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Adaptive Spatially-Distributed Water-Quality Modeling

Permanent Link: http://ufdc.ufl.edu/UFE0042132/00001

Material Information

Title: Adaptive Spatially-Distributed Water-Quality Modeling An Application to Mechanistically Simulate Phosphorus Conditions in the Variable-Density Surface Waters of Coastal Everglades Wetlands
Physical Description: 1 online resource (280 p.)
Language: english
Creator: Muller, Stuart
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: biogeochemistry, complexity, deposition, distributed, everglades, florida, hydrodynamic, macrophytes, mannings, mechanistic, modeling, periphyton, phosphorus, quality, sensitivity, slough, spatially, surfacewater, water, wetlands
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The Everglades region known as the Southern Inland and Coastal Systems is an important area that supports numerous endangered species and plays a crucial role in regulating water-quality conditions in Florida Bay. Taylor Slough is a major feature of this region and represents the primary surface-water pathway for freshwater inputs to Florida Bay. The slough is also subject to intensive flow management under the Comprehensive Everglades Restoration Plan, yet the consequences of such management for water-quality in these oligotrophic and sensitive wetlands are not well understood. A flexible phosphorus water-quality model was therefore developed and tested as an exploratory management tool for the region. Complex local hydrodynamics required that a spatially-distributed hydrodynamic model be used to simulate flow and transport and the USGS model FTLOADDS was selected for this. A user-definable biogeochemical reactive component (aRSE) was then coupled with the hydrodynamic model and the resulting FTaRSELOADDS model was tested against analytical solutions and field data. Hydrodynamic field testing showed that depth-varying Manning s resistance was important for accurately capturing wet and dry conditions during the experimental period. Conceptual water-quality models of increasing complexity were tested against experimental phosphorus field data. Results revealed that a simple daily averaging method was the best approach for atmospheric deposition of phosphorus, which is a crucial but very uncertain water-quality input. A simple conservative transport model provided the best fit between modeled and total phosphorus concentration data. Similar results were also obtained with a more complex and mechanistically justifiable water-quality model. The adaptability of the biogeochemical component was used to study how additional model complexity affects model uncertainty, sensitivity and relevance by evaluating progressively more complex conceptual models using global sensitivity and uncertainty analyses. The framework applying these methods is suggested as a useful way of evaluating models in general, and deciding upon a relevant model structure when the freedom to dictate complexity exists.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Stuart Muller.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Munoz-Carpena, Rafael.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042132:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042132/00001

Material Information

Title: Adaptive Spatially-Distributed Water-Quality Modeling An Application to Mechanistically Simulate Phosphorus Conditions in the Variable-Density Surface Waters of Coastal Everglades Wetlands
Physical Description: 1 online resource (280 p.)
Language: english
Creator: Muller, Stuart
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: biogeochemistry, complexity, deposition, distributed, everglades, florida, hydrodynamic, macrophytes, mannings, mechanistic, modeling, periphyton, phosphorus, quality, sensitivity, slough, spatially, surfacewater, water, wetlands
Agricultural and Biological Engineering -- Dissertations, Academic -- UF
Genre: Agricultural and Biological Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The Everglades region known as the Southern Inland and Coastal Systems is an important area that supports numerous endangered species and plays a crucial role in regulating water-quality conditions in Florida Bay. Taylor Slough is a major feature of this region and represents the primary surface-water pathway for freshwater inputs to Florida Bay. The slough is also subject to intensive flow management under the Comprehensive Everglades Restoration Plan, yet the consequences of such management for water-quality in these oligotrophic and sensitive wetlands are not well understood. A flexible phosphorus water-quality model was therefore developed and tested as an exploratory management tool for the region. Complex local hydrodynamics required that a spatially-distributed hydrodynamic model be used to simulate flow and transport and the USGS model FTLOADDS was selected for this. A user-definable biogeochemical reactive component (aRSE) was then coupled with the hydrodynamic model and the resulting FTaRSELOADDS model was tested against analytical solutions and field data. Hydrodynamic field testing showed that depth-varying Manning s resistance was important for accurately capturing wet and dry conditions during the experimental period. Conceptual water-quality models of increasing complexity were tested against experimental phosphorus field data. Results revealed that a simple daily averaging method was the best approach for atmospheric deposition of phosphorus, which is a crucial but very uncertain water-quality input. A simple conservative transport model provided the best fit between modeled and total phosphorus concentration data. Similar results were also obtained with a more complex and mechanistically justifiable water-quality model. The adaptability of the biogeochemical component was used to study how additional model complexity affects model uncertainty, sensitivity and relevance by evaluating progressively more complex conceptual models using global sensitivity and uncertainty analyses. The framework applying these methods is suggested as a useful way of evaluating models in general, and deciding upon a relevant model structure when the freedom to dictate complexity exists.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Stuart Muller.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Munoz-Carpena, Rafael.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0042132:00001


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ADAPTIVE SPATIALLY-DISTRIBUTED WATER-QUALITY MODELING: AN
APPLICATION TO MECHANISTICALLY SIMULATE PHOSPHORUS CONDITIONS IN
THE VARIABLE-DENSITY SURFACE-WATERS OF COASTAL EVERGLADES
WETLANDS

















By

STUART JOHN MULLER


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2010

































2010 Stuart John Muller






























Dedicated to everyone, for everything, truly. But most of all, it must be said, for Julie.
Elen sila lumenn' omentielvo.









ACKNOWLEDGMENTS

I thank the USGS, SFWMD, and UF for fiscal support throughout this journey. I

thank my committee: Dr. Greg Kiker, for being the original spark that has lead to so

much light; Dr. Andrew James, for his vision for TaRSE; Dr. Mark Brown, for his

example and his conversation; Dr. Jim Jawitz, for his support, both personal and

professional; and dear Dr. Rafael Muioz-Carpena, for the commitment of his generosity

and the conviction of his faith, which have given me more than any Ph.D. is really

supposed to. I thank my incredible family for persistent genes, boundless opportunity,

an enquiring mind, and an open heart; my cats for the peace of their innocence when I

had to let mine go; my friends for making life what it is, even when it isn't; and my Love

for being so patient, and so kind, and so adorable.









TABLE OF CONTENTS

page

A C KN O W LE D G M ENTS ............ ................................................. .. ..............

L IS T O F T A B L E S ................................................................................................................ 9

L IS T O F F IG U R E S ............................................................................................................ 1 0

LIST O F A BBR EV IAT IO N S ................................................................................14

A B S T R A C T ........................................................................................................................ 1 5

CHAPTER

1 IN T R O D U C T IO N ................................................................... ...................... 17

The Southern Inland and Coastal Systems of the Everglades: A Region at Risk.... 17
Opportunities for Spatially-Distributed Mechanistic Modeling of Phosphorus in
SICS ......... .............. .. ............... .......... 20
Hydrologic Modeling of SICS ......... .............. ..... ........................... 20
W ater-Q quality M odeling of S IC S ................................................... 21
M odel S election .................................................................... .......... .... ......... 23
Important SICS Modeling Considerations ..................... ....... ........... 25
M odel R elevance ...................................................................... ..................... 27
Research Questions and Objectives .................. ...................... 28
Research Questions ......................... .... ............ .................. 128
Objectives ............................................... 29

2 FUSION OF FIXED-FORM AND FREE-FORM MODELS FOR ADAPTIVE
SIMULATION OF SPATIALLY-DISTRIBUTED WETLAND WATER-QUALITY ....... 34

Introduction ..................... ........................................................... .. .................... 34
Fixed-Form Versus Free-Form ............................................... 34
Materials and Methods ......................................................... 38
Description of the Models .......................................................................... 39
Fixed-form hydrology and transport model: FTLOADDS ......................... 39
Free-form water-quality reactions model: aRSE ........................... ........... .... 40
Fusing Fixed- and Free-Form Models .................... ..... ................ 41
Analytical Testing of the FTaRSELOADDS Linkage ................. ................42
Analytical solution ......... ...... ............ ................ 42
Setup for testing of SWIFT2D ......... .........................45
Setup for testing of FTaRSELOADDS ................................. 47
R results and D discussion ......... ................... ......... ................ ................ 47
Benchmarking SW IFT2D ...... ............................................................... 47
V erifying FTaRS ELOA D DS ....... .................................................................. 48
C o n c lu s io n s ........................................................ ................ 5 0









3 MODELING HYDROLOGY IN THE SOUTHERN INLAND AND COASTAL
S Y S T E M S .............................................................................................................. 5 8

Introduction ............................... ................ ...................58
Previous Hydrological Modeling of SICS ........................................................ 58
R em modeling the Hydrology of S IC S ........................................... ..................... 60
M ateria ls a nd M methods ........................................................................... 6 1
M o d e l D e s c rip tio n ............... ......................................................... 6 1
SWIFT2D governing equations...................... ...................... 61
SW IFT2D numerical solution technique ............................... 63
SWIFT2D code enhancements and simplifications ................... ........ 63
M odel Setup ........... ................................................................................................ 66
Com putational dom ain ........ .. ......... .. ............ .. ................. 66
B ou nd ary cond itions ........ .. ......................................... .. ............... 67
Stability considerations ......... ..... ...... .... .......... .... .... .... .............. .. 69
R results and D discussion ................ ........................................... 69
W ater-Level R results ......... .................................................. .. ...... ... ..... 70
D discharge R results .................................. ........ .................................73
Salinity R results .......... ............ ................ ........................ .... 74
C conclusions ......................................................................... ........... ..................75

4 MODELING PHOSPHORUS WATER-QUALITY IN THE SOUTHERN INLAND
A N D C O A STA L SY STEM S ......... .................................................. ................ 103

Introduction ............... .................................................................................. 103
M ateria ls a nd M methods ........ ...... ................ .. ................................. .... .. ..... 10 5
B boundary C conditions ..... .... ......... ... .. ............ .. .............. .. ................ 105
Specified w ater-level boundaries...................................... ................... 106
Specified discharge boundaries............... ..... ......... .. .............. 107
A tm ospheric deposition ................ .... ....1.. ............... ................ 108
Conceptual Models of W ater-Quality Processes .................... ... ............. 108
M o d e l 1 ................................ .................. ............................................... 1 0 9
M o d e l 2 .............. ......... ...........................................................................1 10
M o d e l 3 .............. ......... ..................................................................... 1 10
Results and Discussion .............. ..................................... .. ...... ................112
Model 1 .................. ................................... 112
Model 2 .... ......... ......................................112
Model 3 .......................... ..................... 114
C conclusions ............................................................................................ ................115

5 UNRAVELING MODEL RELEVANCE: THE COMPLEXITY-UNCERTAINTY-
SENSITIVITY TRILEMMA .................................................. 135

Intro d uctio n ............... .... .............. .............................. .................13 5
The Complexity-Uncertainty-Sensitivity Trilemma ..................... ................ 137
Uncertainty ............... ........ .. ......... ......... 138
Sensitivity .......................... .. ......... ................ .......... 139


6









C o m p le x ity ................ .................................. .......................................... 1 4 1
R elevance dilem m as ................ ................... .............. ...... ........... ..... 143
The relevance trilem m a .......................... ..................................... .... 145
M materials and M ethods ................................................... ........... ........... .......... .. 146
Global Sensitivity and Uncertainty Analysis Methods..................................... 146
Model Description, Application, and Selection of Complexity Levels .............. 149
Model description: TaRSE ................................ ................ 149
M odel application.. .................................... .......... 150
Levels of com plexity ................................... ........... .............. ... ...... .. 151
Parameterization of Inputs Across Complexity Levels ................................... 152
Results and Discussion ................ .............. ... .... .... ......... ............... 154
Effects of M odel Com plexity on Sensitivity .......... ...................................... 154
Morris method........................................ ................ 154
Extended FA ST ................ .................................... .......... 155
Effects of Model Complexity on Uncertainty................................................... 156
C o n c lu s io n s ............. ......... .. .............. .. ..................................................1 6 0

6 CONCLUDING REMARKS ........................................................................ 172

C o n c lu s io n s ............. ......... .. .............. .. ..................................................1 7 2
Limitations ........................ ........................ 173
Future Research ............. ................................ .............. .......... 174
Philosophical D deliberations ...................... ............... .. ............................. 176

APPENDIX

A MODEL VERSIONS .............. ............................... .......... ........178

Model and Application Versions: Nomenclature............................ 178
Model and Application Versions: Sub-models ................. ................................... 178

B DETAILS OF THE FTARSELOADDS LINKAGE ......... .......... ...............182

S ectio n B 1 ....... .......................... .. .... ....................................................... 18 2
Technical Considerations in the Model Linkage ......... ........................ 182
Consideration 1: Initial setup of aRSE ....................... ..... ..... ............ 183
Consideration 2: Spatially-distributed versus non-spatial ...................... 184
Consideration 3: FORTRAN versus C++ ........... .... ................... 184
Resolution 1: Initial setup of aRSE ......... ............ ............. .............. 186
Resolution 2: Spatially-distributed versus non-spatial ............................. 187
Resolution 3: FORTRAN versus C++ ............................................... 189
General description of the linkage mechanism ................ ............... 189
S ectio n B 2 ................. ................................... .................. ... 19 0
FORTRAN Subroutines for Linkage...................................... ...... .......... 190
M odule aR S E D IM ...................... ............. ................ ............. 190
S ubroutine R EA D IW Q ................................................. .. .................... 19 1
Subroutine CALLaRSE ......................... .... .................................. 193


7









Subroutine aR S E IN ....................................................... ......... .. ... ..... 195
Subroutine aRSEOUT .. .. ......................... ......................197
Subroutine RUNaRSE........................ .............................. ............... 198
Subroutine CELLCO UNT ......... .......................................... ................ 200
S e c tio n B 3 ................................................... ........................................................ 2 0 1
READIW Q Input File .... ... ... .... ............................ ........... 201
S e c tio n B 4 .................................. ....................................................................2 0 2
Nash-Sutcliffe Calculation for Analytical Testing ................... ... ...... ......... 202
Program STUPOSTPROCESS.................................. ............. ............202
Subroutine PO STPRO CESS .......... ..................................... ............... 204
Subroutine CORSTAT.. .. ......................... .......................205

C WATER-QUALITY APPLICATION CODE AND INPUT FILES..............................216

S section C 1 ............ ...................................... ............... .... ...................... 2 16
Additional Subroutines for Water-Quality Inputs .......................... ..........216
Subroutine EDIT INPUTFILE ........................ ......... .. .............. 216
Subroutine STRUCTCONCS .......... ........ .. ............. .................218
S ectio n C 2 ................ ........... .. ..... ............... .. .... ... .......... .................. .. 22 0
Important Input Files for the SICS Water-Quality Simulation........................220
Format for INPUTFLOWCONCS.dat................................ ... ............. 220
Total Phosphorus Atmospheric Deposition Rates for Model 2.....................221
S section C 3 .............. .......... .. ........... ... .. .. ... ..................... 234
XML Input File for Model 3 (XMLINPUT.xml)...... ......... ............ 234
IW Q input File for Model 3 (IW QINPUT.iwq) .................................................238
SWIFT2D Input File (WETLANDS.inp) for Model 3......................................239

LIS T O F R E F E R E N C E S ...................................... ...................................... ... 266

B IO G R A P H IC A L S K ET C H .............................................................................. ..... 280









LIST OF TABLES


Table page

2-1 Quantities and values used in the comparison of SWIFT2D and
FTaRSELOADDS against the analytical solution ......... .................................. 51

2-2 Nash-Sutcliffe efficiencies obtained for different methods of integrating aRSE
reactions into FTLOADS ............... ...................... ...... ...... .. ............ 52

3-1 Nash-Sutcliffe efficiencies for water-level observation points in SICS.................77

3-2 Nash-Sutcliffe statistics for stations in the viciniy of Taylor Slough, stations in
the vicinity of C-111, and all stations in the SICS region.............. ................ 77

4-1 Stations and total phosphorus concentration data used for interpolation of
daily concentrations for specified head boundary conditions in Florida Bay .....118

4-2 Data sources and values used for boundary conditions concentrations at the
L-3 1W discharge source ...................... .. .. ................................ ................ 119

4-3 Data sources and values used for boundary conditions concentrations at the
C-111 discharge source. ................................................... .. .. ...... .... .. 20

4-4 Data sources and values used for boundary conditions concentrations at the
TSB discharge source................................................ ... .............. ... 121

4-5 Parameters used in the model ............. .............. ........... ................122

4-6 State-variables with initial conditions as used in Model 3 ................................ 123

4-7 Nash-Sutcliffe efficiencies for the water-quality models applied to simulate
total phosphorus in the Southern Inland and Coastal Systems ....................... 124

5-1 Process description for the increasing levels of complexity studied .................. 163

5-2 Probability distributions of model input factors used in the global sensitivity
and uncertainty analysis ....... ............... .. ........ .... ............... 164

B-1 Explanation of the READIWQ input file structure and read in parameters ........201

C-1 Atmospheric deposition rates input to Model 2 ....... ................................... 221









LIST OF FIGURES


Figure page

1-1 Location of the Southern Inland and Coastal Systems study area ...................31

1-2 Reviewed phosphorus water-quality models and algorithms from simple to
co m p lex ............... ........... .......................... ........................... 32

1-3 Reviewed phosphorus water-quality models and algorithms from
interim ediate to com plex .......... .......... .................. .......... .............. 33

2-1 Schematic detailing the architecture of the code linking the surface-water
model in FTLOADDS with a Reaction Simulation Engine................................ 52

2-2 Source boundary condition for analytical solution..................... ................ 53

2-3 SWIFT2D model domain used for comparison of conservative and reactive
transport simulations with analytical solutions ...... ........ ..................... 54

2-4 Concentration isolines for 2-D conservative transport from a small
rectangular source as determined by SW IFT2D............................................. 55

2-5 Concentration isolines for 2-D reactive transport from a small rectangular
source as determ ined by SW IFT2D ........................................ ........................ 56

2-6 Spatially-interpolated RMSE and Nash-Sutcliffe efficiencies after 150 minutes
of simulation for the case of transport-reactions-transport-reactions ................ 57

2-7 Spatially-interpolated RMSE and Nash-Sutcliffe efficiencies after 300
minutes of simulation for the case of transport-reactions-transport-reactions .....57

3-1 Location of the Southern Inland and Coastal Systems study area ..................78

3-2 Space-staggered grid system showing relative locations of hydrodynamic
characteristics............. ... ................................. ....... .. .... .............. 79

3-3 The SICS computational grid, showing the location of Taylor Slough, the
Buttonwood Embankment and the coastal creeks.................... ................. 80

3-4 Land-surface elevations. .............. ....................... ......... .. .... .. ...... ...... 81

3-5 Location of SICS model boundary conditions, including specified water-level
boundaries and discharge sources................................................. ... ................... 82

3-6 Specified hydrologic inputs to SWIFT2D................. ................ 83

3-7 Water-levels at the six stations in the vicinity of Taylor Slough, simulated with
depth-varying Manning's n and with constant Manning's n ............................... 84









3-8 Water-levels at the six stations in the vicinity of C-111, simulated with depth-
varying Manning's n and with constant Manning's n .......................................... 85

3-9 Water-levels at the six stations in the vicinity of Taylor Slough, simulated with
depth-varying Manning's n in the current version and the original SICS
application .............. .................................. ...... .. ............... 86

3-10 Water-levels at the six stations in the vicinity of C-111, simulated with depth-
varying Manning's n in the current version and the original SICS application.....87

3-11 Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained
with SICS v1.2.1, for all 12 water-level stations ........... ............................... 88

3-12 Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained
with SICS v1.2.1, for 6 water-level stations in the vicinity of Taylor Slough. .......89

3-13 Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained
with SICS v1.2.1, for 6 water-level stations in the vicinity of C-11 ................... 90

3-12 Trends in prediction bias for the 6 stations in the vicinity of Taylor Slough.........91

3-13 Trends in prediction bias for the 6 stations in the vicinity of C-11 ...................92

3-14 Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the first four months ................ ......................... ............... 93

3-15 Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the m iddle four months ................................... ............. .......... 94

3-16 Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the final four m onths......................................... ...................... 95

3-17 Simulated and measured discharges through five gauged creeks in the
Buttonw ood Em bankm ent............................................. ............................. 96

3-18 Rainfall and discharge inputs, and corresponding 2-D discharge vector
distributions for the first four months ................ ......................... ............... 97

3-19 Rainfall and discharge inputs, and corresponding 2-D discharge vector
distributions for the m iddle four m months. ............ ................... ........... ......... 98

3-20 Rainfall and discharge inputs, and corresponding 2-D discharge vector
distributions for the final four m onths......................................... ...................... 99

3-21 Rainfall and discharge inputs, and corresponding 2-D salinity distributions for
the first four m months ......... ......... .................................... ......... ......... 100

3-22 Rainfall and discharge inputs, and corresponding 2-D salinity distributions for
the m middle four m onths........................................... .... ........ ................ 101









3-23 Rainfall and discharge inputs, and corresponding 2-D salinity distributions for
the final four m months ............... ....... ............... ................ ................ 102

4-2 Location of SICS model boundary conditions ...... ....... ..... ................ 126

4-3 Location of water-quality observation points in Florida Bay ............................... 127

4-4 Model 1: Conservative transport assuming deposition and internal sources
are in equilibrium with biotic uptake and internal sinks................... ................ 128

4-5 Model 2: First-order uptake from the water column using the reactive
transport functionality of SW IFT2D .............. .......... .................. .... .......... 129

4-6 Model 3: Reactions simulated by aRSE with transport by SWIFT2D................ 130

4-7 Mean proportion of total recovered radioisotope (32P) per mesocosm found in
different ecosystem components over time ............................................. 131

4-8 Simulated TP concentrations obtained with Model 1 ................................ .... 132

4-9 Simulated TP concentrations obtained with Model 2................................ .... 133

4-10 Simulated TP concentrations obtained with Model 3................................ .... 134

5-1 Relevance relative to sources of modeling uncertainty and sensitivity in
relation to model complexity ........ ......... ..................... ................ 165

5-2 Hypothesized trends relating complexity to sensitivity from direct effects,
sensitivity from interactions, and total sensitivity ................. ...... ............. 166

5-3 TaRSE application domain, with flow from left to right and bounded above
and below by no-flow boundaries ......................................... ......................... 166

5-4 Levels of modeling complexity studied to represent phosphorus dynamics in
w etla n ds......... .................................................... ........ ....... ................ 16 7

5-5 Morris method global sensitivity analysis results for surface-water soluble
reactive phosphorus outflow ........ ............................. ................ 168

5-6 Results for sensitivity from direct effects, interactions and output uncertainty.. 169

5-7 Output PDFs for SRP concentration in surface-water outflow ......................... 170

5-8 A suggested framework, employing global sensitivity and uncertainty
a n a ly s e s ................................ .................................................... ................ 1 7 1

A-1 SWIFT2D vl.1 comprises the SWIFT2D v1.0 code and additional code from
SICS updates for coastal wetlands ......... ........... ............... ... ............. 179









A-2 FTLOADDS v1.1 comprises the SWIFT2D v1.1. code, leakage code linking
SW IFT2D to SEAWAT, and SEAWAT.................................. ......... .......... 179

A-3 SEAWAT comprises the MODFLOW code and the MT3DMS code............... 179

A-4 FTLOADDS v2.1 comprises SWIFT2D v2.1 and SEAWAT, where SWIFT2D
v2.1 is SWIFT2D v1.1 implemented with integrated leakage........................... 180

A-5 FTLOADDS v1.2 comprises SWIFT2D v2.2 with updates for TIME but with
the ground-water simulation turned off ................................... .......... ......... 180

A-6 FTLOADDS v2.2 contains SWIFT2D v2.1 linked with SEAWAT and
containing TIM E updates. ....... .... ...... .............. ... ... ....... ............ ....181











aRSE

CERP

eFAST

ENP

FAST

FDEP

FTaRSELOADDS


FTLOADDS


GSA

P

PDF

SFRSM

SFWMD

SFWMM

SICS

SRP

SWIFT2D

TaRSE

TIME

TP

UA

USGS


LIST OF ABBREVIATIONS

a Reaction Simulation Engine

Comprehensive Everglades Restoration Plan

extended Fourier Amplitude Sensitivity Test

Everglades National Park

Fourier Amplitude Sensitivity Test

Florida Department of Environmental Protection

Flow, Transport and Reaction Simulation Engine in a Linked
Overland-Aquifer Density Dependent System

Flow and Transport in a Linked Overland-Aquifer Density
Dependent System

Global sensitivity analysis

Phosphorus

Probability Distribution Function

South Florida Regional Simulation Model

South Florida Water Management District

South Florida Water Management Model

Southern Inland and Coastal Systems

Soluble Reactive Phosphorus

Surface-water Integrated Flow and Transport in 2 Dimensions

Transport and Reaction Simulation Engine

Tides and Inflows in the Mangroves of the Everglades

Total phosphorus

Uncertainty Analysis

United States Geological Survey









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ADAPTIVE SPATIALLY-DISTRIBUTED WATER-QUALITY MODELING: AN
APPLICATION TO MECHANISTICALLY SIMULATE PHOSPHORUS CONDITIONS IN
THE VARIABLE-DENSITY SURFACE-WATERS OF COASTAL EVERGLADES
WETLANDS

By

Stuart John Muller

August 2010

Chair: Rafael Muioz-Carpena
Major: Agricultural and Biological Engineering

The Everglades region known as the Southern Inland and Coastal Systems is an

important area that supports numerous endangered species and plays a crucial role in

regulating water-quality conditions in Florida Bay. Taylor Slough is a major feature of

this region and represents the primary surface-water pathway for freshwater inputs to

Florida Bay. The slough is also subject to intensive flow management under the

Comprehensive Everglades Restoration Plan, yet the consequences of such

management for water-quality in these oligotrophic and sensitive wetlands are not well

understood. A flexible phosphorus water-quality model was therefore developed and

tested as an exploratory management tool for the region. Complex local hydrodynamics

required that a spatially-distributed hydrodynamic model be used to simulate flow and

transport and the USGS model FTLOADDS was selected for this. A user-definable

biogeochemical reactive component (aRSE) was then coupled with the hydrodynamic

model and the resulting FTaRSELOADDS model was tested against analytical solutions

and field data.









Hydrodynamic field testing showed that depth-varying Manning's resistance was

important for accurately capturing wet and dry conditions during the experimental

period. Conceptual water-quality models of increasing complexity were tested against

experimental phosphorus field data. Results revealed that a simple daily averaging

method was the best approach for atmospheric deposition of phosphorus, which is a

crucial but very uncertain water-quality input. A simple conservative transport model

provided the best fit between modeled and total phosphorus concentration data. Similar

results were also obtained with a more complex and mechanistically justifiable water-

quality model. The adaptability of the biogeochemical component was used to study

how additional model complexity affects model uncertainty, sensitivity and relevance by

evaluating progressively more complex conceptual models using global sensitivity and

uncertainty analyses. The framework applying these methods is suggested as a useful

way of evaluating models in general, and deciding upon a relevant model structure

when the freedom to dictate complexity exists.









CHAPTER 1
INTRODUCTION

The Southern Inland and Coastal Systems of the Everglades: A Region at Risk

The Southern Inland and Coastal Systems (SICS) region of the southern

Everglades (Figure 1-1) connects Taylor Slough and the C-111 marl prairie wetlands

with Florida Bay, and represents an important region of Everglades study and

management (SFWMD and FDEP, 2004; CRGEE and NRC, 2002). Though Taylor

Slough is substantially smaller than Shark River Slough, in both discharge and areal

extent, it plays an important role in regulating water-quality in Florida Bay (Fourqurean

and Robblee, 1999). Additionally, the region encompasses thousands of acres of

habitat that support dwindling populations of saltwater and freshwater animal species

(van Lent et al., 1998), fifteen of which are listed as threatened or endangered with

extinction (Beccue, 1999), including the Federally protected Cape Sable Seaside

Sparrow (Pimm et al., 2004).

Flow through the southern Everglades has been increased as part of the

Comprehensive Everglades Restoration Plan (CERP), with further increases imminent.

The potential effects of these changes on nutrient conditions in Taylor Slough, the

neighboring wet marl prairies, or the estuaries of Florida Bay is not well understood and

the subject of ongoing research (Childers, 2006). Studies suggest that the SICS area is

already under intense ecological stress from past management decisions that have

impacted flow and nutrient conditions (Childers, 2006; Gaiser et al., 2006; Armentano et

al., 2006). In addition, gradual reductions in freshwater inputs flowing southwards have

contributed to the encroachment of saltwater tolerant species, primarily mangrove

forest, into previously freshwater marsh vegetation (Smith, 1998). Of particular concern









are the possible consequences of additional nutrient loading to Florida Bay (SFWMD

and FDEP, 2004), which has seen an increase in the incidence of harmful algal blooms

and mass seagrass die-off (Fourqurean and Robblee, 1999).

The Everglades are a highly oligotrophic system (Noe et al., 2001) due to a natural

scarcity in bioavailable phosphorus. The concentration of phosphorus in the surface-

water is therefore a principal consideration in the Everglades restoration. Freshwater

marshes in the SICS region are characterized by unique macrophyte and periphyton

communities that are adapted to phosphorus-scarce conditions. Periphyton taxa have

been shown to be very sensitive to phosphorus conditions (Gaiser et al., 2004), with

cascading ecological consequences resulting from even low levels of nutrient

enrichment (Gaiser et al., 2005). Additionally, the low phosphorus loading with

freshwater inputs to the estuaries of Florida Bay means that water from the Gulf of

Mexico is their most important source of phosphorus, as opposed to the upstream

watershed as is normally the case (Chen and Twilley, 1999; Fourqurean et al., 1992).

This reversal in the source of the limiting nutrient, compared with typical estuaries

(biogeochemically speaking), is the reason they are referred to as "upside-down"

estuaries (Childers, 2006). It is believed that phytoplankton and seagrasses in eastern

Florida Bay, which is most isolated from the Gulf of Mexico, are therefore phosphorus-

limited (Fourqurean et al., 1992). Higher natural or anthropogenic loadings of

phosphorus that may accompany increasing freshwater inputs could potentially increase

the frequency, intensity, and duration of phytoplankton blooms in regions of Florida Bay.

However, significant increases in the volume of freshwater inflow relative to the

nutrient additions from upstream sources could make terrestrial phosphorus inputs









negligible, and may possibly even suppress the natural marine phosphorus supply by

dilution. Recent research has shown that freshwater inflows have been found to

enhance oligotrophy where Taylor Slough sufficiently flushes the area and suppresses

the intrusion of water from Florida Bay (Childers, 2006). As such, any increase in

freshwater inflows could enhance oligotrophic conditions in the ecotone between fresh

and marine waters, especially during the wet season.

Time-series water-quality and soil phosphorus data shows a general pattern of low

phosphorus availability along Taylor Slough during the wet season except near the

marine source (Boyer et al., 1999), and the influence of marine phosphorus moving

upstream during the low-flow dry season. This was not expected for the southern

Everglades ecotone as light easily penetrates the clear shallow waters above seagrass

pastures, which are known to efficiently sequester marine phosphorus (Fourqurean and

Robblee, 1999). New research in the area has indicated that surface-water phosphorus

concentrations were unexpectedly high in the Taylor Slough ecotone during the dry

season (Childers, 2006). It is conjectured that relatively phosphorus-rich ground-water

inputs to this ecotone are significant during the dry season, when surface-water

hydraulic heads are lowest and residence times are long enough to deplete dissolved

organic matter, thus reducing productivity and phosphorus consumption (Price et al.,

2006; Childers, 2006). Strong interactions between ground-water and surface-water in

this region mean that increased surface-water heads may impact this ground-water

exchange, and thereby affect phosphorus conditions.









Opportunities for Spatially-Distributed Mechanistic Modeling of Phosphorus in
SICS

A model of spatially-distributed surface-water phosphorus conditions for the region

is required to study these issues. Spatially-distributed mechanistic modeling of wetland

water-quality remains a challenging field of hydrology. Modeling the movement of

solutes both within and with the water is contingent upon reliable flow modeling, which

is a difficult task unto itself in the vegetated and hydrodynamically complex SICS

wetlands (Swain et al., 2004; Langevin et al., 2005). In addition, water-quality

constituents are subject to a multitude of chemical, physical and biological processes in

wetlands where unique biogeochemistry and ecology are drivers of, as much as driven

by, water-quality.

Hydrologic Modeling of SICS

Numerical models for simulating water flow south of Lake Okeechobee have been

developed for three distinct regions. The South Florida Water Management Model

(SFWMM) (SFWMD, 2005) and its successor, the South Florida Regional Simulation

Model (SFRSM) (Lal et al., 2005), simulate the highly managed hydrology between

Lake Okeechobee and Everglades National Park (ENP). The southern and western

offshore waters of Florida Bay are modeled with the Florida Bay Hydrodynamic Model

(Hamrick and Moustafa, 2003). The hydrologically complex region between these

models' domains is encompassed by SICS, and is characterized by surface-

water/ground-water and freshwater/saltwater interactions within a highly vegetated and

hydrodynamically unsteady environment. A further specialized modeling effort was

therefore required (Swain et al., 2004; Langevin et al., 2005; Wang et al., 2007), which

culminated in the Flow and Transport in a Linked Overland-Aquifer Density Dependent









System (FTLOADDS) model (Langevin et al., 2005). FTLOADDS links the managed

hydrology of the mainland with that of Florida Bay; outputs from SFWMM are applied as

boundary conditions in FTLOADDS, the outputs from which are in turn applied as

boundary conditions for the Florida Bay Hydrodynamic Model. In this way, an integrated

hydrologic modeling framework of the region was produced that could propagate the

hydrologic consequences of upstream management scenarios onto the downstream

systems. Furthermore, detailed hydrologic conditions can be simulated for use by

mechanistic ecological models that rely on such information, and which is typically not

practically obtainable at the desired resolution (Swain et al., 2004).

FTLOADDS is itself composed of two models; the Surface-Water Integrated Flow

and Transport in Two Dimensions (SWIFT2D) model (Schaffranek, 2004) adapted for

coastal wetlands (Swain, 2005), and the variable-density ground-water model SEAWAT

(Langevin and Guo, 2006). An application of FTLOADDS to the SICS area that uses

only SWIFT2D, and thus neglects surface-water/ground-water interactions, has been

shown to provide acceptable hydrodynamic results (Swain et al., 2004).

Water-Quality Modeling of SICS

Models of the Everglades hydrology and hydrodynamics have and continue to be

addressed, but analogous tools for water-quality are still needed (McPherson and

Torres, 2006). One approach to addressing this need is to develop a detailed

ecosystem model (Wang and Mitsch, 2000). This approach simulates a large number

of biogeochemical processes and therefore requires many parameters, which make the

model cumbersome to apply and prone to overparameterization (Beven, 2006a). Such

conceptually complex models often use free-form tools such as STELLA (Doerr, 1996),

which can be readily tailored to the specific water-quality considerations at hand.









However, the versatility often comes at the expense of spatial heterogeneity, which is

an untenable simplification in the context of the scale and spatial complexity of SICS.

For instance, the spatial variation in microtopography, landcover, and complex

flow boundaries that include canals, pumping stations, and tidal effects, are known to be

important factors that determine water-level (and therefore whether conditions are wet

or dry) and velocity in SICS (Swain et al., 2004). Flow velocity is crucial for accurate

solute transport when using the advection-dispersion equation. Water-level is

biogeochemically important because it determines whether conditions are dry or wet,

which has implications for the presence or absence of aquatic biota and senescence

and decomposition processes (Reddy et al., 1999). Both velocity and water-level are

important for accurate estimation of discharge, which with concentration determines

loading rates that would be of interest to Florida Bay. Additionally, the original SICS

hydrodynamic modeling effort demonstrated the striking effect of wind shear on water-

levels and the directionality of discharges through coastal creeks, and in turn, important

wind-driven mixing (Swain et al., 2004). In order to accurately capture these transient

effects in the transport solution a mechanistic hydrodynamic model is required that

accounts for their effects. Consequently, a spatially-distributed and mechanistic

hydrodynamic foundation was considered requisite.

A more common and simplified approach is to aggregate all phosphorus cycling

mechanisms into a single lumped process that captures net uptake or release (Kadlec

and Knight, 1996; Mitsch et al., 1995; Walker, 1995), or some combination of lumping

and mechanistic methods (Kadlec, 1997). This simplification in biogeochemistry is

counterbalanced by the complexity of spatial heterogeneity in hydrology. However, the









modeling efforts cited simulated surface-water flow using simplified mass balance

approaches (Walker, 1995; Wang and Mitsch, 2000) or as nondispersive, unidirectional

plug flow (Kadlec, 1997), which are not suitable for the complex conditions in SICS. In

addition to homogeneous hydrology, there is also no accounting for spatial

heterogeneity in wetland components and processes that may be important or desirable

(for example, soil phosphorus concentration or accretion and macrophyte or periphyton

biomass).

With the arrival of spatially-distributed mechanistic models of Everglades

hydrology, the logical step to develop a mechanistic water-quality model that built on

this foundation was undertaken. The result was TaRSE, the Transport and Reaction

Simulation Engine (Muller and Muioz-Carpena, 2005; Jawitz et al., 2008; James et al.,

2009). The term "reaction simulation engine" alludes to a novel characteristic of

TaRSE; the state-variables and equations relating them are user-defined. To our

knowledge, this was the first time a spatially-distributed mechanistic water-quality model

had been developed with the built-in flexibility of a free-form simulation model for

defining the system of biogeochemical water-quality processes. This pairing represents

an important new management and research tool for the SFWMD to address

phosphorus related water-quality issues. Though originally integrated into SFRSM, a

version of TaRSE without the transport (now a Reaction Simulation Engine aRSE) has

subsequently been extricated from SFRSM and modularized.

Model Selection

A critical consideration in the selection of a model is the choice of appropriate

complexity. In the context of mechanistic water-quality modeling, which entails a two-

step process of simulating hydrology and biogeochemistry, this choice must be made









twice. Historically, the complexity of each of these components has often been mutually

exclusive, though the greater prevalence of spatial data and computational power have

seen a move towards models with complex treatments of both hydrology and

biogeochemistry (Costanza et al., 1990). Figures 1-2 and 1-3 present a number of

phosphorus water-quality models that were reviewed and classified according to their

overall complexity. They demonstrate the wide range of complexities and approaches

that exist for modeling phosphorus-related water-quality.

A distinguishing feature in the design of models that is associated with their

complexity is whether they are "fixed-form" (usable as-is only), or "free-form"

(intentionally user-definable). The fixed-form development paradigm is generally

applied for complex spatially-distributed models (of which hydrologic models are a prime

example), which require computationally efficient numerical solutions. Many hydrologic

models are based on fundamental laws of physics, and consequently are quite versatile

despite their rigid design. Free-form models are sometimes referred to as dynamic

systems models, and are more suitable to simulating systems where spatial

heterogeneity can be neglected. The relatively light computational demands of a

spatially-lumped model compared with a spatially-distributed one make it amenable to a

more flexible design. The user is therefore able to specify state-variables of interest and

how they are related, with the result that such tools are highly adaptable to a variety of

system applications, including biogeochemical cycling. The extensive and varied

application of STELLA, a widely used example of a free-from model, is indicative of this

versatility (Doerr, 1996).









The complexity of SICS hydrology calls for a fixed-form spatially-distributed

mechanistic hydrodynamic model. Yet the lack of a clear indication of what, exactly, a

phosphorus water-quality model should look like (Figures 1-2 and 1-3), and the looming

need for models of other water-quality constituents and ecological components, calls for

a free-form solution. It was therefore proposed that a fusion of the fixed-form and free-

form development paradigms be attempted by linking the SWIFT2D model within

FTLOADDS with aRSE.

Important SICS Modeling Considerations

Since the initial application of SWIFT2D to SICS (Swain et al., 2004) the model

has been further adapted for application to the larger Tides and Inflows to the

Mangroves of the Everglades (TIME) domain (Wang et al., 2007), which includes the

SICS model domain but is applied using a somewhat larger cell size (500 m as opposed

to 304.8 m). These changes include a number of potentially important simplifications;

rainfall and evapotranspiration (ET) rates are now applied homogenously, and the

Manning's coefficient no longer varies with flow-depth, though it is now treated

anisotropically where before it was considered isotropic. The implications of the

changes to rainfall and evapotranspiration have been sufficiently justified for SICS

(Wang et al., 2007). The consequences of depth-invariant Manning's coefficients are

unclear though, particularly since this proved to be an important factor in the original

SICS hydrologic modeling effort (Swain et al., 2004). Depth-varying Manning's n was

also found to be important under similar assumptions of homogeneous rainfall and ET in

the ridge and slough Everglades landscape (Min et al., 2010). Of particular concern is

how this change affects the ability of SWIFT2D to accurately capture dry versus wet

conditions, which are important for phosphorus cycling (Reddy et al., 1999).









A second important consideration pertain to atmospheric deposition of total

phosphorus (TP). This is a crucial input for modeling water-quality under the

oligotrophic conditions found in SICS (Sutula et al., 2001; Noe and Childers, 2007).

However, atmospheric deposition of phosphorus is notoriously difficult to quantify due to

persistent sample contamination and limitations in the sampling methods (Redfield,

1998; Ahn, 1999). Bulk phosphorus deposition in Florida is estimated to be comprised

of as much as 30-50% dry deposition from resuspended agricultural soils,

phosphogypsum mining, urban emissions and transported dust (Landing, 1997; Meyers

and Lindberg, 1997). However, rainfall is known to scavenge aerosol phosphorus and

incorporate dry deposition into wet deposition estimates, further complicating

quantification of the process.

Measured rates of bulk atmospheric deposition in the Everglades exhibit great

variability, ranging from 0.017 to 0.07 g TP/m2/yr, with an average of 0.03 g TP/m2/yr

(Sutula et al., 2001). Fitz and Sklar (1999) estimated total phosphorus deposition to be

0.03 g TP/m2/yr for the Everglades, which is similar to an estimate by Davis (1994) of

0.036 g TP/m2/y, and the same as that of 0.03 g TP/m2/yr found for the Kissimmee

region 100 miles north of the Everglades (Moustafa et al.. 1996). Rates as low as

0.0006 g P/m2/yr have been estimated for the Bahamas (Graham and Duce, 1982).

South Florida weather is characterized by frequent convection thunderstorms, which

can scavenge aerosol phosphorus from the upper atmosphere (Poleman et al., 1995),

and the location of SICS in the proximity of Miami could subject it to higher deposition

rates associated with adjacent urban or industrial areas (Paerl, 1995; Redfield, 1998).









Consequently, there is great uncertainty in the quantification of atmospheric

deposition of phosphorus, and the process will therefore represent a major source of

uncertainty in any phosphorus water-quality modeling effort. How best to input this

source remains an open question. Another important open question is, given the free-

form of aRSE, what complexity of water-quality model to select. This raises the issue of

how to balance model complexity and relevance.

Model Relevance

A principal tenet of model development is the establishment of relevance (Zadeh,

1973). Relevance is determined by balancing the complexity of a model against its

uncertainty, given the modeling objectives at hand. This topic is introduced and

discussed in great detail in Chapter 5, which is presented as a standalone paper, but is

briefly reviewed here to clarify the motivation.

Model complexity is a property of the degree of detail implicit to the conceptualized

rendition of reality, including the number of state variables and processes simulated.

Increasing complexity implies ever more variables and processes, and therefore ever

fewer simplifying assumptions. This results in a modeled version of reality with greater

mechanistic integrity and thus less structural uncertainty. However, each new state-

variable and process introduced requires additional calibration and parameterization

data, all of which are subject to some measurement uncertainty. These measurement

uncertainties accumulate and eventually outweigh any reductions in structural

uncertainty gained by increasing complexity (Hanna, 1988). The sensitivity of model

outputs also accumulates with consequences for the practicability of the model

(Snowling and Kramer, 2001). Each added process that exerts some influence over a

state-variable, either directly or through interactions with other processes, represents









additional flexibility in the model that can lead to overparameterization issues that can

seriously undermine the validity of a model (Beven and Binley, 1992).

Two model evaluation methods exist that are ideally suited to elucidating these

relationships. Uncertainty analysis applies Monte Carlo simulations to propagate the

uncertainty inherent to model inputs onto outputs of interest. In this way, the

uncertainties in an output for a given model structure, and subject to the given model

input requirements, can be assessed and compared. Global sensitivity analyses

determine where the uncertainty in an output originates from (Saltelli et al., 2000).

Together, these evaluation methods can shed light on how much uncertainty is in the

model, and why it is there (Muioz-Carpena et al., 2007). When performed in the

context of varying model complexity we are then able study how additional complexity

affects the model's inner workings (Jawitz et al., 2008).

The process of defining a model is also the process of defining a model's

complexity; the ultimate source to which many modeling considerations and challenges

can be traced. This tripartite web of interacting complexity, uncertainty, and sensitivity

has not been well-studied in very complex models (Lindenschmidt, 2006)precisely

because they have typically been fixed-form. A flexible model structure presents a novel

opportunity to subtly experiment with advanced levels of model complexity and to

assess how complexity affects uncertainty, sensitivity, and ultimately relevance.

Research Questions and Objectives

Research Questions

There is urgent need for modeling tools to simulate a variety of water-quality

issues of interest in the southern Everglades, and in particular phosphorus conditions in

the sensitive of oligotrophic freshwater marshes. Assessing likely phosphorus









conditions in the surface-water in response to CERP flow management decisions is a

pressing concern. Though a suitable hydrodynamic model of SICS has been identified

and tested for hydrological outputs (Swain et al., 2004), its suitability to supporting

spatially-distributed water-quality simulations needs to be assessed. Furthermore, as

indicated atmospheric deposition of phosphorus is an important process in the

oligotrophic freshwater Everglades that remains very difficult to quantify. How best to

handle this crucial input is therefore a major source of uncertainty. Finally, with the

flexibility of a free-form water-quality model the definition of the phosphorus conceptual

model becomes a moving target, yet a suitable complexity must eventually be settled

upon. Open questions to be addressed in this dissertation include:

What are the consequences of recent changes to the SWIFT2D code that
included removal of depth-varying Manning's roughness? In particular, how do
these changes affect the hydrodynamic prediction of wet versus dry conditions in
SICS, which are important distinctions for a water-quality simulation?

Given the acknowledged uncertainty associated with quantifying atmospheric
deposition of phosphorus, what methods of inputting this source to the water-
quality model produce the most accurate simulated concentrations?

What is the simplest phosphorus water-quality model that would produce
acceptable results for SICS? Can a more complex and mechanistic model of
water-quality produce comparable or better results than a simpler one?

Given the tradeoffs between complexity and uncertainty, how does one choose
what model complexity is appropriate, and how does uncertainty and sensitivity
change with the addition of further complexity?

Objectives

1. Development of a combined fixed-form/free-form spatially-distributed hydrologic and
biogeochemical model, validated against analytical testing, which is suitable for
application to simulate phosphorus water-quality in SICS (Chapter 2).

2. Application of the new tool to study the importance of depth-varying Manning's
roughness in hydrodynamic simulations of SICS surface-water (Chapter 3).









3. Application of the new tool to determine how best to input phosphorus additions by
atmospheric deposition, and to determine what complexity of phosphorus water-
quality model best captures measured phosphorus conditions in SICS surface-
waters (Chapter 4).

4. Formal evaluation of the effect of using different complexity biogeochemical
conceptual models on output uncertainty, global sensitivity, and model relevance
(Chapter 5).











W830'


Base trUni U S =eo1d 3wney darm dab. 1972
UriKeral TFaref9se Meafttr poedlor Zone it, Dalunm NAD 27 8130' 8100' 8I30' W 8000'
26030' '
EXPLANATION
SEVERGLADES NATIONAL PARK


I I APPROXIMATE AREA OF TAYLOR SLOUGH
- BOUNDARY OF SOUTHERN INLAND AND
COASTALSYSTEMS SICSS STUDYAREA
- BUTTONWOOD EMBANKMENT
A STAGE MEASUREMENT SITE lUSGSp
SRA FALL, WIND AND SOLAR RADIATION
MEASUREMENT SITE (LISGS)
RAINFALL MEASUREMENT SITE (NPS
PUMPSTATION
ET EVAPOTRANSPIRATION


Figure 1-1. Location of the Southern Inland
Swain et al., 2004).


26 '' I


/ '.


24"30
0 40KILOMETERS
O 4 MILES


and Coastal Systems study area (from


25'30'
















25" 5'


W845'


W15'


L


-,. -10


2_. : I-












Cornparlve Table of some existing P lsmulation algorithnm
Model STA Design Model EPGM OMSTA EUTROMOO PHOSMOD GLEAMS
Rivers/Canals
Lakes/Reservairs Y Y
Wettlnds Y Y Y
TP -, T P TP ~ r TP,




Poolng Maximum Very high Very high High High Intermedsale



Simulates Simulates lake Simulates labile,
Simple rate S.iT.i roale sediment bound total P, organic, stable
Simple rate function functions used to functons lfo P and dissolved P percentage of inorganic and active
S Simulated P and used to relate P- predict water uptake, release Iransport to total P in inorganic P in I -e v;i
B related outputs removal to incoming column P, soil P and response by lakes soil P sediment, DO uptake by plants,
water column TP and peat biomass, and melatin and concentrations In d~Islved P n runoff
. accretion peat coretion dissolved P upper soil and sedirnent-bound P
concentration regions in runoff




Complexity rating 1 2 3 4 4 5


Figure 1-2. Reviewed phosphorus water-quality models and algorithms (from simple to
complex from left to right).












sComparittve Table of onme eistina P simulation algorithma cosntIued
Model WASP HSPF ELM CE-QUAL-RIVI CE-QLMA-WZ CE-QUAL-ICM
RiverrsCanals Y VY Y
Lakes Reservoirs Y Y Y Y
Wetlands Y Y Y Y
_SSfR TR TR TR TR TR TR
Adveclion y y y y y
C.
Dispe sion y y y y
Sedirnent-ound y y y y y
Pooling Law Low L Low Lw Lw Very low


Siula Watr S imulates Simulates up o 3
Simulates Simulates dtslved column, soil, floc, Siultes (foc I.D phytoplarton speces of
dissod PN and inorganic and paripyton, ow) p la bc DO lk
organic PN in the organic P in surface mnophyote and baceia DO-caon catron balce, zlopankt,
water column. and soil water. detrital P and C, as
E S beenthic /geje, accunliri for wiel as peat balar", N. P cycle N, Si, P cyde -a,-j,. a C, -ce.ton
S Simulated P and b nthic ar accounting for accounting for rala-nce N 3.
related ulpi_ penphyton and temlperaure, DO. accren linilan :r
r d detrfts, sediment bot d pedphyton salink and s---r ,'d :r" 3:.X.ur,,-g 1,
temperature, Also temprature Ialmrr and
accounting DO. taspo, N communes and accounts for o accounts temperature. Also
sanity zooplankton, biomass and sedlmenlmaletr ON for sediment accounts for
tempeature and phylankton andJ nacrop&l and P flux water O .N and P sedirmntWa 0 N
sediment bonding pH community and ad P ux
bimnass

Complexity rating 8 9 9 9 9 10


Figure 1-3. Reviewed phosphorus water-quality models and algorithms (from
intermediate to complex from left to right).









CHAPTER 2
FUSION OF FIXED-FORM AND FREE-FORM MODELS FOR ADAPTIVE
SIMULATION OF SPATIALLY-DISTRIBUTED WETLAND WATER-QUALITY

Introduction

Spatially-distributed mechanistic water-quality modeling of wetlands, such as

those in southern Florida, requires simulating three distinct, yet inter-related, aspects: 1)

the quantity and timing of water distribution ("hydrodynamics"); 2) the motion of

constituents with and within the water by advection, dispersion and diffusion

("transport"); and 3) local biogeochemical processes that change the nature or state of

constituents ("reactions"). Mechanistic hydrodynamics and transport of large-scale

wetland systems generally requires spatially-distributed modeling. The numerical

considerations associated with this, in conjunction with the generality of the underlying

physics, results in models that are hard-coded or "fixed-form" with little or no

freedom on the part of the user to influence the theoretical concepts driving the

simulation. By contrast, biogeochemical reactions can be more readily conceptualized

as a non-spatial system by relying on hydrodynamics and transport to provide the

spatial connection. Water-quality reactions are therefore more amenable to non-spatial

dynamic systems simulation, for which user-definable or "free-form" modeling tools

are regularly used. The need for spatially-distributed mechanistic water-quality models

therefore offers an excellent opportunity to integrate the versatility of a "free-form"

dynamic systems model with the mechanistic and numerical rigor of a spatially-

distributed fixed-form modeling.

Fixed-Form Versus Free-Form

Truly mechanistic models of hydrology apply theoretically derived equations of

flow dynamics, which are generally well-understood and are based on uniformly









applicable laws of physics. For instance, the Surface-Water Integrated Flow and

Transport in Two Dimensions (SWIFT2D) model (Leendertse, 1987; Schaffranek, 2004;

Swain, 2005) applies the St. Venant equations, which are derived from Newton's

Second Law (Conservation of Momentum) and the Principle of Conservation of Mass.

Spatial discretization of the model domain is necessary to capture variability in space,

and transience is captured by repeatedly solving the equations in successive time-

steps. This approach is contingent on limitations to the size of both spatial and temporal

discretizations in order to maintain mathematical stability of the numerical solutions.

Stability considerations in conjunction with simulations of large areas or long periods

can therefore become computationally intensive, even limiting, despite the modern

computational capacities we have at our disposal.

To ensure numerical efficiency such hydrologic models are generally hard-coded

into a fixed-form. This limits the model's application to only those conditions that meet

the underlying (and fixed) assumptions. However, given the universality of physics,

mechanistic flow models that use equations derived from theoretical principles remain

generally versatile. For example, SWIFT2D has been applied to a multitude of water

bodies and locations, including: Jamaica Bay, New York (Leenderste, 1972), the Dutch

Delta Works of the Netherlands (Dronkers et al., 1981; Leendertse et al., 1981), the

Dutch Wadden Sea (with modifications to evaluate mixing) (Riddererinkhof and

Zimmerman, 1992), the Eastern Scheldt estuary in the Netherlands (Leendertse, 1988),

the Pamlico (Bales and Robbins, 1995) and Neuse River (Robbins and Bales, 1995)

estuaries of North Carolina, Tampa Bay (Goodwin, 1987), Hillsborough Bay (Goodwin,

1991), and the upper Potomac estuary in Maryland (Schaffranek, 1986).









Transport of dissolved and suspended constituents can be mechanistically

simulated with the theoretically derived advection-dispersion equation (Equation 2-1). A

reaction term can be introduced (now the advection-dispersion-reaction equation) to

simulate first-order growth or decay reactions. Given the dependence on velocity,

transport modeling within spatially-distributed systems is often integrated into existing

hydrologic models, and inherits a fixed-form structure. This is the case for both

SWIFT2D (Schaffranek, 2004) and SEAWAT (Langevin and Guo, 2006). However, the

underlying simple and generic mathematical formulation of linear growth and decay

kinetics make the reactive transport universally applicable for any constituent, provided

first-order reaction kinetics are appropriate for the process.

The introduction of biogeochemical processes, which are fundamental to wetland

water-quality (Mitsch and Gosselink, 2000), greatly complicates matters because such

processes are too complex to be mechanistically derived from a physics-based

foundation. The biology, chemistry and physics of the aquatic environment all interact to

form a byzantine web of feedbacks that constitute some of the most complex natural

systems science has endeavored to conceptualize. Simulating such complex

biogeochemical systems requires substantial simplification and abstraction, and even

then presents a significant technical challenge (Arhonditsis and Brett, 2004).

Matters are further confounded by the sheer variety of water-quality subjects -

sediments, nutrients, pesticides, bacteria, pH, salinity, dissolved oxygen, dissolved

organic matter, and algae, to name but a few each of which are involved in their own

unique biogeochemical processes. Spatially-distributed modeling of water-quality issues

has therefore also generally been of the fixed form. Particular water-quality functionality









is to address a particular water-quality issue hard-coded into a given hydrologic model,

which limits the applicability of the water-quality model to the range of appropriate

hydrologic applications, and limits the conceptual model of the water-quality constituent

to the hard-coded form.

Rarely have the power of free-form dynamic system models and fixed-form

spatially-distributed hydrologic models been integrated. The aforementioned

development of TaRSE (Jawitz, et al., 2008; James et al., 2009) in Chapter 1 was, to

the best of our knowledge, the first instance of this. The reasons for this are unclear,

although it is sufficiently intriguing to warrant some conjecture. Dynamic simulation

models have generally been written in object-oriented programming languages since

these are conceptually well matched to the task. By comparison, spatially-distributed

mechanistic models have been written in linear programming languages such as

FORTRAN, which carry benefits for numerically efficient processing of the large arrays

of data associated with a spatially discretized domain.

Many of the most popular hydrologic models have their foundations in the early

days of hydrologic model development, when the fusion of linear and object-oriented

programming philosophies was uncommon because computational limitations of the day

demanded the highest possible efficiencies. More often than not this meant coding in

FORTRAN. The two sub- models of FTLOADDS, both coded in FORTRAN, are classic

examples of this: SIMSYS2D (Leendertse et al., 1987) is based on model development

from the 1970s (Leendertse, 1970) and is the progenitor of SWIFT2D; and SEAWAT is

ultimately an adapted version of a 1983 modular ground-water model that would

become MODFLOW (McDonald and Harbaugh, 1988). Mixed-language programming









has become increasingly common with ever-growing computational capacity

(Zimmermann et al., 1992; Cary et al., 1997). Although languages such as FORTRAN

still offer the greatest control over computational efficiency, many higher-level

programming and even scripting languages are becoming popular alternatives for

applications that are not critically limited by computational considerations (Oliphant,

2007).

It is also the case that model development is never without a purpose, and it is

difficult to conceive of developing a water-quality model without a particular water-

quality issue as the objective. In hindsight, it seems that a combination of serendipity

and naivete was at play in the development of TaRSE. The lack of experience at the

time in both biogeochemistry and water-quality modeling on the part of this author, who

was tasked with researching and formulating the preliminary water-quality

conceptualization (Muller and Muioz-Carpena, 2005), lead to particular attention and

frustration associated with the choice of model complexity. This was amplified by the

express intention of the project to develop a tool for application to water bodies

throughout the Everglades, including wetlands, canals, and reservoirs, all of which are

subject to their own biogeochemical idiosyncrasies (Reddy et al., 1999). It would

appear that these factors combined with the object-oriented programming paradigm

brought to the project by the team programmer to inspire the notion of a truly free-form

spatially-distributed water-quality model.

Materials and Methods

In this section we describe the models selected for linkage and the processes by

which their integration was achieved. Following this we present the results of testing

conducted to validate the reactive transport of the fixed-form model against known









analytical solutions. Validation of the linkage between the fixed- and free-form models

is then presented.

Description of the Models

The fixed-form hydrologic model used was Flow and Transport in a Linked

Overland-Aquifer Density Dependent System (FTLOADDS) (Wang et al., 2007), and the

free-from water-quality model was a Reaction Simulation Engine (aRSE) (Jawitz, et al.,

2008). Together, they constitute a novel and potentially powerful new water-quality

modeling tool for the coastal Everglades wetlands; Flow, Transport and a Reaction

Simulation Engine in a Linked Overland-Aquifer Density Dependent System

(FTaRSELOADDS).

Fixed-form hydrology and transport model: FTLOADDS

The USGS has recently developed FTLOADDS as a tool for simulating linked

surface and subsurface hydrology and transport. Surface hydrology in FTLOADDS is

modeled using the Surface-water Integrated Flow and Transport in Two Dimensions

(SWIFT2D) model (Swain, 2005), which simulates vertically-averaged, variable-density,

transient overland flow and transport of solutes. Subsurface hydrology in FTLOADDS is

modeled using SEAWAT (Langevin, 2001; Guo and Langevin, 2002; Langevin and Guo,

2006), which simulates three-dimensional, variable-density, transient ground-water flow

and transport through a porous media. The two models are linked through the

exchange of water and constituent mass between the surface and subsurface (Langevin

et al., 2005).

A number of different versions and implementations of FTLOADDS, SWIFT2D

within FTLOADDS, and the SICS application using these tools are referred to.

Appendix A contains a detailed breakdown of the distinguishing features of each version









and the nomenclature adopted by the USGS, and adapted herein. In this chapter,

reference to "FTLOADDS" will imply FTLOADDS v1.2, which implements the latest

SWIFT2D code used in FTLOADDS v2.2 (Wang et al., 2007) but with leakage and

ground-water flow disabled, hence FTLOADDS v1.2 and SWIFT2D v1.2 (see Appendix

A). In Chapter 3 some code changes were implemented that constituted a new sub-

version, v1.2.1. Each version of each model is graphically outlined in Appendix A to

facilitate clarification of the sub-models that comprise each model and application

version.

Free-form water-quality reactions model: aRSE

With support from SFWMD and USGS, a group at UF recently developed a

biogeochemical component, the Transport and Reaction Simulation Engine (TaRSE),

for simulating the water-quality processes that control phosphorus concentrations and

fate in Everglades wetlands (Jawitz et al., 2008; James et al., 2009). The term

"simulation engine" alludes to the generic nature of the tool, which permits the user to

define the conceptual biogeochemical system by controlling both the state-variables and

the mathematical form of the processes that connect them. Given the existence of a

number of proven hydrologic models for the Everglades, TaRSE was developed as a

water-quality module, and therefore relies on a suitable hydrologic model to simulate

flow and provide the necessary hydrodynamic inputs. The South Florida Regional

Simulation Model (SFRSM) was selected as the first such hydrologic model. However,

the absence of any solute transport functionality in SFRSM necessitated this be

incorporated into the development of TaRSE. This transport functionality is contingent

on the triangular mesh geometry employed by SFRSM for spatial discretization, which

became a significant restriction on the portability of TaRSE for use by other hydrologic









models, many of which already have transport functionality of their own and a square

spatial discretization geometry. The modularity of TaRSE was therefore re-established

by extricating it from SFRSM and removing the transport functionality, leaving it as

simply a Reaction Simulation Engine (aRSE). Portability of aRSE was finalized through

its modularization into a dynamically linked library (DLL), which is callable by any model,

hydrologic or otherwise, to which it offers a powerful and flexible simulation engine.

Fusing Fixed- and Free-Form Models

Figure 2-1 presents a schematic of the linkage implemented to integrate

FTLOADDS and aRSE. Blue portions correspond to FTLOADDS code, green to aRSE

code, and yellow to the linkage code. Black text and lines indicate FORTRAN, red text

and lines indicate C++, solid lines indicate models, dashed lines indicate subroutines,

solid line arrows indicate calls to subroutines in the same language, and mixed-dash

arrows indicate calls from one language to another.

Full details of the technical considerations in the linkage are presented in

Appendix A, but are briefly reviewed here in reference to Figure 2-1:

An additional method for inputting aRSE parameters and state-variables was
required for this information to be available to FTLOADDS at the beginning of the
simulation. This was important for correctly exchanging hydrodynamic
information between the models, and is achieved through a new input file that is
read by the READIWQ subroutine during setup of SWIFT2D.

FTLOADDS and its sub-models are all coded in FORTRAN, whereas aRSE is
coded in C++. Mixed-language programming methods were therefore required to
facilitate communication between the two models (indicated by the color-coding
and mixed-dash lines in Figure 2-1).

Since aRSE computes water-quality reactions for one cell at a time, it was
necessary to establish a framework that would efficiently repeat this process for
each of the cells in the spatially-distributed hydrodynamic domain. A temporary
storage array is used to hold the latest values required by aRSE for each cell,
which are in turn overwritten after each cell is processed by aRSE and returned
to FTLOADDS once all cells have been reacted.









The general functionality of the linkage is described in detail in Appendix B

(Section B1). The code comprising the various subroutines of the linkage is given in

Appendix B (Section B2). An explanation of the IWQ input file is given in Appendix B

(Section B3).

Analytical Testing of the FTaRSELOADDS Linkage

In order to verify that the code used to integrate FTLOADDS and aRSE was valid,

a series of comparisons between numerically modeled results and known analytical

solutions were conducted. While TaRSE has been previously tested, no published

analysis of aRSE exists. Similarly, though widely used and thoroughly tested in

practice, no published comparison of SWIFT2D reactive transport against known

analytical solutions were identified. Therefore, the procedure outlined was intended to

test both models in addition to their linkage. This process consisted of two main steps:

1) testing the reactive transport of SWIFT2D against an established analytical solution;

and 2) reproducing these results using aRSE to perform the reactions calculations

previously performed by SWIFT2D. In this way, the SWIFT2D code was verified

against an analytical solution and could be used as a benchmark against which to verify

the linkage. If FTaRSELOADDS reproduced the same results by relying on SWIFT2D

for transport and the linked code of aRSE for the reactions, then both the linkage and

the reactions code of aRSE will have been validated since a failure of either would

preclude matching results.

Analytical solution

Reactive transport of dissolved constituents in two dimensions is described

according to the advection-dispersion-reaction (ADR) equation (Equation 2-1):









5XC 5C 5C 2C 72C
= -v v- + D + Dy kC (2-1)
x y x 2 Y 62

where C is concentration of the solute of interest; t is time; x is distance in the x-

direction; y is distance in the y-direction; Vx is local velocity in the x-direction; vy is local

velocity in the y-direction; Dx is effective dispersion in the x-direction; Dy is effective

dispersion in the y-direction; and kr is the solute reaction rate.

The controlled velocity conditions implemented in SWIFT2D to ensure uniform

velocity throughout the domain required using a type-three (flux-averaged)

concentration boundary condition. Leij and Bradford (1994) present a suitable analytical

solution for third-type boundary conditions in three dimensions, with a rectangular

source area (Figure 2-2) of width a (in the y-direction), height b (in the z-direction), and

flow in the x-direction, and provide the 3DADE software for numerically solving the

solution. This software is now available as part of the STANMOD suite of numerical

tools (Simunek et al., 1999; available at http://www.pc-

progress.com/en/Default.aspx?stanmod) for solving various analytical solutions to the

ADR equation.

In order to implement the 3-D solution for the horizontal 2-D conditions that

SWIFT2D simulates, the x-direction was oriented in the direction of horizontal

longitudinal flow, the y-direction as horizontally transverse to the direction of flow, and z-

direction as the vertical plane over which the depth-averaged Navier-Stokes equations

are integrated. In such an orientation vertically integrated conditions can be

approximated by setting b sufficiently large compared with the dimension a to produce

an effectively infinite height. This negated any variability in the z-direction and reduced

the solution to an effective 2-D case. Additionally, the dispersion rate in the z-direction








was set to a value sufficiently low (Table 2-1) compared with that specified for the x-

and y-directions to further negate any solute mass movement in the z-direction that

might have occurred despite the large b-value. The value for vertical dispersion could

not be set to zero exactly because it appears in the denominator of the analytical

solution (see Equation 2-3 below). The analytical solution (Equation 2-2) solved using

3DADE is given in Leij and Bradford (1994) as follows:

C = C A, ()F(r)d A2(r)d (2-2)
4 P R 2R 0

for:

C )yO<,z<0,0 C(x, y, z,| t) Y< < <
C(xzt)x 0 otherwise

where:

F(r) = erfc y a erfc y +a12 x
S(4DD, / R) R 2 (4DzR / 2R)

z-b ( z+b
erfc z-b 12 erfc z(4D7+b
(4Dzrz/R)1/2 (4Dzr/R)'/2

1/2
.r R /ex (Rx vr)2
A,(r) =exp f- R exp f R- X _
S/R e Dx 4RDx ( -
(2-4)
v vx Rx +
exp erfc --Rx + v2
2Dx Dx (4RDjx)l 2


A2 exp= -- erfc 1 -- + +-(x+vr/R) x
R )[ (4RDx )1 / D2 Dx(2 -5
A12 e(2-5)
(vx" ( Rx+vr (4v2 ( (Rx vr)2
exp erfc Rx + -c12 exp (RX -
Dx [(4RDxf) /2 7RDx ) 4RD-,









and where R is the retardation factor; ris time; v is porewater velocity; x is the position

in the direction of flow; Dx, Dy, and Dz are dispersion coefficients in the x-, y-, and z-

directions, p is the first-order decay rate coefficient; and A is the zero-order production

rate coefficient.

Setup for testing of SWIFT2D

An important assumption implicit in the analytical solutions presented is that of

uniform uni-directional velocity. However, given the complexity of SWIFT2D's

mechanistic approach to hydrology, establishing a precisely uniform velocity field was

not possible. To overcome this, and considering that the reactive transport was being

tested and not the underlying hydrology, velocity was controlled by overwriting

hydrodynamic values calculated by SWIFT2D at each time-step. In this way a uniform

velocity was established, and observed discrepancies between numerical and analytical

solutions were therefore known to be attributable to the numerical implementation of the

reactive-transport equation, and not to variability in velocity.

A square test domain was established for SWIFT2D consisting of 101 x 101 cells,

with each cell 100-m in length (Figure 2-3). Such a large domain was necessary given

the decision to test the model for conditions approximating those under which it would

be applied, namely low velocity and high dispersion (Swain et al., 2004), and the

disparity in boundary conditions at the upper and lower borders of the domain. The

analytical solution assumes open boundaries, but modeled domain was applied with no-

flow boundaries. A constant velocity of 0.05 m/s was applied with a molecular diffusion

of 20 m2/s. For these conditions, the central fifty cells, justified to the left and centered

around the source (Figure 2-3), were the focus region of the domain, and ensured









sufficient area remained in the domain to prevent any effect on concentrations within the

focus region due to the discrepancy in boundary conditions.

Molecular diffusion in SWIFT2D is input as a single value that is applied

isotropically in both dimensions of flow. The longitudinal dispersion coefficient (D/) is

computed in each cell (Equation 2-6) and in each principal direction of flow according to

a function established by Elder (1959) relating flow conditions, depth, velocity, and the

Chezy resistance coefficient according to:


D, CdHu ( (2-6)
C

where Cd is a coefficient relating longitudinal dispersion to the local velocity; 0 is

the local velocity; H is the temporal flow depth; g is acceleration due to gravity; and C is

the Chezy resistance coefficient, related to the Manning's n according to (Leendertse,

1987):

H1/6
C= H6 (2-7)
n

A representative value of 14.3 has been determined for Cd (Harleman, 1966). The total

effective dispersion implemented in the advection-dispersion-reaction equation is then

the sum of the longitudinal dispersion, which may be different for each direction, and

diffusion, which is constant.

The 2-D analytical solution is valid for uni-directional flow. The absence of

transverse velocity therefore prevented any dispersion from occurring in the transverse

direction. In order to simulate 2-D solute transport it was therefore necessary to rely on

the diffusion coefficient to generate dispersion in the transverse dimension. A reaction

rate of -0.000001 s-1 was used to generate constituent decay for the reactive transport.









Setup for testing of FTaRSELOADDS

A first-order decay equation was input to aRSE through the XML input file. One

state-variable was specified to represent the transported solute. One parameter, the

reaction rate kr, was input to reproduce the decay reaction. All other conditions were

kept the same as those used for testing SWIFT2D

Results and Discussion

Conservative and reactive transport were simulated using SWIFT2D (Figures 2-4

and 2-5, respectively), and reactive transport using FTaRSELOADDS (Figure 2-4).

Results using SWIFT2D confirm that the model correctly simulates solute transport, and

that these results are reproducible using FTaRSELOADDS.

Benchmarking SWIFT2D

Results for 2-D transport of a non-reactive solute obtained using SWIFT2D (Figure

2-4) compared well with the analytical solution, but showed some disparity at the

concentration front due to the effects of numerical dispersion (Fischer et al., 1979). To

confirm that this was the source of the discrepancy in results the numerical dispersion

(Dn) was calculated as per Swain et al. (2004):

(T.5(2 2- ^
D, 0.5(i-+ (2-8)
At

where C2 is the variance of the constituent concentration distribution and i is the

computational cell number. When numerical dispersion was added to the value for

dispersion allocated to the analytical solution the discrepancy at the concentration front

is absent, confirming that numerical dispersion is the source of the differences. Close to

the source boundary the differences are greater and cannot be mitigated by

compensating for numerical dispersion.









Verifying FTaRSELOADDS

Results of reactive transport obtained using FTaRSELOADDS were essentially

identical to those obtained using SWIFT2D by visual comparison (Figure 2-5). The ADI

solution method implemented by SWIFT2D splits the transport step into two half-steps

for each time-step, with one half-step used to calculate velocity in the x-direction, and

the other the y-direction. This naturally lends itself to comparing the accuracy of

alternate ways of integrating the reactions step of aRSE into the transport step of

SWIFT2D. Three methods were identified and implemented: 1) applying the reactions

after each half-step using the half-step time-step (TRTR, where T=transport and

R=reactions); 2) applying the reaction step once in between the two transport steps,

using the full time-step, (TRT); and 3) applying the reaction step once after both

transport steps using the full time-step (TTR).

Given the closeness of results, visual analysis was unsuitable for comparison. To

quantitatively assess how well the simulated results compared against the analytical

solution throughout the entire model domain, a program was written making use of the

CORSTAT (see Appendix B, Section B4) code (Aitken, 1973) to calculate the Root

Mean Square Error (RMSE) and Nash-Sutcliffe (E) efficiencies (Nash and Sutcliffe,

1970) for each of the concentration points in the SWIFT2D domain, compared with

analytical value at equivalent spatial points in the 2-D analytical domain, according to

Equation 2-9:



E = 1 -=l (2-9)

t=l









where O is the observed, Othe mean observed, and S the simulated value.

Figures 2-6 and 2-7 depict the spatially-interpolated RMSE and Nash-Sutcliffe

results at each grid-point in the domain after 150 and 300 minutes respectively, for the

TRT case. Visual comparison of these results and those obtained using the SWIFT2D

reactions, or either the TTR or TRTR methods, showed no visible differences. To

quantify differences in overall numerical performance between the methods, the

average Nash-Sutcliffe efficiencies for all the domain points were calculated for each

case using the Nash-Sutcliffe values determined for each point after 300 minutes (Table

2-2). In this way it was possible to quantify the performance of each of the linkage

options, from which it appears that the TRTR implementation is the best when taking all

three statistical measures into account.

The two-dimensional presentation of time-variant error statistics in this way also

offers insights into the location of relatively greater and lesser error, as well as its

propagation throughout the domain in time. For instance, in all figures it is clear that the

region closest to the source is subject to the greatest errors. The Nash-Sutcliffe results

in Figure 2-6 also show the expected result of greater discrepancy at the concentration

front (red ring) and the best match in the centre of the domain where source boundary

effects and numerical dispersion effects at the front are least felt. Black regions of the

Nash-Sutcliffe figures indicate that no values were calculated because no solute had yet

reached those points in the domain, thereby generating a null denominator in the Nash-

Sutcliffe calculations.

The Nash-Sutcliffe results in both figures also offer validation of the assumption in

the model setup that an enlarged model domain of 101x101 cells would be sufficient to









prevent any effects from the no-flow boundaries above and below interfering with the

focus region of the fifty cells centered on the source (Figures 2-4 and 2-5). At these

boundaries, the assumption of an infinitely open horizontal plane implicit to the

analytical solution is no longer met, and we see this disparity reflected in degraded

Nash-Sutcliffe efficiencies in the region of the boundary. However, throughout the bulk

of the domain, and certainly within the central 50 cells (25 cells above and below the

source region), we find excellent matching between numerical and analytical results.

Close comparison of Figure 2-5 and 2-6 corroborates the directionality of the error

propagation that is so visually striking in Figure 2-6. The isolines of Figure 2-5 match

best at approximately +/- 45 degrees to the horizontal, taken from the solute source

point. Greater than this angle and we see the numerical (black and orange) solutions

under-predict compared with the analytical isoline (green). Less than 45 degrees (i.e.

towards the extreme right of the concentration front) we see the models over-predict

relative to the analytical solution. This pattern is clearly reflected in the Nash-Sutcliffe

figure, where we see clear darker blue (higher Nash-Sutcliffe efficiency) arms projecting

out into a lighter blue surrounding area.

Conclusions

A free-form, non-spatial water-quality model was integrated with a spatially-

distributed hydrodynamic model. The resultant tool, FTaRSELOADDS, is a novel

water-quality tool that is spatially-distributed, driven by mechanistic hydrodynamics, and

user-definable. Linkage of the models was validated by demonstrating the ability of the

linked tool to replicate results obtained using the reactive transport functionality of

SWIFT2D when using aRSE to perform the reactions and SWIFT2D the transport.










Table 2-1. Quantities and values used in the comparison of SWIFT2D and FTaRSELOADDS against the analytical
solution for 2-D conservative and reactive transport. Variable names as required by SWIFT2D, aRSE or
STANMOD are included where appropriate


Decay rate Longitudinal (x)
[1] dispersion
[s] [m /s]


Transverse
horizontal (y)
dispersion
[m /s]


Transverse
vertical (z)
dispersion
[m /s]


Unit concentration
source dimension [m]


-a to a (y-direction):
Analytical lal = 100 m;
soaltica v= 0.05 RetFac = 1 TO =60000 s = 1E-5 Dx = 20.5332 Dy = 20 Dz = 1E-10 al o0 m
solution -b to b (z-direction):
Ibl= 1E+10m
SWIFT2D TRBNDA = 1
U,UP = 0.05 DIFDEF = 20 2 x 100 m cells (N,M):
transport and = 005 N/A for TITI = 0 to AKK= 1E-5 D = 0.2 DIFDEF = 20 N/A2 c (,)
reactions V,VP = 0.0 D1000 m D = 0.5332* Cell (50,1) and (51,1)
reactions 1000 min

SWIFT2D TRBNDA = 1
U,UP = 0.05 DIFDEF = 20 2 x 100 m cells (N,M):
transport with N/A for TITI = 0 to Kr = 1E-5 DIFDEF = 20 N/A
ea V,VP = 0.0 D min= 0.5332* Cell (50,1) and (51,1)
aRSE reactions Eq = 1000 min
*D1 calculated from Equations 2-6 and 2-7 for n = 0.03 s/m, H = 0.50 mn, 0 = 0.05 mn/s, g = 9.801 m/s Cd = 14.3


Case


Velocity
[m/s]


Retardation
Factor


Pulse length










Table 2-2. Nash-Sutcliffe efficiencies obtained for different methods of integrating
aRSE reactions into FTLOADS
SWIFT2D aRSE: TTR aRSE: TRTR aRSE: TRT
Average 0.92843577 0.94792578 0.94790868 0.94789519
Mode 0.99854711 0.98674260 0.99906814 0.99443873
Median 0.99463456 0.99467713 0.99466211 0.99464882


FTLOADDS aRSE (linkage)

during setup READIWQ Read XML filenames, variables,
Parameters, overrides
at specified Initiae lize nkage using IWQ inputs:
time intervals 1) convert Fortan strings to C++
SCALLaRSE strings; 2) pass variable &
Sparameter values to linkage array
S(C1_aRSE); 3) set time-step
if first cell ----"---------" -
aRSE IN
I Read in current values for
transported constituents if first time
& required hydrodynamics calling aRSE
every cell ------------------------
-- RUN_aRSE -
Fortran interfaces for -
calling C++ subroutines; ca once for
transfer cell data to aRSE each cell
input vector
if last cell r---------------------
aRSE OUT
I
Return updated
constituent values for
Transport & all other aRSE
State variables for printing
1-,,,,-,,,


INITIALIZE
Initializes the
user-defined
reaction
equations

RKSOLVE
Solves the
user-defined
reaction
equations


calls C++
FTLAODDS 4 aRSE linkage
subroutine
subroutines (Fortran) *- -n
I ..... ..... ..... ..... .. .j


Figure 2-1. Schematic detailing the architecture of the code linking the surface-water
model in FTLOADDS (SWIFT2D) with a Reaction Simulation Engine (aRSE).









cO


-C -


-co


Figure 2-2. Source boundary condition for analytical solution: Third-Type, flow in the x-
direction, source dimension a = 100 m in horizontal transverse y-direction,
source dimension b = 1E+10 (~infinity) in the vertical transverse z-direction
(from Leij and Bradford, 1994).












101



.... .. ... .. .. .. .. .. .... ........... ...... .. .... .... ............... .... .. ... .... .....

-- -,----- -- -- -- -- -- --- -- -* .. .. .. .. .. .. .... .. ..


57

56

55

54

53

52

51

50

49

48

47

46

45

44

43

A


I I



N=1

M=1 2 3 4 5 6 7 8 9 ---------------- 93 94 95 96 97 98 99 100 101


Figure 2-3. SWIFT2D model domain used for comparison of conservative and reactive
transport simulations with analytical solutions; red indicate source cells, all
cells 100 m square, total domain 10,000 m, no-flow boundaries at N=1 and
N=101, and M=1.











Conservative, DIFDEF=20: Conc at t=100min
75- 1
SWIFT2D
70 Analytical solution

65 Analytical solution
(corrected)


Column number (x 100m)


Conservative, DIFDEF=20: Conc at t=900min
7.-F, I I I I I


E 60-
o
o
55


0 1
c 4'3

I4(j


5 10 15 20 25 30 35 40 45
Column number (x 100m)


0
0



E
C
0
aY


Conservative, DIFDEF=20: Cone at t=500min


5 10 15 20 25 30 35 40 45
Column number (x 100m)


Figure 2-4. Concentration isolines for 2-D conservative transport from a small
rectangular source as determined by SWIFT2D (black), the analytical solution
(green), and the analytical solution with numerical dispersion effects
accounted for (orange).












Reactive, mu=0.00001, DIFDEF=20: Conc at t=100min


5 10 15 20 25 30 35 40 45
Column number (x 100m)


Reactive, mu=0.00001, DIFDEF=20: Conc at t=900min


5 10 15 20 25 30 35 40 45
Column number (x 100m)


Reactive, mu=0.00001, DIFDEF=20: Cone at t=500min


5 10 15 20 25 30 35 40 45
Column number (x 100m)


Figure 2-5. Concentration isolines for 2-D reactive transport from a small rectangular
source as determined by SWIFT2D (black), the analytical solution (green),
and the coupled version of FTLOADDS and aRSE (orange).











RMSE for Case 10a2_4 (at 150mins)
100
90
80
E
c 70
60 ... .
- 50
E
z 40
6 30-
20
10

10 20 30 40 50 60 70 80 90 100
Column Number (x 100m)


0.01





z
0.0005 S


10 0002



00
0::oo
I O 1JL1U


Nash-Sutcliffe for Case 10a2_4 (at 150r


90
80
70
60
50
40
30
20
10

10 20 30 40 50 60 70 80 90 100
Column Number (x 100m)


mins)




0 99

095


0.7
-10.7


Figure 2-6. Spatially-interpolated RMSE (left) and Nash-Sutcliffe efficiencies (right)
after 150 minutes of simulation for the case of transport-reactions-transport-
reactions.


RMSE for Case 10a2_4 (at 300mins)


10 20 30 40 50 60 70 80 90 100
Column Number (x 100m)


Nash-Sutcliffe for Case 10a2_4 (at 300mins)
100
90 1
0.01 E 80
S70
095
0.001 0.9
n 50 0.9
E
z 40 0.7
0 0005 30
S030


10 0002



0


10 20 30 40 50 60 70 80 90 100
Column Number (x 100m)


Figure 2-7. Spatially-interpolated RMSE (left) and Nash-Sutcliffe efficiencies (right)
after 300 minutes of simulation for the case of transport-reactions-transport-
reactions.









CHAPTER 3
MODELING HYDROLOGY IN THE SOUTHERN INLAND AND COASTAL SYSTEMS

Introduction

There are two major paths of natural freshwater flow from the Everglades into

Florida Bay. One pathway, Taylor Slough, empties directly into the Bay, while the other

pathway, Shark River Slough, contributes a portion of its flow to Florida Bay, but

discharges primarily into the Gulf of Mexico. Freshwater inputs are vital to the coastal

Everglades ecosystem, having important impacts reaching as far as the Florida Keys

(SFWMD and FDEP, 2004). In particular, changes to the flow patterns are expected to

have consequences for water-quality in Taylor Slough, adjacent wet prairies, and the

coastal estuaries into which they empty (Childers, 2006). Modeling the region's

hydrology is the first phase of an effort to model the phosphorus water-quality using a

new water-quality model for the region.

Previous Hydrological Modeling of SICS

Numerous modeling and experimental studies have been undertaken to better

understand the hydrodynamics within the SICS region. For many years, the South

Florida Water Management Model (SFWMM; MacVicar et al., 1984) was used to

provide regional hydrologic information at a 2-mile by 2-mile spatial scale. The coarse

spatial resolution made SFWMM unsuitable for the detailed analysis required to

determine local water management needs and support mechanistic water-quality

modeling efforts.

The South Florida Regional Simulation Model (SFRSM; Brion et al., 2000) was,

and continues to be, developed to replace the SFWMM. Though SFRSM employs a

variable-resolution triangular mesh for spatial discretization, like its predecessor it too









neglects inertial forces, and flow volumes are consequently less accurate. Also

neglected are variable-density and unsteady flow conditions, which are important

characteristics of the SICS region because of tidal interactions with Florida Bay and

wind-shear effects (Swain et al., 2004). Results from efforts to simulate coastal flows to

Florida Bay using SFWMM (Hittle, 2000) were undermined by greatly amplified

freshwater flows, which in turn diluted coastal salinities. Lin et al. (2000) attempted to

use FEMWATER123 for the region, but the computational demands of the model, which

simulates 1-D canal flow, 2-D overland flow, and 3-D finite-element ground-water flow,

were restrictive.

The failure of these models to meet the persistent need for greater accuracy and

spatial resolution of the simulated hydrologic conditions in SICS (as a necessary input

for ecological modeling efforts using ATLSS) and freshwater inputs to Florida Bay

(needed for hydrodynamic modeling of Florida Bay) led to an extensive modeling effort

by the USGS that included a number of field studies to quantify physical parameters.

The major product of this effort was the development of the SICS model, an application

of the USGS-developed Surface-Water Integrated Flow and Transport in 2-Dimensions

(SWIFT2D) hydrodynamic/transport model with additional enhancements specifically for

the coastal wetlands of the Everglades (Swain et al., 2004; Swain 2005).

Variable-density ground-water simulation was integrated into the SICS application

by Langevin et al. (2005). The effort entailed linking SWIFT2D with SEAWAT, a version

of the 3-D modular ground-water flow model MODFLOW integrated with the 3-D

modular transport model MT3DMS, which can simulate variable-density ground-water

hydrology. The resultant tool is known as Flow and Transport in a Linked Overland-









Aquifer Density Dependent System (FTLOADDS), which was subsequently adapted

further for the Tides and Inflows in the Mangroves of the Everglades (TIME) application

(Wang et al., 2007). The TIME application not only encompasses the SICS region, but

greatly expands the domain to include all of Everglades National Park and Big Cypress

National Preserve. Versions 1.0 and 1.1 of FTLOADDS refer to the original SICS

applications using only SWIFT2D. Version 2.1 refers to the coupled surface-

water/ground-water SICS application, and version 2.2 the coupled surface-

water/ground-water TIME application (see Appendix A for further details on versions).

Remodeling the Hydrology of SICS

The proposed effort to model water-quality in the SICS region using

FTaRSELOADDS requires a suitable hydrologic application to provide the necessary

hydrodynamic drivers of water-quality. The original SICS application, which did not

include ground-water simulation, was selected for the inaugural application of

FTaRSELOADDS based on a number of considerations: 1) the surface-water results

obtained with this simplified version of FTLOADDS were considered sufficient for such

testing; 2) the water-quality focus was on surface-water conditions, so only SWIFT2D

had been coupled with aRSE (see Chapter 2); 3) the concerns about compounding

computational times given the addition of aRSE to an already computationally intensive

tool.

However, a number of changes have been made to the SWIFT2D code in

FTLOADDS as the tool has evolved to the current form (version 2.2), which were not

present when the original SICS application (version 1.1) selected for testing

FTaRSELOADDS was established. It was therefore necessary to evaluate the effects of

these changes, many of which were simplifications, on the simulation of surface-water









hydrology in SICS. In particular, the effect of removing depth-varying Manning's n

needed to be evaluated to assess the implications for water-quality modeling.

Materials and Methods

Model Description

The 2-D, vertically integrated, unsteady flow and transport model SWIFT2D has its

origins in SIMSYS2D (Leendertse, 1987), which in turn built on earlier work conducted

throughout the 1970's by Leendertse and his colleagues at The Rand Corporation to

develop a water-quality simulation model for well mixed estuaries and coastal seas

(Leendertse, 1970; Leendertse and Gritton, 1971; Leendertse, 1972).

SWIFT2D governing equations

Thorough descriptions of the SWIFT2D governing equations and their numerical

implementation are variously provided in Leendertse (1987), Goodwin (1987), Bales

and Robbins (1995), and Schaffranek (2004). Four partial-differential equations are

used to describe unsteady, non-uniform, variable-density, turbulent fluid motion

(Equations 3-1 to 3-3) and solute transport (Equation 3-4), which are formulated

according to the laws of Conservation of Mass and Conservation of Momentum.

Hydrodynamics are described with the two-dimensional Saint-Venant equations (de

Saint-Venant, 1871; Equations 3-2 and 3-3), which are derived from the Navier-Stokes

equations by applying temporal averaging of velocity, pressure and mass over time-

intervals that are long relative to the time-scale of turbulent fluctuations, and assuming

negligible vertical accelerations. Transport is described by the advection-dispersion-

reaction equation (Equation 3-4). The resultant formulations retain nonlinear advective

and bottom-stress terms, which permit the simulation of eddies and residual circulation,

and coupled motion and transport with time-varying horizontal density gradients:









a,; O(HU) O(HV)
+ + (HV 0, (3-1)
at ax ay

aU aU U V V +g 8+ gH8p + U2 +V2 OpW2 sin
-+U V fV +g- + +gU
at ax Oy 8x 2pax C2H pH
(3-2)
k2U a2V =
8x2 y2 )


aV aU 8V ag gH8p VU2 + V2 epaW2 cos
-+U-+V-- fU+g-- + +gV
at ax ay ay 2p8y C2H pH
(k 2V+ a2U (3-3)
S-+ --O= 0, and


8(HP) 8(HUP) 8(HVP) 8(HDxP / ax) 8(HDyP /I y) HS
+ + + HS = 0,
at ax ay ax ay (3-4)

where:

C = Chezy resistance coefficient coefficient;
Dx,Dy = diffusion coefficients of dissolved substances;
f = Coriolis parameter;
g = acceleration due to gravity;
h = distance from horizontal reference plane to channel bottom;
H = temporal flow depth (h + C);
k = horizontal exchange coefficient;
P = vector of vertically averaged dissolved constituent concentrations;
S = source of fluid with dissolved substances;
U = vertically averaged velocity component in x direction;
V = vertically averaged velocity component in y direction;
W = wind speed;
S= water surface elevation relative to horizontal reference plane;
0 = wind stress coefficient;
p = density of water;
Pa = density of air; and
i = angle between wind direction and the positive y direction.









SWIFT2D numerical solution technique

The governing differential equations cannot be solved analytically unless

subjected to simplifying assumptions that are unacceptable for the intended

applications. A finite difference numerical solution technique is therefore applied to a

computational domain of equally spaced grid points. The finite-difference equations are

solved on a space-staggered grid (Figure 3-2) using the alternate-direction implicit (ADI)

method. Velocity points are located between water-level points to produce an efficient

solution of the continuity equation (Leendertse, 1987). The ADI method splits the time-

step to obtain a multidimensional implicit solution that provides second-order accuracy,

and requires only the inversion of a tridiagonal matrix in order to solve each set of finite-

difference equations (Roache, 1982). Detailed descriptions of the finite difference

equations are provided in Swain (2005).

Though the ADI method is unconditionally stable (Leendertse, 1987) there are

practical limitations to the time-step (Roache, 1982), particularly when applied to

irregularly shaped domains (Weare, 1979) or complex bathymetries (Benque et al.,

1982).

SWIFT2D code enhancements and simplifications

The FTLOADDS code presently available is that of version 2.2. The original SICS

application represents FTLOADDS version 1.1, which included enhancements to

SWIFT2D but no ground-water linkage (see Chapter 2). These enhancements were

maintained with only minor changes to the SWIFT2D code due to the coupling process

in FTLOADDS version 2.1. However, SWIFT2D code was significantly modified in the

course of the model's evolution to version 2.2. This has implications for this effort to

reproduce SICS surface-water results originally obtained using SWIFT2D v1.1.









SWIFT2D in FTLOADDS v1.1. The original effort to model surface-water flow in

the SICS region required a number of modifications to the SWIFT2D model (Swain et

al., 2004):

* Precipitation: The rainfall code was adapted to permit spatially-distributed values for
rainfall volume to be added to individual cells. Rainfall inputs were calculated at 15-
minute intervals by kriging the rainfall from 14 different rainfall stations in the region.
Rainfall was not added to dry cells, which implicitly assumed that when rainfall fell on
dry cells it infiltrated into the ground-water.

* Evapotranspiration: Evapotranspiration (ET) was not included in the original
SWIFT2D v1.0 code, which was intended for application to estuaries and coastal
waters where evaporation could be considered negligible and macrophytes
sufficiently sparse to ignore transpiration. For SWIFT2D v1.1 an equation regressing
ET with solar radiation and depth (German, 2000) was applied to each cell to
determine spatially-distributed, time varying ET.

* Depth-varying Manning's n: When up-scaling point measurements of frictional
resistance to grid-scale representative values, microtopography can increase the
effective frictional resistance at lower depths. To address this, an empirical relation
was applied to determine an effective Manning's n (neff) based on a reference input
value (n, measured or estimated), a reference depth (dref, the assumed depth at
which measurement or estimation was conducted), the actual depth (d), and a power
variable (p) to capture non-linear effects (Swain et al., 2004):


neff = n d (3-5)



* Wind-sheltering: To account for the sheltering effects of vegetation (Jenter, 1999),
which were not considered for open-water applications of SWIFT2D v1.0, a spatially
uniform sheltering coefficient was applied to all vegetated cells (considered those
having a Manning's n greater than 0.1).

* Other: Other changes included technical modifications to the treatment of flow
adjacent to barriers (which were not previously permitted to go dry), wind friction in
cells adjacent to water-level boundaries (set to zero to avoid numerical oscillations),
and output printing routines.

SWIFT2D in FTLOADDS v2.2. The coupling of SWIFT2D to SEAWAT through

leakage required additional code, but left each of the models intact such that SWIFT2D

could be run without the need to call SEAWAT if so desired. However, the progression









from SICS application to TIME application introduced new changes to SWIFT2D (Wang

et al., 2007):

* Precipitation: Rainfall in version 2.1 was specified at 15-minute intervals and
spatially-interpolated from 14 stations for each cell. Rainfall in version 2.2 is
spatially uniform over defined zones, of which SICS represents one (i.e. uniform
rainfall over the entire domain), and is specified as 6-hour averages. Additionally, the
wetting and drying algorithm has been modified such that rewetting is now permitted
to occur directly from rainfall recharge.

* Evapotranspiration: In analogous fashion to rainfall, ET is now applied regionally,
and therefore uniformly over the SICS domain, also as 6-hour averages.
Additionally, the modified Penman method (Eagelson, 1970) has replaced the cell-
by-cell ET calculations (Swain et al., 2004). When depth of ET is greater than 10
percent of the remaining depth of water then ET is instead removed from the first
layer of the ground-water to avoid making the cell go dry or the depth go negative.
When the ground-water module is turned off this effectively means no ET occurs.

* Manning's n: The functionality to treat variation of Manning's n with depth of flow
was removed from SWIFT2D due to concerns over its empirical nature (E.D. Swain,
U.S. Geological Survey, personal commun., 2010). Frictional resistance (Chezy)
terms, which are calculated using depth and Manning's n, are now defined at cell
faces rather than at cell centers. This permits a different resistance in each of the
principal directions of flow, but also requires a second Manning's n-value for each
cell. In version 2.1 obstruction to surface-water flow, most notably the Buttonwood
Embankment, was defined using the original SWIFT2D barrier formulation intended
to represent weirs. Coastal rivers and creeks were defined as low barriers with
calibrated flow coefficients. In version 2.2 the coastal embankment is defined by a
modified cell-face frictional resistance term, with creeks represented as gaps with
specified (reduced) friction terms.

Considering the important roles played by both precipitation and ET in the south

Florida water budget (Sutula et al., 2001), and of Manning's n in determining flow

velocities and wet/dry conditions, the modifications to v2.2 described above represent

significant hydrological simplifications to the SWIFT2D model. This effort to model

SICS hydrology therefore represented an effort to study the effects of these model

simplifications on the ability of SWIFT2D to simulate hydrodynamics in the SICS region

for future water-quality application.









Model Setup

The SWIFT2D v1.1 model setup used in the original SICS application was

reapplied as consistently as possible in an effort to reproduce the original results for the

period of August 1996 through August 1997. All effort was made to maintain the same

model setup and parameterization, and the integrity of the original SICS application

should be assumed intact unless changes are specified below. Figures from the USGS'

SICS modeling report (cited as Swain et al., 2004) are reproduced where model setup is

appropriately consistent, and original figures have been produced where necessary.

Computational domain

The previously established SICS model (Swain et al., 2004) domain (Figure 3-3),

comprising 9,738 square computational cells of length 304.8 m (1000 ft) for a total

domain area of 905.8 km2, was applied with minimal changes to the model boundary.

The new treatment of frictional resistance terms at cell faces, rather than cell centers,

generated a number of points on the domain boundary where floating point problem

arose due to the underlying space-staggered grid geometry. The original version

required resistance terms for each cell in the computational domain, which is defined

row-by-row, and column-by-column, to produce the irregular boundary required.

Resistance terms were calculated based on input Manning's n values, which were

specified as zero outside the active domain. Since the original computational domain

was not defined to intentionally account for the additional cell face values required by

the current version, and given that the space-staggered grid used by SWIFT2D

attributes values originating in, for example, cell (m, n+1) to cell (m, n), instances of

Chezy resistance terms being calculated using Manning's n values of zero in the









denominator arose. This was resolved by eliminating the offending individual boundary

cells from the computational row or column as the case arose.

