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Title: Development, testing, and sensitivity and uncertainty analyses of a transport and reaction simulation engine (TaRSE) for spatially distributed modelin
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Title: Development, testing, and sensitivity and uncertainty analyses of a transport and reaction simulation engine (TaRSE) for spatially distributed modelin
Alternate Title: Scientific investigations report - United States Geological Survey ; 2008-5029
Physical Description: Book
Language: English
Creator: Jawitz, James W.
Munoz-Carpena, Rafael
Muller, Stuart
Grace, Kevin A.
James, Andrew I.
Publisher: Florida Integrated Science Center, United States Geological Survey
Place of Publication: Ft. Lauderdale, Fla.
Publication Date: 2008
Copyright Date: 2008
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Volume ID: VID00001
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Table of Contents
    Title Page
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    Copyright
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    Table of Contents
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    Front Matter
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Full Text





Development, Testing, and Sensitivity
and Uncertainty Analyses of a Transport
and Reaction Simulation Engine (TaRSE)
for Spatially Distributed Modeling of
Phosphorus in the Peat Marsh Wetlands of
Southern Florida

By James W. Jawitz, Rafael Munoz-Carpena, Stuart Muller, Kevin A. Grace,
and Andrew I. James











Prepared in Cooperation with the South Florida Water Management District





Scientific Investigations Report 2008-5029


U.S. Department of the Interior
U.S. Geological Survey













U.S. Department of the Interior
DIRK KEMPTHORNE, Secretary

U.S. Geological Survey
Mark D. Myers, Director




U.S. Geological Survey, Reston, Virginia: 2008







For product and ordering information:
World Wide Web: http://www.usgs.gov/pubprod
Telephone: 1-888-ASK-USGS





For more information on the USGS--the Federal source for science about the Earth, its natural and living resources,
natural hazards, and the environment:
World Wide Web: http://www.usgs.gov
Telephone: 1-888-ASK-USGS



Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the
U.S. Government.
Although this report is in the public domain, permission must be secured from the individual copyright owners to
reproduce any copyrighted materials contained within this report.
Suggested citation:
Jawitz, J.W., Munoz-Carpena, Rafael, Muller, Stuart, Grace, K.A., and 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 the Peat Marsh Wetlands of Southern Florida: U.S. Geological Survey Scientific Investiga-
tions Report 2008-5029, 109 p.







iii





Contents


A bstra ct ........... ........... ....................................................... 1
Intro d u action .... . .............. ....................................................................................................................... 2
Purpose and Scope .............................................................. . . 3
D description of S tudy A rea .................................................................... 3
P rev io us S tu d ies .......................... ...... ....................................3
Acknowledgments .................... ................................5
M odel Conceptualization.......................................................5
M o d e l N o ta tio n ........................................................................... ......................... .... ... . . 5
S to re s ................. .............................................................. 5
Biom ass ....... . ................................................5
W after C o lu m n ...... . ........... ....................................................................... ....... ............. 9
S o il..... . . .............. ... .............................. ................................................ ............ . . 9
Physical and Biological Transfer M echanism s ........................................ .................... 10
Physical Transfer Processes ..................... ...... ................... 10
W a te r F lo w s ....................................................................................................................... 1 0
Atmospheric Deposition ........................................ 10
Pore-water/Surface-W ater Transfer............................ ... .. .................. 11
Settling and Entrainment of Particulate M aterial............................ ................. 11
Sloughing and Cohesion of Biofilm ................................................. 13
S o rp tio n / D e s o rp tio n .................................................................................................. 13
M in e ral P re c ipitatio n ............................................................ 13
Biological Transfer Processes..............................................14
Grow th of Biological Tissues ...................................................14
Senescence and Decay of Biological Tissues......................... .. .............. 14
Soil Oxidation and M ineralization and Burial................................. ...................15
Feedbacks and External Environmental Factors ............................ ............ 15
Lig ht Lim itatio n ......................... ....................................... ........................... 16
T e m p e ra tu re E ffe c ts .................................................................................................................. 1 6
Vegetation Effects on Flow Restriction .......................... ........ ......... 16
R ea ctio n E qu atio ns .... . ............ ....................................... ...................... .... ........ 17
M odel C alibration and V alidation .........................................................19
Level 1-Soil Cores ..... ....................................... 19
Level 2-O outdoor M esocosm s .................................................................21
Level 3- Stormw ater Treatm ent Area-1W Cell 4 ............................... ................................. 22
G lo b a l S e n s itiv ity A n a ly s is .................................................................................................................. 3 1
Techniques and Screening M ethods...................................................31
M orris M ethod ..... . .......... ...........................................32
Extended Fourier Amplitude Sensitivity Test (FAST) .................. ...32
Effects of Changing Model Structure and Flow Velocity on Global Model
O utput S e nsitiv ity ............................................................ 33
A n a ly s is P ro c e d u re ............................................................................................................ 3 3
Flo w D o m a in ..................................................................3 3













D description of Inputs and O utputs ........................................................ .................. . 34
M o rris M eth o d R esu lts ....................................................... ............ .... .... ..... .......35
S screening of P aram eters .............................................................. ...... . .......... 47
R a n king of P a ra m ete rs .................................................................. ............... . ..... 48
Effect of Flow V velocity .......................................................................... .................. .... 48
Effect of M odel Com plexity ........................................................... .... ......... ...... 48
Extended Fourier Amplitude Sensitivity Test (FAST) Results..................... ............49
Surface-Water Soluble Reactive Phosphorus (CswP]o,t) Case Study.....................49
General Trends Observed in Sensitivity Dynamics ....................................59
Analysis and Assessment of Model Uncertainty from Fourier Amplitude Sensitivity
T est (FA S T ) S im u latio ns ................................................................. .... .... ........... ... .. 60
Level-1 U nc erta inty.............. ....... ................ .... .... ........... .............. ...................... 60
Level-2 Uncertainty ..... .............................. ...................... ....... ....... . ..... 61
Level-3 U nc erta inty.............. ....... ................... . ..... ........... .............. ...................... 67
S u m m a ry a n d C o n c lu s io n s ........................................................ .... ..................... ....... .... ................ .... 68
R efe re n c e s C ite d ..... . ............ .......... ..... ................................................................. 7 0
A appendix 1: M odel N om enclature Used in this Study......................................... ...........................78
Appendix 2: Model Parameter Values for Levels 1, 2, and 3...............................................81
Appendix 3: Equations and XML Input Files for Complexity Levels 1,2, and 3................................ 84
Appendix 4: Fourier Amplitude Sensitivity Test (FAST) for Additional Model Outputs.................106



Figures

1. Map of study area, including Cell 4, Stormwater Treatment Area-1W (STA-1W) ................4
2-4. Diagrams showing:
2. W ater flow s considered in the conceptual m odel ........................... ......................... 6
3. M material flow s considered in the conceptual m odel....................... .........................7
4. Phosphorus flows considered in the conceptual model.................... ... .............. 8
5-10. Graphs showing:
5. Measured water column soluble reactive phosphorus concentrations compared
to model level-1 predictions, including a range of bioturbation factors, and
simulated changes in soil phosphorus storage and pore-water soluble
re a c tiv e p h o s p h o ru s ................... .. ........................ ........................................ 2 1
6. Comparison between observed and simulated water column particulate
phosphorus and soluble reactive phosphorus concentrations for
le v e l-2 s im u la tio n s ....................... .. ..... ... .... .... .... ....... ..... ..... .... .....................2 3
7. Comparison of cumulative phosphorus removal from South Florida Water
Management District water sampling of inflow and outflow waters in Cell 4,
to the phosphorus removal predicted by the model ...................... ..... .............. 25
8. Hydraulic loading rate to Cell 4 for the February 1995 to June 2000
period, relative to the mean hydraulic loading rate applied during level-3 calibration.. 25
9. Measured and predicted change in soil phosphorus storage over time
in the inflow and outflow region of Cell 4, as determined from soil phosphorus
content and bulk density measurements of the newly accrued soil material........... 25
10. Effect of initial biomass on particulate phosphorus and pore-water concentrations
in the calibrated m odel ......................................................................................................... 26













11. Aerial photograph of the modeled Stormwater Treatment Area 1W (STA-1W), Cell 4,
including elevations within the cell, and the model mesh ................... .................... 27
12. Time-series plot showing measured inflow and outflow of total phosphorus, and ...............
simulated outflow from Cell 4 from 1995 to 1997 ................... ... .............. .........28
13. Time-series plot showing measured inflow and outflow of total phosphorus, and ...............
simulated outflow from Cell 4 from 1998 to 2000 .................... .. ... .............. .........28
14. Map showing accumulated total soil phosphorus from samples collected at the end
o f 2 0 0 0 .............................................. .. .... ......... ..... ...... .. ................................ . 2 9
15. Map showing estimated accumulated soil phosphorus at the end of 2000.......................30
16-19. Diagrams showing:
16. Testing dom ain for global sensitivity ................ .... ........................... ................ 34
17. Conceptual m odel for com plexity level 1 ......................................... ...... ............. 35
18. Conceptual m odel for com plexity level 2 ......................................... ...... ............. 36
19. Conceptual model for complexity level 3 .................. ......... ............... 36
20-25. Graphs showing Morris method global sensitivity analysis results for:
20. Surface-water soluble reactive phosphorus outflow (CswP]o,tf) across complexity
levels and velocities tested ........................... ..... ....... .... .... ................. .. 42
21. Soil pore-water soluble reactive phosphorus variation (CpwP]acr) across
complexity levels and velocities tested .................................................... 43
22. Organic soil accretion (So]acr) across complexity levels and velocities tested......44
23. Soil adsorbed phosphorus variation (SsiP]acr) across complexity levels and
velocities tested ............................................... ....................... 45
24. Plankton biomass outflow (Csw'l]o,tf) across complexity levels and velocities
te s te d .......... ......... ............ .. ............ ................................. ...... . . 4 6
25. Macrophyte biomass accumulation (Cmp]acr)across complexity levels and
velocities tested .. ......................... ..................... ............................. 47
26-31. Graphs showing Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis
results for:
26. Surface-water soluble reactive phospho\rus outflow (CswP]o,tf) across complexity
levels and velocities tested ............................................................. ................... 54
27. Soil pore-water soluble reactive phosphorus variation (CpwP]acr) across
complexity levels and velocities tested ................................................................ 55
28. Organic soil accretion (So]acr) across complexity levels and velocities tested...... 56
29. Soil adsorbed phosphorus variation (Ssip]acr) across complexity levels and
velocities tested .................................. .. ................... 57
30. Plankton biomass outflow (Csw'l]o,tf) across complexity levels and velocities ..........
test d ............................. .. ................................ ................. . . . 5 8
31. Macrophyte biomass accumulation (CmP]acr) across complexity levels and
velocities tested ................................. .............. ...... 58
32-34. Graphs showing probability distributions for:
32. Level-1 outputs obtained from the global analysis of uncertainty based on
Fourier Amplitude Sensitivity Test (FAST) results ........................... ............ 61
33. Level-2 outputs obtained from the global analysis of uncertainty based on
Fourier Amplitude Sensitivity Test (FAST) results ............................ ............. 63
34. Level-3 outputs obtained from the global analysis of uncertainty based on
Fourier Amplitude Sensitivity Test (FAST) results ......................... ............ 64













Tables

1. Initial conditions and calibrated parameter values for level-1 model application..............20
2. Initial conditions and calibrated parameter values for level-2 high phosphorus
m o d e l a p p lic a tio n ........................................ ... .......... ....... ...... .................................... .... 2 2
3. Initial conditions and calibrated and algae parameter values for level-3 field-scale
m o d e l a p p lic a tio n ........................................ .. ................................... ........... ..................... 2 4
4. Parameters used in the global sensibility and uncertainty analyses, including
probability distribution functions and parameter use in levels 1 to 3..................................37
5. Fixed model inputs used in the global sensitivity and uncertainty analyses .....................38
6. Model outputs used in the global sensitivity and uncertainty analyses......................... 38
7. Regional Simulation Model/Water Quality Model (RSM/WQ) simulations run in the
global sensitivity and uncertainty analyses.................... ... ............. .............38
8-13. Morris method global sensitivity analysis parameter ranking for the:
8. Surface-water soluble reactive phosphorus outflow outputs................................... 39
9. Pore-water soluble reactive phosphorus variation output....................................... 39
10. O rg an ic so il a cc retio n o utput............................................................. ................. .. .. 4 0
11. Soil adsorbed phosphorus variation output............................ ..................40
12 P la n kto n bio m ass o utflow o utputs ................................................... ...........................4 1
13. M acrophyte biom ass accum ulation output.................................... ..........................41
14-19. Fourier Amplitude Sensitivity Test (FAST) results for the:
14. Surface-water soluble reactive phosphorus outflow outputs................................... 50
15. Pore-water soluble reactive phosphorus variation output...................................... 51
16 O rg a n ic s o il a c c re tio n o u tp u t..................................................... ............... ............ 5 1
17. Soil adsorbed phosphorus variation output .................................... .......................... 52
18. P lankton biom ass o utflow outputs ................................................... ..... .............. 53
19. M acrophyte biom ass accum ulation output.................................... ................... 53
20. Summary statistics for output probability distributions.................... ................... 65
Al. Symbols and notations used to describe formulations of the model ..................................78
A2. Chem ical and m material com ponents used in the m odel..........................................................79
A 3 P a ra m ete rs use d in th e m o d el ............................................................... .... .... ..... .......80















Conversion Factors

Multiply
micrometer (Rm)
centimeter (cm)
meter (m)
kilometer (km)
square meter (m2)
hectare (ha)
square kilometer (km2)
centimeter per second (cm/s)
centimeter per day (cm/d)
meter per second (m/s)
meter per square second (m/s2)
square meter per second (m2/s)
meter per day (m/d)
meter per year (miyr)
gram per square meter (, :1- I
gram per square meter per day g/m2/d
gram per square meter per second g/m2/s
gram per cubic centimeter I
gram per cubic meter (. 1- I


By
0.03937
0.3937
3.281
0.6214
0.0002471
2.471
247.1
0.3937
0.3937
3.281
3.281
10.76
3.281
3.281
10.76
10.76
10.76
62.4220
35.32


To Obtain
inch
inch
foot
mile
acre
acre
acre
inch per second
inch per day
foot per second
foot per square second
square foot per second
foot per day
foot per year
gram per square foot
gram per square foot per day
gram per square foot per second
pound per cubic foot
gram per cubic foot


Abbreviations and Acronyms


CDF cumulative distribution function
EAA Everglades Agricultural Area
FAST Fourier Amplitude Sensitivity Test
DMSTA Dynamic Stormwater Treatment Area Design Model
DOM dissolved organic matter
HRT hydraulic retention time
HSE hydrologic simulation engine
OAT one parameter at a time
PDF probabilistic distribution function
PNG pseudorandom number generation
PP particulate phosphorus
r-LHS replicated Latin hypercube sampling
RSM Regional Simulation Model
RSM/WQ Regional Simulation Model/Water Quality Model
SAV submerged aquatic vegetation
SFWMD South Florida Water Management District
SRP soluble reactive phosphorus
STA stormwater treatment area
TaRSE Transport and Reaction Simulation Engine
TSS Total Suspended Solids
USGS U.S. Geological Survey
WCA Water Conservation Area
XML extensible markup language













Additional abbreviated units


L/kg liter per kilogram
mg/kg milligram per kilogram
mg/L milligram per liter
mg/m2 milligram per square meter
mg/m2/yr milligram per square meter per year
mg/m3 milligram per cubic meter
pg/L microgram per liter

Temperature in degrees Celsius (C) may be converted to degrees Fahrenheit (F) as follows:
F = (1.8 x C)+ 32
Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929
(NGVD 29)
Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83)
Altitude, as used in this report, refers to distance above the vertical datum.













Development, Testing, and Sensitivity and Uncertainty

Analyses of a Transport and Reaction Simulation Engine

(TaRSE) for Spatially Distributed Modeling of Phosphorus

in the Peat Marsh Wetlands of Southern Florida



By James W. Jawitz1, Rafael Muioz-Carpena2, Stuart Muller2, Kevin A. Grace1, and Andrew I. James1


Abstract

Alterations to the redevelopment delivery of water and nutrients into the Everglades of southern Florida have been occurring
for nearly a century. Major regional drainage projects, large-scale agricultural development, and changes to the hydrology
of the Kissimmee River-Lake Okeechobee watershed have resulted in substantial phosphorus transport increases by surface
waters. Excess phosphorus has accumulated in the soils of northern Everglades marshes to levels that have impaired the natural
resources of the region. Regulations now limit the amount of phosphorous that enters the Everglades through an extensive
network of water-control structures.
This study involved the development and application of water-quality modeling components that may be applied to
existing hydrologic models of southern Florida to evaluate the effects of different management scenarios. The result of this
work is a spatially distributed water-quality model for phosphorus transport and cycling in wetlands. The model solves the
advection-dispersion equation on an unstructured triangular mesh and incorporates a wide range of user-selectable mechanisms
for phosphorus uptake and release parameters. In general, the phosphorus model contains transfers between stores; examples of
stores that can be included are soil, water column solutess), pore water, macrophytes, suspended solids (pl.iikil i)n. and biofilm.
Examples of transfers are growth, senescence, L Illil--. diffusion, and so forth, described with first order, second order, and
Monod types of transformations. Local water depths and velocities are determined from an existing two-dimensional, overland-
flow hydrologic model. The South Florida Water Management District Regional Simulation Model was used in this study.
The model is applied to three case studies: intact cores of wetland soils with water, outdoor mesocosoms, and a large
constructed wetland; namely, Cell 4 of Stormwater Treatment Area 1 West (STA-1W Cell 4). Different levels of complexity in the
phosphorus cycling mechanisms were simulated in these case studies using different combinations of phosphorus reaction equa-
tions. Changes in water column phosphorus concentrations observed under the controlled conditions of laboratory incubations, and
mesocosm studies were reproduced with model simulations. Short-term phosphorus flux rates and changes in phosphorus storage
were within the range of values reported in the literature, whereas unknown rate constants were used to calibrate the model output.
In STA-1W Cell 4, the dominant mechanism for phosphorus flow and transport is overland flow. Over many life cycles of
the biological components, however, soils accrue and become enriched in phosphorus. Inflow total phosphorus concentrations
and flow rates for the period between 1995 and 2000 were used to simulate Cell 4 phosphorus removal, outflow concentra-
tions, and soil phosphorus enrichment over time. This full-scale application of the model successfully incorporated parameter
values derived from the literature and short-term experiments, and reproduced the observed long-term outflow phosphorus
concentrations and increased soil phosphorus storage within the system.
A global sensitivity and uncertainty analysis of the model was performed using modern techniques such as a qualitative
screening tool (Morris method) and the quantitative, variance-based, Fourier Amplitude Sensitivity Test (FAST) method.
These techniques allowed an in-depth exploration of the effect of model complexity and flow velocity on model outputs. Three
increasingly complex levels of possible application to southern Florida were studied corresponding to a simple soil pore-water
and surface-water system (level 1), the addition of plankton (level 2), and of macrophytes (level 3). In the analysis for each
complexity level, three surface-water velocities were considered that each correspond to residence times for the selected area
(1-kilometer long) of 2, 10, and 20 days. Various of model outputs were studied that could be potentially useful to the model
user: surface-water soluble reactive phosphorus (SRP) outflow, soil pore-water SRP variation, soil organic accretion, soil
adsorbed phosphorus, plankton outflow, and macrophyte variation.

1Soil and Water Science Department, University of Florida, Gainesville, FL 32611
2Department of Agricultural and Biological Engineering, University of Florida, Gainesville, FL 32611







2 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

Results show that a simple soil pore-water and surface-water system modeled with and without plankton exhibits little
change in sensitivity, owing to the plankton-based processes. Effects in both cases are primarily linear (additive), and the degree
of interactions among parameters is minimal. The sensitivity ranking of the parameters, however, changes with the introduction
of plankton-related modeling processes, because the plankton growth parameters dominate the simulated response of the system
for most outputs studied. The introduction of macrophytes substantially alters the parameter sensitivity, tempering much of
the linear effects and generating nonlinear interactions among all components. Although it is possible to reduce the number of
important parameters to about half of the total model parameters for levels 1 and 2, the presence of interactions prevents such
simplification for level 3.
Among the important parameters for level 1, the organic soil oxidation rate, kox, was consistently ranked most important
followed by three other parameters: diffusion coefficient, kdf, soil bulk density, pb, and mass fraction of phosphorus in organic
soil, XsoP. These results agree well with current understanding of the physical system, because the principal source of new
phosphorus to the level-1 system is from oxidation of the soil (controlled by ko) and the pore-water SRP and, hence, the
adsorbed phosphorus is controlled by the other three parameters. The SRP in the water column is more sensitive to kdf because
this parameter represents the limiting process of diffusion through which the surface water gains new phosphorus. These trends
across outputs persist in the level-2 results, with the only notable difference being the prominence of plankton growth parameters
in the ranking for mobile outputs (outflow of surface-water SRP and plankton biomass). Level-3 results do not exhibit any
pattern of parameter dominance across the different outputs.
Model sensitivity to velocity is correlated with model complexity; that is, as velocity increases, the model sensitivity to the
important parameters changes the most for the most complex case. The complex interactions that occur in level 3 complicate the
process of identifying sensitive parameters with the Morris screening method. This technique, however, was found to be compu-
tationally efficient for qualitatively evaluating global model sensitivity and linear or nonlinear effects of important parameters.
In cases where many parameters appear to be important, as when interactions predominate, the extended FAST method provides
quantitative measures of the linear and nonlinear contributions of each parameter to the observed global output variance.



Introduction

Freshwater wetlands serve a variety of needs by providing habitat, flood control, and water treatment as well as recreational
opportunities. The ability to predict surface-water phosphorus concentrations in freshwater wetlands is of great interest to resource
managers charged with maintaining water quality. Phosphorus is an essential element for all known life forms and is the limiting
nutrient for biological growth in most freshwater ecosystems (Hecky and Kilham, 1988). Excessive external inputs of phosphorus
can stimulate biological productivity in wetlands to a degree that negatively affects these resources. This overstimulation is often
accompanied by an increase in surface-water phosphorus concentration. The Everglades in southern Florida has been found to
be especially sensitive to phosphorous enrichment (Noe and others, 2001). Monitoring and predicting phosphorus concentration
changes are, therefore, important approaches for maintaining water quality and natural resources of freshwater systems.
Several investigators have developed simple predictive models of phosphorus cycling, including Walker (1995) and Kadlec
and Knight (1996), although these steady-state models cannot simulate changes over time. Walker and Kadlec (2005) extended
these steady-state models to account for event-driven behavior of treatment wetlands by also incorporating nutrient storage in
biota in the Dynamic Stormwater Treatment Area Design Model (DMSTA). Other efforts have produced ecological models
that are relatively complex (that is, not restricted to only one or two parameters) at one- or two-dimensional spatial resolution
(Kadlec and Hammer, 1988; Martin and Reddy, 1997; Sklar and others, 2001). In these wetland models, however, solute exchange
between neighboring computational cells is based solely on a water mass balance. Each cell is, thus, considered to be completely
mixed, which can be a severely limiting assumption as the model spatial and temporal discretization interval increases. A preferred,
but more computationally intensive approach is to fully couple water flow and solute transport. This approach recently has been
implemented for phosphorus cycling in a eutrophic lake (Chen and Sheng, 2005), but has yet to be implemented in wetlands.
In 2003, the University of Florida and the U.S. Geological Survey (USGS), in cooperation with the South Florida Water
Management District (SFWMD), initiated a study to develop a transport and reaction simulation engine (TaRSE) to simulate
phosphorus transport and cycling in wetlands. The model developed in this study solves the advection-dispersion equation on an
unstructured triangular mesh and incorporates a wide range of user-selectable mechanisms for biogeochemical cycling between
water, plants, and soils (A.I. James, University of Florida, written commun., 2008).
This model was developed to help assess the effects of management alternatives on large freshwater marsh treatment
wetlands in southern Florida. Important features of the model include the following: (1) ability to select different combina-
tions of phosphorus cycling mechanisms to suit the complexity of the problem under consideration, (2) ability to couple
the phosphorus biogeochemical model to a hydrologic model, and (3) capability for two-dimensional spatially distributed
parameterization and prediction.







Introduction 3


Purpose and Scope

The purpose of this report is to describe the development, testing, and sensitivity and uncertainty analysis of a transport
and reaction simulation engine (TaRSE) designed to simulate phosphorus transport and cycling in wetlands. Model calibration,
validation, and application are discussed, with several combinations of phosphorus cycling mechanisms applied to data sets of
varying scales, culminating with an application of the model to several years of field data from a large constructed wetland-
Cell 4 of Stormwater Treatment Area lWest (STA-1W Cell 4).
A complete global sensitivity and uncertainty analysis of the full model is performed using the Morris method as a
screening tool and the variance-based Fourier Amplitude Sensitivity Test (FAST) method. These techniques can be used to
explore the effects of model complexity on model outputs. In flow-driven systems, such as the Everglades in southern Florida,
it is also important to verify the effect of water velocity on model results. A statistical framework is, therefore, applied in which
the sensitivity and uncertainty of the model are evaluated at three increasingly complex model structures and three surface-
water flow velocities (or residence times). This model evaluation further reinforces the validity of the model, while guiding the
potential user in the parameter selection and application process.


Description of Study Area

The STA-1W study area is a constructed treatment wetland on the eastern perimeter of the Everglades Agricultural
Area (EAA), adjacent to Water Conservation Area (WCA) 1 as shown in figure 1. Cell 4 encompasses 147 ha and acts as a
"polishing" cell before water is discharged into the adjacent WCAs. The cell was constructed in the early 1990s and became
operational in August 1994 (Newman and Pietro, 2001). The spatially uniform vegetation community (dominated by submerged
aquatic vegetation), well-characterized hydrology, and simple geometry of Cell 4 made it a preferable test case for coupled
nutrient-hydrodynamic model development.


Previous Studies

The biogeochemical cycling of phosphorus in wetlands has been studied extensively, and many of the fundamental physical,
chemical, and biological processes involved in the transfer of phosphorus between wetland soil, biomass, and water column are
well documented (Reddy and others, 2005). One approach to mathematical modeling of phosphorus cycling in wetlands has
been to combine mechanistic representations of the fundamental biogeochemical processes into what has been termed a "detailed
ecosystem model" (Wang and Mitsch, 2000). This approach, however, often is considered cumbersome because of the large
number of process parameters required. A second and more common approach to modeling wetland phosphorus dynamics is
to group all phosphorus cycling processes into a single parameter, usually referred to as either an uptake coefficient or settling
velocity (Mitsch and others, 1995; Walker, 1995; Kadlec and Knight, 1996). Models of intermediate complexity that combine
some process lumping and some mechanistic representations also have been employed (Kadlec, 1997).
Although the modeling efforts, just described, represent the phosphorus biogeochemical cycling in wetlands with
varying degrees of complexity, surface-water flow through the wetlands was simulated in these studies as simply a water
mass balance (Walker, 1995; Wang and Mitsch, 2000) or as nondispersive, unidirectional plug flow (Kadlec, 1997). The
spatial variability in the wetland interior of water depth and velocity arising from irregular wetland geometry or irregular
water flow inlet and outlet locations (Persson and others, 1999) are, thus, not captured by such models. Furthermore, these
models treat the entire wetland as a lumped bioreactor with no capability to describe spatial heterogeneity of wetland compo-
nents or processes. Examples of such variables that would be desirable to represent in a spatially distributed manner include
soil phosphorus concentration, vegetation type or density, and process rate coefficients such as biological uptake.
Coupling biogeochemical complexity with hydrologic and spatial simplicity is consistent with most ecological models
designed to predict dynamic behavior while treating the system as spatially homogeneous (Costanza and others, 1990).
Similarly, wetland models that have captured hydrologic complexity and include spatially distributed parameters generally
have been restricted to biogeochemical simplicity. For example, Raghunathan and others (2001) used a spatially distributed
regional-scale hydrologic model coupled with a simple one-parameter settling rate to describe phosphorus transport in the
Everglades. Worman and Kronnas (2005) also used a spatially distributed hydrologic model coupled with a one-parameter,
first-order kinetic model to describe nitrogen transport in a treatment wetland.
Recently, ecological models have been converging toward coupled biogeochemical and spatial complexity. As noted by
Costanza and others (1990), this trend is related to the increased availability of spatial data and advances in computational power.
Concerning the area of study, the STA-1W wetland has been the focus of detailed studies on wetland restoration
(Chimney and Goforth, 2001), surface- and ground-water hydrology (Guardo and Tomasello, 1995; Guardo, 1999; Choi
and Harvey, 2000; Harvey and others, 2004), and nutrient dynamics (Moustafa, 1999; Nungesser and Chimney, 2001). In
particular, STA-1W Cell 4 (147 ha) has been investigated for soil response to flooding (Newman and Pietro, 2001) and
internal hydrodynamics (Dierberg and others, 2005).