Land-surface elevations were measured at about 400-m intervals (Desmond et al.,

2000) and a linear distance-weighted four-point interpolation was applied to assign land

surface elevations to each computational cell (Figure 3-4). The Buttonwood

Embankment (Figure 3-1) is a significant hydrologic barrier in the region, which

separates the freshwater wetlands from Florida Bay. Most exchange of water occurs

through the many creeks that traverse the embankment. Physically, the embankment is

an elevated region, but in SICS it is simulated by barriers based on large resistance

terms in the direction of flow, interspersed with lower resistance values where creeks

cut through the barrier.

Boundary conditions

Boundary conditions (Figure 3-5) were provided at the water surface and lateral

boundaries. The water surface boundary is assumed to be horizontal in each cell; water

is permitted to move vertically but no deformation of the water surface within the cell is

considered. Physically, this implies that high-frequency surface waves are not

accounted for in the model.

A uniform rainfall rate was supplied as a model input file containing values

calculated as the arithmetic mean of all stations in the SICS region, averaged over 6-

hour intervals. A uniform ET rate was similarly supplied as an input file, rather than

calculated within the model. Input ET values were calculated as the regional mean of

ET values calculated according to the modified Penman method (Wang et al., 2007).

Wind conditions are represented as spatially uniform across the entire domain, and the

data from the Old Ingram Highway site was used to define the wind field. A moving









average wind speed was used for the boundary condition since fluctuations in wind

conditions at sub-hourly time-scales are considered to not generally be representative

of regional patterns, which is the scale implied when uniformly applying wind.

Lateral boundaries are described as open (free exchange with water and solutes

across the boundary) or closed (no flow or exchange). Open boundaries were

described by time-series inputs for either discharge or water-level. The SICS model

lateral boundaries are identified in Figure 3-5, and include seven constant head

boundaries and three discharge source boundaries. The discharge sources (Figure 3-

6) are at Taylor Slough Bridge, the C-111 pumping station, and within the L-31W canal.

Inflow at Taylor Slough Bridge was determined from stage-discharge data at the Taylor

Slough Bridge site, and at the L-31W site according to stage-discharge relationship at

the S-175 hydraulic gate structure, where this flow originates. Input of discharge at C-

111 source is based on the discharge from pumping station S-18C, occasionally

adjusted to compensate for flows directly out of the canal and into Florida Bay when the

S-197 structure is opened. The levee on the southern side of the C-111 section has

been removed to promote delivery of additional water to the SICS region. An artificial

topographic low along the SICS boundary was applied to facilitate more uniform flow

distribution along the lower section of C-111.

Several regional model parameters are required and applied as per Swain et al.

(2004): air density, latitude (single value), kinematic viscosity of water, wind stress

coefficient, unadjusted horizontal mixing coefficients, isotropic mass dispersion

coefficient, a coefficient relating mass dispersion to flow conditions, a resistance









coefficient for each computational cell and for tidal creeks, and marginal depth (Swain et

al., 2004).

Stability considerations

Although the ADI method is unconditionally stable (Leendertse, 1987), the

treatment of flow barriers introduces practical limitations. Experimentation with the time-

step eventually lead to selection of a half-step of 1.5 minutes, which demonstrated

sufficiently stability in the region of the creeks and barriers. The next-largest possible

half-step was 2.5 minutes, based on the fact that full time-steps needed to be

compatible with the time-steps defined for tidal boundary conditions, which are read in

at 15-minute intervals, and this proved to be unstable.

Given the simulation of salinity transport it was also necessary to consider

numerical dispersion. A diffusion coefficient of 10 m2/s was applied based on the

previous application of SICS v1.1. (Swain et al., 2004). Considering the cell dimensions

of 304.8 m, and a conservative (high) estimate for average velocities on the order of

0.05 m/s (based on previous results in Swain et al., 2004), a Peclet number of

approximately 1.5 was obtained, which even though conservative was below the

generally applied upper limit of 2.

Results and Discussion

Water-level results at the 12 observation stations in the SICS domain are

presented first, followed by an assessment of the flow through the creeks linking Florida

Bay to Taylor Slough. Following thereafter are 2-D results for water-level, flow, and

salinity.









Water-Level Results

Simulated stages at each of the 12 water-level stations are presented in Figures 3-

7 and 3-8. Results are divided between those stations that fall within Taylor Slough

(Figure 3-7), which are more directly subject to discharges from the TSB source, and

stations east of the slough (Figure 3-8) that are more directly affected by flows

originating from the C-111 canal. The area of the time-series figures shaded in brown

indicates the subsurface. Where brown meets blue corresponds to ground-surface

elevation for the cell containing the location of the station. The area shaded in blue

indicates the maximum observed water-level during the model validation period from

July of 1996 to August 1997. Observed water-levels are depicted in blue, and can drop

below the ground surface because water-level observations are recorded by wells. The

results obtained using SWIFT2D v1.2 are shown in black. Periods where simulated

results are not depicted correspond to conditions that SWIFT2D considers dry, which

occur when water depth drops below 5 cm. As can be seen in both figures, this

happened regularly for a number of locations, including two critical phosphorus

concentration observation locations, the EPGW and P37 stations.

Significant effort was expended attempting to resolve this. The final solution was to

reintroduce the functionality of depth-varying Manning's n, which had been removed in

the present version (v1.2). The reintroduction of depth-varying Manning's constitutes an

updated version of 1.2, and is designated version 1.2.1 (red results in Figures 3-7 to 3-

10). In the original SICS v1.1 modeling effort, the variables applied to the nominal

Manning's input, dref and p (Equation 3-5), were 0.6 m and 2 respectively. In this version

1.2.1 the reference depth was set to 0.4 m given the absence of almost any depths of









0.6 m in the simulated year, making such an assumption for the reference depth

questionable. The simple non-linear quadratic power was maintained.

A comparison of the results obtained in this work with those from the original SICS

modeling effort (Swain et al., 2004) is given in Figures 3-9 and 3-10, with statistics

comparing all three versions original SICS application (v1.1), present SICS application

with depth-constant Manning's n (v1.2), and present SICS application with depth-

varying Manning's n (v1.2.1) are presented in Table 3-1, and summarized in Table 3-

2.

Visual comparison of the results in Figures 3-7 to 3-10 with the statistics in Table

3-1 reveals some contradictions. Visually, it is clear that the results obtained using

depth-varying Manning's n (in both SICS 1.1 and 1.2.1) are a better representation of

reality insomuch as periods of wetness and dryness are captured more reliably,

particularly for the critical water-quality stations EPGW and P37. In SICS v1.1 (Figures

3-9 and 3-10) we see a tendency on the part of the model to over-predict water-levels,

especially at the beginning of the simulation and the beginning of the second wet-

season. The current application performs much better in this regard. Conversely, in

SICS v1.2 (Figures 3-8 and 3-9), the lack of depth-dependency in flow resistance

results in excessively rapid drying out of the system when data clearly shows that wet

conditions prevail. Version 1.2.1 avoids the drawback of both of these versions, better

predicting the dry-down following wet periods compared with SICS v1.2 and avoiding

the over-predictions that were characteristic of SICS v1.1.

The Nash-Sutcliffe efficiencies presented in Table 3-1 and summarized in Table 3-

2 do not capture this, instead implying that v1.2 offers the best results. This is a









consequence of the fact that periods of dry conditions are not accounted for in the

Nash-Sutcliffe calculations because there is no simulated depth value against which to

compare the observed value. The result is a failure to capture the full extent of the

error, and exposes a weakness of this error statistic for assessing results in shallow

systems where wetting and drying is frequent. Additionally, the EP12R station has very

low Nash-Sutcliffe results which disproportionately reduce the Nash-Sutcliffe statistics

(Tables 3-1 and 3-2) considering how little data is actually present for this station

(Figure 3-9). Furthermore, the station is located very close to the boundary of the

model, a region that is known to be susceptible to greater errors due to boundary effects

(Leendertse, 1987).

Figure 3-11 to 3-13 shows the frequency and cumulative distribution of Nash-

Sutcliffe results for all stations, Taylor Slough stations, and C-111 wetlands stations

respectively, from SICS v1.2.1. Over 40 percent of all the stations attained Nash-

Sutcliffe efficiencies of 0.7 or higher, and approximately 60 percent of 0.5 or higher.

Performance of the model for simulating water-levels in Taylor Slough (Figure 3-12) was

comparable to that for the C-111 wetlands (Figure 3-13).

It is known that bias can lead to misleading Nash-Sutcliffe efficiencies (McCuen et

al, 2006). Furthermore, indication of a tendency to over-predict or under-predict would

be useful in interpreting how the changes made to SICS have affected the models

ability to capture particular conditions, which would be useful in future water-quality

modeling efforts.

Simulated results from SICS v1.1. and v1.2.1 were plotted against analogous

observational data. For the 6 stations in the vicinity of Taylor Slough (Figure 3-12) we









see a general reduction in variability about the 1:1 line for SICS v1.2.1 compared with

v1.1. Stations higher up the slough (R127 and TSH) are the exception, tending towards

over-prediction at shallow depths and under-prediction otherwise. For the C-111

stations (Figure 3-13), the current SICS v1.2.1 offers marked improvements, indicating

that v1.2.1 is better equipped to handle the conditions of both slough (Taylor Slough

area of SICS) and marl prairie (C-111 wetlands area). In particular, results were greatly

improved for the EVER4 station and, importantly for water-quality, the EPGW station.

The poor results obtained for EP12R appear to be a problem in both versions of the

model. Since both versions apply some form of depth-varying Manning's coefficient,

while version 1.2, which has better results for EP12R according to the Nash-Sutclife

efficiencies previously discussed, does not account for changing resistance with depth,

this may be a consideration. If the EP12R site is sparsely vegetated then the depth-

varying effect will be less important, and may then be a reason for this discrepancy.

Water-levels throughout the SICS region are presented on the first of each month,

from August 1996 to July 1997, in Figures 3-14 (first wet season), Figure 3-15 (dry

season), and Figure 3-16 (end of dry season and start of wet season). Two-dimensional

results are presented beneath time-series figures depicting precipitation and discharge

source inputs to the domain during that period to facilitate visual comparison between

inputs and hydrologic conditions.

Discharge Results

Discharge data were available for five creeks in the Buttonwood Embankment.

Figure 3-17 compares the simulated daily averaged flow rates in SICS v1.2.1 with the

observed daily averaged flow rates. These results are important for assessing the

accuracy of fluxes, which are critical if loading rates are to be estimated. They are also









an important consolidation of depth and velocity simulations; given the reliable depth

results described above, reliable flux results therefore indicate reliable velocities, which

are important for the transport of solutes in water-quality modeling.

In all creeks except McCormick Creek, the magnitude and timing of daily average

fluxes were satisfactory. Vector diagrams depicting flow direction and magnitude are

given for the first of each month in Figures 3-18 to 3-20. Results reproduce well the

trends found in Swain et al. (2004) that show tendency for flow from both Taylor Slough

and C-111 to congregate in the region of Joe Bay. It is therefore important that the two

primary creeks in this region, Taylor Creek and Mud Creek, are well modeled since they

represent a significant portion of the Taylor Sough flow output to Florida Bay. The large

fluxes through Trout Creek and the directionality of fluxes towards it from the C-111

canal indicate its importance for inputs to Florida Bay originating from the eastern region

of SICS. Fluxes are probably particularly large through Trout Creek because of its

position between two large water bodies that hold relatively deep water permanently

compared with the shallow and intermittently wet/dry conditions on the landward side of

Taylor Creek and Mud Creek.

Salinity Results

Figures 3-21 to 3-23 present the two-dimensional spatial results for salinity

distribution throughout SICS on the first of each month. These results illustrate the

significant diluting effect of freshwater inputs from Taylor Slough and C-111 to Florida

Bay during high flow periods. Salinities were substantially higher throughout the Bay in

the dry season. Dilution emanated from the region of Joe Bay following high freshwater

flows, as would be expected given the previously discussed flow results. During peak

dry periods there is marked intrusion of salinities into the coastal wetlands in the eastern









regions of SICS. Particularly high salinities may be due to evapotranspiration of water

with increased salinity due to tidal influxes during low-flow periods. Such water may

also become trapped in depressed regions by surrounding dry land after tides have

withdrawn.

Conclusions

The current working version of SWIFT2D (v1.2) does not contain depth-varying

Manning's resistance. This proved to undermine the ability of the mode to accurately

capture wet and dry conditions, which are important for both practical considerations

(given the paucity of phosphorus data points for testing in Chapter 4) and

biogeochemical considerations (since wet conditions determine the presence or

absence of aquatic processes). When depth-varying Manning's n was reintroduced into

the model in version 1.2.1 this problem was overcome. Water-levels throughout the

SICS region and discharge rates for important creeks were captured well. The reliable

simulation of wet and dry conditions and velocities therefore established a satisfactory

foundation for mechanistic water-quality modeling of the region.

It is possible that the reintroduction of ground-water exchange may negate the

need for depth-varying Manning's n. Under very shallow flow conditions, which is when

depth-varying Manning's would be most important, the small surface-water hydraulic

head may lead to ground-water upwelling into the water column. Other modeling efforts

in the region have shown that ground-water inputs likely occur during the dry season

(Langevin et al., 2005), with possible implications for phosphorus loading to the surface

water as well (Prince et al., 2006). In the absence of ground-water exchange, the

calibration of the depth-varying Manning's parameters dref and p to maintain surface-

water heads that would otherwise dissipate (as shown in the results for v1.2) equates to









compensating for the lack of ground-water upwelling that may actually be occurring.

Consequently, a fully coupled surface-water/ground-water simulation of SICS using

version 1.2 may be sufficient to justify the assumption of depth-invariant Manning's n.

However, for the purpose of testing the phosphorus water-quality model, water-levels

under shallow conditions are sufficiently sensitive to require that depth-varying

Manning's be included.









Table 3-1. Nash-Sutcliffe efficiencies for water-level observation points in SICS
Station SICS v1.1* SICS v1.2** SICS v1.2.1***
CP 0.7201337 0.901839 0.8771178
P67 0.2144507 0.7837026 0.8087565
TSH 0.7313131 0.8232658 0.7899594
P37 0.7620635 0.863053 2.44E-02
E146 0.778919 0.8662752 0.8897558
EVER5A -0.1176481 0.6932715 0.3337759
EVER7 0.5472993 0.7139693 0.8710759
EPGW 0.4939922 9.81 E-02 0.4452754
EVER6 0.8514937 0.6204761 0.8550127
EP12R -2.930052 -1.618115 -4.148942
EVER4 0.5493984 0.8272943 0.6898439
R127 0.5810636 0.5898135 0.4134087
* Calculated from digitized results in Swain et al., 2004
** Manning's n held constant with depth of flow
*** Manning's n varied with flow depth according to Equation 3-5

Table 3-2. Nash-Sutcliffe statistics for stations in the viciniy of Taylor Slough, s
the vicinity of C-111, and all stations in the SICS region.
SICS v1.1* SICS v1.2** SICS v1.2.1***


stations in


Taylor Slough stations
Mean 0.6313 0.8047 0.6339
Standard Error 0.2159 0.1128 0.3463
Median 0.7257 0.8432 0.7994
Kurtosis 3.7805 3.4693 1.0346
Skewness -1.9502 -1.7921 -1.4219
C-111 stations
Mean -0.1009 0.2225 -0.1590
Mean (excl EP12R) 0.4649 0.5906 0.6390
Standard Error 1.4219 0.9371 1.9666
Median 0.5206 0.6569 0.5676
Kurtosis 4.9453 4.4112 5.7462
Skewness -2.1940 -2.0892 -2.3836
All stations
Mean 0.2652 0.5136 0.2375
Mean (excl EP12R) 0.5557 0.7074 0.6362
Standard Error 1.0423 0.7052 1.4085
Median 0.5652 0.7488 0.7399
Kurtosis 9.9357 9.1905 10.8236
Skewness -3.0767 -2.9601 -3.2369
* Calculated from digitized results in Swain et al., 2004
** Manning's n held constant with depth of flow
*** Manning's n varied with flow depth according to Equation 3-5











W830'


Base trUni U S =eo1d 3wney darm dab. 1972
UriKeral TFaref9se Meafttr poedlor Zone it, Dalunm NAD 27 8130' 8100' 8I30' W 8000'
26030' '
EXPLANATION
SEVERGLADES NATIONAL PARK


I I APPROXIMATE AREA OF TAYLOR SLOUGH
- BOUNDARY OF SOUTHERN INLAND AND
COASTALSYSTEMS SICSS STUDYAREA
- BUTTONWOOD EMBANKMENT
A STAGE MEASUREMENT SITE lUSGSp
SRA FALL, WIND AND SOLAR RADIATION
MEASUREMENT SITE (LISGS)
RAINFALL MEASUREMENT SITE (NPS
PUMPSTATION
ET EVAPOTRANSPIRATION


Figure 3-1. Location of the Southern Inland
Swain et al., 2004).


26 '' I


/ '.


24"30
0 40KILOMETERS
O 4 MILES


and Coastal Systems study area (from


25'30'
















25" 5'


W845'


W15'


L


-,. -10


2_. : I-











0 0




0 0


EXPLANATION

+ WATER LEVEL

O DEPTH

- U-VELOCITY

I V-VELOCITY


j-1 j j+1
Figure 3-2. Space-staggered grid system showing relative locations of hydrodynamic
characteristics.


k+1


k-1













80045' 80040' 80'35'


25025'


ITa'lor I a '-


F,,i Pilm
R,'j,,-, :: :
3lal,,:r,


- r f \ i- r.rlf IJ.tI rl" 7-r ?.- f-*.N ,ji


1.1 .-B 'IT ir. a 1B 1 I 'n i 17,Datm NAD 27

0 1 2 3 4 KILOMETERS
0 1 2 3 4 MILES
0 1 2 3 4 5 MILES


EXPLANATION
SEVERGLADES NATIONAL PARK BUTTONWOOD EMBANKMENT
APPROXIMATE AREAOF LOCATION OF HYDRAULIC BARRIERS
TAYLOR SLOUGH WITH CUTS TO REPRESENT CREEKS
BOUNDARY OF SOUTHERN
INLAND AND COASTAL SYSTEMS
SICSS) STUDY AREA


Figure 3-3. The SICS computational grid, showing the location of Taylor Slough, the

Buttonwood Embankment and the coastal creeks (from Swain et al., 2004).


* S


25020' I-


25010' -


1 .- :r ,r I "r


I I i


80,30' 80,25'












80030' 80025


25'25'


25020 --









25'15 --









25010


-.. r.... ,-. ..4 .h. ...1 .-,.., 1r2 EXPLANATION
.,1,,. lr,,,rr., r., ,pr -jr, Z r, 17. Datum NAD 27 LAND-SURFACE ELEVATION, IN METERS ABOVE AND
BELOW NORTH AMERICAN VERTICAL DATUM OF 1988
0 1 2 3 4 KILOMETERS Greater than 0.30 -0.15 to 0.0 -0.61 to -06 -1.07 to -0.91
0 1 2 3 4 5 MILES 0.15 to 0.3 I -0.30 to -0.15 -0.76 to -0.61 -1.22 to -1.07
0 0.0 to 0.15 -0.46 to -0.30 -0.91 to -0.76 Less than -1.22
BOUNDARY OF SOUTHERN INLAND AND COASTAL SYSTEMS SICSS) STUDY AREA


Figure 3-4. Land-surface elevations (from Swain et al., 2004).


80045'












80050'


80035'


25025'


25'20' -








2515' -








25010, -


i Mile Pdlna


S .a, *::.Aerb cenfluma
LI- I whaler i3 1


A McCornm~ck


*
BK
0 1 2 3 4 KILOMETERS
I-- ,l I ,1 WB
0 1 2 3 4 5MILES

6aI Trt c- U.. C-al.i .jr,, 7 diZolirj daa 1972
IJr..er, l Trsr. ns.l re ell.:or p.Kl4 J .:.r Z.:.re 17, Dalum NAD 27


m EVERGLADES NATIONAL PARK SPECIFIED WATER-LEVEL MODEL BOL
APPROXIMATE AREAOF SPECIFIED FLUX MODEL BOUNDARY
TAYLOR SLOUGH
--- NO-FLOW BOUNDARY OFFSHORE WATER-LEVEL STATION
- BOUNDARY OF SOUTHERN INLAND AND EVERGLADES NATIONAL PARK
COASTAL SYSTEMS SICSS) STUDY AREA WATER-LEVEL STATION
A COASTAL FLOWAND STAGE STATION
(U.S. GEOLOGICAL SURVEY)


INDARY


Figure 3-5. Location of SICS model boundary conditions, including specified water-level
boundaries and discharge sources (from Swain et al., 2004).


EXPLANATION


80o45'


80'30' 80'25'


i


i. i-










First wet season



I


I




--TSB
-L-31W
C-111
-Rain
-I

I
I
I
I


Dry season Second wet season
-------- ---- ---^



0.05



0.1

0.15 -


0.2 1
i

3


---- M ----- *- *
8,'1/96 9,1/96 10/1/96/ 96 1/96 12/1/96 1/1/97 2/11' /97 41/1/9 5/1/9.7 6/1/97 7/1/97 8/1/97

Figure 3-6. Specified hydrologic inputs to SWIFT2D: discharge on the bottom axis and
rainfall on the top axis. The three principal seasons, wet interspersed by dry,
during the course of the simulation are depicted.


I


I


I


_ ______ _____I












0.8
8 -127 maximum SIMULATED SIMULATED ground
0.6 OBSERVED depth SCSv1.2.1 SICSv1.2 surface
0.4
0.2

-0.2
-0.4 AUG96 JUL 97
0.8 NP-P67

0.4
0.2 -,

-0.2
S0.4 AUG9 JUL 97
> 8045 80 8040' 8035' 80"30' 80*25'

Z 0.6
0.4
a 0.2

S02
J 06 Rn Ri27
02 -EVR4

Z 08 P-P .'H EVER7A,
0-- A EVER6A
LU 0.4 .. -R EVER5A T S
S"EPGWISWA .

0.2 25 10
-0.2 c
-0.4 AUG 96 JUL 97 '
-0.2 "-, x. 2'tI-"CP T_ ,: '
0.8 p .. .., -.... EXPLANATION
E-1 4'








0.6 1 EVERGLADES NATIONAL PARK A STAGE MEASUREMENTS SITE (USGS)
0.4TAYLOR SLOUGH STAGE, CONDUCTIVITY AND DISCHARGE










0 -- BuTTONWOOD EMBANKMENT A STAGE MEASUREMENT SITE (NPS)
0.2 STAGE AND CONDUCTIVITY MEASUREMENT
-0.4 AUG96 JUL 97 SITE(NS)
P-C ;.EXPLANATION
-0.4 EVERGLADES NATNAL PARK A DISTAGE MEASUREMENTS SITE (USGS)
I ,1 2 3 4 5 KILOMET APPROXIMATEAREAOF TAYLOR SLOUGH 0 STAGE, CONDUCTIVITY, AND DISCHARGE
0.Figure 2 3-7. W ater-levels at 4 5 MILES the six stations in the vicinity BOUNDARYof Taylor Slough, simulatedSOUTHERN INLANDAND MEASUREMENT SITE (USS)
COASTALSYSTv1.2.1EMS SICS) STUDY AREA constant COASTAL CREEK LOCATION
0 -- BUTTONWOOD EMBANKMENT A STAGE MEASUREMENT SITE (NPS)
-0.2 0 STAGE AND CONDUCTIVITY MEASUREMENT
AUG 96 JUL 9? SITE (NPS)
-0.4 A DISCHARGE MEASUREMENT SITE (SFlMD)


Figure 3-7. Water-levels at the six stations in the vicinity of Taylor Slough, simulated with depth-varying Manning's n
(v1.2.1 red) and with constant Manning's n (v1.2 black).


























0 )

SAUG BE JUL 97
8050' 80045' 8040' 80"35' 80"3(' 8025' 0.
TayIor TSB $175 1 EVERS




REV4 .2 V
25 20' -- o.4AUG 96 JUL 97
slac 0.8 EVRA
2 .I S 5
... 2 EEVER6E 0.6E Z
,AXA. T STAGRE., CNDTIVIT AND D E .4 f' t
S*EPGVWSWA 2
0.2

S25T 15 0 U I -0.2 P
SJnul AUGgB JUL97
> ACP byl -0.4






DEVERTAGE MEASUREMENT S0.4E
SITE (NPS) AUG Ng JUL 97










Figure 3-8. Water-levels at the six stations in the vicinity of C-111, simulated with depth-varying Manning's n (v1.2.1 red)
and with constant Manning's n (v.2 black).1
0 1 2 3 4 5 KILOMETERS I EVERGLADES NATIONAL PARK A STAGE MEASUREMENTS SITE (USES) Z
i 1 11 1 1 1 [^ APPROXIMATE AREA OF TAYLOR SLOUGH 0 STAGE, CONDUCTIVITY, AND DISCHARGE 4
0 1 2 3 5 SMILES BOUNDARY OF SOUTHERN INLAND AND MEASUREMENT SITE (USGS).
COASTAL SYSTEMS SICSS) STUDY AREA 0 COASTAL CREEK LOCATION
-- BUTONWOOD EMBANKMENT A STAGE MEASUREMENT SITE (NPS)
STAGE AND CONDUCTIVITY MEASUREMENT -0.2
SITE (NPS) AUG 96 JUL 97
A DISCHARGE MEASUREMENT SITE (SFWMD) -0.4


Figure 3-8. Water-levels at the six stations in the vicinity of C-1 11, simulated with depth-varying Manning's n (v1.2.1 red)
and with constant Manning's n (v1.2 black).












0.8 SIMULATED
127SICSVI 1 ground
0.6 O D maximu SIUATED SICSvl sul
0.4 OBSERVED SICSv1.2.1 (Swainet al. 2004)j sur"
0.2

-0.2
-0.4 AUG09 JUL97
0.8 NP-P67
0.6
0.4 ,. L

0.2

0.4
0 -.8 40' gOSH' EVER' 1 751'




0.2 EVR
-0. AUG96 JUL 97 .2 -*




0.4













o0.8 NP--- AS r E.v EStaS .EXPLANATION
6 EVERGLADES NATIONAL PARK A STAGE MEASUREMENTS SITE (USGS
S0.4 -2 __5 4KLMER










0.4 APPROXIMATEAREAOFTAYLOR SLOUGH STAGE, CONDUCTIVITY AND DISCHARGE







03 0 1 2 3 4 SMILES BOUNDARY OF SOUTHERN INLAND AND MEASUREMENT SITE (USGS)
COASTAL SYSTEMS SICSS) STUDY AREA COASTAL CREEK LOCATION
0 BUTTONWOOD EMBANKMENT A STAGE MEASUREMENT SITE (NPS)
S-0.2 STAGE AN CONDUCTIVITY MEASUREMENT
-0.4 AUG 6 L A S E MEASUREMENT SITE (SFWMD)











Figure 3-9. Water-levels at the six stations in the vicinity of Taylor Slough, simulated with depth-varying Manning's n in
the current version (v .2.1 red) and the original SIS application (Swain et al., 2004; v .2 black).
0.4 -<
0.2
-0.2
AU 096 JUL97 .. ;" :,
0.8






-0.2 STAGE AND CONDUCTIVITY MEASUREMENT
AUG7SE (NPS)
-0.4 A A DISHARGE MEASUREMENT SITE(SFWMD)




the current version (v.2.1 red) and the original SICS application (Swain et al., 2004; v1.2 black).


T












SIMULATED
maximum SIMULATED SICSvl 1 ground
OBSERVED :, SICSvl.2.1 (Swain et a. 2004) si ce


AUG 96 JUL 97
8050' 8045' 80 040 806~'3 0 -' 80 "25' 4 0.8
25 '25' 0A 2
2] TS1B E175, EVERER


2S r 1 U 0.4 JUL97
S'0.2
I *. *RiAUG

P ., EVER7A 0.8 EVER
S2 3 4 5 K S EVERBAEMS SITE









P. STAGE AND CONDUCTIVITY MEASUREMENT 0
EPWSW .

25TE N15S) J ^
J lr" r. ^S-ll-0.2. -^ r^
-0.2.rpl AUG96 B JUL 7




.. .. .. EXPLANATION 0.4 P







EVERGLADES NATIONAL PARK A DISCHARGE MEASUREMENTS SITE (USFMDS) 0


A DISCHARGE MEASUREMENT SITE (SFWMD) -0.4 '-----------------------------



current version (v1.2.1 red) and the original SICS application (Swain et al., 2004; v1.2 black).



87
87










ALL stations

=Frequency -U-Cumulative %


0.9
0.8

>2 0.7 ~
C 0.6
g I' -0.5 s
SI 0.4 <
LL 1 0.3
l 0.3 o.

0.1
0 -I I I 0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Nash-Sutcliffe Efficiency

Figure 3-11. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies
attained with SICS v1.2.1, for all 12 water-level stations.









Taylor Slough stations
I Frequency --Cumulative %


0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Nash-Sutcliffe Efficiency
Figure 3-12. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies
attained with SICS v1.2.1, for 6 water-level stations in the vicinity of
Taylor Slough.









C-11l stations


SFrequency


-N-Cumulative %


0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Nash-Sutcliffe Efficiency

Figure 3-13. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies
attained with SICS v1.2.1, for 6 water-level stations in the vicinity of C-
111.


2






>1

U
C
LL




0













R-127 0.8

51CS vl.1 0.7
51CS vl.2.1
-l:lline -/ 0,6

0.5
; 0.5

0.4


03
,"' I ,1/ .. 0.3

0.2

0.1




-0.1
0 0.1 0.2 0.3 0.4 0.5 0,6 0,7 0,8 -01
0.6
TSH
0.5

0.4

0.3

0.2

*0.1


NP-P67


0.1 0.3 0.5 0.7 0.9
NP-P37


2 0.2 1'
-...-* 1 '
0-0.2


0 -0.3
0 0.1 0.2 0.3 0.4 0.5 0.6 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0.6 E-146 0.6 NP-P37

0.5 0.5

0.4 0.4

0.3 / 0.3

0.2 0.2

0.1 ,. 0.1 '
J '
0 0

-0.1 -0.1

-0.2 -0.2

-0.3 -0.3
-0.3 -0.1 0.1 0.3 0.5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

OBSERVED WATER-LEVEL


Figure 3-12. Trends in prediction bias for the 6 stations in the vicinity of Taylor

Slough.





91















EVER7


S 0.7


0,6


0.5


0.4


0.3


0.2


0.1


0


-0.1


-0.2
-0.2
0.6


0 0.1 0.2
EPGW


-0.1


-0.2
0.4 0.6 0
0.7

0,6


0.5


0.4

S: 0.3


*0.2


0.1


0

-0.1

-0.2


-0.3
0.3 0.4 0.5 -0.3
0.3

0.25

0.2

0.15

0.1

0.05


-0.05

-0.1

-0.15

-0.2

-0.25
0.2 0.4 0.6 0.8 -025


EVER4


0.1 0.2 0.3 0.4 0.5 0.6 0.7
EVERSA


-0.1 0.1
EP-12R


0.3 0.5 0.7


r

.g'
,4"

'



.'g


-0.2 -0.15 -0.1 -005 0 0.05


OBSERVED WATER-LEVEL



Figure 3-13. Trends in prediction bias for the 6 stations in the vicinity of C-111.


SICS vl.1

SSICS vl.2.1

-1:1 line


0.2
EVER6


0.4



0.3



0.2



0.1



0



-0.1
-0.1
0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2













ICS. Inputs (observed)
-TSB -L31W -Cli -Precipitation








IVW 'y -- Y/-.








F-'


I SEP 96


Stage (meters NGVD88) On 1 Aug 96


iif; .


80


E so

40

S20


0
1 AU


1 NOV 96


Stage (meters NGVD88) On 1 Sep 96


Stage (meters NGVD88) On 1 Oct 96


Stage (meters NGVD88) On 1 Nov 96


Figure 3-14. Rainfall and discharge inputs, and corresponding 2-D water-level

distributions for the first four months (first wet season). White space

within the domain indicates dry cells.


1 OCT '96




















,





-.,
i .I


0



- 0.1 3
0

0.15

-0.2


1 DEC '96


t-- ~I_._
r I



L,

L,
IIICr*
1


G '96











SICS inputs (observed)
-TSB -L31W -C111 -Precipitation
V ~\y- '^ v/'


80



40

5 20

01 DEC 1 JAN
I DEC'96 1 JAN'97


1 FEB 97


1 MAR 97


Stage (meters NGVD88) On 1 Dec 96


Stage (meters NGVD88) On 1 Feb 97


Stage (meters NGVD88) On 1 Jan 97


Stage (meters NGVD88) On 1 Mar 97


Figure 3-15. Rainfall and discharge inputs, and corresponding 2-D water-level
distributions for the middle four months (dry season). White space
within the domain indicates dry cells.








94


0

0.05



0.15 2

0.2


1APR'97


P



-. .1 i
:x >


_________. ______L


_I I















SICS inputs (observed)
-TB -L31W -C111 -Precipitation


1 MAY '97 1JUN'97 1JUL97


Stage (meters NGVD88) On 1 Apr 97


D.5
0.4
.03
0.2
0.1

-0 0




-04
-0.5,


Stage (meters NGVD88) On 1 Jun 97


Stage (meters NGVD88) On 1 May 97


Stage (meters NGVD88) On 1 Jul 97


Figure 3-16. Rainfall and discharge inputs, and corresponding 2-D water-level

distributions for the final four months (up to the second wet season).

White space within the domain indicates dry cells.


80


6o





20



SAPR'97
1 APR '97


0


0.05





0.15 _


0.2


1 AUG '97













15
McCormick Creek


Mud Creek
I0





10

-15

-10


Taylor Creek


20
is West Highway




-5


Trout Creek


-Observed flow -Simulated flow


-60 4 .....
.I *--9$
l-Ain.g96


Figure 3-17. Simulated and measured discharges through five gauged creeks in

the Buttonwood Embankment


0~ "i


1-Aug-97












I5S inputs observed )
-TB -L31W -C111 -Precipitation


1AUG'96 1SEP'96 1 OCT'96 1 NOV96 1 DEC '96


D r i .;tr r scd er f.



-' t1 4 ... ..*..-. / ..





Discharge (cubic meters per second per foot) On 1 Aug 96


*: .. .t- t








Discharge (cubic meters per second per foot) On 1 Sep 96


Reference Vectors [m3/s/ft]
1E-005 0.001


S.....
.4 ;:_,4w4 .. .. 4 ..I..4..-. ,-,





Discharge (cubic meters per second per foot) On 1 Oct96


Discharge (cubic meters per second per foot) On 1 Oct 96


Figure 3-18. Rainfall and discharge inputs, and corresponding 2-D discharge
vector distributions for the first four months (first wet season).










97


.'iA.;j
;: :- ,:.:."- -^..-^:, : ::.!. '-


;'....,,,,. ",-...,,,. .~.._-' .. ,_ ,,
Dis-harge .. ..bi meters p o o 1 ,
,- .. .* t ^ o ^ ,






Discharge (cubic meters per second per foot) On 1 Nov 96


80





CI
- 20


0

0.05 |


0.15


0.2













SICS inputs (observed)
-TSB -L31W -C111 -Precipitation
V


80




40


5 20
0

1 DEC'96 1 JAN 97


1 FEB 97


r .... p










Discharge (cubic meters per second per foot) On 1 Dec 96


t .," ..L ,




Diharge (cubic meters per nd per oot) On 1 Jan 97

Discharge (cubic meters per second per foot) On 1 Jan 97


Reference Vectors [m3/s/ft]
1E-005 0.001


D (d f 0- t n I F 7'

..... .. .........


i g cui er fo) O* b9






Discharge (cubic meters per second per foot) On 1 Feb 97


Figure 3-19. Rainfall and discharge inputs, and corresponding 2-D discharge

vector distributions for the middle four months (dry season).












98


7-" .- ". *; 1
,. i ..*



Discharrge ( m p

/__ .% ." .: ,* / (


Discharge (cubic meters per second per foot) On 1 Mar 97


0

.os
0.05

0.15


0.15

0.2


1 MAR 97


1APR'97


_I I











SICS inputs (observed)
-TSB -L31W --C11 -Precipitation


0

0.5





0.2


1 MAY '97 1JUN'97 7 7U 1 AUG '97


i s 'h1-r \
.., "'.;.;/ i ,, ,t i -,.
X .... ./.\" { *:| i

r" "" i^*"y' -^

^r ^~~n MRILZ;"*^ >-^^*5J''
;' i '" '* ,"

*-~ ~~' >''i; -f
Dic g (



Discharge (cubic meters per second per foot) On 1 Apr 97


I -




Discharge (cubic meters per second per foot) On 1 May 97




Discharge (cubic meters per second per foot) On 1 May 97


Reference Vectors [m3l/sftt
1E-005 0.001


Discharge (cubic meters per second per foot) On 1 Jun 97


Discharge (cubic meters per second per foot) On 1 Jul 97


Figure 3-20. Rainfall and discharge inputs, and corresponding 2-D discharge
vector distributions for the final four months (up to the second wet
season).









99


80



42

20


1 APR'97











51CS inputs (observed)
-T5B -L31W -C11 -Precipitation


1AUG'96 1SEP'96 1CT'96 1 NOV96 1 DEC '96
1AUG96 1SEP'96 1 OCT 96 1 NOV 96 1 DEC9'6


Salinity (psu) On 1 Aug 96


- 25


Salinity (psu) On 1 Oct 96


Salinity (psu) On 1 Sep 96


Salinity (psu) On 1 Nov 96


Figure 3-21. Rainfall and discharge inputs, and corresponding 2-D salinity
distributions for the first four months (first wet season). White space
within the domain indicates dry cells.


100


80





o 20
-20


0

0.05 |
0

0.15


0.2


*dMVL-d
^f^M _*
k C__Z













SICS inputs (observed)
-TSB -L31W -C111 -Precipitation
*v-- -V/~-?~y-/ "r


1 FEB '97


1 MAR '97


SalinItv ips.i On 1 Dec 96


Salinity (psu) On 1 Feb 97


,a-iliniry 'SI 1 On 1 Jan 97


Salinity (psu) On 1 Mar 97


Figure 3-22. Rainfall and discharge inputs, and corresponding 2-D salinity

distributions for the middle four months (dry season). White space

within the domain indicates dry cells.


101


80


S20


0
1 DEC '96


0

.o
0.05


0_15

0
01 g

0.2


1 JAN '97


1APR '97


~













SICS inputs (observed)
-TSB -L31W -C111 -Precipitation


1 MAY '97 1JUN'97 1JUL97


Salinity (psu) On 1 Apr 97


Salinity (psu) On 1 Jun 97


Salinity (psu) On 1 May 97


Salinity (psu) On 1 Jul 97


Figure 3-23. Rainfall and discharge inputs, and corresponding 2-D salinity
distributions for the final four months (up to the second wet season).

White space within the domain indicates dry cells.


102


80

6o
40




20

1 APR'97


0

0.05




0.15 2

0.2


1 AUG '97









CHAPTER 4
MODELING PHOSPHORUS WATER-QUALITY IN THE SOUTHERN INLAND
AND COASTAL SYSTEMS

Introduction

The freshwater Everglades are oligotrophic due to the strong affinity for

phosphorus exhibited by the carbonate substrate underlying the system (de

Kanel & Morse, 1978). The cycling of phosphorus is a complex mix of physical,

chemical, and biological processes (Figure 4-1) that is too complex to describe

based on fundamental physics and chemistry. However, many processes can be

functionally lumped together to simplify and abstract the system of cycling to a

manageable degree of complexity.

The Southern Inland and Coastal Systems (SICS) region encompasses two

principle habitat structures; slough and marl prairie. Taylor Slough, running

southwards through the center of the region (Figure 3-1 in Chapter 3), has

proportionately less emergent macrophyte biomass and more floating

macrophyte and periphyton biomass than adjacent marl prairie, which is a

complex of sawgrass (predominantly) and calcareous periphyton (Swain et al.,

2004). Both systems have significant layers of flocculent material (floc), a loose

conglomerate of bacteria, periphyton and partially decomposed litter (Noe et al.,

2003). Uptake of surface-water phosphorus in both systems is dominated by

periphyton and floc (Noe et al., 2003; Noe and Childers, 2007). Emergent

macrophytes in the marl prairies obtain the majority of their phosphorus from

porewater (Richardson and Marshall, 1986). Floating macrophytes absorb

phosphorus directly from the water column, but turnover is rapid (Mitsch, 1995).


103









In Taylor Slough, periphyton and macrophyte litter accrete and produce

organic soils. The periphyton in the marl prairies co-precipitate phosphorus with

calcium, which accrete to form marl soils. Both forms of soil store phosphorus

and do not readily release it unless conditions become dry (Sutula et al., 2001).

Atmospheric deposition is probably the most important source of nutrients

to the southern Everglades (Noe and Childers, 2007; Sutula et al, 2001). Under

historic conditions atmospheric deposition is estimated to have accounted for up

to 90% of total phosphorus inputs to the Everglades (Davis, 1994). Flow into the

southern Everglades does not generally exhibit the amplified nutrient loading

more prevalent further north, where wetlands receive waters directly from the

EAA.

Ground-water and surface-water in the region are also readily exchanged

because of the combination of shallow topography and particularly high hydraulic

conductivity (Fennema et al., 1994), though the extent to which such exchange

contributes nutrients is unclear. Recently, Price et al. (2006) have suggested

that phosphorus inputs from ground-water may increase during the dry season

due to a reversal of hydraulic gradient that causes upwelling rather than leakage.

Integrated ground-water and surface-water modeling of SICS (Langevin et al.,

2005) have also indicated that there is upwelling during low-flow periods.

However, the effects on productivity that this ground-water input of nutrients is

suggested to drive are found largely in the mangrove/marshland ecotone in the

southern portion of Taylor Slough, and are not thought to be as significant in the

freshwater wetlands that are the focus of this modeling work.


104









Together, these biological, chemical, and physical processes interact to

determine the concentration of phosphorus in the water column, and in turn the

mass exported out of the system. By considering simplified representations of

these processes an abstracted yet functionally mechanistic water-quality model

can be developed that is sufficiently simple to remain manageable and justifiable,

yet sufficiently complex to provide insights into internal biogeochemical

processes that cannot be captured by simple reactive-transport models.

However, such simple models are not without merit, and depending on the

objectives of the modeling exercise may prove sufficient in themselves. We

explore the value of a number of models for the purpose of simulating total

phosphorus concentrations in SICS surface-waters, from the simple reactive-

transport model to a more detailed model of conceptualized biogeochemical

cycling.

Materials and Methods

The integrated surface-water flow, transport and reaction simulation engine

that was described in Chapter 2, and applied to model hydrology in in Chapter 3,

was applied to simulate surface-water total phosphorus concentrations in the

SICS region for the period of August 1996 through October 1997. Two locations

were identified with measured total phosphorus concentrations in the surface-

water against which to compare simulated results. These were the P37 and

EPGW hydrologic stations introduced in Chapter 3, and depicted in Figure 4-2.

Boundary Conditions

Concentration boundary conditions were required for each of the surface-

water boundary locations described in Chapter 3 (Figure 4-2). These boundary


105









conditions were associated with either specified head or specified discharge

boundary conditions at the lateral boundaries. Atmospheric deposition of

phosphorus is input to describe the vertical inputs.

Specified water-level boundaries

For boundaries in Florida Bay (specified head boundaries 1 to 4 in Figure 4-

2), time-series data was obtained for relevant water-quality observation stations

in Florida Bay (Table 4-1). These data were interpolated and input into the

SWIFT2D input file as time-varying data. Time-varying concentration data at

specified water-level boundaries are specified in Record 2A of Part 3 of the

SWIFT2D input file (Swain, 2005) at the same time intervals at which time-

varying tidal (water-level) boundary conditions are read in. A FORTRAN

program was therefore written to do this efficiently and reliably given the very

large number of required inputs at this interval (see Subroutine EDIT_INPUTFILE

in Appendix C, Section C1).

Time-series data for concentrations at specified head boundaries within the

oligotrophic marsh areas (boundaries 6-8) were not available. However, analysis

of long-term concentration trends at stations situated within oligotrophic

marshlands (EPGW and P37) show that concentrations tend to be either below

detection limit (i.e. less than 4 ppb), or on the order of 5 ppb. Total phosphorus

concentrations well below 10 ppb are common in the Everglades (McCormick et

al., 1996) with any excess phosphorus rapidly taken up (Rudnick et al., 1999).

Given that discharge sources are the dominant lateral hydrologic input and that

measured boundary concentrations are available for these (see below), and


106









considering the known importance of atmospheric deposition, a background

concentration of 5 ppb was considered justifiable.

Specified discharge boundaries

Time-series concentration data for discharge sources were obtained for the

pumping stations used to specify boundary condition flow rates. The TSB

discharge source was specified using pumping data from the Taylor Slough

Bridge site, the L-31W source with data from the S-175 pumping station, and the

C-111 source with data from the S18C pumping station (Swain et al., 2004).

Total phosphorus concentrations for these stations were obtained from the

SFWMD water-quality database, DBHydro (Tables 4-2 to 4-4). Additional data

sets used in a Florida Bay water-quality model (Walker, 1998) were identified that

contained supplementary data for the period of interest (Tables 4-2 to 4-4).

These data sources were consolidated and the time-series data interpolated for

daily input to the water-quality model. Additional code had to be written into

SWIFT2D to handle the addition of total phosphorus mass at the discharge

sources. Mass of phosphorus added to the cell containing the discharge source

was calculated based on the volume discharged and the input concentration. The

mass was then added to the existing mass within the cell and the updated cell

concentration determined, accounting for dilution and concentration effects due

to additions and losses of water, from precipitation and ET, respectively. The

subroutine STRUCTCONCS (see Appendix C, Section C1) was written to read

daily discharge source concentration inputs from a new input file

INPUTFLOWCONCS.dat (see Appendix C, Section C2). For consistency with

the existing methods within SWIFT2D for handling sources of water, including


107









discharge sources, the format of the concentration data input file and its

processing by the STRUCTCONCS subroutine were based on the methods used

for input and handling of water sources.

Atmospheric deposition

A value of 0.03 g TP/m2/yr was chosen given past application of this value

for phosphorus budgets in southern Florida (Sutula et al., 2001 ; Noe and

Childers, 2007). Given the known uncertainty of this input and the system's

reported sensitivity to it, the sensitivity of the water-quality model to this input was

explored by evaluating three different options for applying this average annual

rate: Option 1) a fixed daily rate of 8.219E-5 g TP/m2/d based on the annual

deposition of 0.03 g TP/m2/yr distributed evenly over 365 days; Option 2) a fixed

rate of 9.709E-5 g TP/m2/d applied only on days on which rain occurred, based

on the annual deposition of 0.03 g TP/m2/yr and the number (309) of rain days;

and Option 3) a rate proportionate to the rainfall volume on each given day,

summing to 0.03 g TP/m2/yr. In this way, mass of phosphorus added to system

in each case was the same.

Conceptual Models of Water-Quality Processes

Wetland biogeochemical processes are extremely complex. It is therefore

necessary to abstract and simplify the many processes into a conceptual model

of manageable and useful complexity. Noe and Childers (2007) have calculated

annual phosphorus budgets for oligotrophic sloughs that contain phosphorus

pools for water, floc, periphyton, soil, consumers, dead aboveground

macrophytes, live aboveground macrophytes, and live macrophyte root biomass.

Such complexity is unjustifiable in this instance given the absence of data against


108









which to compare the simulated results in a spatially heterogeneous and

transient simulation. Furthermore, without data to constrain the many parameters

that describe the flux of phosphorus between so many pools, fluxes that are

themselves often very uncertain estimates (Noe and Childers, 2007; Noe et al.,

2003; Sutula et al., 2001), there is a likelihood of generating non-identifiability

and non-uniqueness issues in such a complex spatially-distributed model due to

overparameterization (Beven, 1992).

Given the adaptable nature of the water-quality functionality in

FTaRSELOADDS, a number of water-quality models (Figures 4-4, 4-5 and 4-6)

were tested with increasingly complex conceptualizations of phosphorus cycling

following the approach adopted in Jawitz et al. (2008) and recommended as

good practice by Chwif et al. (2000).

Model 1

Applying the principle of Occam's Razor, the most simple case possible

treated total phosphorus as a conservative tracer (Figure 4-4). In this case, the

implicit assumption is that phosphors uptake from the surface-water through the

many processes described in the introduction is balanced with atmospheric

deposition and other internal sources. This is a reasonable assumption given the

efficient uptake of available phosphorus reported for oligotrophic Everglades

wetlands (Davis, 1994; Noe et al., 2001) and the consistently low and relatively

invariant concentrations recorded for the region (McCormick, 1996).

Atmospheric deposition was therefore not added to the water column in this

application, though inputs with lateral flow through the specified head and

concentration boundaries were maintained.


109









Model 2

The second tested model (Figure 4-5) accounted for atmospheric

deposition as a model input, and simulated phosphorus extraction from the

surface-water with a simple first-order sink term, intended to capture the lumped

effect of biotic uptake and physical processes that remove phosphorus from the

water column. This method was used to explore the three atmospheric

deposition options described above. The time-step at which reactions were

applied was that implemented for the transport and hydrology in SWIFT2D, being

1.5 minutes (see Chapter 3). To facilitate comparison, a single uptake rate that

best fit all three methods was determined rather than individual rates for each

case. Manual calibration showed that a rate 1.5E-6 s-1 offered the best result.

Model 3

The most complex case made full use of aRSE to simulate a conceptual

water-quality system of processes including lumped biotic uptake of phosphorus,

senescence, burial, and release of phosphorus from the dead biomass back into

the water column (Figure 4-6).

Although aRSE includes methods to solve partial differential equations

using the Runge-Kutta 4th order solution methods, testing for numerical stability

indicated that a maximum time-step of 15 minutes was permissible. This proved

to be an untenable time-step for computational time considerations.

Alternatively, aRSE offers simple equation solving in two separate steps, known

as resolvev" and "postsolve". This offered a means of solving the system of

equations at a more reasonable daily time-step using a mass-balance approach.

This was the method adopted.


110









Noe et al. (2003) conducted a radioisotope tracing study to examine the

cycling and partitioning of phoshorus in an oligotrophic Everglades wetland

(Figure 4-7). Peak tracer signals were obtained after 10 days (Noe et al., 2003),

at which point the partitioning of the tracer between what remained in the

surface-water and what had been removed was used to estimate an average

daily uptake rate of 0.084375 day-1.

The measured partitioning of phosphorus in Noe et al. (2003) was applied

to determine rates of uptake by living biomass, considered to be the lumped pool

of macrophytes, all forms of periphyton, consumers, and floc. The observed rate

of flux from living to dead material was used to estimate the senescence rate and

burial rate as a function of the uptake rate (Noe et al., 2003). DeBusk and Reddy

report rates for sawgrass decomposition of 0.00067 to 0.003 d-1. McCormick et

al. (1996) reported aerobic decomposition of periphyton mats ranging from 0.006

go 0.11 d-1, and Newman and Pietro (2001) report periphyton decomposition on

the order of 0.0003 d-1. After calibration a value of 0.001 d-1 was chosen.

Parameters, their values and their sources are presented in Table 4-5.

State-variables, their initial conditions, and their definition in the XML input file

are given in Table 4-6. The full system of equations input to aRSE are given in

the XML input file (XMLINPUT.xml) in Appendix C (Section C3). The IWQ input

file (IWQINPUT.iwq) which contains the definitions of model parameters and their

values for access by SWIFT2D (see Chapter 2) is also given in Appendix C

(Section C3), as well as the SWIFT2D input file (WETLANDS.inp).


111









Results and Discussion

Results for each of the 3 model complexities applied are presented. The

simulation periods were extended beyond the 12-month hydrologic period

presented in Chapter 3 up to mid-October of 1997. In this way an additional

validation data-point for the P37 station was obtained. No such data was

available for the EPGW station until much later (and beyond the maximum

simulation length for this work). Table 4-7 summarizes the Nash-Sutcliffe

efficiencies obtained for each of the models applied.

Model 1

Simulated results for a location in Taylor Slough (P37) and the marl prairies

of the C-111 wetlands (EPGW) for the case of conservative transport are shown

in Figure 4-8. The quality of results indicates the assumption that atmospheric

deposition and internal sources are balanced by internal sinks is justifiable. The

model performed better in the marl prairies (Nash-Sutcliffe of 0.74) than in the

slough environment (Nash-Sutcliffe of 0.58), but the average efficiency of 0.66

implies that conservative transport may be an acceptable approximation for

estimating loadings assuming that the mechanistic hydrodynamics are sufficiently

accurate.

Model 2

Figure 4-9 compares the simulated concentrations achieved at stations P37

and EPGW using Model 2 and the three options for atmospheric input. Option 1

input a fixed daily mass irrespective of weather conditions, Option 2 applied a

fixed mass only on rain-days, and Option 3 applied mass relative to the amount

of rainfall on a given day. All three methods were applied such that total mass


112









added over a year summed to 0.03 g TP/m2/yr to ensure comparable loadings to

the system despite the different methods.

Option 1 was the simplest approach to adding deposition, simply dividing

the annual flux equally over each day. This method provided the best results,

with an average Nash-Sutcliffe across both stations of 0.66. Later efforts to

refine the calibrated value of the uptake rate (1.5E-6 s-) produced no significant

improvement in results so this value and these results were used as the final

simulation of total phosphorus concentrations for Model 2.

Nash-Sutcliffe efficiencies for Option 2 ranged fro 0.06 to 0.46, which were

poorer than those of the first method, but still reasonable, especially for EPGW.

Nash-Sutcliffe efficiencies for Option 3 were uniformly less than -5 and therefore

unacceptable. Efforts to improve performance by calibrating the rate constant

specifically for this method proved futile because the lag in peaks could not be

shifted through this factor. This method introduced strong spikes and troughs

during periods of sparse rainfall that degraded results in the dry season. The

lack of input given rare rain events and low volume events when rain did occur

lead to significant reductions in concentrations with time. Rainfall events that

then occurred under drier conditions added a disproportionate amount of

phosphorus to low water-level conditions and produced large spikes in

concentration that tended to lag behind the observed values. During wet periods

this problem was mitigated: peaks were not as high due to the diluting effect of

larger volumes of standing water, and troughs were not as low because the

regular input of mass with frequent rainfall kept the mass topped up. By volume-


113









weighting the deposition with rainfall this method implicitly assumes that

deposition is strongly related to rainfall and therefore disproportionately made up

of wet deposition. The failure of this method corroborates the suggested

importance of dry deposition in the SICS region.

Model 3

Results for the most complex model applied are presented in Figure 4-10.

Results for the prairie (Nash-Sutcliffe = 0.73) were comparable in quality to those

obtained using Model 1 (0.74) and better than those obtained with Model 2

(0.70). However, results for the slough environment (Nash-Sutcliffe = 0.23) were

poorer than those obtained using Model 1 (0.58), though comparable to those

obtained with Model 2 (0.28). The average efficiency for both measurement

stations using Model 3 was a respectable 0.47.

As was the case for all the other models, results for the marl prairie station

(EPGW) were noticeably better than those obtained for the slough station (P37).

While it is unclear why this trend should be present for Models 1 and 2, it can be

explained in Model 3 by noting that the radioisotope study conducted by Noe et

al. (2003) was performed in wet prairie marshes in Shark River Slough. The

location of this study within marshes within a slough was originally thought to be

useful because of the presumed aggregating effect of the habitat being a marsh

within a slough, and the fact that SICS is comprised of marsh and slough.

However, given the modeling results it appears that the measured rates were

more appropriate for marsh/wet prairie conditions than for slough conditions, and

this hoped for aggregating effect was not present, or remained biased towards

marsh conditions.


114









Conclusions

Three different models of increasing complexity were applied to the

modeling of phosphorus water-quality in the SICS region. Average Nash-

Sutcliffe efficiencies ranged from 0.47 to 0.66, indicating that phosphorus water-

quality could be reasonably simulated with multiple models of differing

complexity. Considering this result, the additional complexity inherent to applying

a model akin to Model 3 must be justified by the objectives of the modeling effort

or theoretical considerations pertaining to the underlying conceptual model.

For instance, though the best results were obtained with the simplest

model, this version is subject to the greatest structural uncertainty because of the

sweeping assumptions implicit in its simple form. Model 3 also remains subject to

significant simplifying assumptions, but there is a degree of mechanistic process

to the conceptual model at this higher complexity that imbues the model with

greater theoretical justification. Alternately, if the objectives are to assess how

frequently conditions exceed a specified threshold, say for example the CERP-

mandated maximum TP concentration of 10 ppb, we see that the more dynamic

results from Model 3 capture multiple exceedence events that were missed by

the simpler versions.

The question of how best to handle the problematic but important input of

atmospheric deposition appears to be best answered with the most simple

solution; an annual average evenly distributed across all days of the year.

Occam's Razor would tend to support this approach in any event given the great

uncertainties, but the comparison of input methods yielded some valuable

insights into the problem. Despite the conjectured role of convection storms in


115









harvesting phosphorus from the upper atmosphere, and the regularity of rainfall

in the wet season, results indicated the a rainfall volume-weighted approach was

not advisable. The second deposition method, which assumes rainfall captures

and flushes the dry deposits, performed well but not as well as daily average.

This work, however, remains founded on an annual average that is itself subject

to significant uncertainty, and requires further study and experimentation to

assess the full extent of model sensitivity to this source of uncertainty.

The issue of model complexity is an important one in the context of model

development, and the availability of a tool such as FTaRSELOADDS, which

provides the user with the freedom to define and experiment with model structure

demands of the user a greater understanding of the role of complexity on model

performance. Despite the reduced structural uncertainty, additional complexity is

known to also introduce uncertainty into models through the additional

parameters that are needed, each subject to some measurement uncertainty. In

this case, the uncertainty associated with atmospheric deposition may well be the

underlying reason for the simplest model, which neglected to account for

atmospheric deposition, performing the best. Any effort to mechanistically model

water-quality in the oligotrophic Everglades is surely going to be greatly

hampered using such uncertain measures for such an important input.

Further complexity could be introduced into the water-quality model to

produce more biogeochemically detailed models, and these may well improve

results despite the uncertainty of deposition, but such an effort needs to be

constrained with sufficient data to prevent sensitivity in the model from


116









undermining the integrity of calibration. The paucity of phosphorus data against

which to evaluate model performance in this period is a challenge, though more

recent research in the region of Taylor Slough (Childers, 2006) has produced

much data that would probably be sufficient to test greater complexity. The

following chapter will explore the issue of model complexity, uncertainty and

sensitivity in greater detail.

As discussed in Swain et al. (2004), accurate capture of flow reversals in

the tidal creeks is largely due to wind driven effects and not simply tidal

fluctuations. The importance of wind-shear in this environment has implications

for wind-induced mixing effects in the transport solution that cannot be captured

by hydrologic models that do not account for this hydrodynamic effect. It is

therefore quite possible that the good results obtained in all models, but

particularly the conservative transport approach, would be eroded were a less

hydrodynamic model simulating the transport. This would require further testing

to confirm given that both phosphorus observation stations are located some

distance from the tidal creeks where this effect is most prominent.


117










Table 4-1. Stations and total phosphorus concentration data (g/m3) used for
interpolation of daily concentrations for specified head boundary
conditions in Florida Bay. Station numbers correspond with those of
Figure YY and boundary condition numbers with those of Figure XY.


Date
7/4/96
8/21/96
9/13/96
10/14/96
11/8/96
12/5/96
1/7/97
2/14/97
3/13/97
4/15/97
5/23/97
6/11/97
7/9/97
8/20/97
9/9/97
10/22/97
11/24/97
12/11/97
BC no.


TP [g/m3]
Station 3
0.00597
0.00566
0.00698
0.00612
0.00411
0.00496
0.00419
0.00496
0.00581
0.00411
0.00380
0.01604
0.00667
0.00752
0.00798
0.00860
0.00581
0.00915


TP [g/m3]
Station 6
0.00822
0.00628
0.00698
0.00806
0.00806
0.00581
0.00512
0.00535
0.00605
0.00481
0.00349
0.00636
0.00884
0.00868
0.00822
0.00512
0.00930
0.00977


BC 4**


TP [g/m3]
Station 13
0.01108
0.01651
0.02077
0.01992
0.00891
0.00736
0.01116
0.02534
0.00891
0.00783
0.00845
0.01015
0.02255
0.02108
0.02093
0.01643
0.01232
0.01256
BC 2


* Data provided by the Southeast Environment


TP [g/m3]
Station 15
0.01256
0.03294
0.01333
0.03216
0.01201
0.01744
0.01620
0.01767
0.01240
0.01380
0.00907
0.01116
0.02612
0.02860
0.02031
0.03534
0.01759
0.01411
BC 1
tal Research


TP [g/m3] TP [g/m3]
Station 23 Station 24
0.00481 0.00411
0.00760 0.00395
0.00465 0.00349
0.00581 0.00558
0.00457 0.00434
0.00527 0.00527
0.00388 0.00349
0.00388 0.00473
0.00450 0.00558
0.00349 0.00186
0.00264 0.00271
0.00473 0.00473
0.00767 0.00550
0.00690 0.00837
0.00535 0.00605
0.00729 0.00620
0.00628 0.00496
0.00682 0.00558
BC 3***
1 Center monitoring


program in Florida Bay (http://serc.fiu.edu/wqmnetwork/SFWMD-
CD/Pages/FB.htm)
** Applied the average of station 3 and station 6
*** Applied the average of station 23 and station 24


118









Table 4-2. Data sources and values used for boundary conditions concentrations
at the L-31W discharge source
S175: From DBHYDRO S175: From Walker
(SFWMD) (1998) Averaging per month**
Date TP [ppm] Date TP [ppm] Date TP [ppm]
7/11/96 0.0090
77/11/6 0 0 /96 0.0034 7/96 0.0062
7/24/96 BDL
8/7/96 BDL
8/6 BL 8/96 0.0031 8/96 0.0031
8/20/96 BDL
9/11/96 0.0040
/1/9 0.0040 /96 0.0039 9/96 0.0040
9/24/96 BDL
10/9/96 0.0080
S0000 10/96 0.0050 10/96 0.0065
10/22/96 BDL
11/6/96 BDL
//9 BDL 11/96 0.0033 11/96 0.0033
11/19/96 BDL
12/4/96 0.0070
12/96 BDL 12/96 0.0070
12/17/96 BDL
1/8/97 0.0040
1/97 BDL 1/97 0.0055
1/21/97 0.0070
2/12/97 0.0040 2/97 BDL 2/97 0.0040
3/12/97 BDL 3/97 BDL 3/97 0.0040
-- -- 4/97 BDL 4/97 0.0040
5/21/97 BDL 5/97 0.0084 5/97 0.0062
6/12/97 0.0090
6/2/97 0.006/97 0.0084 6/97 0.0071
6/25/97 0.0040
7/8/97 BDL
7/2/97 0 7/97 0.0035 7/97 0.0043
7/22/97 0.0050
8/5/97 BDL 8/97 0.0063 8/97 0.0052
9/2/97 0.0040
9/17/97 0.0064 9/97 0.0050 9/97 0.0051
9/30/97 BDL
Annual mean 0.0061* 0.0050* 0.0050
BDL="below detection limit"
Excluding BDL
** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the
assumed detection limit of 0.004 ppm was included in the average. If no data
was recorded by SFWMD then the Walker (1998) value was used. If only BDL
records existed then 0.004 ppm was used.
-- No data sampled by SFWMD that month


119









Table 4-3. Data sources and values used for boundary conditions concentrations
at the C-111 discharge source.


S18C: From DBHYDRO
(SFWMD)
Date TP [ppm]
7/11/96 BDL
7/24/96 BDL
8/7/96 BDL
8/20/96 BDL
9/11/96 0.0040
9/24/96 BDL
10/9/96 0.0040
10/22/96 BDL
11/6/96 BDL
11/19/96 0.0050
12/4/96 0.0040
12/17/96 BDL
1/8/97 0.0050
1/21/97 0.0040
2/12/97 BDL
3/12/97 BDL


6/12/97 0.0290
6/25/97 0.0050
7/8/97 BDL
7/22/97 BDL
8/5/97 BDL
09/2/97 0.0041
09/17/97 0.0051
Annual mean 0.0075*
BDL="below detection limit"
* Excluding BDL


S18C: From Walker
(1998)
Date TP [ppm]
7/96 0.0030


8/96

9/96

10/96

11/96

12/96

1/97
2/97
3/97
4/97
5/97
6/97

7/97
8/97
9/97


0.0032


Averaging
Date
7/96

8/96


0.0035 9/96


0.0034


10/96


0.0040 11/96


0.0038

0.0041
0.0031
0.0033
0.0068
0.0115
0.0214

0.0031
0.0063
0.0046
0.0058


12/96

1/97
2/97
3/97
4/97
5/97
6/97

7/97
8/97
9/97


per month**
TP [ppm]
0.0030

0.0032

0.0038

0.0037

0.0045

0.0039

0.0044
0.0031
0.0033
0.0068
0.0115
0.0185

0.0031
0.0052
0.0046
0.0056


** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the
assumed detection limit of 0.004 ppm was included in the average. If no data
was recorded by SFWMD then the Walker (1998) value was used. If only BDL
records existed then 0.004 ppm was used.
-- No data sampled by SFWMD that month.


120









Table 4-4. Data sources and values used for boundary conditions concentrations
at the TSB discharge source.


TSB: From DBHYDRO
(SFWMD)
Date TP [ppm]
7/9/96 BDL
8/6/96 0.0120
9/10/96 0.0040
10/15/96 BDL
11/5/96 BDL
12/3/96 0.016





6/24/97 BDL
7/29/97 BDL
8/19/97 BDL
09/16/97 BDL
Annual mean 0.0107*
BDL="below detection limit"
* Excluding BDL


TSB: From Walker
(1998)
Date TP [ppm]
7/96 0.0047
8/96 0.0081
9/96 0.0041
10/96 0.0031
11/96 0.0045
12/96 0.0152
1/97 0.0138
2/97 BDL
3/97 0.0058
4/97 0.0081
5/97 0.0067
6/97 0.0040
7/97 0.0030
8/97 0.0029
8/97 0.0035
0.0063*


Averaging
Date
7/96
8/96
9/96
10/96
11/96
12/96
1/97
2/97
3/97
4/97
5/97
6/97
7/97
8/97
8/97


per month**
TP [ppm]
0.0044
0.0101
0.0041
0.0031
0.0043
0.0156
0.0138
0.0040
0.0058
0.0081
0.0067
0.0040
0.0030
0.0029
0.0035
0.0062


** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the
assumed detection limit of 0.004 ppm was included in the average. If no data
was recorded by SFWMD then the Walker (1998) value was used. If only BDL
records existed then 0.004 ppm was used.
-- No data sampled by SFWMD that month.


121









Table 4-5. Parameters used in the model
Parameter Definition XML input Value Units Source
Noe et al.,
ku P uptake rate kuptake 0.083475 d-1 2o
2003
Senescence
rate as a Noe et al.,
function of senesc 25 2003
uptake
Calibration;
Debusk and
kd Decomposition kdecomp 0.001 d-1 Reddy,
rate 2005;
Newman et
al.; 2001
Burial rate as a t
Noe et al.,
kb function of k soil 0.13 -- 2
2003
uptake
From
SWIFT2D
Kw Wet/dry factor K wet 1 or 0 SWI
S based on
ICLSTAT*
* ICLSTAT(N,M) is 0 if a cell is considered wet at the time by SWIFT2D, or >0 if
dry.


122









Table 4-6. State-variables with initial conditions as used in Model 3


State
variable
(Figure 4-6)


[TPsw]


TPu






TPbio





TPdead


TPdc

TPb


TPs


Definition


concentration
in the surface-
water at t
Mass of TP in
the surface-
water at t-1
Mass of TP in
the surface-
water at t
TP uptake
from the
surface-water
for t
TP uptake
from the
surface-water
for t-1
TP in live
biomass at
time t
TP in live
biomass at
time t-1
TP in dead
biomass at
time t
TP in dead
biomass at
time t-1
TP flux by
senescence at
time t
TP flux by
decomposition
at time t
TP flux by
burial at time t
TP in the soil
at time t
TP in the soil
at time t-1


XML input


TP sw conc


TPswmass1


TP sw mass2



TP_uptakel



TP_uptake2


TP livel


TP live2


TPdead1


TP_dead2


TPsenesc


TP_decomp

TP_bury

TP soil

TP soil2


123


Initial
condition
(aRSE)

0.005


0.01


0.01


0.0008



0.0008


0.04


0.04


0.014


0.014


0.0002


0.0001

0

0.0001

0.0001


Units



g TP/m3



g TP/m2


g TP/m2



g TP/m2/d



g TP/m2/d



g TP/m2


g TP/m2


g TP/m2


g TP/m2


g TP/m2/d


g TP/m2/d

g TP/m2/d

g TP/m2

g TP/m2









Table 4-7. Nash-Sutcliffe efficiencies for the water-quality models applied to
simulate total phosphorus in the Southern Inland and Coastal Systems
Model 2 Model 2 Model 2 M l
Mode (Option Model 3
(Option 1) (Option 2) (Option 3)


P37
EPGW
Combined


0.583531
0.737771
0.658693


0.285041
0.697249
0.484382


0.062226
0.460871
0.255956


-5.183816
-5.612662
-5.364559


0.226110
0.733882
0.471255


124








































LLM
-- LaeIllng arrow rp,,lrll,, ~
-- HyfOysis P0 C0preopl[-iLin -- E~ eccmrnpostion
MIneraliZation Settlig.~Drial -- Atmospherlc eiposition
S*3l Biological uptake -- Resuspension

Figure 4-1. Schematic of phosphorus cycling processes in Everglades wetlands.


125











80'30' 80025'


25'25'


25020' 1-







2515'


25010'


ii I 1 WB*
0 1 2 3 4 MILES
6Sar vcri U.S. CTjqli J .jr.-, dilir4d dara 1972
IJr..er~sl Trr.s.rer= e ll.: r plja..:T.nr. Z.:re 17, Dalul NAD 27
EXPLANATION
1 EVERGLADES NATIONAL PARK SPECIFIED WATER-LEVEL MODEL BOUNDARY
APPROXIMATE AREAOF SPECIFIED FLUX MODEL BOUNDARY
TAYLOR SLOUGH
--- NO-FLOW BOUNDARY OFFSHORE WATER-LEVEL STATION
BOUNDARY OF SOUTHERN INLAND AND EVERGLADES NATIONAL PARK
COASTAL SYSTEMS SICSS) STUDY AREA WATER-LEVEL STATION
A COASTAL FLOWAND STAGE STATION
(U.S. GEOLOGICAL SURVEY)


Figure 4-2. Location of SICS model boundary conditions including specified head
boundaries (blue), discharge sources (orange), and the associated total
phosphorus concentration boundary conditions (black squares indicate
specified head and circles discharge sources; numeric references refer to
Table 4-1) at each of these (map and hydrologic boundaries from Swain et
al., 2004).


126


80'50'


8045'


80035'



































Figure 4-3. Location of water-quality observation points in Florida Bay. Data are
provided by the Southeast Environmental Research Center
(http://serc.fiu.edu/wqmnetwork/SFWMD-CDIPages/FB.htm)












Atmospheric deposition
and internal sources


I
I I
I I
I I
I I
I I
I I
I I


TP mass transported
in with flow


Biotic uptake and
internal sinks


1 (


I g
---I


TP mass transported
out with flow


Figure 4-4. Model 1: Conservative transport assuming deposition and internal sources
are in equilibrium with biotic uptake and internal sinks. Green fill indicates
total phosphorus, and blue lines indicate the medium is water.


128









TP mass added by
atmospheric
deposition



TP mass transported
in with flow TP mass transported
out with flow






I k[TP,]



TP mass removed by
biotic uptake and sinks

Figure 4-5,. Model 2: First-order uptake from the water column using the reactive
transport functionality of SWIFT2D (Model 2a) or aRSE for reactions and
SWIFT2D for transport (Model 2b).


129








SAtmospheric
deposition


TP mass
transported in
with flow

^^^^^^


TP mass
transported
out with flow


TP, = kK, [TP,~]h,
TPu = kwTP*sw
14
kb7 u
^^^b P^


TPdc = kdcTP dad


STP, T = kTPJ


Figure 4-6. Model 3: Reactions simulated by aRSE with transport by SWIFT2D. For
XML equations see Appendix C (Section C3). Variables and parameters
defined in Tables 4-5 and 4-6.


130


arrrcc~













0.2 Water
Metaphyton
I Epiphyton live
0.4 Epiphyton dead
----_ Consumer
Illl lIll Floc
S0.6 :: : Macrophyte live
02 Macrophyte dead

$ 0.8


1.0
60 min 1 day 4 daN, 10 day 18 days
Time

Figure 4-7. Mean proportion of total recovered radioisotope (32p) per mesocosm found
in different ecosystem components over time (from Noe et al., 2003).













0.03 -Model 1

0.025

o 0.02

c 0.015
ao


0.005 O O

0
Jul-96 Sep-96 Oct-96 Dec-96 Jan-97 Mar-97 May-97 Jun-97 Aug-97 Oct-97

0.03 Model 1: EPGW 0 Data

0.025 -Model 1

0.02


o 0.015

0 005-

0
Jul-96 Sep-96 Oct-96 Dec-96 Jan-97 Mar-97 May-97 Jun-97 Aug-97 Oct-97


Figure 4-8. Simulated TP concentrations obtained with Model 1 at observation stations
in Taylor Slough (P37) and C-111 wetlands (EPGW).


132


Model 1: P37


0 Data












Model 2 Atmospheric deposition options: P37


-Option 2: Rain-day constant
-Option 3: Rainfall weighted
0 Data
-Option 1: Daily constant


0_03

S0.025



0-015
E




r 0.01

0.005

0
Jul-96

0.03


Jul-96 Sep-96 Oct-96 Dec-96 Jan-97 Mar-97 May-97


Jun-97 Aug-97 Oct-97


Figure 4-9. Simulated TP concentrations obtained with Model 2 for each of the
atmospheric deposition options explored at observation stations in Taylor
Slough (P37) and C-111 wetlands (EPGW).


133


Sep-96 Oct-96 Dec-96 Jan-97 Mar-97 May-97 Jun-97 Aug-97 Oct-97


Model 2 Atmospheric deposition options: EPGW 0 Data
-Option 2: Rain-day constant
-Option 3: Rainfall weighted
N -Option 1: Daily constant


- 0.025

0.02



o 0.01
o.
0.005

0










0.03 Model 3: P37 0 Data

a- 0.025 -Model 3



0.015

0.01 --------------- 0-- --- -------------------------
= o.oo 1
0.005

0
Jul-96 Sep-96 Oct-96 Dec-96 Jan-97 Mar-97 May-97 Jun-97 Aug-97 Oct-97


.03 Model 3: EPGW 0 Data
0.025 -Model 3

0.02 ,

0.015

S0.01 .-- --------------- ,-^ -------- --- --------------
0.005



Jul-96 Sep-96 Oct-96 Dec-96 Jan-97 Mar-97 May-97 Jun-97 Aug-97 Oct-97

Figure 4-10. Simulated TP concentrations obtained with Model 3 at observation stations
in Taylor Slough (P37) and C-111 wetlands (EPGW).


134









CHAPTER 5
UNRAVELING MODEL RELEVANCE: THE COMPLEXITY-UNCERTAINTY-
SENSITIVITY TRILEMMA

Introduction

At its heart, our inability to truly simulate environmental (open) systems (Oreskes

et al., 1994; Konikow and Bredehoeft, 1992) is due to our inability to reproduce their

complexity. There are many reasons for this shortcoming: a lack of understanding in

poorly studied systems or the inability to either conceptualize or reproduce the

intricacies of well-studied systems; the inability of our instruments and methods to

obtain true observations needed for parameterization and calibration due to

measurement uncertainties and heterogeneities in space and time and scale; and the

discontinuous nature of numerical solutions that imperfectly reproduce the continuity of

reality. Such limitations prohibit true model validation (Oreskes et al., 1994). In lieu of

confirming such validity, we strive instead for confidence in model results, which we

consider by evaluating the extent of our doubt, as indicated by the degree of uncertainty

associated with the generated results (Naylor and Finger,1967; Beven, 2006a). There

is growing unease among developers and users of dynamic simulation models about

the cumulative effects of various sources of uncertainty on model outputs, which inherit

these underlying uncertainties (Manson, 2007 and 2008; Cressie et al., 2009; Messina

et al., 2008). In particular, this issue has prompted doubt over whether the considerable

effort going into further elaborating complex dynamic system modeling will in fact yield

the expected payback, viz. new insights about the complicated systems they are

intended to simulate (Ascough et al., 2008). The concern is that insufficient heed has

been paid to the balance between investment (complexity) and return (uncertainty),


135









which was succinctly captured by Zadeh (1973), who first presented the notion of

relevance as part of his "principle of incompatibility":

... the conventional quantitative techniques of system analysis are
intrinsically unsuited for dealing with humanistic systems or, for that matter,
any system whose complexity [emphasis added] is comparable to that of
humanistic systems [author's note: e.g. environmental systems]. The basis
for this contention rests on what might be called the "principle of
incompatibility". Stated informally, the essence of this principle is that as
the complexity of a system increases, our ability to make precise and yet
significant statements about its behavior diminishes until a threshold is
reached beyond which precision and significance (or relevance [emphasis
added]) become almost mutually exclusive characteristics.

The relevance of a model is contingent on the balance between its power to

address questions and the power of its answers. The former is dependent on model

complexity the degree of detail to which the real system is reproduced in the model

structure. The latter is dependent on model uncertainty the accuracy, precision and

confidence associated with output results. Our failure to attend more closely to this

balance is due largely to insufficient understanding of how complex models gain and

lose relevance. Failure to advance this understanding has been at least in part due to

the practical limitations associated with complex models. In particular, mechanistic

environmental models are among the most complex, demanding specialized numerical

code of spatially-distributed domains, numerous state variables, and a plethora of input

parameters and data. Such complex tools are typically developed by specialists and,

once complete, are not very amenable to adjustments in structure. The choice of

complexity in such tools has therefore more commonly been the responsibility of model

developers, while users simply have to deal with the consequences. Users do have a

choice between potential tools of differing complexity, but that decision is still based on

fixed choices, and is generally the product of a multitude of other considerations that


136









comprise what most modelers understand as the "art of modeling" (Getz, 1998;

Basmadjian, 1999). We believe that suitable tools now exist to support controlled

experimentation with model complexity, as well as more rigorous investigation into the

consequences for uncertainty. Using such tools, we propose and demonstrate that

meaningful new progress can be achieved toward unraveling the issue of relevance.

The Complexity-Uncertainty-Sensitivity Trilemma

To this point, we have used the term "uncertainty" to encompass various types of

uncertainty, some quantifiable and some less so, which collectively contribute to the

epistemic uncertainty in model results (that is, uncertainty associated with our

knowledge about the state of a simulated system; Regan et al., 2002). To better

investigate total epistemic uncertainty, it becomes necessary to distinguish between

specific forms of uncertainty. The most commonly encountered form of uncertainty in

modeling is error, which is a measure of model accuracy (i.e., the discrepancy between

simulated results and observed data). Another prevalent form of uncertainty is that due

to the uncertainties inherent to the values of input parameters, which are propagated

through a model and onto the outputs and manifest as precision (i.e., the irreducible

uncertainty in any model result that determines the range of possible values the actual

result might inhabit). This is the sense of the word most commonly intended in the

context of uncertainty analysis, and is the meaning adopted in all following sections

unless specified otherwise. Other forms of uncertainty exist, most of which are difficult

to assess because they are conceptually more qualitative, for example: uncertainty due

to the underlying assumptions and structure of a model; uncertainty in the interpretation

of voluminous and complicated results; and uncertainty in the validity of a model's

calibration due to model sensitivity. All are influenced by model complexity, but









sensitivity is particularly interesting in the context of investigating relevance. Methods of

sensitivity analysis now exist to rigorously quantify sensitivity in such a way as to not

only characterize the flexibility inherent to the model, and thereby the risk of

overparameterization issues, but also to illuminate how the sensitivity is caused and

possible ways for improving the precision of results (Saltelli et al., 2004). This

feedback, linking sensitivity and uncertainty, completes a tripartite dialectic between

complexity, uncertainty, and sensitivity the relevance trilemma that guides this work.

Uncertainty

There is growing interest in evaluating the contributions of model inputs

(uncertainty in data) and model structure (uncertainty from the simplifying assumptions

necessary to abstract reality into model design and algorithms) to the overall uncertainty

of model outputs (Beven and Binley, 1992; Beven, 1993; Draper, 1995; Cressie et al.,

2009). However, the sources and magnitude of uncertainty and their effect on dynamic

model outputs have not been comprehensively studied (Haan et al., 1995; Beven,

2006a; Shirmohammadi et al., 2006; Muioz-Carpena et al., 2007; Valle et al., 2009).

Uncertainty analyses endeavor to address this by propagating the various uncertainties

onto a model output, and many methods exist to achieve this end (Haan, 1989;

Shirmohammadi et al., 2006; Cressie et al., 2009). Systems that are better described

and characterized (as physical systems such as hydrology tend to be) are more suitable

for variance-based methods that apply Monte-Carlo simulations, such as the

Generalized Likelihood Uncertainty Estimation method (GLUE; Beven and Binley,

1992). However, many systems (such as ecosystems) are poorly understood and

modeler experience and subjectivity play an important role in their simulation.

Uncertainty assessments that employ Bayesian methods are better suited to


138









incorporate subjectivities and are therefore often favored in such circumstances

(Cressie et al., 2009). Merely quantifying the uncertainty in model outputs is insufficient

to fully understand where and how the uncertainty is propagated or to understand the

role of complexity. Sensitivity analysis can be used to determine how uncertainty in

model outputs is apportioned to different sources of uncertainty in the model inputs

(Saltelli et al., 2008). Whereas uncertainty analysis quantifies the overall uncertainty,

sensitivity analysis identifies the key contributors to uncertainty; together they constitute

a reliability assessment of a model (Scott, 1996).

Sensitivity

The sensitivity of a model output to a given input parameter has traditionally been

expressed in terms of the derivative of the model output with respect to the input

variation (Haan et al., 1995; Cariboni et al., 2007). Such sensitivity measurements are

"local" because they are fixed to a point or narrow range where the derivative is taken.

Local sensitivity indices are generally classified as "one-at-a-time" (OAT) methods,

because they quantify the effect of varying a single parameter by altering only its value

while holding all others fixed. Local OAT sensitivity indices are effective only if all

factors in a model produce linear, direct responses in the output, or interest is in the

model response under specific conditions (Saltelli et al., 2004). However, if changes

produced in an output are non-linear, or parameters exhibit interaction effects on model

output response, or an extensible assessment of sensitivity patterns is required, then a

global sensitivity approach is needed (Leamer, 1990; Saltelli et al., 2004). Global

sensitivity analyses (GSA) simultaneously vary all inputs and explore the entire

parametric space of a model, thereby making no assumptions about linearity, additivity,

or monotonicity. In complex models, the output response is often non-linear and non-


139









additive, so local OAT techniques are not appropriate, and global techniques should be

used (Saltelli et al., 2004). Different GSA methods can be selected based on the

objective and context of the analysis (Saltelli et al., 2000 and 2004; Cacuci, 2003).

Output sensitivity is inextricably tied to uncertainty, representing as it does the

"paths of greatest influence" on the output (those parameters to which the output is

most sensitive). An alternative perspective is that sensitivity represents the "paths of

least resistance" through which input uncertainty will be propagated onto outputs during

an uncertainty analysis. Sensitivity therefore plays an important role in another source

of epistemic uncertainty: model overparameterization, which is variously captured in

both forward and inverse solutions as non-identifiability, non-uniqueness, and

equifinality (Brun et al., 2001; Omlin et al., 2001; Beven, 2006b; Ebel and Loague,

2006). Overparameterization issues are the result of too many degrees of freedom in a

model due to the number of variable parameters. Each additional parameter introduces

an additional source of influence over model outputs. This effect accumulates and can

result in excessive flexibility in the model, which is counterproductive to

parameterization and calibration efforts and can produce poorly defined calibrations or

multiple irresolvable model characterizations (Beven, 2006a).

A poorly calibrated model, or one with a number of calibrated states that may be

physically irreconcilable, undermines confidence in the model's projections. GSA

methods uniquely capture the internal model relationships between input and output, as

well as between different inputs. These can be used as indicators of a model's

flexibility, and thereby the risk of non-identifiability and other overparameterization

issues (Snowling and Kramer, 2001). Though it is an important and neglected (Luo et


140









al., 2009) source of epistemic uncertainty, sensitivity quantified in this form remains a

qualitative measure of uncertainty. However, we can surmise that given sufficient

complexity, uncertainty associated with a model's total sensitivity might be expected to

reach a point that inhibits the model's relevance, overwhelming any gains in accuracy

from added complexity in analogous fashion to Hanna's (1998) usual uncertainty

suspects (Figure 5-2). The sensitivity of outputs to interactions between parameters is

a key contributor to overparameterization, and total sensitivity measures that capture

this effect are therefore a useful proxy for assessing the risk over over-sensitivity. By

contrast, greater direct sensitivity implies stronger direct links between input and output,

which is not only less likely to generate overparameterized conditions, but is also

necessary for identifiability (Brun et al., 2001).

Complexity

Model complexity has proved challenging to quantify, or even define (Chwif et al.,

2000). In a sense, complexity remains an abstract quality that can be assessed

according to many factors, with no single definition proving useful for all contexts.

However, when considering the structural complexity of a model, the number of

parameters is generally considered a useful indication of relative complexity, since the

number of parameters is tied to the number of processes included (Fisher et al., 2002).

Incorporating the complexity of the equations themselves can be achieved using a

Petersen matrix, which accounts for the number of mathematical operations (Snowling

and Kramer, 2001). Subjective allocation of complexity "levels" can also be assigned

based on users' knowledge of the number and nature of the processes included

(Lindenschmidt et al., 2006). In this work, a simple measure of relative complexity is









sufficient, and thus distinct complexity levels were defined according to the number of

parameters required.

Given the limitations inherent to simulating reality with simplified tools, it is not

surprising that more complex models are pursued (Arthur, 1999; Beck, 1987). Models

that are too simple may not capture important processes and cannot be proven to

reproduce the measured data for the correct reasons (Nihoul, 1994). The complexity of

a model fundamentally defines (and limits) the potential realities that can be

reproduced. Environmental systems are particularly challenging to simulate, not only

because they contain profound numbers of processes and constituents, but also

because they can shift between alternate stable states, a complex emergent process

(Scheffer, 2009). Such shifts can fundamentally change the nature of a system (i.e., the

shift from an aquatic system dominated by algae to one dominated by macrophytes).

Models that simulate ecological or biogeochemical systems like these within a

physically dynamic environment, such as a hydrodynamic aquatic environment, are

already highly complex. Yet, as we will show, failure to incorporate sufficient

(additional) complexity can have important consequences for a model's ability to resolve

certain simulated conditions.

The growing interest in optimizing model complexity relative to uncertainty (Cox et

al., 2006; Lawrie and Hearne, 2007) is particularly pertinent today because of the

growing availability of adaptable computational modeling tools, which give the user the

freedom to define model structure, and thus complexity. Dynamic systems that can be

conceptualized without a spatial domain have had such adaptable tools for many years,

with systems such as STELLA finding application in a wide array of fields (Doerr, 1996).


142









Similar versatility has been pursued with GIS modeling tools (e.g., Wesseling et al.,

1996). However, for the case of mechanistic, numerical models of complex

environmental systems, with large, spatially-distributed domains and numerous state

variables, the degree of model complexity has remained largely imposed on model

users.

Nonetheless, the value and amount of specialist time required for such model

development; the dramatic advances in computing capacity (Schaller, 1997) and data

acquisition by remote sensing (Pohl & Van Genderen, 1998); and the economics of

computer code reusability have compelled continued evolution of even the most

complex models toward greater adaptability. Recently, Jawitz et al. (2008) developed a

spatially-distributed numerical water-quality model, the Transport and Reactions

Simulation Engine (TaRSE), with user-definable state variables and biogeochemical

processes. To the authors' knowledge, this degree of control is novel in such a complex

environmental model. Another driver of increased interest in the effects of model

complexity is the development of multi-disciplinary integrated models that combine

environmental and socio-economic drivers, sometimes through coupling of existing

specialty models into a multi-modeling framework that can incorporate larger uncertainty

than conventional models (Lindenschmidt et al., 2007).

Relevance dilemmas

Previous work has sought to begin the process of elucidating the relationships

between complexity and various forms of epistemic uncertainty. Model complexity has

been long recognized as having important consequences for output uncertainty. Hanna

(1998) illustrated (Figure 5-1 a) that increasing complexity by incorporating more state

variables and processes can initially reduce uncertainty, but can have the opposite


143









effect after a certain critical point (Fisher et al., 2002). Greater complexity improves a

model's conceptual rendition of reality, meaning the model has fewer simplifying

assumptions and therefore less structural uncertainty. However, each additional

process requires parameters to characterize the mathematics, and the uncertainty

associated with each of these accumulates, eventually exceeding any gains. This

makes identification of a potential "inflection point" important, for it reveals the optimal

degree of complexity for modeling a system that incorporates sufficient detail to gain

information while avoiding greater uncertainty and loss of relevance.

Snowling and Kramer (2001) proposed general relationships relating complexity

and two forms of uncertainty: error and sensitivity (Figure 5-1 b). The authors showed

that as complexity was increased, model error decreased while model sensitivity

increased. Snowling and Kramer based their hypothesis on the general concept that

reduced structural error increased accuracy in analogous fashion to the reduction of

uncertainty presented by Hanna. Conversely, sensitivity would increase because the

additional parameters required to simulate the additional processes have some effect

on the model outputs, and therefore represent additional degrees of freedom.

This hypothesis has since been supported by work in Lindenschmidt (2006) and

Lindenschmidt et al. (2006). However, all corroborating results presented thus far

(Snowling and Kramer, 2001; Lindenschmidt, 2006; Lindenshcmidt et al., 2006) are

subject to limitations in generality, having been produced for limited ranges of

parameter variation, centralized around calibrated applications, or based on local OAT

sensitivity analyses. Furthermore, existing support for this hypothesis does not address

how the nature of sensitivity changes with model complexity. Improving our


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understanding of these dilemmas, between complexity and uncertainty, complexity and

error, and complexity and sensitivity, is crucial to improving our understanding of

relevance. However, it is also necessary that we acknowledge the links between such

dilemmas, which further complicate the problem but cannot be ignored is we wish to

address it. To this end we propose a trilemma, relating complexity, uncertainty, and

sensitivity, as the first step toward a more integrated assessment of relevance.

The relevance trilemma

In this paper we propose the following relationships relating uncertainty, sensitivity,

and model complexity, which together we believe represent a useful characterization for

model relevance (Figure 5-2): 1) Total global sensitivity, being the net sum of all input

effects on an output, increases with complexity due to the additive influence of

additional parameters; 2) Interactions increase with increasing complexity (for the same

reason), and will diminish the role of direct sensitivity as progressively more parameters

interact to control the output and detract from the direct influence of individual

parameters.

To test these hypotheses, we integrated a step-wise model-building approach

using TaRSE, GSA and UA to investigate the role of complexity, and to better guide

development across multiple levels of model complexity. Given doubt associated with

model input factors, such as structural complexity and uncertainty input parameters,

model development that is closely coupled to GSA and UA can reveal important

unintended effects, not only in terms of model sensitivity and uncertainty, but also the

capacity of a model to reproduce real, and complicated, system responses.


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Materials and Methods

Global Sensitivity and Uncertainty Analysis Methods

Two state-of-the-art global sensitivity and uncertainty methods were used in this

analysis: the qualitative method of Morris (1991) and a quantitative, variance-based

method called the extended Fourier Amplitude Sensitivity Test (FAST; Saltelli, 1999). A

brief summary of each method is given below (further details summarized by Muioz-

Carpena et al. (2007), and an in-depth treatment of the methods is provided in Saltelli et

al., 2004).

The Morris (1991) method, extended by Campolongo and Saltelli (1997), is

intended to elucidate qualitative global sensitivity, sacrificing quantification in lieu of

dramatically improved computational demands. This method is therefore suitable for

assessing the relative importance of input parameters, and for this reason it is an

efficient screening method often used to filter out unimportant parameters before

conducting the more computationally intensive, and quantitative, FAST analysis (Jawitz

et al. 2008; Saltelli et al., 2005). The Morris method applies a frugal sampling technique

to obtain unique sets of parameter values by varying each within their prescribed range

and probability distribution. The multiple simulations then performed using these unique

sets produce "elementary effects" in the outputs, attributable to changes in each input

parameter, the absolute values of which are averaged to produce a qualitative global

sensitivity statistic, p*. The magnitude of p* indicates the relative order of importance

for each parameter with respect to the model output of interest (Campolongo et al.,

2007). The standard deviation of the elementary effects, o, can be used as a statistic

indicating the extent of interactions between inputs. A higher o implies variability in the

elementary effects attributed to a particular parameter. Since the values of all other


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tested parameters are simultaneously varied, this variability implies that the observed

effect is dependent on the values held by other varied parameters (the parametric

context), and thus interaction effects between them. Conversely, an invariant p* implies

that interactions between parameters do not affect the parameter's influence on the

output, and that the output is therefore directly sensitive to it. For each output of

interest, pairs of (p*i, oi) for each input parameter can be plotted in a Cartesian plane to

indicate the relative importance of each output (distance from the origin on the X-axis),

and the prevalence of interaction effects (distance from the origin on the Y-axis).

The variance-based extended FAST method provides a quantitative measure of

the direct sensitivity of a model output to each parameter, using what is termed a first-

order sensitivity index, Si, defined as the fraction of the total output variance attributable

to a single input parameter (i). In the rare case of an additive model, where the total

output variance is explained as a summation of individual variances introduced by

varying each parameter alone, ZSi = 1. Such additivity is a requisite condition if local

sensitivity analysis results are to be generally applied to a model (Saltelli et al., 2004).

Given that even relatively simple models rarely meet this requirement, the application of

global sensitivity methods should be the preferred approach. In addition to the

calculation of first-order indices, the extended FAST method (Saltelli, 1999) calculates

the sum of the first- and all higher-order indices for a given input parameter (i), called

the total sensitivity index (STi), (Equation 5-1),

ST, = Si + S, + Sik... + S...n (5-1)









where Si is the first-order (direct) sensitivity, Syj is the second-order indirect sensitivity

due to interactions between parameters i and j, Sijk the third-order effects to due to

interactions between i and k via j, and so forth to the final varied parameter, n.

Based on Equation 5-1, total interaction effects can then be determined by

calculating STi Si. It is interesting to note that p* of the Morris (1991) method is a close

estimate to the total sensitivity index (STi) (Campolongo et al., 2007). Since the

extended FAST method applies a randomized sampling procedure, it provides an

extensive set of outputs that can then be used in the global uncertainty analysis of the

model. Thus, probability distribution functions (PDFs), cumulative probability

distribution functions (CDFs), and percentile statistics can be derived for each output of

interest with no further simulations required.

In general, the analysis procedure followed six main steps: (1) PDFs were

constructed for uncertain input parameters; (2) input sets were generated by sampling

the multivariate input distribution according to the selected global method; (3) model

simulations were executed for each input set; (4) global sensitivity analysis was

performed according to first the Morris method and then 5) the extended FAST method;

and (6) uncertainty was assessed based on the outputs from the extended FAST

simulations by constructing PDFs and statistics of calculated uncertainty. The free

software Simlab (Saltelli et al., 2004; http://simlab.jrc.ec.europa.eu/) was used for

multivariate sampling of the input parameters and post-processing of the model outputs.

Sample sets were created for all the parameters in each of the complexity levels tested

(see subsequent section and Figure 5-3) and for both methods, resulting in a total of six

sets of analyses. The number of model runs was selected based on the number of


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parameters in each complexity level according to Saltelli et al. (2004). A total of 1,170

simulations were conducted for the Morris method and 45,046 simulations for the

extended FAST method.

Model Description, Application, and Selection of Complexity Levels

Model description: TaRSE

A water-quality numerical modeling framework, the Transport and Reactions

Simulation Engine (TaRSE), has been developed to simulate the biogeochemistry and

transport of phosphorus in the Everglades wetlands of south Florida (Jawitz et al., 2008;

James et al., 2009). The US$10 billion Comprehensive Everglades Restoration Plan

(CERP) is the largest ecosystem restoration effort in the world, and aims to restore

historic flows and P levels to the ecosystem. The freshwater wetlands of the

Everglades have evolved under phosphorus-scarce nutrient conditions and are

especially sensitive to labile phosphorus in the surface-water (Munsen et al., 2002; Noe

et al., 2003). An important component of CERP therefore entails modeling the water-

quality with respect to phosphorus levels, and TaRSE was developed to meet this need.

The design of TaRSE is comprised of two functional modules; one that simulates

the advective and dispersive movement of solutes and suspended particulates in

flowing water (the "Iransport" module; James et al., 2009), and one that simulates the

transfer and transformation of phosphorus between biogeochemical components (the

"Reactions" module) (Jawitz et al., 2008). The term "Simulation Engine" refers to the

generic nature of the reactions module, which has been designed such that the user is

responsible for specifying (in XML input files) the model's state variables and the

equations relating them. State variables cam be grouped in conceptual stores, such as

surface-water or soil, and are classified as "mobile" if they are to be transported or


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"stabile" if they are not. Thus, even though the inaugural implementation of TaRSE was

intended for phosphorus-related water-quality modeling, this variable structure means it

can be easily adapted for different applications. The user selects from a suite of

equations to describe exchanges between state variables, including zeroth-order, first-

order, Michelis-Mentin growth and decay, sorption-desorption kinetics and rule-based

relations (Jawitz et al., 2008). When applied in a hydrodynamic environment, TaRSE

requires that necessary hydrologic state variables, such as stage and velocity, be

provided by a coupled hydrologic model. TaRSE employs a triangular mesh to

discretize the spatial domain for the Godunov-mixed finite element transport algorithm

(James, et el., 2009), but the reactions module is independent of mesh geometry. Once

the reactions have been simulated and mobile quantities updated within each cell, they

are transported.