4 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


26o45'


8045-


80W30'


8015


i. A 1- l ll ITl I FAI
_, -- AFP:A w\\'T F,


26o30' i


I-




i I: I 1I I II: H I: I:I I.ir
-i - --- -i i- .1-, i- i.- I- I-.1 -, -1 - - 1 - 2 - - -
------------------- ;---------'
Base from U.S. Geological Survey digital data i
Universal Transverse Mercator projection, Zone 17 / 0


Figure 1. Study area, including Cell 4, Stormwater Treatment Area-1W (STA-1W).


80O00







Model Conceptualization 5


Acknowledgments

The authors would like to acknowledge the contributions of the following individuals to this project: U.S. Geological
Survey employees Ronnie Best, Alyssa Dausman, Mike Deacon, Rhonda Howard, Barbara Howie, Maggie Irizarry, Christian
Langevin, Robert Renken, Kimberly Swidarski, and Arturo Torres; South Florida Water Management employees Cynthia
Gefvert, Eric Flaig, Zacki Moustafa, Jayahtha Obeysekera, Ken Tarboton and Naiming Wang; and University of Florida staff
Ken Campbell and Yuncong Li.



Model Conceptualization

Phosphorus cycling in wetlands is the transfer of this element in various forms between biota (micro and macro), water
(surface and subsurface), and soil. Various mass stores exist within each of these compartments, and modeled processes basically
are transfers between these stores. Phosphorus may be transferred as a solute in water or as a component of another material.
Modeled water flows, including inflow and outflow, are shown in figure 2, and material flows, such as settling of particulate
matter or decay of plant matter, are shown in figure 3. Figure 4 shows the movement of phosphorus between the various stores, in
either dissolved form or associated with material flow. Each store and transfer process is described in the following discussion.
The modeled phosphorus cycling mechanisms are user selectable and may include subsets of the processes shown in figures
2 to 4 in many possible combinations. Three combinations are selected for demonstration and comparison to measured data.


Model Notation

The basic notation used for the model is presented in table Al (app. 1). Storage in surface water, pore water, and biomass is
represented by C, whereas storage in the soil (such as sorbed solutes) is denoted by S. Both terms have dimensions of [ML-2] (in
the model, the default units are grams per square meter), which is the standard dimension for storage in wetland modeling (for
example, Kadlec and Hammer, 1988; Martin and Reddy, 1997). The mass fractions of phosphorus in some storage is denoted by
X [MM-1], and a material flux is denoted by J [ML-2T -1].
The symbols for storage and mass fractions are modified by superscripts and subscripts (table Al) to indicate what (for
example, P for phosphorus) and where the substance is, respectively. For example, the concentration of particulate organic
matter i( -i in the water column is written Cp", whereas the concentration of phosphorus in that particulate organic matter
is denoted CpoP. Material fluxes J are modified by superscripts indicating what the material is and subscripts indicating the
mechanism involved. For example, the notation for particulate organic material settling (st) from the water column to the soil is
Jsf, and the phosphorus transferred by this settling process to the organic soil (so) is indicated by the product Xso, J's, where X
is a mass fraction.
When volumetric concentration is required in dimensions of [ML-3], such as for determining growth rates, square brackets
are used around the symbol. For example, [CwP] is the mass of phosphorus per volume of surface water. Mass concentration
[MM-1], such as the sorbed phosphorus concentration in soils, is similarly denoted (for example [S P]).


Stores

Living organisms obtain phosphorus during growth and release some of this phosphorus after senescence, death, and
decomposition. The residual partially decomposed biomass may either be exported from the system in flowing water or
contribute to soil accretion. The phosphorus cycle in wetlands may, thus, be characterized as sedimentary instead of, for
example, the gaseous export pathways for nitrogen cycling in wetlands (Mitsch and Gosselink, 2000). Phosphorus that is
accreted in soil, however, may be released to soil pore water and consequently reenter the biogeochemical cycle. The biomass,
water, and soil constituents tracked by the model each contain phosphorus (table A2, app. 1).


Biomass

Wetland biota of interest include small organisms such as bacteria, phytoplankton, algae, and periphyton, as well as macro-
phytes such as sawgrass, cattail, and water hyacinth. In the model, biological organisms are classified as either phytoplankton
(small organisms suspended in the water column), biofilm (primarily periphyton in floating, epiphytic, or benthic forms), or
macrophytes. Phosphorus cycling in the wetland biotic community, which includes phytoplankton, periphyton, and macrophytes,
is closely coupled (Sand-Jensen and Borum, 1991; Havens and others, 2001). Periphyton removes phosphorus from the water








6 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Evaporation
ATMOSPHERE Rainfall


Dead PMacrophytes_D
Dead
SURFACE WATER macrophytes
Sur IIt
,ii i,,[r

PBlofilm outflow
Surficial
flow
Biofilm


SOIL


Ird anqpir [i' ion


a ErI


EXPLANATION
DIRECT TRANSFERS OF WATER
** DIRECT TRANSFERS THAT BYPASS THE ACTIVE SOIL
PBlofilm PHOSPHORUS MASS FRACTION OF BIOFILM
PGW TOTAL PHOSPHORUS CONCENTRATION IN THE GROUND WATER
PMacrophytesD PHOSPHORUS MASS FRACTION OF THE DEAD MACROPHYTE MATERIAL
PMacrophytes_L PHOSPHORUS MASS FRACTION OF THE LIVING MACROPHYTE MATERIAL
Psoll Mn PHOSPHORUS MASS FRACTION OF THE MINERAL SOIL
PsoilOrg PHOSPHORUS MASS FRACTION OF THE ORGANIC SOIL
PPsw PARTICULATE PHOSPHORUS CONCENTRATION IN THE SURFACE WATER
SRPpw SOLUBLE REACTIVE PHOSPHORUS CONCENTRATION IN THE PORE WATER
SRPsw SOLUBLE REACTIVE PHOSPHORUS CONCENTRATION IN THE SURFACE WATER



Figure 2. Water flows considered in the conceptual model.



column and may suppress plankton biomass, whereas high densities of plankton can limit light penetration and suppress the
growth of algae. Macrophytes provide structural support for epiphytic periphyton. Because these classifications are generaliza-
tions, their names can be considered operationally defined; for example, many types of small organisms besides phytoplankton
may be suspended in the water column.
The biological stores considered here are classified as either mobile or stabile (nonmobile). The former includes organisms
that are suspended in the water column such as plankton, algae, and floating plants, whereas the latter include rooted macro-
phytes and epiphytic and benthic periphyton. Of the latter, only rooted macrophytes access phosphorus in the pore water and,
therefore, are capable of translocating soil nutrients.
The turnover rates for phosphorus cycling among wetland stores often are conceptualized as "fast" for water column
organisms, "intermediate" for rooted macrophytes, and "slow" for soil (for example, Kadlec, 1997; Wang and Mitsch, 2000).
Consequently, the relative importance of each of these stores may depend on the temporal scale under consideration.








Model Conceptualization 7


ATMOSPHERE


PPsw inflow/ SURFACE WATER Dead PMacrophes
outflow
outflow macrophytes
PPsw
Plankton growth P- url ,

Suspended Foliageloss r
solids inflow/ Plankton Senescence
outflow P-lofilm
Suspended Sloughing
solids
Cohesion Biofilm
Settling Erosion









I I i iIi /SOIL










EXPLANATION
DIRECT TRANSFERS OF MATERIAL
PBlofilm PHOSPHORUS MASS FRACTION OF BIOFILM
PGW TOTAL PHOSPHORUS CONCENTRATION IN THE GROUND WATER
PMacrophytesD PHOSPHORUS MASS FRACTION OF THE DEAD MACROPHYTE MATERIAL
PMacrophytesL PHOSPHORUS MASS FRACTION OF THE LIVING MACROPHYTE MATERIAL
Poll Min PHOSPHORUS MASS FRACTION OF THE MINERAL SOIL
Psoil_Org PHOSPHORUS MASS FRACTION OF THE ORGANIC SOIL
PPsw PARTICULATE PHOSPHORUS CONCENTRATION IN THE SURFACE WATER
SRPpw SOLUBLE REACTIVE PHOSPHORUS CONCENTRATION IN THE PORE WATER
SRPsw SOLUBLE REACTIVE PHOSPHORUS CONCENTRATION IN THE SURFACE WATER


Figure 3. Material flows considered in the conceptual model.



Phytoplankton (Csw', but incorporated into particulate organic material) acquires phosphorus solely from the water column, and is
transported by surface-water flow as a component of suspended solids. Plankton growth is self-limiting because of competition for light
and nutrients with existing phytoplankton. Macrophyte growth also restricts phytoplankton growth by limiting light and nutrients.
Macrophytes (C"P) are slower growing organisms than phytoplankton, with slower decay and longer turnover times.
These organisms can obtain nutrients from both water column and pore-water phosphorus stores. Rooted macrophytes obtain
the majority of their required phosphorus from pore water (Carignan and Kalff, 1980), whereas floating macrophytes obtain
phosphorus solely from the water column. Above- and below-ground processes for macrophytes are managed in the model using
foliage and root mass fractions, ff and fr, respectively, where fr = 1 -ff. The root fraction becomes incorporated into the soil upon
death, and the foliage fraction decays directly to the water column. The foliage fraction also may restrict light availability in the
water column and at the soil surface.








8 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


EXPLANATION
DIRECT TRANSFERS OF PHOSPHORUS
** DIRECT TRANSFERS THAT BYPASS THE ACTIVE SOIL
PBiofilm PHOSPHORUS MASS FRACTION OF BIOFILM
PGW TOTAL PHOSPHORUS CONCENTRATION IN THE GROUND WATER
PMacrophytesD PHOSPHORUS MASS FRACTION OF THE DEAD MACROPHYTE MATERIAL
PMacrophytesL PHOSPHORUS MASS FRACTION OF THE LIVING MACROPHYTE MATERIAL
Psoll Mi PHOSPHORUS MASS FRACTION OF THE MINERAL SOIL
Psoil_Org PHOSPHORUS MASS FRACTION OF THE ORGANIC SOIL
PPsw PARTICULATE PHOSPHORUS CONCENTRATION IN THE SURFACE WATER
SRPpw SOLUBLE REACTIVE PHOSPHORUS CONCENTRATION IN THE PORE WATER
SRPsw SOLUBLE REACTIVE PHOSPHORUS CONCENTRATION IN THE SURFACE WATER




Figure 4. Phosphorus flows considered in the conceptual model.




For this study, stabile epiphytic and benthic nonrooted organisms are classified as biofilm. Epiphytic and benthic environments
provide large surface area and structural support for organisms that lack differentiated structural tissues. Epiphytic forms, Cpbf,
obtain phosphorus from the water column, rather than from the supporting plants (Carignan and Kalff, 1982). In the littoral
zone of Lake Okeechobee, Havens and others (2001) measured total phosphorus in the combined communities of water column
plankton and epiphytic periphyton to be about 150 mg/m2; about 90 percent of the phosphorus was associated with epiphyton.
Benthic forms, Cbebf, also may intercept nutrients diffusing from pore water to the water column (Carlton and Wetzel,
1988); however, biofilms readily become limited by nutrients in static waters and by light in productive waters. Fast-moving
water can support biofilm growth, but sloughing losses of biofilm tissues can occur when flow velocity changes.







Model Conceptualization 9


Water Column

The water column contains dissolved and particulate constituents. Dissolved components are assumed to be homogeneously mixed
within the water column, and are transported through advection and dispersive fluxes. Suspended particles include inert sediments as
well as living phytoplankton, bacteria, and other dislodged biological constituents that are transported with advective water flows.
Total phosphorus in the water column can be partitioned into phosphorus that is or is not directly available for biological
uptake. Soluble reactive phosphorus (SRP), Cs,,, is well correlated to the biologically available phosphate pool in freshwaters
(Murphy and Riley, 1962), and in standard determinations SRP is measured as filtrate (0.45 rim) that reacts with an ascorbic
acid-molybdenum color reagent (American Public Health Association, 1992). This method of determination is useful in surface
water and pore water because dissolved organic matter (DOM) does not interfere with the reaction (Watanabe and Olsen, 1965).
Phosphorus associated with DOM may be biologically unavailable. The importance of these compounds to phosphorus cycling
currently is not well understood (Turner and others, 2005); therefore, they are not included in the model at this stage.
Organic and inorganic particulate phosphorus molecules, Cpo' and Cpi, are larger than DOM. Because SRP and biologi-
cally unavailable phosphorus compounds have different reactivities, it is necessary to consider the process equations for these
compounds separately. Operationally defined phosphorus fractions are highly exchangeable; for example, when plankton cells
release bioavailable phosphorus upon senescence (Lehman, 1980).
Other dissolved constituents are known to affect phosphorus cycling dynamics. For instance, hydrogen ion concentration (pH),
ionic strength, and alkalinity all describe the chemical environment in which biological processes occur, including phosphorus
uptake and biomass growth. Nutrients other than phosphorus, such as nitrogen, calcium, and iron, are essential nutrients for
biological growth. Because phosphorus is the predominant limiting nutrient in freshwater systems, other constituents were
assumed to have a minimal influence on phosphorus fate and transport in the model. This simplifying assumption was made
recognizing that other dissolved constituents may be more or less important in specific applications.
Surface-water flow transports suspended matter (especially under turbulent flow conditions), measured as total suspended
solids (C" = Cp' + 0O). Much of the suspended load in low-gradient systems, such as those in southern Florida, is either living
plankton (pl), or biological material consisting of nonliving plankton or other organic matter (i,,p (Daroub and others, 2002).
Some inorganic content, 0", can also be attributed to the remains of siliceous and carbonate exteriors of plankton (for example,
diatoms). These remains typically settle out of the water column, but can be resuspended by turbulent flow. High-gradient
systems (for example, mountain streams and large rivers) with large hydraulic potentials have higher maximum flow velocities,
more erosion of inorganic components from the watershed, and a greater portion of inorganic matter in the suspended solids.
Because tracking the three forms of suspended solids is data intensive and may not be warranted by existing data, these forms
either may be lumped into two forms, CpO and CP' (organic and inorganic), or the single form, Cs.


Soil

In peat-forming wetlands, soil organic matter can accumulate to depths of several meters. Such high amounts of organic
matter in the soil represent only a narrow range of hydrologic conditions in which the water table is at or near the land surface.
When drained, peat soils may be depleted completely to expose the underlying mineral bedrock (Davis, 1946). Changes in
hydrology can influence the development and long-term stability of such soils, and can ultimately control soil phosphorus
stability. In southern Florida, surface soils such as Everglades muck and Loxahatchee peat can be composed almost entirely of
organic matter. Drainage of Everglades soils during the past century has resulted in the oxidation (and loss) of more than 2 m of
soil in some areas (Allison, 1956; Snyder, 2005).
Soil pore water is an important nutrient store for macrophyte growth, and as such, can control the distribution of vegeta-
tion in wetland ecosystems. When pore-water phosphorus concentration, CpWP, is high, opportunistic emergent vegetation such
as cattails may have a competitive advantage over phytoplankton, periphyton, and nonrooted or slower growing macrophytes.
This competition is especially acute when column phosphorus is scarce. Pore-water phosphorus may be transported directly to
the water column by molecular diffusion and advection, as with bioturbation for example. Finally, pore-water phosphorus also
is exchanged with solid-phase soil phosphorus, Ssi, through sorption-desorption reactions. Sources of pore-water phosphorus
include surface-water exchange and the mineralization of phosphorus in soil.
Soil solids are composed of eroded and settled minerals, and the remains of biological tissues undergoing decomposition.
The heterogeneous nature of biomass turnover in diverse ecosystems, together with multiple limiting factors (such as space,
i i -.., nutrient, and moisture availability) on decomposer activities, allow for the continuous decomposition of soil constitu-
ents. Mineralization rates can be modified by large changes in nutrient supply, as with soil phosphorus enrichment, or by large
changes in water-table altitude. For the current study, it is assumed that only a portion of deep soil is active in which processes
occur, such as phosphorus uptake by roots and diffusive exchange with the surface water. The active soil depth, zas, is the thick-
ness of soil modified by these processes, and can be considered as some function of root biomass.







10 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

In marsh wetlands, unconsolidated decaying plant matter (sometimes called floc) can accumulate at the soil surface. This
layer has been shown to be important in phosphorus dynamics in southern Florida marsh wetlands (Corstanje and others, 2006).
Floc depths of up to 17 cm with an average total phosphorus concentration of 632 mg/kg (about 50 percent higher than in the
surface soils) was found in WCA 1, which is part of the northern Everglades. Noe and Childers (2007) found that the floc layer
is the second largest store of phosphorus after soil. In the model applications described here, the floc layer is not considered
separately; however, the dynamics in this layer could be considered either as a separate soil layer, or as dead macrophytes.


Physical and Biological Transfer Mechanisms

Each of the transfer mechanisms considered here involve movement of either material or phosphorus between various
stores. The transfer mechanisms and associated stores used in the model are listed in table Al. All transfer rates are modeled as
either zero order, first order, or Michaelis-Menten (Monod equation). Rate constants and half-saturation constants used in the
model are listed in table A3 (app. 1); all other model symbols and parameters are listed in tables Al and A3 (app. 1).


Physical Transfer Processes

Physical transfers of phosphorus or phosphorus-containing materials include particle settling and resuspension, solute transfer
between pore water and surface water advectionn and diffusion), solute sorption and desorption, biofilm cohesion and sloughing,
and mineral precipitation. Ground-water and surface-water inflow and atmospheric deposition are also considered physical trans-
fers, but are only user-defined system inputs. However, the outflow of phosphorus with ground water or surface water is calculated.

Water Flows
The length of time that a given amount of water is retained within a wetland area is known as hydraulic retention time (HRT),
and can influence the potential for phosphorus exchange between flowing water and the other storage (I I iL e I- and others, 2002;
Dierberg and others, 2005). The nominal HRT is the ratio of wetland water storage to flow rate; however, water storage and
flow distribution may change during transient conditions. For example, floodplain wetlands that receive stormwater pulses can
experience conditions of variable flow (including zero flow).
Surface-flow velocities within the wetland are not directly dependent on phosphorus concentrations in the water column.
Indirectly, water column phosphorus may influence macrophyte density, and thus, affect flow velocity (Nepf, 1999; Green,
2006) and sedimentation rates. Water flowing along paths of least resistance preferentially travels toward areas of low macro-
phyte biomass density or greater water depths. Open-water zones can be maintained by continuous or periodic high-flow
velocities that prevent the establishment of macrophytes, creating positive feedback for "channel" creation and maintenance
(Riis and Biggs, 2003). Extensive preferential flow paths in wetlands result in low retention times and concomitant low phos-
phorus removal effectiveness (Martinez and Wise, 2003b; Dierberg and others, 2005; Wang and others, 2006). Additionally, the
prevailing hydraulic conditions can influence accrued soil properties that affect phosphorus dynamics, such as water content,
hydraulic conductivity, and particle size distribution.

Atmospheric Deposition
Atmospheric deposition along with surface-water inputs and ground-water exchange define the conditions under which a
wetland ecosystem develops. Bulk atmospheric phosphorus deposition, including both wet (rainfall) and dry (1, lk iL. dust, and
plant matter) components, is denoted by Jam,,. Hendry and others (1981) reported a mean bulk atmospheric phosphorus deposi-
tion rate in Florida of 59 mg/m2/yr, with a range from 27 mg/m2/yr in nonagricultural rural areas to 96 mg/m2/yr at Belle Glade,
Florida. The latter is an area of intensive agricultural activity where sugar cane fields are burned prior to harvesting. In addition,
dry matter accounted for about 80 percent of the bulk phosphorus deposition, and about 65 percent of the deposited phosphorus
was inorganic. Ahn and James (2001) also reported that bulk atmospheric phosphorus deposition in southern Florida was
dominated by dry deposition, with a range from 11 mg/m2/yr in a remote portion of Everglades National Park, to 77 mg/m2/yr
in an area surrounded by improved pastures. The average from all stations monitored in southern Florida was 40 33 mg/m2/yr.
Grimshaw and Dolske (2002) reported wet atmospheric phosphorus deposition in Florida as 1.3 0.3 mg/m2/yr, with nearly
90 percent of this as SRP. Volume-average phosphorus concentrations in measured rainfall in Florida were 1.3 0.1 pg/L, nearly
all of which was SRP.
Based on these data, atmospheric deposition in the model for the current study comprises constant SRP concentration in
rainfall and constant dry phosphorus deposition that is not dependent on rainfall, but may vary depending on surrounding land
use. Influx of atmospheric deposition is a user-defined input to this model. The particulate deposition is partitioned as 60 percent
inorganic (.Ja,,) and 40 percent (nonliving) organic (Jam") particles.







Model Conceptualization 11


Pore-Water/Surface-Water Transfer
Three mechanisms may enable transfer of phosphorus between pore water and surface water: (1) advective transport
with vertically flowing water, (2) Fickian diffusive transport caused by concentration gradients, and (3) biologically enhanced
transport (bioturbation).
Limestone beneath the southern Florida wetlands is responsible for the high connectivity between surface water and the
surficial aquifer system, although peat sediments underlying the wetlands may restrict surface- and ground-water exchange.
During wet and dry periods, wetland stage is typically above and below land surface, respectively. In the latter case, the wetland
may serve as a recharge basin for the aquifer. A 4-year water budget conducted in STA-1W showed that about 30 percent of the
surface water that is pumped into the wetland is lost to recharge, and that ground-water discharge to the wetland is relatively
minor (Choi and Harvey, 2000). A follow-up study (Harvey and others, 2004) showed that most of the recharge measured in
large wetlands in southern Florida originates near levees separating the wetlands from adjacent water bodies that often have
dissimilar water levels. Ground-water exchange in the central portions of these large wetlands was found to be relatively small-
almost always less than 1 cm/d. Harvey and others (2004) also suggested that traveling waves from inflow water pulsing may be
related to periods of infrequent but substantial recharge to the interior of large wetlands.
These studies highlight the importance of including spatially distributed information for accurate modeling of phosphorus
transport. In the current model, vertical advective flux and horizontal seepage through berms to connecting canals or adjacent
water bodies are determined using Darcy's Law.
Diffusive flux of phosphorus across the soil-water interface is based on Fick's Law and concentration gradients between
pore water and surface water (for example, Fisher and Reddy, 2001). Phosphorus concentrations are typically greater in pore
water than in the water column and, therefore, diffusion is usually from the pore water. Diffusive flux is inversely proportional
to diffusion distance, zdf, which is considered here to be 4 cm, based on concentration gradients observed in the northern
Everglades (Fisher and Reddy, 2001; Newman and Pietro, 2001).
Biological components may cause deviations from predicted phosphorus exchange rates that rely strictly on physical
processes such as diffusion. Rooted macrophytes can deplete soil pore-water nutrients, and benthic biofilms can intercept phos-
phorus diffusing from soil to water. Chironomids can increase water exchange across the soil-water interface with filter-feeding
activities, and can alter soil porosity by creating macropores. Holdren and Armstrong (1980) found phosphorus flux rates from
lake sediment intact cores to be at least an order of magnitude greater than would be expected from diffusion alone. When
the cores were exposed to a poison to kill any chironomids present, phosphorus flux rates were dramatically reduced to levels
consistent with molecular diffusion. Hansen and others (1998) have shown chironomids can increase decomposition of sediment
organic matter and increase sediment phosphorus release.
The pooled contributions of molecular diffusion and enhanced solute mixing due to macrobenthos activity have been
quantified using a Fickian model, with effective diffusion coefficient (D) values of up to 15 times greater than would be
expected from diffusion alone (Van Rees and others, 1996). The flux of phosphorus from pore water to surface water induced by
bioturbation can constitute a substantial portion of the phosphorus budget. In the current model, diffusion and bioturbation are
represented with a Fickian diffusion model, where the diffusion coefficient, D, is multiplied by a bioturbation factor, BF.

Settling and Entrainment of Particulate Material
Suspended particles in wetlands include inorganic particles and organic material such as algae, plankton, or plant debris.
The settling velocity, o, of many inorganic particles is directly related to particle size and can be determined for sand-like
particles using common semianalytic relations such as the following (Sturm, 2001):


9 8v 0.0139*(SG- )gd35 (
(0= 1+ ------ -- 1
d,


where:
v is the kinematic viscosity of water (10-6 m2/s at standard temperature and pressure),
SG is the particle specific gravity,
d is the particle diameter (meters),
g is gravitational acceleration (9.81 m/s2), and
d, is the geometric mean (meters) of the sieve sizes just passing and retaining the particle; this value is often close to d.
Empirically determined values for o are commonly used for wetlands. Kadlec and Knight (1996) have suggested a value of
10 m/d, based on a reported range of 3 to 30 m/d from several wetland studies. Based on equation 1, o = 10 m/d corresponds
to d z 10 pm (silt-size particles).







12 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

Particle depositional flux, JJ0 or J/' for organic and inorganic material respectively, is the product of w and suspended
sediment concentration. This mechanism only applies to nonliving particles, C"', because living suspended organic material
(such as plankton) can exhibit complex behavior such as motility or changing buoyancy.
The flux of sediment particles entrained or resuspended into the water column from the soil, Je,,, is strongly dependent on
water velocity and sediment characteristics. Sediment erosion has been the subject of numerous investigations, and resuspension
has been shown not to occur until the water velocity reaches a minimum threshold with enough i i i- to erode the sediment bed
(Miller and others, 1977; Wiberg and Smith, 1987). The threshold for sediment erosion is measured as the critical shear stress
Tc = pwUc2, where pw is the density of water and Uc is the critical shear velocity, measured just above the viscous no-flow sublayer
at the sediment-water interface.
Critical shear stress has been measured for a range of particle sizes in numerous studies and these data are summarized in
the Shields diagram (Sturm, 2001, p. 384). For silts and sands with d = 10 rpm and 100 tpm, this diagram and the relations above
may be used to determine critical shear velocities uc = 0.006 m/s and 0.01 m/s, respectively (assuming SG = 2.65, pw = 1 g/cm3,
and v = 10-6 m2/s). Shear velocities, however, are always less than mean velocities and often substantially less. The depth-aver-
aged critical velocity for resuspension, vc, is then substantially higher than uc, and can be determined from empirical relations.
Two examples of empirical relations are briefly compared:


1v= 05 (Y)1/6
0.0475 g) and (2)



v,00 =122.6d029 d <0.2cm, (3)

where y is the flow depth, in meters; v,10oo is the velocity (in centimeters per second) 100 cm above the sediment interface,
and d is depth, in centimeters. Equations 2 and 3 are from Sturm (2001) and Miller and others (1977), respectively. Using the
diameters given earlier (10 and 100 rim) and an assumed flow depth of 1 m, these two equations provide nearly identical values
for vc and Vc,100, as noted below:


Diameter i i uii
(pm) (m/s) (m/s) (m/d)
10 0.18 0.17 1.4 x 103
100 0.34 0.32 2.7 x 103


Constructed wetlands typically are designed to have low velocities. For example, at a large treatment wetland in Florida,
velocities of 72 44 m/d were measured in 15 treatment cells based on mean travel lengths and hydraulic retention times reported
by Martinez and Wise (2003a,b). A multiyear water budget for the Everglades Nutrient Removal Project (Guardo, 1999) suggested
velocities of about 400 m/d, based on a mean hydraulic retention time of 20 days and an average travel length of about 8 km. These
velocities are substantially lower than the v, values determined earlier. Steady-flow conditions in treatment wetlands, therefore, are
highly unlikely to generate flow-induced bottom shear stresses sufficient to induce bed erosion and resuspend particles.
Extreme transient conditions can induce resuspension of even cohesive sediments. Such conditions include high winds,
high hydraulic loading rates, or hydraulic "shocks" in areas near pumps. For example, Stuck (1996) found that cohesive organic
sediments in EAA canals were relatively resistant to erosion under steady-flow conditions, but were entrained quickly after
sudden changes in velocity during pump startup. In shallow lakes, wind speed has been found to be a primary driver of sediment
particle entrainment in the water column (Carrick and others, 1993; Hanlon, 1999; Schelske and others, 2000). The presence of
emergent vegetation, however, substantially alters the hydrodynamic conditions. Wind-induced waves and the corresponding
bottom shear stresses are expected to be damped in well-vegetated wetlands compared to shallow lakes. Under equivalent
forcing conditions, such as bed slope or wind speed, water velocities in vegetated systems are substantially less than in unveg-
etated systems, even at moderate vegetation densities (Nepf, 1999).
Observations of steady-state, spatially uniform background concentrations, C*, of total suspended solids (TSS) in wetlands
suggest that a balance exists between settling and the sum of resuspension and internally generated particles, such as from
biological processes (Kadlec and Knight, 1996). For example, Js, = 25 g/m2/d in a wetland with TSS C* = 5 g/m3 and w = 5 m/d.
Suspended solid generation from the combined effects of internal growth and resuspension must equal this value for the steady-
state background concentration to be maintained. Using this logic for a well-characterized wetland, Kadlec and Knight (1996)
found J,,s = 46 g/m2/d. Because the wetland water velocity was well below the critical erosive value, other processes such as
bioturbation were identified as contributing to the observed sediment flux.







Model Conceptualization 13


Erosive flux has been found to increase linearly with bed shear stress above the critical value, rc (Ariathurai and Arulanandan,
1978). Wetland flow velocities are assumed herein to be less than v,, however, and the flux of sediments entrained by flowing
water is zero. A mechanism is included in the present model to enable sediment resuspension enhancement through bioturbation
(discussed later).

Sloughing and Cohesion of Biofilm
Benthic biofilms in southern Florida typically are described as periphyton-a combination of benthic algae, bacteria, and
extracellular mucilage (McCormick and Stevenson, 1998). Periphyton can also grow epiphytically on macrophyte leaves and
stems, although these forms can be considered an extension of macrophyte storage. The cohesive properties of the extracellular
matrix of benthic biofilms can minimize sloughing losses and substrate erosion (Sutherland and others, 1998), and cause the
film to grow by trapping particulates suspended in flowing water. This growth can be counteracted by shearing forces that cleave
overextended macrophytes and biofilms. Benthic biofilms can also slough during large velocity changes (Stuck, 1996). Biofilm
cohesion and sloughing are hypothesized here to be first-order rate processes that (1) exchange material between biofilms and
particulate organic material, and (2) depend on the amount of particulate organic material and biofilm, respectively.

Sorption/Desorption
Dissolved phosphorus adsorbs onto the reactive surfaces of soil solids in a dynamic equilibrium that maintains a
relatively constant ratio of liquid and solid phases within the soil pore-water matrix. This partitioning is accomplished through:
(1) desorption reactions when the liquid phase is depleted, as with root phosphorus uptake; and (2) soil sorption when dissolved
concentration increases, as with soil OM mineralization. In the current model, linear sorption relations are used to "instanta-
neously" partition soil phosphorus between pore-water and solid phases. This partitioning is applied as follows, beginning with
the equation for equilibrium sorption/desorption:


[C,, ]= kd (4)

where k/r is the sorption distribution coefficient, [CP I] is the mass of adsorbed phosphorus per unit volume of soil, and

[CLP i is the mass of pore-water SRP in per unit volume of soil. To convert to mass of adsorbed phosphorus per area
(expressed as SsiP), the active soil depth, zas, bulk density, Pb, and inorganic fraction, f, are multiplied:

S, = zas fkdr cp] (5)

Multiplying [C P I by the porosity, 0, and the active soil depth, zas yields Cpwp in grams per square meter and, thus, equation 5
is rewritten as:


S p = Pbfkds P
0 (6)

Taking the derivative of equation 6 with respect to time yields:

dSj,P pf kd dCP
dt 0 dt (7)


Mineral Precipitation
Carbonates can be precipitated from hard waters by algae, periphyton, and submerged aquatic vegetation (SAV) during
daytime photosynthesis (Otsuki and Wetzel, 1972; Murphy and others, 1983; Scinto and Reddy, 2003). The formation of stable
calcium phosphates from calcium carbonate-phosphate coprecipitates can be hindered by excess humic acid compounds in
solution (Alvarez and others, 2004) produced by decomposing organic matter in soils.
Scinto and Reddy (2003) showed that abiotic uptake (prL ciii.iil ~l of phosphorus by periphyton represents a relatively
small fraction (about 10 percent) of total uptake. The current model computes coprecipitation using the same Michaelis-Menten
reaction kinetics as for biological uptake, with a maximum uptake rate of about 10 percent of the biological value.







14 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Biological Transfer Processes

Because carbon dioxide is exchanged with the atmosphere, aquatic systems may act as either net OM sinks that fix carbon
through photosynthetic productivity, or net sources that emit carbon dioxide following metabolic respiration. Wetlands often are
considered sinks of phosphorus through the accumulation of OM, if OM and nutrient storage increase continuously. Phosphorus
storage capacity in a wetland is finite if OM stores do not increase, whether phosphorus removal is primarily through soil sorption
or biomass uptake (Richardson and Qian, 1999).
Gains to biological storage include growth and import, whereas losses include death and washout (in the case of algae and
other nonrooted organisms). The difference between growth and decay rates for algae, macrophytes, and biofilms determines the
relative contribution of each to soil phosphorus cycling within wetlands. Biological transfers include the uptake and release of
phosphorus during growth and senescence, and mineralization of soil phosphorus.

Growth of Biological Tissues
Biological growth is assumed to be phosphorus limited, as is often the case for algae (Grover, 1989), macrophytes, and
periphyton in freshwater systems. Growth rates are proportional to the existing biomass, with submaximal rates achieved under
limiting conditions. The Michaelis-Menten kinetic formulation for particulate organic growth, Gpo, allows algal growth rates
to be limited by SRP concentration, Cswp. Specifically, the growth of plankton in the water column, GswP,, based on maximum
growth rate, kgp1, and half-saturation constant, I can, therefore, be expressed as:


C p
cw + (8)

This formulation has been widely used to simulate the effect of phosphorus limitation on algal growth in the absence of other
limiting factors, and also has been used to describe phosphorus limitation of periphyton in southern Florida (Hwang and others,
1998; Dong and others, 2002; Scinto and Reddy, 2003).
The Michaelis-Menton formulation was also used in this study to describe phosphorus-limited growth rates for macrophytes
and biofilms as well as plankton. In the current model, new growth is assumed to have a constant phosphorus mass fraction such
that gains in biological storage cause a proportional increase in phosphorus within the storage. Similarly, the decay of living
biomass causes a loss of both organic material and phosphorus storage at a fixed concentration.
Uptake rates for phytoplankton have been found to always be greater than those of periphyton, indicating that the former are
more efficient in assimilating phosphorus (Hwang and others, 1998). Plankton uptake rates may be higher than those for other
organisms because of their large specific surface areas. Although dissolved organic phosphorus usually is considered relatively
unavailable biologically, phosphorus-deficient plankton and periphyton communities have been observed to use this form of phos-
phorus at rates about equal to those for SRP uptake (Havens and others, 2001). For applications in which periphyton are discretized
into epiphytic and benthic pools, the epiphytic periphyton maximum uptake rates and half-saturation constants have been found,
respectively, to be about double and half those of epipelon (Scinto and Reddy, 2003). The greater uptake rates for epiphyton prob-
ably result from its ability to obtain a large portion of its required phosphorus from pore water (Havens and others, 2001).
Factors other than phosphorus also may limit the growth of aquatic organisms (Hecky and Kilham, 1988). Many biological
reaction rates are temperature dependent (Goldman and Carpenter, 1974). Light availability changes with water column attenu-
ation characteristics and seasonal fluctuations in incoming solar radiation and biomass shading, and can also limit photosyn-
thesis and growth rates (Carr and others, 1997). Nutrients other than phosphorus, such as nitrogen or potassium, can also limit
biological growth.

Senescence and Decay of Biological Tissues
Turnover rates for cattail leaves in southern Florida have been estimated to be about 0.011 d-1 (4 yr1) (Kadlec, 1999; Grace,
2003). For algal components, losses caused by mortality may average 0.1 d-1 for diatoms and green algae (Asaeda and Van Bon,
1997). First-order decay coefficients have been reported for standing dead biomass and fallen leaf litter of cattail and sawgrass in
Everglades peat in the range of 10-4 to 10-3 d-1 (DeBusk and Reddy, 1998). Godshalk and Wetzel (1978) reported macrophyte decom-
position rates between 0.002 and 0.06 d-1 under anaerobic conditions, and between 0.004 and 0.085 d1 under aerobic conditions.
Such large differences in decomposition rates between organic detrital materials may be caused by differences in fiber
content, nutrient content, or conditions within the decompositional environment (DeBusk and Reddy, 1998). For this reason,
it is necessary to consider OM sources that have different turnover (decomposition) rates. First-order decay relations are used
in the current model for plankton and macrophytes, with exchanges occurring between plankton, nonplankton particulate OM,
macrophytes, and organic soil:







Model Conceptualization 15


dC pl
j = -k P= C pi
dt "", (9)



dC~wp' ,PIC wpi + kdfoffCmp



dC3"
dt P ke f mp(10)



dCmp- kd, ff +k ff,
dt and (11)


dlSo
d = kd"of,C"
dt (12)

where rate constants (kx,") and fractions (fx) are as defined in table A3. Macrophytic foliage decay increases the particulate
organic store and root decay increases the organic soil store.

Soil Oxidation and Mineralization and Burial
Soil oxidation results from soil drainage and exposure to air or fire, and causes a loss of organic soil, S, primarily through
the conversion of organic carbon to carbon dioxide. Under these conditions, a wetland typically exports phosphorus mineralized
from the OM store as it is depleted. In general, soil mineralization rates are lower than macrophyte and planktonic matter decay
rates because the majority of soil materials are residual compounds resistant to decomposition (Turner and others, 2005). In
the current model when the soil is saturated, oxidation loss is treated as a first-order removal of material from the system, with
the phosphorus contained in the organic soil transferred directly to the pore water, CpP. The oxidation of organic soil and the
mineralization of phosphorus contained in the organic soil, respectively, are modeled as:

dS k
= -koSo
dt (13)



dSsop= -X 'k "So
dt S and (14)


dC P
w_ = XPsksoSo
dt o (15)

where k0ox is the rate of soil oxidation, and Xsov is the phosphorus mass fraction of the organic soil.
Measured mineralization rates of phosphorus from wetland soils range from 1 x 10-6 d-1 for low-productivity meadowlands
to 1.5 x 10-6 d-1 for bogs (Bridgham and others, 1998). The volume of active soil is assumed to be constant over time in the
current model, and additions caused by settling and decay balance the loss caused by burial (that is, movement to deep storage).
The amount buried, therefore, is set equal to the change in soil volume.


Feedbacks and External Environmental Factors

External factors other than phosphorus concentration that may affect the aforementioned physical and biological processes
include hydrology, temperature, and light. The timing, magnitude, duration, and spatial extent of flooding will dictate whether
plankton is present or which macrophytes are prevalent. The absence of water would expose organic soil to the atmosphere,
causing rapid oxidation. Temperature affects the growth rates of many biota, increasing metabolism as well as decomposition.
Macrophytes and some plankton require light for photosynthesis, a process that can be inhibited by particulate matter in the
water and shading from foliage.







16 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Light Limitation

Incident light above the water surface is available to suspended phytoplanktonic and floating and emergent plants. After
some light is reflected by the water surface, light intensity is further reduced by scattering and absorption by suspended matter,
submerged plants and algae, and the bed. The remaining light is reflected upward by the bed surface. In general, light is
available according to the following equation:

PAR = Ioek-k, (16)

where PAR is photosynthetically active radiation; I1 is incident light just below the air-water interface (that is, maximum
available light); ke is the light extinction coefficient for the aquatic system, and zws is depth below the water surface (Carr and
others, 1997). The temporal variability of the limiting control that light has on plant growth has also been modeled dynami-
cally using coefficients from empirical relations; specifically, Secchi depth and turbidity relations (Carr and others, 1997). An
additional extinction coefficient, kwb, can be used to determine the PAR accounting for further loss due to plant biomass, C"P, in
the water column:

PAR = Ioe-k- ,k,Cp (17)

Equation 17 shows that submerged, floating, and emergent macrophyte biomass limits the light available to benthic periphyton.
The formulation also can be used to calculate light availability for organisms such as benthic periphyton-a biotic layer that can
affect phosphorus dynamics strongly across the sediment-water interface.
Because light decreases exponentially with depth and biomass shading and linearly with total suspended solids, Css
(Krause-Jensen and Sand-Jensen, 1998), ke can be used to limit growth and equation 8 is adjusted as follows:


P' = k P'C" pe C_ -k z-kCm
css(CP+k2 ) + (18)



Temperature Effects

Temperature, T, affects biological activities that range from cell and plant growth to decomposition and respiration reactions
and, consequently, is a primary controlling factor on wetland productivity. Shelef and others (1970) showed that the half-saturation
constants used to describe nutrient uptake reactions are temperature dependent. Goldman and Carpenter (1974) related temperature
to maximum algal growth rate, kg, based on a broad range of empirical growth data and the Arrhenius equation:

k" = ab' = 0.851(1.066)', (19)

where a and b are empirical constants, and Tis in degrees Celsius. The effect of temperature on the algal growth rate is
expressed as:


G wP = k pabpC ek ,,z k ,,C'
CS (C ,P + k,") (20)



Vegetation Effects on Flow Restriction

Sessile organisms reduce wave. i -i -' in bottom waters near the soil-water interface and increase flow resistance in the water
column. The effect of vegetation density on Manning's n values can be estimated using common approximations shown in the
following table (Dingman, 1984). More sophisticated methods for relating vegetation and flow restrictions are emerging, including
regressions of Manning's n with vegetation surface area (Green, 2006). The current model is capable of tracking changes in
Manning's n as a function of vegetation density and providing this parameter as feedback to coupled hydrologic models.







Model Conceptualization 17


V n Mannings n values as allecled by
Vegetation
e t vegelalion ol the channel bed surface
densit(Irom Dingman, 1984)
High .025 0.050
Low 0.005 0.010
Medium .010 0.025
Very high .050 0.100


Reaction Equations

The mechanisms described earlier were used to develop a set of reactions among the different constituents, and where
possible, the reactions were simplified by grouping terms. Most of the equations for phosphorus content in materials such as
plankton, Cpf, are redundant if the mass fractions remain constant over time. The phosphorus content equations can be obtained
simply by multiplying the material content by the appropriate mass fraction. For example, CpI can be obtained by multiplying
CPz by Xpf. The number of equations, therefore, can be reduced substantially by eliminating the equations for phosphorus
content in materials where changes in phosphorus are due solely to the movement of material.
The reaction equations for the materials are as follows (variables and parameters are defined in appendixes 1 and 2):


dC +
dt G2;" -(k,," +kc,1) C" +kb(21b


dC _P
dt


SkC pl'-C pn" [C_"- ]+Jso +kpfo pf c JIP"
- "-m c "-st [L ]+ so, +m */cm + Joat,,


dCP'
dt


-k P," [CCP' ]+ JS," + Jppt + Jap


dSt
dt kP"[C "_ko S_ sok kro fC""
d ^ L "" J t <* '


dt = k,,P' [C J "
dt


dC"'
dt


+Go'"p + G"' (kof f + c kro Cmp
o + ro -(k f+ de fr) ,and


dCbf
dt = khP'ICwP' + Gepbf + Gbebf kbf Cbf
-t







18 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

The reaction equations for the solutes are as follows (variables and parameters are defined in appendixes 1 and 2):

dC [CX +- CX kp
"dC~ -XPG i + foPGf +Xbf'Gp kdf l a-- X Jpptk ppt
dt zdf 2


Pw Pk s X Pro PG bf k [cJ L p [C 0 dS[,p
dt sop h ZOdf pZbfkd dt


dC,P
d = P T pi _pl XPI (k P' + kPl) pl + f' Pks, Csf




ct pi ss pn st o en o,pn


dt


-Xp,~kP' [C, '] + XsJ,,'~ +X P J PPt +x ,pjI


dSsoP
dt pn st L s ox so en



i P p
d= X= ,kGJ + Cr'] X"' +V bf+d dfC


dC P
= XfoPGfo +XPGro (X'kd fof +Xrokdro)C C
dt and


dCtp
Y PkchplCswP + pPGep bf +X bnGbf -XbfPk PPbf

The full suite of growth rates is given by the following:



swP1 = + kkg P [



G = k OCfo [CP I
[C s]+k1,f2







Model Calibration and Validation 19


Gro =k roCro l[cp





G = [Cp ]+ kf, and (40)




Ghf = k hfChf [Ciwpl
GC k]+ k,' (41)




Model Calibration and Validation

In this study, model performance and flexibility are demonstrated with applications to laboratory and field experimental
data sets from the following sources, each representing a specific scale and level of complexity.
Level 1-A laboratory core study that measured the flux of SRP released from wetland soils to the water column with-
out interactions influenced by plants or phytoplankton (Grace, 2003).

Level 2-An outdoor mesocosm study that measured phosphorus release to the water column from flooded soils with
different initial phosphorus contents under a natural light environment (DB Environmental, Inc., written commun.,
2004). Both suspended and dissolved phosphorus concentrations were measured.

Level 3-Analysis of data collected from field operations at STA-1W Cell 4 (147 ha) for the period February
1995-June 2000, and stored in the SFWMD DBHYDRO database: hir, "'ri' .th I,.1 .-.v/dbhydroplsql/show_dbkey_
info.main_menu
Some of the important Cell 4 simulation complexities not represented in the first two levels include through-flowing water,
suspended and dissolved components, and active periphyton and macrophtye communities. The level-3 period was considerably
longer (5.4 years) than the 14-day simulation periods for levels 1 and 2. Two model implementations are presented for level 3:
one in which the field-scale system was treated as homogeneous, and another in which the model was coupled with a spatially
distributed hydrologic model.


Level 1-Soil Cores

In this study, five intact soil cores (0.1 m deep and 0.07 m in diameter) were collected from STA-1W Cell 1 outflow region
and incubated with 0.45-im filtered water (initial SRP less than 2 itg L-1) for 28 days (Grace, 2003). The SRP concentrations
were measured in the water column over time to determine the phosphorus flux from the soil. Soil and pore-water phosphorus
concentrations and soil bulk density also were measured during the level-1 study. No periphyton, water column plankton, or
macrophytes were present in the cores, which were incubated in the dark with air continuously stirring the water column but not
resuspending surficial sediments.
The important mechanisms controlling phosphorus flux to the water column included the following:
Soil phosphorus mineralization to the pore water, estimated by the first-order coefficient for organic soil oxidation, kox;

Sorption-desorption equilibrium between pore-water phosphorus and soil surface-exchange sites, estimated by the
partitioning coefficient, k/r;

Phosphorus diffusion from the pore water to the water column, estimated by the diffusion coefficient, D; and

Biologically enhanced phosphorus transfer from the pore water to the water column (bioturbation), estimated by the
bioturbation factor, BF.
All other transfer mechanisms were assumed to be inactive.








20 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


The initial measured soil and water column conditions and model parameters are summarized in table 1. The sorption
partitioning coefficient, kds, was 10 L/kg, based on the study of Richardson and Vaithiyanathan (1995) conducted on soils from
southern Florida wetlands. The value for D is based on results from Fisher and Reddy (2001), and values for ko and BF (table 1)
were calibrated. The bulk density of highly organic soils is often low at the soil surface and increases with depth. Bulk density
values reported for the soils in these core studies were between 0.1 and 0.25 g/cm3 (Grace, 2003). Irons (2001) reported a bulk
density in Cell 4 of 0.29 g/cm3 for cultivated soils, and bulk densities from 0.047 to 0.179 g/cm3 for newly accrued soils; a value
of 0.2 g/cm3 was used for all simulations.
Because the timescale in the level-1 study was only a few weeks, the primary constraints were that soil phosphorus storage
could not be depleted substantially, and that pore-water phosphorus concentrations remained relatively stable. For pore-water
phosphorus concentrations to be stable, the mineralization flux of phosphorus from soil to pore water must be balanced with the
flux of phosphorus from pore water to the water column. Mineralization rates reported in the literature are relatively slow, being
on the order of 10-3 to 10-5 days (Bridgham and others, 1998); a value of kox = 0.0001 d-1 was used in the level-1 study.
Fickian diffusive fluxes of phosphorus calculated from pore water concentration gradients in wetland soils generally have
been lower than fluxes measured from intact core studies (Fisher and Reddy, 2001). Van Rees and others (1996) estimated
that bioturbation increased phosphorus exchange between soil pore water and surface water from 1.5 to 15 times above rates
expected solely from diffusion.
Observed water column SRP concentrations are compared to simulated values in figure 5A. Figure 5a shows comparisons
between predicted water column SRP concentrations based solely on diffusion (BF = 1), and those that consider the combined
effects of diffusion and bioturbation (BF greater than 1). The best fit of these data corresponds to a bioturbation factor of 2.7.
Figure 5B shows the associated change in pore-water SRP concentrations due to the exchange with the water column. This
change is presented relative to the overall soil phosphorus storage for perspective.







Table 1. Initial conditions and calibrated parameter values for level-1 model application.

[Symbols are defined in appendixes 1 and 2. Unit abbreviations are defined on the Conversion Factors page;
BF, bioturbation factor]


Symbol Value

Initial Conditions -Soil
[CpwP] 500 Xg/L
[SV] 3.75 mg/kg
[Ssol] 800 mg/kg
kdsr 10 L/kg
zas .10m
Zdf .04 m
0 .8 [-]
Pb .2 g/cm3
Initial conditions water column
[Csw] 1 ~g/L
Zwc .30 m
Calibrated parameters
BF 2.7
k,,, .0001 1/d









Model Calibration and Validation


A


v--


ooc
0- Q-
0- <0
LU Z



M:


0 3 6 9


a)
D




MrM
CO





z


4
LU

C-)
3 L
oc
LU

CD

a)
2c
LU


LU
w
CD
0_
Q-


I-
w
z._c


LU


M -.
<
co M
CD C


6
TIME, IN DAYS


Figure 5. (A) Measured water column soluble reactive phosphorus
(SRP) concentrations compared to model level-1 predictions, including
a range of bioturbation factors, and (B) simulated changes in soil
phosphorus storage and pore-water soluble reactive phosphorus.






Level 2-Outdoor Mesocosms


Four replicate mesocosms (0.2-m deep soils, 0.4-m deep water column, and 1-m2 surface area) were established for each
of two treatments using soils collected from within STA-1W. The first was a muck soil retrieved during recent excavations for
a new gate structure, which represented "low-P" soils typical of the area prior to STA operations. The second treatment was a
"high-P" soil collected during 2005 near the Cell 4 inlet, where 10 years of flow-through operations at the STA had enriched the
phosphorus content of the soil. The STA-treated water was applied to the soil and allowed to equilibrate for 14 days.
Although no macrophytes nor periphyton were present at the beginning of these mesocosm studies, planktonic communities
did develop from the initial water column population during the experiments. The mechanisms controlling phosphorus flux to
the water column were the same as for level 1, although phosphorus cycling mechanisms influenced by phytoplankton growth
also were included. Additionally, the mesocosms were outdoors rather than in a temperature-controlled laboratory as in level 1.
All other transfer mechanisms were assumed to be inactive.


EXPLANATION
BIOTURBATION FACTOR x2.7
- BIOTURBATION FACTOR x10
- SOIL P STORAGE
PORE-WATER SRP








22 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

Table 2. Initial conditions and calibrated parameter values for level-2
high phosphorus model application.

[Symbols are defined in appendixes 1 and 2. Unit abbreviations are defined on the
Conversion Factors page. Where a range of values is listed, the smallest value
is for low phosphorus soil and largest value is for high phosphorus soil. Additional
components not included in previous level of model application are shaded in blue. BF
bioturbation factor]

Condition or
Symbol Value
Parameter Type
Initial Conditions
[CpwP] 45-700 tg/L Soil
[S,'] .25 7.0 mg/kg Soil
[SsoP] 342- 852 mg/kg Soil
kds 10 L/kg Soil
Zas .20 m Soil
Zdf .04 m Soil
0 .8 [-] Soil
Pb .2 Soil
[Cwp] 43 tg/L Water Column
Csw' 243 tg/L Water Column
Zwc .3 m Water Column
Calibrated Parameters
BF 2.7 20 Soil
koxs .0001 1/d Soil
i '2.005 mg/L Algae
lkgP 2.25 1/d Algae
'ksnpl 2.1 1/d Algae



Initial soil and water column phosphorus storage were based on measured values, but the parameters regulating transfer
mechanisms used in level 1 were maintained for level 2 (table 2). Because the timescale in this case also was only a few weeks,
soil phosphorus storage and pore-water phosphorus concentration were constrained to be relatively stable. Total phosphorus and
SRP concentrations were both measured in the water column over time. Particulate phosphorus (PP) was assumed to be represented
by total phosphorus minus SRP. Concentrations of SRP and PP were measured in the initial floodwater, again 24 hours after the
mesocosms were flooded and after 3, 7, and 14 days. The 24-hour concentrations represent the initial condition for model simula-
tion, because of possible disturbances to the system during the flooding process. This shortened the simulation time to 13 days.
Observed water column PP and SRP concentrations are compared to simulated values in figure 6, and the best fits to these
data indicate that a bioturbation factor of 12 is appropriate. This bioturbation factor is larger than that required to fit the level-1
data, which indicates an increased bioturbation effect with the increased scale of the experiment. Both the simulated SRP and
PP dynamics generally matched the observed trends in the data. The simulation started on day 1 rather than day 0 because of
potential disturbances caused by water additions to the system on day 1.


Level 3-Stormwater Treatment Area 1W, Cell 4

Application of the model to a field-scale system was demonstrated using STA-1W performance data from a 5.4-year period
between February 1995 and June 2000. Some of the important complexities of the field system in level 3, not represented in
levels 1 and 2, include flowing water and active macrophtye communities. Although phosphorus concentrations, flow rates,
and biomass dynamics fluctuated during this period, the long-term performance characteristics of soil, macrophyte, and water
column storage provided a basis for comparison to model output.
Two field-scale model applications are presented: (1) a homogeneous, steady-state flow case that included a more complex
representation of phosphorus cycling, and (2) a spatially distributed, transient flow case that included only a simple representa-
tion of phosphorus cycling. The spatially distributed transport model was validated against known analytical solutions using
nonreactive and reactive solutes (James and Jawitz, 2007).













0 00






) m 0.04
DCD

0.02

OQ




z- 0.10

ILU
^ 0.08



.) 0.04
'-r-



E 0.02
CD


Model Calibration and Validation


A


TIME, IN DAYS


0 5 10 15
TIME, IN DAYS



Figure 6. Comparison between observed and simulated water column particulate
phosphorus (PP) and soluble reactive phosphorus (SRP) concentrations for level-2
simulations.