Model application

This effort to study the effects of increasing model complexity was carried out as

part of a comprehensive testing process during the development of TaRSE. In addition

to the necessary quality control provided by sensitivity and uncertainty analyses, the

intention of this analysis was to study potential consequences resulting from the novel

freedom afforded by TaRSE's flexible design (i.e., user-defined complexity). In order to

isolate the effects of complexity, an artificial domain was created in which the sources of

variability extrinsic to complexity could be controlled and excluded. A 1,000 x 200-m

generic flow domain (Figure 5-3) was created and discretized into 160 equal rectangular

triangles (cells). Flow was set from left to right so that the inflow boundary consisted of

cells 1, 41, 81, and 122, and the outflow boundary consisted of cells 40, 80, 120, and

160. A no-flow boundary was applied to the top and bottom (longer) edges of the


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domain. To exclude the effects of transient flow, steady-state velocity was established,

and the effect of heterogeneities were managed by assuming spatially homogeneous

conditions. A constant velocity of 500 m/d was established to approximate Everglades

flow conditions (Leonard et al., 2006) with an average water depth of 1.0 m.

Simulations were run for 30 days with a 3-hour time-step.

Levels of complexity

Three models of increasing complexity were created (Figure 5-4a-c). Following

the recommendations of Chwif et al. (2000), complexity was progressively added to the

model in an organized and step-wise fashion. Each new complexity level corresponded

to the addition of one new state variable and the associated processes relating the

variable to the pre-existing system. The simplest case (Level 1) contained no biotic

components (Figure 5-4a). The intermediate-complexity case (Level 2) contained

surface-water biota in the form phytoplankton (Figure 5-4b). The most complex case

(Level 3) contained additional macrophytes rooted in the soil (Figure 5-4c). Table 2-1

lists the state variables and processes that appeared in each complexity level, including

the boundary conditions for the mobile state variables (always quantified in g/m3), viz.

soluble reactive phosphorus (SRP) in the surface-water (Csf) and plankton biomass

(Cp). Initial conditions for the stabile state variables (always quantified in g/m2), viz.

SRP in the porewater, adsorbed phosphorus, macrophyte biomass, and organic soil

mass, were 0.05, 0.027, 500, and 30,000 g/m2, respectively. Boundary and initial

conditions were selected to represent reasonable Everglades conditions based on

values cited in the extensive literature review conducted as part of parameterization

effort required for the sensitivity analyses (see following section). For full details of the

model equations and numerical solutions see Jawitz et al. (2008).









Parameterization of Inputs Across Complexity Levels

The application of TaRSE was done without prior calibration in order to avoid

limiting the potential range of physical conditions the model might be applied to, and

through which the effects of new complexity would be expressed. This also facilitated

testing of the model across a wide range of possible scenarios as a necessary step in

the development process prior to evaluation of its performance for a particular

application (Saltelli et al., 2000). Results from the GSA and UA were evaluated to

ensure that simulation results were consistent with the conceptual models and that

unreasonable results did not emerge (see Jawitz et al., 2008 for extensive details).

Before conducting a GSA or UA it is necessary to specify a range and distribution for

each parameter, from which values can be statistically sampled.

The field-scale ambient variability of many inputs has been reported to be

adequately modeled with log-normal or Gaussian distributions (Jury et al. 1991; Haan et

al. 1998; Limpert et al. 2001; Loaiciga et al. 2006). When there is a lack of data to

estimate the mean and standard deviation for such PDFs, the (beta) 3-distribution can

be used as an acceptable approximation (Wyss and Jorgensen 1998). When only the

range and a base (effective) value are known, a simple triangular distribution can be

used (Kotz and van Dorp 2004). Finally, a uniform distribution is recommended in

cases where values are assumed equally distributed along the entire parametric range.

The input parameters used in the analysis of TaRSE (Table 5-2) were assigned

ranges and probability distributions based on an extensive literature review found in

Jawitz et al. (2008). Since the goal of this work was a general model investigation, and

not a specific study of its application to a particular site, parameter ranges were

selected to cover all physically realistic values for the intended target region (the


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Everglades). Given the wide range of physical and ecological conditions that the data

from such an all-encompassing approach include, and considering that values were

derived from relevant literature rather than directly from sets of data, the more general

3-distribution was adopted. Consequently, all biogeochemical parameters (i.e.,

excluding transverse and longitudinal dispersivity) were described using 3-distributions.

Dispersivity is related to the composition of the physical system, such as for example

vegetation density, domain dimensions, and velocity. These characteristics are

contingent on the site selection, rather than natural variation, and their probability was

therefore considered to be random, and accordingly allocated a uniform distribution

(Jawitz et al., 2008).

Several outputs were defined for the analysis, accounting for each of the model's

state variables at each complexity level, and described in Table 5-1. In the context of

this work to investigate the role of complexity, only those outputs that appear in all three

complexity levels permit comparison and are presented. Outputs were defined to

integrate both spatial and temporal effects. For outputs of mobile quantities, averages

across the outflow domain (cells 40, 80, 120, and 160) were calculated at the end of the

simulation period in order to integrate the effects of transport parameters and processes

across the entire domain into the output. For stabile quantities, outputs were expressed

as the difference between the initial and final value of averages across the entire

domain.

Given the constancy of conditions applied to the model across all complexity levels

through fixed parameter ranges and distributions; invariant scale, initial, and boundary


153









conditions; and steady hydrodynamics, any changes observed in the uncertainty and

sensitivity are attributed to the effects of changes in model complexity.

Results and Discussion

Effects of Model Complexity on Sensitivity

Morris method

Figures 5-5a-c depict trends in the results from the Morris method analysis for

soluble reactive phosphorus (SRP) in the surface-water, CswP. This output is generally

considered to be of greatest interest in management of water-quality for CERP (Perry,

2008), and is the official water-quality restoration target mandated by Congress (Sheikh

and Carter, 2005). Immediately apparent is that the relative location of parameters in

the |*-o plane changed as the complexity increased. At lower complexities (Levels 1

and 2) inputs were found closer to the **-axis, almost never approaching, and never

exceeding, the 1:1 line. At Level 3 the parameters were generally above the 1:1

(shaded triangle in each graph) and associated with proportionally larger o-values.

Higher o-values denote a greater role for interactions among input parameters. As the

complexity increased, more parameters were drawn out into the |*-C plane, particularly

at Level 3. Since important parameters (i.e., those to which CswP is most sensitive) are

distinguished from unimportant ones by their relative distance from the origin, these

results indicate that more parameters became relatively important as complexity

increased. Conversely, fewer parameters were uniquely important in the more complex

model. This trend is generalized in Figure 5-5d, a novel presentation of Morris method

results that takes advantage of the geometry inherent to their interpretation. Multiple

outputs were plotted collectively (CsP, Cpw, So, and SP) by normalizing the points to


154









conserve their relative Cartesian positions, and grouping them by complexity level for

comparison. The same patterns observed in the Csw' results are exhibited by all the

outputs lumped together in this way.

These results are in agreement with our hypothesis that as complexity increases,

an increase in interactions is associated with a decrease in direct effects. The

sensitivity of CsW to different parameters at different complexities shows the changing

role of certain parameters as others are added. In Level 1, the stabile parameters kox,

kdf, Pb and Xso (oxidation rate, coefficient of diffusion, soil bulk density, and the soil

phosphorus mass fraction, respectively) were the most important. In Level 2, plankton

in the water column was added to the model, and parameters associated with plankton

growth (kgp and k,/2P'; plankton growth rate and plankton phosphorus half-saturation

constant, respectively) became the most important to Cs,. With the addition of

macrophytes in Level 3, it became difficult to separate obviously important parameters.

Instead, the model became comparably sensitive to many parameters because of the

increased role of interactions.

Extended FAST

Quantitative results for CsP from the extended FAST analysis (Figs. 5-6a-h)

corroborate the qualitative Morris method results. The percentage of total variance

(Figure 5-6a) attributable to direct (first-order) effects (S;) decreased with increasing

complexity, slowly from Level 1 to 2, then rapidly from Level 2 to 3. The same trends

were exhibited by Cp S, SP (Figure 5-6b-d). Conversely, interaction effects (Figure

5-6a-d) rose slowly from Level 1 to 2, then rapidly from Level 2 to 3. These trends were

consistent across all model outputs and provide further quantitative evidence in support


155









of the hypothesized sensitivity-complexity relationship, as posited by Snowling and

Kramer (2001) and extended globally herein.

In Level 1, the sensitivity of CswP to parameters associated with stabile state

variables was limited by the coefficient of diffusion (see Figure 5-3a), because diffusion

was the physical link between mobile surface-water and stabile subsurface state

variables. In Level 2, the total sensitivity (Figure 5-6e) of CswP increased because the

addition of plankton introduced a number of parameters that could affect CswP without

first being channeled through, and thus dampened by, the slow process of diffusion. By

contrast, the Level 2 sensitivity of stabile outputs (CpP, So and SP) to parameters more

closely associated with either of the mobile state variables (CswP or Cpl) remained

mitigated by the diffusion rate (Fig 5-6f-h). This changed in Level 3, however, where the

addition of macrophytes introduced new parameters to the subsurface. At this level of

complexity, macrophytes represented a phosphorus-sink dominant enough to make all

outputs sensitive to even those parameters whose influence was dampened by the slow

rate of diffusion. Consequently, we see a consistent trend across all outputs of

decreasing direct effects, and increasing interactions and total sensitivity. These results

indicate that the system was more sensitive to the addition of macrophytes than to

plankton. Furthermore, when viewed in conjunction with our understanding of the

physical description of the system, they allow us to understand how the model's internal

dynamics, expressed as output sensitivities, are shifting with increasing complexity.

Effects of Model Complexity on Uncertainty

Some of the uncertainty results (Figs. 5-6e-h), presented here using the 95%

confidence interval, seem to question the conceptual trends in Hanna (1988) (Figure 5-

la), indicating that these relationships may not be as simple as proposed. In fact, this is


156









explainable by accounting for the fact that some outputs are integrative, in that all

system components can participate in producing their final outcome, whereas others

have inherent biases that inhibit such integration. The key output, CsP, is an example

of an integrative output, since it is subject to the influence of all other state variables,

and the expected reduction of uncertainty holds. By comparison, accreted organic soil

(So), which is defined in terms of mass that is several orders of magnitude larger than

any other outputs, is not subject to comparable influence by other model components,

and is therefore not integrative. Mechanistically, this discrepancy is due to the relative

influence of turnover rates for the component compared with the fluxes into and out of

the store.

The consistent increase in uncertainty exhibited by SO (Figure 5-6f) therefore does

not follow the conceptual trend. Interestingly, in Level 2 we saw that the stabile outputs

closely associated with SO (Cpw and SP, which we might expect to be more integrated),

followed the SO trend and became more uncertain. This corresponds well with the

physics of the model for that level, however; addition of phosphorus through oxidation is

the predominant contributor to Cpw, to which SP is in turn bound through equilibrium

adsorption-desorption kinetics. Thus, their uncertainties should in fact be coupled with

that of SO. This demonstrates that the uncertainty effects in poorly integrated outputs

can be passed onto related outputs, effectively dis-integrating them. With the

introduction of macrophytes in Level 3, the effect of SO on Cpw and SP was broken by

the addition of a major new sink for phosphorus released through oxidation of the

organic soil, the process that physically linked the three outputs. The previously

affected outputs in turn became more integrated, and we see their uncertainty drop as









originally expected (Figure 5-6h). It is therefore important to consider that outputs can

be effectively dis-integrated, and therefore may not receive the consequences of

increasing complexity in the same way. Similarly, outputs may not be affected by added

complexity in other parts of the model.

Figures 5-7a-c depict the progression of output PDFs across complexity levels for

the same key output, CsfP, from a simpler leptokurtic distribution at the lowest

complexity level (represented by the lowest number of input parameters, eight), through

the platykurtic distribution at the intermediate level (12 parameters), to a bimodal

distribution at the highest complexity (16 parameters). The latter results represent

different system states, combining the further platykurtic nature of the Level 2 stable-

state, with a strongly leptokurtic end-point that corresponds to combinations of

parameter values that push the simulation out of the original stable-state. In this case,

the alternate state appears as a single value, and indicates that the complexity at this

level was sufficient to capture the existence of a second state, but insufficient to capture

any variability within the state.

Mechanistically, the presence of this second state demonstrates that a critical

threshold existed for the state previously simulated as Level 2. Its presence was

caused by combinations of parameter values working in conjunction with initial and

boundary conditions, which resulted in the systemic depletion of the biotic components

(plankton and macrophytes). This occurred because the range of values over which the

parameters were varied was held constant across complexity levels, yet included values

appropriate for both of the known stable-states that shallow water bodies can exhibit in

the Everglades (Scheffer, 1990; Scheffer et al. 1993; Beisner et al., 2003;), namely


158









algae- and macrophyte-dominated systems (Bays et al. 2001; Cichra et al. 1995).

Testing the full range of plankton-dominated conditions in Level 2 presented no

problems to the model because the structure was mechanistically appropriate there

were no macrophytes. However, the incorporation of macrophytes into the model

structure changed the definition of the simulated ecosystem, and without the necessary

feedback mechanisms (i.e., complexity) in place to resolve the extreme conditions

produced by unrealistic combinations of parameter values, phytoplankton biomass is all

but eliminated. Without this surface-water sink for phosphorus, CswP continuously input

at the boundary remained essentially unchanged in these cases, depicted by the spike

in outflow values matching the boundary concentration of 0.05 g/m3 (Figure 5-7c) The

platykurtic area represents model conditions under which the simulated system is not

catastrophically overwhelmed. The results therefore mimic those of Level 2, where

macrophytes were absent and phytoplankton dominated the surface-water phosphorus

dynamics. It is noteworthy that the introduction of macrophytes still acts as a

phosphorus sink in these cases, stressing the phytoplankton in terms of phosphorus

availability and thereby dampening the frequency of lower Cswv values (a sign of greater

phosphorus uptake due to growing plankton). Macrophytes also prevent the majority of

CswP results from exceeding the boundary input concentration (which can only occur

when significant diffusion takes place due to high CpP, as in Level 2, and as was never

the case for Level 3 because of porewater SRP uptake by the macrophytes (Jawitz et

al. 2008).

In this way, the addition of macrophytes to the set of tested model conditions

represented the introduction of an alternate stable-state that could not be resolved. The


159









complexity was insufficient to permit the model to simulate a shift between stable-states,

but (in conjunction with the parameter ranges tested for) was sufficient to simulate the

existence of a second stable-state. Though these results express emergent

characteristics of the simulated systems under the tested conditions, the forcing

"functions" in this case (being the variously sampled parameter sets) are based on real

values (albeit not necessarily real combinations of values) and therefore represent

potential realities that match well with the known biotic states of the Everglades: mixed

algae-macrophyte (the hump in Figure 5-7c) and macrophyte-dominated (the spike).

Given the absence of any suitable feedback in the tested model's mechanisms that

might permit plankton to dominate macrophytes, such a stable state is impossible to

simulate. The emergence of alternate stable-states in the results only occurs once

complexity has reached Level 3, clearly indicating that additional model complexity is

required to capture the complicated, but real, behavior of the system.

Conclusions

Presented results have corroborated the sensitivity-complexity relationship,

proposed by Snowling and Kramer (2001), using true global sensitivity methods and

over a wide range of model conditions, thereby demonstrating the validity of the

relationship in the most general context yet. We have also demonstrated that our

hypotheses relating the global sensitivity indices for direct effects, interactions, and total

sensitivity to model complexity are valid, providing a fresh global perspective to the

relevance trilemma.

The combined GSA and UA framework applied herein produced valuable insights

for interpreting both the meaning of the model results, and the meaning of how they

were generated in the context of model relevance. This methodology is therefore


160









proposed as a useful way to glean insights into the external and internal dimensions of

model performance.

The combined GSA and UA results presented indicate that uncertainty, on

average, decreases with complexity, and that total sensitivity increases. This implies

that we are still within the region of the trilemma space (Figure 5-2) that encourages us

to persist with increasing complexity if so desired. These results emerged from an

exploration of parametric spaces far larger than would be expected for any application

to a specific site, and therefore constitute a worst-case-scenario, which is thus cause for

further optimism. It is therefore reasonable to expect that refinement to a particular

application will reduce uncertainty further and permit additional complexity without loss

of relevance.

Given the benefits derived from the GSA/UA methods, it is proposed that these

methods constitute a valuable framework (Figure 5-8) for exploring the Relevance

Trilemma. In applying it herein, we gained useful information about the tested versions

of TaRSE, including important considerations valuable to future work, such as the

sensitivity of outputs to particular parameters, the strong effects caused by introducing

macrophytes, and the importance of considering integration in output definitions. The

sensitivity of the model to the addition of macrophytes calls for close attention to the

associated initial conditions and parametric ranges. The emergence of alternate stable

states in Level 3 results, and their absence in simpler levels, demonstrates the need for

some minimal complexity if such real world patterns are to be reproduced in

simulations, and highlights the unexpected potential for such patterns in the output

response of even a relatively coarse biogeochemical model. Importantly, these









methods also provide insights into how one might reduce model uncertainty (Saltelli et

al., 2004) by identifying important and unimportant parameters and processes. This

information can be used to guide efforts to better measure important parameters or

remove ineffectual complexity.

Important questions remain after the analyses presented here. Does Level 3

represent the optimum system description? Can this optimum be determined?

Although answers to these questions fall, at least in part, into the subjective realm of the

"art of modeling," the tools presented here offer the modeler an opportunity to better

understand the sometimes unexpected tradeoffs introduced by increasing model

complexity. We suggest that today we are in a better position to unravel the relevance

trilemma, and indeed even to actively incorporate it into our art, than when Zadeh

(1973) first presented his principle of incompatibility.


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Table 5-1. Process description for the increasing levels of complexity studied
Process Levels Key, fig5-2 Affected variables Process equation


Diffusion


1,2, 3


Sorption-desorption



Oxidation of organic soil


Inflow/outflow of surface-
water SRP


Uptake of SRP through
plankton growth


Settling of plankton

Inflow/outflow of
suspended particulates
(plankton)

Uptake of porewater SRP
through macrophyte
growth

Senescence and
deposition of
macrophytes


1,2, 3



1,2, 3


1,2, 3



2,3


2,3


2,3



3


3


Surface-water SRP concentration (mobile),
Cs'P (g/m3)
S Soil porewater SRP concentration (stabile),
CpVP (g/m2)
Soil porewater SRP concentration (stabile),
CP (g/m2)
2 Soil adsorbed P mass (stabile), SP (g/m2)

Soil porewater SRP concentration (stabile),
CwP (g/m2)
Organic soil mass (stabile), S (g/m2)

Surface-water SRP concentration (mobile),
4 CP (g/m3)
Surface-water SRP concentration (mobile),
CsP (g/m3)
Plankton biomass concentration (mobile), C''
(g/m3)
Plankton biomass concentration (mobile), CP'
(g/m3)
6 Organic soil mass (stabile), So (g/m2)

Plankton biomass concentration (mobile), CP'
7 (g/m3)
Soil porewater SRP concentration (stabile),
Cp, (g/m2)
8 Macrophyte biomass (stabile), CmP (g/m2)

Macrophyte biomass (stabile), Cmp (g/m2)

9 Organic soil mass (stabile), S (g/m2)


dCp,
dt



dSP
dt
dS
dt


kdf (cP _cP)
_k pw sw




pbkd dCP
o dt

-koxSo


BC: CsP = 0.05 g/m3


dC p'
dt

dCP'S
dt


BC: CP'

dCmp
dt


dCmp
dt


= -k iC~3 sw
9 + kp'l2

= -kpl'Cp
"xst v


= 0.043 g/m3

mpmp Cpw
S-kmPCmP CaPsk
S Ckp + zasOkc


- ksnCmp


163











Table 5-2. Probability distributions of model input factors used in the global sensitivity
and uncertainty analysis


Parameter
definition

Coefficient of
diffusion

Coefficient of
adsorption

Soil porosity

Soil bulk density

Soil oxidation rate

P mass fraction in
organic soil

Longitudinal
dispersivity
Transverse
dispersivity
Plankton growth
rate

Plankton half
saturation
constant

Plankton settling
rate

P mass fraction in
plankton

Macrophyte
growth rate

Macrophyte half
saturation
constant

Macrophyte
senescence rate
P mass fraction in
macrophytes


Process in
Symbol Fig5-4
Fig5-4


Distribution


P (7x10'10, 4x10 9)


S(8x10-6, 11 x 0-6)

p (.7, 0.98)

p (.05, 0.5)

p (.0001, 0.0015)

p (.0006, 0.0025)


U (70, 270)


U (70, 270)


P (.2, 2.5)


p (.005, 0.08)


p (2.3x10 7, 5.8x10-6)


p (.0008, 0.015)


p (.004, 0.17)


p (.001, 0.01)


p (.001, 0.05)

p (.0002, 0.005)


Input present
Units in
L1 L2 L3

m2/s x x x


m3/g x x x

S x x x

- x x x

1/d x x x


x x x


m x x x


m x x x


1/d


g/m3


m/s


x x


x x


x x


x x


g/m3


1/d


164


kd

0

pb

k,

XSoP
""cc


k,12P1


kspl


XP
i mp

kgmp


kl/2mp


MP
Xmp









b) Relevance relative to error and sensitivity


SSensitivity
RELEVANCE RELEVANCE
LVRELEVANCE


d Total Moddl Uncertainty .
14

N r o.......... ..... ......
7 --- -.1


Number or Parameters in Model Complexity

Figure 5-1. Relevance relative to a) sources of modeling uncertainty in relation to
model complexity (Hanna, 1988 as cited in Fisher et al., 2002), and b)
Snowling and Kramer's (2001) hypothesis relating error and sensitivity to
model complexity.


165


a) Relevance relative to model uncertainty











--- -


Total uncertainty


..--




I -
* --'


t I



'ire ts
_Dect L


- '4


Complexity


Figure 5-2. Hypothesized trends relating complexity to sensitivity from direct effects,
sensitivity from interactions, and total sensitivity. Total uncertainty still follows
the trends of Hanna (1988) but now includes total sensitivity as another
source of uncertainty.


I

Inflow
Inflow a

I:


122 174 126 1,28 \ 130 1 36 138 140' 142 144 \14 8 \148 50 152 \154a 156' 1' 60
121 123 125 127 129 13\ 135\_137\ 139\ 141\ 143\145\ 147\ 149\ 151\ 153\ \1l.7 .r l'
2\1 1\3`\517 211_'24153 1iiT


[3, 8"5/

43\ 45\


91 -. /
/2 rJ
51\ 53\
'II/ I/
/ 1 / 14
a1 *


/I 0 1 I

59 61\
/?n / 2,_
I 001 .ii..r
X,(


Ou rtii iAI


Figure 5-3. TaRSE application domain, with flow from left to right and bounded above
and below by no-flow boundaries. Simulations were run for 30 days with a
time-step of 3 hours.


166


\E 71"
67\>69\

4.


711 117/

75\1 77\
2 ,





















SWater column

F- Soil


1 8 J 9 I Indicates a phosphorus store/flow
......... Indicates a material store/flow

S* S Indicates a simulated process
3 ------- ^ \....
________ Indicates a cell input/output

Figure 5-4. Levels of modeling complexity studied to represent phosphorus dynamics in
wetlands. Levels include a) Level 1: interactions between SRP in the water
column and SRP in the subsurface; b) Level 2: Level 1 with the addition of
plankton growth and settling; c) Level 3: Level 2 with the addition of
macrophyte growth and senescence. Notation and details on processes
included in each Level are given in Table 2-1.


7 j 5 *"""" I
Ssw 5C .
4 *........ ... ..
_,.. ^ :..... |6














LL -

0U-
ow


0>



SL|
.
Z
- ,--i,


_a) C,W: Level 1






kox
*6


Xso* *Pb



es,
S kd

0 0.05 0.1 0.15 0.2 0.25
MEAN OF MODULUS ELEMENTARY
EFFECTS (p*)

c) C(,: Level3



kk
rao
kstp'


pXpb 1/2' k

00

xp,I
-
I I I I I I I
0 0.005 0.01 0.015 0.02 0.025 0.03
MEAN OF MODULUS ELEMENTARY
EFFECTS (p*)


z
O 1


ao 0.8
w
mLL
< W 0.6
0 >
Z:

03 z 0.4
W
NW
S[ 0.2

o 0


0.06
LL -6
SC0-0
Z0

S0.0
5 LL
WW
o >- 0.03

SZ 0.02

0.01

0


0






I I I I I I
0 0.2 0.4 0.6 0.8 1
NORMALIZED MEAN OF MODULUS
ELEMENTARY EFFECTS (p*)


Figure 5-5. Morris method global sensitivity analysis results for surface-water soluble
reactive phosphorus outflow (Csw ) in a) Level 1, b) Level 2, c) Level 3, and
for d) all outputs and all levels combined. The grey triangles indicate the 1:1
line font size of labeled parameters indicates their relative importance to
Csw .


168


b) C,,: Level 2









k 12p


kox
- X

I XI

0 0.01 0.02 0.03 0.04 0.05 0.06
MEAN OF MODULUS ELEMENTARY
EFFECTS (p*)


0.15I


0.05


I1


0.03
LLU
U- ---
0 0.025
O 0.02

0


'E
|L 0.01


I- 0o.005
(Iu~


d) All outputs: Levels 1-3


0 Level 1
* Level 2
* Level 3













100 1300










-0.4 .-0.500 -1080 .... .... -.. ....-.. 1100 CD
0










-- 0.3- -0.375 1020 "-0.9 850
S 0.2 0.250 960 -0,6 600





e) C', ) cp g) h) SP
Complexity, in number of parameters (8=Level 1, 12=Level 2, 16=Level 3)

Figure 5-6. Results for a-d) sensitivity from direct effects (S;, left y-axis) and sensitivity
from interactions (ST- S;, right y-axis, and e-h) output uncertainty expressed
as the 95% Cl (left y-axis) and total sensitivity (S, right y-axis), as model

complexity was increased.
complexity was increased.


169























0 1 j 0
0 0.2 0.4 0.6 0.8 0 0.02 0.04 0.06 0.08 0.1 0.12

S0.5
0- c) Level 3 (16 input parameters)

0.4

0.3-

0.2

0.1

01
0 .......I'
0 0.01 0.02 0.03 0.04 0.05
Concentration of surface water SRP (CP), in grams per cubic meter


Figure 5-7. Output PDFs for SRP concentration in surface-water outflow (Csv) for a)
Level 1, b) Level 2 and c) Level 3.


170











Global UNCERTAINTY Analysis (GUA)


Global SENSITIVITY Analysis (GSA)


Figure 5-8. A suggested framework, employing global sensitivity and uncertainty analyses, for enhancing understanding
of model performance studying model relevance in relation to complexity









CHAPTER 6
CONCLUDING REMARKS

Conclusions

A novel water-quality modeling tool has been developed for the coastal wetlands

of the southern Everglades by linking the hydrologic model FTLOADDS with the water-

quality model aRSE to create FTaRSELOADDS. FTaRSELOADDS combines the

numerical efficiency and mechanistic rigor of a fixed-form spatially-distributed

hydrodynamic model with the adaptability of a flexible free-form biogeochemical cycling

model. In combination, the two models represent a tool that can be adapted and refined

to best capture the water-quality issue of interest while accounting for the complex

variable-density unsteady hydrodynamics that characterize the region's hydrology The

linkage of the FTLOADDS and aRSE was validated by a series of comparisons between

known analytical solutions and numerically simulated results that used FTLOADDS and

a combination of FTLOADDS and aRSE. Thus Objective 1 was satisfied.

The linked models were tested with a field application to the SICS region, which

provided answers to the questions underlying Objectives 2 and 3. Surface-water

hydrodynamics were shown to be sensitive to depth-varying Manning's n, which had to

be reintroduced into the hydrodynamic model in order to accurately capture wetting and

drying processes and their effects on water-quality. Three different water-quality

conceptual models of increasing complexity were implemented and the results

compared. The simplest version employed conservative transport and produced the

best match with data. However, this version also neglected all biogeochemical

processes, including the important input of atmospheric deposition, and was therefore

the weakest of the models from the perspective of mechanistic justifiability. The most


172









complex model produced acceptable results despite being subject to the significant

uncertainty associated with including atmospheric deposition, implying that the greater

mechanistic integrity may have helped mitigate this uncertainty. Experimentation with

how to input atmospheric deposition indicated that the simplest approach of distributing

an annual average equally over all days in the course of a year produced the best

results and is justifiable based on the limited data available.

Given the freedom to manipulate model complexity, and the recognized

relationship between this complexity and model uncertainty, sensitivity and relevance, a

study was conducted to elucidate how additional complexity affects model performance

(Objective 4). Global sensitivity and uncertainty analysis methods were applied, and a

framework for formally exploring their results in the context of complexity was

presented. Direct sensitivity was found to decrease and interaction effects to increase

as complexity was added. Uncertainty was found to decrease in response to increased

complexity, though considerations of turnover rates versus flux rates were shown to

influence this result. The suggested framework demonstrated its value as a useful

means of exploring and explaining model results and of assessing relevance with

respect to complexity, thus satisfying Objective 4.

Limitations

Currently, the computational expense of a fully integrated fixed-form/free-form tool

remains high. The required time-step for hydrodynamic simulations of SICS is small but

the efficiency of solution methods keeps the investment manageable. With the addition

of aRSE comes significant overhead since each cell in the SICS hydrodynamic model

domain is individually processed. This process is exacerbated by the need to prepare

and exchange large amounts of data between the two models. The presented effort


173









was limited to a daily time-step by these computational costs, which precluded using the

Runge-Kutte 4th Order differential equation solution functionality within aRSE, which

required a maximum 15-minute time-step and untenable cumulative computational

times.

The paucity of surface-water phosphorus data was a significant limitation to the

water-quality modeling effort. This was exacerbated by the fact that observed

phosphorus concentrations fluctuated within a relatively small range of variation due to

the oligotrophic conditions. A more rigorous testing of the water-quality against more

phosphorus concentration data points, or against more types of data (such as

biomasses or fluxes), would contribute valuable additional validation of the model.

Additionally, the sensitivity and uncertainty analyses performed did not evaluate

the SICS water-quality application, but rather a theoretical application established in a

generic testing domain. The SICS water-quality application would benefit from such a

sensitivity and uncertainty analysis. Similarly, evaluation the complexity-relevance

relationship for a field-tested application such as SICS would provide additional rigor to

the testing of the suggested relevance framework.

Finally, there is currently no formal documentation for aRSE or FTaRSELOADDS.

Documentation does exist for TaRSE and SWIFT2D individually, but a formal record of

the linkage of the models and a user's manual to guide implementation of the linked

tools is needed. Without this documentation the complexity of the tool prevents its

wider application by any user not already familiar with it.

Future Research

Future work is required to either extend the simulation period to include more data

points, or to shift the simulation period to more recent times when data is being


174









recorded at greater resolution. Additional time-series data pertaining to soil

phosphorus, periphyton and macrophyte biomass in the SICS region would provide

valuable additional testing of the more mechanistic water-quality modeling approaches.

The current treatment of the water-quality reactions as a completely separate step to

the transport means that parallelization of the reactions is possible. Considering that

over 9,000 cells are currently processed in linear sequential order when they could all

theoretically be processed simultaneously, the opportunities for greater computational

efficiency are significant.

The work presented here has demonstrated the significant commitment required to

get to the point of being able to make use of this tool. Future work must now explore

and expose the potential within, especially as it pertains to the flexibility provided by

aRSE. Most immediately, the mechanistic and spatially-distributed modeling of any

number of water-quality issues in the southern Everglades can begin in earnest.

Nitrogen and dissolved organic carbon input to Florida Bay are a major concern that has

not been satisfactorily addressed. The proven ability of the hydrodynamic model to

accurately capture wetting and drying is encouraging for future sulfur and mercury

modeling in the region given the importance of these processes to mercury methylation

(Cleckner et al., 1999).

The development of ecohydrological water-quality modeling is now also possible.

The important role of Manning's n in the hydrological simulations was demonstrated in

Chapter 3. Making the link between simulating biomass growth for water-quality and

changes in flow resistance with seasonal growth and senescence is readily achievable


175









with FTaRSELOADDS. So too is the integration of spatially-distributed nutrient inputs to

ecological models in the region, which have previously been limited to hydrologic inputs.

Finally, such flexibility within complex models is an important launching point for

serious study of how model complexity, uncertainty, and sensitivity interact in complex

spatially-distributed models. Given the paucity of work in this field and the clear benefits

derived from the GSA and UA methodology that was applied in Chapter 5, the

framework that was proposed for tackling questions related to the Relevance Trilemma

should prove fruitful.

Philosophical Deliberations

The freedom to be creative is the source of progress. It is this tenet that underlies

the very notion of Academia, and recognizes the profound role of creative freedom in

advancing our technological, cultural, and intellectual evolution. It is the freedom to be

creative that will prove to be the greatest strength of tools such as FTaRSELOADDS.

One need look no further than the kaleidoscope of problems to which STELLA has

been applied to see the imagination unleashed by a tool that puts creative control in the

user's hands. There is no reason why users of complex models, such as that applied

herein, should be denied such creative freedoms as a matter of course, as has long

been the case with the availability of only fixed-form spatially-distributed models. In

fact, it is precisely because modeling of this highly complex sort is so arduous, and so

challenging, that such freedoms should be encouraged. To have modelers who have

invested such energy and expertise and life time into mastering a tool that is subject to

claustrophobic specificity is to waste a glut of potential and opportunity.

The art of modeling will always entail balancing the pros and cons behind the

choice of an appropriate tool for a given problem, whether it be developed from scratch


176









or picked off a shelf. With the freedom to uniquely tailor complex spatially distributed

models comes a new dimension to the art modeling: the notion of optimizing these high

levels of complexity with respect to uncertainty, sensitivity and relevance. It is important

that we continue to delve more deeply into this tripartite conundrum or risk falling behind

our tools. Modelers, and all who depend on their work, cannot fail to acknowledge and

grasp the limitations to relevance inherent to the nascent generation of "super-complex"

tools, including efforts to integrate many independent and spatially-distributed models

into vast multi-model systems.

As complex model creation and modeler creativity become ever more entangled,

better understanding of how models gain and lose relevance is critical both to the

evolution of our tools and to the evolution of our modelers. We cannot forget that the

science and art of modeling are one and the same.









APPENDIX A
MODEL VERSIONS

Model and Application Versions: Nomenclature

The following rules and naming conventions apply when referring to versions of

either SWIFT2D, FTLOADDS, or their applications as SICS or TIME:

SWIFT2D: specifies only the surface-water model

SEAWAT: specifies only the ground-water model

FTLOADDS: specifies versions in which SWIFT2D and SEAWAT have been linked (one
or the other may be on or off)

SICS: the Southern Inland and Coastal Systems application

TIME: the Tides and Inflows in the Mangroves of the Everglades application

Version 1.X: models or applications simulating only surface-water

Version 2.x: models or applications simulating coupled surface-water/ground-water

Version X.1: models or applications using SWIFT2D code adapted for the SICS
application as per Swain et al. (2004)

Version X.2: models or applications using SWIFT2D code adapted for the TIME
application as per Wang et al. (2007)

Version X.Y. 1: models or applications using SWIFT2D code adapted for TIME but with
variable-Manning's functionality from SICS adaptations reinstated

Model and Application Versions: Sub-models

The following figures offer a graphical overview of the model and application

versions. Consistent colors are used to represent identical versions/models to facilitate

identification across figures. Perpendicular blocks, generally oriented vertically, indicate

models/versions that encompass adjacent horizontal blocks. Blocks crossed out in

white indicate that the submodel is present but not used.


178
















SIC upda tes


Figure A-1. SWIFT2D v1.1 comprises the SWIFT2D v1.0 (Schaffranek, 2004) code and
additional code from SICS updates for coastal wetlands (Swain, 2005).


Figure A-2. FTLOADDS v1.1 comprises the SWIFT2D v1.1. code, leakage code linking
SWIFT2D to SEAWAT, and SEAWAT, but represents applications in which
SEAWAT is not implemented.


Figure A-3. SEAWAT comprises the MODFLOW code and the MT3DMS code
(Langevin and Guo, 2006).


179
























Figure A-4. FTLOADDS v2.1 comprises SWIFT2D v2.1 and SEAWAT, where
SWIFT2D v2.1 is SWIFT2D vl.1 implemented with integrated leakage and
ground-water simulation by SEAWAT.


Figure A-5. FTLOADDS v1.2 comprises SWIFT2D v2.2 with updates for TIME but with
the ground-water simulation turned off (thus SWIFT2D v1.2).


180






















Figure A-6. FTLOADDS v2.2 contains SWIFT2D v2.1 linked with SEAWAT and
containing TIME updates (thus SWIFT2D v2.2).









APPENDIX B
DETAILS OF THE FTARSELOADDS LINKAGE

Section B1

Technical Considerations in the Model Linkage

Since aRSE is callable as a DLL, and considering the primacy of hydrology and

the role of FTLOADDS in controlling the integrated execution of SWIFT2D and

SEAWAT, FTLOADDS was selected as the controlling program. Furthermore, the

decision was taken to link aRSE with the surface-water model only, i.e. to SWIFT2D.

This was done to keep the scope of the task manageable given the effort entailed in

linking aRSE to even one of the two complex FTLOADDS sub-models. The choice of

SWIFT2D is further justified by recognizing that the biogeochemical processes aRSE is

intended to simulate are primarily associated with the surface-water in wetlands

systems. Water-quality in the ground-water is generally not as sensitive to biological

influence given the paucity of autotrophic organisms and was therefore not justified at

this early stage development. Additionally, though vertical flow through the upper soil

cannot be simulated given these assumptions, the flexibility of aRSE does permit soil

phosphorus state-variables to be defined, which would permit soil biogeochemistry to be

modeled under assumptions of negligible vertical advection processes.

A number of fundamental differences in the respective design of FTLOADDS and

aRSE had to be overcome in order to successfully link the two models. These included

an idiosyncratic artifact of the initial setup of aRSE that inhibited its automation within

FTLOADDS, the absence of a spatial distribution in aRSE, and the use of different

programming languages to code the models.


182









Consideration 1: Initial setup of aRSE

In order for the user to specify a unique system of water-quality processes it is

necessary to input the state-variables that comprise the system, the parameters

required to characterize the equations relating the state-variables, and the nature of the

equations themselves. State-variables are classified as mobile if they represent

constituents that would be moved with flow solutess and suspended particulates -

constituents), or stabile if they represent stationary quantities (e.g. rooted macrophytes,

soil, benthos). There are also 30 additional implicit parameters that are always present,

though only used if specified in the equations. These implicit parameters were originally

necessary for transport processes and have been kept because they represent useful

properties (mostly of hydrodynamics) that may be useful in future work and present little

inconvenience with their presence. In the jargon of aRSE, state-variables and

parameters are collectively referred to as components. Given that the number of both

parameters and state-variables is a user choice, the total number of components is

variable.

A single vector, VARS, is used by aRSE to store the values for all components. In

order for updated values of transported constituents or hydrodynamic quantities to be

passed from FTLOADDS to aRSE it is necessary to know which particular element of

this vector corresponds with the given quantity. However, aRSE must be initialized

once in order to determine these locations since they are subject to the number of user-

specified components. In order to exchange information between the two models it is

necessary to have some means to determine what quantity each element of the vector

refers to.


183









Consideration 2: Spatially-distributed versus non-spatial

FTLOADDS is a spatially-distributed model, and therefore performs calculations

on, and stores data about, many individual cells that together comprise the modeled

domain. By contrast, aRSE is non-spatial, assuming that the system of reactions it

simulates is carried out at a singular location with no consideration of spatial

distribution.

Where FTLOADDS stores arrays of data for each model variable, aRSE stores a

single vector containing the single value for each of the model components. The use of

a one-dimensional vector, as opposed to a higher-dimensional array, is possible

because there is essentially only ever one cell (hence non-spatial) under consideration.

By contrast, SWIFT2D maintains two-dimensional arrays, dimensioned to the total

number of cells used to discretize the model domain, for each of the hydrodynamic

variables and three-dimensional arrays for the solute concentration variables (the third

dimension is used to specify the particular constituent, since all concentrations for up to

seven constituents are stored in a single array).

Since aRSE can only ever consider a single cell at a time it must be run repeatedly

for each of the cells in the FTLOADDS domain. This in turn entails updating the VARS

values with data appropriate to the cell in question, and then saving the values after the

reactions step so they are not over-written by the results of the subsequent cell's

reaction step.

Consideration 3: FORTRAN versus C++

The programming languages used to encode each of the models was not

consistent. The FORTRAN language (in the form of both FORTRAN 77 and FORTRAN

90) was used to code FTLOADDS and its constituent sub-models, SWIFT2D and


184









SEAWAT. The generic design of aRSE is the product of object-oriented template

functionality in the C++ language used to code it. The linkage of the two models

therefore represents a mixed-language programming problem in which communication

between the two structurally and syntactically foreign languages must be facilitated.

A number of inter-language calling conventions have been adopted by FORTRAN

and C/C++ (Arnholm, 1997; Wang et al., 2005):

Most FORTRAN compilers convert subroutine names to lower case and append
an underscore. To make a C routine callable in FORTRAN, declare the name of
the routine in lower case and append an underscore.

FORTRAN passes arguments by reference, C++ by value. For a variable name
in a subroutine call from FORTRAN, the corresponding C routine receives a
pointer to that variable. When calling a FORTRAN routine, the C routine must
explicitly pass addresses (pointers) in the argument list.

C routines assume that character strings are delimited by the null character.
From FORTRAN to C, the length of each character string is passed as an implicit
additional INTEGER (KIND=4) value, following the explicit arguments. From C to
FORTRAN, when a function returns a character string, the address of the space
to receive the result is passed as the first implicit argument to the function, and
the length of the result space is passed as the second implicit argument,
preceding all explicit arguments.

Arrays in FORTRAN are stored in a column-major order, whereas in C they are
stored in a row-major order. Two types of communication between FORTRAN
and C++ were required that called for special treatment.

Wang et al. (2005) outline a suggested manual procedure for overcoming these

problems. The principle is to build a "wrapper" for the C++ library that hides the

implementation details of the library from the FORTRAN code. The wrapper handles

the request from a FORTRAN call to create and destroy the objects defined in C++, and

then returns a FORTRAN pointer aliased to the memory allocated in the C++ library with

support function overloading. The "wrapper" itself is made of two components, one "C"

and one FORTRAN 90 component, written in "standard" C++ and FORTRAN 90,


185









together with the conventional inter-language calling method. Changes to the

application source code are minimal and can be automated.

The FORTRAN 90 component contains a module that provides a set of public

functions for the FORTRAN application to call. Each of these public functions

corresponds to a function implemented in the C++ library, and it calls the corresponding

function via the C++ component. The FORTRAN 90 module also holds one- or multi-

dimensional FORTRAN pointers in its global space, and thereby provides an alias

function for the C++ component to call that makes the one- or multi- dimensional

FORTRAN pointer aliased to the memory space allocated dynamically in the C++

library.

Resolution 1: Initial setup of aRSE

To overcome this problem a FORTRAN subroutine, READIWQ, was written to

read a new water-quality input file (IWQINPUT.iwq) that contains the necessary data

also included in the XML input file, but which could be read without the need for aRSE

to be executed. The XML output file was therefore no longer needed. Since aRSE still

relies on reading the XML input file to correctly setup, this method requires that two

input files containing some overlap in data be provided. However, the files are small

and simple to produce, and allow the setup of aRSE to be automated and controlled

from FTLOADDS. Furthermore, having such a file is also useful for overwriting aRSE

parameters and state-variable initial conditions should this be desirable, and introduces

some measure of control from within the calling FORTRAN code over the inputs to

aRSE without having to tamper with the aRSE code at all.

The automation process in READIWQ makes use of the fact that aRSE distributes

components in the VARS vector in an orderly manner that, given knowledge about the


186









number of state-variables and the number of parameters, permits the deduction of their

future location in VARS vector. Mobile state-variables are always positioned first,

followed by stabile state-variables, followed by a fixed number of implicit parameters (27

hydrodynamic and spatial properties), followed by the user-input parameters, followed

by the remaining 3 implicit parameters (temporal properties). The subroutine READIWQ

therefore requires, in order:

The number of mobile state-variables
The number of stabile state-variables
The paired name and initial value for each mobile state-variable
The paired name and initial value for each stabile state-variable
The number of user-specified parameters
The paired name and value for each user-specified parameters

Also permitted are override values for any of the implicit parameters, whose positions in

VARS are fixed relative to each other, though contingent in absolute position on the

number of state-variables that precede them. This process is conducted during the

initial setup of SWIFT2D, thereby ensuring that data is correctly exchange and the

linkage with aRSE is fully functional from the first time it is called from within SWIFT2D

(though aRSE still requires its own initialization step the first time it is called to process

the equations outlined in the XML input).

Resolution 2: Spatially-distributed versus non-spatial

A new two-dimensional vector was established, C1_aRSE, dimensioned to the

number of components (i.e. the same size as the VARS vector) and the total number of

cells in the FTLOADDS domain. Each time aRSE is called, which may or may not be

coincident with the FTLOADDS hydrology and transport time-steps, all the appropriate

data for each of the cells is moved from the various arrays within FTLOADDS to

C1_aRSE prior to the simulation of reactions in the first cell. Since no exchange of









information between cells takes place during the reaction step, the order in which cells

are processed for reactions does not matter with regards to the accuracy of the

simulation. However, the order in which memory is accessed during computations does

affect the speed of the process. It date are therefore transmitted in column-major order

from FTLOADDS arrays to C1_aRSE in order to minimize computational time. Though

FTLOADDS arrays are dimensioned with a rectangular shape (number of rows x

number of columns), the model permits an irregularly shaped domain, which may result

in many points within the rectangular memory array referring to cells that are not

actually used by FTLOADDS. The subroutine CELLCOUNT therefore determines the

number of active cells in the model and this number is used in the reactions step,

thereby minimizing the computational iterations

Prior to each individual cell being processed the data appropriate to that cell is

transmitted to the VARS vector that is used directly by aRSE. Once the reactions have

been simulated the updated VARS values are used to overwrite old values in C1_aRSE.

In this way old values are overwritten and new values stored until reactions have been

performed on all cells. After the final cell has been processed, all updated values in

C1_aRSE used transmitted back to their appropriate FTLOADDS arrays, where they

are then used in subsequent transport calculations.

Currently, concentrations, depths, and velocity in the x- and y-directions are

passed from FTLOADDS to aRSE, where concentrations are analogous to mobile state-

variables, and the hydrodynamic variables to particular implicit parameters. Only

concentrations are transmitted back to FTLOADDS for use in transport, though the

freedom to return updated hydrodynamic variables should the reactions affect them


188









offers potentially exciting opportunities for simulating ecohydrological effects using

these models.

Resolution 3: FORTRAN versus C++

Text strings in FORTRAN and C++ are represented differently. FORTRAN strings

are character variables that are declared as a particular length, which is maintained by

trailing blank space characters irrespective of the length of the text of interest within the

string. By contrast, C++ strings are null-terminated following the final character of text.

If FORTRAN strings are to be understood by C++ they must be converted to a null-

terminated form. A subroutine to do so exists, and was used to convert the XML input

filenames, which are now read in by the FORTRAN subroutine READIWQ, and convert

them to a format acceptable to the C++ code of aRSE.

The second instance necessitating mixed-language communication was the calling

of subroutines. In this case, aRSE is executed by calling one of a three C++

subroutines from within the FORTRAN linkage. FORTRAN 90 contains some built-in

functionality to facilitate mixed-language programming, including the INTERFACE

statement, which is useful for creating interfaces between FORTRAN and external

subroutines. Interfaces were therefore defined for each of the external C++

subroutines. Compiler directives were specified within the interface to attribute C++

calling conventions, to specify the location of the subroutines as within a DLL, and to

specify an alias for the called subroutine that was preceded with an underscore to

match the C++ syntax.

General description of the linkage mechanism

* If aRSE is greater than zero then READIWQ is called during the setup of SWIFT2D
to preprocess aRSE.


189










* The subroutine CALLaRSE is called at the time interval specified by the variable
CaRSE.

* Prior to performing reactions on the first cell the subroutine aRSE_IN is called to
transfer the values for all specified FTLOADDS variables in each of the domain cells
to the storage array variable C1_aRSE.

* For each cell in turn the subroutine RUN_aRSE is called, which updates the vector
VARS with the cell-specific values and calls the C++ subroutines PRESOVE,
RKSOLVE and POSTSOLVE to execute aRSE. If it is the first time aRSE is being
called then the subroutine INITIALIZE is called prior to these subroutines. After each
cell has been processed the array variable C1_aRSE is updated with the updated
values in the vector VARS.

* After reactions have been performed on the final cell the subroutine aRSE_OUT is
called to update all appropriate FTLOADDS variables with the new values in the
array variable C1_aRSE.

Section B2

FORTRAN Subroutines for Linkage

The following subroutines were written specifically for the linkage of aRSE and

FTLOADDS. Additional code that was added to existing SWIFT2D subroutines is given

in Section B3.

Module aRSEDIM

MODULE aRSEDIM


This MODULE is used for declaring variables used in the linkage of aRSE
With SWIFT2D within FTLOADDS


IMPLICIT NONE

INTEGER*4 INITIATE, NCALLS, NCELLS, NCELLST, NCOMPS, NCOMPST, NVARS
INTEGER*4 CALLNO, CELLNO, RKORDER, NPAR, NMOB, NSTAB, NSTABMAX, K WET,
ATM NPAR

PARAMETER (NCALLS = 1, NCELLST = 10201, NCOMPST = 60, RKORDER = 4,
NSTABMAX = 15)

INTEGER*1 XMLINPUTC(50), XMLOUTPUTC(50), XMLREAC SETC(50)
INTEGER NPRZ(NSTABMAX)
CHARACTER*120 PREPROCESS, XMLINPUT, XMLOUTPUT, XMLREAC SET,
COMPNAME(NCOMPST)
REAL*8 DTaRSE,DTFTLOADDS


190












'****************************************************************************



REAL*8, DIMENSION (:), PUBLIC, ALLOCATABLE :: ZR(:,:,:),
Cl aRSE(:,:),ZRIC(:,:,:),RIC(:,:,:)
PUBLIC :: SUB
CONTAINS
SUBROUTINE SUB (en,em,el,ze,comps,activecells)
!integer, intent(in) :: en,em,te
INTEGER :: en,em,el,ze,err,comps,activecells
ALLOCATE ( ZR(en,em,ze), stat=err)
ZR=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
ALLOCATE ( Cl aRSE(comps,activecells), stat=err)
Cl aRSE=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
ALLOCATE ( ZRIC(en,em,ze), stat=err)
ZRIC=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
ALLOCATE ( RIC(en,em,el), stat=err)
RIC=0
!IF (err /=0) PRINT *, "SUB allocate NOT successful."
END SUBROUTINE SUB

END MODULE aRSEDIM



Subroutine READIWQ

SUBROUTINE READIWQ
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccc
!C This subroutine read a .IWQ file to extract the data needed to run RSE.
C
!C The data read are:
C
!C A flag (to be used in vfsmod when RSE is used for simulation of
pollutants C
!C 2 XML files (input [eq's included here, and output [to check indexed])
C
!C the reaction set used declaredd in the XML input file
C
!C number, name and data for the mobile variables (used in the reactions)
C
!C number, name and data for the stabile variables (used in the reactions)
C
!C number, name and data for the parameters (used in the reactions)
C
!C Flag for reading 4 intrinsic parameters (depth, x vel, time step, area)
C
!C that can be used in the equations (XML input files)
C
!C Once data are read, values are passed to the hydrodynamic driving program
C
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc











cccc
USE aRSEDIM
USE SWIFTDIM, ONLY: NMAX,MMAX,LMAX,VARZINT

IMPLICIT NONE

INTEGER(kind=4) :: WQFLAG,M
integer(kind=4) :: s,i,j,k,l,n

PREPROCESS='IWQINPUT.iwq' !Moved this from CALLaRSE since moving READIWQ
to being called from SETUP2

!Opens and read input file .iwq for RSE
OPEN (UNIT=50, FILE=PREPROCESS)
READ(50,*) WQFLAG, NMOB, NSTAB, NPAR, K WET, ATM NPAR
IF(NMOB.NE.LMAX)PRINT*, 'NMAX not equal to NMOB'
NVARS=NMOB+NSTAB
NCOMPS=NMOB+NSTAB+27+NPAR

CALL CELLCOUNT
CALL SUB(NMAX,MMAX,NMOB,NSTAB,NCOMPS,NCELLS)
!Read XML input file, XML outout file to check indexes, react set to be used
in XML input file
READ(50,*) XMLINPUT, XMLOUTPUT, XMLREAC SET
!Read mobile variables
READ(50,*) (COMPNAME(i),C1 aRSE(i,1),i=1,NMOB)

!Read stabile variables
READ(50,*) (COMPNAME(j),C1 aRSE(j,l),j=(NMOB+1),(NMOB+NSTAB))
!Read stabile print flags
READ(50,*) (NPRZ(s),s=1,NSTAB) !Equivalent to the NPRR in FTLOADDS,
but for stabile components
! Output file always has user-defined variables first (j), then 27 intrinsic
params + 1
j=NMOB+NSTAB
n=NMOB+NSTAB
k=j+27+1
j=k
!Read parameter to be used (usually declared to be used in the set of
equatiuons)
READ(50,*) (COMPNAME(k),C1 aRSE(k,1),k=j,(j+NPAR-1))
SRead intrincsic values of depth, x vel ol, time step, area if m="l"
READ(50,*)M
IF(M.EQ.1) THEN
READ(50,*) COMPNAME(n+2),C1 aRSE(n+2,1)& !depth
!&,COMPNAME(n+16),C1 aRSE(n+16,1)& !x-vel
&,COMPNAME(n+20),C1 aRSE(n+20,1)& !time
&,COMPNAME(n+1),C1 aRSE(n+1,1) !area
ENDIF
DTaRSE=Cl aRSE(n+20,1) !time step if not in .iwq

CLOSE(50)

IF(VARZINT.NE.99)THEN !Read in STABILE ICs as uniform
DO L=1,NSTAB
DO N=1,NMAX
DO M=1,MMAX


192











ZR(N,M,L)=Cl aRSE(NMOB+L,1)
ENDDO
ENDDO
ENDDO
ENDIF

END



Subroutine CALLaRSE

SUBROUTINE CALLaRSE
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccc
!C This program emulates a hydrodynamic calling program for using the
Reaction C
!C Simulaiton Engine (RSE). The code structure of this program can be adapted
C
!C to other hydrodynamic calling programs.
C
!C This program reads a text file (.iwq) with the data needed to used
C
!C RSE. This .iwq file contains the name of the XML input file, the name of
C
!C the XML output file to check the indexes used, the name of the reaction
set C
!C to be used (declared in the XML input file), the numberss, name(s) and
C
!C values) for the mobile, stabile and parameters used in the equation(s)
C
!C declared in the XML input file.
C
!C Once data is read, call MyReactionModTest subroutine, which initiate and
C
!C runs RSE.
C
!C RSE is called at each time step. Initiallitation occurs in time step 1
C
!cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccc
USE aRSEDIM
USE SWIFTDIM, ONLY: HALFDT,aRSE,CaRSE,NMAX,MMAX

IMPLICIT NONE

INTEGER(KIND=4) :: i,j,p,r,HALFSTEP
DATA HALFSTEP/O/

IF(INITIATE.EQ.0)THEN
CALL FORT CSTRING(XMLINPUT, XMLINPUTC)
CALL FORT CSTRING(XMLOUTPUT, XMLOUTPUTC)
CALL FORT CSTRING(XMLREAC SET,XMLREAC SETC)
!IF (VARZINT.EQ.99) CALL READIC
DO r=1,NCELLS
DO p=1,NCOMPS
Cl aRSE(p,r)=Cl aRSE(p,l)


193











ENDDO
ENDDO
INITIATE=1
ENDIF

DO 100 CALLNO=1,NCALLS
IF(aRSE.EQ.2) THEN
HALFSTEP=HALFSTEP+1
ELSEIF(aRSE.EQ.1) THEN
HALFSTEP=HALFSTEP+2 !Initiated to zero, so +2 means always even,
so always uses R
ELSEIF(aRSE.EQ.3) THEN
HALFSTEP=1
ELSE
PRINT*, 'aRSE is neither 1, 2 or 3'
PAUSE
ENDIF

Time step used by the controlling program
IF (DTaRSE.GT.0) THEN
DTFTLOADDS=DTaRSE
ELSEIF (aRSE.EQ.1) THEN
!time step in RUNaRSE is DTFTLOADDS*60. If aRSE=0 then no aRSE called so the
/aRSE should
!not be a problem and acts as a check; if aRSE=1 then CaRSE is used to
specify how many full
!time-steps (HALFDT*2) to wait.
DTFTLOADDS=CaRSE*HALFDT*2
ELSEIF (aRSE.EQ.2) THEN
DTFTLOADDS=HALFDT*2/aRSE
ELSEIF (aRSE.EQ.3) THEN !use TRT split-operator
DTFTLOADDS=HALFDT*2
ENDIF

DO 10 CELLNO=1,NCELLS
IF(CELLNO.EQ.1) THEN
CALL aRSE IN(HALFSTEP) !Halfstep needed to determine R or RP
ENDIF

CALL RUNaRSE

IF(CELLNO.EQ.NCELLS) THEN
CALL aRSE OUT(HALFSTEP) !Halfstep needed to determine R or
RP
ENDIF

10 CONTINUE
100 CONTINUE

101 FORMAT(500F8.4)

END


194












Subroutine aRSEIN


SUBROUTINE aRSE IN(HALFSTEPIN)

'********************************************************************
This subroutine moves the necessary values into Cl aRSE for RSE
'********************************************************************


USE SWIFTDIM, ONLY:
IROCOL,NOROWS,MSTART,MEND,SEP,SEMIN,U,UP,V,VP,RP,R,LMAX,ICLSTAT,ATMDEP
USE aRSEDIM

IMPLICIT NONE

INTEGER CELLNUMI, NUMCELLSIRK, CELLNUM, IRK aRSE, HALFSTEPIN
INTEGER M,N,L,S
REAL DEPTHMIN
DATA DEPTHMIN/0.05/


CELLNUMI=0


IF(LMAX.NE.NMOB) THEN
PRINT*,'LMAX (SWIFT2D) not equal to NMOB (aRSE)'
PAUSE
ENDIF
*********************************************************************
!Read in mobile/transported variables from R (u-step) or RP (v-step)
'*********************************************************************
IF(HALFSTEPIN/2*2.EQ.HALFSTEPIN) THEN !Even = v-step, which uses RP to
create R in DIFV, so use R
DO IRK aRSE=1,NOROWS
N=IROCOL(1,IRK aRSE)
START = IROCOL(2,IRK aRSE)
MEND = IROCOL(3,IRK aRSE)
DO M=MSTART,MEND
CELLNUMI=CELLNUMI+1
!Mobile inputs
DO L=1,LMAX
C1 aRSE(L,CELLNUMI)=R(N,M,L)
ENDDO
!Stabile inputs
IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
IF((S.EQ.NSTAB).AND. (K WET.EQ.1)) THEN
IF(ICLSTAT(N,M).EQ.0) THEN
!Cell is wet: K wet=l
C1 aRSE(LMAX+S,CELLNUMI)=1
ELSEIF(ICLSTAT(N,M).NE.0) THEN
!Cell is dry: K wet=0
C1 aRSE(LMAX+S,CELLNUMI)=0
ENDIF
ELSE
C1 aRSE(LMAX+S,CELLNUMI)=ZR(N,M,S)
ENDIF


195











ENDDO
ENDIF
!Hydro inputs
IF(ICLSTAT(N,M).NE.0) THEN
Cl aRSE(NVARS+2,CELLNUMI)=DEPTHMIN
ELSE
Cl aRSE(NVARS+2,CELLNUMI)=(SEP(N,M)-SEMIN(N,M)) !depth
ENDIF


IF(ATM NPAR.GT.O)
Cl aRSE(NVARS+27+ATM NPAR,CELLNUMI)=ATMDEP(2)
!Cl aRSE(NVARS+14,CELLNUMI)=U(N,M)
after u-step, not changed in v-step
!Cl aRSE(NVARS+16,CELLNUMI)=VP(N,M)
SEPV earlier in v-step
ENDDO
ENDDO
ELSE !Odd = u-step, which uses R to create RP
DO IRK aRSE=1,NOROWS
N=IROCOL(1,IRK aRSE)
START = IROCOL(2,IRK aRSE)
MEND = IROCOL(3,IRK aRSE)
DO M=MSTART,MEND
CELLNUMI=CELLNUMI+1
!Conc inputs
DO L=1,LMAX
Cl aRSE(L,CELLNUMI)=RP(N,M,L)
ENDDO
!Stab inputs
IF(NSTAB.GT.0)THEN


Cl aRSE(NVARS+2


!u-vel moved from UP to U

!V-vel updated to VP in




(in DIFU) so use RP


DO S=1,NSTAB
IF((S.EQ.NSTAB).AND. (K WET.EQ.1)) THEN
IF(ICLSTAT(N,M).EQ.0) THEN
Cl aRSE(LMAX+S,CELLNUMI)=1
ELSEIF(ICLSTAT(N,M).NE.0) THEN
Cl aRSE(LMAX+S,CELLNUMI)=0
ENDIF
ELSE
Cl aRSE(LMAX+S,CELLNUMI)=ZR(N,M,S)
ENDIF
ENDDO
ENDIF
!Hydro inputs
IF(ICLSTAT(N,M).NE.0) THEN
Cl aRSE(NVARS+2,CELLNUMI)=DEPTHMIN
ELSE
Cl aRSE(NVARS+2,CELLNUMI)=(SEP(N,M)-SEMIN(N,M)) !depth
ENDIF
IF(ATM NPAR.GT.0)
7+ATM NPAR,CELLNUMI)=ATMDEP(2)
!C1 aRSE(NVARS+14,CELLNUMI)=UP(N,M) !u-vel updated to UP in


SEPU earlier in u-step
!Cl aRSE(NVARS+16,CELLNUMI)=V(N,M)
V after previous v-step, not changed in u-step
ENDDO
ENDDO
ENDIF


!v-vel moved from VP to


196












RETURN
END




Subroutine aRSEOUT

SUBROUTINE aRSE OUT(HALFSTEPOUT)


This subroutine: moves the necessary values out of Cl aRSE for FTL
i********************************************************************


USE SWIFTDIM, ONLY: IROCOL,NOROWS,MSTART,MEND,RP,R,LMAX
USE aRSEDIM

IMPLICIT NONE

INTEGER CELLNUMO, NUMCELLSIRK, CELLNUM, IRK aRSE, HALFSTEPOUT
INTEGER M,N,L,S

i********************************************************************


CELLNUMO=0
IF(LMAX.NE.NMOB) THEN
PRINT*,'LMAX (SWIFT2D) not equal to NMOB (aRSE)'
PAUSE
ENDIF


IF(HALFSTEPOUT/2*2.EQ.HALFSTEPOUT) THEN
to create R in DIFV so use R
DO IRK aRSE=1,NOROWS
N=IROCOL(1,IRK aRSE)
START = IROCOL(2,IRK aRSE)
MEND = IROCOL(3,IRK aRSE)
DO M=MSTART,MEND
CELLNUMO=CEllNUMO+1
!Mobile outputs
DO L=1,LMAX
R(N,M,L)=Cl aRSE(L,CELLNUMO)
ENDDO
!Stabile outputs


!even = v-step, which uses RP


IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
ZR(N,M,S)=Cl aRSE(LMAX+S,CELLNUMO) !Use ZR always
because not transported so no ZRP
ENDDO
ENDIF
ENDDO
ENDDO
ELSE !odd = u-step, which uses R to create RP in DIFU so use RP
DO IRK aRSE=1,NOROWS
N=IROCOL(1,IRK aRSE)
START = IROCOL(2,IRK aRSE)
MEND = IROCOL(3,IRK aRSE)
DO M=MSTART,MEND
CELLNUMO=CEllNUMO+1











!Mobile outputs
DO L=1,LMAX
RP(N,M,L)=C1 aRSE(L,CELLNUMO)


ENDDO
!Stab outputs
IF(NSTAB.GT.0)THEN
DO S=1,NSTAB
ZR(N,M,S)=C1
because not transported so no ZRP
ENDDO
ENDIF
ENDDO
ENDDO
ENDIF

RETURN
END


Subroutine RUNaRSE


aRSE(LMAX+S,CELLNUMO) !Use ZR always


SUBROUTINE RUNaRSE

USE IFPORT
USE aRSEDIM

IMPLICIT NONE


Integer(kind=4)
Integer(kind=4)
Integer(kind=4)
Real(kind=8)
Real(kind=8), Dimension(NCOMPST)
CHARACTER (len=120)
CHARACTER (len=120)
CHARACTER (len=120)
integer*l, Dimension (50):: inpu
reaction setlA


a,x
nvals
rk order !Either 2 or 4
time step
:: vars
input filename,input filenamel
output filename, output filenamel
reaction set, reaction setl
t filenamelA, output filenamelA,


!REMEMBER: change Interfaces to syntax suggested by Steve on IVF forum
Interface to Subroutine Initialize ( input xml, output xml, rsname )
!DEC$ Attributes C, DLLIMPORT, alias: Initialize" :: Initialize
integer*l, Dimension (50):: input xml, output xml, rsname !new input
files as arrays of chars instead of strings

Character*(*) input xml 'old string file name
Character*(*) output xml 'old string file name
Character*(*) rsname
!DEC$ Attributes REFERENCE :: input xml
!DEC$ Attributes REFERENCE :: outputxml
!DEC$ Attributes REFERENCE :: rsname
END

Interface to Subroutine PreSolve ( num var, vars
!DEC$ Attributes C, DLLIMPORT, alias: PreSolve" :: PreSolve
Integer(kind=4) :: num var
Real(kind=8), Dimension(num var) :: vars


198











End


Interface to Subroutine PostSolve ( num var, vars )
!DEC$ Attributes C, DLLIMPORT, alias: PostSolve" :: PostSolve
Integer(kind=4) :: num var
Real(kind=8), Dimension(num var) :: vars
End

Interface to Subroutine RKSolve ( time step, rk order, num var, vars
!DEC$ Attributes C, DLLIMPORT, alias: RKSolve" :: RKSolve
Integer(kind=4) :: num var
Integer(kind=4) :: rk order
Real(kind=8) :: time step
Real(kind=8), Dimension(num var) :: vars
End

Interface to Subroutine SetGlobalValues ( num var, vars
!DEC$ Attributes C, DLLIMPORT, alias: SetGlobalValues"
SetGlobalValues
Integer(kind=4) :: num var
Real(kind=8), Dimension(num var) :: vars
End

nvals = NCOMPS
rk order = RKORDER
time step = DTFTLOADDS*60

Name of the input xml file (here, wq input file.xml)
input filenamelA = XMLINPUTC
Name of the component output file, only used to double check the inputs
output filenamelA = XMLOUTPUTC
Name of the reaction set to use set to the same as in the input xml
file
reaction setlA = XMLREAC SETC

MUST initialize the passed in values to 0.0
New values of conc's are stored here @ vars
IF(INITIATE.EQ.1)THEN
DO a = 1, NCOMPS !NCOMPST
vars(a) = 0.0
ENDDO
INITIATE=2
ENDIF

DO a = 1, NCOMPS
vars(a) = C1 aRSE(a,CELLNO)
ENDDO

IF (INITIATE.EQ.2) THEN
CALL Initialize( input filenamelA, output filenamelA, reaction setlA

INITIATE=3
ENDIF

CALL PreSolve(nvals, vars)

CALL RKSolve(time step, rk order, nvals, vars) !why nvals and not


199












num var?

CALL PostSolve(nvals, vars)

SNvals should be replaced with nvarX equivalent because only vars(1) and
vars(2) are changed
DO a = 1, NCOMPS
IF(a.LE.NVARS) THEN
IF(vars(a).LT.0) vars(a)=0.0
ENDIF
Cl aRSE(a,CELLNO) = vars(a)
ENDDO

20 FORMAT (13, 13, E16.4, E16.4)
RETURN
END




Subroutine CELLCOUNT

SUBROUTINE CELLCOUNT

1********************************************************************
This subroutine: counts the number of active cells
1********************************************************************


USE SWIFTDIM
USE aRSEDIM

IMPLICIT NONE

INTEGER NUMCELLS,NCELLSIRK,IRK aRSE,COUNTCELLS,CELLSCOUNTED,COUNTOFF

i********************************************************************


COUNTOFF = 0
IF(COUNTOFF.EQ.1) GOTO 10

DO IRK=1,NOROWS
START = IROCOL(2,IRK)
MEND = IROCOL(3,IRK)
NCELLSIRK = MEND START + 1
NUMCELLS = NUMCELLS + NCELLSIRK
ENDDO
NCELLS=NUMCELLS



10 RETURN
END


200









Section B3


READIWQ Input File

The nature of the XML interface, on which aRSE relies to obtain the names and values
of the model components (i.e. state variables and parameters), is such that aRSE relies
on the numeric order in which each component appears in order to correctly match
name and value. Given that the number of user-defined state variables and parameters
can change, so too then can the numeric reference and it is therefore necessary to run
aRSE once in order to determine what the appropriate position is for the various
components, unique to the given model setup. This is obviously undesirable for
automated calling of aRSE (and is an artifact of the parent version TaRSE) because it
requires that the user execute the model prior to using it.

This input file's purpose is to avoid the necessity for calling aRSE prior to using it, and is
predicated on the fact that the number of intrinsic parameters in the model is constant
(there are 27), that the state variables appear first in the input XML file, and that the
user-defined parameters appears last. The appropriate numeric positions of all
components can therefore be determined by knowing what and how many state
variables there are, and what and how many user-defined parameters there are. This
information is entered in this .IWQ file, read by the model, and used accordingly.

Table B-1. Explanation of the READIWQ input file structure and read in parameters
Line number Variable Explanation
1 WQFLAG Flag for running water-quality module (unused)

NMOB Number of mobile state-variables specified in input XML

NSTAB Number of stabile state-variables specified in input XML

NPAR Number of user-specified parameters specified in input
XML
Flag to exchange wet/dry conditions. If used, this
K_WET parameter must be specified as the final user-input
parameter (see code in aRSE_IN subroutine)


Flag to indicate atmospheric deposition, read in by
FTLOADDS from ATMDEP.dat input file, must be passed
to aRSE. If then not, if> 0 then the input number must
ATMPAR correspond with the position of the parameter in the list of
user-input parameters e.g. ATM_NPAR=2 indicates that
the second nput parameter in the input XML is the
atmospheric deposition rate parameter (the name must
match that used in Line 6 of the .IWQ)


2 XMLINPUT Name of the XML input file
XMLOUPUT Name of the XML output file (not used)


201










Table B-1. Continued
Line number Variable
2 XMLREACSET

3 VARNAME(i); C2(i)



4 VARNAME(j); C2(j)



5 NPRZ(s)



6 VARNAME(k); C2(k)


VARNAME(x); C2(x)


Explanation
Name of the XML reaction set tag
For i=1 to NMOB, each mobile state-variable name must
be given (VARNAME) along with it's corresponding initial
condition (C2)

Forj=NMOB to NMOB+NSTAB, each stabile state-variable
name must be given (VARNAME) along with its
corresponding initial condition (C2)

For s=1 to NSTAB, the printing interval must be given.
Currently not used, but included for anologous control to
that offered by NPRR for constituent printing in SWIFT2D

For k=j+28 to j+28+NPAR, each user-specified parameter
name must be given (VARNAME) along with its
corresponding constant value (C2)

Flag to specify whether intrinsic variables are read directly
in from .IWQ file in Line 8. If MM=1 then values read in
from Line 8

The position (x) of the desired intrinsic variable in the list of
intrinsiic parmaters must be known, and its name
(VARNAME) and value (C2) given if MM is 1


Section B4

Nash-Sutcliffe Calculation for Analytical Testing

The following program and and subroutines were written for the purpose of

calculating spatially-distributed Nash-Sutcliffe efficiencies in the comparison of

analytical and numerical solutions.

Program STUPOSTPROCESS

PROGRAM StuPOSTPROCESS


PROGRAM: StuPOSTPROCESS

PURPOSE: To run stats on FTLOADDSaRSE results using CORSTAT. When
called, the number of measurements in the time-series to be used in the
statistics (TOTALTIN), and the number of cells to be assessed by rows
(NMAXIN) and columns (MMAXIN)


202












USE GLOBAL
IMPLICIT NONE

integer :: err, SURFERVID,TOTALTI,YES

!Read in the number of measurements in the time-series

55 CALL GETARG(1,ARGUMENT1)
READ(ARGUMENT1,'(A6)') SURFERCASE

CALL GETARG(2,ARGUMENT2)
READ(ARGUMENT2,'(15)') TOTALTF

CALL GETARG(3,ARGUMENT3)
READ(ARGUMENT3,'(I5)') NMAX

CALL GETARG(4,ARGUMENT4)
READ(ARGUMENT4,'(I5)') MMAX

CALL GETARG(5,ARGUMENT5)
READ(ARGUMENT5,'(12)') SURFERVID

50 OPEN(300,FILE="C:\Users\Stuart Muller\Documents\Visual Studio
2008\Projects\FTLOADDSaRSE v2.8\FTLOADDS Test Case v3\FTLOADDS\SurferCases.tx
t",&
STATUS='REPLACE')


IF(SURFERVID.EQ.99) THEN
GOTO 100
ELSE
CALL SUB(NMAX,MMAX,TOTALTF)
TOTALT=TOTALTF
GOTO 200
ENDIF

100 DO TOTALT=2,TOTALTF
CALL SUB(NMAX,MMAX,TOTALTF)

200 IF(TOTALT.LT.10) THEN
TOTALTI=1
WRITE(SURFERSTRING1, (I) ') TOTALT
ELSEIF(TOTALT.LT.100) THEN
TOTALTI=2
WRITE(SURFERSTRING2, (I) ') TOTALT
ELSEIF(TOTALT.GE.100) THEN
TOTALTI=3
WRITE(SURFERSTRING3, (I) ') TOTALT
ENDIF


CALL POSTPROCESS

IF(SURFERVID.NE.99) GOTO 300

DEALLOCATE(C1,C2)


203











ENDDO

300 CONTINUE



END PROGRAM StuPOSTPROCESS



Subroutine POSTPROCESS

SUBROUTINE POSTPROCESS

USE GLOBAL
!C***************************************************************************
********
This subroutine combines the prepared results from FTLOADDSaRSE
(LCONR1 AN.txt)
Sand 3DADE (CXTFIT.OUTe) into CORSTAT.TXT for statistical processing

'****************************************************************************
*******'


IMPLICIT NONE

CHARACTER*50 MODELFILE,MODFILE,ANALFILE,ANALYTFILE

INTEGER t,i,j !!,TOTALT,NMAX,MMAX



!Input files must be of the format INTEGER, REAL(OBS), REAL(SIM)
!The integer is the code for a given time series of data (NCOD in CORSTAT),
and increments up when a new series is encountered (this
!is not used currently)

MODELFILE='..\output\LCONR1 AN.txt'
OPEN(100,FILE=MODELFILE,STATUS='OLD')

ANALYTFILE='..\output\CXTFIT.OUTe'
OPEN(101,FILE=ANALYTFILE,STATUS='OLD')

DO t=1,TOTALT
DO j=1,MMAX
DO i=1,NMAX
READ(100,'(F8.4) ',END=1010) Cl(i,j,t) !Read in model
outputs
READ(101,'(F8.4) ',END=1010) C2(i,j,t) !Read in analytical
model outputs
ENDDO
ENDDO
ENDDO
PRINT*, "Reads complete"
!pause
GOTO 1011

1010PRINT*, "Specified time-series exceeds either observed or simulated data
input"


204












1011CONTINUE


1020CONTINUE
DO j=1,MMAX
DO i= 1,NMAX
CALL CORSTAT(i,j,TOTALT)
ENDDO
ENDDO

1008FORMAT(I3,F8.4,1X,F8.4)

PRINT*, 't:',t,'m:',j,'n:',i

END



Subroutine CORSTAT

SUBROUTINE CORSTAT(NN,MM,TOTALI)


!C************************************************************************
!C* WRITTEN FOR: Paper on VFSMOD development and testing (J.of Hyd) *
!C* Last Updated:June 29, 1998. *
!C* CORSTAT, 5/20/87, VER. 0.1, J.E. PARSONS
!C* REVISED: 5/11/93, VER, 0.3, R. MUNOZ-CARPENA *
!C* UPDATED: 06/04/02, VER, 0.7, R. MUNOZ-CARPENA *
!C* e-mail: carpena@ufl.edu

!C* ADAPTED: 2/7/10 S. MULLER (!SJM) for FTLOADDSaRSE *
!C* CREDITS: (c) 1986-92 Numerical Recipes Software iPJ-5.1:#>OK!. *
!C* USES:(c)Numerical recipes: tptest, avevar, betai,gammaln, betacf *
!ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
!C* CORSTAT, 5/20/87, VER. 0.1, J.E. PARSONS *
!C* REVISED: 5/11/93, VER, 0.3, R. MUNOZ-CARPENA *
!C* LAST UPDATED: 29/6/98, VER, 0.5, R. MUNOZ-CARPENA
!C* THIS PROGRAM COMPUTES A NUMBER OF STATISTICS FOR THE *
!C* COMPARISON OF TWO TIME SERIES, FOR EXAMPLE, AN OBSERVED AND A *
!C* SIMULATED ONE. THE STATISTICS ARE: *
!C* 1) MEAN ERROR *
!C* 2) STANDARD DEVIATION *
!C* 3) SERIAL CORRELATION COEF. *
!C* 4) COEFICIENT OF PERFORMANCE *
!C* 5) COEFICIENT OF PERFORMANCE CORRECTED FOR VARIATION OF THE *
!C* OF THE RECORDED PROCESS *
!C* 6) PEARSON MOMENT AND THE WEIGHTED MOMENT *
!C* RMC-7) Correlation coefficient for the 1:1 line *
!C* RMC-8) Paired t-test to check for differences in series means *
!C* (from Numerical Recipes) *
!C* *
!C* These are computed for the absolute value of the error and the *
!C* error. *
!C* These measures are defined and discussed in: *
C* *
!C* 1. Aitken, A.P. 1973. Assesing systematic errors in rainfall-runoff *


205











!C* models. J. of Hydrology. 20:121-136. *
!C* 2. James, L.D. and S.J. Burges. 1982. Selection, calibration, and *
!C* testing of hydrologic models by. In Hydrologic Modeling of Small *
!C* Watersheds, Chapter 11, ed. C. T. Haan, H. P. Johnson and D. L. *
!C* Brakensiek. pages 435-472. ASAE monograph no. 5. St. Joseph. *
!C* 3. McCuen, R.H. and W.M. Snyder. 1975. A proposed index for *
!C* comparing hydrographs. Water Resour. Res. (AGU).11(6):1021-1024. *
!C* 4. Press et al., 1992. Numerical Recipes in Fortran. 2nd, edition. *
!C* Cambridge: Cambridge University Press *
C* *
!C* Definition of variables *
!C************************************************************************
USE GLOBAL, ONLY:
Cl,C2,SURFERSTRING1,SURFERSTRING2,SURFERSTRING3,TOTALT,SURFERCASE

IMPLICIT DOUBLE PRECISION (A-H,O-Z)
character*16 dummyfl
CHARACTER*6 VARBLE
CHARACTER*50 FLABEL
PARAMETER(NPTS=500)
REAL probl,tl,datal(NPTS),data2(NPTS)
DIMENSION NCOD(5000),OBS(5000),SIM(5000),AERR(5000),&
ERR(5000),NCD(101),NTC(101),SUM(4),SUMSQ(4),CSS(4),DAERR(1000),&
DREC(1000),VAR(4)

INTEGER MM,NN,TOTALI,FILELABELS,ALLOCATEARRAY
DATA FILELABELS/O/
DATA ALLOCATEARRAY/0/


OPEN (UNIT=10,FILE='NUL')

IDIAG=0
I=l
INC=0
KC=0
NC=0
mycount=0
!SJM: Removing FLABEL read because CORSTATIN.txt not being written with
headers
!READ(8,*)FLABEL
!10 READ(8,*,END=20)NCOD(I),OBS(I),SIM(I)

!SJM: Instead of a READ now transferring data between arrays. Note, still
jumps to 20
!when OBS and SIM are filled
DO I=1,TOTALI
NCOD(I)=1
!!OBS(I)=OBSC1(NN,MM,I)
OBS(I)=C1(NN,MM,I)
!!SIM(I)=SIMC2(NN,MM,I)
SIM(I)=C2(NN,MM,I)
!c-- Debug -
!c print*,ncod(i),obs(i),sim(i)
!c-- End Debug ----
ERR(I)=SIM(I)-OBS(I)
AERR(I)=DABS(ERR(I))


206











!C*** COUNT THE DIFFERENT CODES
IF (NC.EQ.NCOD(I)) THEN
INC=INC+1
NTC(KC)=INC
ELSE
KC=KC+1
NC=NCOD(I)
NCD(KC)=NC
INC=1
ENDIF
!SJM: Deleted because DO loop automatically updates I
I=I+1
ENDDO
20 CONTINUE
!C** ZERO OUT THE STATISTICS ARRAYS
NOBS=I
IST=1
DO 25 K=1,KC
DO 24 J=1,4
SUM(J)=0.DO
SUMSQ(J)=0.DO
24 CONTINUE
CROSS=0.DO
cosse=0.dO
NOBK=NTC(K)+IST-1 !!!!!!!!!!!!!GRRR
KOUNT=O
DO 30 I=IST,NOBK
KOUNT=KOUNT+1
DAERR(KOUNT) =AERR(I)
DREC(KOUNT)=OBS(I)
SUM(1)=SUM(1)+ERR(I)
SUM(2)=SUM(2)+AERR(I)
SUM(3)=SUM(3)+OBS(I)
SUM(4)=SUM(4)+SIM(I)
SUMSQ(1)=SUMSQ(1)+ERR(I)*ERR(I)
SUMSQ(2)=SUMSQ(2)+AERR(I)*AERR(I)
SUMSQ(3)=SUMSQ(3)+OBS(I)*OBS(I)
SUMSQ(4)=SUMSQ(4)+SIM(I)*SIM(I)
CROSS=CROSS+OBS(I)*SIM(I)
cosse=cosse+(obs(i)-sim(i))*(obs(i)-sim(i))
datal(KOUNT)=OBS(I)
data2(KOUNT)=SIM(I)
30 CONTINUE
mycount=mycount+1
XPOINT=DFLOAT(NTC(K))
ERMEAN=SUM(1)/XPOINT
AEMEAN=SUM(2)/XPOINT
OBMEAN=SUM(3)/XPOINT
SIMEAN=SUM(4)/XPOINT
!C*** DO RESIDUAL MASS CURVES FOR ACCUMULATED ERRORS
CPAT=0
CPBT=0
CPCT=0
SECOR=0.DO
SAECOR=0.DO
DO 37 I=IST,NOBK
IF (I.GT.IST) THEN


207











SECOR=SECOR+(ERR(I)-ERMEAN)*(ERR(I-1) -ERMEAN)
SAECOR=SAECOR+(AERR(I)-AEMEAN)*(AERR(I-1)-AEMEAN)
ENDIF
ERS=0.DO
ERD=0.DO
ERD2=0.DO
DO 36 II=IST,I
ERS=ERS+ERR(II)
ERD=ERD+OBS(II)
ERD2=ERD2+(OBS(II)-OBMEAN)
36 CONTINUE
XJP=DFLOAT(I-IST+1)
XJP2=XJP*XJP
CPAT=CPAT+ERS*ERS/XJP2
CPBT=CPBT+(ERS/ERD)*(ERS/ERD)/XJP2
!c CPCT=CPCT+(ERS/ERD2)*(ERS/ERD2)/XJP2
37 CONTINUE
!C CPAT=CPAT/XPOINT
!C CPBT=CPBT/XPOINT
!C CPCT=CPCT/XPOINT
IST=NOBK+1
IF (IDIAG.EQ.1) THEN
WRITE(10,90)XPOINT,K,NCD(K)
90 FORMAT(/,/,/,10X,'***** DIAGNOSTICS PRIOR TO CALCULATIONS FOR:',&
/,20X,'NPOINTS=',I6,' SERIES NO.=',I4,' SERIES CODE=',I5,&
/,10X,'SUM OF DATA',10X,'SUM OF SQUARES')
DO 91 KK=1,4
WRITE(10,89)SUM(KK),SUMSQ(KK)
89 FORMAT(5X,F15.5,9X,F15.5)
91 CONTINUE
WRITE(10,88)CROSS
88 FORMAT(/,10X,'CROSS PRODUCT SUM (REC*SIM)=',F15.5,/,/)
ENDIF
CSS(1)=SUMSQ(1)-2*ERMEAN*SUM(1)+XPOINT*ERMEAN*ERMEAN
CSS(2)=SUMSQ(2)-2*AEMEAN*SUM(2)+XPOINT*AEMEAN*AEMEAN
CSS(3)=SUMSQ(3)-2*OBMEAN*SUM(3)+XPOINT*OBMEAN*OBMEAN
CSS(4)=SUMSQ(4)-2*SIMEAN*SUM(4)+XPOINT*SIMEAN*SIMEAN
VAR(1)=CSS(1)/XPOINT
VAR(2)=CSS(2)/XPOINT
VAR(3)=CSS(3)/XPOINT
VAR(4)=CSS(4)/XPOINT
XP1=(XPOINT-1.DO)
SEM=CSS(1)/(XP1)
AEM=SUM(2)/XPOINT
!c RMSE=DSQRT(CSS(1)/XPOINT)
!c----change based on Marion's comments (07/06/93)----------
RMSE=DSQRT(SUMSQ(1)/XPOINT)
ERSTD=DSQRT(CSS(1)/(XP1))
AESTD=DSQRT(CSS(2)/(XP1))
OBSTD=DSQRT(CSS(3)/(XP1))
SISTD=DSQRT(CSS(4)/(XP1))
SECOR=SECOR/(ERSTD*ERSTD*(XP1))
SAECOR=SAECOR/(AESTD*AESTD*(XP1))
!c -rmc-06/02---
!c RPEARM=(CROSS-OBMEAN*SUM(4)-SIMEAN*SUM(3)
!c + XPOINT*OBMEAN*SIMEAN)/(OBSTD*SISTD*XPOINT)
RPEARM=(XPOINT*CROSS-SUM(4)*SUM(3))/SQRT((XPOINT*SUMSQ(3)-SUM(3)*&


208











SUM(3))*(XPOINT*SUMSQ(4)-SUM(4)*SUM(4)))
R2PEAR=RPEARM*RPEARM
W=SISTD/OBSTD
IF (W.GT.1.DO) THEN
WGHTRP=RPEARM/W
ELSE
WGHTRP=RPEARM*W
ENDIF
CPAP=1.DO-SUMSQ(1)/CSS(3)
SLPNI=CROSS/SUMSQ(3)
SLPI=(CROSS-SUM(3)*SUM(4)/XPOINT)/(SUMSQ(3)-SUM(3)*SUM(3)/XPOINT)
YINT=SIMEAN-SLPI*OBMEAN
CORI=SLPI*OBSTD/SISTD
!C*** EJS --- R-SQUARED TO MATCH SAS
SSINT=SUM(4)*SUM(4)/XPOINT
EJDEN1=SUMSQ(3)-SUM(3)*SUM(3)/XPOINT
EJDEN2=SUMSQ(4)-SUM(4)*SUM(4)/XPOINT
EJSNUM=(CROSS-SUM(3)*SUM(4)/XPOINT)
SSB1BO=SLPI*EJSNUM
RESID=SUMSQ(4)-SSINT-SSB1BO
EMSRES=RESID/(XPOINT-2.DO)
STESLP=DSQRT(EMSRES/EJDEN1)
STEINT=DSQRT(EMSRES*SUMSQ(3)/(XPOINT*EJDEN1))
!C*** COMPUTATIONS FOR NO INT ?
SSB1=SLPNI*EJSNUM
RESNI=SUMSQ(4)-SSB1
EMSRNI=RESNI/(XPOINT-1.DO)
SESLPN=DSQRT(EMSRNI/EJDEN1)
CD=SSB1/EJDEN2
CALL GMEDN(KOUNT,DAERR,DREC,OBMEAN,R29)
R21TOP=SUMSQ(3)-2.DO*CROSS+SUMSQ(4)
R21=1.DO R21TOP/CSS(3)
R22TOP=SUMSQ(4)-2.DO*SUM(4)*OBMEAN+ XPOINT*OBMEAN*OBMEAN
R22=R22TOP/CSS(3)
R23=CSS(4)/CSS(3)
R24=1.DO CSS(1)/CSS(3)
R27=1.DO R21TOP/SUMSQ(3)
!c print*,obstd,covaryyc
R28=SUMSQ(4)/SUMSQ(3)

WRITE(10,100)NCD(K),XPOINT
100 FORMAT(/,10X,&
'SUMMARY STATISTICS FOR COMPARING TWO SERIES OF OBSERVED vs.',&
PREDICTED VALUES',/,10X,'SERIES CODE =',I4,10X,&
'NUMBER OF SERIES POINTS=',F6.0,/)
WRITE(10,*)' VARIABLE SUM MEAN SUMSQ&
CORR. SS SAMP.STD. VARIANCE COEF. OF VAR.'
WRITE(10, *)
VARBLE= 'ERROR'
CV=ERSTD/ERMEAN
WRITE(10,102)VARBLE,SUM(1),ERMEAN,SUMSQ(1),CSS(1),ERSTD,VAR(1),CV
VARBLE= 'AERROR'
CV=AESTD/AEMEAN
WRITE(10,102)VARBLE,SUM(2),AEMEAN,SUMSQ(2),CSS(2),AESTD,VAR(2),CV
VARBLE= 'OBSED'
CV=OBSTD/OBMEAN
WRITE(10,102)VARBLE,SUM(3),OBMEAN,SUMSQ(3),CSS(3),OBSTD,VAR(3),CV


209











VARBLE= 'SIMED'
CV=SISTD/SIMEAN
WRITE(10,102)VARBLE,SUM(4),SIMEAN,SUMSQ(4),CSS(4),SISTD,VAR(4),CV
!c 102 FORMAT(5X,A6,5X,E12.3,5X,ell.4,5X,el5.4,5X,ell.4,5X,elO.5,
!c 5X,el0.5,5X,ell.4)
102 FORMAT(5X,A6,E14.4,el4.4,el4.4,el4.4,el4.4,el4.4,el4.4)
WRITE(10,103)RPEARM,WGHTRP,R2PEAR,R21,R22,R23,R24,R27,R28,R29
WRITE(10,105)RMSE,AEM,SEM
103 FORMAT(/,/,5X,'***** CORREL. COMPARISONS ******',&
/,15X,'PEARSON MOMENT =',F10.5,' (FIRST TWO CORREL. TYPES)',&
/,15X,'WGHTED PEAR. MOM. =',F10.5,' (EQN 11.13)',&
/,15X,'PEAR. MOM. SQUAR. =',F10.5,' (KVALSETH R25, R26 MULT. R)',&
(NOTE: FROM HERE DOWN R-SQUARED TYPES)',&
/,15X,'KVALSETH R21 =',F10.5,' (0<=R21<=1, GENERALLY)',&
(1 RATIO OF SUM (OBS-SIM)**2/ CSS-OBS)',&
/,15X,'KVALSETH R22 =',F10.5,' (MAY EXCEED 1)',&
( RATIO OF SUM (SIM-OBMEAN)**2/ CSS-OBS)',&
/,15X,'KVALSETH R23 =',F10.5,' (MAY EXCEED 1)',&
( RATIO OF CSS-SIM/ CSS-OBS)',&
/,15X,'KVALSETH R24 =',F10.5,' (0<=R24<=1, GENERALLY)',&
(1 RATIO OF CSS-ERR/ CSS-OBS)',&
/,15X,'KVALSETH R27 =',F10.5,' (RECOMMEND LINEAR NOINT.)',&
(1 RATIO OF SUM ERR**2/ SUM OBS**2)',&
/,15X,'KVALSETH R28 =',F10.5,' (RECOMMEND LIN. NOINT.)',&
( R28 MAY EXCEED 1, RATIO OF SUM SIM**2/ SUM OBS**2)',&
/,15X,'KVALSETH R29 =',F10.5,' (RESISTANT OR ROBUST FIT)')
105 FORMAT(15X,'ROOT MEAN SQ. ERR.=',E14.5,' [(OBS-SIM)**2/N)**.5]',&
/,15X,'MEAN ABS. ERROR =',E14.5,&
/,15X,'MEAN SQ. ERROR =',E14.5,' (ASS. ONE MODEL PARAMETER)',&
[(OBS-SIM)**2/(N-1)]')
WRITE(10,104)CPAP,SECOR,SAECOR
104 FORMAT(15X,'COEF. OF EFF. (NASH AND SUTCLIFF) =',F15.5,&
(RATIO SS-ERR/ CSS-OBS)',/,&
15X,'SERIAL CORR. (ERROR) =',F10.5,5X,'LAG 1',&
/,15X,'SERIAL CORR. (ABS. ERROR)=',F10.5,5X,'LAG 1')


!SJM: Write results for graphing in Surfer
!@!IF(SURFERVID.EQ.99) THEN !Calculating stats at multiple time to
make a video
IF(TOTALT.LT.10) THEN

OPEN(1100+TOTALT,FILE='Surfer'//SURFERCASE//' T'//SURFERSTRING1//'.dat')
ELSEIF(TOTALT.LT.100) THEN

OPEN(1100+TOTALT,FILE='Surfer'//SURFERCASE//' T'//SURFERSTRING2//'.dat')
ELSEIF(TOTALT.GE.100) THEN

OPEN(1100+TOTALT,FILE='Surfer'//SURFERCASE//' T'//SURFERSTRING3//'.dat')
ENDIF

!Print one line of headers
IF(FILELABELS.EQ.0) THEN
WRITE(1100+TOTALT,'(2A5,4A12)') "X", "Y", "RMSE", "AEM",
"SEM", "CPAP(N-S)"
FILELABELS=1
ENDIF


210












IF(CPAP.NE.CPAP) CPAP=10
WRITE(1100+TOTALT,'(215,4F12.8)') MM,NN,RMSE,AEM,SEM,CPAP
IF(CPAP.NE.CPAP) CPAP=10
WRITE(1100,' (215,4F10.4) ') MM,NN,RMSE,AEM,SEM,CPAP

WRITE(10,106) CPAT,CPBT
!c ,CPCT
106 FORMAT(/,/,5X,'****** RESIDUAL MASS CURVES (ACCUMULATED ERRORS)',&
DIVIDED BY POINTS, SIMILAR TO A VARIANCE',&
/,15X,'CPAT -- EQN 11.31 =',G13.6,&
/,15X,'CPBT -- EQN 11.32 =',G13.6,/)
!c /,15X,'CPCT -- EQN 11.33 =',G13.6,/)
CORI2=CORI*CORI
WRITE(10,109)SLPNI,CD,SESLPN,SLPI,YINT,CORI,CORI2,STESLP,STEINT
109 FORMAT(/,/,5X,'****** REGRESSION ANALYSIS SIM VS OBS *******',&
/,10X,'NO-INTERCEPT MODEL, SLOPE =',F10.5,' JPR-RSQ?=',F10.5,&
JPSTD. ERR. SLP.?=',F10.5,&
/,10X,'INTERCEPT MODEL, SLOPE =',F10.5,' INTERCEPT=',F10.5,&
CORRELATION COEF.=',F8.5,' CORR**2=',F8.5,&
/,25X,'STD. ERR. SLOPE =',F10.5,' STD. ERR. INT. =',F10.5)

!c--rmc----04/93---Error over the 1:1 line, observed vs. predicted --------
WRITE(10,*)
WRITE(10,*)
WRITE(10,*)' ****** ERROR MEASURE FROM THE 1:1 LINE ********'

!c --rmc and arr 06/02--- R2= 1-RSSmodel/RSSnull model, where RSS=res. sum
sq.
!c -- null model= line y=cte=ymean=obs mean; model = 1:1 line = y=x ->
pred=obs
!c -- old-- covaryyc=dsqrt(cosse/(xpoint-2.d0))

covaryyc=dsqrt(cosse/(xpoint-l.dO))
rsqltol=(l.d0-(covaryyc*covaryyc)/(obstd*obstd))
if(rsqltol.lt.0)rsqltol=0
rltol=dsqrt(rsqltol)
if(rsqltol.gt.0) then
WRITE(10,113)covaryyc, rtol,rsqltol
else
WRITE(10,114)covaryyc
endif
113 format(10x,'1:1 COVARIANCE OBSERVED vs. PREDICTED = ',E14.4,&
/,10X,'1:1 SAMPLE COEFFICIENT OF DETERMINATION (R1:l) = ',fl0.4,&
/,10x,'1:1 SAMPLE CORRELATION COEFFICIENT (RSQ1:1) = ',f10.4)
114 format(10x,'1:1 COVARIANCE OBSERVED vs. PREDICTED = ',E14.4,&
/,10X,'1:1 SAMPLE COEFFICIENT OF DETERMINATION (R1:l) < 0.01',&
/,10x,'1:1 SAMPLE CORRELATION COEFFICIENT (RSQ1:1) < 0.01')

!C--------------------------------------------------------------------
!c--rmc----06/98---Paired t-test ---------
WRITE(10,*)
WRITE(10,*)
WRITE(10,*)' ****** PAIRED t-TEST ********'
call tptest(datal,data2,KOUNT,tl,probl)
if(probl.ge..05) then
WRITE(10,120)NCD(K),KOUNT,tl,probl


211











else
WRITE(10,121)NCD(K),KOUNT,tl,probl
endif
tl=0.
probl=0.
120 format(10x,'No. Series= ',i4,'; n= ',i4,'; t= ',f10.6,&
'; Prob= ',f10.4,' Means not significantly different')
121 format(10x,'No. Series= ',i4,'; n= ',i4,'; t= ',f10.6,&
'; Prob= ',f10.4,' Means significantly different')

WRITE (10,111)
111 FORMAT(/,125('-'))
WRITE (10,112)
112 FORMAT('1')
25 CONTINUE
CLOSE (8)
RETURN
END

SUBROUTINE GMEDN(N,ER,REC,RECM,R29)
!C**** COMPUTATION OF MEDIANS FOR R29 FROM KVALSETH
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION ER(*),REC(*),TER(1000),DREC(1000)
DO 5 I=1,N
TER(I)=ER(I)
DREC(I)=DABS(REC(I)-RECM)
5 CONTINUE
DO 10 I=1,N
DO 9 J=I+1,N
IF (TER(J).LT.TER(I)) THEN
TEM=TER(I)
TER(I)=TER(J)
TER(J)=TEM
ENDIF
IF (DREC(J).LT.DREC(I)) THEN
TEM=DREC(I)
DREC(I)=DREC(J)
DREC(J)=TEM
ENDIF
9 CONTINUE
10 CONTINUE
IMED=N/2
DRM=DREC(IMED)
ERM=TER(IMED)
RAT=ERM/DRM
R29=1.DO-RAT*RAT
RETURN
END

SUBROUTINE tptest(datal,data2,n,t,prob)
INTEGER n
REAL prob,t,datal(n),data2(n)
!CU USES avevar,betai
INTEGER j
REAL avel,ave2,cov,df,sd,varl,var2,betai
!c--rmc-
!c write(*,*)n,t,prob


212











!c do 5 i=l,n
!c WRITE(*,*)datal(i),data2(i)
!c5 continue
!c--rmc-
call avevar(datal,n,avel,varl)
call avevar(data2,n,ave2,var2)
cov=0.
do 11 j=l,n
cov=cov+(datal(j)-avel)*(data2(j)-ave2)
11 continue
df=n-1
cov=cov/df
sd=sqrt((varl+var2-2.*cov)/n)
t=(avel-ave2)/sd
prob=betai(0.5*df,0.5,df/(df+t**2))
return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>OK!.
SUBROUTINE avevar(data,n,ave,var)
INTEGER n
REAL ave,var,data(n)
INTEGER j
REAL s,ep
ave=0.0
do 11 j=l,n
ave=ave+data(j)
11 continue
ave=ave/n
var=0.0
ep=0.0
do 12 j=l,n
s=data(j)-ave
ep=ep+s
var=var+s*s
12 continue
var=(var-ep**2/n)/(n-1)
return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>0K!.
FUNCTION betacf(a,b,x)
INTEGER MAXIT
REAL betacf,a,b,x,EPS,FPMIN
PARAMETER (MAXIT=100,EPS=3.e-7,FPMIN=1.e-30)
INTEGER m,m2
REAL aa,c,d,del,h,qab,qam,qap
qab=a+b
qap=a+l.
qam=a-1.
c=l.
d=l.-qab*x/qap
if(abs(d).lt.FPMIN)d=FPMIN
d=l./d
h=d
do 11 m=1,MAXIT
m2=2*m
aa=m*(b-m)*x/((qam+m2)*(a+m2))
d=l.+aa*d


213











if(abs(d) .t.FPMIN)d=FPMIN
c=l.+aa/c
if(abs(c) .lt.FPMIN)c=FPMIN
d=l./d
h=h*d*c
aa=-(a+m)*(qab+m)*x/((a+m2)*(qap+m2))
d=l.+aa*d
if(abs(d) .t.FPMIN)d=FPMIN
c=l.+aa/c
if(abs(c) .lt.FPMIN)c=FPMIN
d=l./d
del=d*c
h=h*del
if(abs(del-l.).lt.EPS)goto 1
11 continue

1 betacf=h
return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>OK!.
FUNCTION betai(a,b,x)
REAL betai,a,b,x
!CU USES betacf,gammln
REAL bt,betacf,gammln
if(x.lt.0..or.x.gt.1.)pause 'bad argument x in betai'
if(x.eq.0..or.x.eq.l.)then
bt=0.
else
bt=exp(gammln(a+b)-gammln(a)-gammln(b)+a*log(x)+b*log(1.-x))
endif
if(x.lt. (a+1.)/(a+b+2.))then
betai=bt*betacf(a,b,x)/a
return
else
betai=l.-bt*betacf(b,a,1.-x)/b
return
endif
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>OK!.
FUNCTION gammln(xx)
REAL gammln,xx
INTEGER j
DOUBLE PRECISION ser,stp,tmp,x,y,cof(6)
SAVE cof,stp
DATA cof,stp/76.18009172947146d0,-86.50532032941677d0,&
24.01409824083091d0,-1.231739572450155d0,.1208650973866179d-2,&
-.5395239384953d-5,2.5066282746310005d0/
x=xx
y=x
tmp=x+5.5d0
tmp=(x+0.5d0)*log(tmp)-tmp
ser=1.000000000190015d0
do 11 j=1,6
y=y+l.d0
ser=ser+cof(j)/y
11 continue
gammln=tmp+log(stp*ser/x)


214











return
END
!C (C) Copr. 1986-92 Numerical Recipes Software iPJ-5.1:#>OK!.


215











APPENDIX C
WATER-QUALITY APPLICATION CODE AND INPUT FILES

Section C1

Additional Subroutines for Water-Quality Inputs

The following two subroutines were required for input of water-quality boundary

conditions. The subroutine EDIT INPUTFILE is used to edit time-series concentrations

at specified head boundaries in the Part 3 of the SWIFT2D input file. The subroutine

STRUNCTCONCS reads in discharge source concentrations from the

INPUTFLOWCONCS.dat input file (see Section C2).




Subroutine EDIT INPUTFILE

PROGRAM Edit inputfile

IMPLICIT NONE
INTEGER X,COUNT1,COUNT2,i,j,NTCT1,LENGTH,DAY,DAYCHK,P3 READ,DAYMAX
REAL TITI
CHARACTER THE REST*60,TEMP*1050,THE REST 19*19
CHARACTER*7 BC1(500),BC2(500),BC3(500),BC4(500)
DATA X,COUNT1,COUNT2,P3 READ,DAYMAX/O,0,0,0,0/

OPEN(10,FILE='wetlands PBC SICS.inp') !original .inp
OPEN(20,FILE='wetlands.inp') !.inp produced by this code
OPEN(30,FILE='BC concs.inp') !source for BC concs

j=0
DO WHILE (X.EQ.0)
j=j+l
READ(30,*,END=100) DAYCHK,BC1(j),BC2(j),BC3(j),BC4(j)
WRITE(40, (I4,,A8,X,A8,XA8X,A8,1X,A8,1X)')
DAYCHK,BC1(j),BC2(j),BC3(j),BC4(j)
ENDDO

100 CONTINUE

'******************************'
Write PART 1 and PART 2 data
'******************************'
DO i=1,1158 !1133 !Look at the .inp file to see what the row number is up
to Part 3 data
IF(i.GE.806.AND.i.LE.903) THEN
READ(10, (A1050) ') TEMP
ELSE
READ(10,'(A100)') TEMP


216











ENDIF
LENGTH=LEN TRIM(TEMP)
WRITE(20, (A) ') TEMP
ENDDO
PAUSE
!READ(10,'(A100)') TEMP
!PRINT*, TEMP
!PAUSE


DO WHILE (X.EQ.O)
READ(10,' (I1,A39)') NTCT1,THE REST
LENGTH=LEN TRIM(THE REST)
IF(NTCT1.EQ.0) P3 READ=P3 READ+1
DAY=P3 READ/96+1
IF(DAY.GE.499) DAYMAX=1 !498 days of BC input data after day 498
completed then just copy and repeat remaining lines.
IF(DAYMAX.EQ.1) GOTO 110
IF(NTCT1.EQ.0) THEN
WRITE(20,'(I1,A)') NTCT1,THE REST
ELSEIF(NTCT1.EQ.1) THEN
THE REST 19=THE REST
COUNT1=COUNT1+1
IF(COUNT1.LE.4) THEN
IF(COUNT1.EQ.1) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE REST 19,BC1(DAY)
IF(COUNT1.EQ.2) WRITE(20,' (I1,A19,1X,A7)')
NTCT1,THE REST 19,BC2(DAY)
IF(COUNT1.EQ.3) WRITE(20,' (I1,A19,1X,A7)')
NTCT1,THE REST 19,BC3(DAY)


IF(COUNT1.EQ.4) WRITE(20,'(I1,A19,1X,A7)')
NTCT1,THE REST 19,BC4(DAY)
ELSEIF(COUNT1.LE.8) THEN
WRITE(20,' (I1A1,A9,A8)') NTCT1,THE REST,'
IF(COUNT1.EQ.8)COUNT1=0
ENDIF
ELSEIF(NTCT1.EQ.2) THEN
THE REST 19=THE REST
COUNT2=COUNT2+1
IF(COUNT2.LE.4) THEN
IF(COUNT2.EQ.1) WRITE(20,' (I1,A19,1X,A7)')
NTCT1,THE REST 19,BC1(DAY)
IF(COUNT2.EQ.2) WRITE(20,' (I1,A19,1X,A7)')
NTCT1,THE REST 19,BC2(DAY)
IF(COUNT2.EQ.3) WRITE(20,' (I1,A19,1X,A7)')
NTCT1,THE REST 19,BC3(DAY)
IF(COUNT2.EQ.4) WRITE(20,' (I1,A19,1X,A7)')
NTCT1,THE REST 19,BC4(DAY)
ELSEIF(COUNT2.LE.8) THEN
WRITE(20,' (I1A1,A98)') NTCT1,THE REST,'
IF(COUNT2.EQ.8)COUNT2=0
ENDIF
ELSEIF(NTCT1.GT.2) THEN
WRITE(20,'(I1,A)') NTCT1,THE REST


0.005'


0.005'


ENDIF
IF(DAYMAX.EQ.1) THEN
IF(NTCT1.EQ.0) WRITE(20,'(I1,A)') NTCT1,THE REST
IF((NTCT1.EQ.1).OR.(NTCT1.EQ.2)) WRITE(20,'(I1,A)')


217











NTCT1,THE REST
IF(NTCT1.GT.2) WRITE(20,'(I1,A)') NTCT1,THE REST
ENDIF
ENDDO

END PROGRAM Edit inputfile



Subroutine STRUCTCONCS

SUBROUTINE STRUCTCONCS
USE SWIFTDIM
USE COUPLING
REAL*4 DAY !STRCFLOWCONC(40),STRCFLOWCONC2(40) moved to SWIFTDIM
REAL*8 DAYCHK
DATA IFIRST/1/,IUSFLOWCONCS/175/
IF(IFIRST .EQ. 1)THEN
OPEN(IUSFLOWCONCS,FILE='..\Input\FLOWS\INPUTFLOWCONCS.DAT',
STATUS='OLD',ACCESS='SEQUENTIAL')
READ(IUSFLOWCONCS,*) NUMSTRUCS
NUMSTRUCS=NUMSTRUCS+1
DO J=2,NUMSTRUCS
READ(IUSFLOWCONCS,*) NFLWPTS(J),NRANGES(J)
DO I=1,NFLWPTS(J)+2*NRANGES(J)
READ(IUSFLOWCONCS,*) MSTRUC(J,I),NSTRUC(J,I),IXYFLOW(J,I)
ENDDO
NTOTPTS(J)=NFLWPTS(J)
IF(NRANGES(J) .GT.0) THEN
DO I=NFLWPTS(J)+1,NFLWPTS(J)+2*NRANGES(J)-1,2
IP1=I+1
MSTRUC(J,IP1)=MSTRUC(J,IP1)-MSTRUC(J,I)
NSTRUC(J,IP1)=NSTRUC(J,IP1)-NSTRUC(J,I)
IF(ABS(MSTRUC(J,IP1)).GT.ABS(NSTRUC(J,IP1)))NSTRUC(J,IP1)=0
IF(ABS(NSTRUC(J,IP1)).GT.ABS(MSTRUC(J,IP1)))MSTRUC(J,IP1)=0
MAXMN=MAX(ABS(MSTRUC(J,IP1)),ABS(NSTRUC(J,IP1)))+1
NTOTPTS(J)=NTOTPTS(J)+MAXMN
ENDDO
ENDIF
ENDDO
!If more than one solute (excl salinity and temp) then need to have
one line in inputfile for each L
!for each day,
!e.g. Linel: Dayl Conc(Ll,strcl) Conc(Ll,strc2) Conc(Ll,strc3)
Line2: Dayl Conc(L2,strcl) Conc(L2,strc2) Conc(L2,strc3)
Line3: Day2 Conc(Ll,strcl) Conc(Ll,strc2) Conc(Ll,strc3)
Line4: Day2 Conc(L2,strcl) Conc(L2,strc2) Conc(L2,strc3)
DO L=1,LMAX
IF(L.EQ.LSAL)GOTO 115 !Skip salinity and temp so don't have to add
these to input file
IF(L.EQ.LTEMP)GOTO 115
READ(IUSFLOWCONCS,*) (STRCFLOWCONC(L,J), J=1,NUMSTRUCS) !Assumes 1
solute
115 CONTINUE
ENDDO
DO L=1,LMAX
IF(L.EQ.LSAL)GOTO 116 !Skip salinity and temp so don't have to add


218











these to input file
IF(L.EQ.LTEMP)GOTO 116
READ(IUSFLOWCONCS,*) (STRCFLOWCONC2(L,J), J=1,NUMSTRUCS) !Assumes
1 solute
116 CONTINUE
ENDDO
IFIRST=0
ENDIF
C SECTION EXECUTED EVERY TIMESTEP
C Convert time in min to Julian days.
DAY=(KBND+1)*HALFDT/1440.+1.+DAYOFFSTSWIFT
C SJM: WRITE DAY to screen to monitor sim progression
!WRITE(*,*)DAY !SJM DELETE!
DO L=1,LMAX
IF((L.EQ.LSAL).OR. (L.EQ.LTEMP)) GOTO 1166
IF(DAY.GT.STRCFLOWCONC(L,1)) DAYCHK=STRCFLOWCONC(L,1) !Assumes data
for different L's given at same time in input file
1166 CONTINUE
ENDDO
!10 IF(DAY .GT. STRCFLOWCONC(1))THEN
10 IF(DAY .GT. DAYCHK)THEN
STRCFLOWCONC=STRCFLOWCONC2
!If more than one solute (excl salinity and temp) then need to have
one line in inputfile for each L
!for each day,
!e.g. Linel: Dayl Conc(Ll,strcl) Conc(Ll,strc2) Conc(Ll,strc3)
Line2: Dayl Conc(L2,strcl) Conc(L2,strc2) Conc(L2,strc3)
Line3: Day2 Conc(Ll,strcl) Conc(Ll,strc2) Conc(Ll,strc3)
Line4: Day2 Conc(L2,strcl) Conc(L2,strc2) Conc(L2,strc3)
DO L=1,LMAX
IF(L.EQ.LSAL)GOTO 117 !Skip salinity and temp so don't have to add
these to input file
IF(L.EQ.LTEMP)GOTO 117
READ(IUSFLOWCONCS,*) (STRCFLOWCONC2(L,J), J=1,NUMSTRUCS) !Assumes
1 solute
DAYCHK=STRCFLOWCONC(L,1)
117 CONTINUE
ENDDO
GO TO 10
ENDIF
RETURN
END


219









Section C2


Important Input Files for the SICS Water-Quality Simulation

Input files and used in the simulation of SICS surface-water phosphorus are

presented. These include the input concentrations at discharge sources

(INPUTFLOWCONCS.dat), the atmospheric deposition data for each of the three

options tested, the SWIFT2D input file (WETLANDS.inp), and the IWQ input file

(IWQINPUT.iwq), which are needed by SWIFT2D. The XML input file (XMLINPUT.xml)

was required for aRSE.

Format for INPUTFLOWCONCS.dat

3
1 0 TSB
90 90 3
1 0 L-31W
100 88 3
1 0 C-111
120 64 3
1.00 0.0044 0.0062 0.003
2.00 0.0044 0.0062 0.003
3.00 0.0044 0.0062 0.003
4.00 0.0044 0.0062 0.003
5.00 0.0044 0.0062 0.003
6.00 0.0044 0.0062 0.003
7.00 0.0044 0.0062 0.003
8.00 0.0044 0.0062 0.003
9.00 0.0044 0.0062 0.003
10.00 0.0044 0.0062 0.003
11.00 0.0044 0.0062 0.003
12.00 0.0044 0.0062 0.003
13.00 0.0044 0.0062 0.003
14.00 0.0044 0.0062 0.003
15.00 0.0044 0.0062 0.003
16.00 0.0044 0.0062 0.003
17.00 0.0044 0.0062 0.003
18.00 0.0101 0.0031 0.0032
19.00 0.0101 0.0031 0.0032
20.00 0.0101 0.0031 0.0032
21.00 0.0101 0.0031 0.0032
22.00 0.0101 0.0031 0.0032


220










23.00
24.00
25.00
26.00
27.00
28.00
29.00
30.00


0.0101
0.0101
0.0101
0.0101
0.0101
0.0101
0.0101
0.0101


0.0031
0.0031
0.0031
0.0031
0.0031
0.0031
0.0031
0.0031


0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032
0.0032


incomplete file

Total Phosphorus Atmospheric Deposition Rates for Model 2

Table C-1 below shows the total phosphorus atmospheric deposition rates applied

to Model 2 for each of the three atmospheric deposition options tested.

Table C-1. Atmospheric deposition rates input to Model 2


Day Date
1 07/15/96
2 07/16/96
3 07/17/96
4 07/18/96
5 07/19/96
6 07/20/96
7 07/21/96
8 07/22/96
9 07/23/96
10 07/24/96
11 07/25/96
12 07/26/96
13 07/27/96
14 07/28/96
15 07/29/96
16 07/30/96
17 07/31/96
18 08/1/96
19 08/2/96
20 08/3/96
21 08/4/96
22 08/5/96
23 08/6/96
24 08/7/96


Variable rate
proportionate to rain
volume [g TP/m2/d]
9.93915E-05
0.000686837
3.68857E-05
1.12111E-05
1.38821 E-05
0.000110112
1.06841 E-06
0
2.1441E-05
4.27002E-06
0
0
2.88908E-05
3.36151E-05
0.000136277
1.92605E-05
2.67103E-06
2.39848E-05
2.1441E-06
0.000190788
1.33552E-05
2.5075E-05
0.000323431
1.06841 E-06


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


221










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
25 08/8/96 0.000174071
26 08/9/96 1.06841 E-05
27 08/10/96 6.41411E-06
28 08/11/96 5.86901E-06
29 08/12/96 0
30 08/13/96 2.83457E-05
31 08/14/96 2.94359E-05
32 08/15/96 8.64906E-05
33 08/16/96 4.76062E-05
34 08/17/96 1.76252E-05
35 08/18/96 0.000174617
36 08/19/96 0.000723178
37 08/20/96 0.000256201
38 08/21/96 0.000159717
39 08/22/96 0.00018352
40 08/23/96 0.000261652
41 08/24/96 4.59709E-05
42 08/25/96 5.34207E-07
43 08/26/96 0.000110657
44 08/27/96 4.90598E-05
45 08/28/96 1.12111E-05
46 08/29/96 2.67103E-06
47 08/30/96 4.48806E-05
48 08/31/96 9.61209E-06
49 09/1/96 6.46863E-05
50 09/2/96 0.000160807
51 09/3/96 7.37714E-05
52 09/4/96 1.38821 E-05
53 09/5/96 0.000120106
54 09/6/96 9.61209E-06
55 09/7/96 7.48616E-06
56 09/8/96 5.92352E-05
57 09/9/96 0.000437904
58 09/10/96 0.000688654
59 09/11/96 2.28946E-05
60 09/12/96 0.000120651
61 09/13/96 6.41411E-06
62 09/14/96 0.000113746
63 09/15/96 1.01572E-05


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


222










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
64 09/16/96 2.56201 E-05
65 09/17/96 0.000174071
66 09/18/96 8.43102E-05
67 09/19/96 9.50307E-05
68 09/20/96 0.000325248
69 09/21/96 0.000190788
70 09/22/96 4.76062E-05
71 09/23/96 0.000170437
72 09/24/96 6.30509E-05
73 09/25/96 0
74 09/26/96 4.27002E-06
75 09/27/96 0
76 09/28/96 3.41602E-05
77 09/29/96 1.54993E-05
78 09/30/96 0.000368857
79 10/1/96 6.52314E-05
80 10/2/96 3.74308E-06
81 10/3/96 0.000107932
82 10/4/96 0.000188971
83 10/5/96 0.000461526
84 10/6/96 0.000132461
85 10/7/96 0.000223495
86 10/8/96 0.000236214
87 10/9/96 0.000130826
88 10/10/96 0
89 10/11/96 0
90 10/12/96 0.001019354
91 10/13/96 0.001010269
92 10/14/96 0.000228946
93 10/15/96 0.000288908
94 10/16/96 6.46863E-05
95 10/17/96 0.000423368
96 10/18/96 0.000310712
97 10/19/96 8.70357E-05
98 10/20/96 3.19797E-06
99 10/21/96 1.60262E-06
100 10/22/96 1.60262E-06
101 10/23/96 0
102 10/24/96 0


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


223










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
103 10/25/96 3.74308E-06
104 10/26/96 1.06841 E-06
105 10/27/96 8.54004E-06
106 10/28/96 1.06841 E-06
107 10/29/96 0
108 10/30/96 1.70982E-05
109 10/31/96 5.34207E-07
110 11/1/96 5.34207E-07
111 11/2/96 3.74308E-06
112 11/3/96 5.34207E-07
113 11/4/96 2.1441E-06
114 11/5/96 1.81703E-05
115 11/6/96 0
116 11/7/96 3.74308E-06
117 11/8/96 1.06841 E-06
118 11/9/96 0
119 11/10/96 0
120 11/11/96 0
121 11/12/96 0
122 11/13/96 0
123 11/14/96 5.015E-05
124 11/15/96 4.59709E-05
125 11/16/96 1.54993E-05
126 11/17/96 0
127 11/18/96 2.1441E-06
128 11/19/96 1.06841 E-06
129 11/20/96 0
130 11/21/96 1.06841 E-06
131 11/22/96 2.67103E-06
132 11/23/96 4.81513E-06
133 11/24/96 0
134 11/25/96 0
135 11/26/96 0
136 11/27/96 0
137 11/28/96 7.21361E-05
138 11/29/96 0
139 11/30/96 0
140 12/1/96 0
141 12/2/96 1.33552E-05


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
0
9.70874E-05
0
0
0
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


224










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
142 12/3/96 1.12111E-05
143 12/4/96 0
144 12/5/96 7.63152E-05
145 12/6/96 1.33552E-05
146 12/7/96 5.34207E-07
147 12/8/96 4.81513E-06
148 12/9/96 0
149 12/10/96 0
150 12/11/96 0
151 12/12/96 0
152 12/13/96 0.000261652
153 12/14/96 4.27002E-06
154 12/15/96 1.06841 E-06
155 12/16/96 0
156 12/17/96 0
157 12/18/96 8.54004E-06
158 12/19/96 4.81513E-06
159 12/20/96 0
160 12/21/96 5.34207E-07
161 12/22/96 6.41411 E-06
162 12/23/96 0


12/24/96
12/25/96
12/26/96
12/27/96
12/28/96
12/29/96
12/30/96
12/31/96
01/1/97
01/2/97
01/3/97
01/4/97
01/5/97
01/6/97
01/7/97
01/8/97
01/9/97
01/10/97


0
1.06841 E-06
8.54004E-06
4.81513E-06
1.06841 E-06
2.67103E-06
4.81513E-06
1.06841 E-06
1.06841 E-06
1.60262E-06
1.06841 E-06
2.1441 E-06
5.34207E-07
1.06841 E-06
6.41411E-06
4.81513E-06
1.60262E-06
9.72111E-05


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


225


163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180










Table C-1. Continued
Variable rate
proportionate to rain Constant rate per rain Constant rate per day
Day Date volume [g TP/m2/d] day [g TP/m2/d] [g TP/m2/d]


181
182


01/11/97
01/12/97
01/13/97
01/14/97
01/15/97
01/16/97
01/17/97
01/18/97
01/19/97
01/20/97
01/21/97
01/22/97
01/23/97
01/24/97
01/25/97
01/26/97
01/27/97
01/28/97
01/29/97
01/30/97
01/31/97
02/1/97
02/2/97
02/3/97
02/4/97
02/5/97
02/6/97
02/7/97
02/8/97
02/9/97
02/10/97
02/11/97
02/12/97
02/13/97
02/14/97
02/15/97
02/16/97
02/17/97
02/18/97


226


1.60262E-05
0.000359772
0.000370674
0.000168802
0.000185337
0.00020169
0
0
0
0
5.34207E-07
1.06841 E-06
5.34207E-07
0
3.74308E-05
3.90661E-05
0
1.44272E-05
0.000134097
8.34017E-05
0
0
2.1441 E-06
3.19797E-06
2.39848E-05
4.81513E-06
1.60262E-06
5.34207E-07
2.1441 E-06
1.65531 E-05
1.06841 E-06
0
0
5.34207E-07
6.41411E-06
1.06841 E-06
0.000152267
9.61209E-06
0.00020169


9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
220 02/19/97 2.39848E-05
221 02/20/97 3.74308E-06
222 02/21/97 5.34207E-07
223 02/22/97 5.34207E-07
224 02/23/97 2.1441E-06
225 02/24/97 2.72554E-05
226 02/25/97 1.60262E-05
227 02/26/97 0
228 02/27/97 0
229 02/28/97 0
230 03/1/97 0
231 03/2/97 0
232 03/3/97 5.34207E-07
233 03/4/97 5.34207E-07
234 03/5/97 0
235 03/6/97 4.27002E-06
236 03/7/97 1.33552E-05
237 03/8/97 5.34207E-07
238 03/9/97 5.34207E-07
239 03/10/97 5.86901 E-06
240 03/11/97 5.34207E-07
241 03/12/97 2.1441E-06
242 03/13/97 5.34207E-07
243 03/14/97 0.000632326
244 03/15/97 8.23114E-05
245 03/16/97 1.06841 E-06
246 03/17/97 5.34207E-07
247 03/18/97 0
248 03/19/97 1.06841 E-06
249 03/20/97 5.34207E-07
250 03/21/97 0.000219861
251 03/22/97 6.41411 E-06
252 03/23/97 5.34207E-07
253 03/24/97 0.000106296
254 03/25/97 1.28282E-05
255 03/26/97 0
256 03/27/97 1.81703E-05
257 03/28/97 2.67103E-06
258 03/29/97 5.34207E-07


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
0
0
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


227










Table C


Day
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297


-1. Continue(


Date
03/30/97
03/31/97
04/1/97
04/2/97
04/3/97
04/4/97
04/5/97
04/6/97
04/7/97
04/8/97
04/9/97
04/10/97
04/11/97
04/12/97
04/13/97
04/14/97
04/15/97
04/16/97
04/17/97
04/18/97
04/19/97
04/20/97
04/21/97
04/22/97
04/23/97
04/24/97
04/25/97
04/26/97
04/27/97
04/28/97
04/29/97
04/30/97
05/1/97
05/2/97
05/3/97
05/4/97
05/5/97
05/6/97
05/7/97


ed
Variable rate
proportionate to rain
volume [g TP/m2/d]
5.34207E-07
2.08958E-05
2.1441E-06
0
0
0
0
0
0
2.1441E-06
3.14346E-05
1.44272E-05
1.70982E-05
5.39658E-05
7.10459E-05
3.19797E-06
0.000117562
0.000141002
1.01572E-05
0
0
0
1.92605E-05
9.08515E-06
5.86901E-06
4.27002E-06
3.19797E-06
0.000129191
2.67103E-06
0.000134097
1.33552E-05
9.55758E-05
5.86901E-05
6.94105E-06
0
6.30509E-05
1.01572E-05
0
0


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
0
0


228


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05










Table C-1. Continued
Variable rate
proportionate to rain Constant rate per rain Constant rate per day
Day Date volume [g TP/m2/d] day [g TP/m2/d] [g TP/m2/d]


298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336


05/8/97
05/9/97
05/10/97
05/11/97
05/12/97
05/13/97
05/14/97
05/15/97
05/16/97
05/17/97
05/18/97
05/19/97
05/20/97
05/21/97
05/22/97
05/23/97
05/24/97
05/25/97
05/26/97
05/27/97
05/28/97
05/29/97
05/30/97
05/31/97
06/1/97
06/2/97
06/3/97
06/4/97
06/5/97
06/6/97
06/7/97
06/8/97
06/9/97
06/10/97
06/11/97
06/12/97
06/13/97
06/14/97
06/15/97


229


0
0
0
1.06841 E-06
0.000466977
0.000145362
0
5.34207E-07
0
2.08958E-05
6.41411E-06
2.1441 E-06
5.34207E-06
1.60262E-05
0.000181158
8.81259E-05
0.000179523
0
4.54257E-05
5.34207E-07
0.000259835
0.000100482
7.05008E-05
0.000119197
0.000122831
0.000739531
7.26812E-05
1.70982E-05
4.81513E-06
0
1.17562E-05
0.000741348
0.004197339
0.001475428
0.000292542
1.92605E-05
2.88908E-05
1.38821 E-05
0.000432453


0
0
0
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
337 06/16/97 0.000115926
338 06/17/97 2.1441E-06
339 06/18/97 3.19797E-06
340 06/19/97 4.27002E-06
341 06/20/97 1.54993E-05
342 06/21/97 7.57701E-05
343 06/22/97 0.000414283
344 06/23/97 7.05008E-05
345 06/24/97 0.000185337
346 06/25/97 0.000101027
347 06/26/97 9.08515E-06
348 06/27/97 1.17562E-05
349 06/28/97 0
350 06/29/97 1.60262E-06
351 06/30/97 5.77815E-05
352 07/1/97 0.000135732
353 07/2/97 0.000247116
354 07/3/97 9.88464E-05
355 07/4/97 0.000321614
356 07/5/97 4.27002E-06
357 07/6/97 3.36151E-05
358 07/7/97 5.86901 E-06
359 07/8/97 5.86901 E-06
360 07/9/97 4.27002E-06
361 07/10/97 0.000108477
362 07/11/97 0.000144272
363 07/12/97 0.000254384
364 07/13/97 0.000205324
365 07/14/97 0.000185337
366 07/15/97 5.34207E-05
367 07/16/97 0.000243482
368 07/17/97 0.000161897
369 07/18/97 0.000156446
370 07/19/97 0.000142092
371 07/20/97 0.000118107
372 07/21/97 3.47053E-05
373 07/22/97 0.00020169
374 07/23/97 0.000120651
375 07/24/97 1.06841 E-05


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


230










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
376 07/25/97 9.61209E-06
377 07/26/97 0.000123376
378 07/27/97 5.77815E-05
379 07/28/97 2.1441E-05
380 07/29/97 5.34207E-07
381 07/30/97 4.27002E-06
382 07/31/97 1.81703E-05
383 08/1/97 0.000160262
384 08/2/97 0.000107386
385 08/3/97 0
386 08/4/97 7.63152E-05
387 08/5/97 7.48616E-06
388 08/6/97 0.000110657
389 08/7/97 4.161E-05
390 08/8/97 5.45109E-05
391 08/9/97 0.000354321
392 08/10/97 0.00021441
393 08/11/97 3.96112E-05
394 08/12/97 2.78006E-05
395 08/13/97 0
396 08/14/97 5.34207E-07
397 08/15/97 0.000153357
398 08/16/97 3.99747E-05
399 08/17/97 6.41411E-06
400 08/18/97 1.60262E-05
401 08/19/97 5.86901E-06
402 08/20/97 7.37714E-05
403 08/21/97 0.000252567
404 08/22/97 2.5075E-05
405 08/23/97 2.19861 E-05
406 08/24/97 4.70611 E-05
407 08/25/97 0.000199873
408 08/26/97 0.000121741
409 08/27/97 0.000128282
410 08/28/97 4.81513E-05
411 08/29/97 6.72301 E-05
412 08/30/97 0.000279823
413 08/31/97 0.000219861
414 09/1/97 0.000138276


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


231










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
415 09/2/97 0.000133552
416 09/3/97 3.25248E-05
417 09/4/97 9.83013E-05
418 09/5/97 0.000321614
419 09/6/97 0.000305261
420 09/7/97 4.27002E-06
421 09/8/97 3.47053E-05
422 09/9/97 1.06841 E-06
423 09/10/97 5.34207E-07
424 09/11/97 9.24868E-05
425 09/12/97 5.72364E-05
426 09/13/97 4.43355E-05
427 09/14/97 0.000100482
428 09/15/97 0.000129191
429 09/16/97 3.52504E-05
430 09/17/97 0.000116472
431 09/18/97 5.86901E-05
432 09/19/97 0.000198056
433 09/20/97 3.30699E-05
434 09/21/97 2.34397E-05
435 09/22/97 2.1441E-06
436 09/23/97 3.41602E-05
437 09/24/97 0.000119742
438 09/25/97 5.72364E-05
439 09/26/97 0.000221678
440 09/27/97 6.03254E-05
441 09/28/97 0.000207141
442 09/29/97 0.000223495
443 09/30/97 0.000332516
444 10/1/97 0.000288908
445 10/2/97 0.000187154
446 10/3/97 4.81513E-06
447 10/4/97 2.1441E-06
448 10/5/97 4.81513E-06
449 10/6/97 9.55758E-05
450 10/7/97 2.1441E-06
451 10/8/97 0
452 10/9/97 4.81513E-06
453 10/10/97 0.000104116


Constant rate per rain
day [g TP/m2/d]
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
9.70874E-05
0
9.70874E-05
9.70874E-05


Constant rate per day
[g TP/m2/d]
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05
8.2192E-05


232










Table C-1. Continued
Variable rate
proportionate to rain
Day Date volume [g TP/m2/d]
454 10/11/97 6.94105E-06
455 10/12/97 2.5075E-05
456 10/13/97 9.61209E-06
457 10/14/97 7.48616E-06
458 10/15/97 2.67103E-06
459 10/16/97 1.28282E-05
460 10/17/97 9.08515E-06
461 10/18/97 1.22831 E-05
462 10/19/97 0
463 10/20/97 1.06841 E-05
464 10/21/97 0
465 10/22/97 0
466 10/23/97 5.34207E-07
467 10/24/97 0
468 10/25/97 5.34207E-07
469 10/26/97 5.34207E-07
470 10/27/97 0
471 10/28/97 0
472 10/29/97 1.01572E-05
473 10/30/97 0.000236214
474 10/31/97 2.1441E-06
475 11/1/97 0
476 11/2/97 9.61209E-06
477 11/3/97 5.72364E-05
478 11/4/97 2.1441E-06
479 11/5/97 1.01572E-05
480 11/6/97 4.81513E-06
481 11/7/97 3.74308E-06
482 11/8/97 0
483 11/9/97 0
484 11/10/97 0
485 11/11/97 1.06841 E-06
486 11/12/97 0


Constant rate per rain day Constant rate per day
[g TP/m2/d] [g TP/m2/d]
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05
0 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05
0 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05
0 8.2192E-05
0 8.2192E-05
9.70874E-05 8.2192E-05
0 8.2192E-05


233










Section C3


XML Input File for Model 3 (XMLINPUT.xml)






all
all


location="element" section="gw" actuator="rsm_wm">
surfacewater



Sal

10.0



TPswconc

10.0



TPswmassl

10.0



TPswmass2

10.0



TP_uptakel

10.0



TP_uptake2

10.0





234










TPsoill

10.0



TPsoil2

10.0



TPlivel

10.0



TPlive2

10.0



TPdeadl

10.0



TPdead2

10.0



TPsenesc

10.0



TP_decomp

10.0



TP_bury

10.0



Kwet



235










10.0





longitudinal_dispersivity

10.0



transverse_dispersivity

10.0



moleculardiffusion

0.00001



surface_porosity

1.0



subsurface_longitudinal_dispersivity

10.0



subsurface_transverse_dispersivity

10.0



subsurface molecular diffusion

0.00001



subsurface_porosity

1.0



k_uptake



236










0.084375



ksenesc

0.25



k_decomp

0.0001



ksoil

0.13








TPswmass2
(1-k_uptake)*TP_sw_conc*depth


TP_uptake2
k_uptake*K_wet*TP_sw_massl


TPsenesc
k_senesc*TP_uptakel


TP_decomp
k_decomp*TP_dead2


TP_bury
k_soil*TP_uptakel


TP live
TP live2


TPdeadl
TPdead2


TPsoill


237










TPsoil2


TP_uptakel
TP_uptake2


TPswmassl
TP sw mass2


TPdead2
TP_deadl +TP_senesc-TP_decomp


TP live2
TP_livel +TP_uptake2-TP_senesc


TPsoil2
TP_soill +TP_bury


TPswconc
(TP_sw_mass2+TP_decomp)/depth









IWQ input File for Model 3 (IWQINPUT.iwq)

1214510
'XMLINPUT.xml' 'XMLOUTPUT.xml' 'rsl'
Sal 5.01 TPswconc 0.005
TP_sw_mass1 0.01 TP_sw_mass2 0.01 TP_uptakel 0.0008 TP_uptake2 0.0008
TP soil 0.0001 TP soil2 0.0001 TP livel 0.04 TP live2 0.04 TP dead 0.014
TP_dead2 0.014 TP_senesc 0.0002 TP_decomp 0.0001 TP_bury 0 K_wet 1
00000000000000
k_uptake 0.084375 k_senesc 0.25 k_decomp 0.0001 k_soil 0.0
0
depth 0.52 time_step 3600 area 92903


238












SWIFT2D Input File (WETLANDS.inp) for Model 3

SOUTHERN INLAND AND COASTAL SYSTEMS MODEL
END NOTE END NOTE
NOSAMV= 1(NUMBER OF DIMENSIONS THAT MUST STAY THE SAME)
NODIMV= 2(NUMBER OF DIMENSIONS TOTAL)
WETMTZ /IDP...R07 00 00 00 00 00
RUN NUMBER 1 R2 TITL
WETLANDS 15 JUL '96 98/8/2517:23:39 IDPV514 R3 DATE
Halfdt Titide Tstart Trst Tstop Tirst Tihisp Tihist DAYOFFSTSWIFT
1.50 15.0 0.0 0.0999999.999999. 1440. 1440. 0 R4TIMEA
99999999999999999999999. 45. 30.999999 60.999999999999999999 0.R5TIMEB
0 0 2 1 0 5 1 0 0 0 0 OR6FLAGS
7 3 4 4 0 4 R7INPR1
1 R8 INPR2
0 1440 1440 1440 0 0 0 0 0 R9OTPR1
1440 1440 1440 1440 0 0 0 R100TPR2
545760545880546000546120546240546360546480546600546720546840546960547080R11 PRT1
547200547320547440547560547680547800547920548040548160548280548400548520R12 PRT2
548640548760548880549000549120549240549360549480549600549720549840549960R13 PRT3
550080550200550320550440550560550680 R14 PRT4
148 98 2 14 33 4 25 3 5 8 0 1R15DIMA
94 128 R16DIMB
0.5 0 1 R17CNST
25.000 0.0304.8 0.20 0.0 0.10 1. 1.00 0.5 1.0 5.0300.0R18PHCH
9.81 0.0012 1.205 998.2 1.0000 14.3 1000.0 0.97 0.0023R19COFA
FR80 35SPRO 1.0 1.0 R20 Ploter D
25 1 0.0 13.0 20.0 14.0K/HR 5 R21 Nctitl D
4.0 170.0 2.00 121.0 163.0 1.25 74.0 89.0 1.00 122.0 103.0 1.00R22 Hx USED
1.0 2.0 2.0 2.0 2.0 R23 Dxpdy ED
1 1 2 0.5 1.0-0.40-0.40 0.25 1.0 0.0 1 1R241plc SED
R25 Linx SED
25.0 1.0250 0.698 1.0 R26 COFB
1 57 36 CP RS1 WL-Sta
2 109 78 EVER4 RS1 WL-Sta
3 100 58 EVER5A RS1 WL-Sta
4 69 45 E146 RS1 WL-Sta
5 98 97 E158 RS1 WL-Sta
6 142 52 EP12R RS1 WL-Sta
7 139 57 EP1R RS1 WL-Sta
8 123 55 EPGW RS1 WL-Sta
9 120 61 EVER6 RS1 WL-Sta
10 110 65EVER7 RS1 WL-Sta
11 74 73 NP67 RS1 WL-Sta
12 62 56 P37 RS1 WL-Sta
13 89 81 R127 RS1 WL-Sta
14 81 66TSH RS1 WL-Sta
1 28 18Alligat_T RS2 Curr-Sta
2 28 17 Alligat_C RS2 Curr-Sta
3 28 16 Alligat_B RS2 Curr-Sta
4 47 14McCorm L RS2 Curr-Sta
5 48 14McCorm C RS2 Curr-Sta
6 49 14McCorm R RS2 Curr-Sta
7 77 23 Taylor_L RS2 Curr-Sta
8 78 23 Taylor_C RS2 Curr-Sta
9 79 23 Taylor_R RS2 Curr-Sta
10 84 26 East L RS2 Curr-Sta
11 85 26 East C RS2 Curr-Sta
12 86 26 East R RS2 Curr-Sta
13 96 27 Mud T RS2 Curr-Sta
14 96 28 Mud C RS2 Curr-Sta
15 96 29 Mud B RS2 Curr-Sta
16 113 32Trout L RS2 Curr-Sta
17 114 32Trout C RS2 Curr-Sta
18 115 32Trout R RS2 Curr-Sta
19 127 30 Shell L RS2 Curr-Sta
20 128 30 Shell C RS2 Curr-Sta
21 129 30 Shell R RS2 Curr-Sta
22 128 36 Stillw L RS2 Curr-Sta


239












36 Stillw C
36 Stillw R
40 Oregon_L
40 Oregon_C
40 Oregon_R
41 WestHi L
41 WestHi C
41 WestHi R
42 EastHi L
42 EastHi C
42 EastHi R
90 TSB
88 L-31W
64 C-11
98 Dummy (ex solar)
36 CP
78 EVER4
58 EVER5A
45 E146
97 E158
52 EP12R
57 EP1R
55 EPGW
61 EVER
65 EVER7
73 NP67
56 P37
81 R127
66 TSH
17 Alligat_c
14 McCorm c
23 Taylor_c
26 East c
28 Mud c
32 Trout c
30 Shell c
36 Stillw c
40 Oregon_c
41 WestHi c
42 EastHi c
31 36 Joe Bay 1
36 40 Joe Bay 2
34 39 Joe Bay 3
93 98 Joe Bay 4
98 101 Joe Bay 5
102 107 Joe Bay 6
108 110 Joe Bay 7
111 116 Joe Bay 8


RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS2 Curr-Sta
RS3 Src
RS3 Src
RS3 Src
RS3 Sol
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS4 Con-Sta
RS5 U-tran-Sta
RS5 U-tran-Sta
RS5 U-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS6 V-tran-Sta
RS7 Dam
RS8 Wind/Temp
RS9 Bar/Sluice


Alligator


240












21 33
22 35
23 36
24 38
25 40
26 41
27 42
28 42
29 43
30 44
31 46
32 46
33 47
34 49
35 50
36 50
37 51
38 52
39 54
40 56
41 57
42 58
43 58
44 59
45 60
46 61
47 63
48 64
49 66
50 68
51 69
52 69
53 70
54 70
55 70
56 71
57 71
58 71
59 71
60 73
61 74
62 74
63 76
64 78
65 80
66 81
67 83
68 84
69 86
70 89
71 91
72 92
73 94
74 96
75 96
76 96
77 98
78 100
79 102
80 104
81 105
82 107
83 109
84 111
85 113
86 114
87 115
88 116
89 118
90 119


Mud Creek


241












1 91 120 32
1 92 121 31
1 93 122 30
1 94 123 29
2 1 4 18
2 2 5 18
2 3 6 18
2 4 7 18
2 5 8 18
2 6 9 18
2 7 10 18
2 8 11 17
2 9 12 17
2 10 13 17
2 11 14 16
2 12 15 16
2 13 16 15
2 14 17 15
2 15 18 14
2 16 19 15
2 17 20 19
2 18 21 20
2 19 22 21
2 20 23 21
2 21 24 20
2 22 25 20
2 23 25 25
2 24 26 19
2 25 27 15
2 26 27 18
2 27 28 14
2 28 29 14
2 29 29 25
2 30 30 14
2 31 31 13
2 32 32 13
2 33 33 13
2 34 34 12
2 35 34 20
2 36 35 12
2 37 36 13
2 38 37 13
2 39 38 13
2 40 39 12
2 41 40 12
2 42 41 11
2 43 43 14
2 44 44 13
2 45 45 13
2 46 46 13
2 47 48 14 McCormick Creek
2 48 49 14
2 49 50 16
2 50 51 12
2 51 52 11
2 52 53 10
2 53 54 10
2 54 55 9
2 55 56 9
2 56 57 10
2 57 59 13
2 58 60 14
2 59 61 15
2 60 62 16
2 61 63 16
2 62 64 17
2 63 65 17
2 64 66 17
2 65 67 17
2 66 68 17


242












2 67 70 14
2 68 71 20
2 69 72 21
2 70 73 21
2 71 75 23
2 72 76 23
2 73 77 23
2 74 78 23 Taylor Creek
2 75 79 23
2 76 80 24
2 77 81 25
2 78 82 25
2 79 83 25
2 80 84 26
2 81 85 26 East Creek
2 82 86 26
2 83 87 26
2 84 88 27
2 85 89 27
2 86 90 27
2 87 91 27
2 88 92 26
2 89 93 26
2 90 94 26
2 91 95 26
2 92 97 30
2 93 98 30
2 94 99 30
2 95 100 30
2 96 101 30
2 97 102 30
2 98 103 30
2 99 104 30
2 100 105 31
2 101 106 31
2 102 107 31
2 103 108 31
2 104 109 30
2 105 110 30
2 106 111 31
2 107 112 31
2 108 113 31
2 109 114 32 Trout Creek
2 110 115 33
2 111 116 34
2 112 117 34
2 113 118 34
2 114 119 33
2 115 120 32
2 116 121 31
2 117 122 30
2 118 123 29
2 119 127 29
2 120 128 30 ShellCreek
2 121 129 36 Stillwater Creek
2 122 130 36
2 123 138 40
2 124 139 40 Oregon Creek
2 125 140 41
2 126 141 41 West Highway
2 127 142 42
2 128 143 42 East Highway
1 1269.9778269.9778269.9778269.9778269.9778269.9778
1 2269.9778269.9778269.9778269.9778269.9778269.9778
1 3269.9778269.9778269.9778269.9778269.9778269.9778
1 4269.9778269.9778269.9778269.9778269.9778269.9778
1 5269.9778269.9778269.9778269.9778269.9778269.9778
1 6269.9778269.9778269.9778269.9778269.9778269.9778
1 7269.9778269.9778269.9778269.9778269.9778269.9778
1 8 43.196443.1964 43.196443.1964 43.196443.1964


243












1 9269.9778269.9778269.9778269.9778269.9778269.9778
1 10269.9778269.9778269.9778269.9778269.9778269.9778
1 11269.9778269.9778269.9778269.9778269.9778269.9778
1 12269.9778269.9778269.9778269.9778269.9778269.9778
1 13269.9778269.9778269.9778269.9778269.9778269.9778
1 14269.9778269.9778269.9778269.9778269.9778269.9778
1 15 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978 Alligator
1 16269.9778269.9778269.9778269.9778269.9778269.9778
1 17269.9778269.9778269.9778269.9778269.9778269.9778
1 18269.9778269.9778269.9778269.9778269.9778269.9778
1 19269.9778269.9778269.9778269.9778269.9778269.9778
1 20 53.9956 53.9956 53.9956 53.9956 53.9956 53.9956
1 21269.9778269.9778269.9778269.9778269.9778269.9778
1 22269.9778269.9778269.9778269.9778269.9778269.9778
1 23269.9778269.9778269.9778269.9778269.9778269.9778
1 24269.9778269.9778269.9778269.9778269.9778269.9778
1 25269.9778269.9778269.9778269.9778269.9778269.9778
1 26269.9778269.9778269.9778269.9778269.9778269.9778
1 27269.9778269.9778269.9778269.9778269.9778269.9778
1 28269.9778269.9778269.9778269.9778269.9778269.9778
1 29269.9778269.9778269.9778269.9778269.9778269.9778
1 30269.9778269.9778269.9778269.9778269.9778269.9778
1 31269.9778269.9778269.9778269.9778269.9778269.9778
1 32 32.3973 32.3973 32.3973 32.3973 32.3973 32.3973
1 33269.9778269.9778269.9778269.9778269.9778269.9778
1 34269.9778269.9778269.9778269.9778269.9778269.9778
1 35 21.5982 21.5982 21.5982 21.5982 21.5982 21.5982
1 36269.9778269.9778269.9778269.9778269.9778269.9778
1 37269.9778269.9778269.9778269.9778269.9778269.9778
1 38269.9778269.9778269.9778269.9778269.9778269.9778
1 39269.9778269.9778269.9778269.9778269.9778269.9778
1 40269.9778269.9778269.9778269.9778269.9778269.9778
1 41269.9778269.9778269.9778269.9778269.9778269.9778
1 42269.9778269.9778269.9778269.9778269.9778269.9778
1 43269.9778269.9778269.9778269.9778269.9778269.9778
1 44269.9778269.9778269.9778269.9778269.9778269.9778
1 45269.9778269.9778269.9778269.9778269.9778269.9778
1 46269.9778269.9778269.9778269.9778269.9778269.9778
1 47269.9778269.9778269.9778269.9778269.9778269.9778
1 48 32.3973 32.3973 32.3973 32.3973 32.3973 32.3973
1 49269.9778269.9778269.9778269.9778269.9778269.9778
1 50269.9778269.9778269.9778269.9778269.9778269.9778
1 51269.9778269.9778269.9778269.9778269.9778269.9778
1 52269.9778269.9778269.9778269.9778269.9778269.9778
1 53269.9778269.9778269.9778269.9778269.9778269.9778
1 54269.9778269.9778269.9778269.9778269.9778269.9778
1 55269.9778269.9778269.9778269.9778269.9778269.9778
1 56269.9778269.9778269.9778269.9778269.9778269.9778
1 57269.9778269.9778269.9778269.9778269.9778269.9778
1 58269.9778269.9778269.9778269.9778269.9778269.9778
1 59269.9778269.9778269.9778269.9778269.9778269.9778
1 60269.9778269.9778269.9778269.9778269.9778269.9778
1 61269.9778269.9778269.9778269.9778269.9778269.9778
1 62269.9778269.9778269.9778269.9778269.9778269.9778
1 63269.9778269.9778269.9778269.9778269.9778269.9778
1 64269.9778269.9778269.9778269.9778269.9778269.9778
1 65269.9778269.9778269.9778269.9778269.9778269.9778
1 66269.9778269.9778269.9778269.9778269.9778269.9778
1 67269.9778269.9778269.9778269.9778269.9778269.9778
1 68269.9778269.9778269.9778269.9778269.9778269.9778
1 69269.9778269.9778269.9778269.9778269.9778269.9778
1 70269.9778269.9778269.9778269.9778269.9778269.9778
1 71269.9778269.9778269.9778269.9778269.9778269.9778
1 72269.9778269.9778269.9778269.9778269.9778269.9778
1 73269.9778269.9778269.9778269.9778269.9778269.9778
1 74269.9778269.9778269.9778269.9778269.9778269.9778
1 7518.898418.8984 18.898418.8984 18.898418.8984 Mud Creek
1 76269.9778269.9778269.9778269.9778269.9778269.9778
1 77269.9778269.9778269.9778269.9778269.9778269.9778
1 78269.9778269.9778269.9778269.9778269.9778269.9778


244












79269.9778269.9778269.9778269.9778269.9778269.9778
80269.9778269.9778269.9778269.9778269.9778269.9778
81269.9778269.9778269.9778269.9778269.9778269.9778
82269.9778269.9778269.9778269.9778269.9778269.9778
83269.9778269.9778269.9778269.9778269.9778269.9778
84269.9778269.9778269.9778269.9778269.9778269.9778
85269.9778269.9778269.9778269.9778269.9778269.9778
86269.9778269.9778269.9778269.9778269.9778269.9778
87269.9778269.9778269.9778269.9778269.9778269.9778
88269.9778269.9778269.9778269.9778269.9778269.9778
89269.9778269.9778269.9778269.9778269.9778269.9778
90269.9778269.9778269.9778269.9778269.9778269.9778
91269.9778269.9778269.9778269.9778269.9778269.9778
92269.9778269.9778269.9778269.9778269.9778269.9778
93269.9778269.9778269.9778269.9778269.9778269.9778
94269.9778269.9778269.9778269.9778269.9778269.9778
1269.9778269.9778269.9778269.9778269.9778269.9778
2269.9778269.9778269.9778269.9778269.9778269.9778
3269.9778269.9778269.9778269.9778269.9778269.9778
4269.9778269.9778269.9778269.9778269.9778269.9778
5269.9778269.9778269.9778269.9778269.9778269.9778
6269.9778269.9778269.9778269.9778269.9778269.9778
7269.9778269.9778269.9778269.9778269.9778269.9778
8269.9778269.9778269.9778269.9778269.9778269.9778
9269.9778269.9778269.9778269.9778269.9778269.9778
10269.9778269.9778269.9778269.9778269.9778269.9778
11269.9778269.9778269.9778269.9778269.9778269.9778
12269.9778269.9778269.9778269.9778269.9778269.9778
13269.9778269.9778269.9778269.9778269.9778269.9778
14269.9778269.9778269.9778269.9778269.9778269.9778
15269.9778269.9778269.9778269.9778269.9778269.9778
16269.9778269.9778269.9778269.9778269.9778269.9778
17269.9778269.9778269.9778269.9778269.9778269.9778
18269.9778269.9778269.9778269.9778269.9778269.9778
19269.9778269.9778269.9778269.9778269.9778269.9778
20269.9778269.9778269.9778269.9778269.9778269.9778
21269.9778269.9778269.9778269.9778269.9778269.9778
22269.9778269.9778269.9778269.9778269.9778269.9778
23 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
24269.9778269.9778269.9778269.9778269.9778269.9778
25269.9778269.9778269.9778269.9778269.9778269.9778
26269.9778269.9778269.9778269.9778269.9778269.9778
27269.9778269.9778269.9778269.9778269.9778269.9778
28269.9778269.9778269.9778269.9778269.9778269.9778
29 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
30269.9778269.9778269.9778269.9778269.9778269.9778
31269.9778269.9778269.9778269.9778269.9778269.9778
32269.9778269.9778269.9778269.9778269.9778269.9778
33269.9778269.9778269.9778269.9778269.9778269.9778
34269.9778269.9778269.9778269.9778269.9778269.9778
35 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964
36269.9778269.9778269.9778269.9778269.9778269.9778
37269.9778269.9778269.9778269.9778269.9778269.9778
38269.9778269.9778269.9778269.9778269.9778269.9778
39269.9778269.9778269.9778269.9778269.9778269.9778
40269.9778269.9778269.9778269.9778269.9778269.9778
41269.9778269.9778269.9778269.9778269.9778269.9778
42269.9778269.9778269.9778269.9778269.9778269.9778
43269.9778269.9778269.9778269.9778269.9778269.9778
44269.9778269.9778269.9778269.9778269.9778269.9778
45269.9778269.9778269.9778269.9778269.9778269.9778
46269.9778269.9778269.9778269.9778269.9778269.9778
47 37.1219 37.1219 37.1219 37.1219 37.1219 37.1219
48269.9778269.9778269.9778269.9778269.9778269.9778
49269.9778269.9778269.9778269.9778269.9778269.9778
50269.9778269.9778269.9778269.9778269.9778269.9778
51269.9778269.9778269.9778269.9778269.9778269.9778
52 18.898418.8984 18.898418.8984 18.898418.8984
53269.9778269.9778269.9778269.9778269.9778269.9778
54269.9778269.9778269.9778269.9778269.9778269.9778


McCormick Creek


245












55269.9778269.9778269.9778269.9778269.9778269.9778
56269.9778269.9778269.9778269.9778269.9778269.9778
57269.9778269.9778269.9778269.9778269.9778269.9778
58269.9778269.9778269.9778269.9778269.9778269.9778
59269.9778269.9778269.9778269.9778269.9778269.9778
60269.9778269.9778269.9778269.9778269.9778269.9778
61269.9778269.9778269.9778269.9778269.9778269.9778
62269.9778269.9778269.9778269.9778269.9778269.9778
63269.9778269.9778269.9778269.9778269.9778269.9778
64269.9778269.9778269.9778269.9778269.9778269.9778
65269.9778269.9778269.9778269.9778269.9778269.9778
66269.9778269.9778269.9778269.9778269.9778269.9778
67809.9334809.9334809.9334809.9334809.9334809.9334
68269.9778269.9778269.9778269.9778269.9778269.9778
69269.9778269.9778269.9778269.9778269.9778269.9778
70269.9778269.9778269.9778269.9778269.9778269.9778
71269.9778269.9778269.9778269.9778269.9778269.9778
72269.9778269.9778269.9778269.9778269.9778269.9778
73269.9778269.9778269.9778269.9778269.9778269.9778
74 11.8790 11.8790 11.8790 11.8790 11.8790 11.8790
75269.9778269.9778269.9778269.9778269.9778269.9778
76269.9778269.9778269.9778269.9778269.9778269.9778
77269.9778269.9778269.9778269.9778269.9778269.9778
78269.9778269.9778269.9778269.9778269.9778269.9778
79269.9778269.9778269.9778269.9778269.9778269.9778
80269.9778269.9778269.9778269.9778269.9778269.9778
81 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978
82269.9778269.9778269.9778269.9778269.9778269.9778
83269.9778269.9778269.9778269.9778269.9778269.9778
84269.9778269.9778269.9778269.9778269.9778269.9778
85269.9778269.9778269.9778269.9778269.9778269.9778
86269.9778269.9778269.9778269.9778269.9778269.9778
87269.9778269.9778269.9778269.9778269.9778269.9778
88269.9778269.9778269.9778269.9778269.9778269.9778
89269.9778269.9778269.9778269.9778269.9778269.9778
90269.9778269.9778269.9778269.9778269.9778269.9778
91269.9778269.9778269.9778269.9778269.9778269.9778
92269.9778269.9778269.9778269.9778269.9778269.9778
93269.9778269.9778269.9778269.9778269.9778269.9778
94269.9778269.9778269.9778269.9778269.9778269.9778
95269.9778269.9778269.9778269.9778269.9778269.9778
96269.9778269.9778269.9778269.9778269.9778269.9778
97269.9778269.9778269.9778269.9778269.9778269.9778
98269.9778269.9778269.9778269.9778269.9778269.9778
99269.9778269.9778269.9778269.9778269.9778269.9778
100269.9778269.9778269.9778269.9778269.9778269.9778
101269.9778269.9778269.9778269.9778269.9778269.9778
102269.9778269.9778269.9778269.9778269.9778269.9778
103269.9778269.9778269.9778269.9778269.9778269.9778
104269.9778269.9778269.9778269.9778269.9778269.9778
105269.9778269.9778269.9778269.9778269.9778269.9778
106269.9778269.9778269.9778269.9778269.9778269.9778
107269.9778269.9778269.9778269.9778269.9778269.9778
108269.9778269.9778269.9778269.9778269.9778269.9778
109 40.4967 40.4967 40.4967 40.4967 40.4967 40.4967
110269.9778269.9778269.9778269.9778269.9778269.9778
111269.9778269.9778269.9778269.9778269.9778269.9778
112269.9778269.9778269.9778269.9778269.9778269.9778
113269.9778269.9778269.9778269.9778269.9778269.9778
114269.9778269.9778269.9778269.9778269.9778269.9778
115269.9778269.9778269.9778269.9778269.9778269.9778
116269.9778269.9778269.9778269.9778269.9778269.9778
117269.9778269.9778269.9778269.9778269.9778269.9778
118269.9778269.9778269.9778269.9778269.9778269.9778
119269.9778269.9778269.9778269.9778269.9778269.9778
120 10.7991 10.7991 10.7991 10.7991 10.7991 10.7991
121 16.1987 16.1987 16.1987 16.1987 16.1987 16.1987
122269.9778269.9778269.9778269.9778269.9778269.9778
123269.9778269.9778269.9778269.9778269.9778269.9778
124 8.0993 8.0993 8.0993 8.0993 8.0993 8.0993


Taylor River






East Creek





























Trout Creek










Shell Creek
Stllwater Creek


Orgeon Creek


246












2 125269.9778269.9778269.9778269.9778269.9778269.9778
2 126 56.6953 56.6953 56.6953 56.6953 56.6953 56.6953
2 127269.9778269.9778269.9778269.9778269.9778269.9778
2 128 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978
1 1 -0.12 10. 1.0 RS11 Bar nit
1 2 0.03 10. 1.0
1 3 -0.12 10. 1.0
1 4 0.03 10. 1.0
1 5 -0.12 10. 1.0
1 6 0.03 10. 1.0
1 7 -0.12 10. 1.0
1 8 1.52 10. 0.08
1 9 -0.12 10. 1.0
1 10 0.03 10. 1.0
1 11 -0.12 10. 1.0
1 12 -0.12 10. 1.0
1 13 0.03 10. 1.0
1 14 -0.12 10. 1.0
1 15 1.52 10. 0.05
1 16 0.03 10. 1.0
1 17 -0.12 10. 1.0
1 18 0.03 10. 1.0
1 19 -0.12 10. 1.0
1 20 1.52 10. 0.080
1 21 0.03 10. 1.0
1 22 -0.12 10. 1.0
1 23 0.03 10. 1.0
1 24 -0.12 10. 1.0
1 25 0.03 10. 1.0
1 26 -0.12 10. 1.0
1 27 0.03 10. 1.0
1 28 -0.12 10. 1.0
1 29 0.03 10. 1.0
1 30 -0.12 10. 1.0
1 31 0.03 10. 1.0
1 32 1.52 10. 0.080
1 33 -0.12 10. 1.0
1 34 0.03 10. 1.0
1 35 1.52 10. 0.080
1 36 0.03 10. 1.0
1 37 -0.12 10. 1.0
1 38 0.03 10. 1.0
1 39 -0.12 10. 1.0
1 40 0.03 10. 1.0
1 41 -0.12 10. 1.0
1 42 0.03 10. 1.0
1 43 -0.12 10. 1.0
1 44 0.03 10. 1.0
1 45 -0.01 10. 1.0
1 46 -0.15 10. 1.0
1 47 -0.30 10. 1.0
1 48 1.52 10. 0.080
1 49 -0.15 10. 1.0
1 50 -0.30 10. 1.0
1 51 -0.15 10. 1.0
1 52 -0.30 10. 1.0
1 53 -0.15 10. 1.0
1 54 -0.30 10. 1.0
1 55 -0.30 10. 1.0
1 56 -0.30 10. 1.0
1 57 -0.30 10. 1.0
1 58 -0.30 10. 1.0
1 59 -0.30 10. 1.0
1 60 -0.30 10. 1.0
1 61 -0.30 10. 1.0
1 62 -0.30 10. 1.0
1 63 -0.30 10. 1.0
1 64 -0.30 10. 1.0
1 65 -0.30 10. 1.0
1 66 -0.30 10. 1.0


West Highway Creek

East Highway Creek


Alligator Creek


247












1 67 -0.30
1 68 -0.30
1 69 -0.30
1 70 -0.30
1 71 -0.30
1 72 -0.30
1 73 -0.30
1 74 -0.30
1 75 1.52
1 76 -0.30
1 77 -0.30
1 78 -0.30
1 79 -0.30
1 80 -0.30
1 81 -0.30
1 82 -0.15
1 83 -0.30
1 84 -0.15
1 85 -0.30
1 86 -0.15
1 87 -0.30
1 88 -0.15
1 89 -0.30
1 90 -0.15
1 91 -0.30
1 92 -0.15
1 93 -0.30
1 94 -0.15
2 1 1.22
2 2 1.22
2 3 1.22
2 4 1.22
2 5 1.22
2 6 1.0
2 7 0.30
2 8 0.03
2 9 -0.12
2 10 0.03
2 11 -0.12
2 12 0.03
2 13 -0.12
2 14 0.03
2 15 -0.12
2 16 0.03
2 17 -0.12
2 18 0.03
2 19 -0.12
2 20 0.03
2 21 -0.12
2 22 0.03
2 23 1.52
2 24 -0.12
2 25 0.03
2 26 -0.12
2 27 0.03
2 28 -0.12
2 29 1.52
2 30 0.03
2 31 -0.12
2 32 0.03
2 33 -0.12
2 34 0.03
2 35 1.52
2 36 -0.12
2 37 0.03
2 38 -0.12
2 39 0.03
2 40 -0.12
2 41 0.03
2 42 -0.12


10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 0.040
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 0.080
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 0.080
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 0.080
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0
10. 1.0


Mud Creek


248












2 43 0.03 10. 1.0
2 44 -0.12 10. 1.0
2 45 0.03 10. 1.0
2 46 -0.12 10. 1.0
2 47 1.52 10. 0.055 McCormick
2 48 0.03 10. 1.0
2 49 -0.12 10. 1.0
2 50 0.03 10. 1.0
2 51 -0.12 10. 1.0
2 52 1.52 10. 0.020
2 53 -0.12 10. 1.0
2 54 0.03 10. 1.0
2 55 -0.12 10. 1.0
2 56 0.03 10. 1.0
2 57 -0.12 10. 1.0
2 58 0.03 10. 1.0
2 59 -0.3 10. 1.0
2 60 -0.15 10. 1.0
2 61 -0.30 10. 1.0
2 62 -0.15 10. 1.0
2 63 -0.30 10. 1.0
2 64 -0.15 10. 1.0
2 65 -0.30 10. 1.0
2 66 -0.15 10. 1.0
2 67 -0.30 10. 1.0
2 68 -0.30 10. 1.0
2 69 -0.30 10. 1.0
2 70 -0.30 10. 1.0
2 71 -0.30 10. 1.0
2 72 -0.30 10. 1.0
2 73 -0.30 10. 1.0
2 74 1.52 10. 0.022 Taylor
2 75 -0.30 10. 1.0
2 76 -0.30 10. 1.0
2 77 -0.30 10. 1.0
2 78 -0.30 10. 1.0
2 79 -0.30 10. 1.0
2 80 -0.30 10. 1.0
2 81 1.52 10. 0.040 East
2 82 -0.30 10. 1.0
2 83 -0.30 10. 1.0
2 84 -0.30 10. 1.0
2 85 -0.30 10. 1.0
2 86 -0.30 10. 1.0
2 87 -0.30 10. 1.0
2 88 -0.30 10. 1.0
2 89 -0.30 10. 1.0
2 90 -0.30 10. 1.0
2 91 -0.30 10. 1.0
2 92 -0.30 10. 1.0
2 93 -0.30 10. 1.0
2 94 -0.30 10. 1.0
2 95 -0.30 10. 1.0
2 96 -0.15 10. 1.0
2 97 -0.30 10. 1.0
2 98 -0.15 10. 1.0
2 99 -0.30 10. 1.0
2 100 -0.15 10. 1.0
2 101 -0.30 10. 1.0
2 102 -0.15 10. 1.0
2 103 -0.30 10. 1.0
2 104 -0.15 10. 1.0
2 105 -0.30 10. 1.0
2 106 -0.15 10. 1.0
2 107 -0.30 10. 1.0
2 108 -0.15 10. 1.0
2 109 1.52 10. 0.120 Trout Creek
2 110 -0.30 10. 1.0
2 111 -0.15 10. 1.0
2 112 -0.30 10. 1.0


249












2 113 -0.15 10. 1.0
2 114 -0.30 10. 1.0
2 115 -0.15 10. 1.0
2 116 -0.30 10. 1.0
2 117 -0.15 10. 1.0
2 118 -0.30 10. 1.0
2 119 -0.1 10. 1.0
2 120 1.52 10. 0.020 Shell Creek
2 121 1.52 10. 0.030 Stillwater Creek
2 122 -0.1 10. 1.0
2 123 -0.1 10. 1.0
2 124 1.52 10. 0.015 Oregon Creek
2 125 -0.1 10. 1.0
2 126 1.52 10. 0.070 West Highway
Creek
2 127 -0.1 10. 1.0
2 128 1.52 10. 0.050 East Highway
Creek
15 1 15 1 20 60.0SOUTHWEST SHORE SOUTHWEST CORNER RS12 1
28 2 178 10 60.0SOUTHWEST CORNER SOUTH OF TAYLOR RS12 2
3 8 79 1137 10 60.0SOUTH OF TAYLOR SOUTHEAST CORNER RS12 3
4714440144380 60.0CULVERTSATUS1 RS12 4
5711869118850 60.0GW INTERACTION WITH C-111 RS12 5
65254425690 60.0CULVERTS ON WEST SIDE RS12 6
76307247720 60.0FROMP46TOCY3 RS12 7
86487268720 60.0FROM CY3TO P67 RS12 8
1 0.200 15.0 40.0 0.0182 RS13 1
2 0.200 15.0 40.0 0.0143 RS13 2
3 0.200 15.0 40.0 0.0048 RS13 3
4 0.200 15.0 3.6 0.0064 RS13 4
5 0.200 15.0 0.0 0.0053 RS13 5
6 0.200 15.0 0.0 0.004 RS13 6
7 0.200 15.0 0.0 0.004 RS13 7
8 0.200 15.0 0.0 0.004 RS13 8
1 0.200 15.0 40.0 0.0182 RS14 1
2 0.200 15.0 40.0 0.0143 RS14 2
3 0.200 15.0 40.0 0.0048 RS14 3
4 0.200 15.0 3.6 0.0064 RS14 4
5 0.200 15.0 0.0 0.0053 RS14 5
6 0.200 15.0 0.0 0.004 RS14 6
7 0.200 15.0 0.0 0.004 RS14 7
8 0.200 15.0 0.0 0.004 RS14 8
1 5.01 salinity RS20_1
2 0.005 TP:TSB water mg/L=g/m3=ppm RS20_2
1 RS21 1
2 RS21 2
1 0.01 0.10 0.20 0.5 1.0 2.0 5.0 RS22 1
2 0.01 0.10 0.20 0.5 1.0 2.0 5.0 RS22 2
0.01 0.10 0.20 0.5 1.0 2.0 5.0 RS23
1.0 2.0 5. 10. 50. 100. 200. 500. 1000. RS24
-0.5 -0.2 -0.1 -0.05 0.001 0.1 0.2 0.5 1.0 RS25
0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.2 1.3
1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.7 0.9 1.0 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.4 1.5 1.2 1.0 0.8 0.6
0.8 1.0 1.2 1.5 1.4 1.4 1.3 1.2 1.2 1.2 1.2 0.9 0.8 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6
0.6 0.7 0.9 1.0 1.1 1.2 1.4 1.5 1.7 1.8 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.3
1.2 1.0 0.9 0.8 0.7 0.6 0.5 0.7 0.9 0.9 1.0 1.1 1.1 1.2 1.2 1.2 1.2 1.3 1.4 1.2 0.9 0.7 0.6
1.3 1.3 1.5 1.5 1.4 1.4 1.3 1.2 1.2 1.2 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6
0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.9 1.9 1.8 1.9
1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9
1.9 1.9 1.9 1.9 1.9 1.9 0.1 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2
1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.7 0.8 0.8 0.7 1.0 1.1 1.1 1.1 1.1 1.2 1.4 1.3 1.3 1.0 0.7 0.6
1.0 1.0 1.0 1.0 1.1 1.0 0.9 0.8 0.7 1.0 1.0 0.9 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.8 1.8 1.7 1.8
1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9


250












1.9 1.8 1.8 1.8 1.8 0.1 0.1 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 0.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.1 1.2
1.1 0.9 0.8 0.7 0.7 0.6 0.5 0.6 0.8 0.7 -0.1 0.9 1.0 1.0 1.1 1.1 1.1 1.2 1.2 1.0 1.0 0.6 0.6
1.0 1.0 1.0 1.0 1.1 1.2 1.2 0.1 0.7 0.8 0.9 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.0 1.0 0.1 0.4 0.5
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.8
1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 0.2 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.1
1.1 0.9 0.7 0.7 0.6 0.5 0.5 0.6 0.8 0.6 0.1 0.2 0.9 1.0 1.0 1.0 1.0 1.1 1.1 1.0 0.5 0.6 0.6
0.6 0.7 1.0 0.9 1.0 1.1 1.0 0.9 1.0 0.7 0.7 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.1 0.2
0.1 -0.2 0.6 0.6 1.0 1.2 1.3 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.6 1.7
1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.1 1.7 1.7 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8
1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 0.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.1
1.0 -0.2 0.7 0.6 0.6 0.5 0.5 0.6 0.7 0.6 0.6 0.1 0.9 0.9 0.9 0.9 0.9 1.1 1.0 0.4 0.1 0.1 0.1
0.1 0.1 0.1 0.7 1.0 1.0 1.0 0.7 1.0 0.1 1.0 1.0 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.0 1.0 0.7 0.6
0.1 0.0 0.4 0.4 0.8 1.2 1.2 1.4 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 0.1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 0.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 1.0
1.0 -0.2 0.6 0.6 0.5 0.5 0.5 0.6 0.7 0.5 0.6 -0.1 0.8 0.8 0.9 0.8 0.8 1.0 0.4 0.1 0.1 0.1 0.1
0.1 0.1 0.1 0.7 0.8 0.9 0.9 1.0 0.1 0.1 1.0 1.0 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.1 1.0 1.0 0.4
0.4 0.1 0.1 0.1 0.4 1.1 1.2 1.4 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 0.1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.7 0.1 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 0.1 0.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9 0.9
0.9 -0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.5 -0.4 -0.2 0.8 0.8 0.8 0.7 0.7 0.2 0.1 0.1 0.1 0.2 0.5
0.7 0.7 0.7 0.8 0.7 1.5 1.5 0.1 0.1 0.1 0.9 0.9 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.0
0.4 0.4 0.0 0.4 1.0 1.1 1.2 1.4 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 0.1 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.9
0.9 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.4 0.1 0.6 0.7 0.7 0.7 0.6 0.1 0.1 0.2 0.1 0.7 0.7 0.7
0.7 0.8 0.7 0.1 0.0 1.5 1.5 0.4 0.2 0.1 0.1 0.1 1.0 1.0 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.1
1.0 0.5 0.5 -0.1 1.0 1.1 1.2 1.3 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 0.1 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.8 0.8
0.8 -0.2 0.4 0.5 0.4 0.4 0.4 0.5 0.6 0.3 0.0 0.6 0.6 0.6 0.6 0.6 0.0 0.1 0.1 0.1 0.7 0.7 0.7
0.7 0.8 0.7 0.1 0.2 1.5 1.5 0.2 0.1 0.1 0.1 0.1 0.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1
1.1 1.0 1.0 -0.1 -0.1 1.1 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 0.0 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7
1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 0.1 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.8
0.8 -0.2 0.0 0.4 0.4 0.4 0.4 0.5 0.6 0.3 0.0 0.6 0.6 0.6 0.6 0.1 0.1 0.1 0.1 0.6 0.7 0.6 0.6
0.4 0.8 0.7 0.6 0.2 1.5 1.5 0.4 0.1 0.1 0.1 0.1 0.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1.1 1.1 1.1 1.0 -0.1 1.2 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4
1.3 1.3 0.9 1.5 1.5 1.5 -0.1 1.5 1.5 1.6 1.6 1.6 1.6 1.6 0.2 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 0.1 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 -0.2 0.4 0.4 0.6 0.6 0.6 0.7 0.7
0.7 0.6 0.1 0.4 0.4 0.4 0.4 0.5 0.6 -0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.6 0.7 0.7 0.1
1.5 1.5 0.7 0.4 0.1 0.2 0.4 0.2 0.1 0.0 0.1 0.1 0.1 1.2 1.1 1.1 1.1 1.2 1.1 1.0 1.0 1.0 1.5
1.5 1.0 1.0 1.0 0.0 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.3 1.2
1.1 1.0 -0.1 0.9 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 0.2 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 0.7 -0.1 0.1 0.0 -0.1 0.4 0.6 0.6 0.7
0.7 0.5 -0.1 0.0 0.1 0.1 -0.2 -0.2 -0.1 0.0 0.0 -0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.0 0.1 0.4 0.1 0.1
1.5 1.5 0.7 0.0 -0.1 -0.1 0.1 0.1 -0.1 0.3 0.2 0.2 -0.1 0.0 1.0 1.1 1.1 1.1 0.9 0.1 1.0 1.0 1.5
1.5 1.0 1.0 1.0 0.1 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.2 0.0
0.0 0.0 0.0 0.9 1.4 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6


251












1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 -99.9 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.7 -0.1 0.0 0.9 0.1 0.1 0.3 0.1 0.6 0.6
0.6 0.5 -0.3 0.0 0.1 0.9 1.5 1.5 1.5 1.5 1.5 0.3 0.4 0.4 0.3 0.2 0.1 0.1 0.1 0.1 0.7 0.8 0.8
1.5 1.5 0.1 0.0 0.0 0.1 0.1 0.2 0.3 0.3 0.3 0.2 0.0 -0.1 -0.1 1.0 1.0 1.1 1.1 0.1 0.1 0.9 1.5
1.5 0.7 1.0 0.1 0.1 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 0.0 0.0
0.0 -0.1 -0.1 1.0 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6
1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.7 -0.2 -0.1 0.1 0.1 1.5 1.5 1.5 1.5 0.1 0.6
0.6 0.4 0.4 0.0 0.1 0.9 1.5 1.5 1.5 1.5 1.5 0.9 0.9 0.9 0.9 0.1 0.1 0.1 0.1 0.1 0.4 1.5 1.5
1.5 1.5 0.6 0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.0 1.0 1.1 0.0 0.1 0.9 1.5
1.5 0.0 0.0 0.1 0.1 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 -0.1 -0.1 -
0.1 0.0 0.0 1.0 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 -0.1 -0.1 0.1 0.1 0.0 1.5 1.5 1.5 1.5 0.6 0.6
0.6 0.6 1.5 1.5 1.5 1.5 1.5 1.5 0.1 1.5 1.5 0.9 0.6 0.9 0.6 0.1 0.1 0.1 0.1 0.4 0.5 1.5 1.5
0.1 1.5 1.5 1.5 1.5 0.3 0.1 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.2 0.1 0.1 1.0 0.0 0.1 0.0 0.1
0.1 0.1 0.1 0.1 0.1 0.1 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 -0.1 0.0 1.0
1.0 1.1 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4
1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 -
99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 0.0 0.1 -0.1 -0.1 -0.1 -0.1 0.0 -0.1 -0.2 -0.2 -0.2 0.1 0.1 0.1 0.1 0.2 0.3 0.3 0.3 0.6 0.6
0.6 0.6 1.5 1.5 1.5 1.5 1.5 1.5 0.1 1.5 1.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.7 0.8 1.5 1.5 1.5
1.5 1.5 1.5 1.5 1.5 0.9 0.0 0.2 0.5 0.2 0.4 0.4 0.5 0.3 0.4 0.4 0.3 0.1 0.2 0.2 0.2 0.2 0.1
0.1 0.9 0.1 0.1 0.1 0.1 0.0 -0.1 -0.1 0.0 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
1.3 1.3 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3
1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.2 -0.2 -0.2 -0.1 -0.2 -0.2 -0.3 -0.3 -0.2 -0.1 -0.1 0.0 0.0 0.1 0.1 0.2 0.1 0.0 0.0 0.3 0.6 0.6
0.6 0.6 0.6 0.6 -0.1 0.3 0.4 0.1 0.0 1.5 1.5 0.1 0.0 0.0 0.1 0.1 0.9 0.9 0.9 0.9 1.5 1.5 1.5
1.5 0.9 0.9 1.5 1.2 0.9 0.1 0.0 0.5 0.6 0.5 0.5 0.4 0.4 0.4 0.5 0.7 0.5 0.5 0.4 0.4 0.2 0.1
0.1 1.0 1.0 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.2 -0.1 -0.1 -0.1 -0.1 1.2 1.2 1.2 1.2
1.2 1.1 1.1 1.1 1.2 1.2 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3
1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 -0.1 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 0.9
-0.4 -0.3 -0.2 -0.1 -0.1 -0.1 0.0 0.0 0.0 1.5 1.5 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.9 0.9 0.8 0.7 0.1
0.9 0.9 0.1 0.0 0.9 0.9 0.9 0.1 0.3 0.5 0.4 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.3 0.2 0.2
0.1 -0.1 1.0 1.1 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.0 -0.1 -0.1 -0.1 -0.1 0.0 0.0 1.0 1.1 1.1 1.1
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2
1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.1 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.1 -0.1 -0.1 -0.4
-0.4 -0.3 -0.2 -0.1 -0.1 -0.1 -0.1 0.0 0.0 1.5 1.5 -0.1 0.0 0.0 0.0 0.0 0.0 0.6 0.1 0.2 0.1 0.1 0.1
0.1 0.1 0.1 0.7 0.9 0.9 0.9 0.9 0.2 0.4 0.3 0.2 0.3 0.4 0.4 0.3 0.2 0.2 0.4 0.4 0.2 0.2 0.2
0.1 0.0 0.1 0.1 1.0 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.3 1.2 1.2 1.1 1.1 1.0 0.0 0.1 1.0 1.0 1.0
1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.0 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.2 0.5 0.4 0.4 1.2 1.2 1.2
1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.2 1.2
1.2 1.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
-0.2 -0.1 -0.1 -0.1 0.1 0.0 -0.1 -0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.0 -0.1 -0.2 -0.2
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 0.1 0.1 0.1
0.9 0.1 0.1 1.0 1.0 0.9 0.9 0.2 0.1 0.3 0.3 0.3 0.4 0.5 0.2 0.2 0.1 0.1 0.4 0.3 0.1 0.0 0.0
0.2 0.4 0.2 0.1 1.2 1.2 1.2 1.5 1.5 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 0.2 0.2 1.0 1.1
1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.3 0.3 1.2
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1
1.1 1.1 1.0 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.1 0.1 0.1 0.0 -0.1 -0.1 -0.1 -0.1 0.1 0.0 0.0 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 -0.1 -0.3 -0.2 -0.1
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 0.0 -0.1 0.1 0.1 0.0
0.1 0.1 1.0 1.0 0.9 0.9 0.9 0.2 0.3 0.2 0.5 0.5 0.3 0.3 0.2 0.2 0.3 0.5 0.7 0.5 0.3 0.0 0.2
0.2 0.2 0.2 0.1 0.1 0.9 0.0 1.5 1.5 1.1 1.2 1.3 1.3 1.4 1.4 1.3 1.3 1.2 1.2 1.1 0.4 0.4 0.3
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.4 1.2 1.2
1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.2 1.2
1.1 1.1 1.0 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.0 0.0 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0
1.5 1.5 0.1 0.0 1.5 1.5 0.9 0.7 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.9 0.9 -0.1 -0.1 -0.1 0.0 0.1 0.9 0.9
0.9 0.9 0.9 0.9 0.9 0.2 0.2 0.2 0.2 0.3 0.4 0.4 0.2 0.4 0.2 0.2 0.2 0.4 0.5 0.5 0.5 0.4 0.2
0.3 0.4 0.2 0.2 0.2 0.2 0.2 1.5 1.5 0.1 -0.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.1 1.1 0.2 0.9 0.9
0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 0.4 1.0 1.1 1.1


252












1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 0.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.0 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.2 -0.2 -0.1 -0.1 -0.1 0.1 0.0
1.5 1.5 0.9 0.9 1.5 1.5 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 -0.1 0.0 0.9 0.9 0.9 0.0 0.4 0.9 0.9 0.9 0.9
0.9 0.9 0.9 0.9 0.1 0.2 0.2 0.2 0.1 0.3 0.4 0.5 0.4 0.4 0.3 0.2 0.2 0.5 0.5 0.5 0.5 0.4 0.3
0.3 0.5 0.2 0.2 0.3 0.4 0.3 1.5 1.5 0.1 -0.1 0.1 1.0 0.2 1.5 1.5 1.1 1.1 1.1 1.1 0.3 0.9 0.9
0.0 1.0 1.0 1.0 1.0 1.0 0.9 0.0 0.1 0.0 0.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1
1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0
1.0 1.0 0.2 0.2 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.1 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.1 0.0 0.1 0.3 0.0
1.5 1.5 0.0 0.9 1.5 1.5 1.5 -0.1 -0.2 -0.2 -0.4 -0.1 0.4 0.9 0.0 0.0 0.9 0.2 0.1 0.9 0.9 0.9 1.0
0.9 0.9 0.9 0.1 0.1 0.2 0.2 0.3 0.1 0.3 0.4 0.5 0.9 0.5 0.4 0.4 0.5 0.9 0.3 0.3 0.3 0.1 0.2
0.2 0.2 0.1 0.2 0.5 0.7 0.3 0.3 0.9 0.3 0.1 0.1 0.2 0.2 1.5 1.5 1.0 1.0 1.0 1.0 0.4 0.3 0.9
0.2 0.2 1.0 1.0 1.0 1.0 0.1 0.0 0.1 0.0 0.1 0.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.1
1.1 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0
1.0 1.0 0.2 0.2 0.2 1.0 -99.9 -99.9 -99.9 -99.9
-99.9 -0.2 -0.1 -0.1 0.0 0.0 -0.1 -0.1 0.0 -0.1 -0.1 -0.1 -0.1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.4 0.3
1.5 1.5 0.9 -0.1 1.5 1.5 1.5 0.9 0.9 0.6 0.6 0.7 0.7 0.5 0.2 0.1 0.2 0.2 0.0 0.2 0.9 0.9 0.9
0.9 0.9 0.9 -0.1 0.1 0.2 0.3 0.4 0.5 0.2 0.2 0.3 0.4 0.5 0.4 0.4 0.5 -0.1 0.5 0.5 0.4 0.2 0.2
0.2 0.2 0.2 0.4 0.4 0.3 0.4 0.4 0.3 0.4 0.4 0.3 0.3 0.4 1.5 1.5 0.4 0.4 0.4 1.0 0.4 0.3 0.6
0.3 0.2 0.0 0.0 1.0 1.0 0.0 1.0 1.0 0.0 0.1 0.2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.4 1.0 1.1 1.1
1.1 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.0 0.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
1.0 0.2 1.0 1.0 1.0 1.0 1.0 -99.9 -99.9 -99.9
-99.9 -99.9 0.0 0.0 0.0 0.0 0.0 -0.1 0.9 0.9 0.9 0.6 0.9 0.9 0.9 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9
0.9 0.9 0.9 -0.1 -0.1 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 0.7 0.4 0.2 0.4 0.4 0.2 0.1 0.7 0.9 0.9
0.9 0.0 -0.1 0.0 0.2 0.1 0.3 0.4 0.4 0.4 0.4 0.4 0.3 0.5 0.5 0.5 0.4 0.3 0.4 0.3 0.2 0.1 0.4
0.4 0.4 0.4 0.4 0.5 0.6 0.3 0.9 0.4 0.3 0.3 0.6 0.3 0.4 1.5 1.5 0.4 0.4 0.4 0.5 0.4 0.9 0.9
0.9 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 0.1 0.1 0.2 1.0 1.0 1.0 1.0 1.0 1.0 0.5 1.0 1.0 1.1 1.1
1.1 1.1 1.1 1.1 1.2 1.0 1.0 1.0 0.1 0.1 1.0 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.1 0.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 -99.9
-99.9 -99.9 -99.9 0.1 0.0 0.0 0.0 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.1 1.1 1.2 1.1 1.1 1.1 1.0 1.0
0.9 0.9 0.9 0.9 -0.1 -0.1 0.9 0.9 0.9 1.0 1.0 1.0 0.9 0.9 0.9 0.3 0.3 0.4 0.4 0.4 0.2 0.1 0.1
0.9 0.9 0.1 0.0 0.0 0.3 0.2 0.3 0.3 0.3 0.5 0.5 0.5 0.5 0.6 0.7 0.6 0.5 0.5 0.5 0.4 0.3 0.3
0.5 0.5 0.5 0.6 0.5 0.7 0.8 1.1 0.6 0.5 0.4 0.4 0.6 0.4 0.9 0.9 0.9 0.5 0.4 0.3 0.4 0.4 0.9
0.9 0.9 1.5 1.5 1.5 1.5 1.0 1.0 1.0 1.0 1.0 0.1 0.1 1.0 1.0 1.0 1.0 0.3 0.3 0.5 1.0 1.0 1.1
1.1 1.1 1.1 1.1 1.1 1.1 1.0 0.2 0.1 0.1 0.1 0.9 1.5 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.1 0.1 1.1 1.1 1.1 1.1 1.2 1.2 1.1 1.1 1.1
-99.9 -99.9 -99.9 -99.9 -99.9 0.0 0.0 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9
0.9 0.9 0.1 0.1 -0.1 -0.1 -0.1 0.0 0.9 0.3 0.4 0.4 0.5 0.7 0.9 0.1 0.5 0.4 0.4 0.5 0.2 0.2 0.1
0.0 0.2 0.2 0.1 0.9 0.3 0.3 0.3 0.3 0.4 0.5 0.5 0.6 0.8 0.8 0.8 0.8 0.8 0.7 0.5 0.5 0.6 0.4
0.8 0.7 0.6 0.8 0.6 0.9 1.1 1.2 1.0 0.5 0.4 0.3 0.3 0.9 0.9 0.9 0.9 0.4 0.3 0.3 0.5 0.9 0.9
0.9 0.9 0.9 0.0 0.7 0.7 1.0 1.0 1.0 1.0 1.0 0.1 0.7 1.0 1.0 1.0 0.4 0.4 0.3 1.0 1.0 1.0 1.1
0.6 1.1 1.1 1.1 1.1 1.1 1.0 0.2 0.1 0.9 0.9 0.6 1.5 1.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.1 0.0
0.1 1.1 1.1 1.1 1.2 1.2 1.2 1.1 1.1 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.1 0.0 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9
0.9 0.1 0.1 0.1 0.3 0.2 0.1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.3 0.5 0.3 0.3 0.3 0.2 0.1 0.1
0.0 0.5 0.4 0.2 0.2 0.4 0.4 0.3 0.2 0.8 0.5 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.2 0.1 0.3 0.4 0.8
0.5 0.5 0.6 0.6 0.6 0.6 0.4 0.4 0.5 0.4 0.3 0.2 0.6 0.9 0.9 0.9 0.2 0.2 0.4 0.9 0.7 0.9 0.3
0.9 0.2 0.1 0.9 1.1 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.2 0.2 1.0 1.0 0.3 0.4 0.3 1.0 1.0 1.5 1.5
1.0 1.0 1.0 1.0 1.1 1.1 0.1 0.2 0.1 0.1 0.1 0.1 1.5 1.5 0.1 0.4 1.0 0.1 0.1 0.1 0.1 0.1 0.0
1.0 1.1 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.0 0.0 0.0 0.0 0.1 -0.1 0.0 0.9 0.2 0.3 0.3 0.2 0.9
0.2 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.7 0.0 0.1 0.1 0.1 0.2 0.4 0.4 0.4 0.3 0.1 0.3 0.2 0.2
0.2 0.4 0.3 0.2 0.2 0.2 0.4 0.4 0.3 0.5 0.2 0.4 0.4 0.2 0.4 0.4 0.4 0.3 -0.1 0.2 0.3 0.3 0.4
0.5 0.4 0.3 0.4 0.4 0.6 0.6 0.6 0.4 0.4 0.3 0.0 0.1 0.2 0.2 0.2 0.2 0.3 0.4 0.5 0.9 0.9 0.3
0.2 0.1 0.1 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.1 0.5 0.1 0.2 0.2 0.4 0.3 0.4 0.4 0.4 0.7 1.5 1.5
1.0 1.0 1.0 1.0 1.1 1.0 0.2 0.4 0.1 0.1 0.2 0.4 1.5 1.5 0.9 0.1 0.1 0.1 0.1 0.0 0.1 0.0 1.0
1.1 1.2 1.3 1.4 1.4 1.4 1.3 1.2 1.1 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.1 0.1 0.0 0.0 0.0 0.1 0.3 0.3 0.3 0.3 0.3 0.3
0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.4 0.5 0.5 0.4 0.3 0.1 0.2 0.2 0.2
0.3 0.3 0.2 0.2 0.3 0.3 0.4 0.4 0.4 0.4 0.3 0.4 0.4 0.2 0.3 0.4 0.4 0.4 0.1 0.2 0.3 0.3 0.4
0.4 0.3 0.2 0.3 0.4 0.6 0.6 0.4 0.3 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.9 0.5 0.9 0.5 0.3
0.2 0.1 0.1 1.4 1.4 1.4 1.4 1.4 1.3 1.2 1.2 1.0 0.2 0.2 0.3 1.0 1.0 0.9 0.9 1.1 0.9 1.5 1.5
0.2 1.0 1.0 1.0 1.0 0.3 0.6 0.6 0.4 0.2 0.1 0.1 1.0 1.0 1.0 1.0 0.5 0.6 0.7 0.5 0.5 0.1 1.0
1.1 1.2 1.4 1.4 1.4 1.4 1.4 1.2 1.2 1.1 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.1 0.9 0.9 0.1 0.1 0.4 0.4 0.3 0.3 0.5
0.5 0.4 0.3 0.2 0.4 0.3 0.2 0.2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.7 0.5 0.4 -0.1 0.2 0.2
0.2 0.3 0.3 0.2 0.3 0.4 0.4 0.5 0.5 0.5 0.4 0.5 0.5 0.5 0.2 0.2 0.3 0.4 0.5 0.3 0.2 0.3 0.4
0.4 0.4 0.3 0.3 0.3 0.6 0.5 0.5 0.2 0.4 0.3 0.3 0.5 0.5 0.4 0.3 0.3 0.3 0.3 0.4 0.5 0.5 0.5
0.3 0.1 0.1 1.4 1.5 1.5 1.4 1.4 1.2 1.3 1.6 1.2 1.2 0.2 0.2 0.2 1.1 1.1 1.0 1.1 1.4 1.0 1.5


253












1.5 1.1 0.2 1.0 1.0 0.2 0.6 1.0 0.9 0.5 0.9 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.1 1.3 1.2 1.0 0.5
0.1 0.4 1.2 1.2 1.4 1.4 1.4 1.4 1.2 1.1 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.1 0.1 0.2 0.2 0.3 0.3 0.8
0.7 0.4 0.3 0.1 0.1 0.1 0.2 0.2 -0.1 0.6 0.5 0.5 0.7 0.6 0.6 0.6 0.5 0.5 0.3 0.2 0.4 0.2 0.1
0.1 0.1 0.3 0.5 0.5 0.5 0.4 0.4 0.5 0.5 0.4 0.5 0.4 0.2 -0.1 0.2 0.0 0.1 0.3 0.4 0.4 0.3 0.3
0.4 0.3 0.3 0.4 0.5 0.7 0.5 0.4 0.7 0.4 0.1 0.1 0.3 0.3 0.4 0.4 0.3 0.3 0.2 0.4 0.3 0.5 0.8
0.9 0.1 1.1 1.4 1.3 1.3 1.4 1.4 1.4 1.3 1.2 1.2 1.2 1.2 0.9 0.9 1.0 1.3 1.0 1.2 1.2 1.4 1.3
1.4 0.7 0.2 0.2 0.2 0.2 0.4 0.9 0.9 0.9 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.3 1.3 1.2
1.1 1.1 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.0 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.2 0.2 0.3 0.4 0.5 0.6
0.5 0.3 0.3 0.4 0.8 0.3 0.2 0.2 0.5 0.6 0.7 0.7 0.3 0.6 0.4 0.4 0.6 0.7 0.5 0.3 -0.1 0.1 0.2
0.2 0.1 0.4 0.3 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.4 0.3 0.2 0.3 0.2 0.2 0.4 0.3 0.3 0.3 0.3
0.4 0.3 0.3 0.3 0.2 0.4 0.3 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.5 0.4 0.4 0.7 0.4
0.3 0.2 1.2 1.2 1.1 1.1 1.2 1.4 1.4 1.3 1.4 1.5 1.3 1.3 1.2 1.4 1.2 1.4 1.4 1.2 1.3 1.5 1.5
1.3 0.9 0.3 0.2 0.3 0.2 0.3 0.9 0.9 0.9 0.2 0.2 0.1 1.0 1.0 1.0 0.0 1.0 1.0 1.1 1.2 1.2 1.3
1.3 1.3 1.2 1.2 0.1 0.1 0.1 0.2 0.2 0.2 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.2 0.3 0.4 0.5
0.4 0.3 0.3 0.4 0.5 0.3 0.3 0.3 0.3 0.6 0.7 0.7 0.5 0.5 0.4 0.4 0.5 0.5 0.5 0.3 0.1 0.1 0.2
0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.5 0.4 0.4 0.3 0.3 0.2 0.3 0.4 0.3 0.3 0.3 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.4 0.4 0.4 0.5 0.4
0.3 0.2 0.5 0.5 0.2 0.1 1.1 1.0 1.2 1.4 1.4 1.3 1.3 1.3 1.3 1.5 1.4 1.5 1.5 1.4 1.5 1.1 1.5
1.2 1.0 0.9 0.2 0.2 0.3 0.9 0.9 0.4 0.9 0.3 0.2 0.1 0.2 0.1 0.1 0.1 0.1 1.0 1.0 1.0 1.0 1.1
1.1 1.1 1.3 1.3 1.2 1.1 1.0 0.2 0.2 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.2 0.2 0.3 0.5
0.3 0.4 0.3 0.2 0.4 0.4 0.4 0.3 0.2 0.6 0.7 0.7 0.7 0.4 0.5 0.5 0.5 0.3 0.4 0.3 0.2 0.1 0.3
0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.4 0.4 0.4 0.3 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.4 0.3 0.3 0.3 0.4
0.4 0.2 0.3 0.3 0.2 0.1 0.1 0.2 1.2 1.2 1.3 1.4 1.2 1.2 1.2 1.4 1.5 1.5 0.9 1.1 1.2 0.8 1.2
1.0 1.2 0.9 0.2 0.3 0.3 0.9 0.9 0.5 0.4 0.3 0.9 0.2 0.2 0.2 0.2 0.2 0.9 0.1 0.1 0.1 1.0 1.1
1.1 1.2 1.2 1.3 1.3 1.2 1.1 1.0 0.2 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 0.3 0.3
0.1 0.9 0.5 0.4 0.3 0.1 0.6 0.4 0.2 0.3 0.4 0.5 0.6 0.6 0.2 0.5 0.5 0.5 0.4 0.2 0.2 0.0 0.5
0.5 0.4 0.3 0.4 0.4 0.4 0.3 -0.1 0.4 0.4 0.4 0.3 0.4 0.4 0.4 0.4 0.5 0.5 0.4 0.4 0.4 0.4 0.3
0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.5 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3
0.5 0.4 0.3 0.3 0.5 0.3 0.2 0.1 0.1 1.1 1.2 1.2 1.3 0.6 1.1 1.1 1.4 1.4 1.4 1.1 0.1 0.5 0.5
0.9 0.9 0.3 0.3 0.3 0.4 0.5 0.3 0.1 0.3 0.2 0.4 0.4 0.5 0.2 0.9 0.9 0.2 0.9 0.2 0.2 0.1 0.2
1.0 1.1 1.2 1.2 1.3 1.3 1.2 1.2 1.1 1.0 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.1 0.2 0.6 0.6 0.8 0.5 0.5 0.5 0.7 0.7 0.1 0.3 0.2 0.6 0.6 0.5 0.4 0.2 0.1 0.2 0.2 0.2 0.5
0.3 0.4 0.5 0.4 0.5 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.5 0.4 0.4 0.3
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.3
0.3 0.2 0.3 0.3 0.3 0.3 0.5 0.3 0.2 0.9 1.1 1.1 1.0 0.3 1.0 1.2 1.4 1.2 1.2 0.1 0.1 0.9 0.9
0.9 0.2 0.4 0.3 0.4 0.9 0.3 0.2 0.5 0.2 0.2 0.9 0.3 0.5 0.4 0.2 0.2 0.4 0.2 0.2 0.1 0.2 0.3
0.1 0.2 0.2 1.5 1.5 1.3 1.2 1.2 1.1 1.0 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 0.2 0.4 0.5 0.4 0.4 0.4 0.5 0.6 0.4 0.4 0.4 0.4 0.4 0.5 0.4 0.3 0.3 0.3 0.3 0.3 0.4 0.4
0.4 0.4 0.5 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.3
0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 1.0 0.2 0.4 1.0 1.1 1.1 0.3 0.3 0.3 0.2 0.1 0.1
0.2 0.2 0.3 0.4 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.5
0.9 0.9 0.2 1.5 1.5 1.1 1.0 1.0 1.0 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 -99.9 -99.9 0.3 0.3 0.2 0.2 0.3 0.4 0.2 0.5 0.5 0.5 0.2 0.4 0.4 0.3 0.3 0.5 0.3 0.3 0.5 0.4
0.3 0.3 0.4 0.5 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.1 0.1 0.2
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 1.0 1.0 0.4 0.4 0.4 0.2 0.2 0.2
0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2 0.1 0.1 0.2 0.2 0.3 0.3 0.3 0.4 0.3 0.3 0.4 0.3 0.3 0.4 0.5
0.4 0.2 0.9 1.5 1.5 0.2 0.2 1.0 1.0 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 -99.9 -99.9 -99.9 0.2 0.1 0.0 0.1 0.2 0.1 0.6 0.5 0.6 0.6 0.3 0.2 0.2 0.2 0.0 0.4 0.4 0.3 0.4
0.3 0.3 0.3 0.4 0.5 0.4 0.3 0.4 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.1 0.2 0.4 0.4 0.3 0.3
0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 -0.1 0.2 0.5 0.2 0.2 0.2 0.2
0.3 0.3 0.3 0.5 0.4 0.3 0.3 0.3 0.2 0.4 0.4 0.6 0.6 0.0 0.2 0.3 0.2 0.2 0.3 0.4 0.5 0.2 0.2
0.2 0.1 0.1 0.2 0.2 0.2 0.1 0.0 0.0 -0.1 0.1 0.2 0.2 0.3 0.4 0.2 0.2 0.2 0.4 0.2 0.3 0.4 0.9
0.3 0.2 0.1 1.5 1.5 0.9 0.2 0.4 0.4 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 -99.9 -99.9 -99.9 0.9 0.9 0.2 0.2 0.3 0.5 0.2 0.4 0.5 0.9 0.5 0.2 0.2 0.5 0.4 0.4 0.3 0.2 0.3
0.4 0.4 0.4 0.6 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.2 0.3 0.4 0.1 0.2 0.2 0.1 0.2 0.3 0.4 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2
0.3 0.2 0.4 0.3 0.2 0.2 0.3 0.3 0.3 0.4 0.5 0.4 0.3 0.2 0.3 0.5 0.5 0.5 0.4 0.5 0.4 0.3 0.2


254












0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.2 0.3 0.2 0.4 0.6 0.3 0.9 0.9 0.2 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 -99.9 -99.9 -99.9 0.9 0.9 0.5 0.4 0.4 0.2 0.4 0.5 0.5 0.5 0.5 0.3 0.2 0.4 0.4 0.4 0.3 0.3 0.4
0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.5 0.4 0.3 0.3 0.4 0.5 0.4 0.4 0.4 0.4 0.3 0.3
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
0.3 0.4 0.5 0.6 0.4 0.4 0.3 0.2 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 -99.9 -99.9 -99.9 0.9 0.9 0.7 0.5 0.4 0.2 0.4 0.5 0.5 0.4 0.5 0.3 0.3 0.4 0.4 0.4 0.3 0.3 0.4
0.4 0.4 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.3
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 0.5 0.4 0.4 0.3 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3
0.3 0.3 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.1
0.2 0.3 0.3 0.4 0.9 0.3 0.4 0.9 -99.9 -99.9 -99.9 -99.9 -99.9
-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
99.9 -99.9 -99.9 -99.9 0.9 0.9 0.5 0.5 0.4 -0.1 0.1 0.4 0.5 0.6 0.5 0.4 0.4 0.5 0.4 0.3 0.3 0.3 0.4
0.4 0.3 0.3 0.5 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.2 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.2 0.3 0.3 0.2
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3
0.3 0.3 0.3 0.2 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.4 0.3 0.4 0.3 0.3 0.3 0.3 0.3
0.3 0.4 0.2 0.2 0.3 0.4 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.2 0.2
0.2 0.2 0.2 0.3 0.4 0.5 0.5 0.5 -99.9 -99.9 -99.9 -99.9 -99.9
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255












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0.1 -0.1 -0.2 -0.2 -0.3 0.9 0.9 0.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
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99.9 -99.9 -99.9 -99.9 -99.9


259












-99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
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0.1 -0.1 -0.1 -0.2 0.9 0.9 0.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -
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99.9 -99.9 0.0 0.0 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
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99.9 -99.9 -99.9 -99.9 -99.9 -99.9 -99.9
0.005 RS28 VIS COEF
RS29 END VISC
0. 1 RS30 DIF COEF
RS31 END DIFF
0.400 RS32 MAN COEF
1 RS33 Flag VEGMANNING


260












RS33 END MANN
0. RS34 BEN VALU
RS35 END BENV
RS36 END CONC
RS37 END TITL
2 2 137 2 1 RS39A COMP ROWS
3 2 137 2 1
4 2 137 2 1
5 2 137 2 1
6 2 137 2 1
7 2 137 2 1
8 2 137 2 1
9 2 137 2 1
10 2 137 2 1
11 2 137 2 1
12 2 137 2 1
13 2 137 2 1
14 2 137 2 1
15 2 138 2 1
16 2 138 1 1
17 2 138 1 1
18 2 139 1 1
19 2 139 1 1
20 2 140 1 1
21 2 140 1 1
22 2 141 1 1
23 2 141 1 1
24 2 142 1 1
25 2 142 1 1
26 3 144 1 1
27 4 145 1 1
28 6 147 1 1
29 7 146 1 1
30 8 146 1 1
31 10 146 1 1
32 11 146 1 1
33 13 145 1 1
34 15 145 1 1
35 16 145 1 1
36 18 145 1 1
37 19 143 1 1
38 20 143 1 2
39 22 143 1 2
40 23 143 1 2
41 25 143 1 1
42 26 143 1 1
43 26 143 1 1
44 26 143 2 1
45 26 143 2 1
46 26 143 2 1
47 26 143 2 1
48 26 143 2 1
49 26 143 2 1
50 26 143 2 1
51 26 143 2 1
52 26 142 2 1
53 26 142 2 1
54 26 142 2 1
55 26 142 2 1
56 26 142 2 1
57 26 140 2 1
58 26 138 2 1
59 26 136 2 1
60 26 133 2 1
61 26 130 2 1
62 26 127 2 1
63 26 125 2 1
64 26 122 2 1
65 26 119 2 1
66 26 117 2 1


261












67 26 115 2 1
68 26 115 2 1
69 26 117 2 2
70 28 117 1 2
71 29 117 1 2
72 69 117 1 2
73 69 117 1 2
74 77 117 1 2
75 77 117 1 2
76 78 117 1 2
77 78 117 1 2
78 79 117 1 2
79 79 117 1 2
80 80 117 1 2
81 80 117 1 2
82 81 117 1 2
83 81 117 1 2
84 82 117 1 2
85 83 117 1 2
86 84 115 1 1
87 84 114 1 1
88 85 113 1 1
89 85 112 1 1
90 86 110 1 1
91 91 109 1 1
92 93 108 1 1
93 95 104 1 1
94 96 104 1 1
95 98 104 1 1
96 99 104 1 1
97 102 104 1 1
END RS39A
2 2 25 2 1 RS40ACOMPCOLS
3 2 26 2 1
4 2 27 2 1
5 2 27 2 1
6 2 28 2 1
7 2 29 2 1
8 2 30 2 1
9 2 31 2 1
10 2 32 2 1
11 2 32 2 1
12 2 33 2 1
13 2 34 2 1
14 2 35 2 1
15 2 35 2 1
16 2 36 2 1
17 2 36 2 1
18 2 37 2 1
19 2 38 2 1
20 2 38 2 1
21 2 39 2 1
22 2 39 2 1
23 2 40 2 1
24 2 41 2 1
25 2 41 2 1
26 2 69 2 1
27 2 70 2 1
28 2 71 2 1
29 2 71 2 1
30 2 71 2 2
31 2 71 2 2
32 2 71 2 2
33 2 71 2 2
34 2 71 2 2
35 2 71 2 2
36 2 71 2 2
37 2 71 2 2
38 2 71 2 2
39 2 71 2 2


262





























































263












110 2 90 2 1
111 2 89 2 1
112 2 89 2 1
113 2 88 2 1
114 2 87 2 1
115 2 86 2 1
116 2 85 2 1
117 2 85 2 1
118 2 66 2 1
119 2 66 2 1
120 2 65 2 1
121 2 65 2 1
122 2 64 2 1
123 2 64 2 1
124 2 63 2 1
125 2 63 2 1
126 2 62 2 1
127 2 62 2 1
128 2 61 2 1
129 2 61 2 1
130 2 61 2 1
131 2 61 2 1
132 2 60 2 1
133 2 60 2 1
134 2 60 2 1
135 2 60 2 1
136 2 59 2 1
137 2 59 2 1
138 11 58 1 1
139 15 58 1 1
140 17 57 1 1
141 19 57 1 1
142 21 57 1 1
143 23 52 1 1
144 24 36 1 1
145 25 36 1 1
146 26 33 1 1
147 26 30 1 1
END RS40A
0 15.000 4 0.00 140.000
1 0.200 22.8200.01722
1 0.200 22.8200.01232
1 0.200 22.820 0.00475
1 0.200 7.310 0.00683
1 0.200 0.000 0.005
1 -0.070 0.000 0.005
1 0.089 0.000 0.005
1 0.269 0.000 0.005
2 0.200 22.8200.01722
2 0.200 22.8200.01232
2 0.200 16.660 0.00475
2 0.200 7.310 0.00683
2 0.200 0.000 0.005
2 0.089 0.000 0.005
2 0.269 0.000 0.005
2 0.314 0.000 0.005
5 1 -1.00 0.00
5 2 0.00 0.00
5 3 -6.94 0.00
5 4 -0.20
0 30.000 1 0.01 136.000
1 0.199 22.7850.01722
1 0.199 22.7850.01232
1 0.199 22.785 0.00475
1 0.199 7.295 0.00683
1 0.200 0.000 0.005
1 -0.070 0.000 0.005
1 0.089 0.000 0.005
1 0.269 0.000 0.005
2 0.199 22.7850.01722


264











2 0.199 22.7850.01232
2 0.199 16.710 0.00475
2 0.199 7.295 0.00683
2 0.200 0.000 0.005
2 0.089 0.000 0.005
2 0.269 0.000 0.005
2 0.314 0.000 0.005
5 4 -0.10
0 45.000 1 0.01 112.000
1 0.199 22.7500.01722
1 0.199 22.7500.01232
1 0.199 22.750 0.00475
1 0.199 7.280 0.00683
1 0.200 0.000 0.005
1 -0.070 0.000 0.005
1 0.089 0.000 0.005
1 0.269 0.000 0.005
2 0.199 22.7500.01722
2 0.199 22.7500.01232
2 0.199 16.760 0.00475
2 0.199 7.280 0.00683
2 0.200 0.000 0.005
2 0.089 0.000 0.005
2 0.269 0.000 0.005
2 0.314 0.000 0.005
5 4 -0.10
0 60.000 1 0.01 127.000
1 0.199 22.7150.01722
1 0.199 22.7150.01232
1 0.199 22.715 0.00475
1 0.199 7.265 0.00683
1 0.200 0.000 0.005
1 -0.070 0.000 0.005
1 0.089 0.000 0.005
1 0.269 0.000 0.005
2 0.199 22.7150.01722
2 0.199 22.7150.01232
2 0.199 16.810 0.00475
2 0.199 7.265 0.00683
2 0.200 0.000 0.005
2 0.089 0.000 0.005
2 0.269 0.000 0.005
2 0.314 0.000 0.005



*incomplete file


265









LIST OF REFERENCES


Ahn, H., 1999. Statistical modeling of total phosphorus concentrations measured in
south Florida rainfall. Ecological Modelling 116:33-44.