A study of the soils within STA-1W prior to construction showed that the average phosphorus content in the upper 10 cm of
soil was about 8.3 g/m2 (Reddy and Graetz, 1991), and this was used as the initial condition for soil phosphorus concentration.
In June 2000, soils were sampled again in the inflow region and outflow region of Cell 4 (Irons, 2001). These data provided a
basis for comparing the predicted increase in soil phosphorus storage.
Shortly after flooding the Cell 4 region of STA-1W in August 1993, pore-water SRP concentrations increased to nearly
4 mg/L at a 10-cm depth, and decreased to less than 1 mg/L by January 1994 (Newman and Pietro, 2001). The simulation was
started in February 1995 so that the effects of cultivation practices would be minimal, and the wetland soil, water, and biomass
dynamics would be more representative of a typical wetland.
In 1995, SFWMD scientists resampled soil and pore-water phosphorus concentrations in 0- to 5-cm and 5- to 10-cm depth
intervals at four locations within Cell 4. The average values for these two depth intervals were used as initial conditions for the
level-3 calibration (table 3). Pore-water SRP concentrations were 346 280 pg/L, and soil total phosphorus concentrations were
355 23 mg/kg. These values are between the high- and low-phosphorus soils of the level-2 calibration (mesocosm) study.
The particulate settling processes simulated in level 2 were limited to representing algal biomass and suspended particulate
transfer from the water column to soil storage. In level 3, the production of particulate phosphorus from macrophyte turnover
also was included. The growth rate coefficient and half saturation concentration for algal biomass growth functions were
consistent between level-2 and level-3 simulations to limit the number of new parameters in level 3.
Model results indicate that 6.2 g/m2 of new soil phosphorus had accumulated over the period of simulation, a value between
the upper and lower estimates of soil phosphorus accrual determined by Irons (2001) (figs. 5 and 6). The predicted biomass
phosphorus storage ranged from 0.1 to 0.31 g/m2, which compared favorably with measurements (0.07-2.0 g/m2) reported in
an assessment of the SAV communities of Cell 4 during winter and summer periods (DB Environmental Inc., 2004). No spatial








24 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table 3. Initial conditions and calibrated and algae parameter values for level-3
field-scale model application.

[Symbols are defined in appendixes 1 and 2, except where noted; HLR, hydraulic loading rate;
BF, bioturbation factor. Unit abbreviations are defined on the Conversion Factors page]

Condition or
Symbol Valuen
parameter type
Initial Conditions
[CP] 346 gg/L Soil
[SsiP] 3.75 mg/kg Soil
[SP] 355 mg/kg Soil
kLr 10 L/kg Soil
kox .0001 1/d Soil
zas .20 m Soil
Zdf .04 m Soil
0 .8 [-] Soil
Pb .2 g/cm3 Soil
CpP 30 gg/L Water column
CsW/ 14 gg/L Water column
HLR .15 m/d Water column
Zwc .8 m Water column
lC", P .1-1.0 g/m2 phosphorus Biomass (phosphorus)
Calibrated Parameters
BF 3 Soil
ks 1 .3 1/d Algae
'kl/2f .050 mg/L Macrophytes
k1/2rm 1.0 mg/L Macrophytes
lkgfo .01 1/d Macrophytes
lkgm .01 1/d Macrophytes
'ksf .002 1/d Macrophytes
'kr .002 1/d Macrophytes
Algae Parameters
.005 mg/L Algae
k/p .25 1/d Algae
1Additional components not included in previous level of model application conditions.


trends in SAV phosphorus storage were observed in that assessment, although higher phosphorus storage was reported for
summer periods than for winter periods. Higher biomass phosphorus storage was typical in areas dominated by water hyacinth
(1.5-4.0 g/m2), although these floating macrophytes were not commonly found in Cell 4 during the calibration period and were
restricted to the inflow region (DB Environmental Inc., 2004). Macrophyte biomass in Cell 4 is dominated by SAV, but also
includes minor amounts of emergent cattails and water hyacinth. The biomass of these plant communities appears to be dynamic
and probably is affected by hydraulics, nutrient loads, and seasonal light and temperature variation. The primary forcing func-
tions that control macrophyte vegetation dynamics, however, have not been determined. Additional datasets are necessary if
interannual variation in macrophyte biomass and species-specific effects are to be incorporated into the model.
Some of the important complexities of the field system not represented in the first two cases include flowthrough of water
and any suspended or dissolved components, and active periphyton and macrophyte communities. The calibrated results and
validation for the homogeneous, steady-state field scenario are presented in figures 7 to 10.
For the spatially distributed exercise, removal of phosphorus (total phosphorus) from the water column and storage within
Cell 4 was modeled using a first-order uptake parameter with coefficient k,. Conversely, phosphorus release from storage into
the water column was modeled using a second first-order parameter, kr. The uptake parameter is assumed to represent a grouping
of several different processes including the settling of particulate phosphorus, SRP uptake by macrophytes, sorption onto soil,
and so forth. The release parameter is assumed to combine such effects as senescence, desorption, resuspension, and so forth.
The uptake was assumed to be proportional to phosphorus content in the water column, whereas the release was proportional to
the phosphorus content in the soil.













EXPLANATION
CELL 4 CUMULATIVE REMOVAL
PREDICTED










995 1996 1997 1998 1999 2000
YEAR


Figure 7. Comparison of cumulative phosphorus removal from South Florida Water
Management District water sampling of inflow and outflow waters in Cell 4, to the
phosphorus removal predicted by the model.


0.4 -


1998
YEAR


Figure 8. Hydraulic loading rate to Cell 4 for the February 1995 to June 2000 period,
relative to the mean hydraulic loading rate applied during level-3 calibration.


1998
YEAR


Figure 9. Measured and predicted change in soil phosphorus storage over time in the
inflow and outflow region of Cell 4, as determined from soil phosphorus content and
bulk density measurements of the newly accrued soil material (Irons, 2001). Values
are mean + 1 standard deviation of four soils per region.


Model Calibration and Validation


, ,



wCD

o -
1^


EXPLANATION
CELL 4
- ASSIGNED MEAN VALUE






'V


16
14
mW 12



Co Lu2
2 E10

Q- C)

5U
cs 2








26 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


:5 1.2 i i i
< EXPLANATION
S 1.0 INITIAL Pnll QQ 1 GRAM PHOSPHORUS
Z L I-'-. lll- I-.l I h1 1 1 -,
IlI -- II ii I-:: I I GRAM PHOSPHORUS
S 0.8 I-H ,. iill-I 111 IHII,.

a 0.6-

0 00






1995 1996 1997 1998 1999 2000 2001

0.7 |--------------------------
-M 0.6 -









a)0-
I" 0.4 -


a00













u., m 0.3


> 0.2 IIlI I- I . .. H I I: 1i .-,- I l- h-II:'ORUS -
'" PER SQUARE METER
0o 0.1 INITIAL BIOMASS 0.1 GRAM PHOSPHORUS -
Q- PER SQUARE METER


1995 1996 1997 1998 1999 2000 2001

0.035

0 0.030 -
)0-
CD








CI 0.45

SMa 0.020











< EXPLANATION
3 -0010 INITIAL BIOMASS 1 GRAM PHOSPHORUS -
:5 PER SQUARE METER
Z 0 INITIAL BIOMASS 0.1 GRAM PHOSPHORUS
0- PER SQUARE METER
0 1 1
1995 1996 1997 1998 1999 2000 2001










YEAR

Figure 10. Effect of initial biomass on particulate phosphorus and pore-water
0.035










concentrations in the calibrated model.
S0.05
w
CD
r 0.020











A nite-element mesh with 208 elements and 130 element vertices was used (g. 11). Data were obtained from a USGSORUS
PER SQUARE METER
0.005 INITIAL BIOMASS 0.1 GRAM PHOSPHORUS


1995 1996 1997 1998 1999 2000 2001








digital elevation map, and the hydrodynamics were provided by the SFWMD Regional Simulation Model (RSM). Water enters
along the northern edge of Cell 4 at structures G-254A-E, flows southward along a gentle altitude gradient, and exits at structure
G-256. Daily inflow and outflow water volumes were obtained for the simulation period from DBHYDRO, along with weekly or
bimonthly phosphorus concentrations.
The parameters k, and kr were chosen to match the first 6 months of 1995; the best-fit values are 2.4 d-1 and 2.4 x 10-4 d-1,
respectively. The inflow and outflow total phosphorus concentrations, as well as simulated total phosphorus outflow concentra-
tions at G-256, are shown for 1995-97 period in figure 12 and the 1998-2000 period in figure 13. Because of the mechanisms of







Model Calibration and Validation 27


Figure 11. Aerial photograph of the modeled Stormwater Treatment Area 1W (STA-1W),
Cell 4, including elevations within the cell, and the model mesh.


phosphorus release from soil included in this application of the model, phosphorus would be in the outflow, as long as phos-
phorus were still present in the soil even if the phosphorus inflow were zero. The simulated outflow total phosphorus concentra-
tions match the measured outflow values for the first 2 years (1995-96) of the simulation (fig. 12), but subsequently overestimate
the values for the majority of the rest of the modeling period (fig. 13).
Maps of spatially distributed values generated from the measured and simulated total accumulated soil phosphorus are
shown in figures 14 and 15, respectively. The basic pattern of accumulation is the same in both cases, with the greatest amount
of accumulated phosphorus in the soil present in the northern part of Cell 4, close to the inflow gages. Although not shown,
phosphorus uptake had a moderately strong influence on the distribution of accumulated soil phosphorus within Cell 4 during
the calibration phase. Lower values of ku resulted in more evenly distributed patterns of soil phosphorus. This information was
not used to calibrate the model, although it may be used for future refinement of the Cell 4 model. Overall, the amount of soil
phosphorus estimated by the simulation underestimates the measured values within the cell. This is expected because the model
overestimated total phosphorus outflow concentrations. Phosphorus, therefore, did not accumulate sufficiently within Cell
4 during the simulation. This overestimation illustrates a limitation of relying on only two temporally and spatially constant
parameters to simulate processes within the cell.










Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)



0.20 1..

EXPLANATION
++ SIMULATED TOTAL PHOSPHORUS OUTFLOW
+ MEASURED TOTAL PHOSPHORUS INFLOW
u- o MEASURED TOTAL PHOSPHORUS OUTFLOW


+o4 + +
+
++
" I 05 +
I ++ o




+

0 . . .


++ + + o +
+ +
o 0 + +

++ 1 +. +



0 0
0 0 0 0 C


JFMAMJ JASON DJ FMAMJ JASON DJ FMAMJ JASON J
1995 1996 1997



Figure 12. Measured inflow and outflow of total phosphorus, and simulated outflow from
Cell 4 from 1995 to 1997.


EXPLANATION
SIMULATED TOTAL PHOSPHOROUS OUTFLOW
+ MEASURED TOTAL PHOSPHOROUS INFLOW
o MEASURED TOTAL PHOSPHOROUS OUTFLOW


1


+ +
+ + I
++ + +


++ +' + 0
++ + + ++ + 0 00 +



+ + +
0 0 + 0 ++ 0 + I0 00 0 0
8 o o o 0 o o o o o o 0 + 0 0 o 0o o
j00 00 000 0 0 0 0 0 000000 0
oo ooo o oo o o'o


J FMAMJ J AS O N DJ FMAMJ J AS O NDJ F MAMJ J AS ONDJ
1998 1999 2000


Figure 13. Measured inflow and outflow of total phosphorus, and simulated outflow from
Cell 4 from 1998 to 2000.


0.20



r-
LU
Ir-

a 0.15
CO
a)







CD



-r
a.
r:
0-


Ca




CD
--
I--


4-

















80027'


80026'


80025'


80'24'


80023'


26041' -


26040' -


26039'






26038'


26037'


26036'


base from u.S. geological Survey digital data
Universal Transverse Mercator projection, Zone 17



EXPLANATION 0 0.5 1 KILOMETER
TOTAL SOIL PHOSPHORUS, IN GRAMS PER METER SQUARED
14 13 12 11 10 9 8 7 6 5 4 3 I I I

SSAM0 0.5 LOMILE

F SAMPLE LOCATION


Figure 14. Accumulated total soil phosphorus from samples collected at the end of 2000.


Model Calibration and Validation


2952000

2951500

2951000

2950500

2950000

2949500

2949000

2948500

2948000

2947500

2947000

2946500

2946000

2945500

2945000

2944500

2944000

2943500

2943000

2942500

2942000

2941500


S I I I I II I I I I I, I I


I . . . .. I I I I











30 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


80027'


26041'


26040'


26039'


26038'


26037'


26036'


80026'


80025'


80024'


80023'


80022'


Base from U.S. Geological Survey digital data
Universal Transverse Mercator projection, Zone 17





EXPLANATION 0 0.5 1 KILOMETER
ACCUMULATED SOIL PHOSPHORUS, IN GRAMS PER METER SQUARED I I
9 8 7 6 5 4 3 2 1I I I

0 0.5 1 MILE



MODEL CELL BOUNDARY


Figure 15. Estimated accumulated soil phosphorus at the end of 2000.


I I I I I I I I I I I I I I I I I I I 1
-


-
-

-


-


-


-
W

-


-


-

-
-


-


-


-
-
-
-

1
-


-


-
F.

-


-


-

-
--


-
F...I...I....I...I...I....I.


2952000


2951500


2951000


2950500


2950000


2949500


2949000


2948500


2948000


2947500


2947000


2946500


2946000

2945500


2945000


2944500


2944000


2943500

2943000


2942500


2942000


2941500







Global Sensitivity Analysis 31


Global Sensitivity Analysis

Mathematical models are built in the presence of uncertainties of various types, such as input variability, model algorithms,
model calibration data, and scale (Beven, 1989; Haan, 1989; Luis and McLaughlin, 1992). Uncertainty analysis is used to
propagate all such uncertainties, using the model, onto the model output of interest. Sensitivity analysis is used to determine
the strength of the relation between a given uncertain input and the output (Saltelli and others, 2004). The evaluation of model
sensitivity and uncertainty is an essential part of the model development and application process (Reckhow, 1994; Beven, 2006).
Although sensitivity analysis is useful in selecting proper parameters and models, and model uncertainty analysis provides an
informative assessment of results, these tools are frequently ignored in current water-quality modeling efforts (Beven, 2006;
Munoz-Carpena and others, 2006). Complex mathematical models, such as the model described herein, often contain a large
number of input parameters and are computationally intensive. To facilitate the evaluation and application of these models, it is
important to identify a subset of parameters that strongly affect model output for several reasons:
Model .N,1ih., ,i,.,, If only a few parameters are important, the model typically can be simplified by eliminating
parts that appear superfluous, or by grouping discrete processes.

Quality Assurance-If the model shows a strong or weak dependence on parameters initially expected to be unimport-
ant or important, respectively, the model structure may need to be revised.

Additional Research-The process may clarify whether important parameters require more accurate quantification
(Saltelli, 2002).
Concerning global sensitivity, an "input factor" broadly refers to anything that changes the model prior to execution. This
not only includes the model parameters, input data, and boundary conditions, but also entirely different conceptualizations of
the system. The model described herein allows for user-defined model complexity through a flexible XML user interface as
described by A.I. James (University of Florida, written commun., 2008). Of particular concern is how model complexity affects
global sensitivity and the uncertainty of different model outputs, especially for those biogeochemical processes that are present
at different complexity levels. Furthermore, in flow-driven systems such as the Everglades, it is necessary to account for the
effect of water velocity in the analysis. A statistical framework applied here follows that presented by Munoz-Carpena and
others (2007) to evaluate a test system at three increasingly complex model structures and three surface-water flow velocities (or
residence times).


Techniques and Screening Methods

Input factors of interest in the sensitivity analysis are those that are uncertain; that is, their value lies within a finite interval
of nonzero width. Traditionally, model sensitivity has been expressed mathematically as the derivative of a model output with
respect to an input variation. These derivatives are typically normalized by either the central value where the derivative is
calculated, or by the standard deviations of the input parameter and output values. These sensitivity measurements are "local"
because they are fixed to a point or narrow range where the derivative is taken. Local sensitivities are used widely and are the
basis of many applications, such as the solution of inverse problems. These local sensitivity indexes, used in "one parameter
at a time" (OAT) methods, quantify the effect of a single parameter, Xi, by assuming all others are fixed (Saltelli and others,
2005). Sometimes a crude variational approach is selected whereby, instead of a derivative, incremental ratios are taken by
moving factors one at a time from the baseline by a fixed amount (for example, 5 percent) without prior knowledge of the factor
uncertainty range.
Local sensitivity indexes are only valid and useful if all factors in a model are linear, or if some type of average can be
used over the parametric space. In the current model, because some of the proposed model equations (or equation combinations)
are nonlinear, an alternative "global" sensitivity approach is more appropriate. Exploring the entire parametric space of the
model may help determine (1) which of the uncertain input parameters largely determine the uncertainty of a specific output, or
(2) which input parameter, if fixed, would reduce output uncertainty by the greatest amount (Saltelli and others, 2005).
Different types of global sensitivity methods can be selected based on the objective of the analysis. For computationally
expensive models or the simultaneous evaluation of many parameters, it is usually most efficient to apply a screening method.
This type of method provides a qualitative parameter ranking in terms of relative effect over output variation and allows the user
to focus the calibration or development effort on the most sensitive parameters. If quantitative information is desired, an analysis
of variance technique usually is required. Each of these methods is applied to the new wetland phosphorus model presented
herein, and the results are compared.







32 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Morris Method

The screening method proposed by Morris (1991), herein referred to as "Morris method" or "Morris," and later modified by
Campolongo and others (2005) was used in this study because it is relatively easy to apply, requires very few simulations, and
its results are easily interpreted (Saltelli and others, 2005). Morris (1991) proposed conducting individually randomized experi-
ments that evaluate the elementary effects (relative output differences) of changing one parameter at a time. Each input may
assume a discrete number of values, called levels, that are selected within an allocated range of variation for the parameter. For
each parameter, two sensitivity measures are proposed: (1) the mean of the elementary effects (u), which estimates the overall
effect of the parameter on a given output; and (2) the standard deviation of the effects (o), which estimates the higher order char-
acteristics of the parameter, such as curvatures and interactions. Because the model output can be nonmonotonic, Campolongo
and others (2005) suggested considering the distribution of absolute values of the elementary effects (y*) to avoid the canceling
of effects of opposing signs. The number of simulations required (N) to perform the Morris analysis is expressed as:

N= r (k + 1) (42)

where r is the sampling size for search trajectory (r = 10 produces satisfactory results), and k is the number of factors. Although
elementary effects are local measures, the method is considered global because the final measure, y*, is obtained by averaging
the elementary effects, and this eliminates the need to consider the specific points at which they are computed (Saltelli and
others, 2005). Morris (1991) recommended applying y (or y* thereof) to rank parameters in order of importance, and Saltelli
and others (2004) suggested applying the original Morris measure, o, when examining the effects induced by interactions. To
interpret the results in a manner that simultaneously provides insight about the parameter ranking and potential presence of
interactions, Morris (1991) suggested plotting the points on a (y**)-a Cartesian plane. Because the Morris method is qualitative
in nature, it should only be used to assess the relative parameter ranking.


Extended Fourier Amplitude Sensitivity Test (FAST)

A variance-based method such as FAST can be used to obtain a quantitative measure of sensitivity (Cukier and others, 1973,
1978; Koda and others, 1979). This technique decomposes the total variance (V= o2y) of the model output Y =fj(X, X, ..., Xk) in
terms of the individual factors Xi, using spectral analysis so that:

V= G2y= V + V2 + V3 +...+ Vk+R, (43)

where V, is the part of the variance that can be attributed to the input factor Xi alone, k is the number of uncertain factors, and R
is a residual corresponding to higher order terms. The first-order sensitivity index, Si, which is defined as a fraction of the total
output variance attributed to a single factor, can then be taken as a measure of global sensitivity of Y with respect to Xi; that is:

Si = Vi / V. (44)

To calculate Si, the FAST technique randomly samples the k-dimensional space of the input parameters using the replicated
Latin hypercube sampling (r-LHS) design (McKay and others, 1979; McKay, 1995). The number of evaluations required in the
analysis can be expressed as:

N = M (k + 2), (45)

where M is a number between 500 and 1,000. For a perfectly additive model, 2Si = 1; that is, no interactions are present and total
output variance is explained as a summation of the individual variances introduced by varying each parameter alone. In general,
models are not perfectly additive, and 2Si < 1.
The FAST analysis was extended to incorporate the calculation of the total order effects through the total sensitivity index,
Sri, calculated as the sum of the first and all higher order indices for a given parameter Xi (Saltelli, 1999; Saltelli and others,
2000). For example, for X1:


ST1 = S1 + Sli + Sljk, + ... + S1 ... and







Global Sensitivity Analysis 33


For a given parameter Xi, interactions can be isolated by calculating STi Si, which makes the extended FAST technique a
powerful method for quantifying the individual effect of each parameter alone (Si) or through interaction with others (SnT Si).
An additional benefit of the extended FAST analysis is that because the results are derived from a randomized sampling proce-
dure, they can be used as the basis for the uncertainty evaluation by constructing cumulative distribution functions (CDFs) for
each of the selected outputs. This could lead to an efficient Monte Carlo type of uncertainty analysis, if only the sensitive param-
eters identified by the Morris screening method are considered as the source of uncertainty (Mufoz-Carpena and others, 2007).


Effects of Changing Model Structure and Flow Velocity on Global Model Output Sensitivity

A.I. James (University of Florida, written commun., 2008) present the implementation of the phosphorus conceptual
water-quality model, TarSE, in the Hydrologic Simulation Engine (HSE) of the SFWMD Regional Simulation Model (RSM).
Documentation of the SFWMD/RSM is available on the RSM web site at https://my.sfw.i./ .!. '.... 't, i l',.i'. ? ,' ,-.. ;. 1= 1314,2
555966,1314_2554338&_dad=portal&_schema=PORT\. SI, i !,-. = ... The RSM/HSE runs on Linux platforms, as does
TaRSE, which is compiled into a static library that can be linked to the RSM. The resulting combined model is referred to as
Regional Simulation Model/Water-Quality model (RSM/WQ). Input data are provided to the RSM/WQ through flexible exten-
sible markup language (XML) input files that define the control parameters, hydrologic boundary conditions, sources, initial
conditions, and so forth. The RSM/WQ is used in the global sensitivity analysis of the proposed phosphorus conceptual model.
Descriptions of the specific water-quality input files used in this evaluation are provided in appendix 3.


Analysis Procedure

A software package, SimLab v2.2 (Saltelli and others, 2004), was used in the global sensitivity analysis. SimLab is
designed for uncertainty and sensitivity analyses using pseudorandom number generation (PNG). The emphasis of the analysis is
to sample a set of points from joint probability distributions of the selected model input factors; that is, the "sample distribution."
PNG-based uncertainty and sensitivity analyses involve performing multiple model evaluations with stochastically selected
values for model inputs, and using the results of these evaluations to determine: (1) degree of uncertainty in model predictions,
and (2) input variables responsible for the uncertainty. The general protocol is as follows:
Step 1-Range and probabilistic distribution functions (PDFs) are selected for each input variable (input factor). If the
analysis is preliminary, then "rough" distribution assumptions may be adequate.

Step 2-A sample of points is generated from the distribution of the inputs specified in Step 1, resulting in a sequence
of sample elements. The SimLab Statistical Pre-Processor module executes this step based on PDFs provided by the
user.

Step 3-Simulations are run with the sample elements, yielding a set of model outputs. The model evaluations map the
input space to the result space, which provides a basis for subsequent uncertainty and sensitivity analyses. A series of
UNIX scripts were prepared to run the RSM/WQ model with a new set of sampled input values for each simulation.
These scripts automatically substitute the new parameter set into the input XML files, run the model, and perform the
necessary postprocessing to obtain the selected model outputs for the analysis. The outputs for each simulation are
stored in a matrix containing the same number of lines as the number of samples generated in Step 2.

Step 4-Sensitivity and uncertainty analysis of the model outputs. The Statistical Post Processor module of Simlab is
used to calculate sensitivity indexes for the Morris and extended FAST methods.


Flow Domain

A 1,000 x 200-m flow domain was selected and discretized into 160 equal rectangular triangles (cells) as shown in
figure 16. Flow was set from left to right so that the inflow boundary consisted of cells 1, 41, 81 and 121, and the outflow
boundary consisted of cells 40, 80, 120, 160. A no-flow boundary was used for the top and bottom (longer) sides of the rect-
angle. A constant velocity across the domain was fixed with an average water depth of 1.0 m. To test the effect of flow velocity
on the transformation and transport of phosphorus in wetlands, three fixed longitudinal flow velocities (0.00579, 0.00116, and
0.000579 m/s) were considered for each batch of sensitivity analysis simulations. These velocities correspond to residence times
of 2, 10 and 20 days, respectively, representative of operational flows within STA-1W Cell 4 (fig. 1).







34 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Inflow

Inflow

1


122' 124 126128 130 132 134 136 138 140 142 144 146 1 48 150152\154 \156 \ 158 10
121 123\ 125 127\ 129\ 131 133\ 135 137\ 139 141 \143 145\ 147 149 151 153 155 15 15
81 83 85 87 89 /91 /93 /95 97 99 /101/ 103 105/ 107 /109/ 111/113/115/117/119
82 84 86 88 /90 /92 /94 /96 /98 00 02 1 04,/106 /108 10l 12 114 16, 118, 120
'r42 \44 \46 \48 50 \52 54 56 \8 60 62 64 66 \ 68 70 \ 72 \ 74 76 \ 78\ 80
41\ 43\ 45\ 47\ 49 51 53 55\ 57 59 61 63 65 67 69 71 73 75 77 79
3 / 5 7 / 9 11/13/15/ 17/19/ 21/23 /25 /27 /29 /31/33/35/37/39
2 /4 /6 /8 10 1/i2 1/4 /16/ / /22 24 /26 / /30 /32 34 /36 38 /40


I.uuu meters


Outflow


EXPLANATION
m INFLOW BOUNDARY CELL
mI OUTFLOW BOUNDARY CELL



Figure 16. Testing domain for global sensitivity. The total simulation time for all model runs was
30 days and the initial time increment selected was At = 3 hour.





Description of Inputs and Outputs

Three model-complexity levels similar to the ones described earlier for model calibration were used in the global sensitivity
analysis. Details of formulation and RSM/WQ model input files used in each case are given in appendix 3. Schematics of the
transfer and transformation processes involved in each complexity level are presented in figures 17 to 19.
The field-scale ambient variability of many inputs has been reported to be modeled adequately using normal or log-normal
distributions (Jury and others, 1991; Haan and others, 1998). Because of the lack of data needed to estimate mean and standard
deviations for PDFs assumed to be Gaussian, the f-distribution was used to assign proper values so that shape factors fit an
approximate log-normal distribution. The f-distribution is generally used as a rough model in the absence of sufficient data
(Wyss and J0rgensen, 1998). When only the range and a base (effective) value are known, a simple triangular distribution can be
used (Kotz and van Dorp, 2004). To characterize sensitivity and uncertainty, each input parameter was assigned a PDF based on
the range of values obtained from a comprehensive literature review summarized in appendix 2. The range for each parameter
was selected to cover all physically realistic values, and all parameters were assigned f-distributions except for A2 and 2,. These
two parameters are related to the composition of the physical system (that is, vegetation density, domain dimensions, velocity,
and so forth), rather than natural variation, so that the probability of the different values within their range can be considered
constant. This corresponds to the uniform distribution (U-distribution) that was selected for them. Table 4 summarizes the sensi-
tivity parameters selected for all complexity levels studied, and table 5 shows the values of the rest of the fixed model parameters
used in the simulations.
Several outputs were selected in the analysis for each one of the conceptual model "stores" considered for each complexity
level. For mobile quantities discussed earlier, averages across the outflow domain were calculated at the end of the simulation
as an average over the entire simulation. Because trends in the results were similar, the average at the end of the simulation
subscriptt "o,tf') was chosen for discussion. For stabile quantities, variation at the end of the simulation was estimated as the
difference across the entire domain between the mean value at the beginning and end of the simulation. Table 6 summarizes the
details of the outputs calculated for the global sensitivity and uncertainty analysis.
Six pseudorandom parameter sample sets were created-one for each complexity level for the Morris and FAST methods.
Each sample set was run three times for each velocity. The number of Morris method runs was selected according to the number of
parameters in each complexity level based on equation 42. For the FAST method, a sufficiently large number of simulations were
selected to allow for both the global sensitivity index calculation and the uncertainty analysis. After some experimentation, the
number of runs for each set of simulations was set to 5,000. The number of simulations run for each level (table 7) illustrates one
of the potential advantages of the Morris method over the FAST method. For an average simulation time of 15 seconds per run, the
total required time to evaluate the model increased from about 15 hours for the Morris method to 16 days with the FAST method.