Aitken, A.P. 1973. Assessing systematic errors in rainfall-runoff models. Journal of
Hydrology 20:121-136.

Arhonditsis, G.B., Brett M.T., 2004. Evaluation of the current state of mechanistic
aquatic biogeochemical modeling. Marine Ecology Progress Series 271:13-26.

Armentano, T.V., Sah, J.P., Ross, M.S., Jones, D.T., Cooley, H.C., Smith, C.S., 2006.
Rapid responses of vegetation to hydrological changes in Taylor Slough,
Everglades National Park, Florida, USA. Hydrobiologia 569:293-309.

Arnholm, C.A., 1997. Mixed language programming using C++ and FORTRAN 77.
Available at: http://arnholm.org/software/cppf77/cppf77.htm. Accessed 10/10,
2009.

Arthur, W.B., 1999. Complexity and the economy. Science 284(5411):107-109.

Ascough, J.C., Maier, H.R., Ravalico, J.K., Strudley, M.W., 2008. Future research
challenges for incorporation of uncertainty in environmental and ecological
decision-making. Ecological Modelling 219:383-399.

Bales, J.D., Robbins, J.C., 1995. Simulation of hydrodynamics and solute transport in
the Pamlico River Estuary, North Carolina. U.S. Geological Survey Open-File
Report 94-454, 85pp.

Basmadjian, D., 1999. The Art of Modeling in Science and Engineering. Boca Raton,
Florida, USA: Chapman and Hall/CRC Press.

Bays, J.S., Knight, R.L., Wenkert, L., Clark, R., Gong, S., 2001. Progress in the
research and demonstration of Everglades periphyton-based stormwater treatment
areas. Water Science and Technology 44:123-130.

Beccue, S., 1999. Endangered species: Everglades National Park. Available at:
http://www.nps.gov/ever/eco/danger.htm. Accessed 08/20, 2003.

Beck, M.B., 1987. Water-quality modeling: a review of the analysis of uncertainty. Water
Resources Research 23(8):1393-1442.

Beisner, B.E., Haydon, D.T., Cuddington, K., 2003. Alternative stable states in ecology.
Frontiers in Ecology and the Environment 1(7):376-382.

Benque, J.P., Cunge, J.A., Feuillet, J., Hauguel, A., Holly, F.M., 1982. New method for
tidal current computation. Journal of the Waterway, Port, Coastal, and Ocean
Division, ASCE 108(3):396-417.


266









Beven, K., 2006a. A manifesto for the equifinality thesis. Journal of Hydrology 320:18-
36.

Beven, K., 2006b. On undermining the science? Hydrological Process 20(14):3141-
3146.

Beven, K., 1993. Prophecy, reality and uncertainty in distributed hydrological modeling.
Advances in Water Resources 16(1):41-51.

Beven, K., Binley, A., 1992. The future of distributed models: model calibration and
uncertainty prediction. Hydrological Processes 6:279-298.

Boyer, J.N., Fourqurean, J.W., Jones, R.D., 1999. Seasonal and long-term trends in the
water-quality of Florida Bay (1989-1997). Estuaries 22(2B):417-430.

Brion, L.M., Senarath, S., Lal, W., 2000. Concepts and algorithms for an integrated
surface-water/ground-water model for natural areas, in Proceedings of the Greater
Everglades Ecosystem Restoration (GEER) Science Conference; Naples, florida,
December 11-15, 2000, p280.

Brun, R., Reichert, P., Kunsch, H.R., 2001. Practical identifiably analysis of large
environmental simulation models. Water Resources Research 37:115-130.

Cacuci, D.G., 2003. Sensitivity and Uncertainty Analysis Volume 1: Theory. Boca
Raton, Florida, USA: Chapman and Hall/CRC Press.

Campolongo, F., Cariboni, J., Saltelli, A., 2007. An effective screening design for
sensitivity analysis of large models. Environmental Modelling and Software
22:1509-1518.

Campolongo, F., Saltelli, A., 1997. Sensitivity analysis of an environmental model: an
application of different analysis methods. Reliability Engineering and System
Safety 57(1):49-69.

Cariboni, J., Gatelli, D., Liska, R., Saltelli, A., 2007. The role of sensitivity analysis in
ecological modeling. Ecological Modelling 203:167-182.

Cary, J.R., Shasharina, S.G., Cummings, J.C., Reynders, J.V.W., Hinker, P.J., 1998.
Comparison of C++ and Fortran 90 for object-oriented scientific programming.
Computer Physics Communications 105(1):20-36.

Chen, R.H., Twilley, R.R., 1999. Patterns of mangrove forest structure and soil nutrient
dynamics along the Shark River estuary, Florida. Estuaries 22(4):955-970.

Childers, D.L., 2006. A synthesis of long-term research by the Florida Coastal
Everglades LTER Program. Hydrobiologia 569:531-544.


267









Chwif, L., Barretto, M., Paul, R., 2000. On simulation model complexity. Proceedings of
the 32nd Conference on Winter Simulation, 449-455.

Cichra, M.F., Badylak, S., Henderson, N., Rueter, B.H., Phlips, E.G., 1995.
phytoplankton community structure in the open water zone of a shallow subtropical
lake (Lake Okeechobee, Florida, USA). Advances in Limnology 45:157-175.

Cleckner, L.B., Gilmour, C.C., Hurley, J.P., Krabbenhoft, D.P., 1999. Mercury
methylation in periphyton of the Florida Everglades. Limnology and
Oceanography 44(7): 1815-1825

Costanza, R., Sklar, F.H., White, M.L., 1990. Modeling coastal landscape dynamics.
Bioscience 40:91-107.

Cox, G.M., Gibbons, J.M., Wood, A.T.A., Craigon, J., Ramsden, S.J., Crout, N.M.J.,
2006. Towards the systematic simplification of models. Ecological Modelling
198:240-246.

Cressie, N., Calder, C.A., Clark, J.S., Ver Hoef, J.M., Wikle, C.K., 2009. Accounting for
uncertainty in ecological analysis: the strengths and limitations of hierarchical
statistical modeling. Ecological Applications 19(3):553-570.

CRGEE, NRC, 2002. Florida Bay Research Programs and their Relation to the
Comprehensive Everglades Restoration Plan. Committee on Restoration of the
Greater Everglades Ecosystem: National Research Council.

Davis SM. 1994. Phosphorous inputs and vegetation sensitivity in the Everglades. In:
Davis SM, Ogden JC, editors. Everglades: the ecosystem and its restoration.
Delray Beach, Florida: St. Lucie Press, p 357-78.

DeBusk, W. F., and K. R. Reddy (1998), Turnover of detrital organic carbon in a
nutrient-impacted Everglades marsh, Soil Science Society Of America Journal, 62,
1460-1468.

de Kanal, J., Morse, J.W., 1978. The chemistry of orthophosphate uptake from
seawater onto calcite and aragonite. Geochimica et Cosmochimica Acta 42:1335-
1340.

Desmond, G., 2000. Topography of the Florida Everglades, in Proceedings of the
Greater Everglades Ecosystem Restoration (GEER) Conference; December 11-
15, 2000: U.S. Geological Survey Open-File Report 00-449.

Doerr, H.M., 1996. Stella ten years later: a review of the literature. International Journal
of Computers for Mathematical Learning 1(2):201-224.

Draper, D., 1995. Assessment and propagation of model uncertainty. Journal of the
Royal Statistical Society Series B-Methodological 57(1):45-97.


268









Dronkers, J., van Os, A.G., Leendertse, J.J., 1981. Predictive salinity modeling of the
Oosterschelde with hydraulic and mathematical models: Transport models for
inland and coastal waters. Proceedings of the Symposium on Predictive Abilities,
New York, N.Y.: Academic Press, p. 451-482.

Eagleson, P.S., 1970. Dynamic Hydrology. New York, NY: McGraw-Hill Book Company.

Ebel, B.A., Loague, K., 2006. Physics-based hydrologic-response simulation: Seeing
through the fog of equifinality. Hydrological Processes 20(13):2887-2900.

Elder, J.W., 1959. The dispersion of marked fluid in turbulent shear flow. Journal of
Fluid Mechanics 5(4):544-560.

Fennema, R.J., Neidrauer, C.J., Johnson, R.A., MacVicar, T.K., Persons, W.A., 1994. A
computer model to simulate natural Everglades hydrology. In: Davis, S.M., Ogden,
J.C. (Eds.), Everglades: The Ecosystem and its Restoration: St. Lucie Press.

Fischer, H.B., List, J.E., Koh, R.C.Y. et al., 1979. Mixing in inland and coastal waters.
New York, N.Y.: Academic Press, p. 126-127.

Fisher, B.E.A., Ireland, M.P., Boyland, D.T., Critten, S.P., 2002. Why use one model?
An approach for encompassing model uncertainty and improving best practice.
Environmental Modeling and Assessment 7(4):291-299.

Fitz, H.C., Sklar, F.H., 1999. Ecosystem analysis of phosphorus impacts and altered
hydrology in the Everglades: a landscape modeling approach. In: Reddy KR,
O'Connor GA, Schelske CL, editors. Phosphorous biogeochemistry in subtropical
ecosystems. Boca Raton (FL): Lewis Publishers, p 585-620.

Fourqurean, J.W., Robblee, M.B., 1999. Florida Bay: A history of recent ecological
changes. Estuaries 22(2B):345-357.

Fourqurean, J.W., Zieman, J.C., Powell, G.V.N., 1992. Phosphorus limitation of primary
production in Florida Bay Evidence from C-N-P ratios of the dominant seagrass
Thalassia-Testudinum. Limnology and Oceanography 37(1):162-171.

Gaiser, E.E., Scinto, L.J., Richards, J.H., Jayachandaran, K., Childers, D.L., Trexler,
J.D., Jones, R.D., 2004. Phosphorus in periphyton mats provides best metric for
detecting low-level nutrient enrichment in an oligotrophic wetland. Water
Resources 38:507-516.

Gaiser, E.E., Trexler, J.C., Richards, Childers, Lee, D., Edwards, A.L., Scinto, L.J., ,
Jayachandaran, K., Noe, G.B., Jones, R.D., 2005. Cascading ecological effects of
low-level phosphorus enrichment in the Florida Everglades. Journal of
Environmental Quality 34:717-723.


269









Gaiser, E.E., Childers, D.L., Jones, R.D., Richards, J.H., Scinto, L.J., Trexler, J.C.,
2006. Periphyton responses to eutrophication in the Florida Everglades: Cross-
system patterns of structural and compositional change. Limnology and
Oceanography 51(1):617-630.

German, E.R., 2000. Regional evaluation of evapotranspiration in the Everglades. U.S.
Geological Survey Water-Resources Investigations Report 00-4217, 48pp.

Getz, W.M., 1998. An introspection on the art of modeling in population ecology.
Bioscience 48(7):540-552.

Goodwin, C.R., 1987. Tidal-flow, circulation, and flushing changes caused by dredge
and fill in Tampa Bay, Florida. U.S. Geological Survey Water-Supply Paper 2282,
88p.

Goodwin, C.R., 1991. Tidal-flow, circulation, and flushing changes caused by dredge
and fill in Hillsborough Bay, Florida. U.S. Geological Survey Water-Supply Paper
2376, 49 p.

Graham, W.F., Duce, R.A., 1982. The atmospheric transport of phosphorus to the
western North Atlantic. Atmospheric Environment 16:1089-1097.

Guo, Weixing, and Langevin, C.D., 2002, User's guide to SEAWAT: A computer
program for simulation of three-dimensional variable-density ground-water flow:
U.S. Geological Survey Techniques of Water-Resources Investigations, book 6,
chap. A7, 77 p.

Haan, C.T., 1989. Parametric uncertainty in hydrologic modeling. Transactions of the
ASAE 32(1):137-146.

Haan, C.T., Allred, B., Storm, D.E., Sabbagh, G.J., Prabhu, S., 1995. Statistical
procedure for evaluating hydrologic water-quality models. Transactions of the
ASAE 38(3):725-733.

Haan, C.T., Storm, D.E., Al-lssa, T., Prabhu, S., Sabbagh, G.J., Edwards, D.R., 1998.
Effect of parameter distributions on uncertainty analysis of hydrologic models.
Transactions of the ASAE 41(1):65-70.

Hamrick, J.M., Moustafa, M.Z., 2003. Florida Bay hydrodynamic and salinity model
analysis, in Proceedings of the Greater Everglades and Florida Bay Ecosystem
Conference, Palm Harbor, Florida, April 13-18, 2003.

Hanna, S.R., 1988. Air-quality model evaluation and uncertainty. International Journal of
Air Pollution Control and Hazardous Waste Management 38(4):406-412.

Harleman D.R.F., 1966. Diffusion Processes in Stratified Flow-Estuary and Coastline
Hydrodynamics. New York, NY: McGraw-Hill Book Company.


270









Heisenberg W., 1958. Physics and Philosophy: The Revolution in Modern Science. New
York, NY: Harper.

Hittle, C.D., 2000. Quantity, timing, and distribution of freshwater flows into northeastern
Florida Bay: U.S. Geological Survey Program on the South Florida Ecosystem, in
Proceedings of the Greater Everglades Ecosystem Restoration (GEER)
Conference; December 11-15, 2000: U.S. Geological Survey Open-File Report 00-
449, pp27-28.

James, A.I., Jawitz, J.W., Muioz-Carpena, R., 2009. Development and implementation
of a transport method for the Transport and Reaction Simulation Engine (TaRSE)
based on the Godunov-Mixed Finite Element Method. U.S. Geological Survey
Scientific Investigations Report 2009-5034, 40pp.

Jawitz, J.W., Muioz-Carpena, R., Muller, S.J., Grace, K.A., James, A.I., 2008.
Development, testing and sensitivity and uncertainty analyses of a Transport and
Reaction Simulation Engine (TaRSE) for spatially-distributed modeling of
phosphorus in south Florida peat marsh wetlands. U.S. Geological Survey
Scientific Investigations Report 2008-5029, 109pp.

Jenter, H., 1999. Laboratory experiments for evaluating the effects of wind forcing on
shallow waters with emergent vegetation, in Coastal Ocean Processes
Symposium: A Tribute to William T. Grant: Woods Hole Oceanographic Institution
Technical Report, 15pp.

Jury, W.A., Gardner, W.R., Gardner, W.H., 1991. Soil Physics. New York, NY: Wiley
and Sons.

Kadlec, R.H., 1997. An autobiotic wetland phosphorus model. Ecological Engineering
8:145-172.

Kadlec, R.H., Knight, R.L., 1996. Treatment Wetlands: Boca Raton, Florida: Lewis
Publishers, 893 p.

Konikow, L.F., Bredehoeft, J.D., 1992. Ground-water models cannot be validated.
Advances in Water Resources 15(1):75-83.

Kotz, S., van Dorp, J.R., 2004. Beyond Beta. Singapore: World Scientific Publishing Co.
Pty. Ltd.

Lal, A.M.W., van Zee, R., Belnap, M., 2005. Case study: Model to simulate regional flow
in South Florida. Journal of Hydraulic Engineering-ASCE 131(4):247-258.

Landing W (1997) Measurements of aerosol phosphorus in South Florida. In: Redfield G
& Urban N (Eds) Atmospheric Deposition into South Florida: Measuring Net
Atmospheric Inputs of Nutrients.: SFWMD Conference on Atmospheric Deposition
into South Florida. West Palm Beach, Florida. October 1997


271









Langevin, C.D., 2001. Simulation of ground-water discharge to Biscayne Bay,
southeastern Florida. U.S. Geological Survey Water-Resources Investigations
Report 00-4251, 137pp.

Langevin, C.D., Swain, E., Wolfert, M., 2005. Simulation of integrated surface-
water/ground-water flow and salinity for a coastal wetland and adjacent estuary.
Journal of Hydrology 314(1-4):212-34.

Langevin, C.D., Guo, W., 2006. MODFLOW/MT3DMS-based simulation of variable-
density ground water flow and transport. Ground Water 44(3):339-351.

Lawrie, J., Hearne, J., 2007. Reducing model complexity via output sensitivity.
Ecological Modelling 207(2-4): 137-44.

Leamer, E.E., 1990. Let's Take the Con Out of Econometrics. In: Granger, C.W.J.,
(Ed.), Modelling Economic Series, Oxford, UK: Clarendon Press.

Leendertse, J.J., 1970, A water-quality simulation model for well-mixed estuaries and
coastal seas: Volume I, Principles of Computation: Santa Monica, Calif., The Rand
Corporation, Report RM-6230-RC, 71 p.

Leendertse, J.J., 1972, A water-quality simulation model for well-mixed estuaries and
coastal seas: Volume IV, Jamaica Bay Tidal Flows: New York, The New York City
Rand Institute, Report R-1009-NYC, 48 p.

Leendertse, J.J., 1987, Aspects of SIMSYS2D, a system for two-dimensional flow
computation: Santa Monica, Calif., The Rand Corporation, Report R-3572-USGS,
80 p.

Leendertse, J.J., 1988, A summary of experiments with a model of the Eastern Scheldt:
Santa Monica, Calif., The Rand Corporation, Report R-3611-NETH, 41 p.

Leendertse, J.J., and Gritton, E.C., 1971, A water-quality simulation model for well-
mixed estuaries and coastal seas: Volume II, Computation Procedures: New York,
The New York City Rand Institute, Report R-708-NYC, 48 p.

Leendertse, J.J., Langerak, A., and de Ras, M.A.M., 1981, Two-dimensional tidal
models for the Delta Works: Transport models for inland and coastal waters:
Proceedings of the Symposium on Predictive Abilities: New York, N.Y., Academic
Press, p. 408-450.

Leij, F.J., Bradford S.A., 1994. 3DADE: A computer program for evaluating three-
dimensional equilibrium solute transport in porous media. U.S. Department of
Agriculture- Salinity Laboratory, 134pp.


272









Leonard, L., Croft, A., Childers, D., Mitchell-Bruker, S., Solo-Gabriele, H., Ross, M,.
2006. Characteristics of surface-water flows in the ridge and slough landscape of
Everglades National Park: Implications for particulate transport. Hydrobiologia
569:5-22.

Limpert, E., Stahel, W.A., Abbot, M., 2001. Log-normal distributions across the
sciences: Keys and clues. Bioscience 51(5):341-352.

Lin, H.C., Talbot, C.A., Richards, D.R., Jones, N.L., 2000. Development of a
multidimensional modeling system for simulating canal, overland, and ground-
water flow in south Florida. Waterways Experiment Station, Vicksburg, Mississippi,
U.S. Army Corps of Engineers report.

Lindenschmidt, K.-E., 2006. The effect of complexity on parameter sensitivity and model
uncertainty in river water-quality modelling. Ecological Modelling 190(1-2):72-86.

Lindenschmidt, K.-E., Wodrich, R., Hesse, C., 2006. The effects of scaling and model
complexity in simulating the transport of inorganic micropollutants in a lowland
river reach. Water-quality Research Journal of Canada 41(1):24-36.

Lindenschmidt, K.-E., Fleischbein, K., Baborowski, M., 2007. Structural uncertainty in a
river water quality modeling system. Ecological Modelling 204:289-300.

Loaiciga, H.A., Yeh, W.W.-G., Ortega-Guerrero, M.A., 2007. Probability density
functions in the analysis of hydraulic conductivity data. Journal of Hydrologic
Engineering. 11(5):442-450.

Luo, Y., Weng, E., Wu, X., Gao, C., Zhou, X., Zhang, L., 2009. Parameter identifiability,
constraint, and equifinality in data assimilation with ecosystem models. Ecological
Applications 19(3):571-574.

MacVicar, T.K., van Lent, T., Castro, A., 1984. South Florida Water Management Model
documentation report. South Florida Water Management District Technical
Publication 84-3, 123pp.

Manson, S.M., 2008. Does scale exist? An epistemological scale continuum for complex
human-environment systems. Geoforum 39(2):776-788.

Manson, S.M., 2007. Challenges in evaluating models of geographic complexity.
Environment and Planning B-Planning and Design 34(2):245-260.

McCormick, P.V., Rawlik, P.S., Lurding, K., Smith, E.P., Sklar, F.H., 1996. Periphyton-
water relationships along a nutrient gradient in the northern Florida Everglades.
Journal of the North American Benthological Society 15(4):433-449.

McCuen, R.H., Knight, Z., Cutter, A.G., 2006. Evaluation of the Nash-Sutcliffe efficiency
index. Journal of Hydrologic Engineering 11(6):597-602.


273









McDonald, M.G., and Harbaugh, A.W., 1988, A modular three-dimensional finite-
difference ground-water flow model: U.S. Geological Survey Techniques of Water-
Resources Investigations Report, book 6, chap. Al.

McPherson, B.F., Torres, A.E., 2006. Freshwater and nutrient fluxes to coastal waters
of Everglades National Park- A synthesis. U.S. Geological Survey Fact Sheet
2006-3076.

Messina, J.P., Evans, T.P., Manson, S.M., Shortridge, A.M., Deadman, P.J., Verburg,
P.H., 2008. Complex systems models and the management of error and
uncertainty. Journal of Land Use Science 3(1): 11-25.

Meyers, T.P., Lindberg, S.E., 1997. An assessment of the relative contribution of dry
deposition to the total atmospheric input of phosphorus. In: Redfield G & Urban N
(Eds) Atmospheric Deposition into South Florida: Measuring Net Atmospheric
Inputs of Nutrients.: SFWMD Conference on Atmospheric Deposition into South
Florida. West Palm Beach, Florida.

Min, J.-H., Paudel, R., Jawitz, J.W., 2010. Spatially distributed modeling of surface
water flow dynamics in the Everglades ridge and slough landscape. Journal of
Hydrology, in press.

Mitsch, W.J., Cronk, J.K., Wu, X.Y., Nairn, R.W., Hey, D.L., 1995. Phosphorus retention
in constructed fresh-water riparian marshes. Ecological Applications 5:830-845.

Mitsch, W.J., Gosselink, J.G., 2000. Wetlands. New York, N.Y.: John Wiley and Sons,
Inc., 920p.

Morris, M.D., 1991. Factorial sampling plans for preliminary computational experiments.
Technometrics 33(2): 161-174.

Moustafa, M.Z., Chimney, M.J., Fontaine, T.D., Shih, G., Davis, S., 1996. The response
of a freshwater wetland to long-term "low level" nutrient loads-marsh efficiency.
Ecol Eng 7:15-33.

Muller, S.J., Muioz-Carpena, R., 2005. Design of a phosphorus model for south Florida
based on a simplified approach. ASAE Paper No. 052252, St. Joseph, MI.

Muroz-Carpena, R., Zajac, Z., Kuo, Y.M., 2007. Global sensitivity and uncertainty
analyses of the water-quality model VFSMOD-W. Transactions of the ASABE
50(5): 1719-1732.

Munson, R.K., Roy, S.B., Gherini, S.A., MacNeil, A.L., Hudson, R.J.M., Blette, V.L.,
2002. Model prediction of the effects of changing phosphorus loads on the
Everglades Protection Area. Water Air and Soil Pollution 134(1-4):255-273.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I
A discussion of principles. Journal of Hydrology 10(3):282-290


274









Naylor, T.H., Finger, J.M., 1967. Verification of computer simulation models.
Management Science 14(2):B92-B101.

Newman, S., and K. Pietro, 2001. Phosphorus storage and release in response to
flooding: implications for Everglades stormwater treatment areas, Ecological
Engineering, 18, 23-38.

Nihoul, J.C.J., 1994. Do not use a simple model when a complex one will do. Journal of
Marine Systems 5(6):401-6.

Noe, G.B., Childers, D.L., 2007. Phosphorus budgets in Everglades wetland
ecosystems: The effects of hydrology and nutrient enrichment. Wetlands Ecology
and Management 15:189-205.

Noe, G.B., Childers, D.L., Jones, R.D., 2001. Phosphorus biogeochemistry and the
impact of phosphorus enrichment: Why is the everglades so unique? Ecosystems
4(7):603-24.

Noe, G.B., Scinto, L.J., Taylor, J., Childers, D.L., Jones, R.D., 2003. Phosphorus cycling
and partitioning in an oligotrophic Everglades wetland ecosystem: A radioisotope
tracing study. Freshwater Biology 48(11):1993-2008.

Oliphant, T.E., 2007. Python for scientific computing. Computing in Science and
Engineering 9(3):10-20.

Omlin, M., Brun, R., Reichert, P., 2001. Biogeochemical model of Lake Zurich:
Sensitivity, identifiability and uncertainty analysis. Ecological Modelling 141(1-
3): 105-123.

Oreskes, N., Shraderfrechette, K., Belitz, K., 1994. Verification, validation, and
confirmation of numerical models in the earth-sciences. Science 263(5147):641-
646.

Paerl H.W., 1995. Coastal eutrophication in relation to atmospheric nitrogen deposition:
current perspectives. Ophelia 41: 237-259.

Perry, W.B., 2008. Everglades restoration and water-quality challenges in south Florida.
Ecotoxicology 17(7):569-578.

Pimm, S.L., Lockwood, J.L., Jenkins, C.N., Curnutt, J.L., Nott, M.P., Powell, R.D., Bass
Jr., O.L., 2002. Sparrow in the grass: A report on the first ten years of research on
the Cape Sable Seaside Sparrow (Ammodramus maritimus mirabilis).
Homestead, Florida: South Florida Natural Resources Center, 204pp.

Pohl, C., van Genderen, J.L., 1998. Multisensor image fusion in remote sensing:
Concepts, methods and applications. International Journal of Remote Sensing
19(5):823-854.


275









Polman, C., Gill, G., Landing, W., Guentzel, J., Bare, D., Porella, D., Zillioux, E.,
Atkeson, T., 1995. Overview of the Florida Atmospheric Deposition Study (FAMS).
Water, Soil, and Air Pollution 80:285-290.

Price, R.M., Swart, P.K., Fourqurean, J.W., 2006. Coastal ground-water discharge An
additional source of phosphorus for the oligotrophic wetlands of the Everglades.
Hydrobiologia 569:23-36.

Reddy, K.R., Kadlec, R.H., Flaig, E., Gale, P.M., 1999. Phosphorus retention in streams
and wetlands: A review: Critical Reviews in Environmental Science and
Technology 29:83-146.

Redfield, G., 1998. Quantifying atmospheric deposition of phosphorus: A conceptual
model and literature review for environmental management. South Florida Water
Management District.

Regan, H.M., Colyvan, M., Burgman, M.A., 2002. A taxonomy and treatment of
uncertainty for ecology and conservation biology. Ecological Applications.
12(2):618-628.

Richardson, C.J., Marshall, P.E., 1986. Processes controlling movement, storage, and
export of phosphorus in a fen peatland. Ecological Monographs 56:279-302.

Ridderinkhof, H., Zimmerman, J.T.F., 1992. Chaotic stirring in a tidal system. Science
258:1107-1111.

Robbins, J.C., Bales, J.D., 1995. Simulation of hydrodynamics and solute transport in
the Neuse River Estuary, North Carolina. U.S. Geological Survey Open-File
Report 94-511, 85 p.

Roache, P.J., 1982. Computational Fluid Dynamics. Albuquerque, NM, USA: Hermosa
Publishers.

Rudnick, D.T., Chen, Z., Childers, D.L., Boyer, J.N., Fontaine III, T.D., 1999.
Phosphorus and nitrogen inputs to Florida Bay: The importance of the Everglades
watershed. Estuaries 22(2B):398-416.

De Saint-Venant, A.J.C., 1871. Theorie du movement non-permanent des eaux, avec
application aux crues des rivieres et a I'introduction des marees dans leur lit. C. R.
Acad. Sc. Paris, 73:147 154.

Saltelli, A., 1999. Sensitivity analysis: Could better methods be used?. Journal of
Geophysical Research 104(D3):3789-3793.

Saltelli, A., Tarantola, S., Campolongo, F., 2000. Sensitivity analysis as an ingredient of
modeling. Statistical Science 15(4):377-395.


276









Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M., 2004. Sensitivity Analysis in
Practice: A Guide to Assessing Scientific Models. Chinchester, UK: John Wiley
and Sons.

Saltelli, A., Ratto, M., Tarantola, S., Campolongo, F., 2005. Sensitivity analysis for
chemical models. Chemical Reviews 105(7):2811-2827.

Saltelli A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., et al., 2008.
Global Sensitivity Analysis: The Primer. Chinchester, UK: Wiley-lnterscience.

Schaffranek, R.W., 1986. Hydrodynamic simulation of the upper Potomac Estuary.
Proceedings of the Water Forum 86: World Water Issues in Evolution, ASCE, New
York, N.Y. 2:1572-1581.

Schaffranek, R.W., 2004. Simulation of surface-water integrated flow and transport in
two dimensions: SWIFT2D user's manual. U.S. Geological Survey Techniques
and Methods Book 6, Chapter B-1, 115pp.

Schaller, P.R., 1997. Moore's Law: Past, present and future. IEEE Spectrum 34(6):52-
58.

Scheffer, M., 2009. Critical Transitions in Nature and Society. Princeton, NY: Princeton
University Press.

Scheffer, M., 1990. Multiplicity of stable states in fresh-water systems. Hydrobiologia
200:475-86.

Scheffer, M., Hosper, S.H., Meijer, M.L., Moss, B., Jeppesen, E., 1993. Alternative
equilibria in shallow lakes. Trends in Ecology and Evolution 8(8):275-279.

Scott, E.M., 1996. Uncertainty and sensitivity studies of models of environmental
systems. In: Charnes, J.M., Morrice, D.J., Brunner, D.T., Swain, J.J., (Eds.),
Proceedings of the 1996 Winter Simulation Conference, Coronado, California,
USA.

SFWMD, 2005. Documentation of the South Florida Water Management Model, Version
5.5. South Florida Water Management District, West Palm Beach, Florida.

SFWMD, FDEP, 2004. Comprehensive Everglades Restoration Plan: 2003 Annual
Report. South Florida Water Management District, West Palm Beach, Florida.

Sheikh, P.A., Carter, N.T., 2005. Everglades restoration: the Federal role in funding.
Congressional Research Service Report for Congress.

Shirmohammadi, A., Chaubey, I., Harmel, R.D., Bosch, D.D., Muioz-Carpena, R.,
Dharmasri, C., et al,, 2006. Uncertainty in TMDL models. Transactions of the
ASABE 49(4): 1033-1049.


277









Simunek, J.M., van Genuchten, T.H., Sejna, M., Toride, N., Leij, F.J., 1999. The
STANMOD computer software for evaluating solute transport in porous media
using analytical solutions of convection-dispersion equation. Versions 1.0 and 2.0.
IGWMC TPS 71. International Ground-water Modeling Center, Colorado School
of Mines, Golden, Colorado, 32pp.

Smith III, T.J., 1998. Imperiled wetlands: Review of mangroves and salt marshes.
Nature 395:131-132.

Snowling, S.D., Kramer, J.R., 2001. Evaluating modelling uncertainty for model
selection. Ecological Modelling 138(1-3):17-30.

Sutula, M., Day, J.W., Cable, J., Rudnick, D., 2001. Hydrological and nutrient budgets of
freshwater and estuarine wetlands of Taylor Slough in southern Everglades,
Florida (USA). Biogeochemistry 56:287-310.

Swain, E.D., 2005. A model for simulation of surface-water integrated flow and transport
in two dimensions: User's guide for application to coastal wetlands. U.S.
Geological Survey Open-File Report 2005-1033, 88pp.

Swain, E.D., Wolfert, M.A., Bales, J.D., Goodwin, C.R., 2004. Two-dimensional
hydrodynamic simulation of surface-water flow and transport to Florida Bay
through the Southern Inland and Coastal Systems (SICS). U.S. Geological Survey
Water-Resources Investigations Report 03-4287, 56pp.

Valle, D., Staudhammer, C.L., Cropper, Jr., W.P., van Gardingen, P.R., 2009. The
importance of multimodel projections to assess uncertainty in projections from
simulation models. Ecological Applications 19(7):1680-1692.

van Lent, T.J., Snow, R.W., Fred, J., 1998. An examination of the Modified Water
Deliveries Project, the C-111 Project and the Experimental Water Deliveries
Project: Hydrologic analyses and effects on endangered species. Everglades
National Park Technical Report, 232pp.

Walker, W.W., 1995. Design basis for Everglades Stormwater Treatment Areas. Water
Resources Bulletin 31:671-685.

Walker, W.W., 1998. Estimation of inputs to Florida Bay. U.S. Army Corps of Engineers
& U.S. Department of the Interior. http://wwwalker.net/flabay.

Wang, N.M., Mitsch, W.J., 2000. A detailed ecosystem model of phosphorus dynamics
in created riparian wetlands. Ecological Modelling 126:101-130.

Wang, Y., Reddy, R., Gomez, R., Lim, J., Sanielevici, S., Ray, J., et al., 2005. A general
approach to creating FORTRAN interface for C++ application libraries. In: Zhang,
W., Tong, W., Chen, Z., Glowinski, R. (Eds.), Current Trends in High Performance
Computing and its Applications, Berlin, Heidelberg: Springer.


278









Wang, J.D., Swain, E.D., Wolfert, M.A., Langevin, C.D., James, D.E., Telis, P.A., 2007.
Application of FTLOADDS to simulate flow, salinity, and surface-water stage in the
southern Everglades, Florida. U.S. Geological Survey Scientific Investigations
Report 2007-5010, 90pp.

Weare, T.J., 1979. Errors arising from irregular boundaries in ADI solutions of the
shallow-water equations. International Journal of Numerical Methods in
Engineering 14(6):921-31.

Wesseling, C.G., van Deursen, W.P.A., Burrough, P.A., 1996. A spatial modelling
language that unifies dynamic environmental models and GIS, in Proceedings of
the Third International Conference/Workshop on Integrating GIS and
Environmental Modeling, Santa Fe, New Mexico, USA, January 21-26.

Wyss, G.D., Jorgensen, K.H., 1998. A user guide to LHS: Sandia's Latin hypercube
sampling software. Sandia National Laboratories Technical Report SAND98-
0210:1-140.

Zadeh, L.A., 1973. Outline of a new approach to the analysis of complex systems and
decision processes. IEEE Transactions on Systems, Man and Cybernetics 3:28-
44.

Zimmermann, T., Dubois-Pelerin, Y., Bomme, P., 1992. Object-oriented finite element
programming: I. Governing principles. Computer Methods in Applied Mechanics
Engineering 98(2):291-303.


279









BIOGRAPHICAL SKETCH

Stuart John Muller hails from South Africa, where he received an excellent

education at Hillcrest High School in KwaZulu-Natal. He matriculated as Head Boy and

proxime accessit dux, before subsequently acquiring a Bachelor of Science degree in

agricultural engineering from the University of Natal (the university and degree have

since been renamed to Bioresources Engineering and the University of KwaZulu-Natal,

respectively). There followed 18 months of global travel to Kenya, Tanzania, Zambia,

Botswana, United Kingdom (where he taught high-school students mathematics and

science), Nepal (where he trekked to Base Camp at Mount Everest), Thailand,

Cambodia, Australia, and New Zealand. In 2003, he moved to Florida to pursue a

Master of Science in Engineering degree in agricultural and biological engineering at the

University of Florida. Before he was able to complete his master's, he was seduced by

an opportunity to embark on a Ph.D. in the same department. That was in 2004. He

would go on to claim the Guinness World Record for the World's Longest Eyelash in

2007, and to eventually become a Doctor of Philosophy in 2010.


280





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1 ADAPTIVE SPATIALLY -DISTRIBUTED WATER -QUALITY MODELING: AN APPLICATION TO MECHANISTICALLY SIMULATE PHOSPHORUS CONDITIONS IN THE VARIABLE-DENSITY SURFACE-WATERS OF COASTAL EVERGLADES WETLANDS By STUART JOHN MULLER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Stuart John Muller

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3 Dedicated t o everyone, for every thing, truly. But most of all, it must be said, for Julie. Elen sila lumenn omentielvo.

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4 ACKNOWLEDGMENTS I thank the USGS, SFWMD, and UF for fiscal support throughout this journey. I thank my committee: Dr. Greg Kiker, for being the original spark that has lead to so much light; Dr. Andrew James, for his vision for TaRSE ; Dr. Mark Brown, for his example and his conversation; Dr. Jim Jawitz, for his support, both personal and professional; and dear Dr. Rafa el Muoz Carpena for the commitment of his generosity and the conviction of his faith, which have given me more than any Ph. D is really supposed to. I thank my incredible family for persistent genes boundless opportunity, an en quiring mind, and an open heart; my cats for the peace of their innocence when I had to let mine go; my friends for making life what it is, even when it isnt; and my Love for being so patient, and so kind and so adorable.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...................................................................................................... 4 LIST OF TABLES ................................................................................................................ 9 LIST OF FIGURES ............................................................................................................ 10 LIST OF ABBREVIATIONS .............................................................................................. 14 ABSTRACT ........................................................................................................................ 1 5 CHAPTER 1 INTRODUCTION ........................................................................................................ 17 The Southern Inland and Coastal Systems of the Everglades: A Region at Risk .... 17 Opportunities for Spatially -Distributed Mechanistic Modeling of Phosphorus in SICS ......................................................................................................................... 20 Hydrologic Modeling of SICS ............................................................................... 20 Water -Quality Modeling of SICS .......................................................................... 21 Model Selection .................................................................................................... 23 Important SICS M odeling Considerations ........................................................... 25 Model Relevance ................................................................................................. 27 Research Questions and Objectives .......................................................................... 28 Research Questions ............................................................................................ 28 Objectives ............................................................................................................. 29 2 FUSION OF FIXED -FORM AND FREE -FORM MODELS FOR ADAPTIVE SIMULATION OF SPATIALLY DISTRIBUTED WETLAND WATER -QUALITY ....... 34 Introduction ................................................................................................................. 34 Fixed -Form Versus FreeForm ............................................................................ 34 Mate rials and Methods ............................................................................................... 38 Description of the Models .................................................................................... 39 Fixed -form hydrology and transport model: FTLOADDS ............................. 39 Free-form water quality reactions model: aRSE .......................................... 40 Fusing Fixed and Free-Form Models ................................................................. 41 Analytical Testing of the FTaRSELOADDS Linkage .......................................... 42 Analytical solution .......................................................................................... 42 Setup for testing of SWIFT2D ....................................................................... 45 Setu p for testing of FTaRSELOADDS .......................................................... 47 Results and Discussion .............................................................................................. 47 Benchmarking SWIFT2D ..................................................................................... 47 Verifying FTaRSELOADDS ................................................................................. 48 Conclusions ................................................................................................................ 50

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6 3 MODELING HYDROLOGY IN THE SOUTHERN INLAND AND COASTAL SYSTEMS ................................................................................................................... 58 Introduction ................................................................................................................. 58 Previous Hydrological Modeling of SICS ............................................................ 58 Remodeling the Hydrology of SICS ..................................................................... 60 Materials and Methods ............................................................................................... 61 Model Description ................................................................................................ 61 SWIFT2D governing equations ..................................................................... 61 SWIF T2D numerical solution technique ....................................................... 63 SWIFT2D code enhancements and simplifications ..................................... 63 Model Setup ......................................................................................................... 66 Computational domain .................................................................................. 66 Boundary conditions ...................................................................................... 67 Stability considerations ................................................................................. 69 Results and Discussion .............................................................................................. 69 Water Level Results ............................................................................................. 70 Discharge Results ................................................................................................ 73 Salinity Results ..................................................................................................... 74 Conclusions ................................................................................................................ 75 4 MODELING PHOSPHORUS WATER-QUALITY IN THE SOUTHERN INLAND AND COASTAL SYSTEMS ...................................................................................... 103 Introduction ............................................................................................................... 103 Materials and Methods ............................................................................................. 105 Boundary Conditions .......................................................................................... 105 Specified water -level boundaries ................................................................ 106 Specified discharge boundaries .................................................................. 107 Atmospheric deposition ............................................................................... 108 Conceptual Models of Water -Quality Processes .............................................. 108 Model 1 ........................................................................................................ 109 Model 2 ........................................................................................................ 110 Model 3 ........................................................................................................ 110 Results and Discussion ............................................................................................ 112 Model 1 ............................................................................................................... 112 Model 2 ............................................................................................................... 112 Model 3 ............................................................................................................... 114 Conclusions .............................................................................................................. 115 5 UNRAVELING MODEL RELEVANCE: THE COMPLEXITY -UNCERTAINTY SENSITIVITY TRILEMMA ........................................................................................ 135 Introduction ............................................................................................................... 135 The Complexity -Uncertainty Sensitivity Trilemma ............................................ 137 Uncertainty ................................................................................................... 138 Sensitivity ..................................................................................................... 139

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7 Complexity ................................................................................................... 141 Relevance dilemmas ................................................................................... 143 The relevance trilemma ............................................................................... 145 Materials and Methods ............................................................................................. 146 Global Sen sitivity and Uncertainty Analysis Methods ....................................... 146 Model Description, Application, and Selection of Complexity Levels .............. 149 Model description: TaRSE .......................................................................... 149 Model application ......................................................................................... 150 Levels of comp lexity .................................................................................... 151 Parameterization of Inputs Across Complexity Levels ..................................... 152 Results and Discussion ............................................................................................ 154 Effects of Model Complexity on Sensitivity ....................................................... 154 Morris method .............................................................................................. 154 Extended FAST ........................................................................................... 155 Effects of Model Complexity on Uncertainty ..................................................... 156 Conclusions .............................................................................................................. 160 6 CONCLUDING REMARKS ...................................................................................... 172 Conclusions .............................................................................................................. 172 Limitations ................................................................................................................. 173 Future Research ....................................................................................................... 174 Philosophical Deliberations ...................................................................................... 176 APPENDIX A MODEL VERSIONS ................................................................................................. 178 Model and Application Versions: Nomenclature ...................................................... 178 Model and Application Versions: Submodels ......................................................... 178 B DETAILS OF THE FTARSELOADDS LINKAGE ..................................................... 182 Section B1 ................................................................................................................. 182 Technical Considerat ions in the Model Linkage ............................................... 182 Consideration 1: Initial setup of aRSE ........................................................ 183 Consideration 2: Spatially distributed versus non-spatial .......................... 184 Consideration 3: FORTRAN versus C++ ................................................... 184 Resolution 1: Initial setup of aRSE ............................................................. 186 Resolution 2: Spatially -distributed versus non-spatial ............................... 187 Resolution 3: FORTRAN versus C++ ......................................................... 189 General description of the linkage mechanism .......................................... 189 Section B2 ................................................................................................................. 190 FORTRAN Subroutines for Linkage .................................................................. 190 Module aRSEDIM ........................................................................................ 190 Subroutine READIWQ ................................................................................. 191 Subroutine CALLaRSE ............................................................................... 193

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8 Subroutine aRSE_IN ................................................................................... 195 Subroutine aRSE_OUT ............................................................................... 197 Subroutine RUNaRSE ................................................................................. 198 Subroutine CELLCOUNT ............................................................................ 200 Section B3 ................................................................................................................. 201 READIWQ Input File .......................................................................................... 201 Section B4 ................................................................................................................. 202 Nash -Sutcliffe Calculation for Analytical Testing .............................................. 202 Program STUPOSTPROCESS ................................................................... 202 Subroutine POSTPROCESS ...................................................................... 204 Subroutine CORSTAT ................................................................................. 205 C WATER -QUALITY APPLICATION CODE AND INPUT FILES ............................... 216 Section C1 ................................................................................................................. 216 Additional Subroutines for Water -Quality Inputs ............................................... 216 Subroutine EDIT_INPUTFILE ..................................................................... 216 Subroutine STRUCTCONCS ...................................................................... 218 Section C2 ................................................................................................................. 220 Important Input Files for the SICS Water -Quality Simulation ........................... 220 Format for INPUTFLOWCONCS.dat .......................................................... 220 Total Phosphorus Atmospheric Deposition Rates for Model 2 ......................... 221 Section C3 ................................................................................................................. 234 XML Input File for Model 3 (XMLINPUT.xml) .................................................... 234 IWQ input File for Model 3 (IWQINPUT.iwq) .................................................... 238 SWIFT2D Input File (WETLANDS.inp) for Model 3 .......................................... 239 LIST OF REFERENCES ................................................................................................. 266 BIOGRAPHICAL SKETCH .............................................................................................. 280

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9 LIST OF TABLES Table page 2 -1 Quantities and values used in the comparison of SWIFT2D and FTaRSELOADDS against the analytical solution ................................................. 51 2 -2 Nash -Sutcliffe efficiencies obtained for different methods of integrating aRSE reactions into FTLOADS ........................................................................................ 52 3 -1 Nash -Sutcliffe efficiencies for water -level observation points in SICS ................. 77 3 -2 Nash -Sutcliffe statistics for stations in the viciniy of Taylor Slough, stations in the vicinity of C 111, and all stations in the SICS region. ..................................... 77 4 -1 Stations and total phosphorus concentration data used for interpolation of daily concentrations for specified head boundary conditions in Florida Bay ..... 118 4 -2 Data sources and values used for boundary conditions concentrations at the L -31W discharge source ...................................................................................... 119 4 -3 Data sources and values used for boundary conditions concentrations at the C -111 discharge source. ...................................................................................... 120 4 -4 Data sources and values used for boundary conditions concentrations at the TSB discharge source. ......................................................................................... 121 4 -5 Parameters used in the model ............................................................................. 122 4 -6 State variables with initial conditions as used in Model 3 ................................... 123 4 -7 Nash -Sutcliffe efficiencies for the water quality models applied to simulate total phosphorus in the Southern Inland and Coastal Systems .......................... 124 5 -1 Process description for the increasing levels of complexity studied .................. 163 5 -2 Probability distributions of model input factors used in the global sensitivity and uncertainty analysis ...................................................................................... 164 B-1 Explanation of the READIWQ input file structure and read in parameters ........ 201 C -1 Atmospheric deposition rates input to Model 2 ................................................... 221

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10 LIST OF FIGURES Figure page 1 -1 Location of the Southern Inland and Coastal Systems study area ...................... 31 1 -2 Reviewed phosphorus water -quality models and algorithms from simple to complex .................................................................................................................. 32 1 -3 Reviewed phosphorus water -quality models and algorithms from intermediate to complex ......................................................................................... 33 2 -1 Schematic detailing the architecture of the code linking the surface water model in FTLOADDS with a Reaction Simulation Engine .................................... 52 2 -2 Source boundary condition for analytical solution ................................................. 53 2 -3 SWIFT2D model domain used for comparison of conservative and reactive transport simulations with analytical solutions ...................................................... 54 2 -4 Concentration isolines for 2-D conservative transport from a small rectangular source as determined by SWIFT2D ................................................... 55 2 -5 Concentration isolines for 2-D reactive transport from a small rectangular source as determined by SWIFT2D ...................................................................... 56 2 -6 Sp atially -interpolated RMSE and Nash-Sutcliffe efficiencies after 150 minutes of simulation for the case of transport reactions -transport -reactions. .................. 57 2 -7 Spatially -interpolated RMSE and Nash-Sutcliffe efficiencies after 300 minutes of simulation for the case of transport -reactions -transport -reactions. .... 57 3 -1 Location of the Southern Inland and Coastal Systems study area ...................... 78 3 -2 Space -staggered grid system showing relative locations of hydrodynamic characteristics. ........................................................................................................ 79 3 -3 The SICS computational grid, showing the location of Taylor Slough, the Buttonwood Embankment and the coastal creeks ................................................ 80 3 -4 Land-surface elev ations ........................................................................................ 81 3 -5 Location of SICS model boundary conditions, including specified water -level boundaries and discharge sources ........................................................................ 82 3 -6 Specified hydrologic inputs to SWIFT2D ............................................................... 83 3 -7 Water -levels at the six stations in the vicinity of Taylor Slough, simulated with depth varying Mannings n and with constant Mannings n ................................. 84

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11 3 -8 Water -levels at the six stations in the vicinity of C 111, simulated with depthvarying Mannings n and with constant Mannings n ............................................ 85 3 -9 Water -levels at the six stations in the vicinity of Taylor Slough, simulated with depth varying Mannings n in the current version and the original SICS application ............................................................................................................... 86 3 -10 Water -levels at the six stations in the vicinity of C 111, simulated with depthvarying Mannings n in the current version and the original SICS application ..... 87 3 -11 Frequency and cumulative distribution of Nash -Sutcliffe efficiencies attained wit h SICS v1.2.1, for all 12 water -level stations. ................................................... 88 3 -12 Frequency and cumulative distribution of Nash -Sutcliffe efficiencies attained with SICS v1.2.1, for 6 water level stations in the vicinity of Taylor Slough. ....... 89 3 -13 Frequency and cumulative distribution of Nash -Sutcliffe efficiencies attained with SICS v1.2.1, for 6 water level stations in the vicinity of C -111. .................... 90 3 -12 Trends in prediction bias for the 6 stations in the vicinity of Taylor Slough. ........ 91 3 -13 Trends in prediction bias for the 6 stations in the vicinity of C 111. ..................... 92 3 -14 Rainfall and discharge inputs, and corresponding 2D water level distributions for the first four months ..................................................................... 93 3 -15 Rainfall and discharge inputs, and corresponding 2D water level distributions for the middle four months ................................................................ 94 3 -16 Rainfall and discharge inputs, and corresponding 2D water level distributions for the final four months ..................................................................... 95 3 -17 Simulated and measured discharges through five gauged creeks in the Buttonwood Embankment ...................................................................................... 96 3 -18 Rainfall and discharge inputs, and corresponding 2D discharge vector distributions for the first four months ..................................................................... 97 3 -19 Rainfall and discharge inputs, and corresponding 2D discharge vector distributions for the middle four months. ............................................................... 98 3 -20 Rainfall and discharge inputs, and corresponding 2D discharge vector distributions for the final four months ..................................................................... 99 3 -21 Rainfall and discharge inputs, and corresponding 2D salinity distributions for the first four months ............................................................................................. 100 3 -22 Rainfall and discharge inputs, and corresponding 2D salinity distributions for the middle four months ......................................................................................... 101

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12 3 -23 Rainfall and discharge inputs, and corresponding 2D salinity distributions for the final four months ............................................................................................. 102 4 -2 Location of SICS model boundary conditions ..................................................... 126 4 -3 Location of water -quality observation points in Florida Bay ............................... 127 4 -4 Model 1: Conservative transport assuming deposition and internal sources are in equilibrium with biotic uptake and internal sinks. ...................................... 128 4 -5 Model 2: First order uptake from the water column using the reactive transport functionality of SWIFT2D ...................................................................... 129 4 -6 Model 3: Reactions simulated by aRSE with transport by SWIFT2D ................. 130 4 -7 Mean proportion of total rec overed radioisotope (32P) per mesocosm found in different ecosystem components over time. ........................................................ 131 4 -8 Simulated TP concentrations obtained with Model 1 .......................................... 132 4 -9 Simulated TP concentrations obtained with Model 2 .......................................... 133 4 -10 Simulated TP concentrations obtained with Model 3 .......................................... 134 5 -1 Relevance relative to sources of modeling uncertainty and sensitivity in relation to model complexity ................................................................................ 165 5 -2 Hypothesized trends relating complexity to sensitivity from direct effects, sensitivity from interactions, and total sensitivity ................................................ 166 5 -3 TaRSE application domain, with flow from left to right and bounded above and below by no -flow boundaries ........................................................................ 166 5 -4 Levels of modeling complexity studied to represent phosphorus dynamics in wetlands. ............................................................................................................... 167 5 -5 Morris method global sensitivity analysis results for surface water soluble reactive phosphorus outflow ................................................................................ 168 5 -6 Results for sensitivity from direct effects interactions and output uncertainty .. 169 5 -7 Output PDFs for SRP concentration in surfacewater outflow ........................... 170 5 -8 A suggested framework, employing global sensitivity and uncertainty analyses ................................................................................................................ 1 71 A-1 SWIFT2D v1.1 comprises the SWIFT2D v1.0 code and additional code from SICS updates for coastal wetlands. ..................................................................... 179

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13 A-2 FTLOADDS v1.1 comprises the SWIFT2D v1.1. code, leakage code linki ng SWIFT2D to SEAWAT, and SEAWAT ................................................................ 179 A-3 SEAWAT comprises the MODFLOW code and the MT3DMS code .................. 179 A-4 FTLOADDS v2.1 comprises SWIFT2D v2.1 and SEAWAT, where SWIFT2D v2.1 is SWIFT2D v1.1 implemented with integrated leakage ............................. 180 A-5 FTLOADDS v1.2 comprises SWIFT2D v2.2 with updates for TIME but with the groundwater simulation turned off. ............................................................... 180 A-6 FTLOADDS v2.2 contains SWIFT2D v2.1 linked with SEAWAT and containing TIME updates. .................................................................................... 181

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14 LIST OF ABBREVIATION S aRSE a Reaction Simulation Engine CERP Comprehensive Everglades Restoration Plan eFAST extended Fourier Amplitude Sensitivity Test ENP Everglades National Park FAS T Fourier Amplitude Sensitivity Test FDEP Florida Department of Environmental Protection FTaRSELOADDS Flow, Transport and Reaction Simulation Engine in a Linked OverlandAquifer Density Dependent System FTLOADDS Flow and Transport in a Linked Overland-Aquifer Density Dependent System GSA Global sensitivity analysis P Phosphorus PDF Probability Distribution Function SFRSM South Florida Regional Simulation Model SFWMD South Florida Water Management District SFWMM South Florida Water Management Mo del SICS Southern Inland and Coastal Systems SRP Soluble Reactive Phosphorus SWIFT2D Surface water Integrated Flow and Transport in 2 Dimensions TaRSE Transport and Reaction Simulation Engine TIME Tides and Inflows in the Mangroves of the Everglades TP Tot al phosphorus UA Uncertainty Analysis USGS United States Geological Survey

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15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ADAPTIVE SPATIALLY -DISTRIBUTED WATER -QUALITY MODELING: AN APPLICATION TO MECHANISTICALLY SIMULATE PHOSPHORUS CONDITIONS IN THE VARIABLE-DENSITY SURFACE-WATERS OF COASTAL EVERGLADES WETLANDS By Stuart John Muller August 2010 Chair: Rafael Muoz -Carpena Major: Agricultural and Biological Engineering The Everglades region known as the Southern Inland and Coastal Systems is an important area that supports numerous endangered species and plays a crucial role in regulating water quality conditi ons in Florida Bay. Taylor Slough is a major feature of this region and represents the primary surface water pathway for freshwater inputs to Florida Bay. The slough is also subject to intensive flow management under the Comprehensive Everglades Restorat ion Plan, yet the consequences of such management for water -quality in these oligotrophic and sensitive wetlands are not well understood. A flexible phosphorus water quality model was therefore developed and tested as an exploratory management tool for th e region. Complex local hydrodynamics required that a spatially -distributed hydrodynamic model be used to simulate flow and transport and the USGS model FTLOADDS was selected for this A user definable biogeochemical reactive component (aRSE) was then coupled with the hydrodynamic model and the resulting FTaRSELOADDS model was tested against analytical solutions and field data.

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16 Hydrodynamic field testing showed that depthvarying Mannings resistance was important for accurately capturing wet and dry condi tions during the experimental period Conceptual water -quality models of increasing complexity were tested against experimental phosphorus field data. Results revealed that a simple daily averaging method was the best approach for atmospheric deposition of phosphorus, which is a crucial b ut ve r y uncertain water quality input. A simple conservative transport model provided the best fit between model ed and total phosphorus concentration data. Similar results were also obtained with a more complex and mechanistically justifiable water quality model. The adaptability of the biogeochemical component was used to study how additional model complexity affects model uncertainty, sensitivity and relevance by evaluating progressi vely more complex conceptual models using global sensitivity and uncertainty analyses. The framework applying these methods is suggested as a useful way of evaluating models in general, and deciding upon a relevant model structure when the freedom to dictate complexity exists.

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17 CHAPTER 1 INTRODUCTION The Southern Inland and Coastal Systems of the Everglades: A Region at Risk The Southern Inland and Coastal Systems (SICS) region of the southern Everglades (Figure 11) connects Taylor Slough and the C -111 marl prairie wetlands with Florida Bay, and represents an important region of Everglades study and management (SFWMD and FDEP 2004; CRGEE and NRC, 2002 ). Though Taylor Slough is substantially smaller than Shark River Slough, in both discharge and ar e al extent, it plays an important role in regulating water quality in Florida Bay (Fourqurean and Robblee, 1999). Additionally, t he region encompasses thousands of acres of habitat that support dwindling populations of saltwater and freshwater animal species (van Lent et al., 1998), fifteen of which are listed as threatened or endangered with extinction (Beccue, 1999), including the Federally protected Cape Sable Seaside Sparrow (Pimm et al., 2004). Flow through the southern Everglades has been increased as part of the Comprehensive Everglades Restoration Plan (CERP), with further increases imminent. The potential effects of these c hanges on nutrient conditions in Taylor Slough, the neighboring wet marl prairies, or the estuaries of Florida Bay is not well understood and the subject of ongoing research (Childers, 2006). Studies suggest that the SICS area is already under intense ecol ogical stress from past management decisions that have impacted flow and nutrient conditions (Childers, 2006; Gaiser et al., 2006; Armentano et al., 2006). In addition, gradual reductions in freshwater inputs flowing southwards have contributed to the encr oachment of saltwater tolerant species, primarily mangrove forest, into previously freshwater marsh vegetation (Smith, 1998). Of particular concern

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18 are the possible consequences of additional nutrient loading to Florida Bay (SFWMD and FDEP, 2004), which h as seen an increase in the incidence of harmful algal blooms and mass seagrass dieoff (Fourqurean and Robblee, 1999). The Everglades are a highly oligotrophic system (Noe et al., 2001) due to a natural scarcity in bioavailable phosphorus. The concentration of phosphorus in the surface water is therefore a principal consideration in the Everglades restoration. Freshwater ma rshes in the SICS region are characterized by unique macrophyte and periphyton communities that are adapted to phosphorus -scarce con ditions. Periphyton taxa have been shown to be very sensitive to phosphorus conditions (Gaiser et al., 2004), with cascading ecological consequences resulting from even low levels of nutrient enrichment (Gaiser et al., 2005). Additionally, the low phosph orus loading with freshwater inputs to the estuaries of Florida Bay means that water from the Gulf of Mexico is their most important source of phosphorus, as opposed to the upstream watershed as is normally the case (Chen and Twilley, 1999; Fourqurean et al., 1992). This reversal in the source of the limiting nutrient, compared with typical estuaries (biogeochemically speaking), is the reason they are referred to as upside-down estuaries (Childers, 2006). It is believed that phytoplankton and seagrasses in eastern Florida Bay, which is most isolated from the Gulf of Mexico, are therefore phosphorus limited (Fourqurean et al., 1992). Higher natural or anthropogenic loadings of phosphorus that may accompany increasing freshwater inputs could potentially i ncrease the frequency, intensity, and duration of phytoplankton blooms in regions of Florida Bay. How ever, s ignificant increases in the volume of freshwater inflow relative to the nutrient additions from upstream sources could make terrestrial phosphorus inputs

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19 negligible, and may possibly even suppress the natural marine phosphorus supply by dilution. Recent research has shown that freshwater inflows have been found to enhance oligotrophy where Taylor Slough sufficiently flushes the area and suppresses the intrusion of water from Florida Bay (Childers, 2006). As such, any increase in freshwater inflows could enhance oligotrophic conditions in the ecotone between fresh and marine waters, especially during the wet season. Time -series water -quality and soil phosphorus data shows a general pattern of low phosphorus availability along Taylor S lough during the wet season except near the marine source (Boyer et al., 1999), and the influence of marine phosphorus moving upstream during the low -flow dry season. This was not expected for the southern Everglades ecotone as light easily penetrates the clear shallow waters above seagrass pastures, which are known to efficiently sequester marine phosphorus (Fourqurean and Robblee, 1999) New research in the area has indicated that surface -water phosphorus concentrations were unexpectedly high in the Taylor Slough ecotone during the dry season (Childers, 2006). It is conjectured that relatively phosphorus rich groundwater inputs to thi s ecotone are significant during the dry season, when surfacewater hydraulic heads are lowest and residence times are long enough to deplete dissolved organic matter, thus reducing productivity and phosphorus consumption (Price et al., 2006; Childers, 2006). Strong interactions between groundwater and surface water in this region mean that increased surfacewater heads may impact this groundwater exchange, and thereby affect phosphorus conditions

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20 Opportunities for Spatially Distributed Mechanistic Modeling of Phosphorus in SICS A model of spatially distributed surface water phosphorus conditions for the region is required to study these issu es. Spatially -distributed mechanistic modeling of wetland water -quality remains a challenging field of hydrology. Modeling the movement of solutes both within and with the water is contingent upon reliable flow modeling, which is a difficult task unto itself in the vegetated and hydrodynamically complex SICS wetlands (Swain et al., 2004; Langevin et al., 2005) In addition, water -quality constituents are subject to a multitude of chemical, physical and biological processes in wetlands where unique biogeochemistry and ecology are drivers of, as much as driven by, water quality. Hydrologic Modeling of SICS Numerical models for simulating water flow south of Lake Okeechobee have been developed for three distinct regions. The South Florida Water Management Model (SFWMM) (SFWMD, 2005) and its successor, the South Florida Regional Simulation Model (SFRSM) (Lal et al., 2005), simulate the highly managed hydrology between Lake Okeechobee and E verglades N ational P ark (ENP). The southern and western offshore waters of Florida Bay are modeled with the Florida Bay Hydrodynamic Model (Hamrick and Moustafa, 2003). The hydrologically complex region between these models domains is encompassed by SICS, and is characterized by surfacewater/groundwater and freshwater/salt water interactions within a highly vegetated and hydrodynamically unsteady environment. A further specialized modeling effort was therefore required (Swain et al., 2004; Langevin et al., 2005; Wang et al., 2007), which culminated in the Flow and Transport in a Linked OverlandAquifer Density Dependent

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21 System (FTLOADDS) model (Langevin et al., 2005). FTLOADDS links the managed hydrology of the mainland with that of Florida Bay; outputs from SFWMM are applied as boundary conditions in FTLOADDS, the outputs fr om which are in turn applied as boundary conditions for the Florida Bay Hydrodynamic Model. In this way, an integrated hydrologic modeling framework of the region was produced that could propagate the hydrologic consequences of upstream management scenario s onto the downstream systems. Furthermore, detailed hydrologic conditions can be simulated for use by mechanistic ecological models that rely on such information, and which is typically not practically obtainable at the desired resolution (Swain et al., 2004) FTLOADDS is itself composed of two model s ; the Surface Water Integrated Flow and Transport in Two Dimensions (SWIFT2D) model (Schaffranek, 2004) adapted for coastal wetlands (Swain, 2005), and the variabledensity groundwater model SEAWAT (Langevin and Guo, 2006). An application of FTLOADDS to the SICS area that uses only SWIFT2D, and thus neglects surface water/groundwater interactions has been shown to provide acceptable hydrodynamic results (Swain et al., 2004). Water Quality Modeling of SICS Models of the Everglades hydrology and hydrodynamics have and continue to be addressed, but analogous tools for water quality are still needed (McPherson and Torres, 2006). One approach to addressing this need is to develop a detailed ecosystem model (Wan g and Mitsch, 2000). This approach simulates a large number of biogeochemical processes and therefore requires many parameters, which make the model cumbersome to apply and prone to overparameterization (Beven, 200 6 a ). Such conceptually complex models of ten use free -form tools such as STELLA (Doerr, 1996) which can be readily tailored to the specific water quality considerations at hand.

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22 However, the versatility often comes at the expense of spatial heterogeneity, which is an untenable simplification in the context of the scale and spatial complexity of SICS. For instance, the spatial variation in microtopography, landcover, and complex flow boundaries that include canals, pumping stations, and tidal effects, are known to be important factors that deter mine water level (and therefore whether conditions are wet or dry) and velocity in SICS (Swain et al., 2004). Flow velocity is crucial for accurate solute transport when using the advectiondispers ion equation. Water -level is bi ogeoch e mically important b ecause it determines whether conditions are dry or wet, which has implications for the presence or absence of aquatic biota and senescence and decomposition processes (Reddy et al., 1999). Both velocity and water level are important for accurate estimation of discharge, which with concentration determines loading rates that would be of interest to Florida Bay. Additionally, the original SICS hydrodynamic modeling effort demonstrated the striking effect of wind shear on water levels and the direction ality o f discharges through coastal creeks, and in turn important wind -driven mixing (Swain et al., 2004). In order to accurately capture these transient effects in the transport solution a mechanistic hydrodynamic model is required that accounts for the ir effe cts. Consequently, a spatially distributed and mechanistic hydro dynamic foundation was considered requisite. A more common and simplified approach is to aggregate all phosphorus cycling mechanisms into a single lumped process that captures net uptake or release (Kadlec and Knight, 1996; Mitsch et al. 1995; Walker, 1995), or some combination of lumping and mechan istic methods (Kadlec, 1997). This simplification in biogeochemistry is counterbalanced by the complexity of spatial heterogeneity in hydrology. However, the

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23 modeling efforts cited simulate d surfacewater flow using simplified mass balance approaches (Wa lker, 1995; Wang and Mitsch, 2000) or as nondispersive, unidirectional plug flow (Kadlec, 1997), which are not suitable for the complex conditions in SICS. In addition to homogeneous hydrology, there is also no accounting for spatial heterogeneity in wetl and components and processes that may be important or desirable (for example, soil phosphorus concentration or accretion an d macrophyte or periphyton bioma ss). With the arrival of spatially distributed mechanistic models of Everglades hydrology, the logical step to develop a mechanistic water quality model that built on this foundation was undertaken. The result was TaRSE, the Transport and Reaction Simulation Engine (Muller and Muoz -Carpena, 2005; Jawitz et al., 2008; James et al., 2009). The term reac tion simulation engine alludes to a novel characteristic of TaRSE; the state variables and equations relating them are user defined. To our knowledge, this was the first time a spatially -distributed mechanistic water -quality model had been developed with the built -in flexibility of a free -form simulation model for defining the system of biogeochemical water -quality processes. This pairing represents an important new management and research tool for the SFWMD to address phosphorus related water quality is sues. Though originally integrated into SF RSM, a version of TaRSE without the transport (now a Reaction Simulation Engine aRSE) has subsequently been extricated from SF RSM and modularized. Model Selection A critical consideration in the selection of a m odel is the choice of appropriate complexity. In the context of mechanistic water quality modeling, which entails a twostep process of simulating hydrology and biogeochemistry, this choice must be made

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24 twice. Historically, the complexity of each of thes e components has often been mutually exclusive, though the greater prevalence of spatial data and computational power have seen a move towards models with complex treatments of both hydrology and biogeochemistry (Costanza et al., 1990). Figures 1-2 and 13 present a number of phosphorus water quality models that were reviewed and classified according to their overall complexity. They demonstrate the wide range of complexities and approaches that exist for modeling phosphorus -related water quality. A disti nguishing feature in the design of models that is associated with their complexity is whether they are fixed-form (usable as -is only), or free-form (intentionally user definable). The fixed-form development paradigm is generally applied for complex sp atially -distributed models (of which hydrologic models are a prime example), which require computationally efficient numerical solutions. Many hydrologic models are based on fundamental laws of physics, and consequently are quite versatile despite their r igid design. Free -form models are sometimes referred to as dynamic systems models, and are more suitable to simulating systems where spatial heterogeneity can be neglected. The relatively light computational demands of a spatially -lumped model compared wi th a spatially distributed one make it amenable to a more flexible design. The user is therefore able to specify state variables of interest and how they are related, with the result that such tools are highly adaptable to a variety of system applications, including biogeochemical cycling. The extensive and varied application of STELLA, a widely used example of a free-from model, is indicative of this versatility (Doerr, 1996).

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25 The complexity of SICS hydrology calls for a fixed -form spatially distributed me chanistic hydrodynamic model. Yet the lack of a clear indication of what, exactly, a phosphorus water quality model should look like (Figures 1-2 and 13), and the looming need for models of other water quality constituents and ecological components, call s for a free -form solution. It was therefore proposed that a fusion of the fixed-form and free form development paradigms be attempted by linking the SWIFT2D model within FTLOADDS with aRSE. Important SICS Modeling Considerations Since the initial applica tion of SWIFT2D to SICS (Swain et al., 2004) the model has been further adapted for application to the larger Tides and Inflows to the Mangroves of the Everglades (TIME) domain (Wang et al., 2007), which includes the SICS model domain but is applied using a somewhat larger cell size (500 m as opposed to 304.8 m). These changes include a number of potentially important simplifications; rainfall and evapotranspiration (ET) rates are now applied homogenously, and the Mannings coefficient no longer varies wit h flow -depth, though it is now treated anisotropically where before it was considered isotropic. The implications of the changes to rainfall and evapotranspiration have been sufficiently justified for SICS (Wang et al., 2007). The consequences of depth-i nvariant Mannings coefficients are unclear though, particularly since this proved to be an important factor in the original SICS hydrologic modeling effort (Swain et al., 2004) Depthvarying Mannings n was also found to be important under similar assum ptions of homogeneous rainfall and ET in the ridge and slough Everglades landscape (Min et al., 2010) Of particular concern is how this change affects the ability of SWIFT2D to accurately capture dry versus wet conditions, which are important for phosphorus cycling (Reddy et al., 1999).

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26 A second important consideration pertain to atmospheric deposition of total phosphorus (TP). This is a crucial input for modeling water -quality under the oligotrophic conditions found in SICS (Sutula et al., 2001; Noe and Childers, 2007). However, atmospheric deposition of phosphorus is notoriously difficult to quantify due to persistent sample contamination and limitations in the sampling methods (Redfield 1998; Ahn, 1999 ). Bulk phosphorus deposition in Florida is estim ated to be comprised of as much as 30 -50% dry deposition from resuspended agricultural soils, phosphogypsum mining, urban emissions and transported dust (Landing, 1997; Meyers and Lindberg, 1997). However, rainfall is known to scavenge aerosol phosphorus and incorporate dry deposition into wet deposition estimates, further complicating quantification of the process. Measured rates of bulk atmospheric deposition in the Everglades exhibit great variability, ranging from 0.017 to 0.07 g TP/m2/yr, with an av erage of 0.03 g TP/m2/yr (Sutula et al., 2001). Fitz and Sklar (1999) estimated total phosphorus deposition to be 0.03 g TP/m2/yr for the Everglades, which is similar to an estimate by Davis (1994) of 0.036 g TP/m2/y, and the same as that of 0.03 g TP/m2/ yr found for the Kissimmee region 100 miles north of the Everglades (Moustafa et al.. 1996). Rates as low as 0.0006 g P/m2/yr have been estimated for the Bahamas (Graham and Duce, 1982). South Florida weather is characterized by frequent convection thunder storms, which can scavenge aerosol phosphorus from the upper atmosphere (Poleman et al., 1995), and the location of SICS in the proximity of Miami could subject it to higher deposition rates associated with adjacent urban or industrial areas (Paerl, 1995; Redfield, 1998).

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27 Consequently, there is great uncertainty in the quantification of atmospheric deposition of phosphorus, and the process will therefore represent a major source of uncertainty in any phosphorus water -quality modeling effort. How best to i nput this source remains an open question. Another important open question is, given the free form of aRSE, what complexity of water -quality model to select. This raises the issue of how to balance model complexity and relevance. Model Relevance A princi pal tenet of model development is the establishment of relevance (Zadeh, 1973) Relevance is determined by balancing the complexity of a model against its u ncertainty given the modeling objectives at hand. This topic is introduced and discussed in great detail in Chapter 5, which is presented as a standalone paper, but is briefly reviewed here to clarify the motivation. Model complexity is a property of the degree of detail implicit to the conceptualized re ndition of reality, including the number of state variables and processes simulated. Increasing complexity implies ever more variables and processes, and therefore ever fewer simplifying assumptions. This results in a modeled version of reality with greater mechanistic integrity and thus less structural uncertainty. However, each new statevariable and process introduced requires additional calibration and parameterization data, all of which are subject to some measurement uncertainty. These meas urement uncertainties accumulate and eventually outweigh any reductions in structural uncertainty gained by increasing complexity (Hanna, 1988). The sensitivity of model outputs also accumulates with consequences for the practicability of the model (Snowling and Kr amer, 2001) Each added process that exerts some influence over a state variable, either directly or through interactions with other processes, represents

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28 additional flexibility in the model that can lead to overparameterization issues that can seriously u ndermine the validity of a model (Beven and Binley, 1992) Two model evaluation methods exist that are ideally suited to elucidating these relationships. Uncertainty analysis applies Monte Carlo simulations to propagate the uncertainty inherent to model inputs onto outputs of interest. In this way, the uncertainties in an output for a given model structure, and subject to the given model input requirements, can be assessed and compared. Global sensitivity analyses determine where the uncertainty in an output originates from (Saltelli et al., 2000) Together, these evaluation methods can shed light on how much uncertainty is in the model, and why it is there (Muoz -Carpena et al., 2007) When performed in the context of varying model complexity we are t hen able study how additional complexity affects the model s inner workings (Jawitz et al., 2008) The process of defining a model is also the process of defining a models complexity; the ultimate source to which many modeling considerations and challenges can be traced. This tripartite web of interacting complexity, uncertainty, and sensitivity has not been well -studied in very complex models (Lindenschmidt, 2006) precisely because they have typically been fixed -form. A flexible model structure presents a novel opportunity to subtly experiment with advanced levels of model complexity and to assess how complexity affects uncertainty, sensitivity, and ultimately relevance. Research Questions and Objectives Research Questions There is urgent need for modeling tools to simulate a variety of water -quality issues of interest in the southern Everglades and in particular phosphorus conditions in the sensitiv e of oligotrophic freshwater marshes A ssessing likely phosphorus

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29 conditions in the surfacewater in respons e to CERP flow management decisions is a pressing concern. Though a suitable hydrodynamic model of SICS has been identified and tested for hydrological outputs (Swain et al., 2004) its suitability to supporting spatially -distributed water quality simulat ions need s to be assessed. Furthermore, as indicated atmospheric deposition of phosphorus is an important process in the oligotrophic freshwater Everglades that remains very difficult to quantify. How best to handle this crucial input is therefore a major source of uncertainty. Finally, with the flexibility of a free-form water quality model the definition of the phosphorus conceptual model becomes a moving target yet a suitable complexity must eventually be settled upon. Open questions to be addressed in this dissertation include: What are the consequences of recent changes to the SWIFT2D code that included removal of depthvarying Mannings roughness? In particular, how do these changes affect the hydrodynamic predictio n of wet versus dry conditions in SICS, which are important distinctions for a water quality simulation? Given the acknowledged uncertainty associated with quantifying atmospheric deposition of phosphorus w hat methods of input ting this source to the water quality model produce the most accurate simulated concentrations ? What is the simplest phosphorus water quality model that would produce acceptable results for SICS? Can a more complex and mechanistic model of water -quality produce comparable or better r esults than a simpler one? G iven the tradeoffs bet ween complexity and uncertainty, how does one choose what model complexity is appropriate, and h ow does uncertainty and sensitivity change with the addition of further complexity? Objectives 1 Development of a combined fixed -form /free -form spatially -distributed hydrologi c and biogeochemical model validated against analytical testing which is suitable for application to simulate phosphorus water quality in SICS (Chapter 2). 2 Application of the new tool to stu dy the importance of depth varying Mannings roughness in hydrodynamic simulations of SICS surface water (Chapter 3)

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30 3 Application of the new tool to determine how best to input phosphorus additions by atmospheric deposition and to determine what complexit y of phosphorus water quality model best captures measured phosphorus conditions in SICS surface waters (Chapter 4). 4 Formal evaluation of the effect of using different complexity biogeochemical conceptual models on output uncertainty global sensitivity, a nd model relevance (Chapter 5).

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31 Figure 11. Location of the Southern Inland and Coastal Systems study area (from Swain et al., 2004)

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32 Figure 12 Reviewed phosphorus water quality models and algorithms (from simple to complex from left to right).

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33 Figure 13 Reviewed phosphorus water quality models and algorithms (from intermediate to complex from left to right).

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34 CHAPTER 2 FUSION OF FIXED -FORM AND FREE -FO R M MODELS FOR ADAPTIV E SIMULATION OF SPATIA LLY DISTRIBUTED WETLAND WATER -QUALITY Introduction Spatially distributed mechanistic water -quality modeling of wetlands, such as those in southern Florida, requires simulating three distinct, yet inter related, aspects: 1) the quantity and timing of water distribution (hydrodynamics); 2) the motion of constituents with and within the water by advection, dispersion and diffusion (transport); and 3) local biogeochemical processes that change the nature or state of constituents (reactions). Mechanistic hydrodynamics and transport of large -s cale wetland systems generally requires spatially distributed modeling. The numerical considerations associated with this, in conjunction with the generality of the underlying physics, results in models that are hard-coded or fixed-form with little o r no freedom on the part of the user to influence the theoretical concepts driving the simulation. By contrast, biogeochemical reactions can be more readily conceptualized as a non-spatial system by relying on hydrodynamics and transport to provide the sp atial connection. Water -quality reactions are therefore more amenable to non-spatial dynamic systems simulation, for which user -definable or free-form modeling tools are regularly used. The need for spatially distributed mechanistic water quality m odels therefore offers an excellent opportunity to integrate the versatility of a free -form dynamic systems model with the mechanistic and numerical rigor of a spatially distributed fixed -form modeling. FixedForm Versus Free-Form Truly mechanistic mod els of hydrology apply theoretically derived equations of flow dynamics, which are generally well -understood and are based on uniformly

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35 applicable laws of phys ics. For instance, the Surface -W ater Integrated Flow and Transport in Two Dimensions (SWIFT2D) model (Leendertse, 1987; Schaffranek, 2004; Swain, 2005) applies the St Venant equations, which are derived from Newtons Second Law (Conservation of Momentum) and the Pri nciple of Conservation of Mass Spatial discretization of the model domain is necessary to capture variability in space, and transience is captured by repeatedly solving the equations in successive time steps. This approach is contingent on limitations to the size of both spatial and temporal discretizations in order to maintain mathematic al stability of the numerical solutions. Stability considerations in conjunction with simulations of large areas or long periods can therefore become computationally intensive, even limiting, despite the modern computational capacities we have at our dispo sal. To ensure numerical efficiency such hydrologic models are generally hard-coded into a fixed-form. This limits the models application to only those conditions that meet the underlying (and fixed) assumptions. However, given the universality of phys ics, mechanistic flow models that use equations derived from theoretical principles remain generally versatile. For example, SWIFT2D has been applied to a multitude of water bodies and locations, including: Jamaica Bay, New York (Leenderste, 1972), the Dut ch Delta Works of the Netherlands (Dronkers et al., 1981; Leendertse et al., 1981), the Dutch Wadden Sea (with modifications to evaluate mixing) (Riddererinkhof and Zimmerman, 1992), the Eastern Scheldt estuary in the Netherlands (Leendertse, 1988), the Pamlico (Bales and Robbins, 1995) and Neuse River (Robbins and Bales, 1995) estuaries of North Carolina, Tampa Bay (Goodwin, 1987), Hillsborough Bay (Goodwin, 1991), and the upper Potomac estuary in Maryland (Schaffranek, 1986).

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36 Transport of dissolved and suspended constituents can be mechanistically simulated with the theoretically derived advectiondispersion equation (Equation 2 1). A reaction term can be introduced (now the advection-dispersion -reaction equation) to simulate first order growth or decay reactions. Given the dependence on velocity transport modeling within spatially distributed systems is often integrated into existing hydrologic models, and inherits a fixed -form structure. This is the case for both SWIFT2D (Schaffranek, 2004) and SEAWAT (Langevin and Guo, 2006). However, the underlying simple and generic mathematical formulation of linear growth and decay kinetics make the reactive transport universally applicable for any constituent, provided first -order reaction kinetics are appropriate for the process. The introduction of biogeochemical processes, which are fundamental to wetland water -quality (Mitsch and Gosselink, 2000) greatly complicates matters because such processes are too complex to be mechanistically derived from a physics -bas ed foundation. The biology, chemistry and physics of the aquatic environment all interact to form a byzantine web of feedbacks that constitute some of the most complex natural systems science has endeavored to conceptualize. Simulating such complex biogeochemical systems requires substantial simplification and abstraction, and even then presents a significant technical challenge (Arhonditsis and Brett, 2004). Matters are further confounded by the sheer variety of water -quality subjects sediments, nutri ents, pesticides, bacteria, pH, salinity, dissolved oxygen, dissolved organic matter, and algae, to name but a few each of which are involved in their own unique biogeochemical processes. Spatially -distributed modeling of water -quality issues has therefo re also generally been of the fixed form. Particular water quality functionality

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37 is to address a particular water -quality issue hard-coded into a given hydrologic model, which limits the applicability of the water quality model to the range of appropriate hydrologic applications, and limits the conceptual model of the water quality constituent to the hard-coded form R arely have the power of free -form dynamic system models and fixed-form spatially -distributed hydrologic models been integrated. The aforementioned development of Ta RSE (Jawitz, et al., 2008; James et al., 2009) in Chapter 1 was, to the best of our knowledg e, the first instance of this. The reasons for this are unclear, although it is sufficiently intriguing to warrant some conjecture. Dynamic simulation models have generally been written in object oriented programming languages since these are conceptuall y well matched to the task. By comparison, spatially -distributed mechanistic models have been written in linear programming languages such as FORTRAN, which carry benefits for numerically efficient processing of the large arrays of data associated with a s patially discretized domain. Many of the most popular hydrologic models have their foundations in the early days of hydrologic model development, when the fusion of linear and object oriented programming philosophies was uncommon because computational lim itations of the day demanded the highest possible efficiencies. More often than not this meant coding in FORTRAN. The two submodels of FTLOADDS, both coded in FORTRAN, are classic examples of this: SIMSYS2D (Leendertse et al., 1987) is based on model dev elopment from the 1970s (Leendertse, 1970) and is the progenitor of SWIFT2D; and SEAWAT is ultimately an adapted version of a 1983 modular ground water model that would become MODFLOW (McDonald and Harbaugh, 1988 ). Mixed language programming

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38 has become in creasingly common with ever -growing computational capacity (Zimmermann et al., 1992; Cary et al., 1997). Although languages such as FORTRAN still offer the greatest control over computational efficiency, many higher level programming and even scripting languages are becoming popular alternatives for applications that are not critically limited by computational considerations (Oliphant, 2007). It is also the case that model development is never without a purpose, and it is difficult to conceive of developing a water -quality model without a particular water quality issue as the objective. In hindsight, it seems that a combination of serendipity and navet was at play in the development of TaRSE. The lack of experience at the time in both biogeochemistry and water -quality modeling on the part of this author, who was tasked with researching and formulating the preliminary water quality conceptualization (Muller and Muoz -Carpena, 2005), lead to particular attention and frustration associated with the choice of model complexity. This was amplified by the express intention of the project to develop a tool for application to water bodies throughout the Everglades, including wetlands, canals, and reservoirs, all of which are subject to their own biogeochemical idios yncrasies (Reddy et al., 1999) It would appear that these factors combined with the object oriented programming paradigm brought to the project by the team programmer to inspire the notion of a truly free-form spatially -distributed water quality model. M aterials and Methods In this section we describe the models selected for linkage and the processes by which their integration was achieved. Following this we present the results of testing conducted to validate the reactive transport of the fixed -form mo del against known

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39 analytical solutions. Validation of the linkage between the fixed and free-form models is then presented. Description of the Models The fixed-form hydrologic model used was Flow and Transport in a Linked OverlandAquifer Density Dependent System (FTLOADDS) (Wang et al., 2007), and the free-from water quality model was a Reaction Simulation Engine (aRSE) (Jawitz, et al., 2008). Together, they constitute a novel and potentially powerful new water -quality modeling tool for the coastal Ever glades wetlands; Flow, Transport and a Reaction Simulation Engine in a Linked Overland-Aquifer Density Dependent System (FTaRSELOADDS). Fixed-form hydrology and transport model: FTLOADDS The USGS has recently developed FTLOADDS as a tool for simulating linked surface and subsurface hydrology and transport Surface hydrology in FTLOADDS is modeled using the Surfacewater Integrated Flow and Transport in Two Dimensions (SWIFT2D) model (Swain, 2005), which simulates vertically averaged, variable-density, tran sient overland flow and transport of solutes. Subsurface hydrology in FTLOADDS is modeled using SEAWAT (Langevin, 2001; Guo and Langevin, 2002; Langevin and Guo, 2006), which simulates threedimensional, variable-density, transient groundwater flow and t ransport through a porous media. The two models are linked through the exchange of water and constituent mass between the surface and subsurface (Langevin et al., 2005). A number of different versions and implementations of FTLOADDS, SWIFT2D within FTLOAD DS, and the SICS application using these tools are referred to. Appendix A contains a detailed breakdown of the distinguishing features of each version

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40 and the nomenclature adopted by the USGS, and adapted herein. In this chapter, reference to FTLOADDS will imply FTLOADDS v1.2, which implements the latest SWIFT2D code used in FTLOADDS v2.2 (Wang et al., 2007) but with leakage and groundwater flow disabled hence FTLOADDS v1.2 and SWIFT2D v1.2 ( see Appendix A). In Chapter 3 some code changes were implem ented that constituted a new subversion v 1.2.1. Each version of each model is graphically outlined in Appendix A to facilitate clarification of the submodels that comprise each model and application version Freeform water -quality reactions model: aRSE With support from SFWMD and USGS, a group at UF recently developed a biogeochemical component the Transport and Reaction Simulation Engine ( T aRSE), for simulating the water -quality processes that control phosphorus concentrations and fate in Everglades wetlands (Jawitz et al., 2008; James et al., 2009). The term simulation engine alludes to the generic nature of the tool, which permits the user to define the conceptual biogeochemical system by controlling both the state variables and the mathematical form of the processes that connect them. Given the existence of a number of proven hydrologic models for the Everglades, TaRSE was developed as a water -quality module, and therefore relies on a suitable hydrologic model to simulate flow and provide the nec essary hydrodynamic inputs. The South Florida Regional Simulation Model (SFRSM) was selected as the first such hydrologic model. However, the absence of any solute transport functionality in SFRSM necessitated this be incorporated into the development of TaRSE. This transport functionality is contingent on the triangular mesh geometry employed by SFRSM for spatial discretization, which became a significant restriction on the portability of TaRSE for use by other hydrologic

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41 models, many of which already ha ve transport functionality of their own and a square spatial discretization geometry. The modularity of TaRSE was therefore re established by extricating it from SFRSM and removing the transport functionality, leaving it as simply a Reaction Simulation En gine (aRSE). Portability of aRSE was finalized through its modularization into a dynamically linked library (DLL), which is callable by any model, hydrologic or otherwise, to which it offers a powerful and flexible simulation engine. Fusing Fixedand Free -F o r m M odels Figure 21 presents a schematic of the linkage implemented to integrate FTLOADDS and aRSE. Blue portions correspond to FTLOADDS code, green to aRSE code, and yellow to the linkage code. Black text and lines indicate FORTRAN, red text and l ines indicate C++, solid lines indicate models, dashed lines i ndicate subroutines, solid line arrows indicate calls to subroutines in the same language, and mixeddash arrows indicate calls from one language to another. Full details of the technical consi derations in the linkage are presented in Appendix A but are briefly reviewed here in reference to Figure 21: An additional method for inputting aRSE parameters and state variables was required for this information to be available to FTLOADDS at the beg inning of the simulation. This was important for correctly exchanging hydrodynamic information between the models, and is achieved through a new input file that is read by the READIWQ subroutine during setup of SWIFT2D. FTLOADDS and its submodels are all coded in FORTRAN, whereas aRSE is coded in C++. Mixed -language programming methods were therefore required to facilitate commu nication between the two models ( indicated by the color -coding and mixed -dash lines in Figure 2-1 ) Since aRSE computes water qu ality reactions for one cell at a time, it was necessary to establish a framework that would efficiently repeat this process for each of the cells in the spatially distributed hydrodynamic domain. A temporary storage array is used to hold the latest values required by aRSE for each cell, which are in turn overwritten after each cell is processed by aRSE and returned to FTLOADDS once all cells have been reacted.