I







Global Sensitivity Analysis 35


Morris Method Results

Results of the global sensitivity analysis obtained from the screening Morris method are presented for each of the selected
model outputs identified in table 6. The rankings of importance of parameters for each respective output, based on the relative
value of Morris p*, are presented in tables 8 to 13. As suggested by Morris, only parameters separated from the origin of the
p**-o plane were considered important. Figures 20 to 25 graphically present the Morris method results for the selected outputs.
As previously noted, the choice of parameters deemed to be important for sensitivity when using the Morris method is subjec-
tive. The decision is based on using this graphical presentation, and the user must decide whether a parameter is sufficiently far
from the origin to warrant ranking. Choosing parameters becomes increasingly difficult when the parameters are more widely
distributed throughout the p*-a plane, as was the case for many level-3 results (for example, fig. 22G-I). Consequently, without
quantified measures to more accurately compare the contribution of each parameter, it becomes challenging to identify their true
importance in these complex cases, and the advantages of an alternate approach such as the extended FAST method become
apparent. Though the number of key parameters identified is an important outcome (sensitivity to parameters), so too are any
noticeable changes in the ranking of these parameters across either velocities (sensitivity to environmental structure) or levels of
complexity (sensitivity to model structure), noting the limitations described above.
These initial screening results illustrate four products of the global sensitivity analysis: (1) an indication of the importance
of some common parameters for all outputs; (2) an indication of how changing the modeling structure affects the sensitivity of
the model outputs to parameters, environment conditions, and the model structure itself; (3) a verification of model behavior
and absence of errors; and (4) an indication of how important parameters influence the model outputs, either directly or through
their interaction with other parameters. Results are discussed in terms of four broad considerations that include screening of
parameters, ranking of parameters, effect of flow velocity on sensitivity, and effect of complexity on sensitivity.










Inflow Outflow
CGswP

SURFACE WATER EXPLANATION
EXPLANATION
MATERIAL FLOW
PHOSPHORUS FLOW
CpwP SOIL PORE WATER SRP
CswP SURFACE-WATER SRP
SO ORGANIC SOIL
SSiP SOILADSORBED PHOSPHORUS
II S







Figure 17. Conceptual model for complexity level 1. SRP is soluble reactive phosphorus. Notation definitions
are presented in table 6.








36 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Inflow


Outflow


C,.1 pl


SURFACE WATER





S1111


CpwP
CswP
Cswpl
SO
SsiP


EXPLANATION
MATERIAL FLOW
PHOSPHORUS FLOW
SOIL PORE WATER SRP
SURFACE-WATER SRP
PLANKTON BIOMASS
ORGANIC SOIL
SOIL ADSORBED PHOSPHORUS


Figure 18. Conceptual model for complexity level 2. SRP is soluble reactive phosphorus. Notation definitions
are presented in table 6.









Inflow SURFACE WATER Outflow

i CswP C.,, -,
C cswP C," EXPLANATION

MATERIAL FLOW
PHOSPHORUS FLOW
Cmp MACROPHYTE BIOMASS
CpwP SOIL PORE WATER SRP
CswP SURFACE-WATER SRP
S'IL- Cswpl PLANKTON BIOMASS
S- So ORGANIC SOIL
SSsiP SOIL ADSORBED PHOSPHORUS


Figure 19. Conceptual model for complexity level 3. SRP is soluble reactive phosphorus. Notation definitions
are presented in table 6.








Global Sensitivity Analysis 37


Table 4. Parameters used in the global sensitivity and uncertainty analyses, including probability distribution functions and
parameter use in levels 1 to 3.

[Ranges and distributions are based on the literature review presented in appendix 2. Complete parameter descriptions are provided in the model calibration and
validation section and appendix 1 of this report. Unit abbreviations are defined on the Conversion Factors page]


Parameter Parameter present in
Parameter Coded notation' description Distribution Units
description Level 1 Level 2 Level 3


Pb bulk density


Bulk density


p (0.05, 0.5)


Unitless x x x


S Mass fraction of phosphorus in
Xnzp chi mp
-X c p macrophytes

Schior l Mass fraction of phosphorus in
XoP chi_org_soil s
organic soil

Mass fraction of phosphorus in
XpP chi_pl plankton
plankton
kd k_d Coefficient of adsorption
kdf k_df Coefficient of diffusion
Half saturation constant for
kl/2mp k_halfsat_mp
macrophyte growth
Half saturation constant for
k_halfsat pl
plankton growth
kgnm k_mp_growth Macrophyte growth rate
ksnmp k_mp_senesc Macrophyte senescence rate

kox k_ox Soil oxidation rate
kg1 kplgrowth Plankton growth rate
kj k_pl_settle Plankton illi rate
S long_disp Longitudinal dispersivity
0 soil_porosity Soil porosity
t tran_disp Transverse dispersivity
'Code implementation is provided in appendix 2.


p (0.0002, 0.005)


p (0.0006, 0.0025)


p (0.0008, 0.015)

p (8x10-6, 11x10-6)
p (7xl0-10, 4xl0-9)

p (0.001, 0.01)


p (0.005, 0.08)

p (0.004, 0.17)
p (0.001, 0.05)
p (0.0001, 0.0015)
p (0.2, 2.5)
p (2.3x10-7, 5.8x10-6)
U (70, 270)
p (0.7, 0.98)
U (70, 270)


Unitless


Unitless x x x


Unitless


x x


m3/g
m2/s

g/m3


x x


1/d
1/d
1/d
1/d
m/s
m
Unitless
m


x x
x
x
x x
x x
x x








38 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table 5. Fixed model inputs used in the global sensitivity and uncertainty analyses.

[Notations are defined in appendix 1. Units: g/m2, gram per square meter; g/m3, gram per cubic meter; m, meter]


Type Description
Type Value Level 1 Level 2 Level 3
(unils)
(7C (, .i. 500 x
CsY (: .r.i .043 x x
Initial and CpwP (g/m2) .071 x x x
boundary
conditions CSw' ,. ,- I .05 x x x
S'( ., 30,000 x x x
,Ssi' .1 .027 x x x
ki (day) 1 x x x
Surface porosity
Parameters (unitless)
Zas (m) .1 x x x
zdf(m) .04 x x x


Table 6. Model outputs used in the global sensitivity and uncertainty analyses.

[Notations are defined in appendix 1. SRP, soluble reactive phosphorus]


Class Type Output Description

Average of CwP for outlet cells (boundary cells 40, 80, 120, and
Surface-water SRP (CswP) outflow s 160 in fig. 16) at the final time step
Mobile CsPo,t Average of CsWP for outlet across all simulation time steps
CswPlo,tf Average of CsW' for outlet cells at the final time step
Plankton biomass (C5swP) outflow
wCs]o,t Average of CsW' for outlet cells across all simulation time steps
Soil pore war SP v n Difference in averages of CpwP across the domain (all cells) be-
Soil pore-water SRP (Clw) variation Cw ]acr
(r tween initial and end time step
Difference in averages of So across the domain (all cells) between
Organic soil (So) accretion S]cr
Stabile
S. Difference in averages of SsP across the domain (all cells) between
Soil adsorbed P (Si') variation SJ']acr
initial and end time step
Difference in averages of C"P across the domain (all cells) between
Macrophyte biomass (CP) accumulation C]ad t
initial and end time step


Table 7. Regional Simulation Model/Water Quality Model (RSM/WQ) simulations run in the
global sensitivity and uncertainty analyses.

[FAST, Fourier amplitude sensitivity test; RSM/WQ, Regional Simulation Model/Water Quality Model]

Number ol Number ol Number ol simulations
Level
velocities parameters Morris FAST Total

1 3 8 90 x 3 5,000 x 3 15,270
2 3 12 130 x 3 5,004 x 3 15,402
3 3 16 170 x 3 5,008 x 3 15,534
Total simulations 1,170 45,046 46,206








Global Sensitivity Analysis 39


Table 8. Morris method global sensitivity analysis parameter ranking for the surface-water soluble reactive phosphorus (SRP) outflow
outputs (CswPo,tf and Cs]o,t).

[Parameter descriptions are provided in table 4. Numbers for each parameter represent the parameter ranking in decreasing order of importance for each
output (1 = most important for that level, "-" no significant influence). Missing values or symbols indicate that they are not part of the simulation]

Velocity Parameter
Complexity (melers Oulpul
p e r d a y ) .. ', ' .' .. -.
50 C,,P], 2 1 4 3
100 CjwP]o,j 2 1 4 3
500 CwJ]o, 2 1 4 3
Level 1
50 CswP],, 2 1 4 3
100 Cwplo,t 2 1 4 3
500 CwP]0,, 2 1 4 3
50 CJP]i 5 3 4 6 1 2
100 CJwp]o, 5 3 4 6 7 -- 1 2
500 CwP]o, 7 4 5 6 3 1 2 8
Level 2
50 CsP],, 4 3 6 5 1 2
100 Cj]o,t 4 3 5 6 1 2 7
500 Cj,]o,t 7 4 5 6 3 1 2 8
50 CP]o, -- 7 6 1 11 9 10 13 5 12 -- 3 2 4 8
100 CwP]o,t 11 -- 8 -- 10 -- 9 6 5 12 1 4 7 2 3
Level 500 C ], 10 4 3 -- 12 9 8 -- 1 2 5 6 7 11
Level 3
50 Cp]o,, -- 8 7 1 12 10 11 -- 6 5 13 14 3 2 4 9
100 Cplo,t 12 -- 9 -- 10 -- 11 6 4 8 1 5 7 2 3
500 Cs]o,, 10 4 3 -- 12 9 8 -- 1 2 5 6 7 11



Table 9. Morris method global sensitivity analysis parameter ranking for the pore-water soluble reactive phosphorus variation output
( CpwP acr)

[Parameter descriptions are provided in table 4. Numbers 1-6 for each parameter represents the ranking of parameter in decreasing order of importance for each
output (1 = most important for that level, "-" no significant influence). Missing values or symbols indicate that they are not part of the simulation]


Velocity Parameter
Complexity meterss Oulpul t ,i
per day) .' .; '- / .:' '' -.

50 Cpwp]acr 4 1 2 6 5 3
Level 1 100 CwP]pacr 4 1 2 6 5 3
500 CwP]acr 4 1 2 6 5 3
50 CpwP]ac 4 1 2 6 5 3
Level 2 100 CwP]acr 4 1 2 6 5 3
500 Cwp]acr 4 1 2 6 5 3
50 CpwP]acr 5 -- 3 -- 4 -- 2 -- 1
Level 3 100 CpwP]acr 1 4 3 2
500 CpwP]acr 3 2 4 1- -- 1








40 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table 10. Morris method global sensitivity analysis parameter ranking for the organic soil accretion output (SOacr).

[Parameter descriptions are provided in table 4. Numbers 1-6 for each parameter represents the ranking of parameter in decreasing order of importance for each
output (1 = most important for that level, "--" no significant influence). Missing values or symbols indicate that they are not part of the simulation]


Velocity
Complexity (meters Oulput
per day)


Parameter


S A ., \ ..1 .


50 S]ac -- 1
Level 1 100 S]acr -- 1
500 S]ac -- 1
50 S]a -- 1
Level 2 100 S]acr 1
500 S]ac -- 1
50 S]ac -- 1 4 3 10 8 9 -- 11 5 7 2 6
Level 3 100 So]ac' 13 1 6 9 12 10 14 7 11 2 8 4 3 5
500 S]acr 10 1 2 -- 7 5 8 9 4 3 6




Table 11. Morris method global sensitivity analysis parameter ranking for the soil adsorbed phosphorus variation output (SsPIacr)

[Parameter descriptions are provided in table 4. Numbers 1-6 for each parameter represents the ranking of parameter in decreasing order of importance for each
output (1 = most important for that level, "-" no significant influence). Missing values or symbols indicate that they are not part of the simulation]


Velocity Parameter
Complexity meterss Oulpul
per day) i. .. / ' i, I

50 S/,,]c 4 1 2 3

Level 1 100 Ssi]acr 4 1 2 3
500 SP],,, 4 1 2 3

50 S/,,]c 4 1 2 3

Level 2 100 S,,s]ac 4 1 2 -- 3

500 S,,]ac 4 1 2 3

50 Ssilacr 5 6 2 3 -- 4 -- 1
Level 3 100 Ssi,]acr 1 -- 3 -- 4 -- -- -- 2

500 S i]acr 3 4 2 -- 1


n
. I,' 1..'


I ,








Global Sensitivity Analysis 41


Table 12. Morris method global sensitivity analysis parameter ranking for the plankton biomass outflow outputs (Csw]o,tf and Cswpo,t).

[Parameter descriptions are provided in table 4. Numbers 1-6 for each parameter represents the ranking of parameter in decreasing order of importance for each
output (1 = most important for that level, "-" no significant influence). Missing values or symbols indicate that they are not part of the simulation]

Velocity Parameter
Complexity meterss Oulput ,
per day) .r
50 CPl]o,g 4 1 2 6 -- 3 -- -- 5
100 C ']o,,f 3 1 2 4 5
500 C5'],wtf 6 3 4 7 5 1 2 8
Level 2
50 C 'P1],, 3 2 4 6 1 -- -- -- 5
100 CP1'],0 4 1 3 6 2 7 -- 5
500 C~1],, 5 4 7 6 3 1 2 8
50 CPl]o,g 7 11 5 12 2 15 1 16 8 10 3 6 4 9 13 14
100 C ]o,,f 3 15 7 14 12 13 2 10 8 11 1 4 5 -- 6 9
500 CWv]o,tf 8 4 5 -- 12 10 7 -- 1 3 2 9 6 -- 11
Level 3
50 CP1]0,, 9 10 6 8 3 15 2 -- 13 12 1 5 4 7 11 14
100 C P1],0 4 14 9 15 11 12 2 8 10 13 1 3 6 -- 5 7
500 C~ ],, 8 4 5 -- 12 10 7 -- 1 3 2 9 6 -- 11



Table 13. Morris method global sensitivity analysis parameter ranking for the macrophyte biomass accumulation output (CmPacr)

[Parameter descriptions are provided in table 4. Numbers 1-6 for each parameter represents the ranking of parameter in decreasing order of importance for each
output (1 = most important for that level, "-" no significant influence). Missing values or symbols indicate that they are not part of the simulation]

Velocity Parameter
Complexity meterss Oulpul r.
p e r d a y ) ,' i .". .o :.
50 P]acr -- 3 4 5 9 8 10 11 6 7 2 1
Level 3 100 CP]a. 11 4 5 10 7 12 9 13 3 8 6 1 2
500 CP]cr 9 3 1 7 6 8 10 5 4 2














0.20

0.15

0.10


LEVEL 500 m/d








Pso


0.05 0.10 0.15 0.20 0.25 0.30
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


U.UO
LEVEL2 -500 m/d
0.05

0.04

0.03 gP
k
0.02 k,1pl *
ko
0.01 o x /1


0 0.01 0.02 0.03 0.04 0.05 0.C
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
G
D.035
LEVEL 3 500 m/d
).030 ko
p
D.025 *Xs

).020 k mp

.015 kdf s ) pi
*P *kl/ pl
).010 X P 2

.005 mp

0 I I I I


0 0.005 0.010 0.015 0.020 0.025
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


0.16 LEVEL 1 100 m/d
0.14
0.12
0.10 -
k.
0.08
0.06 P
0.04 X Pb
0.02

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


n nnc


o 0.005
Z CJ
0.004
U-
- 0.003

z 0.002
z 2
n 0.001
LU


U-

>oL
LU

S^I


0 LU
Ca LU


0.030 0.035


LEVEL 2 -100 m/d



kgpI


pi
k


k1/2


P

0.001 0.002 0.003 0.004 0.005
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


LEVEL3-100m/d
0.05 X pP snmp
k mp Lt k p
0.04 g \ p

0.03 k X- k p

0.02 kd- 'P g

0.01 p

0


0 0.01 0.02 0.03 0.04 0.05
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


C
0.045 I I I i
0.040 -LEVEL 1 50 m/d
0.035
0.030
0.025
0.020
0.015 P k
0.010
0.005

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


0.0030

c 0.0025
Z Co
P L 0.0020 -

>- 0.0015


z I
< z 0.0010 -

0.0005


06 0


LEVEL 2 50 m/d




k

k pl
kox,



0.0005 0.0010 0.0015 0.0020 0.0025 0.(
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


LEVEL3-50m/d k mp k
10 k mp-
40 X- P kg k mp
Smp sn
35 x-Pb k pl

?5- x\ 12
0 so
15




0 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.05
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


0.06


Figure 20. Morris method global sensitivity analysis results for surface-water soluble reactive phosphorus outflow (CswP]o,tf) across complexity levels and
velocities tested. Parameter descriptions are provided in table 4.


Z CO
0
oI-
U

< >z
a LU











0.35 I
LEVEL 1 500 m/d
F 0.30
z o
1- 0.25

0.2 0.20

0 0.15
z ox
O 0.10 P
I -b o
m i 0.05
0 I I
0 0.05 0.10 0.15 0.20 0.25 0.30 0.;
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
D
0.30 I
LEVEL 2 500 m/d
o L 0.25
z C
i 0.20

S> 0.15

z 0.10 -

0.05 x -
k,,


ii iii ii II II ii.-
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


0 0.01


0.02 0.03 0.04 0.05 U.U6 0.07
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


S0.3
Z to
o t 0.2

- 0.2

M S 0.1

_ 0.1
< U
C5 Gi 0.0


0.3

L 0.2
z c.
I 0.2

C > 0.1

z 0.1

c- 0.0
(/2 Ii


LEVEL 1 -100 m/d
0

5

0


kox
0 Pb Xso

5 kdf


0 0.05 0.10 0.15 0.20 0.25 0.30 0.3
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
E
0
LEVEL 2 100 m/d
5

0

5


P kox
0 b X
5P b o -
k,,


1130 111 1 I II :
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


oU



LU
0z
5-


oQ LU
CO LU


z
Z C
SLU



za
i3 L
.cz


Co LUJ


o >O

.-,i





C3I


1130


LEVEL3- ii....i -, mp
7 \

6 I df
SP
5 X so

4

3

2


0 L I I I L
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


Zc





z5
z|
o Lii

I-
rn LU


C
0.35 ,i I
LEVEL 1 50 m/d
0.30

0.25

0.20

0.15 -
kox
0.10 PPb -

0.05 k
*kdf
0 0.05 0.10 0.15 0.20 0.25 0.30 0.3
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
F
0.30 i
LEVEL 2 50 m/d
0.25

0.20

0.15

0.10
Pb Xso x
0.05 Pb
.k,,
II I 11' i III I I Ii .1 II 113
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)

0.08
LEVEL 3 -50 md "P
0.07

0.06 p

0.50 E- so

0.40

0.30

0.20

0.10 *kdf

0 L L I I I I
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.C
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


Figure 21. Morris method global sensitivity analysis results for soil pore-water soluble reactive phosphorus variation (CpwP]acr) across complexity levels and
velocities tested. Parameter descriptions are provided in table 4.


oU
Ce




LU
I-
CO LU
Co LU


LEVEL 3 500 m/d kg mp
17 g8

6 Xo P
5

4

3

d2 k


0
0 L L L L














oo
U- u

. -









. -
a L

.Pu














I-








oC

z,









o LU



2D


z,
0' LU
U-



5-
U|













-iS


ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


'U i i i i
S LEVEL 3 500 m/d
10 -

10 I

10 -Xso

10


10 k P1p
sn
0 S
0 100 200 300 400 500 600 700 800 900
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(A*)


S LEVEL 1 500 m/d

10
10
10
10
10
10
10
10 kox

0 100 200 300 400 500 600 700 800 900 1,0
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


LEVEL 2 500 m/d
10
10
10 -

10
10
10 -
10
10

0
0 100 200 300 400 500 600 700 800 900 1,0
0 100 200 300 400 500 600 700 800 900 1,0(


0-



Z
U-
U|


SLU
I-

C LU


O0


Z C4
CDo



U< -

0 2
< LU
I- -


Ca
5 LU
2u-
"ED
LL
LU


z z
z I-
D LU

II
CO LU


uu iii
800 LEVEL3 -100 m/d kgp sp
800 k st
700

600 kd
500 Pb k pl k nmp
g g
400 t
300 Xpl
xp
200- I X P kox
100

0 100 200 300 400 500 600 700 800 900
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(9*)


I,UUU
900 LEVEL 1 100 m/d
800
700
600
500
400
300
200
100 kox

0 100 200 300 400 500 600 700 800 900 1,(
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
E
1,000 i i i i
0 LEVEL 2 100 m/d
900
800
700
600
500
400
300
200
100 kox

0 100 200 300 400 500 600 700 800 900 1,0(
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(p*)


Z -
o 0
z Z

S-
U|


Sul

-.II


30


z -,



LU
SU
5-



oz
S.LU
Cw3 LU


a o
2

lL



. z


0 100


200 300 400 500 600 700
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


800 900


Figure 22. Morris method global sensitivity analysis results for organic soil accretion (SO",r) across complexity levels and velocities tested. Parameter
descriptions are provided in table 4.


I ,UUU
900 LEVEL 1 50 m/d

800
700
600
500
400
300
200
100 kox

100 200 300 400 500 600 700 800 900 1,000
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
F
1,000 i,,i
900 LEVEL 2 50 m/d
800
700
600
500
400
300
200
100 ko
0
0 100 200 300 400 500 600 700 800 900 1,000
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)

900 i i i
800 LEVEL 3-50 m/d
800 -
kd
700 -
600 k mp
P
500 Xso
400 Pb k /mp
P
300 1 X mp
200 *k P k ox
100 kl/2
o












0.9
U- 0.8
Z G 0.7
S 0.6
,^ 0.5
5 0.4
4z 0.3
ou
Z 2 0.2
C LU 0.1

0




0.9
u 0.8
zj c 0.7

|a 0.6
Cu
L L 0.5
0 0.4
Sz 0.3
I 0.2
Cz L 0.1

0




0.12

o 0.10
zco
L 0.08
SW
U-
> 0.06

4 Z 0.04
= LU
o 0.02
Ca U


0.1 0.2 0.3 0.4 0.5 0.6 0.7
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


0 0.02 0.04 0.06 0.08 0.10
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


Z Co
0I-.
Cu.
LU
>LLJ
uia
a -

4z
Q LU

CU LU


LL
CO

2E

o I-
5L
LU
o -




V I-
4z
o ui
I- -
wa Ui


0.8 0.9



G


0 L 0.10
z co
S0.08

0.06

,Z 0.04

I 0.02
Ca U


0.12


LEVEL1 -500 m/d









-
Pb o P




0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


X P
so

kdf b

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


0 0.02 0.04 0.06 0.08 0.10
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


CO
z c


5-

- LJ

C3I


L
ss





zcz
2 i


, g


B
0.9 I I II
LEVEL 1 -100 m/d
0.8 -
0.7 zo

0.6 z
U -
0.5 -
0.4
0.3 ox -
p 0 LU
0.2
0.1 kf G Lw

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
E
no


Figure 23. Morris method global sensitivity analysis results for soil adsorbed phosphorus variation (SsP]ac,) across complexity levels and velocities
tested. Parameter descriptions are provided in table 4.


0.9 i i i i i i i
LEVEL 1 50 m/d
0.8
0.7
0.6
0.5
0.4
0.3 -
0.2 P ,
0.1
0 I
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)
F
0.9
0.8
0.7
0.6
0.5
0.4
0.3 P
0.2 "
*Pb
0.1 kdf
0 1 1 1 1 1 1 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)

).12 i
LEVEL 3- 50 m/d
).10 k mp

).08 -

).06

).04

).02 -kdf


0 0.02 0.04 0.06 0.08 0.10 0.1
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


LEVEL2 -500 m/d






k--


x"PP

/df
- kf b ,*
i i i i i


LEVEL 3 500 m/d




-so






-*k
kox


LEVEL 3 -100 m/d


- k d
\ g


Sso










46 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


4

Sz3
z co
Zs3
L)

o >-
0 2
2
z 2-

.LU
C3 LU















oC

-0
LU



4z
o LU

I-
Wa LU


SIII, I Ij 16
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


3.5

- 3.0
z cj
o
2I l.5
LU
>- 2.0

SI-
Z 1.5

- LU 1.0
SLU


LEVEL 2 500 m/d
.0

.5

.0

.5

.0

.5 -P p
.0 -
.0 Pb '

.5 -ox
kdf

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.!
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


C

LEVEL 2 -100 m/d
9

8



6 Xso
5
4 Pb
kox
3 -

2 Xp P kdf
-k




ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


E

LEVEL 2- 50 m/d
4

2 -

80 P
so


6 P
ox
4 XplI

2 kd

I t I t I


ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


Figure 24. Morris method global sensitivity analysis results for plankton biomass outflow (Csjo,,,t) across

complexity levels and velocities tested. Parameter descriptions are provided in table 4.


LEVEL 3 500 m/d


kg mp

kdf
'^


kl pl
1/2


*P
.Xrrp


0.5 e


0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.(
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


D
i i
LEVEL3 -100m/d
14 -

12

10 kdf
10

8

kmp
6 g P1
xP .

+ ksnmp
2 P
XplI

0 2 4 6 8 10 12 14
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


F

LEVEL3 50m/d
14 8

12

10
k
kst

6 *kgmp
6- g

*X
4 so

kdf
-


1
zS
z c
oI-
-



0 z
o LU

CO LU


I


II II-~









Global Sensitivity Analysis


50

45
0 40
C 35
L 30
5L
n 25
z LU
z 5
0-
Eo ul 10
5






45

40

2D 35
Z C





0 01
5&3
...i 10

5 U


o0
Z Cn
0c 40
>iLU

M >- 30
0<
0 u 20

zI
US LUJ


I LEVEL3 -100 meters m/d
Pb k mp
st

10
x mp
0 kd Xso

0 kdf P ksnmp

k X1
0
10 -I I I


0 100 200 300 400 500 60
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(g*)


Figure 25. Morris method global sensitivity analysis results for macrophyte biomass accumulation (mC"]cr)
across complexity levels and velocities tested. Parameter descriptions are provided in table 4.




Screening of Parameters

In almost all instances, the number of important parameters identified using the Morris method was substantially smaller
than the full set of model parameters tested, especially for levels 1 and 2, as shown by the maximum recorded rankings for these
levels in tables 8 to 13. The following summarizes the number of input parameters identified as being important for each level
(range is due to variation across velocities as discussed later):




Number ol input parameters considered important

Level Initial number ol (parameters declined in appendix 1)
input parameters


1 8 4 6 4 1

2 12 6-81 6 4 1 6-8

3 16 11-14 4-5 10-13 4-6 12-15 10-11


0
LEVEL3 500 meters m/d
0 kgmP XsoP -


0 -
O0 rp -X

0 E-

0 -
,0 kox

0o kdf
o kstpl ksp
I I I I I
0 50 100 150 200 250 300 350 400 450 50
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(u*)

50
LEVEL3 50 meters m/d
0 -

0- X -

0 P- krp p
kl/2 Xso


0 -

O0 -


0 /2 mp -


0 50 100 150 200 250 300 350 400 45(
ABSOLUTE VALUE OF MEAN
ELEMENTARY EFFECTS(*)







48 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

Ranking of Parameters
Comparing parameter rankings in tables 8 to 11 over all outputs, by level, indicates that for level 1, soil oxidation rate,
kox, is consistently ranked most important. Three other parameters, kdf, Pb and XsoP, repeatedly appear to be of intermediary
importance, sharing ranking positions 2 to 4 depending on the output. These results are in good agreement with current under-
standing of the physical system, because the principal source of new phosphorus to the level-1 system is from oxidation of the
soil, controlled by kox. Of the parameters ranked 2 to 4, the stabile outputs associated with the soil, CpwI]acr and Ssie]acn are
sensitive to Xso' and pb. These two parameters play a direct role in the amount of SRP contributed to the pore water through
oxidation, and in turn to the amount of adsorbed phosphorus. The SRP concentration in the water column is more sensitive to kdf
than Xso' and Pb, because this parameter represents the limiting process of diffusion through which the surface water gains new
phosphorus originating from the pore water.
These trends across outputs persist in the level-2 results (tables 8-12), with the only notable difference being the previously
mentioned prominence of plankton growth parameters in the ranking for mobile outputs Cswp]o, and C~sw'o,,,. Level-3 results
(tables 8-13) do not exhibit any pattern of parameter dominance across the different outputs.