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42 The general functionality of the linkage is described in detail in Appendix B (Section B1 ) The code comprising the various subroutines of the linkage is given in Appendix B (Section B2 ). An explanation of the IWQ input file is given in Appendix B (Section B3 ) Analytical Testing of the FTaRSELOADDS Linkage In order to verify that the code used to i ntegrate FTLOADDS and aRSE was valid, a series of comparisons between numerically modeled results and known analytical solutions were conducted. While TaRSE has been previously t ested, no published analysis of aRSE exists. Similarly, though widely used and thoroughly tested in practice, no published comparison of SWIFT2D reactive transport against known analytical solutions were identified. Therefore, the procedure outlined was intended to test both models in addition to their linkage. This process cons isted of two main steps: 1) testing the reactive transport of SWIFT2D against an established analytical solution; and 2) reproducing these results using aRSE to perform the reactions calculations previously performed by SWIFT2D. In this way, the SWIFT2D c ode was verified against an analytical solution and could be used as a benchmark against which to verify the linkage. If FTaRSELOADDS reproduced the same results by relying on SWIFT2D for transport and the linked code of aRSE for the reactions, then both the linkage and the reactions code of aRSE will have been validated since a failure of either would preclude matching results. Analytical solution Reactive transport of dissolved constituents in two dimensions is described according to the advectiondisper sion-reaction (ADR) equation (Equation 2-1):

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43 C k y C D x C D t C v t C v t Cr y x y x 2 2 2 2 (2 -1) where C is concentration of the solute of interest; t is time; x is distance in the x direction; y is distance in the y -direction; vx is local velocity in the x direction; vy is local velocity in the y -direction; Dx is effective dispersion in the x direction ; Dy is effective dispersion in the y -direction ; and kr is the solute reaction rate. The controlled velocity conditions implemented in SWIFT2D to ensure uniform velocity throughout the domain required using a type -three (flux averaged) concentration boundary condition. Leij and Bradford (1994) present a suitable analytical solution for third-type boundary conditions in three dimensions, with a rectangular source area ( Figure 2 -2) of width a (in the y direction), height b (in the z -direction), and flow in the x direction, and provide the 3DADE software for numerically solving the solution. This software is now available as part of the STANMOD suite of numerical tools (Simunek et al., 1999; available at http://www.pc progress.com/en/Default.aspx?stanmod) for solving various analytical solutions to the ADR equation. In order to implement the 3-D solution for the horizontal 2-D conditions that SWIFT2D simulates the x direction was oriented in the direction of horizontal longitudinal flow, the y direction as horizontally transverse to the direction of flow, and z direction as the vertical plane over which the depth averaged Navier Stokes equations are integrated. In such an orientation vertically integrated conditions can be approximated by setting b sufficiently large compared with the dimension a to produce an effectively infinite height. This negated any variability in the z -direction and reduced the solutio n to an effective 2-D case. Additionally, the dispersion rate in the z -direction

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44 was set to a value sufficiently low (Table 2 -1) compared with that specified for the x and y -directions to further negate any solute mass movement in the z -direction that mi ght have occurred despite the large b value. The value for vertical dispersion could not be set to zero exactly because it appears in the denominator of the analytical solution (see Equation 2-3 below). The analytical solution (Equation 2-2) solved using 3DADE is given in Leij and Bradford (1994) as follows: t t t P od R d R v C C0 2 ) ( 1) ( 2 ) ( ) ( 4 (2 -2) for: otherwise 0 0 0 0 ) (0 0 0t t z y C t z y x Cx where: 2 / 1 2 / 1 2 / 1 2 / 1) / 4 ( erfc ) / 4 ( erfc ) / 4 ( erfc ) / 4 ( erfc ) ( R D b z R D b z R D a y R D a yz z y y (2 -3) 2 / 1 2 1/2 1) 4 ( exp 2 4 ) ( exp exp ) ( x x x x xRD v Rx erfc D vx D v RD v Rx D R R (2 -4) x x x x x xRD v Rx RD v RD v Rx D vx R v x D v RD Rx v R 4 ) ( exp 4 ) 4 ( erfc exp ) / ( 1 ) 4 ( erfc exp ) (2 1/2 2 2 / 1 2 / 1 2 (2 -5)

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45 and where R is the retardation factor; is time ; v is porewater velocity; x is the position in the direction of flow; Dx, Dy, and Dz are dispersion coefficients in the x -, y -, and z directions, is the first order decay rate coefficient; and is the zero order production rate coefficient. Setup for testing of SWIFT2D An important assumption implicit in the analytical solutions presented is that of uniform uni directional velocity. However, given the complexity of SWIFT2Ds mechanistic approach to hydrology, establishing a precisely uniform velocity field was not possi ble. To overcome this, and considering that the reactive transport was being tested and not the underlying hydrology, velocity was controlled by overwriting hydrodynamic values calculated by SWIFT2D at each time -step In this way a uniform velocity was e stablished, and observed discrepancies between numerical and analytical solutions were therefore known to be attributable to the numerical implementation of the reactive -transport equation, and not to variability in velocity. A square test domain was estab lished for SWIFT2D consisting of 101 x 101 cells, with each cell 100m in length (Figure 2-3). Such a large domain was necessary given the decision to test the model for conditions approximating those under which it would be applied, namely low velocity and high dispersion (Swain et al., 2004), and the disparity in boundary conditions at the upper and lower borders of the domain. The analytical solution assumes open boundaries, but modeled domain was applied with noflow boundaries. A constant velocity o f 0.05 m/s was applied with a molecular diffusion of 20 m2/s. For these conditions, the central fifty cells, justified to the left and centered around the source (Figure 23) were the focus region of the domain, and ensured

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46 sufficient area remained in th e domain to prevent any effect on concentrations within the focus region due to the discrepancy in boundary conditions. Molecular diffusion in SWIFT2D is input as a single value that is applied isotropically in both dimensions of flow. The longitudinal di spersion coefficient ( Dl) is computed in each cell (Equation 26) and in each principal direction of flow according to a function established by Elder (1959) relating flow conditions, depth, velocity, and the Chezy resistance coefficient according to: C g u H C Dd l) 2 ( (2 -6) where Cd is a coefficient relating longitudinal dispersion to the local velocity; is the local velocity; H is the temporal flow depth; g is acceleration due to gravity; and C is the Chezy resistance coefficient, related to the Mannings n according to (Leendertse, 1987): n H C6 / 1 (2 -7) A representative value of 14.3 has been determined for Cd (Harleman, 1966). The total effective dispersion implemented in the advection dispersion-reaction equation is then the sum of the longitudinal dispersion, which may be different for each direction, and diffusion, which is constant. The 2-D analytical solution is valid for uni -directional flow. The absence of transverse velocity therefore prevented any dispersion from occurring in the transverse direction. In order to simulate 2-D solute transport it was therefore necessary to rely on the diffusion coefficient to generate dispersion in the transverse dimension. A reaction rate of -0.000001 s1 was used to generate constituent decay for the reactive transport.

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47 Setup for testing of FTaRSELOADDS A first order decay equation was input to aRSE through the XML input file. One state variable was specified to represent the transported solute. One parameter, the reaction rate kr, was input to reproduce the decay r eaction. All other conditions were kept the same as those used for testing SWIFT2D Results and Discussion Conservative and reactive transport were simulated using SWIFT2D (Figures 24 and 2 -5, respectively), and reactive transport using FTaRSELOADDS (Figure 2-4). Results using SWIFT2D confirm that the model correctly simulates solute transport, and that these results are reproducible using FTaRSELOADDS. Benchmarking SWIFT2D Results for 2 -D transport of a non-reactive solute obtained using SWIFT2D (Figure 2 -4) compared well with the analytical solution, but showed some disparity at the concentration front due to the effects of numerical dispersion (Fischer et al., 1979). To confirm that this was the source of the discrepancy in results the numerical disper sion (Dn) was calculated as per Swain et al. (2004): t Di i n 2 2 15 0 (2 -8) where 2 is the variance of the constituent concentration distribution and i is the computational cell number. When numerical dispersion was added to the value for dispersion allocated to the analytical solution the discrepancy at the concentration front is absent, confirming that numerical dispersion is the source of the differences. Close to the source boundary the differences are greater and cannot be mitigated by compensating for numerical dispersion.

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48 Verifying FTaRSELOADDS Results of reactive transport obtained using FTaRSELOADDS were essentially identical to those obtained using SWIFT2D by visual comparison (Figure 25). The ADI solution method implemented by SWIFT2D splits the transport step into two half -steps for each time-step, with one half -step used to calculate velocity in the x direction, and the other the y direction. This naturally lends itself to comparing the accuracy of alternate ways of integrating the reactions step of aRSE into the transport step of SWIFT2D. Three methods were identified and implemented: 1) applying the reactions after each half -step using the half -step time -step (TRTR, where T=transport and R=reactions); 2) applying the reaction step once in between the tw o transport steps, using the full time -step, (TRT); and 3) applying the reaction step once after both transport steps using the full time -step (TTR). Given the closeness of results, visual analysis was unsuitable for comparison. To quantitatively assess how well the simulated results compared against the analytical solution throughout the entire model domain, a program was written making use of the CORSTAT (see Appendix B, Section B 4 ) code (Aitken, 1973) to calculate the Root Mean Square Error (RMSE) and Nash-Sutcliffe ( E) efficiencies (Nash and Sutcliffe, 1970) for each of the concentration points in the SWIFT2D domain, compared with analytical value at equivalent spatial points in the 2-D analytical domain, according to Equation 29: E 1 Ot St 2 t 1 TOt O 2 t 1 T (2 -9)

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49 where O i s the observed, O the mean observed, and S the simulated value. Figures 2 6 and 27 depict the spatially interpolated RMSE and Nash -Sutcliffe results at each grid-point in the domain after 150 and 300 minutes respectively, for the TRT case. Visual comparis on of these results and those obtained using the SWIFT2D reactions, or either the TTR or TRTR methods, showed no visible differences. To quantify differences in overall numerical performance between the methods, the average Nash-Sutcliffe efficiencies for all the domain points were calculated for each case using the Nash-Sutcliffe values determined for each point after 300 minutes (Table 2 -2). In this way it was possible to quantify the performance of each of the linkage options, from which it appears that the TRTR implementation is the best when taking all three statistical measures into account. The two-dimensional presentation of timevariant error statistics in this way also offers insights into the location of relatively greater and lesser error, as well as its propagation throughout the domain in time. For instance, in all figures it is clear that the region closest to the source is subject to the greatest errors. The Nash-Sutcliffe results in Figure 2 -6 also show the expected result of greater discr epancy at the concentration front (red ring) and the best match in the centre of the domain where source boundary effects and numerical dispersion effect s at the front are least felt Black regions of the Nash -Sutcliffe figures indicate that no values wer e calculated because no solute had yet reached those points in the domain, thereby generating a null denominator in the NashSutcliffe calculations. The Nash -Sutcliffe results in both figures also offer validation of the assumption in the model setup that an enlarged model domain of 101x101 cells would be sufficient to

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50 prevent any effects from the no-flow boundaries above and below interfering with the focus region of the fifty cells centered on the source (Figures 2-4 and 2-5). At these boundaries, the as sumption of an infinitely open horizontal plane implicit to the analytical solution is no longer met, and we see this disparity reflected in degraded Nash -Sutcliffe efficiencies in the region of the boundary. However, throughout the bulk of the domain, an d certainly within the central 50 cells (25 cells above and below the source region) we find excellent matching between numerical and analytical results. Close comparison of Figure 25 and 2-6 corroborates the directionality of the error propagation that is so visually striking in Figure 2 -6. The isolines of Figure 2 5 match best at approximately +/ 45 degrees to the horizontal, taken from the solute source point. Greater than this angle and we see the numerical (black and orange) solutions under p redict compared with the analytical isoline (green). Less than 45 degrees (i.e. towards the extreme right of the concentration front) we see the models over -predict relative to the analytical solution. This pattern is clearly reflected in the Nash-Sutcli ffe figure, where we see clear darker blue (higher Nash-Sutcliffe efficiency) arms projecting out into a lighter blue surrounding area. Conclusions A free -form, non -spatial water quality model was integrated with a spatially distributed hydrodynamic model. The resultant tool, FTaRSELOADDS, is a novel water -quality tool that is spatially -distributed, driven by mechanistic hydrodynamics, and user -definable. Linkage of the models was validated by demonstrating the ability of the linked tool to replicate resul ts obtained using the reactive transport functionality of SWIFT2D when using aRSE to perform the reactions and SWIFT2D the transport.

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51 Table 2 1. Quantities and values used in the comparison of SWIFT2D and F TaRSELOADDS against the analytical solution for 2-D conservative and reactive transport. Variable names as required by SWIFT2D, aRSE or STANMOD are included where appropriate Case Velocity [m/s] Retardation Factor Pulse length Decay rate [s-1] Longitudinal (x) dispersion [m2/s] Transverse horizontal (y) dispersion [m2/s] Transverse vertical (z) dispersion [m2/s] Unit concentration source dimension [m] Analytical solution v = 0.05 RetFac = 1 T0 = 60000 s = 1E 5 Dx = 20.5332 Dy = 20 Dz = 1E 10 a to a (y direction): |a| = 100 m; b to b (z direction): |b| = 1E+10 m SWIFT2D transport and reactions U,UP = 0.05 V,VP = 0.0 N/A TRBNDA = 1 for TITI = 0 to 1000 min AKK = 1E5 DIFDEF = 20 Dl = 0.5332* DIFDEF = 20 N/A 2 x 100 m cells (N,M): Cell (50,1) and (51,1) SWIFT2D transport with aRSE reactions U,UP = 0.05 V,VP = 0.0 N/A TRBNDA = 1 for TITI = 0 to 1000 min Kr = 1E 5 DIFDEF = 20 Dl = 0.5332* DIFDEF = 20 N/A 2 x 100 m cells (N,M): Cell (50,1) and (51,1) Dl calculated from Equations 2 6 and 2 7 for n = 0.03 s/m1/3, H = 0.50 m, = 0.05 m/s, g = 9.801 m/s2, Cd = 14.3

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52 Table 2 2. Nash Sutcliffe efficiencies obtained for different methods of integrating aRSE reactions into FTLOADS SWIFT2D aRSE: TT R aRSE: TRTR aRSE: TRT Average 0.92843577 0.94792578 0.94790868 0.94789519 Mode 0.99854711 0.98674260 0.99906814 0.99443873 Median 0.99463456 0.99467713 0.99466211 0.99464882 Figure 21. Schematic detailing the architecture of the code linking the surfacewater model in FTLOADDS (SWIFT2D) with a Reaction Simulation Engine (aRSE).

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53 Figure 22. Source boundary condition for analytical solution: Third-Type, flow in the x direction, source dimension a = 100 m in horizontal transverse y -direction, source dimension b = 1E+10 (~infinity) in the vertical transverse z direction (from Leij and Bradford, 1994).

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54 Figure 23. SWIFT2D model domain used for comparison of conservative and reactive transport simulations with analytical solutions; red indicate source cells, all cells 100 m square, total domain 10,000 m, no-flow boundaries at N=1 and N=101, and M=1.

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55 Figure 24. Concentration isolines for 2-D conservative transport from a small rectangular source as determined by SWIFT2D (black), the analy tical solution (green), and the analytical solution with numerical dispersion effects accounted for (orange).

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56 Figure 25. Concentration isolines for 2-D reactive transport from a small rectangular source as determined by SWIFT2D (black), the analy tical solution (green), and the coupled version of FTLOADDS and aRSE (orange).

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57 Figure 26. Spatially -interpolated RMSE (left) and NashSutcliffe efficiencies (right) after 150 minutes of simulation for the case of transport -reactions -transport reactions. Figure 27. Spatially -interpolated RMSE (left) and NashSutcliffe efficiencies (right) after 300 minutes of simulation for the case of transport -reactions -transport reactions.

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58 CHAPTER 3 MODELING HYDROLOGY IN THE SOUTHERN INLA ND AND COASTAL SYSTE MS Introduction There are two major paths of natural freshwater flow from the Everglades into Florida Bay. One pathway, Taylor Slough, empties directly into the Bay, while the other pathway, Shark River Slough, contributes a portion of its flow to Florida Bay, but discharges primarily into the Gulf of Mexico. Freshwater inputs are vital to the coastal Everglades ecosystem, having important impacts reaching as far as the Florida Keys (SFWMD and FDEP, 2004). In part icular, changes to the flow patterns are expected to have consequences for water quality in Taylor Slough, adjacent wet prairies, and the coastal estuaries into which they empty (Childers, 2006). Modeling the regions hydrology is the first phase of an ef fort to model the phosphorus water -quality using a new water quality model for the region. Previous Hydrological Modeling of SICS Numerous modeling and experimental studies have been undertaken to better understand the hydrodynamics within the SICS region. For many years, the South Florida Water Management Model (SFWMM; MacVicar et al., 1984) was used to provide regional hydrologic information at a 2mile by 2 -mile spatial scale. T he coarse spatial resolution mad e SFWMM unsuitable for the detailed analysis required to determine local water management needs and support mechanistic water -quality modeling efforts. The South Florida Regional Simulation Model (SFRSM; Brion et al., 2000) was, and continues to be, developed to replace the SFWMM. Though SFRSM em ploys a variable-resolution triangular mesh for spatial discretization, like its predecessor it too

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59 neglects inertial forces, and flow volumes are consequently less accurate. Also neglected are variabledensity and unsteady flow conditions, which are impor tant characteristics of the SICS region because of tidal interactions with Florida Bay and wind -shear effects (Swain et al., 2004) Results from e fforts to simulate coastal flows to Florida Bay using SFWMM (Hittle, 2000) were undermined by greatly amplifi ed freshwater flows, which in turn diluted coastal salinities. Lin et al. (2000) attempted to use FEMWATER123 for the region, but the computational demands of the model, which simulates 1 -D canal flow, 2-D overland flow, and 3-D finite element groundwater flow, were restrictive. The failure of these models to meet the persistent need for greater accuracy and spatial resolution of the simulated hydrologic conditions in SICS (as a necessary input for ecological modeling efforts using ATLSS) and freshwater inputs to Florida Bay (needed for hydrodynamic modeling of Florida Bay) led to an extensive modeling effort by the USGS that included a number of field studies to quantify physical parameters. The major product of this effort was the development of the S ICS model, an application of the USGS developed Surface -Water Integrated Flow and Transport in 2-Dimensions (SWIFT2D) hydrodynamic/transport model with additional enhancements specifically for the coastal wetlands of the Everglades (Swain et al., 2004; Sw ain 2005). Variable density groundwater simulation was integrated into the SICS application by Langevin et al. (2005). The effort entailed linking SWIFT2D with SEAWAT, a version of the 3 -D modular groundwater flow model MODF L OW integrated with the 3-D modular transport model MT3DMS, which can simulate variable density groundwater hydrology. The resultant tool is known as Flow and Transport in a Linked Overland-

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60 Aquifer Density Dependent System (FTLOADDS), which was subsequently adapted further for the T ides and Inflows in the Mangroves of the Everglades (TIME) application (Wang et al., 2007) The TIME application not only encompasses the SICS region, but greatly expands the domain to include all of Everglades National Park and Big Cypress National Prese rve. Versions 1.0 and 1.1 of FTLOADDS refer to the original SICS applications using only SWIFT2D. Version 2.1 refers to the coupled surface water/groundwater SICS application, and version 2.2 the coupled surfacewater/groundwater TIME application (see Appendix A for further details on versions) Remodeling the Hydrology of SICS The proposed effort to model water -quality in the SICS region using FTaRSELOADDS requires a suitable hydrologic application to provide the necessary hydrodynamic drivers of water -quality. The original SICS application, which did not include groundwater simulation, was selected for the inaugural application of FTaRSELOADDS based on a number of considerations: 1) the surface water results obtained with this simplified version of FT LOADDS were considered sufficient for such testing; 2) the water -quality focus was on surfacewater conditions, so only SWIFT2D had been coupled with aRSE (see Chapter 2) ; 3) the concerns about compounding computational times given the addition of aRSE to an already computationally intensive tool. However, a number of changes have been made to the SWIFT2D code in FTLOADDS as the tool has evolved to the current form (version 2.2), which were not present when the original SICS application (version 1.1) select ed for testing FTaRSELOADDS was established. It was therefore necessary to evaluate the effects of these changes, many of which were simplifications, on the simulation of surface water

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61 hydrology in SICS. In particular, the effect of removing depthvarying Mannings n needed to be evaluated to assess the implications for water quality modeling. Materials and Methods Model Description The 2-D, vertically integrated, unsteady flow and transport model SWIFT2D has its origins in SIMSYS2D (Leendertse, 1987), whi ch in turn built on earlier work conducted throughout the 1970s by Leendertse and his colleagues at The Rand Corporation to develop a water quality simulation model for well mixed estuaries and coastal seas (Leendertse, 1970; Leendertse and Gritton, 1971; Leendertse, 1972). SWIFT2D governing equations Thorough descriptions of the SWIFT2D governing equations and their numerical implementation are variously provided in Leendertse (1987), Goodwin (1987), Bales and Robbins (1995), and Schaffranek (2004). Four partial differential equations are used to describe unsteady, nonuniform, variable-density, turbulent fluid motion (Equations 31 to 3-3) and solute transport (Equation 34), which are formulated according to the laws of Conservation of Mass and Conservation of Momentum. Hydrodynamics are described with the two dimensional Saint Venant equations (de Saint -Venant, 1871; Equations 32 and 33), which are derived from the Navier -Stokes equations by applying temporal averaging of velocity, pressure and mass over timeintervals that are long relative to the time -scale of turbulent fluctuations, and assuming negligible vertical accelerations. Transport is described by the advection -dispersionreaction equation (Equation 3 -4). The resultant formulations retain no nlinear advective and bottom -stress terms, which permit the simulation of eddies and residual circulation, and coupled motion and transport with time varying horizontal density gradients:

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62 0 ) ( ) ( y HV x HU t (3 -1) H W H C V U gU x gH x g fV y V V x U U t Ua sin 22 2 2 2 02 2 2 2 y V x U k (3 -2) H W H C V U gV y gH y g fU y V V x U U t Va cos 22 2 2 2 02 2 2 2 y U x V k and (3 -3) 0 ) / ( ) / ( ) ( ) ( ) ( HS y y P HD x x P HD y HVP x HUP t HPy x (3 -4) where: direction. positive the and direction wind between angle and air; of density water; of density t; coefficien stress wind plane; reference horizontal to relative elevation surface water speed; wind direction; in component velocity averaged vertically direction; in component velocity averaged vertically ; substances dissolved with fluid of source ions; concentrat t constituen dissolved averaged vertically of vector t; coefficien exchange horizontal ); ( depth flow temporal bottom; channel to plane reference horizontal from distance gravity; to due on accelerati parameter; Coriolis ; substances dissolved of ts coefficien diffusion t; coefficien t coefficien resistance Chezy ay W y V x U S P k h H h g f ,D D Cy x

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63 SWIFT2D numerical solution technique The governing differential equations cannot be solved analytically unless subjected to simplifying assumptions that are unacceptable for the intended applications. A finite difference numerical solution technique is therefore applied to a computational domain of equally spaced grid points. The finite difference equations are solved on a space-staggered grid (Figure 3 -2) using the alternate-direction implicit (ADI) method. Velocity points are located between water -level p oints to produce an efficient solution of the continuity equation (Leendertse, 1987). The ADI method splits the time step to obtain a multidimensional implicit solution that provides secondorder accuracy, and requires only the inversion of a tridiagonal m atrix in order to solve each set of finitedifference equations (Roache, 1982). Detailed descriptions of the finite difference equations are provided in Swain (2005). Though the ADI method is unconditionally stable (Leendertse, 1987) there are practical l imitations to the time -step (Roache, 1982), particularly when applied to irregularly shaped domains (Weare, 1979) or complex bathymetries (Benque et al., 1982). SWIFT2D code enhancements and simplifications The FTLOADDS code presently available is that of version 2.2. The original SICS application represents FTLOADDS version 1.1, which included enhancements to SWIFT2D but no groundwater linkage (see Chapter 2). These enhancements were maintained with only minor changes to the SWIFT2D code due to the coupling process in FTLOADDS version 2.1. However, SWIFT2D code was significantly modified in the course of the models evolution to version 2.2. This has implications for this effort to reproduce SICS surfacewater results originally obtained using SWIFT2D v 1.1.

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64 SWIFT2D in FTLOADDS v1.1 The original effort to model surface water flow in the SICS region required a number of modifications to the SWIFT2D model (Swain et al., 2004): Precipitation: The rainfall code was adapted to permit spatially distributed values for rainfall volume to be added to individual cells. Rainfall inputs were calculated at 15minute intervals by kriging the rainfall from 14 different rainfall stations in the region. Rainfall was not added to dry cells, which implicitly assumed that w hen rainfall fell on dry cells it infiltrated into the groundwater Evapotranspiration: Evapotranspiration (ET) was not included in the original SWIFT2 D v1.0 code, which was intended for application to estuaries and coastal waters where evaporation could be considered negligible and macrophytes sufficiently sparse to ignore transpiration. For SWIFT2D v1.1 an equation regressing ET with solar radiation and depth (German, 2000 ) was applied to each cell to determine spatially distributed, time varying ET. Dep th varying Mannings n : When up-scaling point measurements of frictional resistance to grid-scale representative values, microtopography can increase the effective frictional resistance at lower depths. To address this, an empirical relation was applied to determine an effective Mannings n (neff) based on a reference input value ( n measured or estimated), a reference depth ( dref, the assumed depth at which measurement or estimation was conducted), the actual depth ( d ), and a power variable ( p ) to capture nonlinear effects (Swain et al., 2004): p ref effd d n n (3 -5) Wind-sheltering: To account for the sheltering effects of vegetation (Jenter, 1999) which were not considered for openwater applications of SWIFT2D v1.0, a spatially uniform sheltering coefficient was applied to all vegetated cells (considered those having a Mannings n greater than 0.1). Other: Other changes included technical modifications to the treatment of flow adjacent to barriers (which were not previously permitted to go dry), wind friction in ce lls adjacent to water -level boundaries (set to zero to avoid numerical oscillations), and output printing routines. SWIFT2D in FTLOADDS v2.2 The coupling of SWIFT2D to SEAWAT through leakage required additional code, but left each of the models intact such that SWIFT2D could be run without the need to call SEAWAT if so desired. However, the progression

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65 from SICS application to TIME application introduced new changes to SWIFT2D (Wang et al., 2007): Precipitation: Rainfall in version 2.1 was specified at 15minute intervals and spatially -interpolated from 14 stations for each cell. Rainfall in version 2.2 is spatially uniform over defined zones, of which SICS represents one (i.e. uniform rainfall over the entire domain), and is specified a s 6 -hour averages. Additionally, the wetting and drying algorithm has been modified such that rewetting is now permitted to occur directly from rainfall recharge. Evapotranspiration: In analogous fashion to rainfall, ET is now applied regionally, and therefore uniformly over the SICS domain, also a s 6 hour averages. Additionally, the modified Penman method (Eagelson, 1970) has replaced the cell by -cell ET calculations (Swain et al., 2004) When depth of ET is greater than 10 percent of the remaining depth of water then ET is instead removed from the first layer of the groundwater to avoid making the cell go dry or the depth go negative. When the groundwater module is turned off this effec tively means no ET occurs. Mannings n : The functionality to treat variation of Mannings n with depth of flow was removed from SWIFT2D due to concerns over its empirical nature (E.D. Swain, U.S. Geological Survey, personal commun., 2010). Frictional resi stance (Chezy) terms, which are calculated using depth and Mannings n are now defined at cell faces rather than at cell centers. This permits a different resistance in each of the principal directions of flow, but also requires a second Mannings n valu e for each cell. In version 2.1 obstruction to surface water flow, most notably the Buttonwood Embankment, was defined using the original SWIFT2D barrier formulation intended to represent weirs. Coastal rivers and creeks were defined as low barriers with calibrated flow coefficients. In version 2.2 the coastal embankment is defined by a modified cell -face frictional resistance term, with creeks represented as gaps with specified (reduced) friction terms. Considering the important roles played by both pr ecipitation and ET in the south Florida water budget (Sutula et al., 2001), and of Mannings n in determining flow velocities and wet/dry conditions the modifications to v2.2 described above represent significant hydrological simplifications to the SWIFT2D model. This effort to model SICS hydrology therefore re presented an effort to study the effects of these model simplifications on the ability of SWIFT2D to simulate hydrodynamics in the SICS region for future water quality application.

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66 Model Setup The S WIFT2D v1.1 model setup used in the original SICS application was reapplied as consistently as possible in an effort to reproduce the original results for the period of August 1996 through August 1997. All effort was made to maintain the same model setup and parameterization, and the integrity of the original SICS application should be assumed intact unless changes are specified below. Figures from the USGS SICS modeling report (cited as Swain et al., 2004) are reproduced where model setup is appropriately consistent, and original figures have been produced where necessary. Computational domain The previously established SICS model (Swain et al., 2004) domain (Figure 33), comprising 9,738 square computational cells of length 304.8 m (1000 ft) for a total d omain area of 905.8 km2, was applied with minimal changes to the model boundary. The new treatment of frictional resistance terms at cell faces, rather than cell centers, generated a number of points on the domain boundary where floating point problem aro se due to the underlying space -staggered grid geometry. The original version required resistance terms for each cell in the computational domain, which is defined row -by -row, and column-by -column, to produce the irregular boundary required. Resistance ter ms were calculated based on input Mannings n values, which were specified as zero outside the active domain. Since the original computational domain was not defined to intentionally account for the additional cell face values required by the current vers ion, and given that the space-staggered grid used by SWIFT2D attributes values originating in, for example, cell (m, n+1) to cell (m, n), instances of Chezy resistance terms being calculated using Mannings n values of zero in the

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67 denominator arose. This was resolved by eliminating the offending individual boundary cells from the computational row or column as the case arose. Land-surface elevations were measured at about 400 -m intervals (Desmond et al., 2000) and a linear distance weighted four point inte rpolation was applied to assign land surface elevations to each computational cell (Figure 3 -4). The Buttonwood Embankment (Figure 31) is a significant hydrologic barrier in the region, which separates the freshwater wetlands from Florida Bay. Most exch ange of water occurs through the many creeks that traverse the embankment. Physically, the embankment is an elevated region, but in SICS it is simulated by barriers based on large resistance terms in the direction of flow, interspersed with lower resistance values where creeks cut through the barrier. Boundary conditions Boundary conditions (Figure 3-5) were provided at the water surface and lateral boundaries. The water surface boundary is assumed to be horizontal in each cell; water is permitted to move vertically but no deformation of the water surface within the cell is considered. Physically, this implies that high -frequency surface waves are not accounted for in the model. A uniform rainfall rate was supplied as a model input file containing values calculated as the arithmetic mean of all stations in the SICS region, averaged over 6hour intervals. A uniform ET rate was similarly supplied as an input file, rather than calculated within the model. Input ET values were calculated as the regional mean of ET values calculated according to the modified Penman method (Wang et al., 2007) Wind conditions are represented as spatially uniform across the entire domain, and the data from the Old Ingram Highway site was used to define the wind field. A moving

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68 average wind speed was used for the boundary condition since fluctuations in wind conditions at subhourly time -scales are considered to not generally be representative of regional patter n s, which is the scale implied when uniformly applying wind. Lateral boundaries are described as open (free exchange with water and solutes across the boundary) or closed (no flow or exchange). Open boundaries were described by time -series inputs for either discharge or water -level The SICS model lateral boundaries are identified in Figure 3-5, and include seven constant head boundaries and three discharge source boundaries. The discharge sources (Figure 36) are at Taylor Slough Bridge, the C -111 pumping station, and within the L31W canal. Inflow at Taylor Slough B ri dge was determined from stage-discharge data at the Taylor Slough Bridge site, and at the L31W site according to stage-discharge relationship at the S -175 hydraulic gate structure, where this flow originates. Input of discharge at C 111 source is based on the discharge from pumping station S 18C, occasionally adjusted to compensate for flows directly out of the canal and into Florida Bay when the S-197 structure is opened. The levee on the southern side of the C 111 section has been removed to promote delivery of additional water to the SICS region. An artificial topographic low along the SICS boundary was applied to facilitate more uniform flow distribution along the lower section of C -111. Several regional model parameters are required and applied as p er Swain et al. (2004) : air density, latitude (single value), kinematic viscosity of water, w ind stress coefficient, unadjusted horizontal mixing coefficients, isotropic mass dispersion coefficient, a coefficient relating mass dispersion to flow conditions a resistance

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69 coefficient for each computational cell and for tidal creeks, and marginal depth (Swain et al., 2004). Stability considerations Although the ADI method is unconditionally stable (Leendertse, 1987), the treatment of flow barriers introduces p ractical limitations. Experimentation with the timestep eventually lead to selection of a half -step of 1.5 minutes, which demonstrated sufficiently stability in the region of the creeks and barriers. The next -largest possible half -step was 2.5 minutes, based on the fact that full time -steps needed to be compatible with the time -steps defined for tidal boundary conditions, which are read in at 15minute intervals, and this proved to be unstable. Given the simulation of salinity transport it was also neces sary to consider numerical dispersion. A diffusion coefficient of 10 m2/s was applied based on the previous application of SICS v1.1. (Swain et al., 2004). Considering the cell dimensions of 304.8 m, and a conservative (high) estimate for average velocit ies on the order of 0.05 m/s (based on previous results in Swain et al., 2004), a Pclet number of approximately 1.5 was obtained, which even though conservative was below the generally applied upper limit of 2. Results and Discussion Water -level results at the 12 observation stations in the SICS domain are presented first, followed by an assessment of the flow through the creeks linking Florida Bay to Taylor Slough. Following thereafter are 2-D results for water -level, flow, and salinity.

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70 Water -Level Res ults Simulated stages at each of the 12 water -level stations are presented in Figures 37 and 38. Results are divided between those stations that fall within Taylor Slough (Figure 37), which are more directly subject to discharges from the TSB source, and stations east of the slough (Figure 3-8) that are more directly affected by flows originating from the C -111 canal. The area of the time -series figures shaded in brown indicates the subsurface. Where brown meets blue corresponds to ground-surface elevation for the cell containing the location of the station. The area shaded in blue indicates the maximum observed water -level during the model validation period from July of 1996 to August 1997. Observed water levels are depicted in blue, and can drop bel ow the ground surface because water level observations are recorded by wells. The results obtained using SWIFT2D v1.2 are shown in black. Periods where simulated results are not depicted correspond to conditions that SWIFT2D considers dry, which occur whe n water depth drops below 5 cm. As can be seen in both figures, this happened regularly for a number of locations, including two critical phosphorus concentration observation locations, the EPGW and P37 stations. Significant effort was expended attempting to resolve this. The final solution was to reintroduce the functionality of depthvarying Mannings n which had been removed in the present version (v1.2). The reintroduction of depthvarying Mannings constitutes a n updated version of 1.2, and is designated version 1.2.1 (red results in Figures 37 to 310). In the original SICS v1.1 modeling effort, the variables applied to the nominal Mannings input, dref and p (Equation 3-5), were 0.6 m and 2 respectively. In this version 1.2.1 the reference depth was set to 0.4 m given the absence of almost any depths of

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71 0.6 m in the simulated year, making such an assumption for the reference depth questionable. The simple non-linear quadratic power was maintained. A comparison of the results obtained in this work with those from the original SICS modeling effort (Swain et al., 2004) is given in Figures 3-9 and 3-10, with statistics comparing all three versions original SICS application (v1.1), present SICS application with depth -constant Man nings n (v1.2), and present SICS application with depthvarying Mannings n (v1.2.1) are presented in Table 31, and summarized in Table 32. Visual comparison of the results in Figures 3-7 to 310 with the statistics in Table 3 -1 reveals some contradic tions Visually, it is clear that the results obtained using depth varying Mannings n (in both SICS 1.1 and 1.2.1) are a better representation of reality insomuch as periods of wetness and dryness are captured more reliably, particularly for the critical water quality stations EPGW and P37. In SICS v1.1 (Figures 3 -9 and 3-10) we see a tendency on the part of the model to over -predict water -levels, especially at the beginning of the simulation and the beginning of the second wet season. The current applic ation performs much better in this regard. Conversely, in SICS v1.2 (Figures 38 and 3-9), the lack of depth -dependency in flow resistance results in excessively rapid drying out of the system when data clearly shows that wet conditions prevail. Version 1. 2.1 avoids the drawback of both of these versions, better predicting the dry -down following wet periods compared with SICS v1.2 and avoiding the over -predictions that were characteristic of SICS v1.1. The Nash -Sutcliffe efficiencies presented in Table 31 and summarized in Table 32 do not capture this, instead implying that v1.2 offers the best results. This is a

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72 consequence of the fact that periods of dry conditions are not accounted for in the Nash -Sutcliffe calculations because there is no simulated depth value against which to compare the observed value. The result is a failure to capture the full extent of the error, and exposes a weakness of this error statistic for assessing results in shallow systems where wetting and drying is frequent. Additi onally, the EP12R station has very low Nash-Sutcliffe results which disproportionately reduce the NashSutcliffe statistics (Tables 31 and 32) considering how little data is actually present for this station (Figure 39). Furthermore, the station is loc ated very close to the boundary of the model, a region that is known to be susceptible to greater errors due to boundary effects (Leendertse, 1987). Figure 311 to 313 shows the frequency and cumulative distribution of NashSutcliffe results for all stati ons, Taylor Slough stations, and C -111 wetlands stations respectively, from SICS v1.2.1. Over 40 percent of all the stations attained NashSutcliffe efficiencies of 0.7 or higher, and approximately 60 percent of 0.5 or higher. Performance of the model for simulating water -level s in Taylor Slough (Figure 312) was comparable to that for the C 111 wetlands (Figure 313). It is known that bias can lead to misleading Nash-Sutcliffe efficiencies (McCuen et al, 2006). Furthermore, indication of a tendency to ov er -predict or under predict would be useful in interpreting how the changes made to SICS have affected the models ability to capture particular conditions, which would be useful in future water -quality modeling efforts. Simulated results from SICS v1.1. an d v1.2.1 were plotted against analogous observational data. For the 6 stations in the vicinity of Taylor Slough (Figure 312) we

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73 see a general reduction in variability about t he 1:1 line for SICS v1.2.1 com p a red with v1.1. Stations higher up the slough (R 127 and TSH) are the exception, tending towards over -prediction at shallow depths and under -prediction otherwise. For the C 111 stations (Figure 3 -13), the current SICS v1.2.1 offers marked improvements, indicating that v1.2.1 is better equipped to handle the conditions of both slough (Taylor Slough area of SICS) and marl prairie (C 111 wetlands area). In particular, results were greatly improved for the EVER4 station and, importantly for water quality, the EPGW station. The poor results obtained for EP1 2R appear to be a problem in both versions of the model. Since both versions apply some form of depthvarying Mannings coefficient, while version 1.2, which has better results for EP12R according to the Nash-Sutclife efficiencies previously discussed, does not account for changing resistence with depth, this may be a cons i deration. If the EP12R site is sparsely vegetated then the depthvarying effect will be less important, and may then be a reason for this discrepancy. Water -levels throughout the SICS r egion are presented on the first of each month, from August 1996 to July 1997, in Figures 3-14 (first wet season), Figure 315 (dry season), and Figure 316 (end of dry season and start of wet season). Two-dimensional results are presented beneath time -ser ies figures depicting precipitation and discharge source inputs to the domain during that period to facilitate visual comparison between inputs and hydrologic conditions. Discharge Results Discharge data were available for five creeks in the Buttonwood Emb ankment. Figure 317 compares the simulated daily averaged flow rates in SICS v1.2.1 with the observed daily averaged flow rates. These results are important for assessing the accuracy of fluxes, which are critical if loading rates are to be estimated. They are also

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74 an important consolidation of depth and velocity simulations; given the reliable depth results described above, reliable flux results therefore indicate reliable velocities, which are important for the transport of solutes in water -quality m odeling. In all creeks except McCormick Creek, the magnitude and timing of daily average fluxes were satisfactory. Vector diagrams depicting flow direction and magnitude are given for the first of each month in Figures 318 to 320. Results reproduce wel l the trends found in Swain et al. ( 2004 ) that show tendency for flow from both Taylor Slough and C 111 to congregate in the region of Joe Bay. It is therefore important that the two primary creeks in this region, Taylor Creek and Mud Creek, are well modeled since they represent a significant portion of the Taylor Sough flow output to Florida Bay. The large fluxes through Trout Creek and the directionality of fluxes towards it from the C 111 canal indicate its importance for input s to Florida Bay originat ing from the eastern region of SICS. Fluxes are probably particularly large through Trout Creek because of its position between two large water bodies that hold relatively deep water permanently compared with the shallow and intermittently wet/dry conditions on the landward side of Taylor Creek and Mud Creek. Salinity Results Figures 3 21 to 323 present the two dimensional spatial results for salinity distribution throughout SICS on the first of each month. These results illustrate the significant diluting effect of freshwater inputs from Taylor Slough and C -111 to Florida Bay during high flow periods. Salinities were substantially higher throughout the Bay in the dry season. Dilution emanated from the region of Joe Bay following high freshwater flows, a s would be expected given the previously discussed flow results. During peak dry periods there is marked intrusion of salinities into the coastal wetlands in the eastern

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75 regions of SICS. Particularly high salinities may be due to evapotranspiration of water with increased salinity due to tidal influxes during low -flow periods. Such water may also become trapped in depressed regions by surrounding dry land after tides have withdrawn. Conclusions The current working version of SWIFT2D (v1.2) does not contain depthvarying Mannings resistance. This proved to undermine the ability of the mode to accurately capture wet and dry conditions which are important for both practical considerations (given the paucity of phosphorus data points for testing in Chapter 4) and biogeochemical considerations (since wet conditions determine the presence or absence of aquatic processes) When depthvarying Mannings n was reintroduced into the model in version 1.2.1 this problem was overcome. W ater levels throughout the SI CS region and discharge rates for important creeks were captured well. The reliable simulation of wet and dry conditions and velocities therefore established a satisfactory foundation for mechanistic water -quality modeling of the region. It is possible th at the reintroduction of groundwater exchange may negate the need for depthvarying Mannings n Under very shallow flow conditions, which is when depth varying Mannings would be most important, the small surface water hydraulic head may lead to groundwater upwelling into the water column. Other modeling efforts in the region have shown that ground water inputs likely occur during the dry season (Langevin et al., 2005), with possible implications for phosphorus loading to the surface water as well (Prince et al., 200 6). In the absence of groundwater exchange, the calibration of the depthvarying Mannings parameters dref and p to maintain surface water heads that would otherwise dissipate (as shown in the results for v1.2) equates to

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76 compensating for the lack of groundwater upwelling that may actually be occurring. Consequently, a fully coupled surface water/groundwater simulation of SICS using version 1.2 may be sufficient to justify the assumption of depth-invariant Mannings n However, for the purpose of test ing the phosphorus water -quality model, water -levels under shallow conditions are sufficiently sensitive to require that depthvarying Mannings be included.

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77 Table 3 1. Nash-Sutcliffe efficiencies for water -level observation points in SICS Station SICS v 1.1* SICS v1.2** SICS v1.2.1*** CP 0.7201337 0.901839 0.8771178 P67 0.2144507 0.7837026 0.8087565 TSH 0.7313131 0.8232658 0.7899594 P37 0.7620635 0.863053 2.44E 02 E146 0.778919 0.8662752 0.8897558 EVER5A 0.1176481 0.6932715 0.3337759 EVER7 0.5472993 0.7139693 0.8710759 EPGW 0.4939922 9.81E 02 0.4452754 EVER6 0.8514937 0.6204761 0.8550127 EP12R 2.930052 1.618115 4.148942 EVER4 0.5493984 0.8272943 0.6898439 R127 0.5810636 0.5898135 0.4134087 Calculated from digitized results in Swain et al., 2004 ** Mannings n held constant with depth of flow *** Mannings n varied with flow depth according to Equation 35 Table 3 2. Nash Sutcliffe statistics for stations in the viciniy of Taylor Slough, stations in the vicinity of C 111, and all stations in the SICS region. SICS v1.1* SICS v1.2** SICS v1.2.1*** Taylor Slough stations Mean 0.6313 0.8047 0.6339 Standard Error 0.2159 0.1128 0.3463 Median 0.7257 0.8432 0.7994 Kurtosis 3.7805 3.4693 1.0346 Skewness 1.9502 1.7921 1.4219 C 111 stations Mean 0.1009 0.2225 0.1590 Mean (excl EP12R) 0.4649 0.5906 0.6390 Standard Error 1.4219 0.9371 1.9666 Median 0.5206 0.6569 0.5676 Kurtosis 4.9453 4.4112 5.7462 Skewness 2.1940 2.0892 2.3836 All stations Mean 0.2652 0.5136 0.2375 Mean (excl EP12R) 0.5557 0.7074 0.6362 Standard Error 1.0423 0.7052 1.4085 Median 0.5652 0.7488 0.7399 Kurtosis 9.9357 9.1905 10.8236 Skewness 3.0767 2.9601 3.2369 Calculated from digitized results in Swain et al., 2004 ** Mannings n held constant with depth of flow *** Mannings n varied with flow depth according to Equation 35

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78 Figure 31. Location of the Southern Inland and Coastal Systems study area (from Swain et al., 2004)

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79 Figure 32. Space -staggered grid system showing relative locations of hydrodynamic characteristics.

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80 Figure 33. The SICS computational grid, showing the location of Taylor Slough, the Buttonwood Embankment and the coastal creeks (from Swain et al., 2004).

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81 Figure 34. Land-surface elevations (from Swain et al., 2004).

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82 Figure 35. Location of SICS model boundary conditions, including specified water -level boundaries and discharge sources (from Swain et al., 2004).

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83 Figure 36. Specified hydrologic inputs to SWIFT2D: discharge on the bott om axis and rainfall on the top axis. The three principal seasons, wet interspersed by dry, during the course of the simulation are depicted.

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84 Figure 37. Water -levels at the six stations in the vicinity of Taylor Slough, simulated with depth varying Mannings n (v1.2.1 red) and with constant Mannings n (v1.2 black).

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85 Figure 38. Water levels at the six stations in the vicinity of C -111, simulated with depth varying Mannings n (v1.2.1 red) and with constant Mannings n (v1.2 black).

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86 Figure 39. Water -levels at the six stations in the vicinity of Taylor Slough, simulated with depth varying Mannings n in the current version (v1.2.1 red) and the original SICS application (Swain et al., 2004; v1.2 black).

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87 Figure 310. Water -levels at the six stations in the vicinity of C 111, simulated with depth varying Mannings n in the current version (v1.2.1 red) and the original SICS application (Swain et al., 2004; v1.2 black).

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88 Figure 311. Frequency and cumulative distribution of Nash-Sutcliffe efficiencies attained with SICS v1.2.1, for all 12 water level stations.

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89 Figure 312. Frequency and cumulative distribution of NashSutcliffe efficiencies attained with S ICS v1.2.1, for 6 water level stations in the vicinity of Taylor Slough.

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90 Figure 313. Frequency and cumulative distribution of NashSutcliffe efficiencies attained with SICS v1.2.1, for 6 water level stations in the vicinity of C 111.

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91 Figure 312. Trends in prediction bias for the 6 stations in the vicinity of Taylor Slough. OBSERVED WATER LEVEL

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92 Figure 313. Trends in prediction bias for the 6 stations in the vicinity of C -111. OBSERVED WATER LEVEL

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93 Figure 314. Rainfall and discharge inputs, and corresponding 2-D water -level distributions for the first four months (first wet season). White space within the domain indicates dry cells.

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94 Figure 315. Rainfall and discharge inputs, and correspond ing 2-D water -level distributions for the middle four months (dry season). White space within the domain indicates dry cells.

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95 Figure 316. Rainfall and discharge inputs, and corresponding 2-D water -level distributions for the final four months (up t o the second wet season). White space within the domain indicates dry cells.

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96 Figure 317. Simulated and measured discharges through five gauged creeks in the Buttonwood Embankment Creek discharge (cubic meters per second)

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97 Figure 3 18. Rainfall and discharge inputs, and corresponding 2-D discharge vector distributions for the first four months (first wet season).

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98 Figure 319. Rainfall and discharge inputs, and corresponding 2-D discharge vector distributions for the middl e four months (dry season).

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99 Figure 320. Rainfall and discharge inputs, and corresponding 2-D discharge vector distributions for the final four months (up to the second wet season).

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100 Figure 321. Rainfall and discharge inputs, and corresponding 2-D salinity distributions for the first four months (first wet season). White space within the domain indicates dry cells.

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101 Figure 322. Rainfall and discharge inputs, and corresponding 2-D salinity distributions for the middle four m onths (dry season). White space within the domain indicates dry cells.

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102 Figure 323. Rainfall and discharge inputs, and corresponding 2-D salinity distributions for the final four months (up to the second wet season). White space within the domain in dicates dry cells.

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103 CHAPTER 4 MODELING PHOSPHORUS WATER -QUALITY IN THE SOUTH ERN INLAND AND COASTAL SYSTEMS Introduction The freshwater Everglades are oligotrophic due to the strong affinity for phosphorus exhibited by the carbonate substrate underlying the system (de Kanel & Morse, 1978). The cycling of phosphorus is a complex mix of physical, chem ical, and biological processes (Figure 4-1) that is too complex to describe based on fundamental physics and chemistry. However, many processes can be functionall y lumped together to simplify and abstract the system of cycling to a manageable degree of complexity. The Southern Inland and Coastal Systems (SICS) region encompasses two principle habitat structures; slough and marl prairie. Taylor Slough, running sout hwards through the center of the region (Figure 31 in Chapter 3), has proportionately less emergent macrophyte biomass and more floating macrophyte and periphyton biomass than adjacent marl prairie, which is a complex of sawgrass (predominantly) and calca reous periphyton (Swain et al., 2004). Both systems have significant layers of flocculent material (floc), a loose conglomerate of bacteria, periphyton and partially decomposed litter (Noe et al., 2003). Uptake of surface water phosphorus in both systems is dominated by periphyton and floc (Noe et al., 2003; Noe and Childers, 2007). Emergent macrophytes in the marl prairies obtain the majority of their phosphorus from porewater (Richardson and Marshall, 1986). Floating macrophytes absorb phosphorus direct ly from the water column, but turnover is rapid (Mitsch, 1995).

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104 In Taylor Slough, periphyton and macrophyte litter accrete and produce organic soils. The periphyton in the marl prairies co precipitate phosphorus with calcium, which accrete to form marl soi ls. Both forms of soil store phosphorus and do not readily release it unless conditions become dry (Sutul a et al., 2001). Atmospheric deposition is probably the most important source of nutrients to the southern Everglades (Noe and Childers, 2007; Sutula et al, 2001). Under historic conditions atmospheric deposition is estimated to have accounted for up to 90% of total phosphorus inputs to the Everglades (Davis, 1994). Flow into the southern Everglades does not generally exhibit the amplified nutrient loading more prevalent further north, where wetlands receive waters directly from the EAA. Ground water and surface water in the region are also readily exchanged because of the combination of shallow topography and particularly high hydraulic conductivity (Fennema et al., 1994), though the extent to which such exchange contributes nutrients is unclear. Recently, Price et al. (2006) have suggested that phosphorus inputs from groundwater may increase during the dry season due to a reversal of hydraulic gradient that causes upwelling rather than leakage. Integrated groundwater and surface water modeling of SICS (Langevin et al., 2005) have also indicated that there is upwelling during low -flow periods. However, the effects on productivity that this groundwater input of nutrients is suggested to drive are found largely in the mangrove/marshland ecotone in the southern portion of Taylor Slough, and are not thought to be as significant in the freshwater wetlands that are the focus of this modeling work.

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105 Toget her, these biological, chemical, and physical processes interact to determine the concentration of phosphorus in the water column, and in turn the mass exported out of the system. By considering simplified representations of these processes an abstracted yet functionally mechanistic water -quality model can be developed that is sufficiently simple to remain manageable and justifiable, yet sufficiently complex to provide insights into internal biogeochemical processes that cannot be captured by simple reacti ve transport models. However, such simple models are not without merit, and depending on the objectives of the modeling exercise may prove sufficient in themselves. We explore the value of a number of models for the purpose of simulating total phosphorus concentrations in SICS surface waters, from the simple reactivetransport model to a more detailed model of conceptualized biogeochemical cycling. Materials and Methods The integrated surfacewater flow, transport and reaction simulation engine that was d escribed in Chapter 2, and applied to model hydrology in in Chapter 3, was applied to simulate surface water total phosphorus concentrations in the SICS region for the period of August 1996 through October 1997. Two locations were identified with measured total phosphorus concentrations in the surface water against which to compare simulated results. These were the P37 and EPGW hydrologic stations introduced in Chapter 3, and depicted in Figure 42. Boundary Conditions Concentration boundary conditions were required for each of the surfacewater boundary locations described in Chapter 3 (Figure 4-2). These boundary

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106 conditions were associated with either specified head or specified discharge boundary conditions at the lateral boundaries. Atmospheric dep osition of phosphorus is input to describe the vertical inputs. Specified water -level boundaries For boundaries in Florida Bay (specified head boundaries 1 to 4 in Figure 42 ), time -series data was obtained for relevant water -quality observation stations i n Florida Bay (Table 41). These data were interpolated and input into the SWIFT2D input file as time varying data. Timevarying concentration data at specified water level boundaries are specified in Record 2A of Part 3 of the SWIFT2D input file (Swain, 2005) at the same time intervals at which timevarying tidal ( water -level ) boundary conditions are read in. A FORTRAN program was therefore written to do this efficiently and reliably given the very large number of required inputs at this interval (see S ubroutine EDIT_INPUTFILE in Appendix C, Section C 1 ). Time -series data for concentrations at specified head boundaries within the oligotrophic marsh areas (boundaries 68) were not available. However, analysis of long -term concentration trends at stations s ituated within oligotrophic marshlands (EPGW and P37) show that concentrations tend to be either below detection limit (i.e. less than 4 ppb), or on the order of 5 ppb. Total phosphorus concentrations well below 10 ppb are common in the Everglades (McCorm ick et al., 1996) with any excess phosphorus rapidly taken up (Rudnick et al., 1999). Given that discharge sources are the dominant lateral hydrologic input and that measured boundary concentrations are available for these (see below), and

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107 considering the known importance of atmospheric deposition, a background concentration of 5 ppb was considered justifiable. Specified discharge boundaries Time -series concentration data for discharge sources were obtained for the pumping stations used to specify boundary condition flow rates. The TSB discharge source was specified using pumping data from the Taylor Slough Bridge site, the L31W source with data from the S -175 pumping station, and the C -111 source with data from the S18C pumping station (Swain et al., 2004). Total phosphorus concentrations for these stations were obtained from the SFWMD water -quality database, DBHydro (Tables 42 to 4 -4). Additional data sets used in a Florida Bay water quality model (Walker, 1998) were identified that contained supplementary data for the period of interest (Tables 42 to 4-4). These data sources were consolidated and the time -series data interpolated for daily input to the water -quality model. Additional code had to be written into SWIFT2D to handle the addition of tot al phosphorus mass at the discharge sources. Mass of phosphorus added to the cell containing the discharge source was calculated based on the volume discharged and the input concentration. The mass was then added to the existing mass within the cell and t he updated cell concentration determined, accounting for dilution and concentration effects due to additions and losses of water from precipitation and ET respectively. The subroutine STRUCTCONCS (see Appendix C, Section C 1 ) was written to read daily discharge source concentration inputs from a new input file INPUTFLOWCONCS.dat (see Appendix C, Section C 2 ). For consistency with the existing methods within SWIFT2D for handling sources of water, including

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108 discharge sources, the format of the concentrat ion data input file and its processing by the STRUCTCONCS subroutine were based on the methods used for input and handling of water sources. Atmospheric deposition A value of 0.03 g TP/m2/yr was chosen given past application of this value for phosphorus budgets in southern Florida (Sutula et al., 2001 ; Noe and Childers, 2007). Given the known uncertainty of this input and the systems reported sensitivity to it, the sensitivity of the water -quality model to this input was explored by evaluating three diffe rent options for applying this average annual rate: Option 1) a fixed daily rate of 8.219E 5 g TP/m2/d based on the annual deposition of 0.03 g TP/m2/yr distributed evenly over 365 days; Option 2) a fixed rate of 9.709E 5 g TP/m2/d applied only on days on which rain occurred, based on the annual deposition of 0.03 g TP/m2/yr and the number (309) of rain days; and Option 3) a rate proportionate to the rainfall volume on each given day, summing to 0.03 g TP/m2/yr. In this way, mass of phosphorus added to sys tem in each case was the same. Conceptual Models of Water Quality Processes Wetland biogeochemical processes are extremely complex. It is therefore necessary to abstract and simplify the many processes into a conceptual model of manageable and useful compl exity. Noe and Childers (2007) have calculated annual phosphorus budgets for oligotrophic sloughs that contain phosphorus pools for water, floc, periphyton, soil, consumers, dead aboveground macrophytes, live aboveground macrophytes, and live macrophyte r oot biomass. Such complexity is unjustifiable in this instance given the absence of data against

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109 which to compare the simulated results in a spatially heterogeneous and transient simulation. Furthermore, without data to constrain the many parameters that describe the flux of phosphorus between so many pools, fluxes that are themselves often very uncertain estimates (Noe and Childers, 2007; Noe et al., 2003; Sutula et al., 2001), there is a likelihood of generating non-identifiability and non -uniqueness iss ues in such a complex spatially -distributed model due to overparameterization (Beven, 1992). Given the adaptable nature of the water -quality functionality in FTaRSELOADDS, a number of water quality models (Figures 44, 45 and 46) were tested with increas ingly complex conceptualizations of phosphorus cycling following the approach adopted in Jawitz et al. (2008) and recommended as good practice by Chwif et al. (2000). Model 1 Applying the principle of Occams Razor, the most simple case possible treated total phosphorus as a conservative tracer (Figure 44). In this case, the implicit assumption is that phosphors uptake from the surface water through the many processes described in the introduction is balanced with atmospheric deposition and other internal sources. This is a reasonable assumption given the efficient uptake of available phosphorus reported for oligotrophic Everglades wetlands (Davis, 1994; Noe et al., 2001) and the consistently low and relatively invariant concentrations recorded for the r egion (McCormick, 1996). Atmospheric deposition was therefore not added to the water column in this application, though inputs with lateral flow through the specified head and concentration boundaries were maintained.

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110 Model 2 The second tested model (Figu re 4 -5) accounted for atmospheric deposition as a model input, and simulated phosphorus extraction from the surfacewater with a simple first order sink term, intended to capture the lumped effect of biotic uptake and physical processes that remove phosphorus from the water column. This method was used to explore the three atmospheric deposition options described above. The time-step at which reactions were applied was that implemented for the transport and hydrology in SWIFT2D, being 1.5 minutes (see Chapter 3). To facilitate comparison, a single uptake rate that best fit all three methods was determined rather than individual rates for each case. Manual calibration showed that a rate 1.5E -6 s1 offered the best result. Model 3 The most complex case m ade full use of aRSE to simulate a conceptual water -quality system of processes including lumped biotic uptake of phosphorus, senescence, burial, and release of phosphorus from the dead biomass back into the water column (Figure 4 -6). Although aRSE inclu des methods to solve partial differential equations using the Runge-Kutta 4th order solution methods, testing for numerical stability indicated that a maximum time -step of 15 minutes was permissible. This proved to be an untenable time -step for computational time considerations. Alternatively, aRSE offers simple equation solving in two separate steps, known as presolve and postsolve. This offered a means of solving the system of equations at a more reasonable daily time-step using a mass -balance appr oach. This was the method adopted.

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111 Noe et al. (2003) conducted a radioisotope tracing study to examine the cycling and partitioning of phoshorus in an oligotrophic Everglades wetland (Figure 47). Peak tracer signals were obtained after 10 days (Noe et al. 2003), at which point the partitioning of the tracer between what remained in the surfacewater and what had been removed was used to estimate an average daily uptake rate of 0.084375 day1. The measured partitioning of phosphorus in Noe et al. (2003) wa s applied to determine rates of uptake by living biomass, considered to be the lumped pool of macrophytes, all forms of periphyton, consumers, and floc. The observed rate of flux from living to dead material was used to estimate the senescence rate and burial rate as a function of the uptake rate (Noe et al., 2003). DeBusk and Reddy report rates for sawgrass decomposition of 0.00067 to 0.003 d1. McCormick et al. (1996) reported aerobic decomposition of periphyton mats ranging from 0.006 go 0.11 d1, and Newman and Pietro (2001) report periphyton decomposition on the order of 0.0003 d1. After calibration a value of 0.001 d1 was chosen. Parameters, their values and their sources are presented in Table 45. State variables, their initial conditions, and their definition in the XML input file are given in Table 4-6. The full system of equations input to aRSE are given in the XML input file (XMLINPUT.xml) in Appendix C (Section C 3 ). The IWQ input file (IWQINPUT.iwq) which contains the definitions of model parameters and their values for access by SWIFT2D (see Chapter 2) is also given in Appendix C (Section C 3 ), as well as the SWIFT2D input file (WETLANDS.inp).

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112 Results and Discussi on Results for each of the 3 model complexities applied are presented. The simulation periods were extended beyond the 12month hydrologic period presented in Chapter 3 up to mid -October of 1997. In this way an additional validation data point for the P3 7 station was obtained. No such data was available for the EPGW station until much later (and beyond the maximum simulation length for this work). Table 4 7 summarizes the Nash Sutcliffe efficiencies obtained for each of the models applied. Model 1 Simu lated results for a location in Taylor Slough (P37) and the marl prairies of the C -111 wetlands (EPGW) for the case of conservative transport are shown in Figure 4 -8. The quality of results indicates the assumption that atmospheric deposition and internal sources are balanced by internal sinks is justifiable. The model performed better in the marl prairies (Nash-Sutcliffe of 0.74) than in the slough environment (Nash-Sutcliffe of 0.58), but the average efficiency of 0.66 implies that conservative transpor t may be an acceptable approximation for estimating loadings assuming that the mechanistic hydrodynamics are sufficiently accurate. Model 2 Figure 49 compares the simulated concentrations achieved at stations P37 and EPGW using Model 2 and the three options for atmospheric input. Option 1 input a fixed daily mass irrespective of weather conditions, Option 2 applied a fixed mass only on rain-days, and Option 3 applied mass relative to the amount of rainfall on a given day. All three methods were appli ed such that total mass

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113 added over a year summed to 0.03 g TP/m2/yr to ensure comparable loadings to the system despite the different methods. Option 1 was the simplest approach to adding deposition, simply dividing the annual flux equally over each day. This method provided the best results, with an average NashSutcliffe across both stations of 0.66. Later efforts to refine the calibrated value of the uptake rate (1.5E 6 s1) produced no significant improvement in results so this value and these resul ts were used as the final simulation of total phosphorus concentrations for Model 2. Nash -Sutcliffe efficiencies for Option 2 ranged fro 0.06 to 0.46, which were poorer than those of the first method, but still reasonable, especially for EPGW. Nash -Sutclif fe efficiencies for Option 3 were uniformly less than -5 and therefore unacceptable. Efforts to improve performance by calibrating the rate constant specifically for this method proved futile because the lag in peaks could not be shifted through this fact or. This method introduced strong spikes and troughs during periods of sparse rainfall that degraded results in the dry season. The lack of input given rare rain events and low volume events when rain did occur lead to significant reductions in concentrat ions with time. Rainfall events that then occurred under drier conditions added a disproportionate amount of phosphorus to low water level conditions and produced large spikes in concentration that tended to lag behind the observed values. During wet per iods this problem was mitigated: peaks were not as high due to the diluting effect of larger volumes of standing water, and troughs were not as low because the regular input of mass with frequent rainfall kep t the mass topped up. By volume-

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114 weighting the d eposition with rainfall this method implicitly assumes that deposition is strongly related to rainfall and therefore disproportionately made up of wet deposition. The failure of this method corroborates the suggested importance of dry deposition in the SIC S region Model 3 Results for the most complex model applied are presented in Figure 4-10. Results for the prairie (Nash-Sutcliffe = 0.73) were comparable in quality to those obtained using Model 1 (0.74) and better than those obtained with Model 2 (0.70). However, results for the slough environment (Nash-Sutcliffe = 0.23) were poorer than those obtained using Model 1 (0.58), though comparable to those obtained with Model 2 (0.28). The average efficiency for both measurement stations using Model 3 was a respectable 0.47. As was the case for all the other models, results for the marl prairie station (EPGW) were noticeably better than those obtained for the slough station (P37). While it is unclear why this trend should be present for Models 1 and 2, it c an be explained in Model 3 by noting that the radioisotope study conducted by Noe et al. (2003) was performed in wet prairie marshes in Shark River Slough. The location of this study within marshes within a slough was originally thought to be useful because of the presumed aggregating effect of the habitat being a marsh within a slough, and the fact that SICS is comprised of marsh and slough. However, given the modeling results it appears that the measured rates were more appropriate for marsh/wet prairie conditions than for slough conditions, and this hoped for aggregating effect was not present, or remained biased towards marsh conditions.

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115 Conclusions Three different models of increasing complexity were applied to the modeling of phosphorus water -quality in the SICS region. Average NashSutcliffe efficiencies ranged from 0.47 to 0.66, indicating that phosphorus water quality could be reasonably simulated with multiple models of differing complexity. Considering this result, the additional complexity inher ent to applying a model akin to Model 3 must be justified by the objectives of the modeling effort or theoretical considerations pertaining to the underlying conceptual model. For instance, though the best results were obtained with the simplest model, this version is subject to the greatest structural uncertainty because of the sweeping assumptions implicit in its simple form. Model 3 also remains subject to significant simplifying assumptions, but there is a degree of mechanistic process to the conceptual model at this higher complexity that imbues the model with greater theoretical justification. Alternately, if the objectives are to assess how frequently conditions exceed a specified threshold, say for example the CERP mandated maximum TP concentration of 10 ppb, we see that the more dynamic results from Model 3 capture multiple exceedence events that were missed by the simpler versions. The question of how best to handle the problematic but important input of atmospheric deposition appears to be best answered with the most simple solution; an annual average evenly distributed across all days of the year. Occams Razor would tend to support this approach in any event given the great uncertainties, but the comparison of input methods yielded some valuabl e insights into the problem. Despite the conjectured role of convection storms in

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116 harvesting phosphorus from the upper atmosphere, and the regularity of rainfall in the wet season, results indicated the a rainfall volume weighted approach was not advisable. The s econd deposition method, which assumes rainfall captures and flushes the dry deposits, performed well but not as well as daily average. This work, however, remains founded on an annual average that is itself subject to significant uncertainty, an d requires further study and experimentation to assess the full extent of model sensitivity to this source of uncertainty. The issue of model complexity is an important one in the context of model development, and the availability of a tool such as FTaRSELOADDS, which provides the user with the freedom to define and experiment with model structure demands of the user a greater understanding of the role of complexity on model performance. Despite the reduced structural uncertainty, additional complexity is known to also introduce uncertainty into models through the additional parameters that are needed, each subject to some measurement uncertainty. In this case, the uncertainty associated with atmospheric deposition may well be the underly ing reason for the simplest model, which neglected to account for atmospheric deposition, performing the best. Any effort to mechanistically model water -quality in the oligotrophic Everglades is surely going to be greatly hampered using such uncertain measures for such an important input. Further complexity could be introduced into the water -quality model to produce more biogeochemically detailed models, and these may well improve results despite the uncertainty of deposition, but such an effort needs to be constrained with sufficient data to prevent sensitivity in the model from

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117 undermining the integrity of calibration. The paucity of phosphorus data against which to evaluate model performance in this period is a challenge, though more recent research in the region of Tayl or Slough (Childers, 2006) has produced much data that would probably be sufficient to test greater complexity. The following chapter will explore the issue of model complexity, uncertainty and sensitivity in greater detail. As discussed in Swain et al. ( 2004), accurate capture of flow reversals in the tidal creeks is largely due to wind driven effects and not simply tidal fluctuations. The importance of wind-shear in this environment has implications for wind -induced mixing effects in the transport solut ion that cannot be captured by hydrologic models that do not account for this hydrodynamic effect. It is therefore quite possible that the good results obtained in all models, but particularly the conservative transport approach, would be eroded were a le ss hydrodynamic model simulating the transport. This would require further testing to confirm given that both phosphorus observation stations are located some distance from the tidal creeks where this effect is most prominent.

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118 Table 4 1. Stations and t otal phosphorus concentration data (g/m3) used for interpolation of daily concentrations for specified head boundary conditions in Florida Bay. Station numbers correspond with those of Figure YY and boundary condition numbers with those of Figure XY. TP [ g/m 3 ] TP [g/m 3 ] TP [g/m 3 ] TP [g/m 3 ] TP [g/m 3 ] TP [g/m 3 ] Date Station 3 Station 6 Station 13 Station 15 Station 23 Station 24 7/4/96 0.00597 0.00822 0.01108 0.01256 0.00481 0.00411 8/21/96 0.00566 0.00628 0.01651 0.03294 0.00760 0.00395 9/13/96 0.00698 0.00698 0.02077 0.01333 0.00465 0.00349 10/14/96 0.00612 0.00806 0.01992 0.03216 0.00581 0.00558 11/8/96 0.00411 0.00806 0.00891 0.01201 0.00457 0.00434 12/5/96 0.00496 0.00581 0.00736 0.01744 0.00527 0.00527 1/7/97 0.00419 0.00512 0.01116 0.01620 0.00388 0.00349 2/14/97 0.00496 0.00535 0.02534 0.01767 0.00388 0.00473 3/13/97 0.00581 0.00605 0.00891 0.01240 0.00450 0.00558 4/15/97 0.00411 0.00481 0.00783 0.01380 0.00349 0.00186 5/23/97 0.00380 0.00349 0.00845 0.00907 0.00264 0.00271 6/11/97 0.01604 0.00636 0.01015 0.01116 0.00473 0.00473 7/9/97 0.00667 0.00884 0.02255 0.02612 0.00767 0.00550 8/20/97 0.00752 0.00868 0.02108 0.02860 0.00690 0.00837 9/9/97 0.00798 0.00822 0.02093 0.02031 0.00535 0.00605 10/22/97 0.00860 0.00512 0.01643 0.03534 0.00729 0.00620 11/24/97 0.00581 0.00930 0.01232 0.01759 0.00628 0.00496 12/11/97 0.00915 0.00977 0.01256 0.01411 0.00682 0.00558 BC no. BC 4** BC 2 BC 1 BC 3*** Data provided by the Southeast Environmental Research Center monitoring program in Florida Bay ( http://serc.fiu.edu/wqmnetwork/SFWMD CD/Pages/FB.htm ) ** Applied the average of station 3 and station 6 *** Applied the average of station 23 and station 24

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119 Table 4 2. Da ta sources and values used for boundary conditions concentrations at the L31W discharge source S175: From DBHYDRO (SFWMD) S175: From Walker (1998) Averaging per month** Date TP [ppm] Date TP [ppm] Date TP [ppm] 7/11/96 0.0090 7/96 0.0034 7/96 0.0062 7/24/96 BDL 8/7/96 BDL 8/96 0.0031 8/96 0.0031 8/20/96 BDL 9/11/96 0.0040 9/96 0.0039 9/96 0.0040 9/24/96 BDL 10/9/96 0.0080 10/96 0.0050 10/96 0.0065 10/22/96 BDL 11/6/96 BDL 11/96 0.0033 11/96 0.0033 11/19/96 BDL 12/4/96 0.0070 12/96 BDL 12/96 0.0070 12/17/96 BDL 1/8/97 0.0040 1/97 BDL 1/97 0.0055 1/21/97 0.0070 2/12/97 0.0040 2/97 BDL 2/97 0.0040 3/12/97 BDL 3/97 BDL 3/97 0.0040 --4/97 BDL 4/97 0.0040 5/21/97 BDL 5/97 0.0084 5/97 0.0062 6/12/97 0.0090 6/97 0.0084 6/97 0.0071 6/25/97 0.0040 7/8/97 BDL 7/97 0.0035 7/97 0.0043 7/22/97 0.0050 8/5/97 BDL 8/97 0.0063 8/97 0.0052 9/2/97 0.0040 9/97 0.0050 9/97 0.0051 9/17/97 0.0064 9/30/97 BDL Annual mean 0.0061* 0.0050* 0.0050 BDL="below detection limit" Excluding BDL ** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the assumed detection limit of 0.004 ppm was included in the average. If no data was recorded by SFWMD then the Walker (1998) value was used. If only BDL records existed then 0.004 ppm was used. -No data sampled by SFWMD that month

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120 Table 4 3. Data sources and values used for boundary conditions concentrations at the C -111 discharge source. S18C: From DBHYDRO (SFWMD) S18C: From Walker (1998) Averaging per month** Date TP [ppm] Date TP [ppm] Date TP [ppm] 7/11/96 BDL 7/96 0.0030 7/96 0.0030 7/24/96 BDL 8/7/96 BDL 8/96 0.0032 8/96 0.0032 8/20/96 BDL 9/11/96 0.0040 9/96 0.0035 9/96 0.0038 9/24/96 BDL 10/9/96 0.0040 10/96 0.0034 10/96 0.0037 10/22/96 BDL 11/6/96 BDL 11/96 0.0040 11/96 0.0045 11/19/96 0.0050 12/4/96 0.0040 12/96 0.0038 12/96 0.0039 12/17/96 BDL 1/8/97 0.0050 1/97 0.0041 1/97 0.0044 1/21/97 0.0040 2/12/97 BDL 2/97 0.0031 2/97 0.0031 3/12/97 BDL 3/97 0.0033 3/97 0.0033 --4/97 0.0068 4/97 0.0068 --5/97 0.0115 5/97 0.0115 6/12/97 0.0290 6/97 0.0214 6/97 0.0185 6/25/97 0.0050 7/8/97 BDL 7/97 0.0031 7/97 0.0031 7/22/97 BDL 8/5/97 BDL 8/97 0.0063 8/97 0.0052 09/2/97 0.0041 9/97 0.0046 9/97 0.0046 09/17/97 0.0051 Annual mean 0.0075* 0.0058 0.0056 BDL="below detection limit" Excluding BDL ** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the assumed detection limit of 0.004 ppm was included in the average. If no data was recorded by SFWMD then the Walker (1998) value was used. If only BDL records existed then 0.004 ppm was used. -No data sampled by SFWMD that month.

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121 Table 4 4. Data sources and values used for boundary conditions concentrations at the TSB discharge source. TSB: From DBHYDRO (SFWMD) TSB: From Walker (1998) Averaging per month** Date TP [ppm] Date TP [ppm] Date TP [ppm] 7/9/96 BDL 7/96 0.0047 7/96 0.0044 8/6/96 0.0120 8/96 0.0081 8/96 0.0101 9/10/96 0.0040 9/96 0.0041 9/96 0.0041 10/15/96 BDL 10/96 0.0031 10/96 0.0031 11/5/96 BDL 11/96 0.0045 11/96 0.0043 12/3/96 0.016 12/96 0.0152 12/96 0.0156 --1/97 0.0138 1/97 0.0138 --2/97 BDL 2/97 0.0040 --3/97 0.0058 3/97 0.0058 --4/97 0.0081 4/97 0.0081 --5/97 0.0067 5/97 0.0067 6/24/97 BDL 6/97 0.0040 6/97 0.0040 7/29/97 BDL 7/97 0.0030 7/97 0.0030 8/19/97 BDL 8/97 0.0029 8/97 0.0029 09/16/97 BDL 8/97 0.0035 8/97 0.0035 Annual mean 0.0107* 0.0063* 0.0062 BDL="below detection limit" Excluding BDL ** If value from Walker (1998) > 0.004 ppm and all SFWMD records BDL then the assumed detection limit of 0.004 ppm was included in the average. If no data was recorded by SFWMD then the Walker (1998) value was used. If only BDL records existed then 0.004 ppm was used. -No data sampled by SFWMD that month.

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122 Table 4 5. Parameters used in the model Parameter Definition XML input Value Units Source ku P uptake rate k_uptake 0.083475 d -1 Noe et al., 2003 ksn Senescence rate as a function of uptake k_senesc 0.25 -Noe et al., 2003 kdc Decomposition rate k_decomp 0.001 d -1 Calibration; Debusk and Reddy, 2005; Newman et al.; 2001 kb Burial rate as a function of uptake k_soil 0.13 -Noe et al., 2003 Kw Wet/dry factor K_wet 1 or 0 -From SWIFT2D based on ICLSTAT* ICLSTAT(N,M) is 0 if a cell is considered wet at the time by SWIFT2D, or >0 if dry.

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123 Table 4 6. State variables with initial conditions as used in Model 3 State variable (Figure 4 6) Definition XML input Initial condition (aRSE) Units [TPsw] TP concentration in the surfacewater at t TP_sw_conc 0.005 g TP/m3 TPsw Mass of TP in the surfacewater at t 1 TP_sw_mass1 0.01 g TP/m2 Mass of TP in the surfacewater at t TP_sw_mass2 0.01 g TP/m2 TPu TP uptake from the surfacewater for t TP_uptake1 0.0008 g TP/m2/d TP uptake from the surfacewater for t 1 TP_uptake2 0.0008 g TP/m2/d TPbio TP in live biomass at time t TP_live1 0.04 g TP/m2 TP in live biomass at time t 1 TP_live2 0.04 g TP/m2 TPdead TP in dead biomass at time t TP_dead1 0.014 g TP/m2 TP in dead biomass at time t 1 TP_dead2 0.014 g TP/m2 TPsn TP flux by senescence at time t TP_senesc 0.0002 g TP/m2/d TPdc TP flux by decomposition at time t TP_decomp 0.0001 g TP/m2/d TPb TP flux by burial at time t TP_bury 0 g TP/m2/d TPs TP in the soil at time t TP_soil1 0.0001 g TP/m2 TP in the soil at time t 1 TP_soil2 0.0001 g TP/m2

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124 Table 4 7. Nash Sutcliffe efficiencies for the water -quality models applied to simulate total phosphorus in the Southern Inland and Coastal Systems Model1 Model 2 (Option 1) Model 2 (Option 2) Model 2 (Option 3) Model 3 P37 0.583531 0.285041 0.062226 5.183816 0.226110 EPGW 0.737771 0.697249 0.460871 5.612662 0.733882 Combined 0.658693 0.484382 0.255956 5.364559 0.471255

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125 Figure 41. Schematic of phosphorus cycling processes in Everglades wetlands.

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126 Figure 42. Location of SICS model boundary conditions including specified head boundaries (blue), discharge sources (orange), and the associated total phosphorus concentration boundary conditions (black sq uares indicate specified head and circles discharge sources; numeric references refer to Table 4 1) at each of these (map and hydrologic boundaries from Swain et al., 2004). 1 2 3 4 6 7 8 11 5 9 10 P37 EPGW

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127 Figure 43. Location of water -quality observation points in Florida Bay. Data are provided by the Southeast Environmental Research Center (http://serc.fiu.edu/wqmnetwork/SFWMD -CD/Pages/FB.htm )

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128 Figure 44. Model 1: Conservative transport assuming deposition and internal sources are in equilibrium with biotic uptake and internal sinks. Green fill indicates total phosphorus, and blue lines indicate the medium is water.

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129 Figure 45,. Model 2: First order uptake from the water column using the reactive transport functionality of SWIFT2D (Model 2a) or aRSE for reactions and SWIFT2D for transport (Model 2b).

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130 Figure 46. Model 3: Reactions simulated by aRSE with transport by SWIFT2D. For XML equations see Appendix C (Section C 3 ) Variables and parameters define d in Tables 4 -5 and 46.

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131 Figure 47. Mean proportion of total recovered radioisotope (32P) per mesocosm found in different ecosystem components over time (from Noe et al., 2003)

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132 Figure 48. Simulated TP concentrations obtained with Model 1 at observation stations in Taylor Slough (P37) and C -111 wetlands (EPGW).

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133 Figure 49. Simulated TP concentrations obtained with Model 2 for each of the atmospheric deposition options explored at observation stations in Taylor Slough (P37) and C -111 we tlands (EPGW).

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134 Figure 410. Simulated TP concentrations obtained with Model 3 at observation stations in Taylor Slough (P37) and C -111 wetlands (EPGW).

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135 CHAPTER 5 UNRAVELING MODEL REL EVANCE: THE COMPLEXI TY -UNCERTAINTY SENSITIVITY TRILEMMA Introduction At its heart, our inability to truly simulate environmental (open) systems (Oreskes et al., 1994; Konikow and Bredehoeft, 1992) is due to our inability to reproduce their complexity. There are many reasons for this shortcoming: a lack of understanding in poorly studied systems or the inability to either conceptualize or reproduce the intricacies of well -studied systems; the inability of our instruments and methods to obtain true observations needed for parameterization and calibration due to m easurement uncertainties and heterogeneities in space and time and scale; and the discontinuous nature of numerical solutions that imperfectly reproduce the continuity of reality. Such limitations prohibit true model validation (Oreskes et al., 1994). In lieu of confirming such validity, we strive instead for confidence in model results, which we consider by evaluating the extent of our doubt, as indicated by the degree of uncertainty associated with the generated results (Naylor and Finger,1967; Beven, 2006a). There is growing unease among developers and users of dynamic simulation models about the cumulative effects of various sources of uncertainty on model outputs, which inherit these underlying uncertainties (Manson, 2007 and 2008; Cressie et al., 20 09; Messina et al., 2008). In particular, this issue has prompted doubt over whether the considerable effort going into further elaborating complex dynamic system modeling will in fact yield the expected payback, viz. new insights about the complicated sy stems they are intended to simulate (Ascough et al., 2008). The concern is that insufficient heed has been paid to the balance between investment (complexity) and return (uncertainty),

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136 which was succinctly captured by Zadeh (1973), who first presented the notion of relevance as part of his principle of incompatibility: ... the conventional quantitative techniques of system analysis are intrinsically unsuited for dealing with humanistic systems or, for that matter, any system whose complexity [emphasis ad ded] is comparable to that of humanistic systems [authors note: e.g. environmental systems]. The basis for this contention rests on what might be called the "principle of incompatibility". Stated informally, the essence of this principle is that as the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance (or relevance [emphasis added]) become almost mutually exclusive characteristics. The relevance of a model is contingent on the balance between its power to address questions and the power of its answers. The former is dependent on model complexity the degree of detail to which the real system is reproduced in the m odel structure. The latter is dependent on model uncertainty the accuracy, precision and confidence associated with output results. Our failure to attend more closely to this balance is due largely to insufficient understanding of how complex models gain and lose relevance. Failure to advance this understanding has been at least in part due to the practical limitations associated with complex models. In particular, mechanistic environmental models are among the most complex, demanding specialized numerical code of spatially distributed domains, numerous state variables, and a plethora of input parameters and data. Such complex tools are typically developed by specialists and, once complete, are not very amenable to adjustments in structure. The choic e of complexity in such tools has therefore more commonly been the responsibility of model developers, while users simply have to deal with the consequences. Users do have a choice between potential tools of differing complexity, but that decision is stil l based on fixed choices, and is generally the product of a multitude of other considerations that

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137 comprise what most modelers understand as the art of modeling (Getz, 1998; Basmadjian, 1999). We believe that suitable tools now exist to support controll ed experimentation with model complexity, as well as more rigorous investigation into the consequences for uncertainty. Using such tools, we propose and demonstrate that meaningful new progress can be achieved toward unraveling the issue of relevance. The Complexity -Uncertainty -Sensitivity Trilemma To this point, we have used the term uncertainty to encompass various types of uncertainty, some quantifiable and some less so, which collectively contribute to the epistemic uncertainty in model results (that is, uncertainty associated with our knowledge about the state of a simulated system; Regan et al., 2002). To better investigate total epistemic uncertainty, it becomes necessary to distinguish between specific forms of uncertainty. The most commonly enc ountered form of uncertainty in modeling is error, which is a measure of model accuracy (i.e., the discrepancy between simulated results and observed data). Another prevalent form of uncertainty is that due to the uncertainties inherent to the values of i nput parameters, which are propagated through a model and onto the outputs and manifest as precision (i.e., the irreducible uncertainty in any model result that determines the range of possible values the actual result might inhabit). This is the sense of the word most commonly intended in the context of uncertainty analysis, and is the meaning adopted in all following sections unless specified otherwise. Other forms of uncertainty exist, most of which are difficult to assess because they are conceptually more qualitative, for example: uncertainty due to the underlying assumptions and structure of a model; uncertainty in the interpretation of voluminous and complicated results; and uncertainty in the validity of a models calibration due to model sensitivi ty. All are influenced by model complexity, but

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138 sensitivity is particularly interesting in the context of investigating relevance. Methods of sensitivity analysis now exist to rigorously quantify sensitivity in such a way as to not only characterize the flexibility inherent to the model, and thereby the risk of overparameterization issues, but also to illuminate how the sensitivity is caused and possible ways for improving the precision of results (Saltelli et al., 2004). This feedback, linking sensitivi ty and uncertainty, completes a tripartite dialectic between complexity, uncertainty, and sensitivity the relevance trilemma that guides this work. Uncertainty There is growing interest in evaluating the contributions of model inputs (uncertainty in data) and model structure (uncertainty from the simplifying assumptions necessary to abstract reality into model design and algorithms) to the overall uncertainty of model outputs (Beven and Binley, 1992; Beven, 1993; Draper, 1995; Cressie et al., 2009). Howe ver, the sources and magnitude of uncertainty and their effect on dynamic model outputs have not been comprehensively studied (Haan et al., 1995; Beven, 2006a; Shirmohammadi et al., 2006; Muoz -Carpena et al., 2007; Valle et al., 2009). Uncertainty analys es endeavor to address this by propagating the various uncertainties onto a model output, and many methods exist to achieve this end (Haan, 1989; Shirmohammadi et al., 2006; Cressie et al., 2009). Systems that are better described and characterized (as ph ysical systems such as hydrology tend to be) are more suitable for variance based methods that apply Monte-Carlo simulations, such as the Generalized Likelihood Uncertainty Estimation method (GLUE; Beven and Binley, 1992). However, many systems (such as ecosystems) are poorly understood and modeler experience and subjectivity play an important role in their simulation. Uncertainty assessments that employ Bayesian methods are better suited to

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139 incorporate subjectivities and are therefore often favored in such circumstances (Cressie et al., 2009). Merely quantifying the uncertainty in model outputs is insufficient to fully understand where and how the uncertainty is propagated or to understand the role of complexity. Sensitivity analysis can be used to determine how uncertainty in model outputs is apportioned to different sources of uncertainty in the model inputs (Saltelli et al., 2008). Whereas uncertainty analysis quantifies the overall uncertainty, sensitivity analysis identifies the key contributors to uncertainty; together they constitute a reliability assessment of a model (Scott, 1996). Sensitivity The sensitivity of a model output to a given input parameter has traditionally been expressed in terms of the derivative of the model output with respect to the input variation (Haan et al., 1995; Cariboni et al., 2007). Such sensitivity measurements are "local" because they are fixed to a point or narrow range where the derivative is taken. Local sensitivity indices are generally classified as "one at a time" (OAT) methods, because they quantify the effect of varying a single parameter by altering only its value while holding all others fixed. Local OAT sensitivity indices are effective only if all factors in a model produce linear, direct responses in t he output, or interest is in the model response under specific conditions (Saltelli et al., 2004). However, if changes produced in an output are non-linear, or parameters exhibit interaction effects on model output response, or an extensible assessment of sensitivity patterns is required, then a global sensitivity approach is needed (Leamer, 1990; Saltelli et al., 2004). Global sensitivity analyses (GSA) simultaneously vary all inputs and explore the entire parametric space of a model, thereby making no assumptions about linearity, additivity, or monotonicity. In complex models, the output response is often non-linear and non-

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140 additive, so local OAT techniques are not appropriate, and global techniques should be used (Saltelli et al., 2004). Different GSA methods can be selected based on the objective and context of the analysis (Saltelli et al., 2000 and 2004; Cacuci, 2003). Output sensitivity is inextricably tied to uncertainty, representing as it does the paths of greatest influence on the output (tho se parameters to which the output is most sensitive). An alternative perspective is that sensitivity represents the paths of least resistance through which input uncertainty will be propagated onto outputs during an uncertainty analysis. Sensitivity th erefore plays an important role in another source of epistemic uncertainty: model overparameterization, which is variously captured in both forward and inverse solutions as non-identifiability, non -uniqueness, and equifinality (Brun et al., 2001; Omlin et al., 2001; Beven, 2006b; Ebel and Loague, 2006). Overparameterization issues are the result of too many degrees of freedom in a model due to the number of variable parameters. Each additional parameter introduces an additional source of influence over model outputs. This effect accumulates and can result in excessive flexibility in the model, which is counterproductive to parameterization and calibration efforts and can produce poorly defined calibrations or multiple irresolvable model characterizations (Beven, 2006a). A poorly calibrated model, or one with a number of calibrated states that may be physically irreconcilable, undermines confidence in the models projections. GSA methods uniquely capture the internal model relationships between input and output, as well as between different inputs. These can be used as indicators of a models flexibility, and thereby the risk of nonidentifiability and other overparameterization issues (Snowling and Kramer, 2001). Though it is an important and neglected ( Luo et

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141 al., 2009) source of epistemic uncertainty, sensitivity quantified in this form remains a qualitative measure of uncertainty. However, we can surmise that given sufficient complexity, uncertainty associated with a models total sensitivity might be expected to reach a point that inhibits the models relevance, overwhelming any gains in accuracy from added complexity in analogous fashion to Hannas (1998) usual uncertainty suspects (Figure 5 2). The sensitivity of outputs to interactions between par ameters is a key contributor to overparameterization, and total sensitivity measures that capture this effect are therefore a useful proxy for assessing the risk over over -sensitivity. By contrast, greater direct sensitivity implies stronger direct links between input and output, which is not only less likely to generate overparameterized conditions, but is also necessary for identifiability (Brun et al., 2001). Complexity Model complexity has proved challenging to quantify, or even define (Chwif et al., 2000). In a sense, complexity remains an abstract quality that can be assessed according to many factors, with no single definition proving useful for all contexts. However, when considering the structural complexity of a model, the number of parameters is generally considered a useful indication of relative complexity, since the number of parameters is tied to the nu mber of processes included (Fis her et al., 2002). Incorporating the complexity of the equations themselves can be achieved using a Petersen matrix, which accounts for the number of mathematical operations (Snowling and Kramer, 2001). Subjective allocation of complexity levels can also be assigned based on users knowledge of the number and nature of the processes included (Lindenschmidt et al., 2006). In this work, a simple measure of relative complexity is

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142 sufficient, and thus distinct complexity levels were defined according to the number of parameters required. Given the limitations inherent to simulating reality with simplified tools, it is not surprising that more complex models are pursued (Arthur, 1999; Beck, 19 87). Models that are too simple may not capture important processes and cannot be proven to reproduce the measured data for the correct reasons (Nihoul, 1994). The complexity of a model fundamentally defines (and limits) the potential realities that can be reproduced. Environmental systems are particularly challenging to simulate, not only because they contain profound numbers of processes and constituents, but also because they can shift between alternate stable states, a complex emergent process (Scheffer, 2009). Such shifts can fundamentally change the nature of a system (i.e., the shift from an aquatic system dominated by algae to one dominated by macrophytes). Models that simulate ecological or biogeochemical systems like these within a physically dynamic environment, such as a hydrodynamic aquatic environment, are already highly complex. Yet, as we will show, failure to incorporate sufficient (additional) com plexity can have important consequences for a models ability to resolve certain simulated conditions. The growing interest in optimizing model complexity relative to uncertainty (Cox et al., 2006; Lawrie and Hearne, 2007) is particularly pertinent today b ecause of the growing availability of adaptable computational modeling tools, which give the user the freedom to define model structure, and thus complexity. Dynamic systems that can be conceptualized without a spatial domain have had such adaptable tools for many years, with systems such as STELLA finding application in a wide array of fields (Doerr, 1996).

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143 Similar versatility has been pursued with GIS modeling tools (e.g., Wesseling et al., 1996). However, for the case of mechanistic, numerical models of complex environmental systems, with large, spatially distributed domains and numerous state variables, the degree of model complexity has remained largely imposed on model users. Nonetheless, the value and amount of specialist time required for such m odel development; the dramatic advances in computing capacity (Schaller, 1997) and data acquisition by remote sensing (Pohl & Van Genderen, 1998); and the economics of computer code reusability have compelled continued evolution of even the most complex mo dels toward greater adaptability. Recently, Jawitz et al. (2008) developed a spatially -distributed numerical water -quality model, the Transport and Reactions Simulation Engine (TaRSE), with user -definable state variables and biogeochemical processes. To the authors knowledge, this degree of control is novel in such a complex environmental model. Another driver of increased interest in the effects of model complexity is the development of multi disciplinary integrated models that combine environmental and socio economic drivers, sometimes through coupling of existing specialty models into a multi modeling framework that can incorporate larger uncertainty than conventional models (Lindenschmidt et al., 2007). Relevance dilemmas Previous work has sought to begin the process of elucidating the relationships between complexity and various forms of epistemic uncertainty. Model complexity has been long recognized as having important consequences for output uncertainty. Hanna (1998) illustrated (Figure 5-1a) th at increasing complexity by incorporating more state variables and processes can initially reduce uncertainty, but can have the opposite

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144 effect after a certain critical point (Fisher et al., 2002). Greater complexity improves a models conceptual rendition of reality, meaning the model has fewer simplifying assumptions and therefore less structural uncertainty. However, each additional process requires parameters to characterize the mathematics, and the uncertainty associated with each of these accumulate s, eventually exceeding any gains. This makes identification of a potential inflection point important, for it reveals the optimal degree of complexity for modeling a system that incorporates sufficient detail to gain information while avoiding greater uncertainty and loss of relevance. Snowling and Kramer (2001) proposed general relationships relating complexity and two forms of uncertainty: error and sensitivity (Figure 5-1b). The authors showed that as complexity was increased, model error decreased while model sensitivity increased. Snowling and Kramer based their hypothesis on the general concept that reduced structural error increased accuracy in analogous fashion to the reduction of uncertainty presented by Hanna. Conversely, sensitivity would i ncrease because the additional parameters required to simulate the additional processes have some effect on the model outputs, and therefore represent additional degrees of freedom. This hypothesis has since been supported by work in Lindenschmidt (2006) and Lindenschmidt et al. (2006). However, all corroborating results presented thus far (Snowling and Kramer, 2001; Lindenschmidt, 2006; Lindenshcmidt et al., 2006) are subject to limitations in generality, having been produced for limited ranges of paramet er variation, centralized around calibrated applications, or based on local OAT sensitivity analyses. Furthermore, existing support for this hypothesis does not address how the nature of sensitivity changes with model complexity. Improving our

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145 understand ing of these dilemmas, between complexity and uncertainty, complexity and error, and complexity and sensitivity, is crucial to improving our understanding of relevance. However, it is also necessary that we acknowledge the links between such dilemmas, whi ch further complicate the problem but cannot be ignored is we wish to address it. To this end we propose a trilemma, relating complexity, uncertainty, and sensitivity, as the first step toward a more integrated assessment of relevance. The relevance trilemma In this paper we propose the following relationships relating uncertainty, sensitivity, and model complexity, which together we believe represent a useful characterization for model relevance (Figure 52): 1) Total global sensitivity, being the net sum of all input effects on an output, increases with complexity due to the additive influence of additional parameters; 2) Interactions increase with increasing complexity (for the same reason), and will diminish the role of direct sensitivity as progressively more parameters interact to control the output and detract from the direct influence of individual parameters. To test these hypotheses, we integrated a stepwise model -building approach using TaRSE, GSA and UA to investigate the role of complexity, and to better guide development across multiple levels of model complexity. Given doubt associated with model input factors, such as structural complexity and uncertainty input parameters, model development that is closely coupled to GSA and UA can reveal im portant unintended effects, not only in terms of model sensitivity and uncertainty, but also the capacity of a model to reproduce real, and complicated, system responses.

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146 Materials and Methods Global Sensitivity and Uncertainty Analysis Methods Two state o f -the art global sensitivity and uncertainty methods were used in this analysis: the qualitative method of Morris (1991) and a quantitative, variance based method called the extended Fourier Amplitude Sensitivity Test (FAST; Saltelli, 1999). A brief summa ry of each method is given below (further details summarized by Muoz Carpena et al. (2007), and an in-depth treatment of the methods is provided in Saltelli et al., 2004). The Morris (1991) method, extended by Campolongo and Saltelli (1997), is intended to elucidate qualitative global sensitivity, sacrificing quantification in lieu of dramatically improved computational demands. This method is therefore suitable for assessing the relative importance of input parameters, and for this reason it is an effici ent screening method often used to filter out unimportant parameters before conducting the more computationally intensive, and quantitative, FAST analysis (Jawitz et al. 2008; Saltelli et al., 2005). The Morris method applies a frugal sampling technique t o obtain unique sets of parameter values by varying each within their prescribed range and probability distribution. The multiple simulations then performed using these unique sets produce elementary effects in the outputs, attributable to changes in each input parameter, the absolute values of which are averaged to produce a qualitative global for each parameter with respect to the model output of interest (Campol ongo et al., elementary effects attributed to a particular parameter. Sinc e the values of all other

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147 tested parameters are simultaneously varied, this variability implies that the observed effect is dependent on the values held by other varied parameters (the parametric context), and thus interaction effects between them. Conver that interactions between parameters do not affect the parameters influence on the output, and that the output is therefore directly sensitive to it. For each output of an be plotted in a Cartesian plane to indicate the relative importance of each output (distance from the origin on the X axis), and the prevalence of interaction effects (distance from the origin on the Y axis). The variance based extended FAST method pr ovides a quantitative measure of the direct sensitivity of a model output to each parameter, using what is termed a first order sensitivity index, Si, defined as the fraction of the total output variance attributable to a single input parameter (i). In th e rare case of an additive model, where the total output variance is explained as a summation of individual variances introduced by i = 1. Such additivity is a requisite condition if local sensitivity analysis results are t o be generally applied to a model (Saltelli et al., 2004). Given that even relatively simple models rarely meet this requirement, the application of global sensitivity methods should be the preferred approach. In addition to the calculation of first order indices, the extended FAST method (Saltelli, 1999) calculates the sum of the first and all higher order indices for a given input parameter (i), called the total sensitivity index (STi), (Equation 51), n i ijk ij i TiS S S S S...... (5 -1)

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148 where Si is the first order (direct) sensitivity, Sij is the second order indirect sensitivity due to interactions between parameters i and j Sijk the thirdorder effects to due to interactions between i and k via j and so forth to the final varied parameter, n Based on Equation 5 -1, total interaction effects can then be determined by calculating STi Si estimate to the total sensitivity index ( STi) (Campolongo et al., 2007). Since the extended FAST method applies a randomized sampling procedure, it provides an extensive set of outputs that can then be used in the global uncertainty analysis of the model. Thus, probability distribution functions (PDFs), cumulative probability distributi on functions (CDFs), and percentile statistics can be derived for each output of interest with no further simulations required. In general, the analysis procedure followed six main steps: (1) PDFs were constructed for uncertain input parameters; (2) input sets were generated by sampling the multivariate input distribution according to the selected global method; (3) model simulations were executed for each input set; (4) global sensitivity analysis was performed according to first the Morris method and th en 5) the extended FAST method; and (6) uncertainty was assessed based on the outputs from the extended FAST simulations by constructing PDFs and statistics of calculated uncertainty. The free software Simlab (Saltelli et al., 2004; http://simlab.jrc.ec.europa.eu/) was used for multivariate sampling of the input parameters and post processing of the model outputs. Sample sets were created for all the parameters in each of the complexity levels tested (see subsequent section and Figure 5-3) and for both met hods, resulting in a total of six sets of analyses. The number of model runs was selected based on the number of

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149 parameters in each complexity level according to Saltelli et al. (2004). A total of 1,170 simulations were conducted for the Morris method and 45,046 simulations for the extended FAST method. Model Description, Application, and Selection of Complexity Levels Model description: TaRSE A water quality numerical modeling framework, the Transport and Reactions Simulation Engine (TaRSE), has been dev eloped to simulate the biogeochemistry and transport of phosphorus in the Everglades wetlands of south Florida (Jawitz et al., 2008; James et al., 2009). The US$10 billion Comprehensive Everglades Restoration Plan (CERP) is the largest ecosystem restorati on effort in the world, and aims to restore historic flows and P levels to the ecosystem. The freshwater wetlands of the Everglades have evolved under phosphorus -scarce nutrient conditions and are especially sensitive to labile phosphorus in the surface w ater (Munsen et al., 2002; Noe et al., 2003). An important component of CERP therefore entails modeling the water quality with respect to phosphorus levels, and TaRSE was developed to meet this need. The design of TaRSE is comprised of two functional modules; one that simulates the advective and dispersive movement of solutes and suspended particulates in flowing water (the T ransport module; James et al., 2009), and one that simulates the transfer and transformation of phosphorus between biogeochemical components (the R eactions module) (Jawitz et al., 2008). The term S imulation E ngine refers to the generic nature of the reactions module, which has been designed such that the user is responsible for specifying (in XML input files) the models state variables and the equations relating them. State variables cam be grouped in conceptual stores, such as surfacewater or soil, and are classified as mobile if they are to be transported or

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150 stabile if they are not. Thus, even though the inaugural impl ementation of TaRSE was intended for phosphorus -related water quality modeling, this variable structure means it can be easily adapted for different applications. The user selects from a suite of equations to describe exchanges between state variables, including zerothorder, first order, Michelis Mentin growth and decay, sorptiondesorption kinetics and rule based relations (Jawitz et al., 2008). When applied in a hydrodynamic environment, TaRSE requires that necessary hydrologic state variables, such as stage and velocity, be provided by a coupled hydrologic model. TaRSE employs a triangular mesh to discretize the spatial domain for the Godunov mixed finite element transport algorithm (James, et el., 2009), but the reactions module is independent of mes h geometry. Once the reactions have been simulated and mobile quantities updated within each cell, they are transported. Model application This effort to study the effects of increasing model complexity was carried out as part of a comprehensive testing process during the development of TaRSE. In addition to the necessary quality control provided by sensitivity and uncertainty analyses, the intention of this analysis was to study potential consequences resulting from the novel freedom afforded by TaRSEs flexible design (i.e., user -defined complexity). In order to isolate the effects of complexity, an artificial domain was created in which the sources of variability extrinsic to complexity could be controlled and excluded. A 1,000 200m generic flow do main (Figure 53) was created and discretized into 160 equal rectangular triangles (cells). Flow was set from left to right so that the inflow boundary consisted of cells 1, 41, 81, and 122, and the outflow boundary consisted of cells 40, 80, 120, and 160. A no -flow boundary was applied to the top and bottom (longer) edges of the

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151 domain. To exclude the effects of transient flow, steady -state velocity was established, and the effect of heterogeneities were managed by assuming spatially homogeneous conditi ons. A constant velocity of 500 m/d was established to approximate Everglades flow conditions (Leonard et al., 2006) with an average water depth of 1.0 m. Simulations were run for 30 days with a 3 -hour time-step. Levels of complexity Three models of incr easing complexity were created (Figure 54a -c). Following the recommendations of Chwif et al. (2000), complexity was progressively added to the model in an organized and stepwise fashion. Each new complexity level corresponded to the addition of one new state variable and the associated processes relating the variable to the preexisting system. The simplest case (Level 1) contained no biotic components (Figure 54a). The intermediate -complexity case (Level 2) contained surfacewater biota in the form phytoplankton (Figure 5-4b). The most complex case (Level 3) contained additional macrophytes rooted in the soil (Figure 5-4c). Table 2 1 lists the state variables and processes that appeared in each complexity level, including the boundary conditions fo r the mobile state variables (always quantified in g/m3), viz. soluble reactive phosphorus (SRP) in the surface water ( Csw P) and plankton biomass (Cpl). Initial conditions for the stabile state variables (always quantified in g/m2), viz. SRP in the porewater, adsorbed phosphorus, macrophyte biomass, and organic soil mass, were 0.05, 0.027, 500, and 30,000 g/m2, respectively. Boundary and initial conditions were selected to represent reasonable Everglades conditions based on values cited in the extensive literature review conducted as part of parameterization effort required for the sensitivity analyses (see following section). For full details of the model equations and numerical solutions see Jawitz et al. (2008).

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152 Pa rameterization of Inputs Across Complexity Levels The application of TaRSE was done without prior calibration in order to avoid limiting the potential range of physical conditions the model might be applied to, and through which the effects of new complexi ty would be expressed. This also facilitated testing of the model across a wide range of possible scenarios as a necessary step in the development process prior to evaluation of its performance for a particular application (Saltelli et al., 2000). Result s from the GSA and UA were evaluated to ensure that simulation results were consistent with the conceptual models and that unreasonable results did not emerge (see Jawitz et al., 2008 for extensive details). Before conducting a GSA or UA it is necessary t o specify a range and distribution for each parameter, from which values can be statistically sampled. The field-scale ambient variability of many inputs has been reported to be adequately modeled with log -normal or Gaussian distributions (Jury et al. 1991; Haan et al. 1998; Limpert et al. 2001; Loiciga et al. 2006). When there is a lack of data to -distribution can be used as an acceptable approximation (Wyss and Jrgensen 1998). When only the range and a base (effective) value are known, a simple triangular distribution can be used (Kotz and van Dorp 2004). Finally, a uniform distribution is recommended in cases where values are assumed equally distributed along the entire parametr ic range. The input parameters used in the analysis of TaRSE (Table 5-2) were assigned ranges and probability distributions based on an extensive literature review found in Jawitz et al. (2008). Since the goal of this work was a general model investigat ion, and not a specific study of its application to a particular site, parameter ranges were selected to cover all physically realistic values for the intended target region (the

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153 Everglades). Given the wide range of physical and ecological conditions that the data from such an all encompassing approach include, and considering that values were derived from relevant literature rather than directly from sets of data, the more general -distribution was adopted. Consequently, all biogeochemical parameters (i .e., -distributions. Dispersivity is related to the composition of the physical system, such as for example vegetation density, domain dimensions, and velocity. These characteristi cs are contingent on the site selection, rather than natural variation, and their probability was therefore considered to be random, and accordingly allocated a uniform distribution (Jawitz et al., 2008). Several outputs were defined for the analysis, acc ounting for each of the models state variables at each complexity level, and described in Table 5 -1. In the context of this work to investigate the role of complexity, only those outputs that appear in all three complexity levels permit comparison and ar e presented. Outputs were defined to integrate both spatial and temporal effects. For outputs of mobile quantities, averages across the outflow domain (cells 40, 80, 120, and 160) were calculated at the end of the simulation period in order to integrate the effects of transport parameters and processes across the entire domain into the output. For stabile quantities, outputs were expressed as the difference between the initial and final value of averages across the entire domain. Given the constancy of conditions applied to the model across all complexity levels through fixed parameter ranges and distributions; invariant scale, initial, and boundary

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154 conditions; and steady hydrodynamics, any changes observed in the uncertainty and sensitivity are attribut ed to the effects of changes in model complexity. Results and Discussion Effects of Model Complexity on Sensitivity Morris method Figures 5 5a -c depict trends in the results from the Morris method analysis for soluble reactive phosphorus (SRP) in the surfa ce water, Csw P. This output is generally considered to be of greatest interest in management of water -quality for CERP (Perry, 2008), and is the official water -quality restoration target mandated by Congress (Sheikh and Carter, 2005). Immediately apparent is that the relative location of parameters in the plane changed as the complexity increased. At lower complexities (Levels 1 and 2) inputs were found closer to the axis, almost never approaching, and never exceeding, the 1:1 line. At Level 3 t he parameters were generally above the 1:1 (shaded triangle in each graph) and associated with proportionally larger values. Higher values denote a greater role for interactions among input parameters. As the complexity increased, more parameters wer e drawn out into the plane, particularly at Level 3. Since important parameters (i.e., those to which Csw P is most sensitive) are distinguished from unimportant ones by their relative distance from the origin, these results indicate that more paramet ers became relatively important as complexity increased. Conversely, fewer parameters were uniquely important in the more complex model. This trend is generalized in Figure 55d, a novel presentation of Morris method results that takes advantage of the g eometry inherent to their interpretation. Multiple outputs were plotted collectively ( Csw P, Cpw P, So, and SP) by normalizing the points to

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155 conserve their relative Cartesian positions, and grouping them by complexity level for comparison. The same patterns observed in the Csw P results are exhibited by all the outputs lumped together in this way. These results are in agreement with our hypothesis that as complexity increases, an increase in interactions is associated with a decrease in direct effects. The sensitivity of Csw P to different parameters at different complexities shows the changing role of certain parameters as others are added. In Level 1, the stabile parameters kox, kdf, b and Xso (oxidation rate, coefficient of diffusion, soil bulk density, and the soil phosphorus mass fraction, respectively) were the most important. In Level 2, plankton in the water column was added to the model, and parameters associated with plankton growth ( kg pl and k1/2 pl; plankton growth rate and plankton phosphorus half -saturation constant, respectively) became the most important to Csw P. With the addition of macrophytes in Level 3, it became difficult to separate obviously important parameters. Instead, the model became comparably sensitive to many parameters because of the increased role of interactions. Extended FAST Quantitative results for Csw P from the extended FAST analysis (Figs. 5-6a -h) corroborate the qualitative Morris method results. The perce ntage of total variance (Figure 56a) attributable to direct (first order) effects ( Si) decreased with increasing complexity, slowly from Level 1 to 2, then rapidly from Level 2 to 3. The same trends were exhibited by Cpw P, So, SP (Figure 56bd). Conver sely, interaction effects (Figure 5 -6a -d) rose slowly from Level 1 to 2, then rapidly from Level 2 to 3. These trends were consistent across all model outputs and provide further quantitative evidence in support

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156 of the hypothesized sensitivity -complexity relationship, as posited by Snowling and Kramer (2001) and extended globally herein. In Level 1, the sensitivity of Csw P to parameters associated with stabile state variables was limited by the coefficient of diffusion (see Figure 53a), because diffusion was the physical link between mobile surface water and stabile subsurface state variables. In Level 2, the total sensitivity (Figure 56e) of Csw P increased because the addition of plankton introduced a number of parameters that could affect Csw P without first being channeled through, and thus dampened by, the slow process of diffusion. By contrast, the Level 2 sensitivity of stabile outputs ( Cpw P, So and SP) to parameters more closely associated with either of the mobile state variables ( Csw P or Cpl) rem ained mitigated by the diffusion rate (Fig 5-6f -h). This changed in Level 3, however, where the addition of macrophytes introduced new parameters to the subsurface. At this level of complexity, macrophytes represented a phosphorus -sink dominant enough to make all outputs sensitive to even those parameters whose influence was dampened by the slow rate of diffusion. Consequently, we see a consistent trend across all outputs of decreasing direct effects, and increasing interactions and total sensitivity. T hese results indicate that the system was more sensitive to the addition of macrophytes than to plankton. Furthermore, when viewed in conjunction with our understanding of the physical description of the system, they allow us to understand how the models internal dynamics, expressed as output sensitivities, are shifting with increasing complexity. Effects of Model Complexity on Uncertainty Some of the uncertainty results (Figs. 5-6e h), presented here using the 95% confidence interval, seem to question th e conceptual trends in Hanna (1988) (Figure 51a), indicating that these relationships may not be as simple as proposed. In fact, this is

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157 explainable by accounting for the fact that some outputs are integrative, in that all system components can participa te in producing their final outcome, whereas others have inherent biases that inhibit such integration. The key output, Csw P, is an example of an integrative output, since it is subject to the influence of all other state variables, and the expected reduc tion of uncertainty holds. By comparison, accreted organic soil (So), which is defined in terms of mass that is several orders of magnitude larger than any other outputs, is not subject to comparable influence by other model components, and is therefore not integrative. Mechanistically, this discrepancy is due to the relative influence of turnover rates for the component compared with the fluxes into and out of the store. The consistent increase in uncertainty exhibited by So (Figure 56f) therefore does not follow the conceptual trend. Interestingly, in Level 2 we saw that the stabile outputs closely associated with So (Cpw P and SP, which we might expect to be more integrated), followed the So trend and became more uncertain. This corresponds well with the physics of the model for that level, however; addition of phosphorus through oxidation is the predominant contributor to Cpw P, to which SP is in turn bound through equilibrium adsorption-desorption kinetics. Thus, their uncertainties should in fact be coupled with that of So. This demonstrates that the uncertainty e ffects in poorly integrated outputs can be passed onto related outputs, effectively dis -integrating them. With the introduction of macrophytes in Level 3, the effect of So on Cpw P and SP was broken by the addition of a major new sink for phosphorus releas ed through oxidation of the organic soil, the process that physically linked the three outputs. The previously affected outputs in turn became more integrated, and we see their uncertainty drop as

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158 originally expected (Figure 5-6h). It is therefore import ant to consider that outputs can be effectively dis -integrated, and therefore may not receive the consequences of increasing complexity in the same way. Similarly, outputs may not be affected by added complexity in other parts of the model. Figures 5 7a -c depict the progression of output PDFs across complexity levels for the same key output, Csw P, from a simpler leptokurtic distribution at the lowest complexity level (represented by the lowest number of input parameters, eight), through the platykurtic distribution at the intermediate level (12 parameters), to a bimodal distribution at the highest complexity (16 parameters). The latter results represent different system states, combining the further platykurtic nature of the Level 2 stablestate, with a strongly leptokurtic end-point that corresponds to combinations of parameter values that push the simulation out of the original stable-state. In this case, the alternate state appears as a single value, and indicates that the complexity at this level was sufficient to capture the existence of a second state, but insufficient to capture any variability within the state. Mechanistically, the presence of this second state demonstrates that a critical threshold existed for the state previously simulated as Level 2. Its presence was caused by combinations of parameter values working in conjunction with initial and boundary conditions, which resulted in the systemic depletion of the biotic components (plankton and macrophytes). This occurred because the range of values over which the parameters were varied was held constant across complexity levels, yet included values appropriate for both of the known stable -states that shallow water bodies can exhibit in the Everglades (Scheffer, 1990; Scheffer et al. 1993; B eisner et al., 2003;), namely

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159 algae and macrophytedominated systems (Bays et al. 2001; Cichra et al. 1995). Testing the full range of plankton -dominated conditions in Level 2 presented no problems to the model because the structure was mechanistically appropriate there were no macrophytes. However, the incorporation of macrophytes into the model structure changed the definition of the simulated ecosystem, and without the necessary feedback mechanisms (i.e., complexity) in place to resolve the extreme conditions produced by unrealistic combinations of parameter values, phytoplankton biomass is all but eliminated. Without this surface water sink for phosphorus, Csw P continuously input at the boundary remained essentially unchanged in these cases, depict ed by the spike in outflow values matching the boundary concentration of 0.05 g/m3 (Figure 57c) The platykurtic area represents model conditions under which the simulated system is not catastrophically overwhelmed. The results therefore mimic those of L evel 2, where macrophytes were absent and phytoplankton dominated the surface water phosphorus dynamics. It is noteworthy that the introduction of macrophytes still acts as a phosphorus sink in these cases, stressing the phytoplankton in terms of phosphor us availability and thereby dampening the frequency of lower Csw P values (a sign of greater phosphorus uptake due to growing plankton). Macrophytes also prevent the majority of Csw P results from exceeding the boundary input concentration (which can only occur when significant diffusion takes place due to high Cpw P, as in Level 2, and as was never the case for Level 3 because of porewater SRP uptake by the macrophytes (Jawitz et al. 2008). In this way, the addition of macrophytes to the set of tested model conditions represented the introduction of an alternate stable-state that could not be resolved. The

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160 complexity was insufficient to permit the model to simulate a shift between stable-states, but (in conjunction with the parameter ranges tested for) was sufficient to simulate the existence of a second stable-state. Though these results express emergent characteristics of the simulated systems under the tested conditions, the forcing functions in this case (being the variously sampled parameter sets) ar e based on real values (albeit not necessarily real combinations of values) and therefore represent potential realities that match well with the known biotic states of the Everglades: mixed algae -macrophyte (the hump in Figure 5-7c) and macrophyte-dominate d (the spike). Given the absence of any suitable feedback in the tested models mechanisms that might permit plankton to dominate macrophytes, such a stable state is impossible to simulate. The emergence of alternate stable-states in the results only occ urs once complexity has reached Level 3, clearly indicating that additional model complexity is required to capture the complicated, but real, behavior of the system. Conclusions Presented results have corroborated the sensitivity -complexity relationship, proposed by Snowling and Kramer (2001), using true global sensitivity methods and over a wide range of model conditions, thereby demonstrating the validity of the relationship in the most general context yet. We have also demonstrated that our hypotheses relating the global sensitivity indices for direct effects, interactions, and total sensitivity to model complexity are valid, providing a fresh global perspective to the relevance trilemma. The combined GSA and UA framework applied herein produced valuabl e insights for interpreting both the meaning of the model results, and the meaning of how they were generated in the context of model relevance. This methodology is therefore

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161 proposed as a useful way to glean insights into the external and internal dimens ions of model performance. The combined GSA and UA results presented indicate that uncertainty, on average, decreases with complexity, and that total sensitivity increases. This implies that we are still within the region of the trilemma space (Figure 5-2) that encourages us to persist with increasing complexity if so desired. These results emerged from an exploration of parametric spaces far larger than would be expected for any application to a specific site, and therefore constitute a worst -case-scena rio, which is thus cause for further optimism. It is therefore reasonable to expect that refinement to a particular application will reduce uncertainty further and permit additional complexity without loss of relevance. Given the benefits derived from the GSA/UA methods, it is proposed that these methods constitute a valuable framework (Figure 58) for exploring the Relevance Trilemma. In applying it herein, we gained useful information about the tested versions of TaRSE, including important considerations valuable to future work, such as the sensitivity of outputs to particular parameters, the strong effects caused by introducing macrophytes, and the importance of considering integration in output definitions. The sensitivity of the model to the addition of macrophytes calls for close attention to the associated initial conditions and parametric ranges. The emergence of alternate stable states in Level 3 results, and their absence in simpler levels, demonstrates the need for some minimal complexity if such real world patterns are to be reproduced in simulations, and highlights the unexpected potential for such patterns in the output response of even a relatively coarse biogeochemical model. Importantly, these

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162 methods also provide insights into how one mi ght reduce model uncertainty (Saltelli et al., 2004) by identifying important and unimportant parameters and processes. This information can be used to guide efforts to better measure important parameters or remove ineffectual complexity. Important questi ons remain after the analyses presented here. Does Level 3 represent the optimum system description? Can this optimum be determined? Although answers to these questions fall, at least in part, into the subjective realm of the "art of modeling," the tool s presented here offer the modeler an opportunity to better understand the sometimes unexpected tradeoffs introduced by increasing model complexity. We suggest that today we are in a better position to unravel the relevance trilemma, and indeed even to ac tively incorporate it into our art, than when Zadeh (1973) first presented his principle of incompatibility.

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163 Table 5 1. Process description for the increasing levels of complexity studied Process Levels Key, fig5 2 Affected variables Process equation Diffusion 1, 2, 3 1 Surface water SRP concentration (mobile), Csw P (g/m3) P sw P pw df w df P swC C z z k dt dC Soil porewater SRP concentration (stabile), Cpw P (g/m2) Sorption desorption 1, 2, 3 2 Soil porewater SRP concentration (stabile), C pw P (g/m 2 ) dt dC k dt dSP pw d b P Soil adsorbed P mass (stabile), SP (g/m2) Oxidation of organic soil 1, 2, 3 3 Soil porewater SRP concentration (stabile), C pw P (g/m 2 ) o ox oS k dt dS Organic soil mass (stabile), So (g/m2) Inflow/outflow of surface water SRP 1, 2, 3 4 Surface water SRP concentration (mobile), Csw P (g/m3) BC: Csw P = 0.05 g/m3 Uptake of SRP through plankton growth 2, 3 5 Surface water SRP concentration (mobile), C sw P (g/m 3 ) pl P sw P sw pl pl g plk C C C k dt dC2 / 1 Plankton biomass concentration (mobile), Cpl (g/m3) Settling of plankton 2, 3 6 Plankton biomass concentration (mobile), C pl (g/m3) pl pl st pl swC k dt dC Organic soil mass (stabile), So (g/m2) Inflow/outflow of suspended particulates (plankton) 2, 3 7 Plankton biomass concentration (mobile), Cpl (g/m3) BC: Cpl = 0.043 g/m3 Uptake of porewater SRP through macrophyte growth 3 8 Soil porewater SRP concentration (stabile), Cpw P (g/m2) mp as P pw P pw mp mp g mpk z C C C k dt dC2 / 1 Macrophyte biomass (stabile), Cmp (g/m2) Senescence and deposition of macrophytes 3 9 Macrophyte biomass (stabile), C mp (g/m 2 ) mp sn mpC kdt dC Organic soil mass (stabile), So (g/m2)

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164 Table 5 2. Probability distributions of model input factors used in the global sensitivity and uncertainty analysis Parameter definition Symbol Process in Fig5 4 Distribution Units Input present in L1 L2 L3 Coefficient of diffusion kdf 1 (710-10, 410-9) m2/s x x x Coefficient of adsorption kd 2 (810-6, 1110-6) m3/g x x x Soil porosity (.7, 0.98) x x x Soil bulk density b (.05, 0.5) x x x Soil oxidation rate kox 3 (.0001, 0.0015) 1/d x x x P mass fraction in organic soil so P (.0006, 0.0025) x x x Longitudinal dispersivity l U (70, 270) m x x x Transverse dispersivity t U (70, 270) m x x x Plankton growth rate kg pl 5 (.2, 2.5) 1/d x x Plankton half saturation constant k1/2 pl 5 (.005, 0.08) g/m3 x x Plankton settling rate kst pl 6 (2.310-7, 5.810-6) m/s x x P mass fraction in plankton pl P (.0008, 0.015) x x Macrophyte growth rate kg mp 8 (.004, 0.17) 1/d x Macrophyte half saturation constant k1/2 mp 8 (.001, 0.01) g/m3 x Macrophyte senescence rate ksn mp 9 (.001, 0.05) 1/d x P mass fraction in macrophytes mp P (.0002, 0.005) x

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165 Figure 51. Relevance relative to a) sources of modeling uncertainty in relation to model complexity (Hanna, 1988 as cited in Fisher et al., 2002), and b) Snowling and Kramers (2001) hypothesis relating error and sensitivity to model complexity.

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166 Figure 52. Hypothesized trends relating complexity to sensitivity from direct effects, sensitivity from interactions, and total sensitivity. Total uncertainty still follows the trends of Hanna (1988) but now includes total sensitivity as another source of uncertainty. Figure 53. TaRSE application domai n, with flow from left to right and bounded above and below by no -flow boundaries. Simulations were run for 30 days with a time -step of 3 hours.

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167 Figure 54. Levels of modeling complexity studied to represent phosphorus dynamics in wetlands. Levels include a) Level 1: interactions between SRP in the water column and SRP in the subsurface; b) Level 2: Level 1 with the addition of plankton growth and settling; c) Level 3: Level 2 with the addition of macrophyte growth and senescence. Notation and detail s on processes included in each Level are given in Table 2-1.

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168 Figure 55. Morris method global sensitivity analysis results for surface water soluble reactive phosphorus outflow ( Csw P) in a) Level 1, b) Level 2, c) Level 3, and for d) all outputs and all levels combined. The grey triangles indicate the 1:1 line, font size of labeled parameters indicates their relative importance to Csw P.

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169 Figure 56. Results for a -d) sensitivity from direct effects ( Si, left y axis) and sensitivity from interactions ( ST Si, right y axis, and e-h) output uncertainty expressed as the 95% CI (left y axis) and total sensitivity ( ST, right y axis), as model complexity was increased.

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170 Figure 57. Output PDFs for SRP concentration in surface water outflow ( Csw P) for a) Level 1, b) Level 2 and c) Level 3.

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171 Figure 58. A suggested framework, employing global sensitivity and uncertainty analyses, for enhancing understanding of model performance studying model relevance in relation to complexity

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172 CHAPTER 6 CONCLUDING REMARKS Conclusions A novel water quality modeling tool has been developed for the coastal wetlands of the southern Everglades by linking the hydrologic model FTLOADDS with the water quality model aRSE to create FTaRSELOADDS FTaRSELOADDS comb ines the numerical efficiency and mechanistic rigor of a fixed-form spatially -distributed hydrodynamic model with the adaptability of a flexible free-form biogeochemical cycling model. In combination, the two models represent a tool that can be adapted an d refined to best capture the water -quality issue of interest while accounting for the complex variable-density unsteady hydrodynamics that characterize the regions hydrology The linkage of the FTLOADDS and aRSE was validated by a series of comparisons b etween known analytical solutions and numerically simulated results that used FTLOADDS and a combination of FTLOADDS and aRSE. Thus Objective 1 was satisfied. The linked models were tested with a field application to the SICS region, which provided answers to the questions underlying Objectives 2 and 3. Surfacewater hydrodynamics were shown to be sensitive to depthvarying Mannings n which had to be reintroduced into the hydrodynamic model in order to accurately capture wetting and drying process es and their effects on water -quality Three different water -quality conceptual models of increasing complexity were implemented and the results compared. The simplest version employed conservative transport and produced the best match with data. However, this version also neglected all biogeochemical processes, including the important input of atmospheric deposition, and was therefore the weakest of the models from the perspective of mechanistic justifiability. The most

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173 complex model produced acceptabl e results despite being subject to the significant uncertainty associated with including atmospheric deposition, implying that the greater mechanistic integrity may have helped mitigate this uncertainty. Experimentation with how to input atmospheric depos ition indicated that the simplest approach of distributing an annual average equally over all days in the course of a year produced the best results and is justifiable based on the limited data available Given the freedom to manipulate model complexity, and the recognized relationship between this complexity and model uncertainty, sensitivity and relevance, a study was conducted to elucidate how additional complexity affects model performance (Objective 4) Global sensitivity and uncertainty analysis meth ods were applied, and a framework for formally exploring their results in the context of complexity was presented. Direct sensitivity was found to decrease and interaction effects to increase as complexity was added. Uncertainty was found to decrease in response to increased complexity, though considerations of turnover rates versus flux rates were shown to influence this result. The suggested framework demonstrated its value as a useful means of exploring and explaining model results and of assessing relevance with respect to complexity, thus satisfying Objective 4. Limitations Currently, the computational expense of a fully integrated fixed -form/free-form tool remains high. The required time -step for hydrodynamic simulations of SICS is small but the ef ficiency of solution methods keeps the investment manageable. With the addition of aRSE comes significant overhead since each cell in the SICS hydrodynamic model domain is individually processed. This process is exacerbated by the need to prepare and exc hange large amounts of data between the two models. The presented effort

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174 was limited to a daily time-step by these computational costs, which precluded using the Runge Kutte 4th Order differential equation solution functionality within aRSE, which require d a maximum 15 minute time -step and untenable cumulative computational times. The paucity of surfacewater phosphorus data was a significant limitation to the water -quality m odeling effort. This was exacerbated by the fact that observed phosphorus concent rations fluctuated within a relatively small range of variation due to the oligotrophic conditions. A more rigorous testing of the water quality against more phosphorus concentration data points, or against more types of data (such as biomasses or fluxes) would contribute valuable additional validation of the model. Additionally, the sensitivity and uncertainty analyses performed did not evaluate the SICS water quality application, but rather a theoretical application established in a generic testing domain. The SICS water quality application would benefit from such a sensitivity and uncertainty analysis. Similarly, evaluation the complexity -relevance relationship for a field-tested application such as SICS would provide additional rigor to the testing o f the suggested relevance framework. Finally, t here is currently no formal documentation for aRSE or FTaRSELOADDS. D ocumentation does exist for TaRSE and SWIFT2D individually, but a formal record of the linkage of the models and a users manual to guide i mplementation of the linked tools is needed. Without this documentation the complexity of the tool prevents its wider application by any user n ot already familiar with it Future Research Future work is required to either extend the simulation period to i nclude more data points, or to shift the simulation period to more recent times when data is being

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175 recorded at greater resolution. Additional time-series data pertaining to soil phosphorus, periphyton and macrophyte biomass in the SICS region would provid e valuable additional testing of the more mechanistic water quality modeling approaches. The current treatment of the water -quality reactions as a completely separate step to the transport means that parallelization of the reactions is possible. Consider ing that over 9,000 cells are currently processed in linear sequential order when they could all theoretically be processed simultaneously, the opportunities for greater computational efficiency are significant. Th e work presented here has demonstrated the significant commitment required to get to the point of being able to make use of this tool Future work must now explore and expose the potential within, especially as it pertains to the flexibility provided by aRSE Most immediatel y, the mechanistic and spatially -distributed modeling of any number of water -quality issues in the southern Everglades can begin in earnest. Nitrogen and dissolved organic carbon input to Florida Bay are a major concern that has not been satisfactorily ad dressed T he proven ability of the hydrodynamic model to accurately capture wetting and drying is encouraging for future sulfur and mercury modeling in the region given the importance of these processes to mercury methylation (Cleckner et al., 1999) The development of ecohydrological water quality modeling is now also possible. The important role of Mannings n in the hydrological simulations was demonstrated in Chapter 3. Making the link between simulating biomass growth for water -quality and changes i n flow resistance with seasonal growth and senescence is readily achievable

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176 with FTaRSELOADDS. So too is the integration of spatially distributed nutrient inputs to ecological models in the region, which have previously been limited to hydrologic inputs. Finally, such flexibility within complex models is an important launching point for serious study of how model complexity, uncertainty, and sensitivity interact in complex spatially -distributed models Given the paucity of work in this field and the clear benefits derived from the GSA and UA methodology that was applied in Chapter 5, the framework that was proposed for tackling questions related to the Relevance Trilemma should prove fruitful Philoso phical Deliberations The freedom to be creative is the source of progress. It is this tenet that underlies the very notion of Academia, and recognizes the profound role of creative freedom in advancing our technological, cultural, and intellectual evoluti on. It is the freedom to be creative that will prove to be the greatest strength of tools such as FTaRSELOADDS. One need look no further than the kaleidoscope of problems to which STELLA has been applied to see the imagination unleashed by a tool that put s creative c ontrol in the users hands. There is no reason why users of complex models, such as that applied herein, should be denied such creative freedoms as a matter of course, as has long been the case with the availability of only fixed -form spatiall y distributed models In fact, it is precisely because modeling of this highly complex sort is so arduous and so challenging that such freedoms should be encouraged. To have modelers who have invested such energy and expertise and life time into master ing a tool that is subject to claustrophobic specificity is to waste a glut of potential and opportunity. The art of modeling will always entail balancing the pros and cons behind the choice of an appropriate tool for a given problem, whether it be develop ed from scratch

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177 or picked off a shelf. With th e freedom to uniquely tailor complex spatially distributed models comes a new dimension to the art modeling: the notion of optimizing these high levels of complexity with respect to uncertainty, sensitivity and relevance It is important that we continue to delve more deeply into this tripartite conundrum or risk falling behind our tools. Modelers, and all who depend on their work, cannot fail to acknowledge and grasp the limitations to relevance inherent to t he nascent generation of super -complex tools including efforts to integrate many independent and spatially distributed models into vast multi model systems. As complex model creation and modeler creativity become ever more entangled, better understandi ng of how models gain and lose relevance is critical both to the evolution of our tools and to the evolution of our modelers. We cannot forget that the science and art of modeling are one and the same.

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178 APPENDIX A MODEL VERSIONS Model and Application Versions: Nomenclature The following rules and naming conventions apply when referring to versions of either SWIFT2D, FTLOADDS, or their applications as SICS or TIME: SWIFT2D: specifies only the surfacewater model SEAWAT: specifies only the groundwater m odel FTLOADDS: specifies versions in which SWIFT2D and SEAWAT have been linked (one or the other may be on or off) SICS: the Southern Inland and Coastal Systems application TIME: the Tides and Inflows in the Mangroves of the Everglades application Version 1.X: models or applications simulating only surfacewater Version 2.x: models or applications simulating coupled surface water/groundwater Version X.1: models or applications using SWIFT2D code adapted for the SICS a pplication as per Swain et al. ( 2004) V ersion X.2: models or applications using SWIFT2D code adapted for the TIME application as per Wang et al. ( 2007 ) Version X.Y.1: models or applications using SWIFT2D code adapted for TIME but with variableManning's functionality from SICS adaptations reins tated Model and Application Versions: Submodels The following figures offer a graphical overview of the model and application versions. Consistent colors are used to represent identical versions/models to facilitate identification across figures. Perpendicular blocks, generally oriented vertically, indicate models/versions that encompass adjacent horizontal blocks. Blocks crossed out in white indicate that the submodel is present but not used.

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179 Figure A 1. SWIFT2D v1.1 comprises the SWIFT2D v1.0 (Schaffranek, 2004) code and additional code from SICS updates for coastal wetlands (Swain, 2005). Figure A 2. FTLOADDS v1.1 comprises the SWIFT2D v1.1. code, leakage code linking SWIFT2D to SEAWAT, and SEAWAT, but represents applications in which SEA WAT is not implemented. Figure A 3. SEAWAT comprises the MODFLOW code and the MT3DMS code (Langevin and Guo, 2006).

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180 Figure A 4. FTLOADDS v2.1 comprises SWIFT2D v2.1 and SEAWAT, where SWIFT2D v2.1 is SWIFT2D v1.1 implemented with integrated leakage and groundwater simulation by SEAWAT. Figure A 5. FTLOADDS v1.2 comprises SWIFT2D v2.2 with updates for TIME but with the groundwater simulation turned off (thus SWIFT2D v1.2).

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181 Figure A 6. FTLOADDS v2.2 contains SWIFT2D v2.1 linked with SEAWAT and containing TIME updates (thus SWIFT2D v2.2).

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182 APPENDIX B DETAILS OF THE FTARSELOADDS LINKAGE Section B1 Technical Considerations in the Model Linkage Since aRSE is callable as a DLL, and considering the primacy of hydrology and the role of FTLOADDS in controlling the integrated execution of SWIFT2D and SEAWAT, FTLOADDS was selected as the controlling program. Furthermore, the decision was taken to link aRSE with the surface water model only, i.e. to SWIFT2D. This was done to keep the scope of the task manageable given the effort entailed in linking aRSE to even one of the two complex FTLOADDS sub -models. The choice of SWIFT2D is further justified by r ecognizing that the biogeochemical processes aRSE is intended to simulate are primarily associated with the surface water in wetlands systems. Water quality in the groundwater is generally not as sensitive to biological influence given the paucity of aut otrophic organisms and was therefore not justified at this early stage development. Additionally, though vertical flow through the upper soil cannot be simulated given these assumptions, the flexibility of aRSE does permit soil phosphorus statevariables t o be defined, which would permit soil biogeochemistry to be modeled under assumptions of negligible vertical advection processes. A number of fundamental differences in the respective design of FTLOADDS and aRSE had to be overcome in order to successfully link the two models. These included an idiosyncratic artifact of the initial setup of aRSE that inhibited its automation within FTLOADDS, the absence of a spatial distribution in aRSE, and the use of different programming languages to code the models.

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183 Co nsideration 1: Initial setup of aRSE In order for the user to specify a unique system of water -quality processes it is necessary to input the state variables that comprise the system, the parameters required to characterize the equations relating the state variables, and the nature of the equ ations themselves. State variables are classified as mobile if they represent constituents that would be moved with flow (solutes and suspended particulates constituents), or stabile if they represent stationary quantities (e.g. rooted macrophytes, soil benthos). There are also 30 additional implicit parameters that are always present, though only used if specified in the equations. These implicit parameters were originally necessary for transport processes and have been kept because they represent us eful properties (mostly of hydrodynamics) that may be useful in future work and present little inconvenience with their presence. In the jargon of aRSE, state variables and parameters are collectively referred to as components Given that the number of bo th parameters and statevariables is a user choice, the total number of components is variable. A single vector, VARS, is used by aRSE to store the values for all components. In order for updated values of transported constituents or hydrodynamic quantitie s to be passed from FTLOADDS to aRSE it is necessary to know which particular element of this vector corresponds with the given quantity. However, aRSE must be initialized once in order to determine these locations since they are subject to the number of user specified components. In order to exchange information between the two models it is necessary to have some means to determine what quantity each element of the vector refers to.

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184 Consideration 2: Spatially -distributed versus non-spatial FTLOADDS is a spatially -distributed model, and therefore performs calculations on, and stores data about, many individual cells that together comprise the modeled domain. By contrast, aRSE is non-spatial, assuming that the system of reactions it simulates is carried ou t at a singular location with no consideration of spatial distribution. Where FTLOADDS stores arrays of data for each model variable, aRSE stores a single vector containing the single value for each of the model components. The use of a one-dimensional vector, as opposed to a higher dimensional array, is possible because there is essentially only ever one cell (hence non-spatial) under consideration. By contrast, SWIFT2D maintains two-dimensional arrays, dimensioned to the total number of cells used to discretize the model domain, for each of the hydrodynamic variables and threedimensional arrays for the solute concentration variables (the third dimension is used to specify the particular constituent, since all concentrations for up to seven constituent s are stored in a single array). Since aRSE can only ever consider a single cell at a time it must be run repeatedly for each of the cells in the FTLOADDS domain. This in turn entails updating the VARS values with data appropriate to the cell in question, and then saving the values after the reactions step so they are not over written by the results of the subsequent cells reaction step. Consideration 3: FORTRAN versus C++ The programming languages used to encode each of the models was not consistent. Th e FORTRAN language (in the form of both FORTRAN 77 and FORTRAN 90) was used to code FTLOADDS and its constituent submodels, SWIFT2D and

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185 SEAWAT. The generic design of aRSE is the product of object oriented template functionality in the C++ language used t o code it. The linkage of the two models therefore represents a mixedlanguage programming problem in which communication between the two structurally and syntactically foreign languages must be facilitated. A number of inter -language calling conventions have been adopted by FORTRAN and C/C++ (Arnholm, 1997; Wang et al., 2005): Most FORTRAN compilers convert subroutine names to lower case and append an underscore. To make a C routine callable in FORTRAN, declare the name of the routine in lower case and ap pend an underscore. FORTRAN passes arguments by reference, C++ by value. For a variable name in a subroutine call from FORTRAN, the corresponding C routine receives a pointer to that variable. When calling a FORTRAN routine, the C routine must explicitly pass addresses (pointers) in the argument list. C routines assume that character strings are delimited by the null character. From FORTRAN to C, the length of each character string is passed as an implicit additional INTEGER (KIND=4) value, following the ex plicit arguments. From C to FORTRAN, when a function returns a character string, the address of the space to receive the result is passed as the first implicit argument to the function, and the length of the result space is passed as the second implicit ar gument, preceding all explicit arguments. Arrays in FORTRAN are stored in a columnmajor order, whereas in C they are stored in a row -major order. Two types of communication between FORTRAN and C++ were required that called for special treatment. Wang et a l. (2005) outline a suggested manual procedure for overcoming these problems. The principle is to build a wrapper for the C++ library that hides the implementation details of the library from the FORTRAN code. The wrapper handles the request from a FOR TRAN call to create and destroy the objects defined in C++, and then returns a FORTRAN pointer aliased to the memory allocated in the C++ library with support function overloading. The wrapper itself is made of two components, one C and one FORTRAN 90 component, written in standard C++ and FORTRAN 90,

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186 together with the conventional inter -language calling method. Changes to the application source code are minimal and can be automated. The FORTRAN 90 component contains a module that provides a set of public functions for the FORTRAN application to call. Each of these public functions corresponds to a function implemented in the C++ library, and it calls the corresponding function via the C++ component. The FORTRAN 90 module also holds one or multi dimensional FORTRAN pointers in its global space, and thereby provides an alias function for the C++ component to call that makes the oneor multi dimensional FORTRAN pointer aliased to the memory space allocated dynamically in the C++ library. Resoluti on 1: Initial s etup of aRSE To overcome this problem a FORTRAN subroutine, READIWQ, was written to read a new water -quality input file (IWQINPUT.iwq) that contains the necessary data also included in the XML input file, but which could be read without the need for aRSE to be executed. The XML output file was therefore no longer needed. Since aRSE still relies on reading the XML input file to correctly setup, this method requires that two input files containing some overlap in data be provided. However, t he files are small and simple to produce, and allow the setup of aRSE to be automated and controlled from FTLOADDS. Furthermore, having such a file is also useful for overwriting aRSE parameters and statevariable initial conditions should this be desirabl e, and introduces some measure of control from within the calling FORTRAN code over the inputs to aRSE without having to tamper with the aRSE code at all. The automation process in READIWQ makes use of the fact that aRSE distributes components in the VARS vector in an orderly manner that, given knowledge about the

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187 number of statevariables and the number of parameters, permits the deduction of their future location in VARS vector. Mobile state variables are always positioned first, followed by stabile sta te variables, followed by a fixed number of implicit parameters (27 hydrodynamic and spatial properties), followed by the user -input parameters, followed by the remaining 3 implicit parameters (temporal properties). The subroutine READIWQ therefore require s, in order: The number of mobile state variable s The number of stabile state variable s The paired name and initial value for each mobile state variable The paired name and initial value for each stabile state variable The number of user -specified paramete rs The paired name and value for each user -specified parameter s Also permitted are override values for any of the implicit parameters, whose positions in VARS are fixed relative to each other, though contingent in absolute position on the number of statevariables that precede them. This process is conducted during the initial setu p of SWIFT2D, thereby ensuring that data is correctly exchange and the linkage with aRSE is fully functional from the first time it is called from within SWIFT2D (though aRSE still requires its own initialization step the first time it is called to process the equations outlined in the XML input). Resolution 2: Spatially -distributed v ersus non-spatial A new two -dimensional vector was established, C1_aRSE, dimensioned to the number of components (i.e. the same size as the VARS vector) and the total number of cells in the FTLOADDS domain. Each time aRSE is called, which may or may not be coincident with the FTLOADDS hydrology and transport time-steps, all the appropriate data for each of the cells is moved from the various arrays within FTLOADDS to C1_aRSE pr ior to the simulation of reactions in the first cell. Since no exchange of

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188 information between cells takes place during the reaction step, the order in which cells are processed for reactions does not matter with regards to the accuracy of the simulation. However, the order in which memory is accessed during computations does affect the speed of the process. It date are therefore transmitted in columnmajor order from FTLOADDS arrays to C1_aRSE in order to minimize computational time. Though FTLOADDS arra ys are dimensioned with a rectangular shape (number of rows x number of columns), the model permits an irregularly shaped domain, which may result in many points within the rectangular memory array referring to cells that are not actually used by FTLOADDS. The subroutine CELLCOUNT therefore determines the number of active cells in the model and this number is used in the reactions step, thereby minimizing the computational iterations Prior to each individual cell being processed the data appropriate to tha t cell is transmitted to the VARS vector that is used directly by aRSE. Once the reactions have been simulated the updated VARS values are used to overwrite old values in C1_aRSE. In this way old values are overwritten and new values stored until reactio ns have been performed on all cells. After the final cell has been processed, all updated values in C1_aRSE used transmitted back to their appropriate FTLOADDS arrays, where they are then used in subsequent transport calculations. Currently, concentrations depths, and velocity in the x and y directions are passed from FTLOADDS to aRSE, where concentrations are analogous to mobile statevariables, and the hydrodynamic variables to particular implicit parameters. Only concentrations are transmitted back to FTLOADDS for use in transport, though the freedom to return updated hydrodynamic variables should the reactions affect them

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189 offers potentially exciting opportunities for simulating ecohydrological effects using these models. Resolution 3: FORTRAN v ersus C ++ Text strings in FORTRAN and C++ are represented differently. FORTRAN strings are character variables that are declared as a particular length, which is maintained by trailing blank space characters irrespective of the length of the text of interest wit hin the string. By contrast, C++ strings are null terminated following the final character of text. If FORTRAN strings are to be understood by C++ they must be converted to a null terminated form. A subroutine to do so exists, and was used to convert the XML input filenames, which are now read in by the FORTRAN subroutine READIWQ, and convert them to a format acceptable to the C++ code of aRSE. The second instance necessitating mixed -language communication was the calling of subroutines. In this case, aR SE is executed by calling one of a three C++ subroutines from within the FORTRAN linkage. FORTRAN 90 contains some built in functionality to facilitate mixed -language programming, including the INTERFACE statement, which is useful for creating interfaces between FORTRAN and external subroutines. Interfaces were therefore defined for each of the external C++ subroutines. Compiler directives were specified within the interface to attribute C++ calling conventions, to specify the location of the subroutines as within a DLL, and to specify an alias for the called subroutine that was preceded with an underscore to match the C++ syntax. General description of the linkage mechanism If aRSE is greater than zero then READIWQ is called during the setup of SWIFT2D t o preprocess aRSE.

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190 The subroutine CALLaRSE is called at the time interval specified by the variable CaRSE. Prior to performing reactions on the first cell the subroutine aRSE_IN is called to transfer the values for all specified FTLOADDS variables in each of the domain cells to the storage array variable C1_aRSE. For each cell in turn the subroutine RUN_aRSE is called, which updates the vector VARS with the cell -specific values and calls the C++ subroutines PRESOVE, RKSOLVE and POSTSOLVE to execute aRSE. If it is the first time aRSE is being called then the subroutine INITIALIZE is called prior to these subroutines. After each cell has been processed the array variable C1_aRSE is updated with the updated values in the vector VARS. After reactions have been p erformed on the final cell the subroutine aRSE_OUT is called to update all appropriate FTLOADDS variables with the new values in the array variable C1_aRSE. Section B2 FORTRAN Subroutines for Linkage The following subroutines were written specifically for the linkage of aRSE and FTLOADDS. Additional code that was added to existing SWIFT2D subroutines is given in Section B3. Module aRSEDIM MODULE aRSEDIM !**************************************************************************** This MODULE is used for declaring variables used in the linkage of aRSE with SWIFT2D within FTLOADDS !**************************************************************************** IMPLICIT NONE INTEGER*4 INITIATE, NCALLS, NCELLS, NCELLST, NCOMPS, NCOMPST, NVARS INTEGER*4 CALLNO, CELLNO, RKORDER, NPAR, NMOB, NSTAB, NSTABMAX, K_WET, ATM_NPAR PARAMETER (NCALLS = 1, NCELLST = 10201, NCOMPST = 60, RKORDER = 4, NSTABMAX = 15) INTEGER*1 XMLINPUTC(50), XMLOUTPUTC(50), XMLREAC_SETC(50) INTEGER NPRZ(NSTABMAX) CHARACTER *120 PREPROCESS, XMLINPUT, XMLOUTPUT, XMLREAC_SET, COMPNAME(NCOMPST) REAL*8 DTaRSE,DTFTLOADDS

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191 !**************************************************************************** **** REAL*8 DIMENSION (:), PUBLIC, ALLOCATABLE :: ZR(:,:,:), C1_aRSE(:,:),ZRIC(:,:,:),RIC(:,:,:) PUBLIC :: SUB CONTAINS SUBROUTINE SUB (en,em,el,ze,comps,activecells) !integer, intent(in) :: en,em,te INTEGER :: en,em,el,ze,err,comps,activecells ALLOC ATE ( ZR(en,em,ze), stat=err) ZR=0 !IF (err /=0) PRINT *, "SUB allocate NOT successful." ALLOCATE ( C1_aRSE(comps,activecells), stat=err) C1_aRSE=0 !IF (err /=0) PRINT *, "SUB allocate NOT successful." ALLOCATE ( ZRIC(en,em,ze), stat=err) ZRIC=0 !IF (err /=0) PRINT *, "SUB allocate NOT successful." ALLOCATE ( RIC(en,em,el), stat=err) RIC=0 !IF (err /=0) PRINT *, "SUB allocate NOT successful." END SUBROUTINE SUB END MODULE aRSEDIM Subroutine READIWQ SUBROUTINE READIWQ !cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc cccc !C This subroutine read a .IWQ file to extract the data needed to run RSE. C !C The data read are: C !C A flag (to be used in vfsmod when RSE is used for simulation of pollutants C !C 2 XML files (input [eq's included here, and output [to check indexed]) C !C the reac tion set used (delclared in the XML input file C !C number, name and data for the mobile variables (used in the reactions) C !C number, name and data for the stabile variables (used in the reactions) C !C number, name and data for the parameters (used in the reactions) C !C Flag for reading 4 intrinsic parameters (depth, x_vel, time_step, area) C !C that can be used in the equations (XML input files) C !C Once data are read, values are passed to the hydrodynamic driving program C !cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

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192 cccc USE aRSEDIM USE SWIFTDIM, ONLY : NMAX,MMAX,LMAX,VARZINT IMPLICIT NONE INTEGER(kind=4) :: WQFLAG,M integer(kind=4) :: s,i,j,k,l,n PREPROCESS='IWQINPUT.iwq' !Moved this from CALLaRSE since moving READIWQ to being called from SETUP2 !Opens and read input file .iwq for RSE OPEN (UNIT=50, FILE=PREPROCESS) READ(50,*) WQFLAG, NMOB, NSTAB, NPAR, K_WET, ATM_NPAR IF(NMOB.NE.LMAX)PRINT *, 'NMAX not equal to NMOB' NVARS=NMOB+NSTAB NCOMPS=NMOB+NSTAB+27+NPAR CALL CELLCOUNT CALL SUB(NMAX,MMAX,NMOB,NSTAB,NCOMPS,NCELLS) !Read XML input file, XML outo ut file to check indexes, react set to be used in XML input file READ(50,*) XMLINPUT, XMLOUTPUT, XMLREAC_SET !Read mobile variables READ(50,*) (COMPNAME(i),C1_aRSE(i,1),i=1,NMOB) !Read stabile variables READ(50,*) (COMPNAME(j),C1_aRSE(j,1),j=(NMOB+1),(NMOB+NSTAB)) !Read stabile print flags READ(50,*) (NPRZ(s),s=1,NSTAB) !Equivalent to the NPRR in FTLOADDS, but for stabile components Output file always has userdefined variables first (j), then 27 intrinsic params + 1 j=NMOB+NSTAB n=NMOB+NSTAB k=j+27+1 j=k !Read parameter to be used (usually declared to be used in the set of equatiuons) READ(50,*) (COMPNAME(k),C1_aRSE(k,1),k=j,(j+NPAR 1)) Read intrincsic values of depth, x_vel_ol, time_step, area if m="1" READ(50,*)M IF(M.EQ.1) THEN READ(50,*) COMPNAME(n+2),C1_aRSE(n+2,1)& !depth !&,COMPNAME(n+16),C1_aRSE(n+16,1)& !x vel &,COMPNAME(n+20),C1_aRSE(n+20,1)& !time &,COMPNAME(n+1),C1_aRSE(n+1,1) !area ENDIF DTaRSE=C1_aRSE(n+20,1) !time step if not in .iwq CLOSE(50) IF(VARZINT.NE.99)THEN !Read in STABILE ICs as uniform DO L=1,NSTAB DO N=1,NMAX DO M=1,MMAX

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193 ZR(N,M,L)=C1_aRSE(NMOB+L,1) ENDDO ENDDO ENDDO ENDIF END Subroutine CALLaRSE SUBROUTINE CALLaRSE !cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc cccc !C This program emulates a hydrodynamic calling program for using the Reaction C !C Simulaiton Engine (RSE). The code structure of this program can be adapted C !C to othe r hydrodynamic calling programs. C !C This program reads a text file (.iwq) with the data needed to used C !C RSE. This .iwq file contains the name of the XML input file, the name of C !C the XML output file to check the indexes used, the name of the reaction set C !C to be used (declared in the XML input file), the number(s), name(s) and C !C value(s) for the mobile, stabile and parameters used in the equation(s) C !C declared in the XML input file. C !C Once data is read, call MyReactionModTest subroutine, which initiate and C !C runs RSE. C !C RSE is called at each time step. Init iallitation occurs in time step 1 C !cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc cccc USE aRSEDIM USE SWIFTDIM, ONLY : HALFDT,aRSE,CaRSE,NMAX,MMAX IMPLICIT NONE INTEGER(KIND=4) :: i,j,p,r,HA LFSTEP DATA HALFSTEP/0/ IF(INITIATE.EQ.0)THEN CALL FORT_CSTRING(XMLINPUT, XMLINPUTC) CALL FORT_CSTRING(XMLOUTPUT, XMLOUTPUTC) CALL FORT_CSTRING(XMLREAC_SET,XMLREAC_SETC) !IF (VARZINT.EQ.99) CALL READIC DO r=1,NCELLS DO p=1,NCOMPS C1_aRSE(p,r)=C1_aRSE(p,1)

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194 ENDDO ENDDO INITIATE=1 ENDIF DO 100 CALLNO=1,NCALLS IF (aRSE.EQ.2) THEN HALFSTEP=HALFSTEP+1 ELSEIF(aRSE.EQ.1) THEN HALFSTEP=HALFSTEP+2 !Initiated to zero, so +2 means always even, so always uses R ELSEIF(aRSE.EQ.3) THEN HALFSTEP=1 ELSE PRINT *, 'aRSE is neither 1, 2 or 3' PAU SE ENDIF Time step used by the controlling program IF (DTaRSE.GT.0) THEN DTFTLOADDS=DTaRSE ELSEIF (aRSE.EQ.1) THEN !time_step in RUNaRSE is DTFTLOADDS*60. If aRSE=0 then no aRSE called so the /aRSE should !not be a problem and acts as a check; if aRSE=1 then CaRSE is used to specify how many full !timesteps (HALFDT*2) to wait. DTFTLOADDS=CaRSE*HALFDT*2 ELSEIF (aRSE.EQ.2) THEN DTFTLOADDS=HALFDT*2/aRSE ELSEI F (aRSE.EQ.3) THEN !use TRT splitoperator DTFTLOADDS=HALFDT*2 ENDIF DO 10 CELLNO=1,NCELLS IF (CELLNO.EQ.1) THEN CALL aRSE_IN(HALFSTEP) !Halfstep needed to determine R or RP ENDIF CALL RUNaRSE IF (CELLNO.EQ.NCELLS) THEN CALL aRSE_OUT(HALFSTEP) !Halfstep needed to determine R or RP ENDIF 10 CONTINUE 100 CO NTINUE 101 FORMAT(500F8.4) END

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195 Subroutine aRSE_IN SUBROUTINE aRSE_IN(HALFSTEPIN) !******************************************************************** This subroutine moves the necessary values into C1_aRSE for RSE !******************************************************************** USE SWIFTDIM, ONLY: IROCOL,NOROWS,MSTART,MEND,SEP,SEMIN,U,UP,V,VP,RP,R,LMAX,ICLSTAT,ATMDEP USE aRSEDIM IMPLICIT NONE INTEGER CELLNUMI, NUMCELLSIRK, CELLNUM, IRK_aRSE, HALFSTE PIN INTEGER M,N,L,S REAL DEPTHMIN DATA DEPTHMIN/0.05/ !******************************************************************** CELLNUMI=0 IF(LMAX.NE.NMOB) THEN PRINT *,'LMAX (SWIFT2D) not equal to NMOB (aRSE)' PAUSE ENDIF !********************************************************************* !Read in mobile/transported variables from R (ustep) or RP (v step) !********************************************************************* IF(HALFSTEPIN/2*2.EQ.HALFSTEPIN) THEN !Even = v step, which uses RP to create R in DIFV, so use R DO IRK_aRSE=1,NOROWS N=IROCOL(1,IRK_aRSE) MSTART = IROCOL(2,IRK_aRSE) MEND = IROCOL(3,IRK_aRSE) DO M=MSTART,MEND CELLNUMI=CELLNUMI+1 !Mobile inputs DO L=1,LMAX C1_aRSE(L,CELLNUMI)=R(N,M,L) ENDDO !Stabile inputs IF(NSTAB.GT.0)THEN DO S=1,NSTAB IF ((S.EQ.NSTAB).AND.(K_WET.EQ.1)) THEN IF(ICLSTAT(N,M).EQ.0) THEN !Cell is wet: K_wet=1 C1_aRSE(LMAX+S,CELLNUMI)=1 ELSEIF (ICLSTAT(N,M).NE.0) THEN !Cell is dry: K_wet=0 C1_aRSE(LMAX+S,CELLNUMI)=0 ENDIF ELSE C1_aRSE(LMAX+S,CELLNUMI)=ZR(N,M,S) ENDIF

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196 ENDDO ENDIF !Hydro inputs IF(ICLSTAT(N,M).NE.0) THEN C1_aRSE(NVARS+2,CELLNUMI)=DEPTHMIN ELSE C1_aRSE(NVARS+2,CELLNUMI)=(SEP(N,M) SEMIN(N,M)) !depth ENDIF IF(ATM_NPAR.GT.0) C1_aRSE(NVARS+27+ATM_NPAR,CELLNUMI)=ATMDEP(2) !C1_aRSE(NVARS+14,CELLNUMI)=U(N,M) !uvel moved from UP to U after u step, not changed in vstep !C1_aRSE(NVARS+16,CELLNUMI)=VP(N,M) !Vvel updated to VP in SEPV earlier in vstep ENDDO ENDDO ELSE !Odd = u step, wh ich uses R to create RP (in DIFU) so use RP DO IRK_aRSE=1,NOROWS N=IROCOL(1,IRK_aRSE) MSTART = IROCOL(2,IRK_aRSE) MEND = IROCOL(3,IRK_aRSE) DO M=MSTART,MEND CELLNUMI=CELLNUMI+1 !Conc inputs DO L=1,LMAX C1_aRSE(L,CELLNUMI)=RP(N,M,L) ENDDO !Stab inputs IF(NSTAB.GT.0)THEN DO S=1,NSTAB IF ((S.EQ.NSTAB).AND.(K_WET.EQ.1)) THEN IF(ICLSTAT(N,M).EQ.0) THEN C1_aRSE(LMAX+S,CELLNUMI)=1 ELSEIF (ICLSTAT(N,M).NE.0) THEN C1_aRSE(LMAX+S,CELLNUMI)=0 ENDIF ELSE C1_aRSE(LMAX+S,CELLNUMI)=ZR(N,M,S) ENDIF ENDDO ENDIF !Hydro inputs IF(ICLSTAT(N,M).NE.0) THEN C1_aRSE(NVARS+2,CELLNUMI)=DEPTHMIN ELSE C1_aRSE(NVARS+2,CELLNUMI)=(SEP(N,M) SEMIN(N,M)) !depth ENDIF IF(ATM_NPAR.GT.0) C1_aRSE(NVARS+27+ATM_NPAR,CELLNUMI)=ATMDEP(2) !C1_aRSE(NVARS+14,CELLNUMI)=UP(N,M) !u vel updated to UP in SEPU earlier in ustep !C1_aRSE(NVARS+16,CELLNUMI)=V(N,M) !v vel moved from VP to V after previous vstep, not changed in ustep ENDDO ENDDO ENDIF

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197 RETURN END Subroutine aRSE_OUT SUBROUTINE aRSE_OUT(HALFSTEPOUT) !******************************************************************** This subroutine: moves the necessary values out of C1_aRSE for FTL !******************************************************************** USE SWIFTDIM, ONLY: IROCOL,NOROWS,MSTART,MEND,RP,R,LMAX USE aRSEDIM IMPLICIT NONE INTEGER CELLNUMO, NUMCELLSIRK, CELLNUM, IRK_aRSE, HALFSTEPOUT INTEGER M,N,L,S !******************************************************************** CELLNUMO=0 IF (LMAX.NE.NMOB) THEN PRINT *,'LMAX (SWIFT2D) not equal to NMOB (aRSE)' PAUSE ENDIF IF (HALFSTEPOUT/2*2.EQ.HALFSTEPOUT) THEN !even = v step, which uses RP to create R in DIFV so use R DO IRK_aRSE=1,NOROWS N=IROCOL(1,IRK_aRSE) MSTART = IROCOL(2,IRK_aRSE) MEND = IROCOL(3,IRK_aRSE) DO M=MSTART,MEND CELLNUMO=CEllNUMO+1 !Mobile outputs DO L=1,LMAX R(N,M,L)=C1_aRSE(L,CELLNUMO) ENDDO !Stabile outputs IF(NSTAB.GT.0)THEN DO S=1,NSTAB ZR(N,M,S)=C1_aRSE(LMAX+S,CELLNUMO) !Use ZR always because not transported so no ZRP ENDDO ENDIF ENDDO ENDDO ELSE !odd = ustep, which uses R to create RP in DIFU so use RP DO IRK_aRSE=1,NOROWS N=IROCOL(1,IRK_aRSE) MSTART = IROCOL(2,IRK_aRSE) MEND = IROCOL(3,IRK_aRSE) DO M=MSTART,MEND CELLNUMO=CEllNUMO+1

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198 !Mobile outputs DO L=1,LMAX RP(N,M,L)=C1_aRSE(L,CELLNUMO) ENDDO !Stab outputs IF(NSTAB.GT.0)THEN DO S=1,NSTAB ZR(N,M,S)=C1_aRSE(LMAX+S,CELLNUMO) !Use ZR always because not transported so no ZRP ENDDO ENDIF ENDDO ENDDO ENDIF RETURN END Subroutine RUNaRSE SUBROUTINE RUNaRSE USE IFPORT USE aRSEDIM IMPLICIT NONE Integer(kind=4) :: a,x Integer(kind=4) :: nvals Integer(kind=4) :: rk_order !Either 2 or 4 Real(kind=8) :: time_step Real(kind=8), Dimension(NCOMPST) :: vars CHARACTER (len=120) :: input_filename,input_filenam e1 CHARACTER (len=120) :: output_filename, output_filename1 CHARACTER (len=120) :: reaction_set, reaction_set1 integer*1 Dimension (50):: input_filename1A, output_filename1A, reaction_set1A !REMEMBER: change Interfaces to syntax suggested by Steve on IVF forum Interface to Subroutine Initialize ( input_xml, output_xml, rsname ) !DEC$ Attributes C, DLLIMPORT, alias: "_Initialize" :: Initialize integer*1, Dimension (50):: input_xml, output_xml, rsname !new inp ut files as arrays of chars instead of strings Character*(*) input_xml 'old string file name Character*(*) output_xml 'old string file name Character*(*) rsname !DEC$ Attributes REFERENCE :: input_xml !DEC$ Attributes REFERENCE :: output_xml !DEC$ Attributes REFERENCE :: rsname END Interface to Subroutine PreSolve ( num_var, vars ) !DEC$ Attributes C, DLLIMPORT, alias: "_PreSolve" :: PreSolve Integer (kind=4) :: num_var Real (kind=8), Dimension(num_var) :: vars

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199 End Interface to Subroutine PostSolve ( num_var, vars ) !DEC$ Attributes C, DLLIMPORT, alias: "_PostSolve" :: PostSolve Integer (kind=4) :: num_var Real (kind=8), Dimension(num_var) :: vars End Interface to Subroutine RKSolve ( time_step, rk_order, num_var, vars ) !DEC$ Attributes C, DLLIMPORT, alias: "_RKSolve" :: RKSolve Integer (kind=4) :: num_var Integer (kind=4) :: rk_order Real (kind=8) :: time_step Real (kind=8), Dimension(num_var) :: vars End Interface to Subroutine SetGlobalValues ( num_var, vars ) !DEC$ Attributes C, DLLIMPORT, alias: "_SetGlobalValues" :: SetGlobalValues Integer (kind=4) :: num_var Real (kind=8), Dimension(num_var) :: vars End nvals = NCOMPS rk_order = RKORDER time_step = DTFTLOADDS*60 Name of the input xml file (here, wq_input_file.xml) input_filename1A = XMLINPUTC Name of the component output file, only used to double check the inputs output_filename1A = XMLOUTPUTC Name of the reaction set to use set to the same as in the input xml file reaction_set1A = XMLREAC_SETC MUST initialize the passed in values to 0.0 New values of conc's are stored here @ vars IF(INITIATE.EQ.1)THEN DO a = 1, NCOMPS !NCOMPST vars(a) = 0.0 ENDDO INITIATE=2 ENDIF DO a = 1, NCOMPS vars(a) = C1_aRSE(a,CELLNO) ENDDO IF (INITIATE.EQ.2) THEN CALL Initialize( input_filename1A, output_filename1A, reaction_set1A ) INITIATE=3 ENDIF CALL PreSolve(nvals, vars) CALL RKSolve(time_step, rk_order, nvals, vars) !why nvals and not

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200 num_var? CALL PostSolve(nvals, vars) Nvals should be replaced with nvarX equivalent because only vars(1) and vars(2) are changed DO a = 1, NCOMPS IF (a.LE.NVARS) THEN IF (vars(a).LT.0) vars(a)=0.0 ENDIF C1_aRSE(a,CELLNO) = vars(a) ENDDO 20 FORMAT (I3, I3, E16.4, E16.4) RETURN END Subroutine CELLCOUNT SUBROUTINE CELLCOUNT !******************************************************************** This subroutine: counts the number of active cells !******************************************************************** USE SWIFTDIM USE aRSEDIM IMPLICIT NONE INTEGER NUMCELLS,NCELLSIRK,IRK_aRSE,COUNTCELLS,CELLSCOUNTED,COUNTOFF !******************************************************************** COUNTOFF = 0 IF(COUNTOFF.EQ.1) GOTO 10 DO IRK=1,NOROWS MSTART = IROCOL(2,IRK) MEND = IROCOL(3,IRK) NCELLSIRK = MEND MSTART + 1 NUMCELLS = NUMCELLS + NCELLSIRK ENDDO NCELLS=NUMCELLS 10 RETURN END

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201 Section B3 READIWQ Input File The nature of the XML interface, on which aRSE relies to obtain the names and values of the model components (i.e. state variables and parameters), is such that aRSE relies on the numeric order in which each component appears in order to correctly match name and value. Given that the number of user -defined stat e variables and parameters can change, so too then can the numeric reference and it is therefore necessary to run aRSE once in order to determine what the appropriate position is for the various components, unique to the given model setup. This is obvious ly undesirable for automated calling of aRSE (and is an artifact of the parent version TaRSE) because it requires that the user execute the model prior to using it. This input file's purpose is to avoid the necessity for calling aRSE prior to using it, an d is predicated on the fact that the number of intrinsic parameters in the model is constant (there are 27), that the state variables appear first in the input XML file, and that the user -defined parameters appears last. The appropriate numeric positions of all components can therefore be determined by knowing what and how many state variables there are, and what and how many user defined parameters there are. This information is entered in this .IWQ file, read by the model, and used accordingly. Table B -1. Explanation of the READIWQ input file structure and read in parameters Line number Variable Explanation 1 WQFLAG Flag for running water quality module (unused) NMOB Number of mobile statevariables specified in input XML NSTAB Number of stabile state variables specified in input XML NPAR Number of user specified parameters specified in input XML K_WET Flag to exchange wet/dry conditions. If used, this parameter must be specified as the final user input parameter (see code in aRSE_IN subroutin e) ATM_NPAR Flag to indicate atmospheric deposition, read in by FTLOADDS from ATMDEP.dat input file, must be passed to aRSE. If 0, then not, if > 0 then the input number must correspond with the position of the parameter in the list of user input parameters e.g. ATM_NPAR=2 indicates that the second nput parameter in the input XML is the atmospheric deposition rate parameter (the name must match that used in Line 6 of the .IWQ) 2 XMLINPUT Name of the XML input file XMLOUPUT Name of the XML output file (not used)

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202 Table B -1. Continued Line number Variable Explanation 2 XMLREAC_SET Name of the XML reaction set tag 3 VARNAME(i); C2(i) For i=1 to NMOB, each mobile statevariable name must be given (VARNAME) along with it's corresponding initial condition (C2) 4 VARNAME(j); C2(j) For j=NMOB to NMOB+NSTAB, each stabile statevariable name must be given (VARNAME) along with its corresponding initial condition (C2) 5 NPRZ(s) For s=1 to NSTAB, the printing interval must be given. Currently not used, but included for anologous control to that offered by NPRR for constituent printing in SWIFT2D 6 VARNAME(k); C2(k) For k=j+28 to j+28+NPAR, each user specified parameter name must be given (VARNAME) along with its corresponding constant value (C2) 7 MM Flag to specify whether intrinsic variables are read directly in from .IWQ file in Line 8. If MM=1 then values read in from Line 8 8 VARNAME(x); C2(x) The position (x) of the desired intrinsic variable in the list of intrinsiic parmaters must be known, an d its name (VARNAME) and value (C2) given if MM is 1 Section B4 Nash -Sutcliffe Calculation for Analytical Testing The following program and and subroutines were written for the purpose of calculating spatially distributed Nash-Sutcliffe efficiencies in the comparison of analytical and numerical solutions. Program STUPOSTPROCESS PROGRAM StuPOSTPROCESS !***************************************************************************! PROGRAM: StuPOSTPROCESS ! PURPOSE: To run stats on FTLOADDSaRSE results using CORSTAT. When called, the number of measurements in the time series to be used in the statistics (TOTALTIN), and the number of cells to be assessed by rows (NMAXIN) and columns (MMAXIN)

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203 !***************************************************************************! USE GLOBAL IMPLICIT NONE integer :: err, SURFERVID,TOTALTI,YES !Read in the number of measurements in the timeseries 55 CALL GETARG(1,ARGUMENT1) READ(ARGUMENT1, '(A6)' ) SURFERCASE CALL GETARG(2,ARGUMENT2) READ(ARGUMENT2, '(I5)' ) TOTALTF CALL GETARG(3,ARGUMENT3) READ(ARGUMENT3, '(I5)' ) NMAX CALL GETARG(4,ARGUMENT4) READ(ARGUMENT4, '(I5)' ) MMAX CALL GETARG(5,ARGUMENT5) READ(ARGUMENT5, '(I2)' ) SURFERVID 50 OPEN(300,FILE="C: \ Users\ Stuart Muller\ Documents\ Visual Studio 2008 \ Projects \ FTLOADDSaRSE_v2.8 \ FTLOADDS_Test_Case_v3\ FTLOADDS\ SurferCases.tx t",& STATUS= 'REPLACE' ) IF(SURFERVID.EQ.99) THEN GOTO 100 ELSE CALL SUB(NMAX,MMAX,TOTALTF) TOTALT=TOTALTF GOTO 200 ENDIF 100 DO TOTALT=2,TOTALTF CALL SUB(NMAX,MMAX,TOTALTF) 200 IF (TOTALT.LT.10) THEN TOTALTI=1 WRITE (SURFERSTRING1,'(I)' ) TOTALT ELSEIF(TOTALT.LT.100) THEN TOTALTI=2 WRITE (SURFERSTRING2,'(I)' ) TOTALT ELSEIF(TOTALT.GE.100) THEN TOTALTI=3 WRITE (SURFERSTRING3,'(I)' ) TOTALT ENDIF CALL POSTPROCESS IF (SURFERVID.NE.99) GOTO 300 DEALLOCATE(C1,C2)

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204 ENDDO 300 CONTINUE END PROGRAM StuPOSTPROCESS Subroutine POSTPROCESS SUBROUTINE POSTPROCESS USE GLOBAL !C*************************************************************************** ******** This subroutine combines the prepared results from FTLOADDSaRSE (LCONR1_AN.txt) and 3DADE (CXTFIT.OUTe) into CORSTAT.TXT for statistical processing !**************************************************************************** *******! IMPLICIT NONE CHARACTER *50 MODELFILE,MODFILE,ANALFILE,ANALYTFILE INTEGER t,i,j !!,TOTALT,NMAX,MMAX !Input files must be of the format INTEGER, REAL(OBS), REAL(SIM) !The integer is the code for a given time series of data (NCOD in CORSTAT), and increments up when a new series is encountered (this !is not used currently) MODELFILE='.. \ output\ LCONR1_AN.txt' OPEN(100,FILE=MODELFILE,STATUS='OLD' ) ANALYTFILE='.. \ output \ CXTFIT.OUTe' OPEN(101,FILE=ANALYTFILE,STATUS='OLD' ) DO t=1,TOTALT DO j=1,MMAX DO i=1,NMAX READ(100, '(F8.4)', END =1010) C1(i,j,t) !Read in model outputs READ(101, '(F8.4)', END =1010) C2(i,j,t) !Read in analytical model outputs ENDDO ENDDO ENDDO PRINT*, "Reads complete" !pause GOTO 1011 1010 PRINT*, "Specified timeseries exceeds either observed or simulated data input"

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2 05 1011 CONTINUE 1020 CONTINUE DO j=1,MMAX DO i= 1,NMAX CALL CORSTAT(i,j,TOTALT) ENDDO ENDDO 1008 FORMAT (I3,F8.4,1X,F8.4) PRINT*, 't:' ,t, 'm:',j, 'n:',i END Subroutine CORSTAT SUBROUTINE CORSTAT(NN,MM,TOTALI) !C************************************************************************ !C* WRITTEN FOR: Paper on VFSMOD development and testing (J.of Hyd) !C* Last Updated:June 29, 1998. !C* CORSTAT, 5/20/87, VER. 0.1, J.E. PARSONS !C* REVISED: 5/11/93, VER, 0.3, R. MUNOZCARPENA !C* UPDATED: 06/04/02, VER, 0.7, R. MUNOZCARPENA !C* e mail: carpena@ufl.edu !C* ADAPTED: 2/7/10 S. MULLER (!SJM) for FTLOADDSaRSE !C* CREDITS: (c) 1986 92 Numerical Recipes Software iPJ5.1:#>0K!. !C* USES:(c)Numerical recipes: tptest, avevar, betai,gammaln, betacf !ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc !C* CORSTAT, 5/20/87, VER. 0.1, J.E. PARSONS !C* REVISED: 5/11/93, VER, 0.3, R. MUNOZCARPENA !C* LAST UPDATED: 29/6/98, VER, 0.5, R. MUNOZ CARPENA !C* THIS PROGRAM COMPUTES A NUMBER OF STATISTICS FOR THE !C* COMPARISON OF TWO TIME SERIES, FOR EXAMPLE, AN OBSERVED AND A !C* SIMULATED ONE. THE STATISTICS ARE: !C* 1) MEAN ERROR !C* 2) STANDARD DEVIATION !C* 3) SERIAL CORELATION COEF. !C* 4) COEFICIENT OF PERFORMANCE !C* 5) COEFICIENT OF PERFORMANCE CORRECTED FOR VARIATION OF THE !C* OF THE RECORDED PROCESS !C* 6) PEARSON MOMENT AND THE WEIGHTED MOMENT !C* RMC7) Correlation coefficient for the 1:1 line !C* RMC8) Paired ttest to check for differences in series means !C* (from Numerical Recipes) !C* !C* These are computed for the absolute value of the error and the !C* error. !C* These measures are defined and discussed in: !C* !C* 1. Aitken, A.P. 1973. Assesing systematic errors in rainfallrunoff

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206 !C* models. J. of Hydrology. 20:121136. !C* 2. James, L.D. and S.J. Burges. 1982. Selection, calibration, and !C* testing of hydrologic models by. In Hydrologic Modeling of Small !C* Watersheds, Chapter 11, ed. C. T. Haan, H. P. Johnson and D. L. !C* Brakensiek. pages 435472. ASAE m onograph no. 5. St. Joseph. !C* 3. McCuen, R.H. and W.M. Snyder. 1975. A proposed index for !C* comparing hydrographs. Water Resour. Res. (AGU).11(6):1021 1024. !C* 4. Press et al., 1992. Numerical Recipes in Fortran. 2nd, edition. !C* Cambridge: Cambridge University Press !C* !C* Definition of variables !C************************************************************************ USE GLOBAL, ONLY : C1,C2,SURFERSTRING1,SURFERSTRING2,SURFERSTRING3,TOTALT,SURFERCASE IMPLICIT DOUBLE PRECISION (A H,O Z) character*16 dummyf1 CHARACTER*6 VARBLE CHARACTER*50 FLABEL PARAMETER(NPTS=500) REAL prob1,t1,data1(NPTS),data2(NPTS) DIMENSION NCOD(5000),OBS(5000),SIM(5000),AERR(5000),& ERR(5000),NCD(101),NTC(101), SUM (4),SUMSQ(4),CSS(4),DAERR(1000),& DREC(1000),VAR(4) INTEGER MM,NN,TOTALI,FILELABELS,ALLOCATEARRAY DATA FILELABELS/0/ DATA ALLOCATEARRAY/0/ OPEN (UNIT=10,FILE= 'NUL') IDIAG=0 I=1 INC=0 KC=0 NC=0 mycount=0 !SJM: Removing FLABEL read because CORSTATIN.txt not being written with headers !READ(8,*)FLABEL !10 READ(8,*,END=20)NCOD(I),OBS(I),SIM(I) !SJM: Instead of a READ now transferring data between arrays. Note, still jumps to 20 !when OBS and SIM are filled DO I=1,TOTALI NCOD(I)=1 !!OBS(I)=OBSC1(NN,MM,I) OBS(I)=C1(NN,MM,I) !!SIM(I)=SIMC2(NN,MM,I) SIM(I)=C2(NN,MM,I) !c-Debug ---!c print*,ncod(i),obs(i),sim(i) !c-End Debug ---ERR(I)=SIM(I) OBS(I) AERR(I)=DABS(ERR(I))

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207 !C*** COUNT THE DIFFERENT CODES IF (NC.EQ.NCOD(I)) THEN INC=INC+1 NTC(KC)=INC ELSE KC=KC+1 NC=NCOD(I) NCD(KC)=NC INC=1 ENDIF !SJM: Deleted because DO loop automatically updates I I=I+1 ENDDO 20 CONTINUE !C** ZERO OUT THE STATISTICS ARRAYS NOBS=I IST=1 DO 25 K=1,KC DO 24 J=1,4 SUM (J)=0.D0 SUMSQ(J)=0.D0 24 CONTINUE CROSS=0.D0 cosse=0.d0 NOBK=NTC(K)+IST 1 !!!!!!!!!!!!!GRRR KOUNT=0 DO 30 I=IST,NOBK KOUNT=KOUNT+1 DAERR(KOUNT)=AERR(I) DREC(KOUNT)=OBS(I) SUM (1)= SUM (1)+ERR(I) SUM (2)= SUM (2)+AERR(I) SUM (3)= SUM (3)+OBS(I) SUM (4)= SUM (4)+SIM(I) SUMSQ(1)=SUMSQ(1)+ERR(I)*ERR(I) SUMSQ(2)=SUMSQ(2)+AERR(I)*AERR(I) SUMSQ(3)=SUMSQ(3)+OBS(I)*OBS(I) SUMSQ(4)=SUMSQ(4)+SIM(I)*SIM(I) CROSS=CROSS+OBS(I)*SIM(I) cosse=cosse+(obs(i) sim(i))*(obs(i)sim(i)) data1(KOUNT)=OBS(I) data2(KOUNT)=SIM(I) 30 CO NTINUE mycount=mycount+1 XPOINT=DFLOAT(NTC(K)) ERMEAN=SUM (1)/XPOINT AEMEAN=SUM (2)/XPOINT OBMEAN=SUM (3)/XPOINT SIMEAN=SUM (4)/XPOINT !C*** DO RESIDUAL MASS CURVES FOR ACCUMMULATED ERRORS CPAT=0 CPBT=0 CPCT=0 SECOR=0.D0 SAECOR=0.D0 DO 37 I=IST,NOBK IF (I.GT.IST) THEN

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208 SECOR=SECOR+(ERR(I)ERMEAN)*(ERR(I1) ERMEAN) SAECOR=SAECOR+(AERR(I)AEMEAN)*(AERR(I1)AEMEAN) ENDIF ERS=0.D0 ERD=0.D0 ERD2=0.D0 DO 36 II=IST,I ERS=ERS+ERR(II) ERD=ERD+OBS(II) ERD2=ERD2+(OBS(II)OBMEAN) 36 CONTINUE XJP= DFLOAT (IIST+1) XJP2=XJP*XJP CPAT=CPAT+ERS*ERS/XJP2 CPBT=CPBT+(ERS/ERD)*(ERS/ERD)/XJP2 !c CPCT=CPCT+(ERS/ERD2)*(ERS/ERD2)/XJP2 37 CONTINUE !C CPAT=CPAT/XPOINT !C CPBT=CPBT/XPOINT !C CPCT=CPCT/XPOINT IST=NOBK+1 IF (IDIAG.EQ.1) THEN WRITE (10,90)XPOINT,K,NCD(K) 90 FORMAT(/,/,/,10X,'***** DIAGNOSTICS PRIOR TO CALCULATIONS FOR:',& /,20X,'NPOINTS=' ,I6,' SERIES NO.=' ,I4,' SERIES CODE=' ,I5,& /,10X,'SUM OF DATA' ,10X,'SUM OF SQUARES' ) DO 91 KK=1,4 WRITE(10,89) SUM (KK),SUMSQ(KK) 89 FORMAT (5X,F15.5,9X,F15.5) 91 CONTINUE WRITE (10,88)CROSS 88 FORMAT(/,10X, 'CROSS PRODUCT SUM (REC*SIM)=' ,F15.5,/,/) ENDIF CSS(1)=SUMSQ(1)2*ERMEAN*SUM (1)+XPOINT*ERMEAN*ERMEAN CSS(2)=SUMSQ(2)2*AEMEAN*SUM (2)+XPOINT*AEMEAN*AEMEAN CSS(3)=SUMSQ(3)2*OBMEAN*SUM (3)+XPOINT*OBMEAN*OBMEAN CSS(4)=SUMSQ(4)2*SIMEAN*SUM (4)+XPOINT*SIMEAN*SIMEAN VAR(1)=CSS(1)/XPOINT VAR(2)=CSS(2)/XPOINT VAR(3)=CSS(3)/XPOINT VAR(4)=CSS(4)/XPOINT XP1=(XPOINT 1.D0) SEM=CSS(1)/(XP1) AEM=SUM (2)/XPOINT !c RMSE=DSQRT(CSS(1)/XPOINT) !c----change based on Marlon's comments (07/06/93)---------RMSE=DSQRT (SUMSQ(1)/XPOINT) ERSTD= DSQRT(CSS(1)/(XP1)) AESTD= DSQRT(CSS(2)/(XP1)) OBSTD= DSQRT(CSS(3)/(XP1)) SISTD= DSQRT(CSS(4)/(XP1)) SECOR=SECOR/(ERSTD*ERSTD*(XP1)) SAECOR=SAECOR/(AESTD*AESTD*(XP1)) !c rmc 06/02 --!c RPEARM=(CROSS OBMEAN*SUM(4)SIMEAN*SUM(3) !c + XPOINT*OBMEAN*SIMEAN)/(OBSTD*SISTD*XPOINT) RPEARM=(XPOINT*CROSSSUM (4)*SUM (3))/ SQRT((XPOINT*SUMSQ(3) SUM (3)*&

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209 SUM (3))*(XPOINT*SUMSQ(4)SUM (4)* SUM (4))) R2PEAR=RPEARM*RPEARM W=SISTD/OBSTD IF (W.GT.1.D0) THEN WGHTRP=RPEARM/W ELSE WGHTRP=RPEARM*W ENDIF CPAP=1.D0 SUMSQ(1)/CSS(3) SLPNI=CROSS/SUMSQ(3) SLPI=(CROSSSUM (3)*SUM (4)/XPOINT)/(SUMSQ(3)SUM (3)* SUM (3)/XPOINT) YINT=SIMEANSLPI*OBMEAN CORI=SLPI*OBSTD/SISTD !C*** EJS --R SQUARED TO MATCH SAS SSINT= SUM (4)*SUM (4)/XPOINT EJDEN1=SUMSQ(3) SUM (3)*SUM (3)/XPOINT EJDEN2=SUMSQ(4) SUM (4)*SUM (4)/XPOINT EJSNUM=(CROSSSUM (3)* SUM (4)/XPOINT) SSB1B0=SLPI*EJSNUM RESID=SUMSQ(4)SSINTSSB1B0 EMSRES=RESID/(XPOINT2.D0) STESLP=DSQRT (EMSRES/EJDEN1) STEINT=DSQRT (EMSRES*SUMSQ(3)/(XPOINT*EJDEN1)) !C*** COMPUTATIONS FOR NO INT ? SSB1=SLPNI*EJSNUM RESNI=SUMSQ(4)SSB1 EMSRNI=RESNI/(XPOINT1.D0) SESLPN=DSQRT (EMSRNI/EJDEN1) CD=SSB1/EJDEN2 CALL GMEDN(KOUNT,DAERR,DREC,OBMEAN,R29) R21TOP=SUMSQ(3) 2.D0*CROSS+SUMSQ(4) R21=1.D0 R21TOP/CSS(3) R22TOP=SUMSQ(4) 2.D0* SUM (4)*OBMEAN+ XPOINT*OBMEAN*OBMEAN R22=R22TOP/CSS(3) R23=CSS(4)/CSS(3) R24=1.D0 CSS(1)/CSS(3) R27=1.D0 R21TOP/SUMSQ(3) !c print*,obstd,covaryyc R28=SUMSQ(4)/SUMSQ(3) WRITE (10,100)NCD(K),XPOINT 100 FORMAT(/,10X,& 'SUMMARY STATISTICS FOR COMPARING TWO SERIES OF OBSERVED vs.',& PREDICTED VALUES',/,10X, 'SERIES CODE =' ,I4,10X,& 'NUMBER OF SERIES POINTS=' ,F6.0,/) WRITE (10,*) VARIABLE SUM MEAN SUMSQ& CORR. SS SAMP.STD. VARIANCE COEF. OF VAR.' WRITE (10,*) VARBLE='ERROR' CV=ERSTD/ERMEAN WRITE(10,102)VARBLE,SUM (1),ERMEAN,SUMSQ(1),CSS(1),ERSTD,VAR(1),CV VARBLE= 'AERROR' CV=AESTD/AEMEAN WRITE(10,102)VARBLE,SUM (2),AEMEAN,SUMSQ(2),CSS(2),AESTD,VAR(2),CV VARBLE='OBSED' CV=OBSTD/OBMEAN WRITE(10,102)VARBLE,SUM (3),OBMEAN,SUMSQ(3),CSS(3),OBSTD,VAR(3),CV

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210 VARBLE='SIMED' CV=SISTD/SIMEAN WRITE(10,102)VARBLE,SUM (4),SIMEAN,SUMSQ(4),CSS(4),SISTD,VAR(4),CV !c 102 FORMAT(5X,A6,5X,E12.3,5X,e11.4,5X,e15.4,5X,e11.4,5X,e10.5, !c 5X,e10.5,5X,e11.4) 102 FORMAT(5X,A6,E14.4,e14.4,e14.4,e14.4,e14.4,e14.4,e14.4) WRITE(10,103)RPEARM,WGHTRP,R2PEAR,R21,R22,R23,R24,R27,R28,R29 WRITE (10,105)RMSE,AEM,SEM 103 FORMAT(/,/,5X, '***** CORREL. COMPARISONS ******',& /,15X,'PEARSON MOMENT =',F10.5,' (FIRST TWO CORREL. TYPES)' ,& /,15X,'WGHTED PEAR. MOM. =',F10.5,' (EQN 11.13)',& /,15X,'PEAR. MOM. SQUAR. =',F10.5,' (KVALSETH R25, R26 MULT. R)',& (NOTE: FROM HERE DOWN R SQUARED TYPES)',& /,15X,'KVALSETH R21 =',F10.5,' (0<=R21<=1, GENERALLY)' ,& (1 RA TIO OF SUM (OBS SIM)**2/ CSSOBS)' ,& /,15X,'KVALSETH R22 =',F10.5,' (MAY EXCEED 1)',& ( RATIO OF SUM (SIM OBMEAN)**2/ CSSOBS)' ,& /,15X,'KVALSETH R23 =',F10.5,' (MAY EXCEED 1)',& ( RATIO OF CSSSIM/ CSS OBS)' ,& /,15X,'KVALSETH R24 =',F10.5,' (0<=R24<=1, GENERALLY)' ,& (1 RATIO OF CSSERR/ CSS OBS)' ,& /,15X,'KVALSETH R27 =',F10.5,' (RECOMMEND LINEAR NOINT.)' ,& (1 RATIO OF SUM ERR**2/ SUM OBS**2)',& /,15X,'KVALSETH R28 =',F10.5,' (RECOMMEND LIN. NOINT.)',& ( R28 MAY EXCEED 1, RATIO OF SUM SIM**2/ SUM OBS**2)' ,& /,15X,'KVALSETH R29 =',F10.5,' (RESISTANT OR ROBUST FIT)' ) 105 FORMAT(15X, 'ROOT MEAN SQ. ERR.=' ,E14.5,' [(OBS SIM)**2/N)**.5]',& /,15X,'MEAN ABS. ERROR =',E14.5,& /,15X,'MEAN SQ. ERROR =',E14.5,' (ASS. ONE MODEL PARAMETER)',& [(OBSSIM)**2/(N 1)]') WRITE(10,104)CPAP,SECOR,SAECOR 104 FORMAT(15X, 'COEF. OF EFF. (NASH AND SUTCLIFF) =',F15.5,& (RATIO SSERR/ CSS OBS)' ,/,& 15X,'SERIAL CORR. (ERROR) =' ,F10.5,5X,'LAG 1',& /,15X,'SERIAL CORR. (ABS. ERROR)=',F10.5,5X, 'LAG 1') !SJM: Write results for graphing in Surfer !@!IF(SURFERVID.EQ.99) THEN !Calculating stats at multiple time to make a video IF (TOTALT.LT.10) THEN OPEN (1100+TOTALT,FILE= 'Surfer'//SURFERCASE//'_T'//SURFERSTRING1// '.dat' ) ELSEIF(TOTALT.LT.100) THEN OPEN (1100+TOTALT,FILE= 'Surfer'//SURFERCASE//'_T'//SURFERSTRING2// '.dat' ) ELSEIF(TOTALT.GE.100) THEN OPEN (1100+TOTALT,FILE= 'Surfer'//SURFERCASE//'_T'//SURFERSTRING3// '.dat' ) ENDIF !Print one line of headers IF (FILELABELS.EQ.0) THEN WRITE(1100+TOTALT, '(2A5,4A12)' ) "X" "Y" "RMSE", "AEM" "SEM", "CPAP(NS)" FILELABELS=1 ENDIF

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211 IF (CPAP.NE.CPAP) CPAP=10 WRITE (1100+TOTALT,'(2I5,4F12.8)') MM,NN,RMSE,AEM,SEM,CPAP IF(CPAP.NE.CPAP) CPAP=10 WRITE (1100,'(2I5,4F10.4)' ) MM,NN,RMSE,AEM,SEM,CPAP WRITE(10,106)CPAT,CPBT !c ,CPCT 106 FORMAT(/,/,5X, '****** RESIDUAL MASS CURVES (ACCUMULATED ERRORS)',& DIVIDED BY NPOINTS, SIMILAR TO A VARIANCE',& /,15X,'CPAT -EQN 11.31 =',G13.6,& /,15X,'CPBT -EQN 11.32 =',G13.6,/) !c /,15X,'CPCT -EQN 11.33 =',G13.6,/) CORI2=CORI*CORI WRITE(10,109)SLPNI,CD,SESLPN,SLPI,YINT,CORI,CORI2,STESLP,STEINT 109 FORMAT(/,/,5X, '****** REGRESSION ANALYSIS SIM VS OBS *******',& /,10X,'NO INTERCEPT MODEL, SLOPE =' ,F10.5,' JPRRSQ?=',F10.5,& JPSTD. ERR. SLP.?=' ,F10.5,& /,10X,'INTERCEPT MODEL, SLOPE =' ,F10.5,' INTERCEPT=',F10.5,& CORRELATION COEF.=',F8.5,' CORR**2=',F8.5,& /,25X,'STD. ERR. SLOPE =',F10.5, STD. ERR. INT. =',F10.5) !c-rmc ----04/93 --Error over the 1:1 line, observed vs. predicted --------WRITE(10,*) WRITE(10,*) WRITE(10,*)' ****** ERROR MEASURE FROM THE 1:1 LINE ********' !c -rmc and arr 06/02 --R2= 1 RSSmodel/RSSnull model, where RSS=res. sum sq. !c -null model= line y=cte=ymean=obs_mean; model = 1:1 line = y=x > p red=obs !c -old -covaryyc=dsqrt(cosse/(xpoint2.d0)) covaryyc= dsqrt(cosse/(xpoint1.d0)) rsq1to1=(1.d0(covaryyc*covaryyc)/(obstd*obstd)) if(rsq1to1.lt.0)rsq1to1=0 r1to1= dsqrt(rsq1to1) if(rsq1to1.gt.0) then WRITE(10,113)covaryyc,r1to1,rsq1to1 else WRITE(10,114)covaryyc endif 113 format(10x, '1:1 COVARIANCE OBSERVED vs. PREDICTED = ,E14.4,& /,10X,'1:1 SAMPLE COEFFICIENT OF DETERMINATION (R1:1) = ,f10.4,& /,10x,'1:1 SAMPLE CORRELATION COEFFICIENT (RSQ1:1) = ,f10.4) 114 format(10x, '1:1 COVARIANCE OBSERVED vs. PREDICTED = ,E14.4,& /,10X,'1:1 SAMPLE COEFFICIENT OF DETERMINATION (R1:1) < 0.01',& /,10x,'1:1 SAMPLE CORRELATION COEFFICIENT (RSQ1:1) < 0.01' ) !C-------------------------------------------------------------------!c-rmc ----06/98 --Paired ttest --------WRITE(10,*) WRITE(10,*) WRITE(10,*)' ****** PAIRED t TEST ********' call tptest(data1,data2,KOUNT,t1,prob1) if(prob1.ge..05) then WRITE(10,120)NCD(K),KOUNT,t1,prob1

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212 else WRITE(10,121)NCD(K),KOUNT,t1,prob1 endif t1=0. prob1=0. 120 format (10x,'No. Series= ',i4,'; n= ',i4,'; t= ,f10.6,& '; Prob= ',f10.4, Means not significantly different' ) 121 format (10x,'No. Series= ',i4,'; n= ',i4,'; t= ,f10.6,& '; Prob= ',f10.4, Means significantly different' ) WRITE(10,111) 111 FORMAT(/,125(' )) WRITE(10,112) 112 FORMAT( '1' ) 25 CONTINUE CLOSE(8) RETURN END SUBROUTINE GMEDN(N,ER,REC,RECM,R29) !C**** COMPUTATION OF MEDIANS FOR R29 FROM KVALSETH IMPLICIT REAL*8 (AH,O Z) DIMENSION ER(*),REC(*),TER(1000),DREC(1000) DO 5 I=1,N TER(I)=ER(I) DREC(I)=DABS(REC(I) RECM) 5 CONTINUE DO 10 I=1,N DO 9 J=I+1,N IF (TER(J).LT.TER(I)) THEN TEM=TER(I) TER(I)=TER(J) TER(J)=TEM ENDIF IF (DREC(J).LT.DREC(I)) THEN TEM=DREC(I) DREC(I)=DREC(J) DREC(J)=TEM ENDIF 9 CONTINUE 10 CONTINUE IMED=N/2 DRM=DREC(IMED) ERM=TER(IMED) RAT=ERM/DRM R29=1.D0RAT*RAT RETURN END SUBROUTINE tptest(data1,data2,n,t,prob) INTEGER n REAL prob,t,data1(n),data2(n) !CU USES avevar,betai INTEGER j REAL ave1,ave2,cov,df,sd,var1,var2,betai !c-rmc !c write(*,*)n,t,prob

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213 !c do 5 i=1,n !c WRITE(*,*)data1(i),data2(i) !c5 continue !c-rmc call avevar(data1,n,ave1,var1) call avevar(data2,n,ave2,var2) cov=0. do 11 j=1,n cov=cov+(data1(j) ave1)*(data2(j)ave2) 11 continue df=n1 cov=cov/df sd= sqrt((var1+var2 2.*cov)/n) t=(ave1ave2)/sd prob=betai(0.5*df,0.5,df/(df+t**2)) return END !C (C) Copr. 198692 Numerical Recipes Software iPJ 5.1:#>0K!. SUBROUTINE avevar( data,n,ave,var) INTEGER n REAL ave,var,data(n) INTEGER j REAL s,ep ave=0.0 do 11 j=1,n ave=ave+ data(j) 11 continue ave=ave/n var=0.0 ep=0.0 do 12 j=1,n s= data(j) ave ep=ep+s var=var+s*s 12 continue var=(varep**2/n)/(n1) return END !C (C) Copr. 198692 Numerical Recipes Software iPJ 5.1:#>0K!. FUNCTION betacf(a,b,x) INTEGER MAXIT REAL betacf,a,b,x,EPS,FPMIN PARAMETER (MAXIT=100,EPS=3.e7,FPMIN=1.e30) INTEGER m,m2 REAL aa,c,d,del,h,qab,qam,qap qab=a+b qap=a+1. qam=a1. c=1. d=1.qab*x/qap if( abs (d).lt.FPMIN)d=FPMIN d=1./d h=d do 11 m=1,MAXIT m2=2*m aa=m*(bm)*x/((qam+m2)*(a+m2)) d=1.+aa*d

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214 if ( abs (d).lt.FPMIN)d=FPMIN c=1.+aa/c if ( abs (c).lt.FPMIN)c=FPMIN d=1./d h=h*d*c aa= (a+m)*(qab+m)*x/((a+m2)*(qap+m2)) d=1.+aa*d if ( abs (d).lt.FPMIN)d=FPMIN c=1.+aa/c if ( abs (c).lt.FPMIN)c=FPMIN d=1./d del=d*c h=h*del if ( abs (del1.).lt.EPS)goto 1 11 continue 1 betacf=h return END !C (C) Copr. 198692 Numerical Recipes Software iPJ 5.1:#>0K!. FUNCTION betai(a,b,x) REAL betai,a,b,x !CU USES betacf,gammln REAL bt,betacf,gammln if(x.lt.0..or.x.gt.1.)pause 'bad argument x in betai' if(x.eq.0..or.x.eq.1.)then bt=0. else bt= exp (gammln(a+b)gammln(a)gammln(b)+a* log (x)+b* log (1.x)) endif if(x.lt.(a+1.)/(a+b+2.)) then betai=bt*betacf(a,b,x)/a return else betai=1. bt*betacf(b,a,1.x)/b return endif END !C (C) Copr. 198692 Numerical Recipes Software iPJ 5.1:#>0K!. FUNCTION gammln(xx) REAL gammln,xx INTEGER j DOUBLE PRECISION ser,stp,tmp,x,y,cof(6) SAVE cof,stp DATA cof,stp/76.18009172947146d0, 86.50532032941677d0,& 24.01409824083091d0,1.231739572450155d0,.1208650973866179d2,& .5395239384953d5,2.5066282746310005d0/ x=xx y=x tmp=x+5.5d0 tmp=(x+0.5d0)*log (tmp) tmp ser=1.000000000190015d0 do 11 j=1,6 y=y+1.d0 ser=ser+cof(j)/y 11 continue gammln=tmp+log (stp*ser/x)

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215 return END !C (C) Copr. 198692 Numerical Recipes Software iPJ 5.1:#>0K!.