Effect of Flow Velocity
Changes in flow velocity appear to have no effect on the ranking of parameters for all outputs in level 1 (tables 8-11).
Negligible velocity effects on ranking are also evident in level 2 for all outputs except Csw,]o,f (table 12 and fig. 24A, C, E),
which shows the plankton growth parameters kgP/ and k1/1P to be the most important at 500 m/d (fig. 24A), and the soil phos-
phorus parameters kox and Xso' to be the most important at slower velocities of 50 and 100 m/d (fig. 24C, E). This unexpected
relation is discussed later, together with the additional information provided from the extended FAST and uncertainty results.
Outputs in the level-3 case exhibit a much greater sensitivity to velocity than outputs in the level 1 and 2 cases, and parameter
rankings changed with velocity for all outputs (tables 8-13). As previously noted, however, the dispersed positioning of so many
of the parameters in the p*-o plane means that there may be little quantifiable difference between parameters that are ranked
differently, as discussed later.

Effect of Model Complexity
The parameter ranking in tables 8 to 12 is the same between levels 1 and 2 for stabile outputs Cpwelacr, So]acr and Ssi]acr,
although the mobile output associated with the water column Cswj]o, was observed to become most sensitive to the plankton
growth parameters, kgP1 and k1/2, introduced in level 2. This is to be expected because the additional complexity of level 2 is
due to the incorporation of suspended solids in the form of plankton, which should have an influence on surface-water SRP
concentration through uptake kinetics. Plankton grows rapidly and extracts SRP from the water column, and accordingly SRP
concentration becomes more sensitive to losses from uptake by growing plankton than to parameters associated with the much
slower process of diffusion, which were important when plankton was absent in level 1. Except indirectly through longitudinal
dispersivity (A;) in the transport equation, diffusion is the only process that influences SRP concentration in the water column for
level 1. This explains the importance of kdf and parameters such as kox, Xso' and pb that directly influence pore-water SRP and, as
a consequence, diffusion (fig. 20A-C).
At level 2, a subtle rise in the prominence of A, occurs between 100 and 500 m/d for both CswP]o,, and Cs,]o,(f (figs. 20D
and 24A). This is an informative confirmation of realistic transport dynamics because dispersion is a function of Ai and velocity,
and would directly increase the amount of SRP or plankton biomass transported to the output cells under higher velocity condi-
tions. An increase from 50 to 100 m/d was seemingly insufficient to register a similar increase in rank.
Rankings changed markedly for nearly all outputs with the introduction of level-3 parameters associated with macrophytes.
The more complicated system dynamics caused an extensive reordering of parameter rankings, although as previously
mentioned, there was probably little quantifiable difference between similar positions. Many more parameters are also spread out
across the p*-a plane to form "clouds" that make it difficult to clearly identify truly sensitive parameters. Only S]acr maintains
a similar trend in level 3 to that observed for previous levels, with kox remaining linearly dominant (fig. 22). Mobile components
in the water column (Csw]o, and CswP]o,f) remain sensitive to plankton growth parameters k1F and kg/1, as they were in level 2,
but are comparably sensitive to macrophyte parameters k12rmp, kgmp, and ks,,n (figs. 20G-I, and 24B, D, F). As in levels 1 and 2,
the remaining stabile components (figs. 21G-I, 22G-I, 23G-I and 25A-C) appear sensitive to a variety of soil parameters, such as
XsoP, kox, and Pb, but here too the macrophyte parameters become comparably important.
Compared with the level-1 and level-2 Morris results, the level-3 plots show a general parameter shift away from the
/P*-axis and toward the a-axis, indicating an increase in the contribution of higher order effects. Results from the simpler systems
for levels 1 and 2 were more closely associated with the p/*-axis than level-3 results, with proportionately more first-order influ-
ence on sensitivity. The initial increase in complexity to level 2 does not appear to change the dominance of first-order effects
substantially, but the introduction of the macrophytes for level 3 greatly reduced the additivity of the model by substantially







Global Sensitivity Analysis 49


increasing the role of interactions. This in turn diminishes the first-order contribution to overall variance and, thus, the propor-
tionate first-order contributions of many similarly ranked parameters are also expected to decrease. Because the quantifiable
difference between closely grouped parameters is expected to be small, calculated variances (using extended FAST results) are
necessary to determine the importance of the observed changes in ranking.


Extended Fourier Amplitude Sensitivity Test (FAST) Results

Results of the global sensitivity analysis obtained from the variance-based FAST method for each of the selected model
outputs are discussed herein and presented in tables 14 to 19 and figures 26 to 31. Also considered are the effects of complexity
level and velocity on the sensitive parameters affecting each of the model outputs. A threshold value of greater than 5 percent of
total output variance was selected to distinguish sensitive from nonsensitive parameters. Significant contributions exceeding 5
percent are highlighted in blue in tables 14 to 19.
The extended FAST results reinforce and quantify those obtained with the Morris method and, in many cases, eliminate the
subjectivity inherent to that qualitative approach. The list of important parameters is also further reduced in many instances.
In an effort to simplify the presentation of FAST results, one output of particular interest in the Everglades, surface-water
SRP outflow (Csw]o,f), is discussed here in detail. Detailed sensitivity trends for each individual output, corresponding to
figures 26 to 31 as well as tables 14 to 19, are discussed in the appendix 4.

Surface-Water Soluble Reactive Phosphorus (CswP]otf Case Study
For level 1, depending on the velocity case, 35.1 to 37.5 percent of the variance can be attributed to the first order effects
of kox, 18.6 to 21.9 percent to pb, 15.4 to 16.9 percent to Xso and 15.4 to 15.7 percent to kdf. The greater number of simulations
required to obtain these results, compared to the Morris method, improves their accuracy, and some reordering of parameter
importance occurs as a result. Although Pb was previously ranked third by the Morris method, the results presented here indicate
that it is in fact the second most important parameter. Conversely, kdf decreases in rank from second to third (at 500 m/d) or
fourth (at 50 and 100 m/d), whereas X,,P rises from fourth to third at 50 and 100 m/d. This reordering demonstrates the fine
tuning that can be performed using the extended FAST results. In this case, however, the reordering is of little importance
because the actual difference between the contributions of parameters ranked second, third, or fourth is negligible relative to
the actual difference of the unranked parameters. Irrespective of their order, all four of the listed parameters would typically
be included for the extended FAST analysis based on the Morris results. However, if a user were required to select only two
parameters to better measure in the field, then the choice of pb (as per the extended FAST results) instead of kdf (as per the
Morris results) for the second parameter could potentially reduce variance by up to 6 percent more.
Level-2 results show that kgP1 accounts for 46.7, 37.0, and 67.1 percent of the change in Cw,,]of, and k1/I for another
22.6, 10.2, and 15.8 percent for the 50, 100, and 500 m/d cases, respectively (table 14). Because the next highest contribution is
only 3.4 percent (kox at 500 m/d), kgPl and k1/ z are the critical parameters, and accordingly, the remaining parameters that were
originally ranked using the Morris method can be disregarded. This reduces the number of important parameters from 6-8 to 2.
The extended FAST results also confirm the relative importance of direct effects as opposed to indirect effects through
interactions. Close to 89 percent of the total variation in Cw,,]o, for level 1 was consistently due to first order effects, and
73.5, 53.4, and 94.6 percent of the variation in level 2 at 50, 100, and 500 m/d, respectively. This dominance of linear effects
corroborates earlier conclusions from the Morris plots, where proximity of parameters to the fp*-axis was used to deduce the
same result. Specifically, the pattern shown in table 14, of falling and then rising total first order effects over increasing velocity,
is further demonstration of the high qualitative accuracy of the Morris method. Taking into account the variable scales of the p*
and o-axes in figures 24A, C, and E, the relative magnitudes of p and a for the two plankton parameters are found to follow
the same order observed in the extended FAST results; if figure 24E was plotted within figure 24C, the points of the latter figure
would be comparatively farther from the jp*-axis (that is, less linear), and similarly so if the points of figure 24A were plotted in
figure 24A. This apparent importance of interactions at 100 m/d in level 2 seems somewhat anomalous, but closer examination
of the uncertainty analysis results (pit. ii. later) provides useful explanatory information.
For level 3, combined first-order effects account for only 47.2, 39.2, and 55.2 percent over increasing velocity, indicating
that about 45 to 60 percent of the variation is due to interactions. Except for kgP1 and kl/fz, which are responsible for 18.2 and
14.6 percent, respectively, of the total variation at 500 m/d, all the first-order contributions of the level-3 parameters are less
than 6 percent. This result implies that the 500-m/d water velocity creates a unique environment; the uncertainty analysis results
presented later provide further insight on this case.
This comparison between the Morris and extended FAST results demonstrates the accuracy of the Morris results for iden-
tifying qualitative trends, and for screening out unimportant parameters. It also illustrates the need, however, for quantitative
measures to guarantee accurate ranking of parameters, and for further screening.








50 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table 14. Fourier Amplitude Sensitivity Test (FAST) results for the surface-water soluble reactive phosphorus outflow outputs (Cs/]o,tff
and CsP]o,t).

[Parameter descriptions are provided in table 4. Values for all results except velocity are shown as percentages. Values greater than 5 percent of the total output
variance are shaded]

Velocity Parameter
Complexity meterss Oulpul .. Total
per day)
First order index, Si
50 C P]o, 15.4 37.5 16.9 0.3 0.1 18.6 0.0 0.0 88.8
Level 1 100 C w]o,g 15.6 36.2 16.1 .3 .1 20.4 .1 .0 88.8
500 CJw]of 15.7 35.1 15.4 .4 .1 21.9 .4 .0 88.9
50 C ]o,y .1 2.0 .6 .6 .1 .4 .3 .0 46.7 22.6 .1 .1 73.5
Level 2 100 Csw]o,g .3 1.3 .7 1.9 .3 .4 .5 .2 37.0 10.2 .3 .4 53.4
500 Cw]o,tf 1.7 3.4 2.0 .0 .0 1.5 2.6 .0 67.1 15.8 .0 .4 94.6
50 CJP]o,i 2.7 1.8 3.1 5.3 4.1 4.3 4.3 2.1 4.8 1.1 1.8 2.4 2.2 2.0 2.7 2.5 47.2
Level 3 100 CpP]o,f 3.0 1.7 1.7 3.7 1.9 2.3 1.7 1.9 4.2 3.1 5.4 1.5 2.8 .7 1.1 2.8 39.2
500 CwP]of .8 .6 1.6 1.2 .9 .5 1.9 .8 18.2 14.6 1.2 4.2 2.6 2.2 1.3 2.7 55.2
Interactions, S T,- Si
50 CP]o,f 4.2 7.5 7.3 .5 .3 4.4 .2 .2
Level 1 100 CplPo,t 4.4 7.6 7.2 .6 .3 4.7 .4 .5
500 Cp]o,tf 4.6 7.7 7.0 .6 .4 4.9 .7 .5
50 CJ ]o,4 7.8 7.3 5.0 12.6 23.3 22.6 11.8 11.8 13.7 8.2 15.6 9.4
Level 2 100 CpP]o,t 21.0 27.1 16.6 43.7 44.1 47.6 37.9 36.7 35.7 24.2 38.8 36.8
500 CP]otf 2.2 3.9 2.3 .7 8.4 4.4 .8 .9 .9 2.6 1.8 .8
50 CjP]o,f 88.9 85.9 84.3 82.9 85.5 83.8 87.3 86.1 74.5 85.6 82.9 83.4 84.6 85.7 78.6 81.3
Level3 100 CwJ]o,4 78.7 79.7 83.1 81.9 85.7 82.0 81.4 77.8 78.9 85.8 86.8 84.5 81.2 79.8 82.5 75.9
500 CP]o,tf 52.1 61.7 67.1 59.5 66.8 55.0 52.9 67.3 63.9 63.1 66.0 61.0 28.4 57.7 62.6 54.7
First order index, Si
50 Cj]o,, 18.3 32.2 14.1 .4 .1 24.1 .1 .0 89.3
Level 1 100 CJP]o, 18.3 31.4 13.6 .4 .1 25.4 .2 .0 89.4
500 CjP],, 18.4 30.7 13.2 .4 .1 26.4 .3 .0 89.6
50 CjP]o, .3 .9 0.4 .5 .0 1.1 .1 .0 64.9 14.5 .0 .4 83.2
Level 2 100 CJ]o,t .1 .8 .4 .9 .1 .9 .1 .1 59.2 11.8 .1 .3 74.7
500 CJP]o, 1.5 2.0 1.1 .0 .0 1.5 2.0 .0 67.9 18.7 .0 .6 95.1
50 Cj]o,, 2.7 1.7 3.0 5.0 4.2 4.5 4.5 1.9 6.6 1.2 1.8 2.1 2.0 2.2 2.9 2.5 48.6
Level 3 100 CsP]o, 2.9 1.7 1.7 4.0 1.8 2.1 1.6 1.8 5.6 3.1 5.2 1.5 2.4 .7 1.1 2.9 40.2
500 CJ ]o,, 1.0 .6 1.6 1.3 .9 .5 1.7 .9 18.7 14.9 1.1 4.9 1.2 2.1 1.2 2.6 55.1
Interactions, S T,- Si
50 CsP]o, 5.0 7.5 6.8 .6 .4 5.1 .6 .4
Level 1 100 CsP]o, 5.2 7.5 6.6 .6 .4 5.3 .5 .4
500 CJP]o, 5.2 7.4 6.5 .7 .4 5.4 .2 .2
50 Cj]o,, 4.3 5.5 4.9 9.1 14.3 16.2 10.6 8.9 10.6 8.9 11.5 8.4
Level 2 100 CsP]o, 7.0 11.1 8.9 17.8 23.0 24.7 19.9 15.9 17.1 14.8 17.2 18.6
500 CsP],, 2.0 2.3 1.6 .8 7.6 4.8 .9 1.0 1.0 2.3 1.6 .9
50 CJI]o, 86.9 85.7 83.1 83.2 83.6 81.6 86.2 84.7 71.5 84.3 81.4 83.2 83.6 84.4 78.3 78.9
Level3 100 CP]o,t 77.4 78.2 81.8 80.1 84.4 80.6 80.7 76.0 78.7 85.4 86.3 84.5 80.2 78.8 80.9 74.2
500 Cj']o, 51.4 62.0 67.1 59.0 66.4 55.3 53.0 67.7 64.1 62.7 65.9 60.9 30.2 58.1 62.3 56.4








Global Sensitivity Analysis


Table 15. Fourier Amplitude Sensitivity Test (FAST) results for the pore-water soluble reactive phosphorus variation output (CwP]acr).

[Parameter descriptions are provided in table 4. Values for all results except velocity are shown as percentages. Values greater than 5 percent of the total output
variance are shaded]


Velocity
Complexity (meters
per day)


Parameter

,, _


I, .. I


50
Level 1 100
500
50
Level 2 100
500
50
Level 3 100
500


2.0 43.5 20.9
1.9 43.5 20.9
1.8 43.5 20.9
1.6 42.4 19.7
1.6 42.4 19.7
1.6 42.4 19.7
.8 5.9 3.0
1.2 4.6 1.2
1.9 2.9 2.7


First order index, St
0.4 1.2 17.5 0.0 0.0 85.5
.4 1.2 17.7 .0 .0 85.6
.4 1.2 17.9 .0 .0 85.7
.3 1.8 17.3 .0 .0 .0 .0 .0 .0 83.2
.3 1.8 17.3 .0 .0 .0 .0 .0 .0 83.2
.3 1.8 17.5 .0 .0 .0 .0 .0 .0 83.3
1.6 1.7 3.0 1.7 1.1 .7 1.9 1.4 .9 11.6 1.9 2.5 8.9 48.6
.9 .8 1.8 2.0 1.7 1.3 .8 .9 .9 16.8 2.3 2.7 8.6 48.5
1.6 .5 1.7 2.0 1.2 2.6 1.1 1.9 1.4 12.7 3.0 2.2 9.9 49.2
Interactions, S T- Si


50
Level 1 100
500
50
Level 2 100
500
50
Level 3 100
500


1.3 9.6 5.4 .6 .7 4.2 .4 .5
1.2 9.6 5.4 .6 .7 4.2 .8 .5
1.2 9.6 5.4 .6 .7 4.2 .7 .4
1.8 6.7 5.7 .6 .9 .6 .6 .6 1.0 5.1 .7 .7
1.8 6.7 5.7 .6 .9 .6 .6 .6 1.0 5.1 .7 .7
1.8 6.7 5.7 .6 .9 .6 .6 .6 1.0 5.1 .7 .7
51.4 76.3 55.8 75.9 58.0 47.6 62.2 75.2 77.6 79.9 65.5 59.1 46.3 57.3 69.7 42.6
60.6 63.8 31.6 60.8 64.0 51.2 56.4 78.6 72.3 76.0 59.7 54.0 55.8 51.5 80.6 59.1
61.9 59.5 58.0 53.1 69.2 71.4 66.2 68.1 71.3 79.2 60.2 65.0 17.3 54.4 80.3 58.9


Table 16. Fourier Amplitude Sensitivity Test (FAST) results for the organic soil accretion output (SO]acr)

[Parameter descriptions are provided in table 4. Values for all results except velocity are shown as percentages. Values greater than 5 percent of the total output
variance are shaded]

Velocity Parameter
Complexity (meters Total
per day) .. .. .. T
First order index, Si
50 0.0 98.7 0.0 0.0 0.0 0.0 0.0 0.0 98.7
Level 1 100 .0 98.7 .0 .0 .0 .0 .0 .0 98.7
500 .0 98.7 .0 .0 .0 .0 .0 .0 98.7
50 .0 98.6 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 98.6
Level 2 100 .0 98.6 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 98.6
500 .0 98.6 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 98.6
50 1.7 13.0 3.6 3.5 4.8 3.5 3.9 2.2 3.2 .7 1.8 2.4 1.8 2.1 9.1 3.3 60.4
Level3 100 2.7 15.1 1.6 2.9 .6 1.6 2.1 2.5 .9 1.6 3.1 2.4 2.6 .7 5.5 4.7 50.4
500 2.8 14.6 1.7 3.6 1.6 .9 1.7 1.3 2.3 1.8 3.7 1.4 1.9 2.1 4.1 3.9 49.4
Interactions, S 7- St
50 .2 1.3 .2 .2 .2 .2 .6 .5
Level 1 100 .2 1.3 .2 .2 .2 .2 .5 .4
500 .2 1.3 .2 .2 .2 .2 .5 .4
50 .3 1.4 .3 .3 .3 .3 .3 .3 .3 .3 .3 .3
Level 2 100 .3 1.4 .3 .3 .3 .3 .3 .3 .3 .3 .3 .3
500 .3 1.4 .3 .3 .3 .3 .3 .3 .3 .3 .3 .3
50 83.1 68.3 76.1 75.3 63.0 64.9 81.3 82.0 68.9 80.1 69.7 74.8 70.7 73.5 68.4 57.4
Level3 100 70.9 72.7 76.6 79.4 59.3 72.7 81.5 79.6 76.3 79.1 72.2 69.3 66.2 60.7 82.1 73.2
500 72.8 73.7 85.5 79.9 65.5 63.9 82.9 85.1 74.4 77.0 77.3 73.3 40.9 59.3 72.2 74.3








52 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table 17. Fourier Amplitude Sensitivity Test (FAST) results for the soil adsorbed phosphorus variation output (SsP]acr).

[Parameter descriptions are provided in table 4. Values for all results except velocity are shown as percentages. Values greater than 5 percent of the total output
variance are shaded]

Velocity Parameter
Complexity (meters Total
perday) t,, ': ". ,, ,.. ,, .' ,'' .* .,, t,. ,' ,
First order index, Si
50 1.9 51.1 24.6 0.4 0.1 12.1 0.0 0.0 90.3
Level 1 100 1.8 51.3 24.7 .4 .1 12.1 .0 .0 90.4
500 1.7 51.4 24.7 .4 .1 12.0 .0 .0 90.4
50 2.5 49.4 25.5 .6 .1 12.5 .0 .0 .0 .0 .0 .0 90.4
Level 2 100 2.5 49.3 25.5 .6 .1 12.5 .0 .0 .0 .0 .0 .0 90.4
500 2.4 49.3 25.5 .6 .1 12.6 .0 .0 .0 .0 .0 .0 90.3
50 1.0 6.0 3.1 1.2 1.7 2.3 1.6 .9 .6 1.7 1.3 .9 18.1 1.9 2.6 9.4 54.4
Level 3 100 1.2 4.2 1.0 1.2 .8 1.8 1.8 2.1 .9 1.0 .9 1.2 23.9 2.0 2.6 9.4 56.0
500 1.9 3.3 3.4 2.0 .5 0.9 2.0 1.2 2.2 1.4 1.9 1.4 18.2 2.7 1.9 11.3 56.3
Interactions, Sn- Si
50 .7 8.1 5.6 .5 0.4 2.4 0.5 0.4
Level 1 100 .7 8.1 5.6 0.5 0.4 2.3 0.2 0.2
500 .7 8.1 5.6 0.5 0.4 2.3 0.4 0.5
50 1.0 7.9 6.7 1.2 0.3 0.6 0.7 0.5 0.5 3.1 0.6 0.6
Level 2 100 1.0 7.9 6.7 1.2 0.3 0.6 0.7 0.5 0.5 3.1 0.6 0.6
500 1.0 7.9 6.7 1.2 0.3 0.6 0.7 0.5 0.5 3.1 0.6 0.6
50 59.4 79.3 62.0 78.6 57.6 42.1 59.1 71.1 72.1 79.3 67.4 58.6 47.0 61.3 68.2 40.7
Level 3 100 54.1 72.6 33.8 75.8 61.2 49.9 58.1 79.5 66.6 73.7 57.8 54.1 54.7 51.8 78.1 57.3
500 59.6 66.1 64.5 62.4 66.0 71.7 65.3 65.9 68.2 78.7 58.0 64.2 16.8 55.9 76.2 60.3








Global Sensitivity Analysis


Table 18. Fourier Amplitude Sensitivity Test (FAST) results for the plankton biomass outflow outputs (Cswiio,tf and Csw]o,t).

[Parameter descriptions are provided in table 4. Values for all results except velocity are shown as percentages. Values greater than 5 percent of the total output
variance are shaded]

Velocity Parameter
Complexity (meters Output Total
per day) ,, ,
First order index, Si
50 C w1]o, 15.2 43.1 15.8 0.4 0.1 14.7 0.3 0.0 0.5 0.0 0.0 9.4 99.6
Level 2 100 C l],o, 14.0 44.0 16.0 .0 .0 13.0 .0 .0 .0 .0 .0 11.0 98.0
500 CYw']o,, 4.0 8.2 3.5 .1 .0 4.0 1.6 .0 61.8 13.6 .0 1.5 98.2
50 C P'],o, 2.4 3.8 1.2 3.9 3.6 2.3 3.0 2.4 2.3 1.8 12.2 7.5 11.8 1.4 2.6 2.7 64.9
Level3 100 C w1]o,y 2.1 2.1 2.4 1.2 1.1 2.2 .6 1.6 1.4 1.7 11.2 15.9 5.3 .3 2.6 1.3 52.8
500 C w ]o,,f .8 2.1 2.0 1.6 2.0 .5 1.9 1.1 12.7 11.3 3.2 3.1 1.5 2.3 2.1 4.1 52.3
Interactions, S 77- S
50 CJP']o, 4.5 9.0 5.7 .5 1.1 .6 .7 2.0 .5 6.0 .9 .8 32.4
Level 2 100 CwP]o,4 5.0 9.0 6.0 1.0 1.0 .0 .0 2.0 .0 5.0 1.0 .0 30.0
500 CW']o,4 2.7 4.5 3.9 .6 6.7 4.1 1.4 2.4 .7 4.1 1.7 .8 33.6
50 CJ'],,f 72.7 71.9 58.0 67.1 49.2 66.7 69.7 77.3 71.4 65.5 74.5 72.5 57.2 65.1 65.0 62.3
Level3 100 Cs'],, 72.1 55.7 45.7 51.0 57.4 56.7 70.8 66.3 67.1 56.0 59.3 73.9 67.4 62.5 63.8 71.3
500 CwP1]o, 62.6 73.5 76.7 66.2 71.1 69.4 64.9 72.6 73.4 74.3 61.2 67.7 51.1 47.2 65.0 50.5
First order index, Si
50 Cwi]o,t 18.0 39.0 14.0 .0 .0 16.0 .0 .0 .0 .0 .0 13.0 100.0
Level 2 100 Cw']o,r 17.0 40.0 14.0 .0 .0 15.0 .0 .0 .0 .0 .0 16.0 100.0
500 C,']o,, 2.7 4.1 2.0 .1 .0 2.8 1.3 .0 64.8 17.8 .0 1.4 97.0
50 C Plo,, 2.6 2.9 1.5 4.5 4.4 2.6 2.3 2.1 2.4 1.6 14.7 17.5 4.8 1.4 2.3 2.0 69.5
Level 3 100 Cs']o,t 1.9 1.3 2.3 1.4 1.2 2.1 .7 1.7 1.2 2.2 11.2 17.0 2.8 .3 2.5 1.1 51.0
500 CP']o,, .7 2.2 1.7 1.8 2.1 .5 1.9 1.2 12.5 11.1 3.1 2.9 1.4 2.3 1.9 4.4 51.8
Interactions, S T- S,
50 Cw']o,, 5.2 9.5 5.6 1.1 1.6 .6 .6 2.8 .6 7.4 1.4 1.0 37.4
Level 2 100 CwP']o, 6.0 10.0 6.0 1.0 1.0 .0 .0 2.0 .0 6.0 1.0 1.0 34.0
500 Cw]o,t 2.1 2.9 2.8 .7 6.5 4.8 1.4 2.4 .8 3.5 1.5 .9 30.4
50 Cw']o,, 73.5 72.3 64.6 63.0 50.4 66.0 68.5 70.2 75.7 72.1 75.2 75.7 66.9 72.5 69.4 69.1
Level 3 100 Csw]o, 71.9 55.2 54.4 52.3 58.6 58.3 70.4 64.8 68.4 60.8 59.0 75.0 69.2 64.7 63.5 70.1
500 Cs]o,t 63.3 74.1 79.2 67.9 71.6 69.0 64.6 74.4 73.7 74.7 61.8 68.3 54.5 47.9 65.7 52.5




Table 19. Fourier Amplitude Sensitivity Test (FAST) results for the macrophyte biomass accumulation output (CmPacr)

[Parameter descriptions are provided in table 4. Values greater than 5 percent of the total output variance are shaded]

S Velocity Parameter
Complex -
(x meters A Total
ity 1 ' . .'' '. ,
per day)
First order index, Si
50 1.0 5.8 5.9 3.4 2.6 2.3 1.3 1.3 1.5 1.5 1.9 3.8 2.2 1.9 11.8 16.1 64.2
Level 3 100 2.5 4.9 3.0 1.0 1.3 1.5 1.4 1.7 .4 1.4 1.8 1.6 3.1 .6 6.6 10.3 43.0
500 2.5 7.9 5.1 3.5 2.0 .5 1.4 1.0 2.2 1.6 2.2 1.4 3.8 2.3 4.9 29.1 71.2
Interactions, S Si
50 65.6 60.0 75.3 61.4 60.0 65.0 57.1 70.2 73.1 85.4 59.4 73.1 78.2 72.2 55.6 58.0
Level 3 100 58.7 55.8 76.1 80.6 39.9 65.1 59.3 69.3 73.3 75.2 68.4 73.1 65.8 65.1 64.8 62.6
500 67.3 64.6 63.4 65.8 56.3 59.3 78.1 78.2 54.1 71.3 70.8 57.9 54.0 71.3 62.4 60.8









54 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


0.40
0.35

o 0.30

o 0.25
z -
, 0.20
H- )
o.15
S0.10
0.05
n


0 100 200 300 400
VELOCITY, IN METERS PER DAY


0.8 I I
FIRST ORDER LEVEL 2
0.7

0.6

0.5

0.4

0.3

0.2



0.1
0 100 200 300 400 500 6(
VELOCITY, IN METERS PER DAY


0.10
S 0.09
0.08
c, 0.07
a 0.06
< i

S0.04
g z 0.03
0.02
E 0.01
0


500 600 0 100 200 300 400
VELOCITY, IN METERS PER DAY


0 0 100 200 300 400
VELOCITY, IN METERS PER DAY


0 100 200 300 40
VELOCITY, IN METERS PEI


10 500 600 0
R DAY
EXPLANATION
Skdf kox XsP

4- e Pb -+
kgp' k1/2 ksf

Skg p kl/2 p ksnmp


100 200 300 400
VELOCITY, IN METERS PER DAY


y P

XP
^mp


Figure 26. Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis results for surface-water
soluble reactive phosphorus outflow (Cs,]o,tf) across complexity levels and velocities tested. Parameter
descriptions are provided in table 4.