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216 APPENDIX C WATER -QUALITY APPLICATION CODE AND INPUT FILES Section C1 Additional Subroutines for Water Quality Inputs The following two subroutines were required for input of water -quality boundary conditions. The subroutine EDIT_INPUTFILE is used to edit time -series concentrations at specified head boundaries in the Part 3 of the SWIFT2D input file. The subroutine STRU NCTCONCS reads in discharge source concentrations from the INPUTFLOWCONCS.dat input file (see Section C2). Subroutine EDIT_INPUTFILE PROGRAM Edit_inputfile IMPLICIT NONE INTEGER X,COUNT1,COUNT2,i,j,NTCT1,LENGTH,DAY,DAYCHK,P3_READ,DAYMAX REAL TITI CHARACTER THE_REST*60,TEMP*1050,THE_REST_19*19 CHARACTER *7 BC1(500),BC2(500),BC3(500),BC4(500) DATA X,COUNT1,COUNT2,P3_READ,DAYMAX/0,0,0,0,0/ OPEN(10,FILE='wetlands_PBC_SICS.inp' ) !original .inp OPEN(20,FILE='wetlands.inp' ) !.inp produced by this code OPEN(30,FILE='BC_concs.inp' ) !source for BC concs j=0 DO WHILE (X.EQ.0) j=j+1 READ(30,*,END =100) DAYCHK,BC1(j),BC2(j),BC3(j),BC4(j) WRITE (40,'(I4,1X,A8,1X,A8,1X,A8,1X,A8,1X)') DAYCHK,BC1(j),BC2(j),BC3(j),BC4(j) ENDDO 100 CONTINUE !******************************! Write PART 1 and PART 2 data !******************************! DO i=1,1158 !1133 !Look at the .inp file to see what the row number is up to Part 3 data IF (i.GE.806.AND.i.LE.903) THEN READ (10,'(A1050)') TEMP ELSE READ (10,'(A100)' ) TEMP

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217 ENDIF LENGTH=LEN_TRIM(TEMP) WRITE (20,'(A)') TEMP ENDDO PAUSE !READ(10,'(A100)') TEMP !PRINT*, TEMP !PAUSE DO WHILE (X.EQ.0) READ(10, '(I1,A39)') NTCT1,THE_REST LENGTH=LEN_TRIM(THE_REST) IF (NTCT1.EQ.0) P3_READ=P3_READ+1 DAY=P3_READ/96+1 IF (DAY.GE.499) DAYMAX=1 !498 days of BC input data after day 498 completed then just copy and repeat remaining lines. IF (DAYMAX.EQ.1) GOTO 110 IF (NTCT1.EQ.0) THEN WRITE (20,'(I1,A)' ) NTCT1,THE_REST ELSEIF(NTCT1.EQ.1) THEN THE_REST_19=THE_REST COUNT1=COUNT1+1 IF (COUNT1.LE.4) THEN IF(COUNT1.EQ.1) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC1(DAY) IF(COUNT1.EQ.2) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC2(DAY) IF(COUNT1.EQ.3) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC3(DAY) IF(COUNT1.EQ.4) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC4(DAY) ELSEIF(COUNT1.LE.8) THEN WRITE(20, '(I1,A19,A8)') NTCT1,THE_REST, 0.005' IF(COUNT1.EQ.8)COUNT1=0 ENDIF ELSEIF(NTCT1.EQ.2) THEN THE_REST_19=THE_REST COUNT2=COUNT2+1 IF (COUNT2.LE.4) THEN IF(COUNT2.EQ.1) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC1(DAY) IF(COUNT2.EQ.2) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC2(DAY) IF(COUNT2.EQ.3) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC3(DAY) IF(COUNT2.EQ.4) WRITE (20,'(I1,A19,1X,A7)') NTCT1,THE_REST_19,BC4(DAY) ELSEIF(COUNT2.LE.8) THEN WRITE(20, '(I1,A19,A8)') NTCT1,THE_REST, 0.005' IF(COUNT2.EQ.8)COUNT2=0 ENDIF ELSEIF(NTCT1.GT.2) THEN WRITE (20,'(I1,A)' ) NTCT1,THE_REST ENDIF 110 IF (DAYMAX.EQ.1) THEN IF (NTCT1.EQ.0) WRITE (20,'(I1,A)' ) NTCT1,THE_REST IF ((NTCT1.EQ.1).OR.(NTCT1.EQ.2)) WRITE (20,'(I1,A)')

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218 NTCT1,THE_REST IF (NTCT1.GT.2) WRITE (20,'(I1,A)' ) NTCT1,THE_REST ENDIF ENDDO END PROGRAM Edit_inputfile Subroutine STRUCTCONCS SUBROUTINE STRUCTCONCS USE SWIFTDIM USE COUPLING REAL*4 DAY !STRCFLOWCONC(40),STRCFLOWCONC2(40) moved to SWIFTDIM REAL*8 DAYCHK DATA IFIRST/1/,IUSFLOWCONCS/175/ IF (IFIRST .EQ. 1)THEN OPEN(IUSFLOWCONCS,FILE= '.. \ Input \ FLOWS \ INPUTFLOWCONCS.DAT', 1 STATUS='OLD' ,ACCESS='SEQUENTIAL') READ(IUSFLOWCONCS,*) NUMSTRUCS NUMSTRUCS=NUMSTRUCS+1 DO J=2,NUMSTRUCS READ(IUSFLOWCONCS,*) NFLWPTS(J),NRANGES(J) DO I=1,NFLWPTS(J)+2*NRANGES(J) READ (IUSFLOWCONCS,*) MSTRUC(J,I),NSTRUC(J,I),IXYFLOW(J,I) ENDDO NTOTPTS(J)=NFLWPTS(J) IF(NRANGES(J).GT.0) THEN DO I=NFLWPTS(J)+1,NFLWPTS(J)+2*NRANGES(J)1,2 IP1=I+1 MSTRUC(J,IP1)=MSTRUC(J,IP1)MSTRUC(J,I) NSTRUC(J,IP1)=NSTRUC(J,IP1)NSTRUC(J,I) IF ( ABS (MSTRUC(J,IP1)).G T.ABS (NSTRUC(J,IP1)))NSTRUC(J,IP1)=0 IF ( ABS (NSTRUC(J,IP1)).GT. ABS (MSTRUC(J,IP1)))MSTRUC(J,IP1)=0 MAXMN=MAX ( ABS (MSTRUC(J,IP1)), ABS (NSTRUC(J,IP1)))+1 NTOTPTS(J)=NTOTPTS(J)+MAXMN ENDDO ENDIF ENDDO !If more than one solute (excl salinity and temp) then need to have one line in inputfile for each L !for each day, !e.g. Line1: Day1 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3) Line2: Day1 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3) Line3: Day2 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3) Line4: Day2 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3) DO L=1,LMAX IF(L.EQ.LSAL)GOTO 115 !Skip salinity and temp so don't have to add these to input f ile IF(L.EQ.LTEMP)GOTO 115 READ(IUSFLOWCONCS,*)(STRCFLOWCONC(L,J), J=1,NUMSTRUCS) !Assumes 1 solute 115 CONTINUE ENDDO DO L=1,LMAX IF(L.EQ.LSAL)GOTO 116 !Skip salinity and temp so don't have to add

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219 these to input file IF(L.EQ.LTEMP)GOTO 116 READ(IUSFLOWCONCS,*)(STRCFLOWCONC2(L,J), J=1,NUMSTRUCS) !Assumes 1 solute 116 CONTINUE ENDDO IFIRST=0 ENDIF C SECTION EXECUTED EVERY TIMESTEP C Convert time in min to Julian days. DAY=(KBND+1)*HALFDT/1440.+1.+DAYOFFSTSWIFT C SJM: WRITE DAY to screen to monitor sim progression !WRITE(*,*)DAY !SJM DELETE! DO L=1,LMAX IF ((L.EQ.LSAL).OR.(L.EQ.LTEMP)) GOTO 1166 IF (DAY.GT.STRCFLOWCONC(L,1)) DAYCHK=STRCFLOWCONC(L,1) !Assumes data for different L's given at same time in input file 1166 CONTINUE ENDDO !10 IF(DAY .GT. STRCFLOWCONC(1))THEN 10 IF (DAY .GT. DAYCHK) THEN STRCFLOWCONC=STRCFLOWCONC2 !If mo re than one solute (excl salinity and temp) then need to have one line in inputfile for each L !for each day, !e.g. Line1: Day1 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3) Line2: Day1 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3) Line3: Day2 Conc(L1,strc1) Conc(L1,strc2) Conc(L1,strc3) Line4: Day2 Conc(L2,strc1) Conc(L2,strc2) Conc(L2,strc3) DO L=1,LMAX IF(L.EQ.LSAL)GOTO 117 !Skip salinity and temp so don't have to add these to input file IF(L.EQ.LTEMP)GOTO 117 READ(IUSFLOWCONCS,*)(STRCFLOWCONC2(L,J), J=1,NUMSTRUCS) !Assumes 1 solute DAYCHK=STRCFLOWCONC(L,1) 117 CONTINUE ENDDO GO TO 10 ENDIF RETURN END

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220 Section C2 Important Input Files for the SICS Water -Quality Simulation Input files and used in the simulation of SICS surface water phosphorus are presented. These include the input concentrations at discharge sources (INPUTFLOWCONCS.dat), the atmospheri c deposition data for each of the three options tested, the SWIFT2D input file (WETLANDS.inp), and the IWQ input file (IWQINPUT.iwq), which are needed by SWIFT2D. The XML input file (XMLINPUT.xml) was required for aRSE. Format for INPUTFLOWCONCS.dat 3 1 0 TSB 90 90 3 1 0 L -31W 100 88 3 1 0 C -111 120 64 3 1.00 0.0044 0.0062 0.003 2.00 0.0044 0.0062 0.003 3.00 0.0044 0.0062 0.003 4.00 0.0044 0.0062 0.003 5.00 0.0044 0.0062 0.003 6.00 0.0044 0.0062 0.003 7.00 0.0044 0.0062 0.003 8.00 0.0044 0.0062 0.003 9.00 0.0044 0.0062 0.003 10.00 0.0044 0.0062 0.003 11.00 0.0044 0.0062 0.003 12.00 0.0044 0.0062 0.003 13.00 0.0044 0.0062 0.003 14.00 0.0044 0.0062 0.003 15.00 0.0044 0.0062 0.003 16.00 0.0044 0.0062 0.003 17.00 0.0044 0.0062 0.003 18.00 0.0101 0.0031 0.0032 19.00 0.0101 0.0031 0.0032 20.00 0.0101 0.0031 0.0032 21.00 0.0101 0.0031 0.0032 22.00 0.0101 0.0031 0.0032

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221 23.00 0.0101 0.0031 0.0032 24.00 0.0101 0.0031 0.0032 25.00 0.0101 0.0031 0.0032 26.00 0.0101 0.0031 0.0032 27.00 0.0101 0.0031 0.0032 28.00 0.0101 0.0031 0.0032 29.00 0.0101 0.0031 0.0032 30.00 0.0101 0.0031 0.0032 *incomplete f i le Total P hosphorus A tmospheric D eposition Rates for Model 2 Table C -1 below shows the total phosphorus atmospheric deposition rates applied to Model 2 for each of the three atmospheric deposition options tested. Table C -1. Atmospheric deposition rates input to Model 2 Day Date Variable rate proportionate to rain volume [g T P/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 1 07/15/96 9.93915E 05 9.70874E 05 8.2192E 05 2 07/16/96 0.000686837 9.70874E 05 8.2192E 05 3 07/17/96 3.68857E 05 9.70874E 05 8.2192E 05 4 07/18/96 1.12111E 05 9.70874E 05 8.2192E 05 5 07/19/96 1.38821E 05 9.70874E 05 8.2192E 05 6 07/20/96 0.000110112 9.70874E 05 8.2192E 05 7 07/21/96 1.06841E 06 9.70874E 05 8.2192E 05 8 07/22/96 0 0 8.2192E 05 9 07/23/96 2.1441E 05 9.70874E 05 8.2192E 05 10 07/24/96 4.27002E 06 9.70874E 05 8.2192E 05 11 07/25/96 0 0 8.2192E 05 12 07/26/96 0 0 8.2192E 05 13 07/27/96 2.88908E 05 9.70874E 05 8.2192E 05 14 07/28/96 3.36151E 05 9.70874E 05 8.2192E 05 15 07/29/96 0.000136277 9.70874E 05 8.2192E 05 16 07/30/96 1.92605E 05 9.70874E 05 8.2192E 05 17 07/31/96 2.67103E 06 9.70874E 05 8.2192E 05 18 08/1/96 2.39848E 05 9.70874E 05 8.2192E 05 19 08/2/96 2.1441E 06 9.70874E 05 8.2192E 05 20 08/3/96 0.000190788 9.70874E 05 8.2192E 05 21 08/4/96 1.33552E 05 9.70874E 05 8.2192E 05 22 08/5/96 2.5075E 05 9.70874E 05 8.2192E 05 23 08/6/96 0.000323431 9.70874E 05 8.2192E 05 24 08/7/96 1.06841E 06 9.70874E 05 8.2192E 05

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222 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 25 08/8/96 0.000174071 9.70874E 05 8.2192E 05 26 08/9/96 1.06841E 05 9.70874E 05 8.2192E 05 27 08/10/96 6.41411E 06 9.70874E 05 8.2192E 05 28 08/11/96 5.86901E 06 9.70874E 05 8.2192E 05 29 08/12/96 0 0 8.2192E 05 30 08/13/96 2.83457E 05 9.70874E 05 8.2192E 05 31 08/14/96 2.94359E 05 9.70874E 05 8.2192E 05 32 08/15/96 8.64906E 05 9.70874E 05 8.2192E 05 33 08/16/96 4.76062E 05 9.70874E 05 8.2192E 05 34 08/17/96 1.76252E 05 9.70874E 05 8.2192E 05 35 08/18/96 0.000174617 9.70874E 05 8.2192E 05 36 08/19/96 0.000723178 9.70874E 05 8.2192E 05 37 08/20/96 0.000256201 9.70874E 05 8.2192E 05 38 08/21/96 0.000159717 9.70874E 05 8.2192E 05 39 08/22/96 0.00018352 9.70874E 05 8.2192E 05 40 08/23/96 0.000261652 9.70874E 05 8.2192E 05 41 08/24/96 4.59709E 05 9.70874E 05 8.2192E 05 42 08/25/96 5.34207E 07 9.70874E 05 8.2192E 05 43 08/26/96 0.000110657 9.70874E 05 8.2192E 05 44 08/27/96 4.90598E 05 9.70874E 05 8.2192E 05 45 08/28/96 1.12111E 05 9.70874E 05 8.2192E 05 46 08/29/96 2.67103E 06 9.70874E 05 8.2192E 05 47 08/30/96 4.48806E 05 9.70874E 05 8.2192E 05 48 08/31/96 9.61209E 06 9.70874E 05 8.2192E 05 49 09/1/96 6.46863E 05 9.70874E 05 8.2192E 05 50 09/2/96 0.000160807 9.70874E 05 8.2192E 05 51 09/3/96 7.37714E 05 9.70874E 05 8.2192E 05 52 09/4/96 1.38821E 05 9.70874E 05 8.2192E 05 53 09/5/96 0.000120106 9.70874E 05 8.2192E 05 54 09/6/96 9.61209E 06 9.70874E 05 8.2192E 05 55 09/7/96 7.48616E 06 9.70874E 05 8.2192E 05 56 09/8/96 5.92352E 05 9.70874E 05 8.2192E 05 57 09/9/96 0.000437904 9.70874E 05 8.2192E 05 58 09/10/96 0.000688654 9.70874E 05 8.2192E 05 59 09/11/96 2.28946E 05 9.70874E 05 8.2192E 05 60 09/12/96 0.000120651 9.70874E 05 8.2192E 05 61 09/13/96 6.41411E 06 9.70874E 05 8.2192E 05 62 09/14/96 0.000113746 9.70874E 05 8.2192E 05 63 09/15/96 1.01572E 05 9.70874E 05 8.2192E 05

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223 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 64 09/16/96 2.56201E 05 9.70874E 05 8.2192E 05 65 09/17/96 0.000174071 9.70874E 05 8.2192E 05 66 09/18/96 8.43102E 05 9.70874E 05 8.2192E 05 67 09/19/96 9.50307E 05 9.70874E 05 8.2192E 05 68 09/20/96 0.000325248 9.70874E 05 8.2192E 05 69 09/21/96 0.000190788 9.70874E 05 8.2192E 05 70 09/22/96 4.76062E 05 9.70874E 05 8.2192E 05 71 09/23/96 0.000170437 9.70874E 05 8.2192E 05 72 09/24/96 6.30509E 05 9.70874E 05 8.2192E 05 73 09/25/96 0 0 8.2192E 05 74 09/26/96 4.27002E 06 9.70874E 05 8.2192E 05 75 09/27/96 0 0 8.2192E 05 76 09/28/96 3.41602E 05 9.70874E 05 8.2192E 05 77 09/29/96 1.54993E 05 9.70874E 05 8.2192E 05 78 09/30/96 0.000368857 9.70874E 05 8.2192E 05 79 10/1/96 6.52314E 05 9.70874E 05 8.2192E 05 80 10/2/96 3.74308E 06 9.70874E 05 8.2192E 05 81 10/3/96 0.000107932 9.70874E 05 8.2192E 05 82 10/4/96 0.000188971 9.70874E 05 8.2192E 05 83 10/5/96 0.000461526 9.70874E 05 8.2192E 05 84 10/6/96 0.000132461 9.70874E 05 8.2192E 05 85 10/7/96 0.000223495 9.70874E 05 8.2192E 05 86 10/8/96 0.000236214 9.70874E 05 8.2192E 05 87 10/9/96 0.000130826 9.70874E 05 8.2192E 05 88 10/10/96 0 0 8.2192E 05 89 10/11/96 0 0 8.2192E 05 90 10/12/96 0.001019354 9.70874E 05 8.2192E 05 91 10/13/96 0.001010269 9.70874E 05 8.2192E 05 92 10/14/96 0.000228946 9.70874E 05 8.2192E 05 93 10/15/96 0.000288908 9.70874E 05 8.2192E 05 94 10/16/96 6.46863E 05 9.70874E 05 8.2192E 05 95 10/17/96 0.000423368 9.70874E 05 8.2192E 05 96 10/18/96 0.000310712 9.70874E 05 8.2192E 05 97 10/19/96 8.70357E 05 9.70874E 05 8.2192E 05 98 10/20/96 3.19797E 06 9.70874E 05 8.2192E 05 99 10/21/96 1.60262E 06 9.70874E 05 8.2192E 05 100 10/22/96 1.60262E 06 9.70874E 05 8.2192E 05 101 10/23/96 0 0 8.2192E 05 102 10/24/96 0 0 8.2192E 05

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224 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 103 10/25/96 3.74308E 06 9.70874E 05 8.2192E 05 104 10/26/96 1.06841E 06 9.70874E 05 8.2192E 05 105 10/27/96 8.54004E 06 9.70874E 05 8.2192E 05 106 10/28/96 1.06841E 06 9.70874E 05 8.2192E 05 107 10/29/96 0 0 8.2192E 05 108 10/30/96 1.70982E 05 9.70874E 05 8.2192E 05 109 10/31/96 5.34207E 07 9.70874E 05 8.2192E 05 110 11/1/96 5.34207E 07 9.70874E 05 8.2192E 05 111 11/2/96 3.74308E 06 9.70874E 05 8.2192E 05 112 11/3/96 5.34207E 07 9.70874E 05 8.2192E 05 113 11/4/96 2.1441E 06 9.70874E 05 8.2192E 05 114 11/5/96 1.81703E 05 9.70874E 05 8.2192E 05 115 11/6/96 0 0 8.2192E 05 116 11/7/96 3.74308E 06 9.70874E 05 8.2192E 05 117 11/8/96 1.06841E 06 9.70874E 05 8.2192E 05 118 11/9/96 0 0 8.2192E 05 119 11/10/96 0 0 8.2192E 05 120 11/11/96 0 0 8.2192E 05 121 11/12/96 0 0 8.2192E 05 122 11/13/96 0 0 8.2192E 05 123 11/14/96 5.015E 05 9.70874E 05 8.2192E 05 124 11/15/96 4.59709E 05 9.70874E 05 8.2192E 05 125 11/16/96 1.54993E 05 9.70874E 05 8.2192E 05 126 11/17/96 0 0 8.2192E 05 127 11/18/96 2.1441E 06 9.70874E 05 8.2192E 05 128 11/19/96 1.06841E 06 9.70874E 05 8.2192E 05 129 11/20/96 0 0 8.2192E 05 130 11/21/96 1.06841E 06 9.70874E 05 8.2192E 05 131 11/22/96 2.67103E 06 9.70874E 05 8.2192E 05 132 11/23/96 4.81513E 06 9.70874E 05 8.2192E 05 133 11/24/96 0 0 8.2192E 05 134 11/25/96 0 0 8.2192E 05 135 11/26/96 0 0 8.2192E 05 136 11/27/96 0 0 8.2192E 05 137 11/28/96 7.21361E 05 9.70874E 05 8.2192E 05 138 11/29/96 0 0 8.2192E 05 139 11/30/96 0 0 8.2192E 05 140 12/1/96 0 0 8.2192E 05 141 12/2/96 1.33552E 05 9.70874E 05 8.2192E 05

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225 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 142 12/3/96 1.12111E 05 9.70874E 05 8.2192E 05 143 12/4/96 0 0 8.2192E 05 144 12/5/96 7.63152E 05 9.70874E 05 8.2192E 05 145 12/6/96 1.33552E 05 9.70874E 05 8.2192E 05 146 12/7/96 5.34207E 07 9.70874E 05 8.2192E 05 147 12/8/96 4.81513E 06 9.70874E 05 8.2192E 05 148 12/9/96 0 0 8.2192E 05 149 12/10/96 0 0 8.2192E 05 150 12/11/96 0 0 8.2192E 05 151 12/12/96 0 0 8.2192E 05 152 12/13/96 0.000261652 9.70874E 05 8.2192E 05 153 12/14/96 4.27002E 06 9.70874E 05 8.2192E 05 154 12/15/96 1.06841E 06 9.70874E 05 8.2192E 05 155 12/16/96 0 0 8.2192E 05 156 12/17/96 0 0 8.2192E 05 157 12/18/96 8.54004E 06 9.70874E 05 8.2192E 05 158 12/19/96 4.81513E 06 9.70874E 05 8.2192E 05 159 12/20/96 0 0 8.2192E 05 160 12/21/96 5.34207E 07 9.70874E 05 8.2192E 05 161 12/22/96 6.41411E 06 9.70874E 05 8.2192E 05 162 12/23/96 0 0 8.2192E 05 163 12/24/96 0 0 8.2192E 05 164 12/25/96 1.06841E 06 9.70874E 05 8.2192E 05 165 12/26/96 8.54004E 06 9.70874E 05 8.2192E 05 166 12/27/96 4.81513E 06 9.70874E 05 8.2192E 05 167 12/28/96 1.06841E 06 9.70874E 05 8.2192E 05 168 12/29/96 2.67103E 06 9.70874E 05 8.2192E 05 169 12/30/96 4.81513E 06 9.70874E 05 8.2192E 05 170 12/31/96 1.06841E 06 9.70874E 05 8.2192E 05 171 01/1/97 1.06841E 06 9.70874E 05 8.2192E 05 172 01/2/97 1.60262E 06 9.70874E 05 8.2192E 05 173 01/3/97 1.06841E 06 9.70874E 05 8.2192E 05 174 01/4/97 2.1441E 06 9.70874E 05 8.2192E 05 175 01/5/97 5.34207E 07 9.70874E 05 8.2192E 05 176 01/6/97 1.06841E 06 9.70874E 05 8.2192E 05 177 01/7/97 6.41411E 06 9.70874E 05 8.2192E 05 178 01/8/97 4.81513E 06 9.70874E 05 8.2192E 05 179 01/9/97 1.60262E 06 9.70874E 05 8.2192E 05 180 01/10/97 9.72111E 05 9.70874E 05 8.2192E 05

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226 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 181 01/11/97 1.60262E 05 9.70874E 05 8.2192E 05 182 01/12/97 0.000359772 9.70874E 05 8.2192E 05 183 01/13/97 0.000370674 9.70874E 05 8.2192E 05 184 01/14/97 0.000168802 9.70874E 05 8.2192E 05 185 01/15/97 0.000185337 9.70874E 05 8.2192E 05 186 01/16/97 0.00020169 9.70874E 05 8.2192E 05 187 01/17/97 0 0 8.2192E 05 188 01/18/97 0 0 8.2192E 05 189 01/19/97 0 0 8.2192E 05 190 01/20/97 0 0 8.2192E 05 191 01/21/97 5.34207E 07 9.70874E 05 8.2192E 05 192 01/22/97 1.06841E 06 9.70874E 05 8.2192E 05 193 01/23/97 5.34207E 07 9.70874E 05 8.2192E 05 194 01/24/97 0 0 8.2192E 05 195 01/25/97 3.74308E 05 9.70874E 05 8.2192E 05 196 01/26/97 3.90661E 05 9.70874E 05 8.2192E 05 197 01/27/97 0 0 8.2192E 05 198 01/28/97 1.44272E 05 9.70874E 05 8.2192E 05 199 01/29/97 0.000134097 9.70874E 05 8.2192E 05 200 01/30/97 8.34017E 05 9.70874E 05 8.2192E 05 201 01/31/97 0 0 8.2192E 05 202 02/1/97 0 0 8.2192E 05 203 02/2/97 2.1441E 06 9.70874E 05 8.2192E 05 204 02/3/97 3.19797E 06 9.70874E 05 8.2192E 05 205 02/4/97 2.39848E 05 9.70874E 05 8.2192E 05 206 02/5/97 4.81513E 06 9.70874E 05 8.2192E 05 207 02/6/97 1.60262E 06 9.70874E 05 8.2192E 05 208 02/7/97 5.34207E 07 9.70874E 05 8.2192E 05 209 02/8/97 2.1441E 06 9.70874E 05 8.2192E 05 210 02/9/97 1.65531E 05 9.70874E 05 8.2192E 05 211 02/10/97 1.06841E 06 9.70874E 05 8.2192E 05 212 02/11/97 0 0 8.2192E 05 213 02/12/97 0 0 8.2192E 05 214 02/13/97 5.34207E 07 9.70874E 05 8.2192E 05 215 02/14/97 6.41411E 06 9.70874E 05 8.2192E 05 216 02/15/97 1.06841E 06 9.70874E 05 8.2192E 05 217 02/16/97 0.000152267 9.70874E 05 8.2192E 05 218 02/17/97 9.61209E 06 9.70874E 05 8.2192E 05 219 02/18/97 0.00020169 9.70874E 05 8.2192E 05

PAGE 227

227 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 220 02/19/97 2.39848E 05 9.70874E 05 8.2192E 05 221 02/20/97 3.74308E 06 9.70874E 05 8.2192E 05 222 02/21/97 5.34207E 07 9.70874E 05 8.2192E 05 223 02/22/97 5.34207E 07 9.70874E 05 8.2192E 05 224 02/23/97 2.1441E 06 9.70874E 05 8.2192E 05 225 02/24/97 2.72554E 05 9.70874E 05 8.2192E 05 226 02/25/97 1.60262E 05 9.70874E 05 8.2192E 05 227 02/26/97 0 0 8.2192E 05 228 02/27/97 0 0 8.2192E 05 229 02/28/97 0 0 8.2192E 05 230 03/1/97 0 0 8.2192E 05 231 03/2/97 0 0 8.2192E 05 232 03/3/97 5.34207E 07 9.70874E 05 8.2192E 05 233 03/4/97 5.34207E 07 9.70874E 05 8.2192E 05 234 03/5/97 0 0 8.2192E 05 235 03/6/97 4.27002E 06 9.70874E 05 8.2192E 05 236 03/7/97 1.33552E 05 9.70874E 05 8.2192E 05 237 03/8/97 5.34207E 07 9.70874E 05 8.2192E 05 238 03/9/97 5.34207E 07 9.70874E 05 8.2192E 05 239 03/10/97 5.86901E 06 9.70874E 05 8.2192E 05 240 03/11/97 5.34207E 07 9.70874E 05 8.2192E 05 241 03/12/97 2.1441E 06 9.70874E 05 8.2192E 05 242 03/13/97 5.34207E 07 9.70874E 05 8.2192E 05 243 03/14/97 0.000632326 9.70874E 05 8.2192E 05 244 03/15/97 8.23114E 05 9.70874E 05 8.2192E 05 245 03/16/97 1.06841E 06 9.70874E 05 8.2192E 05 246 03/17/97 5.34207E 07 9.70874E 05 8.2192E 05 247 03/18/97 0 0 8.2192E 05 248 03/19/97 1.06841E 06 9.70874E 05 8.2192E 05 249 03/20/97 5.34207E 07 9.70874E 05 8.2192E 05 250 03/21/97 0.000219861 9.70874E 05 8.2192E 05 251 03/22/97 6.41411E 06 9.70874E 05 8.2192E 05 252 03/23/97 5.34207E 07 9.70874E 05 8.2192E 05 253 03/24/97 0.000106296 9.70874E 05 8.2192E 05 254 03/25/97 1.28282E 05 9.70874E 05 8.2192E 05 255 03/26/97 0 0 8.2192E 05 256 03/27/97 1.81703E 05 9.70874E 05 8.2192E 05 257 03/28/97 2.67103E 06 9.70874E 05 8.2192E 05 258 03/29/97 5.34207E 07 9.70874E 05 8.2192E 05

PAGE 228

228 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 259 03/30/97 5.34207E 07 9.70874E 05 8.2192E 05 260 03/31/97 2.08958E 05 9.70874E 05 8.2192E 05 261 04/1/97 2.1441E 06 9.70874E 05 8.2192E 05 262 04/2/97 0 0 8.2192E 05 263 04/3/97 0 0 8.2192E 05 264 04/4/97 0 0 8.2192E 05 265 04/5/97 0 0 8.2192E 05 266 04/6/97 0 0 8.2192E 05 267 04/7/97 0 0 8.2192E 05 268 04/8/97 2.1441E 06 9.70874E 05 8.2192E 05 269 04/9/97 3.14346E 05 9.70874E 05 8.2192E 05 270 04/10/97 1.44272E 05 9.70874E 05 8.2192E 05 271 04/11/97 1.70982E 05 9.70874E 05 8.2192E 05 272 04/12/97 5.39658E 05 9.70874E 05 8.2192E 05 273 04/13/97 7.10459E 05 9.70874E 05 8.2192E 05 274 04/14/97 3.19797E 06 9.70874E 05 8.2192E 05 275 04/15/97 0.000117562 9.70874E 05 8.2192E 05 276 04/16/97 0.000141002 9.70874E 05 8.2192E 05 277 04/17/97 1.01572E 05 9.70874E 05 8.2192E 05 278 04/18/97 0 0 8.2192E 05 279 04/19/97 0 0 8.2192E 05 280 04/20/97 0 0 8.2192E 05 281 04/21/97 1.92605E 05 9.70874E 05 8.2192E 05 282 04/22/97 9.08515E 06 9.70874E 05 8.2192E 05 283 04/23/97 5.86901E 06 9.70874E 05 8.2192E 05 284 04/24/97 4.27002E 06 9.70874E 05 8.2192E 05 285 04/25/97 3.19797E 06 9.70874E 05 8.2192E 05 286 04/26/97 0.000129191 9.70874E 05 8.2192E 05 287 04/27/97 2.67103E 06 9.70874E 05 8.2192E 05 288 04/28/97 0.000134097 9.70874E 05 8.2192E 05 289 04/29/97 1.33552E 05 9.70874E 05 8.2192E 05 290 04/30/97 9.55758E 05 9.70874E 05 8.2192E 05 291 05/1/97 5.86901E 05 9.70874E 05 8.2192E 05 292 05/2/97 6.94105E 06 9.70874E 05 8.2192E 05 293 05/3/97 0 0 8.2192E 05 294 05/4/97 6.30509E 05 9.70874E 05 8.2192E 05 295 05/5/97 1.01572E 05 9.70874E 05 8.2192E 05 296 05/6/97 0 0 8.2192E 05 297 05/7/97 0 0 8.2192E 05

PAGE 229

229 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 298 05/8/97 0 0 8.2192E 05 299 05/9/97 0 0 8.2192E 05 300 05/10/97 0 0 8.2192E 05 301 05/11/97 1.06841E 06 9.70874E 05 8.2192E 05 302 05/12/97 0.000466977 9.70874E 05 8.2192E 05 303 05/13/97 0.000145362 9.70874E 05 8.2192E 05 304 05/14/97 0 0 8.2192E 05 305 05/15/97 5.34207E 07 9.70874E 05 8.2192E 05 306 05/16/97 0 0 8.2192E 05 307 05/17/97 2.08958E 05 9.70874E 05 8.2192E 05 308 05/18/97 6.41411E 06 9.70874E 05 8.2192E 05 309 05/19/97 2.1441E 06 9.70874E 05 8.2192E 05 310 05/20/97 5.34207E 06 9.70874E 05 8.2192E 05 311 05/21/97 1.60262E 05 9.70874E 05 8.2192E 05 312 05/22/97 0.000181158 9.70874E 05 8.2192E 05 313 05/23/97 8.81259E 05 9.70874E 05 8.2192E 05 314 05/24/97 0.000179523 9.70874E 05 8.2192E 05 315 05/25/97 0 0 8.2192E 05 316 05/26/97 4.54257E 05 9.70874E 05 8.2192E 05 317 05/27/97 5.34207E 07 9.70874E 05 8.2192E 05 318 05/28/97 0.000259835 9.70874E 05 8.2192E 05 319 05/29/97 0.000100482 9.70874E 05 8.2192E 05 320 05/30/97 7.05008E 05 9.70874E 05 8.2192E 05 321 05/31/97 0.000119197 9.70874E 05 8.2192E 05 322 06/1/97 0.000122831 9.70874E 05 8.2192E 05 323 06/2/97 0.000739531 9.70874E 05 8.2192E 05 324 06/3/97 7.26812E 05 9.70874E 05 8.2192E 05 325 06/4/97 1.70982E 05 9.70874E 05 8.2192E 05 326 06/5/97 4.81513E 06 9.70874E 05 8.2192E 05 327 06/6/97 0 0 8.2192E 05 328 06/7/97 1.17562E 05 9.70874E 05 8.2192E 05 329 06/8/97 0.000741348 9.70874E 05 8.2192E 05 330 06/9/97 0.004197339 9.70874E 05 8.2192E 05 331 06/10/97 0.001475428 9.70874E 05 8.2192E 05 332 06/11/97 0.000292542 9.70874E 05 8.2192E 05 333 06/12/97 1.92605E 05 9.70874E 05 8.2192E 05 334 06/13/97 2.88908E 05 9.70874E 05 8.2192E 05 335 06/14/97 1.38821E 05 9.70874E 05 8.2192E 05 336 06/15/97 0.000432453 9.70874E 05 8.2192E 05

PAGE 230

230 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 337 06/16/97 0.000115926 9.70874E 05 8.2192E 05 338 06/17/97 2.1441E 06 9.70874E 05 8.2192E 05 339 06/18/97 3.19797E 06 9.70874E 05 8.2192E 05 340 06/19/97 4.27002E 06 9.70874E 05 8.2192E 05 341 06/20/97 1.54993E 05 9.70874E 05 8.2192E 05 342 06/21/97 7.57701E 05 9.70874E 05 8.2192E 05 343 06/22/97 0.000414283 9.70874E 05 8.2192E 05 344 06/23/97 7.05008E 05 9.70874E 05 8.2192E 05 345 06/24/97 0.000185337 9.70874E 05 8.2192E 05 346 06/25/97 0.000101027 9.70874E 05 8.2192E 05 347 06/26/97 9.08515E 06 9.70874E 05 8.2192E 05 348 06/27/97 1.17562E 05 9.70874E 05 8.2192E 05 349 06/28/97 0 0 8.2192E 05 350 06/29/97 1.60262E 06 9.70874E 05 8.2192E 05 351 06/30/97 5.77815E 05 9.70874E 05 8.2192E 05 352 07/1/97 0.000135732 9.70874E 05 8.2192E 05 353 07/2/97 0.000247116 9.70874E 05 8.2192E 05 354 07/3/97 9.88464E 05 9.70874E 05 8.2192E 05 355 07/4/97 0.000321614 9.70874E 05 8.2192E 05 356 07/5/97 4.27002E 06 9.70874E 05 8.2192E 05 357 07/6/97 3.36151E 05 9.70874E 05 8.2192E 05 358 07/7/97 5.86901E 06 9.70874E 05 8.2192E 05 359 07/8/97 5.86901E 06 9.70874E 05 8.2192E 05 360 07/9/97 4.27002E 06 9.70874E 05 8.2192E 05 361 07/10/97 0.000108477 9.70874E 05 8.2192E 05 362 07/11/97 0.000144272 9.70874E 05 8.2192E 05 363 07/12/97 0.000254384 9.70874E 05 8.2192E 05 364 07/13/97 0.000205324 9.70874E 05 8.2192E 05 365 07/14/97 0.000185337 9.70874E 05 8.2192E 05 366 07/15/97 5.34207E 05 9.70874E 05 8.2192E 05 367 07/16/97 0.000243482 9.70874E 05 8.2192E 05 368 07/17/97 0.000161897 9.70874E 05 8.2192E 05 369 07/18/97 0.000156446 9.70874E 05 8.2192E 05 370 07/19/97 0.000142092 9.70874E 05 8.2192E 05 371 07/20/97 0.000118107 9.70874E 05 8.2192E 05 372 07/21/97 3.47053E 05 9.70874E 05 8.2192E 05 373 07/22/97 0.00020169 9.70874E 05 8.2192E 05 374 07/23/97 0.000120651 9.70874E 05 8.2192E 05 375 07/24/97 1.06841E 05 9.70874E 05 8.2192E 05

PAGE 231

231 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 376 07/25/97 9.61209E 06 9.70874E 05 8.2192E 05 377 07/26/97 0.000123376 9.70874E 05 8.2192E 05 378 07/27/97 5.77815E 05 9.70874E 05 8.2192E 05 379 07/28/97 2.1441E 05 9.70874E 05 8.2192E 05 380 07/29/97 5.34207E 07 9.70874E 05 8.2192E 05 381 07/30/97 4.27002E 06 9.70874E 05 8.2192E 05 382 07/31/97 1.81703E 05 9.70874E 05 8.2192E 05 383 08/1/97 0.000160262 9.70874E 05 8.2192E 05 384 08/2/97 0.000107386 9.70874E 05 8.2192E 05 385 08/3/97 0 0 8.2192E 05 386 08/4/97 7.63152E 05 9.70874E 05 8.2192E 05 387 08/5/97 7.48616E 06 9.70874E 05 8.2192E 05 388 08/6/97 0.000110657 9.70874E 05 8.2192E 05 389 08/7/97 4.161E 05 9.70874E 05 8.2192E 05 390 08/8/97 5.45109E 05 9.70874E 05 8.2192E 05 391 08/9/97 0.000354321 9.70874E 05 8.2192E 05 392 08/10/97 0.00021441 9.70874E 05 8.2192E 05 393 08/11/97 3.96112E 05 9.70874E 05 8.2192E 05 394 08/12/97 2.78006E 05 9.70874E 05 8.2192E 05 395 08/13/97 0 0 8.2192E 05 396 08/14/97 5.34207E 07 9.70874E 05 8.2192E 05 397 08/15/97 0.000153357 9.70874E 05 8.2192E 05 398 08/16/97 3.99747E 05 9.70874E 05 8.2192E 05 399 08/17/97 6.41411E 06 9.70874E 05 8.2192E 05 400 08/18/97 1.60262E 05 9.70874E 05 8.2192E 05 401 08/19/97 5.86901E 06 9.70874E 05 8.2192E 05 402 08/20/97 7.37714E 05 9.70874E 05 8.2192E 05 403 08/21/97 0.000252567 9.70874E 05 8.2192E 05 404 08/22/97 2.5075E 05 9.70874E 05 8.2192E 05 405 08/23/97 2.19861E 05 9.70874E 05 8.2192E 05 406 08/24/97 4.70611E 05 9.70874E 05 8.2192E 05 407 08/25/97 0.000199873 9.70874E 05 8.2192E 05 408 08/26/97 0.000121741 9.70874E 05 8.2192E 05 409 08/27/97 0.000128282 9.70874E 05 8.2192E 05 410 08/28/97 4.81513E 05 9.70874E 05 8.2192E 05 411 08/29/97 6.72301E 05 9.70874E 05 8.2192E 05 412 08/30/97 0.000279823 9.70874E 05 8.2192E 05 413 08/31/97 0.000219861 9.70874E 05 8.2192E 05 414 09/1/97 0.000138276 9.70874E 05 8.2192E 05

PAGE 232

232 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 415 09/2/97 0.000133552 9.70874E 05 8.2192E 05 416 09/3/97 3.25248E 05 9.70874E 05 8.2192E 05 417 09/4/97 9.83013E 05 9.70874E 05 8.2192E 05 418 09/5/97 0.000321614 9.70874E 05 8.2192E 05 419 09/6/97 0.000305261 9.70874E 05 8.2192E 05 420 09/7/97 4.27002E 06 9.70874E 05 8.2192E 05 421 09/8/97 3.47053E 05 9.70874E 05 8.2192E 05 422 09/9/97 1.06841E 06 9.70874E 05 8.2192E 05 423 09/10/97 5.34207E 07 9.70874E 05 8.2192E 05 424 09/11/97 9.24868E 05 9.70874E 05 8.2192E 05 425 09/12/97 5.72364E 05 9.70874E 05 8.2192E 05 426 09/13/97 4.43355E 05 9.70874E 05 8.2192E 05 427 09/14/97 0.000100482 9.70874E 05 8.2192E 05 428 09/15/97 0.000129191 9.70874E 05 8.2192E 05 429 09/16/97 3.52504E 05 9.70874E 05 8.2192E 05 430 09/17/97 0.000116472 9.70874E 05 8.2192E 05 431 09/18/97 5.86901E 05 9.70874E 05 8.2192E 05 432 09/19/97 0.000198056 9.70874E 05 8.2192E 05 433 09/20/97 3.30699E 05 9.70874E 05 8.2192E 05 434 09/21/97 2.34397E 05 9.70874E 05 8.2192E 05 435 09/22/97 2.1441E 06 9.70874E 05 8.2192E 05 436 09/23/97 3.41602E 05 9.70874E 05 8.2192E 05 437 09/24/97 0.000119742 9.70874E 05 8.2192E 05 438 09/25/97 5.72364E 05 9.70874E 05 8.2192E 05 439 09/26/97 0.000221678 9.70874E 05 8.2192E 05 440 09/27/97 6.03254E 05 9.70874E 05 8.2192E 05 441 09/28/97 0.000207141 9.70874E 05 8.2192E 05 442 09/29/97 0.000223495 9.70874E 05 8.2192E 05 443 09/30/97 0.000332516 9.70874E 05 8.2192E 05 444 10/1/97 0.000288908 9.70874E 05 8.2192E 05 445 10/2/97 0.000187154 9.70874E 05 8.2192E 05 446 10/3/97 4.81513E 06 9.70874E 05 8.2192E 05 447 10/4/97 2.1441E 06 9.70874E 05 8.2192E 05 448 10/5/97 4.81513E 06 9.70874E 05 8.2192E 05 449 10/6/97 9.55758E 05 9.70874E 05 8.2192E 05 450 10/7/97 2.1441E 06 9.70874E 05 8.2192E 05 451 10/8/97 0 0 8.2192E 05 452 10/9/97 4.81513E 06 9.70874E 05 8.2192E 05 453 10/10/97 0.000104116 9.70874E 05 8.2192E 05

PAGE 233

233 Table C -1. Continued Day Date Variable rate proportionate to rain volume [g TP/m 2 /d] Constant rate per rain day [g TP/m 2 /d] Constant rate per day [g TP/m 2 /d] 454 10/11/97 6.94105E 06 9.70874E 05 8.2192E 05 455 10/12/97 2.5075E 05 9.70874E 05 8.2192E 05 456 10/13/97 9.61209E 06 9.70874E 05 8.2192E 05 457 10/14/97 7.48616E 06 9.70874E 05 8.2192E 05 458 10/15/97 2.67103E 06 9.70874E 05 8.2192E 05 459 10/16/97 1.28282E 05 9.70874E 05 8.2192E 05 460 10/17/97 9.08515E 06 9.70874E 05 8.2192E 05 461 10/18/97 1.22831E 05 9.70874E 05 8.2192E 05 462 10/19/97 0 0 8.2192E 05 463 10/20/97 1.06841E 05 9.70874E 05 8.2192E 05 464 10/21/97 0 0 8.2192E 05 465 10/22/97 0 0 8.2192E 05 466 10/23/97 5.34207E 07 9.70874E 05 8.2192E 05 467 10/24/97 0 0 8.2192E 05 468 10/25/97 5.34207E 07 9.70874E 05 8.2192E 05 469 10/26/97 5.34207E 07 9.70874E 05 8.2192E 05 470 10/27/97 0 0 8.2192E 05 471 10/28/97 0 0 8.2192E 05 472 10/29/97 1.01572E 05 9.70874E 05 8.2192E 05 473 10/30/97 0.000236214 9.70874E 05 8.2192E 05 474 10/31/97 2.1441E 06 9.70874E 05 8.2192E 05 475 11/1/97 0 0 8.2192E 05 476 11/2/97 9.61209E 06 9.70874E 05 8.2192E 05 477 11/3/97 5.72364E 05 9.70874E 05 8.2192E 05 478 11/4/97 2.1441E 06 9.70874E 05 8.2192E 05 479 11/5/97 1.01572E 05 9.70874E 05 8.2192E 05 480 11/6/97 4.81513E 06 9.70874E 05 8.2192E 05 481 11/7/97 3.74308E 06 9.70874E 05 8.2192E 05 482 11/8/97 0 0 8.2192E 05 483 11/9/97 0 0 8.2192E 05 484 11/10/97 0 0 8.2192E 05 485 11/11/97 1.06841E 06 9.70874E 05 8.2192E 05 486 11/12/97 0 0 8.2192E 05

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234 Section C3 XML Input File for Model 3 (XMLINPUT.xml) < reaction_set name="rs1" full_name="Reaction Set Number 1"> all all surface_water Sal < initial_distribution type="constant"> 10.0 TP_sw_conc 10.0 TP_sw_mass1 10.0 TP_sw_mass2 10.0 TP_uptake1 < initial_distribution type="constant"> 10.0 TP_uptake2 10.0

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235 TP_soil1 10.0
TP_soil2 10.0 TP_live1 10.0 TP_live2 < initial_distribution type="constant"> 10.0 TP_dead1 10.0 TP_dead2 10.0 TP_senesc 10.0 TP_decomp 10.0 TP_bury < initial_distribution type="constant"> 10.0 K_wet

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236 10.0
longitudinal_dispersivity< /name> 10.0 transverse_dispersivity 10.0 molecular_diffusion 0.00001 surface_porosity 1.0 subsurface_longitudinal_dispersivity 10.0 subsurface_transverse_dispersivity 10.0 subsurface_molecular_diffusion 0.00001 subsurface_porosity 1.0 < /initial_distribution> k_uptake

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237 0.084375
k_senesc 0.25 k_decomp 0.0001 k_soil 0.13
TP_sw_mass2 (1 k_uptake)*TP_sw_conc*depth TP_uptake2 k_uptake*K_wet*TP_sw_mass1 TP_senesc k_senesc*TP_uptake1 TP_decomp k_decomp*TP_dead2 TP_bury k_soil*TP_uptake1 TP_live1 TP_live2 TP_dead1 TP_dead2 TP_soil1

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238 TP_soil2
TP_uptake1 TP_uptake2 TP_sw_mass1 TP_sw_mass2 TP_dead2 TP_dead1+TP_senesc TP_decomp TP_live2 TP_live1+TP_uptake2TP_senesc TP_soil2 TP_soil1+TP_bury TP_sw_conc (TP_sw_mass2+TP_decomp)/depth
IWQ input File for Model 3 ( IWQINPUT.iwq) 1 2 14 5 1 0 'XMLINPUT.xml' 'XMLOUTPUT.xml' 'rs1' Sal 5.01 TP_sw_conc 0.005 TP_sw_mass1 0.01 TP_sw_mass2 0.01 TP_uptake1 0.0008 TP_uptake2 0.0008 TP_soil1 0.0001 TP_soil2 0.0001 TP_live1 0.04 TP_live2 0.04 TP_dead1 0.014 TP_dead2 0.014 TP_senesc 0.0002 TP_decomp 0.0001 TP_bury 0 K_wet 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 k_uptake 0.084375 k_senesc 0.25 k_decomp 0.0001 k_soil 0.0 0 depth 0.52 time_step 3600 area 92903

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239 SWIFT2D Input File (WETLANDS.inp) for Model 3 SOUTHERN INLAND AND COASTAL SYSTEMS MODEL END NOTE END NOTE NOSAMV= 1(NUMBER OF DIMENSIONS THAT MUST STAY THE SAME) NODIMV= 2(NUMBER OF DIMENSIONS TOTAL) WETMTZ /IDP...R07 00 00 00 00 00 RUN NUMBER 1 R2 TITL WETLANDS 15 JUL '96 98/ 8/2517:23:39 IDPV514 R3 DATE Halfdt Titide Tstart Trst Tstop Tirst Tihisp Tihist DAYOFFSTSWIFT 1.50 15.0 0.0 0.0 999999. 999999. 1440. 1440. 0 R4 TIMEA 99999999999999999999999. 45. 30.999999 60.999999999999999999 0.R5 TIMEB 0 0 2 1 0 5 1 0 0 0 0 0R6 FLAGS 7 3 4 4 0 4 R7 INPR1 1 R8 INPR2 0 1440 1440 1440 0 0 0 0 0 R9 OTPR1 1440 1440 1440 1440 0 0 0 R10OTPR2 545760545880546000546120546240546360546480546600546720546840546960547080R11 PRT1 54720054732054744054756054 7680547800547920548040548160548280548400548520R12 PRT2 548640548760548880549000549120549240549360549480549600549720549840549960R13 PRT3 550080550200550320550440550560550680 R14 PRT4 148 98 2 14 33 4 25 3 5 8 0 1R15 DIMA 94 128 R16 DIMB 0.5 0 1 R17 CNST 25.000 0.0 304.8 0.20 0.0 0.10 1. 1.00 0.5 1.0 5.0 300.0R18 PHCH 9.81 0.0012 1.205 998.2 1.0000 14.3 1000.0 0.97 0.0023R19 COFA FR80 35SPRO 1.0 1.0 R20 Ploter D 25 1 0.0 13.0 20.0 14.0K/HR 5 R21 Nct itl D 4.0 170.0 2.00 121.0 163.0 1.25 74.0 89.0 1.00 122.0 103.0 1.00R22 Hx USED 1.0 2.0 2.0 2.0 2.0 R23 Dxpdy ED 1 1 2 0.5 1.0 0.40 0.40 0.25 1.0 0.0 1 1R24Iplc SED R25 Linx SED 25.0 1.0250 0.698 1.0 R26 COFB 1 57 36 CP RS1 WLSta 2 109 78 EVER4 RS1 WL Sta 3 100 58 EVER5A RS1 WLSta 4 69 45 E146 RS1 WL Sta 5 98 97 E158 RS1 WL Sta 6 142 52 EP12R RS1 WLSta 7 139 57 EP1R RS1 WLSta 8 123 55 EPGW RS1 WL Sta 9 120 61 EVER6 RS1 WL Sta 10 110 65 EVER7 RS1 WL Sta 11 74 73 NP67 RS1 WL Sta 12 62 56 P37 RS1 WL Sta 13 89 81 R127 RS1 WLSta 14 81 6 6 TSH RS1 WL Sta 1 28 18 Alligat_T RS2 Curr Sta 2 28 17 Alligat_C RS2 Curr Sta 3 28 16 A lligat_B RS2 Curr Sta 4 47 14 McCorm_L RS2 Curr Sta 5 48 14 McCorm_C RS2 Curr Sta 6 49 14 Mc Corm_R RS2 CurrSta 7 77 23 Taylor_L RS2 Curr Sta 8 78 23 Taylor_C RS2 Curr Sta 9 79 23 Tay lor_R RS2 Curr Sta 10 84 26 East_L RS2 Curr Sta 11 85 26 East_C RS2 Curr Sta 12 86 26 East _R RS2 Curr Sta 13 96 27 Mud_T RS2 Curr Sta 14 96 28 Mud_C RS2 Curr Sta 15 96 29 Mud_B RS2 Curr Sta 16 113 32 Trout_L RS2 Curr Sta 17 114 32 Trout_C RS2 Curr Sta 18 115 32 Trout_R RS2 Curr Sta 19 127 30 Shell_L RS2 Curr Sta 20 128 30 Shell_C RS2 Curr Sta 21 129 30 Shell_R RS2 Curr Sta 22 128 36 Stillw_L RS2 Curr Sta

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240 23 129 36 Stillw_C RS2 Curr Sta 24 130 36 Stillw_R RS2 Curr Sta 25 138 40 Oregon_L RS2 Curr Sta 26 139 40 Oregon_C RS2 Curr Sta 27 140 40 Oregon_R RS2 Curr Sta 28 140 41 WestHi_L RS2 Curr Sta 29 141 41 WestHi_C RS2 Curr Sta 30 142 41 WestHi_R RS2 Curr Sta 31 142 42 EastHi_L RS2 Curr Sta 32 143 42 EastHi_C RS2 Curr Sta 33 144 42 EastHi_R RS2 Curr Sta 1 90 90 TSB RS3 Src 2 100 88 L 31W RS3 Src 3 120 6 4 C 111 RS3 Src 4 148 98 Dummy (ex solar) RS3 Sol 1 57 36 CP RS4 Con Sta 2 109 78 EVER4 RS4 Con Sta 3 100 58 EVER5A RS4 ConSta 4 69 45 E146 RS4 Con Sta 5 98 97 E158 RS4 Con Sta 6 142 52 EP12R RS4 ConSta 7 139 57 EP1R RS4 Con Sta 8 123 55 EPGW RS4 Con Sta 9 120 61 EVER6 RS4 Con Sta 10 110 65 EVER7 RS4 Con Sta 11 74 73 NP67 RS4 Con Sta 12 62 56 P37 RS4 Con Sta 13 89 81 R127 RS4 ConSta 14 81 66 TSH RS4 Con Sta 15 28 17 Alligat_c RS4 ConSta 16 48 14 McCorm_c RS4 Con Sta 17 78 23 Taylor_c RS4 Con Sta 18 85 26 East_c RS4 Con Sta 19 96 28 Mud_c RS4 Con Sta 2 0 114 32 Trout_c RS4 Con Sta 21 128 30 Shell_c RS4 Con Sta 22 129 36 Stillw_c RS4 Con Sta 23 139 40 Oregon_c RS4 Con Sta 24 141 41 WestHi_c RS4 Con Sta 25 143 42 EastHi_c RS4 ConSta 1 93 31 36 Joe Bay 1 RS5 U tran Sta 2 98 36 40 Joe Bay 2 RS5 U tran Sta 3 116 34 39 Joe Bay 3 RS5 U tran Sta 1 36 93 98 Joe Bay 4 RS6 V tran Sta 2 40 98 101 Joe Bay 5 RS6 V tran Sta 3 41 102 107 Joe Bay 6 RS6 V tran Sta 4 40 108 110 Joe Bay 7 RS6 V tran Sta 5 39 111 116 Joe Bay 8 RS6 V tran Sta RS7 Dam RS8 Wind/Temp 1 1 13 17 RS9 Bar/Sluice 1 2 15 16 1 3 17 15 1 4 18 14 1 5 19 17 1 6 19 18 1 7 20 15 1 8 20 16 1 9 20 19 1 10 21 20 1 11 23 21 1 12 26 19 1 13 27 18 1 14 27 15 1 15 28 17 Alligator 1 16 28 16 1 17 28 14 1 18 30 14 1 19 31 13 1 20 32 15

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241 1 21 33 13 1 22 35 12 1 23 36 13 1 24 38 13 1 25 40 12 1 26 41 11 1 27 42 12 1 28 42 13 1 29 43 14 1 30 44 13 1 31 46 13 1 32 46 18 1 33 47 14 1 34 49 14 1 35 50 16 1 36 50 17 1 37 51 12 1 38 52 11 1 39 54 10 1 40 56 9 1 41 57 10 1 42 58 11 1 43 58 12 1 44 59 13 1 45 60 14 1 46 61 15 1 47 63 16 1 48 64 17 1 49 66 17 1 50 68 17 1 51 69 16 1 52 69 15 1 53 70 14 1 54 70 18 1 55 70 19 1 56 71 15 1 57 71 16 1 58 71 17 1 59 71 20 1 60 73 21 1 61 74 22 1 62 74 23 1 63 76 23 1 64 78 23 1 65 80 24 1 66 81 25 1 67 83 25 1 68 84 26 1 69 86 26 1 70 89 27 1 71 91 27 1 72 92 26 1 73 94 26 1 74 96 27 1 75 96 28 Mud Creek 1 76 96 29 1 77 98 30 1 78 100 30 1 79 102 30 1 80 104 30 1 81 105 31 1 82 107 31 1 83 109 30 1 84 111 31 1 85 113 31 1 86 114 32 1 87 115 33 1 88 116 34 1 89 118 34 1 90 119 33

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242 1 91 120 32 1 92 121 31 1 93 122 30 1 94 123 29 2 1 4 18 2 2 5 18 2 3 6 18 2 4 7 18 2 5 8 18 2 6 9 18 2 7 10 18 2 8 11 17 2 9 12 17 2 10 13 17 2 11 14 16 2 12 15 16 2 13 16 15 2 14 17 15 2 15 18 14 2 16 19 15 2 17 20 19 2 18 21 20 2 19 22 21 2 20 23 21 2 21 24 20 2 22 25 20 2 23 25 25 2 24 26 19 2 25 27 15 2 26 27 18 2 27 28 14 2 28 29 14 2 29 29 25 2 30 30 14 2 31 31 13 2 32 32 13 2 33 33 13 2 34 34 12 2 35 34 20 2 36 35 12 2 37 36 13 2 38 37 13 2 39 38 13 2 40 39 12 2 41 40 12 2 42 41 11 2 43 43 14 2 44 44 13 2 45 45 13 2 46 46 13 2 47 48 14 McCormick Creek 2 48 49 14 2 49 50 16 2 50 51 12 2 51 52 11 2 52 53 10 2 53 54 10 2 54 55 9 2 55 56 9 2 56 57 10 2 57 59 13 2 58 60 14 2 59 61 15 2 60 62 16 2 61 63 16 2 62 64 17 2 63 65 17 2 64 66 17 2 65 67 17 2 66 68 17

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243 2 67 70 14 2 68 71 20 2 69 72 21 2 70 73 21 2 71 75 23 2 72 76 23 2 73 77 23 2 74 78 23 Taylor Creek 2 75 79 23 2 76 80 24 2 77 81 25 2 78 82 25 2 79 83 25 2 80 84 26 2 81 85 26 East Creek 2 82 86 26 2 83 87 26 2 84 88 27 2 85 89 27 2 86 90 27 2 87 91 27 2 88 92 26 2 89 93 26 2 90 94 26 2 91 95 26 2 92 97 30 2 93 98 30 2 94 99 30 2 95 100 30 2 96 101 30 2 97 102 30 2 98 103 30 2 99 104 30 2 100 105 31 2 101 106 31 2 102 107 31 2 103 108 31 2 104 109 30 2 105 110 30 2 106 111 31 2 107 112 31 2 108 113 31 2 109 114 32 Trout Creek 2 110 115 33 2 111 116 34 2 112 117 34 2 113 118 34 2 114 119 33 2 115 120 32 2 116 121 31 2 117 122 30 2 118 123 29 2 119 127 29 2 120 128 30 Shell Creek 2 121 129 36 Stillwater Creek 2 122 130 36 2 123 138 40 2 124 139 40 Oregon Creek 2 125 140 41 2 126 141 41 West Highway 2 127 142 42 2 128 143 42 East Highway 1 1269.9778269.9778269.9778269.9778269.9778269.9778 1 2269.9778269.9778269.9778269.9778269.9778269.9778 1 3269.9778269.9778269.9778269.9778269.9778269.9778 1 4269.9778269.9778269.9778269.9778269.9778269.9778 1 5269.9778269.9778269.9778269.9778269.9778269.9778 1 6269.9778269.9778269.9778269.9778269.9778269.9778 1 7269.9778269.9778269.9778269.9778269.9778269.9778 1 8 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964

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244 1 9269.9778269.9778269.9778269.9778269.9778269.9778 1 10269.9778269.9778269.9778269.9778269.9778269.9778 1 11269.9778269.9778269.9778269.9778269.9778269.9778 1 12269.9778269.9778269.9778269.9778269.9778269.9778 1 13269.9778269.9778269.9778269.9778269.9778269.9778 1 14269.9778269.9778269.9778269.9778269.9778269.9778 1 15 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978 Alligator 1 16269.9778269.9778269.9778269.9778269.9778269.9778 1 17269.9778269.9778269.9778269.9778269.9778269.9778 1 18269.9778269.9778269.9778269.9778269.9778269.9778 1 19269.9778269.9778269.9778269.9778269.9778269.9778 1 20 53.9956 53.9956 53.9956 53.9956 53.9956 53.9956 1 21269.9778269.9778269.9778269.9778269.9778269.9778 1 22269.9778269.9778269.9778269.9778269.9778269.9778 1 23269.9778269.9778269.9778269.9778269.9778269.9778 1 24269.9778269.9778269.9778269.9778269.9778269.9778 1 25269.9778269.9778269.9778269.9778269.9778269.9778 1 26269.9778269.9778269.9778269.9778269.9778269.9778 1 27269.9778269.9778269.9778269.9778269.9778269.9778 1 28269.9778269.9778269.9778269.9778269.9778269.9778 1 29269.9778269.9778269.9778269.97 78269.9778269.9778 1 30269.9778269.9778269.9778269.9778269.9778269.9778 1 31269.9778269.9778269.9778269.9778269.9778269.9778 1 32 32.3973 32.3973 32.3973 32.3973 32.3973 32.3973 1 33269.9778269.9778269.9778269.9778269.9778269.9778 1 34269.9778269.9778269.9778269.9778269.9778269.9778 1 35 21.5982 21.5982 21.5982 21.5982 21.5982 21.5982 1 36269.9778269.9778269.9778269.9778269.9778269.9778 1 37269.9778269.9778269.9778269.9778269.9778269.9778 1 38269.9778269.9778269.9778269.9778269.9778269.9778 1 39269.9778269.9778269.9778269.9778269.9778269.9778 1 40269.9778269.9778269.9778269.9778269.9778269.9778 1 41269.9778269.9778269.9778269.9778269.9778269.9778 1 42269.9778269.9778269.9778269.9778269.9778269.9778 1 43269.9778269.9778269.9778269.9778269.9778269.9778 1 44269.9778269.9778269.9778269.9778269.9778269.9778 1 45269.9778269.9778269.9778269.9778269.9778269.9778 1 46269.9778269.9778269.9778269.9778269.9778269.9778 1 47269.9778269.9778269.9778269.9778269.9778269.9778 1 48 32.3973 32.3973 32.3973 32.3973 32.3973 32.3973 1 49269.9778269.9778269.9778269.9778269.9778269.9778 1 50269.9778269.9778269.9778269.9778269.9778269.9778 1 51269.9778269.9778269.9778269.9778269.9778269.9778 1 52269.9778269.9778269.9778269.9778269.9778269.9778 1 53269.9778269.9778269.9778269.9778269.9778269.9778 1 54269.9778269.9778269.9778269.9778269.9778269.9778 1 55269.9778269.9778269.9778269.9778269.9778269.9778 1 56269.9778269.9778269.9778269.9778269.9778269.9778 1 57269.9778269.9778269.9778269.9778269.9778269.9778 1 58269.9778269.9778269.9778269.9778269.9778269.9778 1 59269.9778269.9778269.9778269.97 78269.9778269.9778 1 60269.9778269.9778269.9778269.9778269.9778269.9778 1 61269.9778269.9778269.9778269.9778269.9778269.9778 1 62269.9778269.9778269.9778269.9778269.9778269.9778 1 63269.9778269.9778269.9778269.9778269.9778269.9778 1 64269.9778269.9778269.9778269.9778269.9778269.9778 1 65269.9778269.9778269.9778269.9778269.9778269.9778 1 66269.9778269.9778269.9778269.9778269.9778269.9778 1 67269.9778269.9778269.9778269.9778269.9778269.9778 1 68269.9778269.9778269.9778269.9778269.9778269.9778 1 69269.9778269.9778269.9778269.9778269.9778269.9778 1 70269.9778269.9778269.9778269.9778269.9778269.9778 1 71269.9778269.9778269.9778269.9778269.9778269.9778 1 72269.9778269.9778269.9778269.9778269.9778269.9778 1 73269.9778269.9778269.9778269.9778269.9778269.9778 1 74269.9778269.9778269.9778269.9778269.9778269.9778 1 75 18.8984 18.8984 18.8984 18.8984 18.8984 18.8984 Mud Creek 1 76269.9778269.9778269.9778269. 9778269.9778269.9778 1 77269.9778269.9778269.9778269.9778269.9778269.9778 1 78269.9778269.9778269.9778269.9778269.9778269.9778

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245 1 79269.9778269.9778269.9778269.9778269.9778269.9778 1 80269.9778269.9778269.9778269.9778269.9778269.9778 1 81269.9778269.9778269.9778269.9778269.9778269.9778 1 82269.9778269.9778269.9778269.9778269.9778269.9778 1 83269.9778269.9778269.9778269.9778269.9778269.9778 1 84269.9778269.9778269.9778269.9778269.9778269.9778 1 85269.97782 69.9778269.9778269.9778269.9778269.9778 1 86269.9778269.9778269.9778269.9778269.9778269.9778 1 87269.9778269.9778269.9778269.9778269.9778269.9778 1 88269.9778269.9778269.9778269.9778269.9778269.9778 1 89269.9778269.9778269.9778269.9778269.9778269.9778 1 90269.9778269.9778269.9778269.9778269.9778269.9778 1 91269.9778269.9778269.9778269.9778269.9778269.9778 1 92269.9778269.9778269.9778269.9778269.9778269.9778 1 93269.9778269.9778269.9778269.9778269.9778269.9778 1 94269.9778269.9778269.9778269.9778269.9778269.9778 2 1269.9778269.9778269.9778269.9778269.9778269.9778 2 2269.9778269.9778269.9778269.9778269.9778269.9778 2 3269.9778269.9778269.9778269.9778269.9778269.9778 2 4269.977826 9.9778269.9778269.9778269.9778269.9778 2 5269.9778269.9778269.9778269.9778269.9778269.9778 2 6269.9778269.9778269.9778269.9778269.9778269.9778 2 7269.9778269.9778269.9778269.9778269.9778269.9778 2 8269.9778269.9778269.9778269.9778269.9778269.9778 2 9269.9778269.9778269.9778269.9778269.9778269.9778 2 10269.9778269.9778269.9778269.9778269.9778269.9778 2 11269.9778269.9778269.9778269.9778269.9778269.9778 2 12269.9778269.9778269.9778269.9778269.9778269.9778 2 13269.9778269.9778269.9778269.9778269.9778269.9778 2 14269.9778269.9778269.9778269.9778269.9778269.9778 2 15269.9778269.9778269.9778269.9778269.9778269.9778 2 16269.9778269.9778269.9778269.9778269.9778269.9778 2 17269.9778269.9778269.9778269.9778269.9778269.9778 2 18269.9778269.9778269.9778269.9778269.9778269.9778 2 19269.9778269.9778269.9778269.9778269.9778269.9778 2 20269.9778269.9778269.9778269.9778269.9778269.9778 2 21269.9778269.9778269.9778269.97 78269.9778269.9778 2 22269.9778269.9778269.9778269.9778269.9778269.9778 2 23 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964 2 24269.9778269.9778269.9778269.9778269.9778269.9778 2 25269.9778269.9778269.9778269.9778269.9778269.9778 2 26269.9778269.9778269.9778269.9778269.9778269.9778 2 27269.9778269.9778269.9778269.9778269.9778269.9778 2 28269.9778269.9778269.9778269.9778269.9778269.9778 2 29 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964 2 30269.9778269.9778269.9778269.9778269.9778269.9778 2 31269.9778269.9778269.9778269.9778269.9778269.9778 2 32269.9778269.9778269.9778269.9778269.9778269.9778 2 33269.9778269.9778269.9778269.9778269.9778269.9778 2 34269.9778269.9778269.9778269.9778269.9778269.9778 2 35 43.1964 43.1964 43.1964 43.1964 43.1964 43.1964 2 36269.9778269.9778269.9778269.9778269.9778269.9778 2 37269.9778269.9778269.9778269.9778269.9778269.9778 2 38269.9778269.9778269.9778269.9778269.9778269.9778 2 39269.9778269.9778269.9778269.9778269.9778269.9778 2 40269.9778269.9778269.9778269.9778269.9778269.9778 2 41269.9778269.9778269.9778269.9778269.9778269.9778 2 42269.9778269.9778269.9778269.9778269.9778269.9778 2 43269.9778269.9778269.9778269.9778269.9778269.9778 2 44269.9778269.9778269.9778269.9778269.9778269.9778 2 45269.9778269.9778269.9778269.9778269.9778269.9778 2 46269.9778269.9778269.9778269.9778269.9778269.9778 2 47 37.1219 3 7.1219 37.1219 37.1219 37.1219 37.1219 McCormick Creek 2 48269.9778269.9778269.9778269.9778269.9778269.9778 2 49269.9778269.9778269.9778269.9778269.9778269.9778 2 50269.9778269.9778269.9778269.9778269.9778269.9778 2 51269.9778269.9778269.9778269.9778269.9778269.9778 2 52 18.8984 18.8984 18.8984 18.8984 18.8984 18.8984 2 53269.9778269.9778269.9778269.9778269.9778269.9778 2 54269.9778269.9778269.9778269.9778269.9778269.9778

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246 2 55269.9778269.9778269.9 778269.9778269.9778269.9778 2 56269.9778269.9778269.9778269.9778269.9778269.9778 2 57269.9778269.9778269.9778269.9778269.9778269.9778 2 58269.9778269.9778269.9778269.9778269.9778269.9778 2 59269.9778269.9778269.9778269.9778269.9778269.9778 2 60269.9778269.9778269.9778269.9778269.9778269.9778 2 61269.9778269.9778269.9778269.9778269.9778269.9778 2 62269.9778269.9778269.9778269.9778269.9778269.9778 2 63269.9778269.9778269.9778269.9778269.9778269.9778 2 64269.9778269.9778269.9778269.9778269.9778269.9778 2 65269.9778269.9778269.9778269.9778269.9778269.9778 2 66269.9778269.9778269.9778269.9778269.9778269.9778 2 67809.9334809.9334809.9334809.9334809.9334809.9334 2 68269.9778269.9778269.9778269.9778269.9778269.9778 2 69269.9778269.9778269.9778269.9778269.9778269.9778 2 70269.9778269.9778269.9778269.9778269.9778269.9778 2 71269.9778269.9778269.9778269.9778269.9778269.9778 2 72269.9778269.9778269.9778269.9778269.9778269.9778 2 73269.9778269.9778269.9778269.9778269.9778269.9778 2 74 11.8790 11.8790 11.8790 11.8790 11.8790 11.8790 Taylor River 2 75269.9778269.9778269.9778269.9778269.9778269.9778 2 76269.9778269.9778269.9778269.9778269.9778269.9778 2 77269.9778269.9778269.9778269.9778269.9778269.9778 2 78269.9778269.9778269.9778269.9778269.9778269.9778 2 79269.9778269.9778269.9778269.9778269.9778269.9778 2 80269. 9778269.9778269.9778269.9778269.9778269.9778 2 81 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978 East Creek 2 82269.9778269.9778269.9778269.9778269.9778269.9778 2 83269.9778269.9778269.9778269.9778269.9778269.9778 2 84 269.9778269.9778269.9778269.9778269.9778269.9778 2 85269.9778269.9778269.9778269.9778269.9778269.9778 2 86269.9778269.9778269.9778269.9778269.9778269.9778 2 87269.9778269.9778269.9778269.9778269.9778269.9778 2 88269.9778269.9778269. 9778269.9778269.9778269.9778 2 89269.9778269.9778269.9778269.9778269.9778269.9778 2 90269.9778269.9778269.9778269.9778269.9778269.9778 2 91269.9778269.9778269.9778269.9778269.9778269.9778 2 92269.9778269.9778269.9778269.9778269.9778269.9778 2 93269.9778269.9778269.9778269.9778269.9778269.9778 2 94269.9778269.9778269.9778269.9778269.9778269.9778 2 95269.9778269.9778269.9778269.9778269.9778269.9778 2 96269.9778269.9778269.9778269.9778269.9778269.9778 2 97269.9778269.9778269.9778269.9778269.9778269.9778 2 98269.9778269.9778269.9778269.9778269.9778269.9778 2 99269.9778269.9778269.9778269.9778269.9778269.9778 2 100269.9778269.9778269.9778269.9778269.9778269.9778 2 101269.9778269.9778269.9778269.9778269.9778269.9778 2 102269.9778269.9778269.9778269.9778269.9778269.9778 2 103269.9778269.9778269.9778269.9778269.9778269.9778 2 104269.9778269.9778269.9778269.9778269.9778269.9778 2 105269.9778269.9778269.9778269.9778269.9778269.9778 2 106269.9778269.9778269.9778269.9778269.9778269.9778 2 107269.9778269.9778269.9778269.9778269.9778269.9778 2 108269.9778269.9778269.9778269.9778269.9778269.9778 2 109 40.4967 40.4967 40.4967 40.4967 40.4967 40.4967 Trout Creek 2 110269.9778269.9778269.9778269.9778269.9778269.9778 2 111269.9778269.9778269.9778269.9778269.9778269.9778 2 112269.9778269.9778269.9778269.9778269.9778269.9778 2 113269.9778269.9778269.9778269.9778269.9778269.9778 2 114269.9778269.9778269.9778269.9778269.9778269.9778 2 115269.9778269.9778269.9778269.9778269.9778269.9778 2 116269.9778269.9778269.9778269.9778269.9778269.9778 2 117269.9778269.9778269.9778269.9778269.9778269.9 778 2 118269.9778269.9778269.9778269.9778269.9778269.9778 2 119269.9778269.9778269.9778269.9778269.9778269.9778 2 120 10.7991 10.7991 10.7991 10.7991 10.7991 10.7991 Shell Creek 2 121 16.1987 16.1987 16.1987 16.1987 16.1987 16.1987 Stllwater Creek 2 122269.9778269.9778269.9778269.9778269.9778269.9778 2 123269.9778269.9778269.9778269.9778269.9778269.9778 2 124 8.0993 8.0993 8.0993 8.0993 8.0993 8.0993 Orgeon Creek

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247 2 125269.9778269.9778269.9778269.9778269.9778269.9778 2 126 56.6953 56.6953 56.6953 56.6953 56.6953 56.6953 West Highway Creek 2 127269.9778269.9778269.9778269.9778269.9778269.9778 2 128 26.9978 26.9978 26.9978 26.9978 26.9978 26.9978 East Highway Creek 1 1 0.12 10. 1.0 RS11 Bar Init 1 2 0.03 10. 1.0 1 3 0.12 10. 1.0 1 4 0.03 10. 1.0 1 5 0.12 10. 1.0 1 6 0.03 10. 1.0 1 7 0.12 10. 1.0 1 8 1.52 10. 0.08 1 9 0.12 10. 1.0 1 10 0.03 10. 1.0 1 11 0.12 10. 1.0 1 12 0.12 10. 1.0 1 13 0.03 10. 1.0 1 14 0.12 10. 1.0 1 15 1.52 10. 0.05 Alligator Creek 1 16 0.03 10. 1.0 1 17 0.12 10. 1.0 1 18 0.03 10. 1.0 1 19 0.12 10. 1.0 1 20 1.52 10. 0.080 1 21 0.03 10. 1.0 1 22 0.12 10. 1.0 1 23 0.03 10. 1.0 1 24 0.12 10. 1.0 1 25 0.03 10. 1.0 1 26 0.12 10. 1.0 1 27 0.03 10. 1.0 1 28 0.12 10. 1.0 1 29 0.03 10. 1.0 1 30 0.12 10. 1.0 1 31 0.03 10. 1.0 1 32 1.52 10. 0.080 1 33 0.12 10. 1.0 1 34 0.03 10. 1.0 1 35 1.52 10. 0.080 1 36 0.03 10. 1.0 1 37 0.12 10. 1.0 1 38 0.03 10. 1.0 1 39 0.12 10. 1.0 1 40 0.03 10. 1.0 1 41 0.12 10. 1.0 1 42 0.03 10. 1.0 1 43 0.12 10. 1.0 1 44 0.03 10. 1.0 1 45 0.01 10. 1.0 1 46 0.15 10. 1.0 1 47 0.30 10. 1.0 1 48 1.52 10. 0.080 1 49 0.15 10. 1.0 1 50 0.30 10. 1.0 1 51 0.15 10. 1.0 1 52 0.30 10. 1.0 1 53 0.15 10. 1.0 1 54 0.30 10. 1.0 1 55 0.30 10. 1.0 1 56 0.30 10. 1.0 1 57 0.30 10. 1.0 1 58 0.30 10. 1.0 1 59 0.30 10. 1.0 1 60 0.30 10. 1.0 1 61 0.30 10. 1.0 1 62 0.30 10. 1.0 1 63 0.30 10. 1.0 1 64 0.30 10. 1.0 1 65 0.30 10. 1.0 1 66 0.30 10. 1.0

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248 1 67 0.30 10. 1.0 1 68 0.30 10. 1.0 1 69 0.30 10. 1.0 1 70 0.30 10. 1.0 1 71 0.3 0 10. 1.0 1 72 0.30 10. 1.0 1 73 0.30 10. 1.0 1 74 0.30 10. 1.0 1 75 1.52 10. 0.040 Mud Creek 1 76 0.30 10. 1.0 1 77 0.30 10. 1.0 1 78 0.30 10. 1.0 1 79 0.30 10. 1.0 1 80 0.30 10. 1.0 1 81 0.30 10. 1.0 1 82 0.15 10. 1.0 1 83 0.30 10. 1.0 1 84 0.15 10. 1.0 1 85 0.30 10. 1.0 1 86 0.15 10. 1.0 1 87 0.30 10. 1.0 1 88 0.15 10. 1.0 1 89 0.30 10. 1.0 1 90 0.15 10. 1.0 1 91 0.30 10. 1.0 1 92 0.15 10. 1.0 1 93 0.30 10. 1.0 1 94 0.15 10. 1.0 2 1 1.22 10. 1.0 2 2 1.22 10. 1.0 2 3 1.22 10. 1.0 2 4 1.22 10. 1.0 2 5 1.22 10. 1.0 2 6 1.0 10. 1.0 2 7 0.30 10. 1.0 2 8 0.03 10. 1.0 2 9 0.12 10. 1.0 2 10 0.03 10. 1.0 2 11 0.12 10. 1.0 2 12 0.03 10. 1.0 2 13 0.12 10. 1.0 2 14 0.03 10. 1.0 2 15 0.12 10. 1.0 2 16 0.03 10. 1.0 2 17 0.12 10. 1.0 2 18 0.03 10. 1.0 2 19 0.12 10. 1.0 2 20 0.03 10. 1.0 2 21 0.12 10. 1.0 2 22 0.03 10. 1.0 2 23 1.52 10. 0.080 2 24 0.12 10. 1.0 2 25 0.03 10. 1.0 2 26 0.12 10. 1.0 2 27 0.03 10. 1.0 2 28 0.12 10. 1.0 2 29 1.52 10. 0.080 2 30 0.03 10. 1.0 2 31 0.12 10. 1.0 2 32 0.03 10. 1.0 2 33 0.12 10. 1.0 2 34 0.03 10. 1.0 2 35 1.52 10. 0.080 2 36 0.12 10. 1.0 2 37 0.03 10. 1.0 2 38 0.12 10. 1.0 2 39 0.03 10. 1.0 2 40 0.12 10. 1.0 2 41 0.03 10. 1.0 2 42 0.12 10. 1.0

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249 2 43 0.03 10. 1.0 2 44 0.12 10. 1.0 2 45 0.03 10. 1.0 2 46 0.12 10. 1.0 2 47 1.52 10. 0.055 McCormick 2 48 0.03 10. 1.0 2 49 0.12 10. 1.0 2 50 0.03 10. 1.0 2 51 0.12 10. 1.0 2 52 1.52 10. 0.020 2 53 0.12 10. 1.0 2 54 0.03 10. 1.0 2 55 0.12 10. 1.0 2 56 0.03 10. 1.0 2 57 0.12 10. 1.0 2 58 0.03 10. 1.0 2 59 0.3 10. 1.0 2 60 0.15 10. 1.0 2 61 0.30 10. 1.0 2 62 0.15 10. 1.0 2 63 0.30 10. 1.0 2 64 0.15 10. 1.0 2 65 0.30 10. 1.0 2 66 0.15 10. 1.0 2 67 0.30 10. 1.0 2 68 0.30 10. 1.0 2 69 0.30 10. 1.0 2 70 0.30 10. 1.0 2 71 0.30 10. 1.0 2 72 0.30 10. 1.0 2 73 0.30 10. 1.0 2 74 1.52 10. 0.022 Taylor 2 75 0.30 10. 1.0 2 76 0.30 10. 1.0 2 77 0.30 10. 1.0 2 78 0.30 10. 1.0 2 79 0.30 10. 1.0 2 80 0.30 10. 1.0 2 81 1.52 10. 0.040 East 2 82 0.30 10. 1.0 2 83 0.30 10. 1.0 2 84 0.30 10. 1.0 2 85 0.30 10. 1. 0 2 86 0.30 10. 1.0 2 87 0.30 10. 1.0 2 88 0.30 10. 1.0 2 89 0.30 10. 1.0 2 90 0.30 10. 1.0 2 91 0.30 10. 1.0 2 92 0.30 10. 1.0 2 93 0.30 10. 1.0 2 94 0.30 10. 1.0 2 95 0.30 10. 1.0 2 96 0.15 10. 1.0 2 97 0.30 10. 1.0 2 98 0. 15 10. 1.0 2 99 0.30 10. 1.0 2 100 0.15 10. 1.0 2 101 0.30 10. 1.0 2 102 0.15 10. 1.0 2 103 0.30 10. 1.0 2 104 0.15 10. 1.0 2 105 0.30 10. 1.0 2 106 0.15 10. 1.0 2 107 0.30 10. 1.0 2 108 0.15 10. 1.0 2 109 1.52 10. 0.120 Trout Creek 2 110 0.30 10. 1.0 2 111 0.15 10. 1.0 2 112 0.30 10. 1.0

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250 2 113 0.15 10. 1.0 2 114 0.30 10. 1.0 2 115 0.15 10. 1.0 2 116 0.30 10. 1.0 2 117 0.15 10. 1.0 2 118 0.30 10. 1.0 2 119 0.1 10. 1.0 2 120 1.52 10. 0.020 Shell Creek 2 121 1.52 10. 0.030 Stillwater Creek 2 122 0.1 10. 1.0 2 123 0.1 10. 1.0 2 124 1.52 10. 0.015 Oregon Creek 2 125 0.1 10. 1.0 2 126 1.52 10. 0.070 W est Highway Creek 2 127 0.1 10. 1.0 2 128 1.52 10. 0.050 East Highway Creek 1 5 1 15 1 2 0 60.0SOUTHWEST SHORE SOUTHWEST CORNER RS12_1 2 8 2 1 78 1 0 60.0SOUTHWEST CORNER SOUTH OF TAYLOR RS12_2 3 8 79 1137 1 0 60.0SOUTH OF TAYLOR SOUTHEAST CORNER RS12_3 4 7144 40144 38 0 60.0CULVERTS AT US 1 RS12_4 5 7118 69118 85 0 60.0GW INTERACTION WITH C 111 RS12_5 6 5 25 44 25 69 0 60.0CULVERTS ON WEST SIDE RS12_6 7 6 30 72 47 72 0 60.0FROM P46 TO CY3 RS12_7 8 6 48 72 68 72 0 60.0FROM CY3 TO P67 RS12_8 1 0.200 15.0 40.0 0.0182 RS13_1 2 0.200 15.0 40.0 0.0143 RS13_2 3 0.200 15.0 40.0 0.0048 RS13_3 4 0.200 15.0 3.6 0.0064 RS13_4 5 0.200 15.0 0.0 0.0053 RS13_5 6 0.200 15.0 0.0 0.004 RS13_6 7 0.200 15.0 0.0 0.004 RS13_7 8 0.200 15.0 0.0 0.004 RS13_8 1 0.200 15.0 40.0 0.0182 RS14_1 2 0.200 15.0 40.0 0.0143 RS14_2 3 0.200 15.0 40.0 0.0048 RS14_3 4 0.200 15.0 3.6 0.0064 RS14_4 5 0.200 15.0 0.0 0.0053 RS14_5 6 0.200 15.0 0.0 0.004 RS14_6 7 0.200 15.0 0.0 0.004 RS14_7 8 0.200 15.0 0.0 0.004 RS14_8 1 5.01 salinity RS20_1 2 0.005 TP:TSB water mg/L=g/m3=ppm RS20_2 1 RS21_1 2 RS21_2 1 0.01 0.10 0.20 0.5 1.0 2.0 5.0 RS22_1 2 0.01 0.10 0.20 0.5 1.0 2.0 5.0 RS22_2 0.01 0.10 0.20 0.5 1.0 2.0 5.0 RS23 1.0 2.0 5. 10. 50. 100. 200. 500. 1000. RS24 0.5 0.2 0.1 0.05 0.001 0.1 0.2 0.5 1.0 RS25 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.2 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.7 0.9 1.0 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.4 1.5 1.2 1.0 0.8 0.6 0.8 1.0 1.2 1.5 1.4 1.4 1.3 1.2 1.2 1.2 1.2 0.9 0.8 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.9 1.0 1.1 1.2 1.4 1.5 1.7 1.8 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2. 0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2 .0 2.0 2.0 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.3 1.2 1.0 0.9 0.8 0.7 0.6 0.5 0.7 0.9 0.9 1.0 1.1 1.1 1.2 1.2 1.2 1.2 1.3 1. 4 1.2 0.9 0.7 0.6 1.3 1.3 1.5 1.5 1.4 1.4 1.3 1.2 1.2 1.2 1.0 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.8 0.9 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.9 1.9 1.8 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 0.1 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 0.9 0.9 1.0 1.0 1.1 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.7 0.8 0.8 0.7 1.0 1.1 1.1 1.1 1.1 1.2 1.4 1.3 1.3 1.0 0.7 0.6 1.0 1.0 1.0 1.0 1.1 1.0 0.9 0.8 0.7 1.0 1.0 0.9 0.8 0.8 0.8 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.8 1.8 1.7 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9

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0.2 0.2 0.1 0.1 0.1 0.1 0.2 0.3 0.3 0.3 0.6 0.6 0.6 0.6 1.5 1.5 1.5 1.5 1.5 1.5 0.1 1.5 1.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.7 0.8 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.9 0.0 0.2 0.5 0.2 0.4 0.4 0.5 0.3 0.4 0.4 0.3 0.1 0.2 0.2 0.2 0.2 0.1 0.1 0.9 0.1 0.1 0.1 0.1 0.0 0.1 0.1 0.0 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1. 4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.3 0.3 0.2 0.1 0.1 0.0 0.0 0.1 0.1 0.2 0.1 0.0 0.0 0.3 0.6 0.6 0.6 0.6 0.6 0.6 0.1 0.3 0.4 0.1 0.0 1.5 1.5 0.1 0.0 0.0 0.1 0.1 0.9 0.9 0.9 0.9 1.5 1.5 1.5 1.5 0.9 0.9 1.5 1. 2 0.9 0.1 0.0 0.5 0.6 0.5 0.5 0.4 0.4 0.4 0.5 0.7 0.5 0.5 0.4 0.4 0.2 0.1 0.1 1.0 1.0 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.2 0.1 0.1 0.1 0.1 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.2 1.2 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 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0.4 0.3 0.2 0.2 0.4 0.4 0.2 0.2 0.2 0.1 0.0 0.1 0.1 1.0 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.3 1.2 1 .2 1.1 1.1 1.0 0.0 0.1 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.0 1.0 1.0 1.1 1.2 1.2 1.2 1.2 1.2 0.5 0.4 0.4 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 99.9 99.9 99.9 99.9 99.9 99.9 99.9 99.9 0.2 0.1 0.1 0.1 0.1 0.0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.1 0.0 0.1 0.2 0.2 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.0 0.0 0.1 0.1 0.1 0.9 0.1 0.1 1.0 1.0 0.9 0.9 0.2 0.1 0.3 0.3 0.3 0.4 0.5 0.2 0.2 0.1 0.1 0.4 0.3 0.1 0.0 0.0 0.2 0.4 0.2 0.1 1.2 1.2 1.2 1.5 1.5 1.2 1.3 1.3 1. 3 1.3 1.3 1.3 1.3 1.3 1.2 0.2 0.2 1.0 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.3 0.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.0 99.9 99.9 99.9 99.9 99.9 99.9 99.9 0.1 0.1 0.1 0.0 0.1 0.1 0. 1 0.1 0.1 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.0 0.0 0.1 0.3 0.2 0.1 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 0.0 0.1 0.1 0.1 0.2 0.2 0.1 0.0 0.1 0.1 0.1 0.0 0.1 0.1 1.0 1.0 0.9 0.9 0.9 0.2 0.3 0.2 0.5 0.5 0.3 0.3 0.2 0.2 0.3 0.5 0.7 0.5 0.3 0.0 0.2 0.2 0.2 0.2 0.1 0.1 0.9 0.0 1.5 1.5 1.1 1.2 1.3 1.3 1.4 1.4 1.3 1.3 1.2 1.2 1.1 0.4 0.4 0.3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.1 1.0 1.0 1.0 1.0 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 0.4 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 99.9 99.9 99.9 99.9 99.9 99.9 99.9 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.1 0.0 0.0 0.1 0.1 0.1 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.0 0.0 1.5 1.5 0.1 0.0 1.5 1.5 0.9 0.7 0.1 0.1 0.1 0.1 0.1 0.1 0.9 0.9 0.1 0.1 0.1 0.0 0.1 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.2 0.2 0.2 0.2 0.3 0.4 0.4 0.2 0.4 0.2 0.2 0.2 0.4 0.5 0.5 0.5 0.4 0.2 0.3 0.4 0.2 0.2 0.2 0.2 0.2 1.5 1.5 0.1 0.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 1.1 1.1 0.2 0.9 0.9 0.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 1.0 1.0 1.0 1.0 1.0 1.1 1.0 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