FIRST ORDER LEVEL 1





---

- r---- -
chiorgsoil

I-I -I


1. 4 I I I 4
INTERACTIONS-LEVEL 1






.




*-*----
-
- A !


I-


500 600


500 600


FIRST ORDERLEVEL 3
FIRST ORDER LEVEL 3


0.20
0.18
c 0.16
S0.14
- 0.12
Z 0.10
0.08
S 0.06
>0.04
0.02


INTERACTIONS- LEVEL 3


500 600


u'


I I I


I I I









Global Sensitivity Analysis


0.50
0.45
S0.40
S 0.35
- 0.30
z t 0.25
u 0.20
- 0.15
> 0.10
0.05
0






0.50
0.45
S0.40
S 0.35
- 0.30
Sz 0.25
-- 0.20
' 0.15
> 0.10
0.05
0


0.10
0.09
= 0.08
| 0.07
0.06
z 0.05
S0.04
S0.03
S0.02
0.01
n


FIRST ORDER LEVEL 1

*












0 100 200 300 400 500 61
VELOCITY, IN METERS PER DAY



C

FIRST ORDER -LEVEL 2
*
.















0 100 200 300 400 500 61
VELOCITY, IN METERS PER DAY


U. lu


0.09
S0.08
- 0.07
0.06
0.05
S0.04
| 0.03
S0.02
0.01
n


00


FIRST ORDER LEVEL















0 100 200 300 400 500 61
VELOCITY, IN METERS PER DAY


500 600


0 100 200 300 400 500 60
VELOCITY, IN METERS PER DAY



F
0
INTERACTIONS- LEVEL 3



.7
6


4
3
2


0 100 200 300 400
VELOCITY, IN METERS PER DAY


500 600


EXPLANATION
-kdf ko Xso kd

0- -Pb -- -X
k g kl2mpl k pk P Xmp
knp kl/ p + ksn p XpP
fk~l~ I/2 "';M


Figure 27. Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis results for soil pore-water
soluble reactive phosphorus variation (CP]acr) across complexity levels and velocities tested. Parameter
descriptions are provided in table 4.


INTERACTIONS LEVEL 1


00 0 100 200 300 400
VELOCITY, IN METERS PER DAY


0.20
0.18
c 0.16
a 0.14
/ 0.12
z t 0.10
U 0.08
: 0.06
> 0.04
0.02
0


INTERACTIONS- LEVEL 2


A A
-------------


* ----------
i ~ i i i____________i_








56 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


FIRST ORDER LEVEL 1













S 100 200 300 400 500 60
VELOCITY, IN METERS PER DAY



C

FIRST ORDER LEVEL 2













S 100 200 300 400 500 60
VELOCITY, IN METERS PER DAY


200 300 400
VELOCITY, IN METERS PER DAY


0.10
0.09
0 0.08
o
S0.07
` 0.06
z 0.05
F 0.04
< 0.03
0.02
0.01

0 0





0.10
0.09
= 0.08
z 0.07
0.06
= 0.05
F- 0.04
L-) U)
< 0.03
S0.02
0.01

0 0


EXPLANATION

- kdf -- k XsP -- k


INTERACTIONS-LEVEL 1













0 100 200 300 400 500 60
VELOCITY, IN METERS PER DAY



D

INTERACTIONS- LEVEL 2













0 100 200 300 400 500 60
VELOCITY, IN METERS PER DAY



F
INTERACTIONS- LEVEL


K-











0 100 200 300 400 500 60
VELOCITY, IN METERS PER DAY


0 e + PA +
k fp kl/ ks/
4 k mp kl/2mp P ksnmp


P
mp
;i;V~p


Figure 28. Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis results for organic soil
accretion (So]acr) across complexity levels and velocities tested. Parameter descriptions are provided
in table 4.


0.20
0.18
0.16
S0.14
S' 0.12
=z 0.10
o 0.08
S0.06
> 0.04
0.02









Global Sensitivity Analysis


0.6

0.5

=, 0.4

z 0.3
UL
< 0.2

0.1

0






0.6

0.5

S0.4

C-,
z 0.3

,z 0.2

> 0.1


0


0 100


200 300 400
VELOCITY, IN METERS PER DAY


FIRST ORDER -LEVEL 1













*
0 100 200 300 400 500 6(
VELOCITY, IN METERS PER DAY



C
FIRSTORDER -LEVEL 2



-





.




0 100 200 300 400 500 6(
VELOCITY, IN METERS PER DAY



E
FIRSTORDER-LEVEL3












p P


500 600 0

EXPLANATION
kdf/ k Xso -
e Pb --' 1
kgp kl/2 ks
kgmp k mp ksnmp


0.10
0.09
z 0.08
. 0.07
0.06
z 0.05
P 0.04
< 0.03
S0.02
0.01
0






0.10
0.09
a 0.08
o 0.07
0.06
;z 0.05
P 0.04
< 0.03

| 0.02
0.01
0


100 200 300 400
VELOCITY, IN METERS PER DAY


500 600


Xp

mp


Figure 29. Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis results for soil adsorbed
phophorus variation (SsPP]ac) across complexity levels and velocities tested. Parameter descriptions are
provided in table 4.


INTERACTIONS-LEVEL 1














0 100 200 300 400 500 6C
VELOCITY, IN METERS PER DAY



D
INTERACTIONS-LEVEL 2














0 100 200 300 400 500 6C
VELOCITY, IN METERS PER DAY



F
I INTERACTIONS- LEVEL I


0.30

S0.25

c 0.20

S 0.15
UJ

S< 0.10

0.05


n


A.









58 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


<1 0.5

U 0.4

C 0.3

_ 0.2

0.1


VELOCITY, IN METERS PER DAY


2
VELO


C- ) U.

- o.
0.
0.
CD 0.

_o.
I -K



00 300 400 500 600
CITY, IN METERS PER DAY
EXPLANATION
kdi kf 9 kox kl/21P XsoP

e kgmp p b k1/2mp l


0 100 200 300 400
VELOCITY, IN METERS PER DAY
1 n


500 600


INTERACTIONS -LEVEL 3

8 -
B





4 -
3
2

1 -

0 100 200 300 400 500 61
VELOCITY, IN METERS PER DAY


kst, 4- k k +k Xpi^

ks t -X,


Figure 30. Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis results for plankton biomass
outflow (Cs/P'o,1, across complexity levels and velocities tested. Parameter descriptions are provided in table 4.


100 201
VELOCI


1.0
INTERACTIONS LEVEL 3
0.9


C 0.7
S0.6
z 0.5
S0.4 -
C-) U_)
< 0.3
0.2
0.1
0
0 300 400 500 600 0 100 200
TY, IN METERS PER DAY VELOCITY, IN I\
EXPLANATION
kf k/ P1 kox o kl/2P1 XSo t i kd + XIp

S -e kg Pb kl1/2m X mp ksm X t XmpP


300 400
METERS PER DAY


Figure 31. Fourier Amplitude Sensitivity Test (FAST) global sensitivity analysis results for macrophyte biomass
accumulation (Cm]acr) across complexity levels and velocities tested. Parameter descriptions are provided in table


0.20
0.18
c 0.16
S0.14
0.12
= 0.10
' < 0.06


0.04
0.02
0


0.25

S0.20
o- ~
S0.15
I- 0
C = 0.10

0.05


500 600


I I I







Global Sensitivity Analysis 59


General Trends Observed in Sensitivity Dynamics
The model discussed herein generally appears to be additive for levels 1 and 2, and outputs are predominantly dependent
on first-order effects, as indicated by the high sums of first order contributions. As noted earlier, soil pore-water SRP (Cswe]o,f)
has 88.8 to 88.9 and 53.4 to 94.6 percent of its variation attributed to first-order effects in levels 1 and 2, respectively, depending
on velocity (table 14). Between 85.5 and 85.7 percent of all variation in Cpwe]acr in level 1 and between 83.2 and 83.3 percent
in level 2 are due to linear effects (table 15). With no discernible velocity effects, CpwP]acr at both levels is strongly dependent on
kox (43.5 percent in level 1 and 42.4 percent in level 2), followed by Xso' (20.9 and 19.7 percent for levels 1 and 2, respectively)
and Pb (between 17 and 18 percent depending on level and velocity). The final number of important parameters for Cpw]acr was,
therefore, reduced from 6 to 3 for levels 1 and 2 (table 15). Accrued organic soil (S]acr) was almost exclusively dependent on kox;
more than 98 percent of all variation in S]acr was attributed to this parameter for both levels and at all velocities, as predicted by
the Morris results (table 16). Similarly, Ssi]acr also showed high sensitivity to kox, which is responsible for 49.3 to 51.4 percent
of the variation for both levels (table 17). Of the overall linear effects on Ss~lacr, which totaled about 90 percent, only two other
parameters contributed substantially: Xso' (24.6 to 25.5 percent for both levels), and Pb (12.1 to 12.6 percent). These results
indicate 11i.I / can be removed from the list of the four parameters originally identified as important by the Morris method.
The effect of the parameters on Cswj']o, for level 2 largely appears to be additive, with first-order effects totaling 98.2
to 99.6 percent across all velocities (table 18). At 50 and 100 m/d, ko and Xso' consistently account for between 43.1 and
44.0 percent, and about 16 percent of the variation, respectively, with most of the remaining variation at these respective veloci-
ties accounted for by kdf (14.0 to 15.2 percent), Pb (13.0 to 14.7 percent) and X p1 (9.4 to 11.0 percent). Sensitivity dynamics are
very different at 500 m/d, with kgP1, kl/1', and kox, accounting for 61.8, 13.6, and 8.2 percent, respectively, of the variation.
There is a clear decrease in the role of first-order effects for all outputs in level 3. Over the three velocities, total first-order
contributions were 39.2 to 55.2 percent for CswP]o,f, 48.5 to 49.2 percent for Cpwe]acr, 49.4 to 60.4 percent for S]acr, 54.4 to
56.3 percent for Ssi]acr, 52.3 to 64.9 percent for CIlof, and 43.0 to 71.2 percent for C"P]acr (tables 14-19). Although only one
output at one velocity had a total first-order effect less than 70 percent in levels 1 and 2 (most were greater than 80 percent), only
one output at one velocity had total first order effects greater than 70 percent in level 3, with most about or less than 50 percent.
Thus, the role of interactions is substantially more important for all outputs in level 3.
Concerning sensitivity to changing velocity, level-1 outputs were found to be relatively insensitive (tables 14-17, and
figs. 26-29A, B). Outputs for mobile components exhibit some sensitivity to velocity in level 2; Csw]o,f is more susceptible to
higher order effects at 100 m/d than at other velocities (table 14), and Cw'p]o,t is only sensitive to plankton growth parameters
at 500 m/d (table 18 and fig. 30A). Noteworthy changes in sensitivity at different velocities is apparent in the level-3 results
of three outputs, namely, Cswp]o,f, So]acr, CswJ]o,f (tables 14, 16, and 18, respectively). Although no parameters are clearly
dominant for C,,P]o, at 50 and 100 m/d, kgP1 and k1/2 account for 18.2 and 14.6 percent, respectively, at 500 m/d (fig. 26E and
table 14); the minor individual first-order effects of the other 14 parameters together account for the remaining 22 parameters.
As for levels 1 and 2, level-3 first-order effects for S]acr were dominated by kox (table 16 and fig. 28E), but to a lesser extent
(13.0 to 15.1 percent in level 3 compared with more than 98 percent in levels 1 and 2). Furthermore, at the slowest velocity, ksn,,
contributes almost 10 percent of the total variation, but only 5.5 and 4.1 percent at 100 and 500 m/d, respectively (table 16).
This result presumably is due to the greater role of settling on soil storage in slow-flowing water; faster flowing water carries
more of the decomposing material out of the simulation cell before it has time to settle in the soil. About half of the variation in
S]acr at 100 and 500 m/d is due to interactions, but only 40 percent at 50 m/d.
The first-order effects on Cswpjo,f (table 18) are dominated at 50 and 100 m/d by kJ1 (12.2 and 11.2 percent, respectively),
Xpt (7.5 and 15.9 percent, respectively) and kgmp (11.8 and 5.3 percent, respectively). At 500 m/d, kgP1 and k1/2I become the major
contributors (12.7 and 11.3 percent, respectively). CnP]acr is subject to stronger first-order influence at 50 and 500 m/d, for which
Xmpe contributes the largest portion of the total variation at these velocities (64.2 and 71.2 percent, respectively) (table 19). At
100 m/d, contributions are more diffuse; linear effects total 43 percent, of which only Xmp accounts for more than 10 percent.
The tabulated values for the interaction effects of each parameter represent their total contribution to output variation
through interactions with all other parameters, and shading indicates exceedence of a relatively low threshold value of 5 percent.
The comparative lack of shaded cells for the interactions portion of level 1 and 2 results (tables 14-18) is indicative of a substan-
tially lower contribution to variability from interactions at these levels. Level-3 results differ greatly in that interaction effects for
every parameter are shaded for all outputs at this level (tables 14-19), corroborating the strong dominance of interactions at this
level noted from the Morris method results and lower first-order totals. In one exception, extensive shading of level-2 results of
interaction effects for Csw]o,f (table 14) show the increased role of such interactions at this level under slower velocities. This
trend was expected given the reduced total first-order contributions at the lower velocities.







60 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Analysis and Assessment of Model Uncertainty from Fourier Amplitude

Sensitivity Test (FAST) Simulations

Mathematical models provide an alternative to field monitoring that potentially can save time, reduce cost, and minimize
the need for testing management alternatives, although the uncertainty of the model results is a major concern. If model uncer-
tainty is not evaluated formally, the science and value of the model will be undermined (Beven, 2006). The issue of uncertainty
of model outputs has implications for policy, regulation, and management, but the source and magnitude of uncertainty and
its effect on water-quality assessment has not been studied comprehensively (Beven, 2006; Munoz-Carpena and others, 2006;
Shirmohammadi and others, 2006). Reckhow (1994) proposed that although uncertainty assessment can improve risk assess-
ment and decision making, it does not eliminate uncertainty nor change the fact that, because of uncertainty, some decisions will
have consequences other than those anticipated. Rather, the explicit integration of uncertainty in water-quality modeling studies
should help improve environmental management and decision making.
Following the approach used in Morgan and Henrion (1990), probabilistic and cumulative distribution functions (PDFs and
CDFs, respectively) were constructed to communicate the uncertainty graphically. The CDFs are useful for depicting probabili-
ties of exceedance and confidence. The model was applied to a generic site, however, and parameters were tested over the entire
range of feasible values for southern Florida wetland ecosystems, with the purpose of evaluating the sensitivity and uncertainty
trends across the range of possible conditions. Given the intentional generality of this sensitivity and uncertainty analysis,
meaningful interpretation of specific outcomes, such as the chance of exceeding a particular output value or defining confidence
intervals, is not practically useful, and a separate uncertainty analysis is needed for each individual application of the model
(Mufoz-Carpena and others, 2007). The application herein remains important, however, and is included to (1) guide future such
applications in which uncertainty measures are the goal, and (2) complement the exploration of the wetland system dynamics
achieved during the global sensitivity analysis of the model.
The primary focus of this particular uncertainty analysis is the PDFs, which help provide the insight needed to explain some
unexpected trends previously mentioned in the sensitivity analysis, and to further explore how model structure and flow velocity
affect sensitivity and uncertainty. Results of this analysis correspond to a "worst case scenario" in which all of the potentially
sensitive model parameters, from 8 to 16 depending on complexity level, are allowed to vary across the complete parametric
space identified in an extensive literature review; parameters and their associated distributions are presented in table 4.
Measures of output uncertainty were obtained directly from the FAST analysis conducted to quantify sensitivity. Figures
32 to 34 depict both the probability and cumulative distribution functions for the outputs of levels 1, 2 and 3, respectively, and
table 20 presents summary statistics of the uncertainty results. Three main elements can be observed and interpreted from the
probability distributions obtained. First, the slope and range of the PDFs are indicative of the uncertainty and range in the model
output results. In addition, any shifting between PDFs for different velocities provides information about the effects of velocity
on output uncertainties. Finally, any apparent discontinuities in the PDFs, indicating bimodality of output distributions, also will
be helpful for interpreting model results.


Level-1 Uncertainty

The sensitivity analysis provides insight about the strength of the relation between a parameter and an output, and how that
relation may vary with changing flow velocity or structure; it does not identify the actual relation between an output and the
velocity or structure itself. Results of the earlier Morris and extended FAST analyses indicated no apparent influence of velocity
on the sensitivity of outputs to parameters in level 1. Although the sensitivity to parameters may not have changed significantly, the
uncertainty analysis results show that in the case of CwP]o,f, the output itself is indeed sensitive to velocity (fig. 32A); as velocity
increases, so too does the uncertainty of CswP]o,. This effect on uncertainty is absent for the remaining outputs at this level (Cpw,,lcr,
S]acr, and Sie]acr) (figs. 32B-D), which can be explained by the fact that they represent the stabile components. These components
do not move with the flowing water and are largely isolated from the water column in level 1 by the slow process of diffusion.
Consequently, velocity effects are secondary, whereas the mobile SRP concentration in the surface water is directly affected by
changes in velocity through the dispersion term of the transport equation (A.I. James, University of Florida, written commun., 2008).
The process of dispersion is embodied by the dispersion coefficient (D1), which is itself a function of the product of
dispersivity (predominantly A2) and flow velocity (D; = A2 v1). Because the distribution and range of the dispersivity are consistent
across velocities, the dispersion becomes a function of velocity. At low velocities, there is little dispersive spreading of the SRP
that enters through the boundary; the phosphorus remains "together" as it moves through the model in a quasi-plug flow manner.
With increased velocity, and hence, dispersion, some of the SRP travels through the system at different rates, introducing the
log-normal effect seen in the PDF for this output in level 1 (fig. 32). Further increasing the velocity increases this spread and
associated skewness, hence the observed difference between CDFs and PDFs with velocity. The observed spread in Cw],, f and
the absence of this spread for the stabile components is, therefore, an important validation of the dispersion mechanics in the
transport code of the model, further illustrating the usefulness of this analysis as a general verification of model performance.








Analysis and Assessment of Model Uncertainty from Fourier Amplitude Sensitivity Test (FAST) Simulations 61


1.2 A 1.2 B

S1.0 1.0 -

So.8 / / 0.8

S0.6- 0.6

0.4 0.4-

0.2 0.2

0
0 0.2 0.4 0.6 0.8 1.0 01.5 -1.0 -0.5 0 0.5 1.0 1.5
SURFACE-WATER SRP OUTFLOW (CsF]o,tt), SOIL POREWATER SRP OUTFLOW (CpwPlacr),
IN GRAMS PER CUBIC METER IN GRAMS PER SQUARE METER
1.2 .. c 1.2 ,

1.0 1.0 -

CQ 0.8 0.8

0.6 0.6

S0.4 0.4 -

= 0.2 0.2

0 0
-1,400 -1,200 -1,000 -800 -600 -400 -200 0 0 0.5 1.0 1.5 2.0
ORGANIC SOIL ACCRETION (Sacr), SOILABSORBED PHOSPHORUS VARIATION
IN GRAMS PER CUBIC METER (SsiPacr), IN GRAMS PER SQUARE METER
EXPLANATION
50 METERS PER DAY VELOCITY
100 METERS PER DAY VELOCITY
500 METERS PER DAY VELOCITY

Figure 32. Probability distributions for level-1 outputs obtained from the global analysis of
uncertainty based on Fourier Amplitude Sensitivity Test (FAST) results. SRP is soluble reactive
phosphorus. Parameters are defined in appendix 1.

For level 1, the results indicate that the CDF slope for surface-water SRP decreases as velocity increases. The sharp rise in
surface-water SRP at 50 m/d indicates a narrow range of possible outcomes, with nearly 100-percent certainty that the output
will be less than 0.1 g/cm3. As velocity increases, so too does the uncertainty and possibility of exceeding an arbitrary value for
Cswp]o,tf, such as 0.2 g/m3. For 100 m/d, about 80 percent of the outcomes will be less than this value, whereas at 500 m/d this
likelihood drops to about 40 percent. Because no values as large as 0.2 g/m3 were obtained at 50 m/d, there is no possibility of
exceeding the stipulated value at this velocity.


Level-2 Uncertainty

These fundamental relations with velocity would be expected to persist in the level-2 results, and figure 33 shows this
is indeed the case. Outputs for stabile components remain insensitive to velocity changes; mobile outputs, which include
Csl]o,lf at this level, are again seen to be affected by velocity. The change in complexity appears to have no effect on the
uncertainty of any stabile outputs, and their range and distribution for level 2 appear almost identical to those observed for
level 1 (table 20). The influence of velocity on CP]o,f persists, but the distinction is substantially less obvious between 50 and
100 m/d than between 100 and 500 m/d (fig. 33). The uncertainty in Cw,]o,f is reduced at all velocities in level 2, as indicated
by the reduced standard deviations listed in table 20, but the general trend of increasing uncertainty with increasing velocity is
still evident. Initially, this result was unexpected because increasing the number of parameters, each with their own intrinsic
uncertainty, should increase uncertainty in the model output. Also unexpected is the large change in the profile of the distribu-
tions. Specifically, the respective skewness for the 50- and 100-m/d cases increases from 1.3 and 1.4 in level 1 to 3.4 and 7.9 in
level 2; for the 500 m/d case, skewness drops from 1.4 to 0.2. This latter observation indicates that the high velocity creates a
system with very different phosphorus dynamics than those for lower velocities.








62 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


0.06

0.05

0.04

0.03

0.02

0.01-

0

-0.01
0 0.2 0.4 0.6 0.8 1


SURFACE-WATER SRP OUTFLOW (Csw/]o,tt),
IN GRAMS PER CUBIC METER
G
0.016 .
0.014
0.012
0.010
0.008
0.006
0.004
0.002
n


-1,400 -1,200 -1,000 -800 -600 -400 -200
ORGANIC SOIL ACCRETION (S]oacr),
IN GRAMS PER CUBIC METER


1.5 -1.0 -0.5 0 0.5 1.0 1.5
SOIL POREWATER SRP OUTFLOW (Cpvi]acr),
IN GRAMS PER SQUARE METER
H
0.030

0.025 -

0.020
C-,

S0.015

S0.010

0.005

0
0 0.5 1.0 1.5 2.0
SOILABSORBED PHOSPHORUS VARIATION
(SsiPlacr), IN GRAMS PER SQUARE METER


EXPLANATION
-50 METERS PER DAY VELOCITY
- 100 METERS PER DAY VELOCITY
-500 METERS PER DAY VELOCITY


Figure 32. Probability distributions for level-1 outputs obtained from the global analysis of
uncertainty based on Fourier Amplitude Sensitivity Test (FAST) results-Continued. SRP is soluble
reactive phosphorus. Parameters are defined in appendix 1.



These unexpected trends can be explained through close examination of figure 33. As noted for the sensitivity analysis
results, C,,s]o,f sensitivity dynamics in level 2 changed substantially with velocity, as indicated by the output uncertainty results.
Although the quantified differences mean little given the generality of the application, the trends are important. The PDF at
500 m/d is clearly diverging from those of the lesser velocities, and ultimately becomes negatively skewed relative to them in
level 3 (table 20). This inversion of output dynamics is due to the introduction of an interdependent sink for surface-water SRP
in the form of uptake by plankton. Compared with the observed results for CsP]o,f, plankton mass (C,,W'jo,f) has an inverted
relation with velocity, and actually exhibits decreased uncertainty with increasing velocity. At slower velocities (50 and 100 m/d)
planktons take longer to reach the output cells when exiting the modeled domain and, thus, remain in the system longer and
consume more SRP. A slower flow rate also means slower replenishment of SRP supplied to the modeled system by means of
the boundary conditions. Because a constant concentration for C,, of 0.05 g/m3 was set for the initial and boundary conditions,
a faster flow rate inputs more SRP to the system.
This combination of less supply and greater uptake depleted nearly all of the SRP in the water column in many of the
simulations, as indicated by the means for level 2 C,,P]o, in table 20. The initial mass of plankton selected would also have
influenced these dynamics; specifically, a larger population would deplete the SRP more quickly than a smaller population.
However, this initial condition was consistent for all cases studied, and meaningful conclusions can, therefore, be made. A
velocity of 500 m/d appears sufficient to maintain SRP levels in the water column throughout the simulation by supplying more
SRP at the boundary, given the faster flow at the same concentration, and by transporting plankton away before the population in
a given cell grows large enough to consume all of the available SRP. This conclusion appears to be supported by the results for
Csw'o,tf, which show that at 500 m/d, the mean for CswQjo, is substantially less than that obtained at 50 and 100 m/d (table 20).


.









Analysis and Assessment of Model Uncertainty from Fourier Amplitude Sensitivity Test (FAST) Simulations


S1.0

a 0.8
0
0.6

S0.4

S0.2
3


0 0.02 0.04 0.06 0.08 0.10 0.12 0.14
SURFACE-WATER SRP OUTFLOW (Cswio,tt),
IN GRAMS PER CUBIC METER


1.2

t 1.0

S0.8
o
0.6

S0.4

I0.2
i_


SOILABSORBED PHOSPHORUS VARIATION
(SsiPacr), IN GRAMS PER SQUARE METER

F
0.40
0.35
0.30
S0.25
S0.20 -
S0.15 -
0.10
0.05
0
-0.05
O 0.02 0.04 0.06 0.08 0.10 0.12 0.14
SURFACE-WATER SRP OUTFLOW (Csw]o,tt),
IN GRAMS PER CUBIC METER


S1.0

c 0.8
-
a
. 0.6

t 0.4

I 0.2
3


-1.5 -1.0 -0.5 0 0.5 1.0 1.5
SOIL POREWATER SRP OUTFLOW (CpwP]acr),
IN GRAMS PER SQUARE METER

E
1.2 ,

S1.
















0.090---------------G
0.8 -

0.6 -

0.4 -

0.2 -

001
0 5 10 15 20 25 30 35
PLANKTON BIOMASS OUTFLOW
(Csw']o,, IN GRAMS PER CUBIC METER

G
0.09
0.08
0.07
0.06 >
0.05 z
0.04
0.03 -.
0.02
0.01

1.5 -1.0 -0.5 0 0.5 1.0 1.5
SOIL POREWATER SRP OUTFLOW (Cpvi]acr),
IN GRAMS PER SQUARE METER


. z

.0

.8

.6

.4

.2

0


EXPLANATION
- 50 METERS PER DAY VELOCITY
- 100 METERS PER DAY VELOCITY
- 500 METERS PER DAY VELOCITY


-1,400-1,200-1,000 -800 -600 -400 -200
ORGANIC SOILACCRETION (So]acr),
IN GRAMS PER CUBIC METER


EXPLANATION
- 50 METERS PER DAY VELOCITY
- 100 METERS PER DAY VELOCITY
- 500 METERS PER DAY VELOCITY


SOIL ABSORBED PHOSPHORUS VARIATION
(SsiPlacr), IN GRAMS PER SQUARE METER


PLANKTON BIOMASS OUTFLOW
(CsWlo,tf), IN GRAMS PER CUBIC METER


Figure 33. Probability distributions for level-2 outputs obtained from the global analysis of uncertainty based on
Fourier Amplitude Sensitivity Test (FAST) results. SRP is soluble reactive phosphorus. Parameters are defined
in appendix 1.


-1,400 -1,200 -1,000 -800 -600 -400 -200
ORGANIC SOIL ACCRETION (So]acr),
IN GRAMS PER CUBIC METER


0.030

0.025

S0.020

2 0.015

0.010

0.005









64 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


1.U

0.8 -

0.6

0.4

0.2

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14
SURFACE-WATER SRP OUTFLOW (CswP]o,tf),
IN GRAMS PER CUBIC METER
D


SOILABSORBED PHOSPHORUS VARIATION
(SsiPlacr), IN GRAMS PER SQUARE METER


-0.1 I 1
0 0.02 0.04 0.06 0.08 0.10 0.12
SURFACE-WATER SRP OUTFLOW (Cswp]o,tf),
IN GRAMS PER CUBIC METER


J


.0 -

).8

).6

).4 -

).2 -

0 I I
-1.0 -0.5 0 0.5 1.0
SOIL ABSORBED PHOSPHORUS VARIATION
(Ssil]acr), IN GRAMS PER SQUARE METER


u
-1.5 -1.0 -0.5 0 0.5 1.0
SOIL POREWATER SRP OUTFLOW (CpwPvacr),
IN GRAMS PER SQUARE METER


0 20 40 60 80 100
PLANKTON BIOMASS OUTFLOW
(Csv']o,tf), IN GRAMS PER CUBIC METER

EXPLANATION
50 METERS PER DAY VELOCITY
100 METERS PER DAY VELOCITY
500 METERS PER DAY VELOCITY


1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4
SOIL POREWATER SRP OUTFLOW (CpwPvacr),
IN GRAMS PER SQUARE METER
K
n q --- -- -- -- -


0.8
0.7
> 0.6
~0.5
0.4
0.3
0.2
0.1
0
-n 1


0 10 20 30 40 50
PLANKTON BIOMASS OUTFLOW
(Csv'o,tt), IN GRAMS PER CUBIC METER


).8

).6

).4

).2


-1,500-1,000 -500 0 500 1,000 1,500 2,000 2,500
ORGANIC SOIL ACCRETION (So]acr),
IN GRAMS PER CUBIC METER


- 1.0

, 0.8
o
0.6

t 0.4

| 0.2
i_


2,000 0 2,000 4,000 6,000 8,000
MACROPHYTE BIOMASS ACCUMULATION
(Cmplacr), IN GRAMS PER SQUARE METER


U. bU i
0.45
0.40
. 0.35
S0.30
S0.25
S0.20
.- 0.15
0.10
0.05


-1,500-1,000 -500 0 500 1,000 1,500 2,000 2,500
ORGANIC SOIL ACCRETION (So]acr),
IN GRAMS PER CUBIC METER
L
0.6

0.5

0.4

0.3

0.2

0.1 -


-1,000 0 1,000 2,000 3,000 4,000
MACROPHYTE BIOMASS ACCUMULATION
(Cmplacr), IN GRAMS PER SQUARE METER


Figure 34. Probability distributions for level-3 outputs obtained from the global analysis of uncertainty based
on Fourier Amplitude Sensitivity Test (FAST) results. SRP is soluble reactive phosphorus. Parameters are
defined in appendix 1.


.2



.8

.6

.4

.2


-1.5 -1.0 -0.5 0 0.5 1.0 1.!


71 . . . .


'


5








Analysis and Assessment of Model Uncertainty from Fourier Amplitude Sensitivity Test (FAST) Simulations 65


Table 20. Summary statistics for output probability distributions.

[Parameter descriptions are provided in table 4. Units for mobile outputs are grams per cubic meter (CsPlf, CsPot, C1wp1o,, Csl]o,t). Units for stabile
outputs are grams per square meter (Cpw']aL, S]acr, Ssiacr, CP]acr). SD, standard deviation; SE, standard error; Q, quartile]


Velocity SE
Output Level y Range Mean Median SD Minimum 01 02 03 Maximum Skew Kurtosis
(m/d) mean
1 50 0.11 0.08 0.07 0.02 0.00 0.05 0.07 0.07 0.09 0.16 1.3 5.0
1 100 .47 .17 .15 .07 .00 .06 .12 .15 .20 .54 1.4 5.4

1 500 .77 .24 .21 .11 .00 .07 .16 .21 .29 .84 1.4 5.7
2 50 .02 .00 .00 .00 .00 .00 .00 .00 .00 .02 3.4 24.4

CswP]o,, 2 100 .10 .00 .00 .01 .00 .00 .00 .00 .00 .10 7.9 104.7
2 500 .12 .04 .04 .02 .00 .00 .02 .04 .06 .12 .2 2.5
3 50 .08 .03 .02 .02 .00 .00 .00 .02 .05 .08 .0 1.1

3 100 .12 .03 .03 .02 .00 .00 .00 .03 .05 .12 .0 1.2
3 500 .08 .04 .05 .01 .00 .00 .04 .05 .05 .08 -1.8 6.7
1 50 .07 .07 .06 .01 .00 .05 .06 .06 .07 .12 1.4 5.5

1 100 .25 .11 .10 .04 .00 .06 .08 .10 .13 .30 1.5 5.8

1 500 .35 .13 .12 .05 .00 .06 .10 .12 .15 .41 1.5 5.9
2 50 .05 .01 .01 .00 .00 .00 .01 .01 .01 .05 2.6 15.4

Csw]o, 2 100 .08 .01 .01 .01 .00 .00 .01 .01 .01 .08 3.8 27.2
2 500 .09 .04 .04 .02 .00 .00 .03 .04 .05 .09 -.1 2.4

3 50 .07 .03 .03 .02 .00 .00 .01 .03 .05 .07 .0 1.1
3 100 .08 .03 .03 .02 .00 .00 .01 .03 .05 .08 -.1 1.2

3 500 .06 .04 .05 .01 .00 .00 .04 .05 .05 .06 -2.0 7.0
1 50 1.16 .18 .15 .14 .00 -.04 .08 .15 .24 1.13 1.6 7.1

1 100 1.17 .18 .15 .14 .00 -.04 .08 .15 .25 1.13 1.6 7.1
1 500 1.17 .18 .15 .14 .00 -.04 .08 .15 .25 1.13 1.6 7.1

2 50 1.01 .18 .15 .14 .00 -.04 .08 .15 .25 .97 1.4 5.9

Cpw]acr 2 100 1.01 .18 .15 .14 .00 -.04 .08 .15 .25 .97 1.4 5.9
2 500 1.01 .18 .15 .14 .00 -.04 .08 .15 .25 .97 1.4 5.9
3 50 .56 -.07 -.07 .04 .00 -.07 -.07 -.07 -.07 .49 8.3 84.8
3 100 .59 -.06 -.07 .04 .00 -.07 -.07 -.07 -.07 .51 7.8 75.2
3 500 .57 -.06 -.07 .04 .00 -.07 -.07 -.07 -.07 .50 7.7 70.8

1 50 1,212.0 -710.1 -711.4 275.1 3.9 -1,314.5 -924.5 -711.4 -497.0 -102.4 0.0 2.1
1 100 1,212.0 -710.1 -711.4 275.1 3.9 -1,314.5 -924.5 -711.4 -497.0 -102.4 0.0 2.1
1 500 1,212.0 -710.1 -711.4 275.1 3.9 -1,314.5 -924.5 -711.4 -497.0 -102.4 0.0 2.1
2 50 1,206.4 -710.3 -712.0 275.3 3.9 -1,305.9 -924.4 -712.0 -496.6 -99.5 0.0 2.1

S]acr 2 100 1,206.4 -710.3 -712.0 275.3 3.9 -1,305.9 -924.4 -712.0 -496.6 -99.5 0.0 2.1
2 500 1,206.4 -710.3 -712.0 275.3 3.9 -1,305.9 -924.4 -712.0 -496.6 -99.5 0.0 2.1
3 50 3,178.6 21.4 177.5 377.0 5.3 -1,154.5 -289.5 177.5 351.2 2,024.1 -0.6 2.3

3 100 3,199.7 17.3 149.2 376.1 5.3 -1,174.3 -289.6 149.2 351.3 2,025.4 -0.6 2.3
3 500 3,196.5 14.1 140.6 379.9 5.4 -1,178.7 -293.8 140.6 351.9 2,017.7 -0.6 2.2








66 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table 20. Summary statistics for output probability distributions.-Continued

[Parameter descriptions are provided in table 4. Units for mobile outputs are grams per cubic meter (Csj,4f, Cswj ,t, Cwplo,, Cs,1lo,). Units for stabile
outputs are grams per square meter (CpwP]a,, S]acr, Sslacr, CP]acr). SD, standard deviation; SE, standard error; Q, quartile]


Velocity SE
Output Level Range Mean Median SD Minimum 01 02 03 Maximum Skew Kurtosis
(m/d) mean
1 50 1.81 .66 .62 .34 .01 .06 .41 .62 .88 1.86 .6 3.0
1 100 1.81 .67 .62 .34 .01 .06 .41 .62 .88 1.86 .6 2.9
1 500 1.81 .67 .62 .34 .01 .06 .42 .62 .88 1.87 .6 2.9
2 50 2.07 .66 .61 .35 .01 .04 .41 .61 .86 2.12 .8 3.4
SsiP]acr 2 100 2.08 .66 .61 .35 .01 .04 .41 .61 .86 2.12 .8 3.4
2 500 2.08 .66 .61 .35 .01 .05 .41 .61 .86 2.12 .8 3.4
3 50 1.23 -.01 -.03 .09 .00 -.03 -.03 -.03 -.03 1.20 6.9 57.0
3 100 1.23 -.01 -.03 .09 .00 -.03 -.03 -.03 -.03 1.20 6.8 56.2
3 500 1.10 -.01 -.03 .09 .00 -.03 -.03 -.03 -.03 1.08 6.7 54.1
2 50 61.19 21.37 19.74 9.28 .13 6.04 14.28 19.74 26.21 67.22 1.0 4.1
2 100 38.06 14.94 13.94 5.76 .08 5.02 10.55 13.94 18.06 43.08 1.0 4.0
2 500 11.73 3.76 3.39 1.84 .03 1.02 2.29 3.39 4.85 12.75 1.0 4.0
Cs/lo,tr
3 50 151.07 .77 .13 3.34 .05 .00 .00 .13 .80 151.07 26.8 999.8
3 100 92.34 1.53 .72 3.48 .05 .00 .00 .72 2.08 92.34 12.3 244.0
3 500 52.85 1.06 .83 1.86 .03 .01 .01 .83 1.55 52.86 10.1 200.4
2 50 26.97 11.88 11.19 4.01 .06 5.11 8.84 11.19 14.01 32.08 1.0 4.4
2 100 19.43 9.54 9.08 2.85 .04 4.57 7.39 9.08 11.06 24.00 1.0 4.3
2 500 7.95 3.00 2.74 1.34 .02 .96 1.92 2.74 3.86 8.91 .9 3.4
CsJ l]o,r
3 50 82.89 1.10 .60 2.28 .03 .00 .00 .60 1.60 82.89 14.8 414.6
3 100 55.36 1.56 1.00 2.66 .04 .00 .00 1.00 2.31 55.36 7.3 104.8
3 500 34.48 .97 .80 1.49 .02 .01 .01 .80 1.47 34.49 6.8 103.2
3 50 7,380.8 -91.6 -212.2 382.2 5.4 -348.7 -348.7 -212.2 58.7 7,032.2 4.2 44.8
CP]acr 3 100 4,772.3 -92.9 -208.1 361.1 5.1 -348.7 -348.7 -208.1 57.2 4,423.6 3.1 22.3
3 500 7,388.1 -83.5 -192.2 388.5 5.5 -348.7 -348.7 -192.2 63.3 7,039.5 4.1 43.0


The consequences of these dynamics for the quantified uncertainty measures are deduced from the CDFs shown in figure 33.
As expected, the CDFs for the stabile outputs are essentially unchanged. For Csw]o,f, there is almost a 100-percent likelihood that
velocities up to 100 m/d will result in almost zero surface-water SRP by the end of the 1-month simulation period. At 500 m/d,
the CDF resembles that from a PDF with a f-distribution, as seen in the PDF and CDF for S]acr in level 1 (fig. 32). In that case,
the only influence on the organic soil store is the oxidation rate, kox, which was given a f-distribution as shown in table 4, and the
resulting output PDF would, thus, be expected to follow the same pattern. Given the earlier conclusion that increased velocity
negated the limiting effect of depleted surface-water SRP on plankton growth, it is possible to assume that the plankton growth
occurs largely at rates stipulated by the growth parameters, which themselves were also assigned P-distributions. With respect to
Cswlo,tf, if 10 g/m3 was chosen as an arbitrary value of interest for plankton (suspended solids) output, then 100 percent of the
simulations at 500 m/d would have outputs less than this, about 60 percent at 100 m/d, and about 40 percent at 50 m/d.







Analysis and Assessment of Model Uncertainty from Fourier Amplitude Sensitivity Test (FAST) Simulations 67


Level-3 Uncertainty

Velocity does not appear to substantially affect uncertainty results for any of the outputs except CswP]o,f (fig. 34). Along with
S],cr and C"],acr, however, Cswoif exhibits bimodality, which indicates that the system is characterized by a set of critical condi-
tions (flow velocity, parameter values, and initial and boundary conditions) that, when exceeded, create distinct sets of results. Three
of the six outputs (CwP] r,,, Ssi],acr and Cspl'],of) do not exhibit bimodality, and although their respective ranges are very large, the
standard deviations are low, and consequently, the uncertainty is reduced by the increased complexity in this case. As in level 2, this
seems somewhat contradictory, because increasing the number of uncertain parameters in a model typically increases the net uncer-
tainty of the results. However, a large proportion of the simulations provide similar results, due to the collapse of one or more pools
as the critical conditions mentioned above were exceeded, thereby reducing the range of final values and, thus, the net uncertainty.
C, P]o,fhas two distinct phases in level 3 (fig. 34), one analogous to that shown in level 2 (fig. 33) where SRP results at
500 m/d are distinctly different to those at 50 and 100 m/d (and is now in fact negatively skewed), and another where results
are consistently about 0.05 g/m3, which is the value set for the initial and boundary conditions. The fact that the value has not
changed by the end of the simulation implies that the plankton population is small. This explanation is supported by the PDF for
Csl],otf in level 3 (fig. 33), which shows that a large proportion of the results was close to zero. The macrophytes, Cmp]ac,, also
exhibit a bimodal response (fig. 34); a negative net accumulated mass appears to occur almost half of the time, which implies
that conditions were such that the initial macrophyte store could not be maintained over the simulation and that a large propor-
tion of the original mass was lost. The remainder of the simulations produced a more continuous set of results, ranging from
negative to positive growth outcomes.
These trends are mirrored by results for S],ac (fig. 34), which show a large spike representing the many cases in which
the macrophyte population failed to grow and the senesced material was deposited and incorporated into the organic soil store.
The shallower portion of the PDF is more akin to the results for levels 1 and 2, and represents the cases in which macrophytes
continued to grow and hold the bulk of their foliage. Results for CpwP],ac (fig. 34) provide further support for this explanation;
almost all simulations resulted in completely depleted pore-water SRP. As presented in table 20, the median value at all veloci-
ties was -0.07 g/m2 compared with the initial condition of 0.071 g/m2. Under these conditions, macrophytes would have been
limited by phosphorus, and could not have grown any faster than diffusion rates would permit SRP to reenter the soil, assuming
surface-water SRP was not depleted at the time, or oxidation of the soil would release SRP into the pore water. It appears that
in half of the cases, conditions were insufficient to support the initial macrophyte density, resulting in depleted pore-water
phosphorus, minimal growth, and subsequent widespread senescence. In half of the cases, however, it appears that conditions
were able to support a macrophyte population; such results must represent values for combinations of factors that might include
higher soil oxidation rates (releasing more SRP into the pore water), lower growth rates or senescence rates, and even reduced
adsorption and diffusion. In almost all simulations, adsorbed phosphorus was completely depleted (the median value for SsiP]acr
is -0.03 g/m2, which equates to a loss of all 0.03 g/m2 input as the initial condition), and implies that pore-water SRP must have
been low for a long time.
The bimodality complicates interpretation of the uncertainty measures for many of the CDFs. The frequencies indicated
by the PDF spikes are corroborated by the cumulative measures. In this hypothetical case, and almost 100 percent of the
time, results for CpwP and SsiP were about 0 g/m2, regardless of velocity. The outputs Cpw],acr and SsiP]acr were in deficit by
amounts equal to their respective initial conditions. Plankton mass would be expected to drop to zero marginally less than
50 percent of the time at 500 m/d, just more than 50 percent of the time at 100 m/d, and about 80 percent of the time at 50 m/d.
Regardless of velocity, there would be about a 55-percent probability that organic soil accretion (S],acr) would be consistently
in the region of 300 g/m2, but about a 50-percent probability there would be no net gain in soil mass. Macrophytes would have
almost a 100-percent probability of losing net mass in this system, with about a 50-percent likelihood of specifically losing
about 300 g/m2. Finally, there is nearly a 100-percent probability of surface-water SRP at the output being less than the initial
and boundary condition input; if 0.045 g/m3 is the chosen limit (initial/boundary condition is 0.05 g/m3), there is a 50-percent
probability that the output will be less at 50 and 100 m/d, but only a 20-percent probability at 500 m/d.
These results highlight the importance of initial conditions within the simulation lengths used in this study, particularly for
plankton and macrophytes. If the initial population of plankton is too large, it will rapidly take up all of the SRP in the water
column and then cease to grow any further, dying off until the end of the simulation or until a population level is reached that
can be supported by the minimal phosphorus added to the water column through diffusion, assuming macrophytes have not
depleted pore-water SRP. Similarly, an initial macrophyte population that is too large to be realistically supported will rapidly
extract all of the phosphorus from the pore water and then similarly cease to grow and progressively senesce, adding to the soil
much of the initial mass and that accumulated through the rapid but brief growth phase until a density is reached that can be
supported by the soil pore-water SRP.







68 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Summary and Conclusions

Phosphorus is an essential element for all life and frequently is the limiting nutrient in oligotrophic wetlands. Although
many models exist for the simulation of wetland hydrology, few suitable computational models exist for nutrient modeling. The
current study focuses on the conceptualization, development, and application of a spatially distributed water-quality model to
simulate phosphorus dynamics and transport in wetlands. An integral component of this research involved the calibration and
validation of the model, which was applied to the Everglades of southern Florida. A global analysis of sensitivity and uncer-
tainty was also conducted.
Conceptually, the model considers physical and biogeochemical transfers between stores, and transports those elements that
move with flowing surface water. Three main compartments can be defined containing stores that are modeled: biomass (phyto-
plankton, macrophytes, and biofilm), the water column (dissolved constituents, suspended solids), and soil (soil pore water and
soil solids). Physical transfers include surface-water flow, atmospheric deposition, pore-water/surface-water interactions, settling
and entrainment of particulate matter, sloughing and cohesion of biofilm, sorption and desorption, and mineral precipitation.
Biological transfers include growth; senescence and decay of biological tissues; and soil oxidation, mineralization, and burial.
The model has been developed to be flexible in its application. Through the input interface, the user may choose which
stores and processes to include or exclude, as well as what particular equation to use to describe a process. The model was
calibrated for three different experimental datasets, representing three increasingly complex levels of potential application. For
the simplest case (level 1), the model was calibrated to data from a laboratory soil core study, which measured SRP flux out
of the soil and into the water column without the influence of macrophytes or phytoplankton. From this, a bioturbation factor
was determined and found to control the model predictions when compared to the dataset. Data from an outdoor mesocosm
study was used for an application of intermediate complexity (level 2). The model was calibrated against data for phosphorus
released from flooded soil to the water column, under natural conditions, and for surface-water suspended solids and dissolved
phosphorus. The third, most complex (level 3) case was a 147-ha field site-Cell 4 of STA-1W. This application incorporated
new complexities such as through-flowing water, suspended and dissolved components, and active periphyton and macrophyte
communities. Using some values obtained from calibration for the two simpler previous cases and data from a number of
STA-1W studies, a successful calibration and validation for this field-site case was conducted. Finally, a spatially distributed
application of the model on Cell 4 of STA-1W is presented using the same dataset referenced earlier. Overall the model was
found to respond well to the case studies.
The model applications described herein have demonstrated a flexible modeling framework that enables simulation of
phosphorus cycling using a variety of model complexity levels. For example, in level 1, phosphorus exchange was considered
only between soil and water. The same general framework was extended in levels 2 and 3 to include phosphorus exchange
with plankton and macrophytes. Furthermore, the level-2 applications demonstrated the ability of such a flexible framework to
accurately capture phosphorus cycling dynamics in systems with different initial conditions. The first level-3 application showed
that this phosphorus modeling framework can be applied even at the field scale. This application also showed the limitations of
modeling field-scale systems as homogeneous units, because such approaches are unable to capture spatial trends that have been
observed in field data. Finally, the second level-3 application demonstrated the potential utility of coupling hydrodynamic and
biogeochemical models to simulate spatially and temporally varying processes. This model was able to capture general temporal
trends in phosphorus import/export from a treatment wetland while also accurately simulating the transient spatial trends in soil
phosphorus accrual.
Although sensitivity and uncertainty analyses are an essential part of the development and application of hydrologic and
water-quality models, they are frequently overlooked. "One-at-a-time," derivative-based techniques do not evaluate sensitivity
over the entire parametric space of a given parameter, and their validity relies on linear output response. This is rarely encoun-
tered in hydrologic or water-quality models and, thus, an alternative "global" sensitivity approach is more appropriate. A modem
model evaluation framework for hydrologic and water-quality models is applied to the new wetland phosphorus water-quality
model for the purpose of conducting a comprehensive evaluation of the model sensitivity and uncertainty dynamics, and the
susceptibility of these dynamics to effects from changing model structure or velocity. This framework combines two types of
global sensitivity analysis techniques, a "Morris" screening method and a variance-based FAST technique, in conjunction with
an uncertainty analysis that is based on extended FAST results.
One outcome of these analyses is quality assurance of the computer code generated from the conceptual model presented;
that is, the model response to changes in input factors over their expected range matches the underlying conceptual model. This
model assurance is generally difficult to achieve, because the users typically do not formally explore such a large number of
combinations as those included in the global analyses.








References Cited 69


For the purpose of calibration, the analyses provided the identification of the important model parameters. The Morris
method efficiently screened the model parameters in levels 1 and 2, and predicted trends in sensitivity that were corroborated
well with FAST results. For level 1, the organic soil oxidation rate, kox, was consistently ranked most important, followed by
three other parameters: the diffusion coefficient, kdf; the soil bulk density, Pb; and the mass fraction of phosphorus in organic
soil, XsoP. These results are in agreement with current understanding of the physical system, because the principal source of
new phosphorus to the level-1 system is from oxidation of the soil (controlled by k,,), and the pore-water SRP (and, hence, the
adsorbed phosphorus) is controlled by the other three parameters. The SRP in the water column is more sensitive to kdf, because
this parameter represents the limiting process of diffusion through which the surface water gains new phosphorus. These trends
persist across outputs in the level-2 results, with the only notable difference being the prominence of plankton growth parameters
in the ranking for mobile outputs (outflow of surface-water SRP and plankton biomass). Level-3 results do not exhibit any
pattern of parameter dominance across the different outputs. The Morris qualitative results for the more complex level 3 indicate
that the majority of the level-3 variance is due to interactions and that a quantitative investigation of the output variance using the
FAST analysis is required to more clearly understand the sensitivity dynamics. The stronger additivity of the model in the level-1
and level-2 cases suggests that an efficient calibration in most field situations is possible.
Model sensitivity to velocity is correlated with model complexity. Velocity had no discernible effect on the sensitivity of
outputs for stabile components in levels 1 and 2. Mobile components were similarly unaffected in level 1; but in level 2, surface-
water SRP was subject to variable effects from interactions, depending on velocity. Plankton mass was much more sensitive
to plankton growth parameters at higher velocities and with soil parameters at lower velocities. Velocity effects in level 3
became apparent for stabile outputs, and remained important for mobile cases. Increasing the velocity increased the uncertainty
in surface-water SRP, but reduced the uncertainty in plankton biomass. The first result is expected, given the direct relation
between SRP transport as a solute and velocity in the dispersion term of the transport equation. The second result, however,
is less intuitive and only became apparent through the uncertainty analysis. A nonlinear relation between plankton mass and
velocity exists as plankton takes up SRP from the water column with growth, but is simultaneously transported much like the
SRP itself.
The uncertainty analysis provided important support for accurate interpretation of the sensitivity results, and the combined
analyses served as a powerful tool for analyzing wetland system dynamics. Increased velocity increased the uncertainty in
surface-water SRP, but decreased the uncertainty in plankton mass. Uncertainty of stabile components is largely unaffected by
velocity. Critical states of the system were apparent due to the observed decrease in uncertainty with increased complexity for
many cases. Increasing the number of parameters, each with an inherent uncertainty, typically is expected to increase output
uncertainty. However, PDFs and CDFs examined in the uncertainty analysis indicated that many of the simulations ended in the
collapse of one or more stores to a fixed output value, thereby reducing the net range and deviation of the output distributions.
This outcome was determined to be caused by the combined effect of sets of values for input parameters, in conjunction with
initial conditions that together exceeded sustainable conditions for the system. The model sensitivity to initial conditions of the
biological stores that accumulate mass and extract phosphorus is an important outcome of this process.
The results indicate that the inclusion of macrophytes in more complex representations of wetland systems of southern
Florida substantially affect the model dynamics. When included, the macrophyte component tends to dictate much of the phos-
phorus dynamics, and can greatly reduce the role of plankton. A number of other important considerations can be drawn from
these analyses. First, it is necessary to accurately measure the oxidation rates and the labile phosphorus content of the oxidizing
soil and sediments in areas where surface-water phosphorus input is low and the oxidation of the organic soil is an important
contributor of phosphorus, such as in Everglades National Park. Second, the role of plankton is expected to be different under
faster flowing conditions, such as in sloughs, than under slower flow conditions. In areas with faster flow velocities, better
measurements of plankton growth parameters would be more beneficial compared with plankton settling rates and phosphorus
mass fractions in low-flow environments. Finally, plankton, to the exclusion of macrophytes, dominates few wetlands in the
Everglades, but examples do exist, such as in the experimental stormwater treatment areas adjacent to the EAA. In most real
applications, a system more similar to level 3 is expected, with both macrophytes and plankton present. However, because
the same plankton growth parameters are important for SRP in the water column, particularly when velocities are high, such
measurements would be beneficial at multiple complexity levels. Similarly, predictions of plankton would be improved substan-
tially by more accurate values for plankton growth parameters at high velocities, particularly in the absence of macrophytes, and
phosphorous mass fractions at low velocities. It appears that plankton settling rates are more important for plankton outputs
when macrophytes are present than when they are absent.







70 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


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78 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Appendix 1. Model Nomenclature Used in this Study

This appendix describes the model nomenclature used in the stydy. The symbols and notation used to describe formulations
of the model are presented in table Al. The chemical and material components used in the model are given in table A2. Finally,
the parameters used in the model are presented in table A3.

Table Al. Symbols and notation used to describe formulations of the model.

Symbol Description Symbol Description


Main symbols used in the model
Solute concentration
Growth
Material flux
Soil concentration
Mass fraction
Subscripts and superscripts for modeled stores
Phosphorus
Biofilm
Benthic
Epiphytic
Foliage
Inorganic (applied to soil S)
Macrophyte
Organic (applied to soil S)
Particulate inorganic material
Phytoplankton (subset ofpo)
Nonphytoplankton po (po pl)

Particulate organic material
Pore water
Roots
Inorganic soil
Organic soil
Suspended solids
Surface water
Water (generic)


Subscripts and superscripts for modeled processes'
Atmospheric deposition: inflow -> (pn, pi)
Burial of soil: (so, si) -> removal
Cohesion: po -> bf
Decay: (fo, ro) -> (po, so)
Diffusion of phosphorus: sw <- pw
Entrainment of soil: so po
Growth: (sw, pw) (pl,fo, ro)
Mineralization of phosphorus: so -> pw
Oxidation of soil: so -> removal
Precipitation: sw -> pi
Sloughing: bf -po
Sorption/desorption: si -> pw
'illiidi po -> so
Flux and biomass growth notation2
Growth rate of material M: k MCMCwP/([CP] +k M)
Sorption from pore water onto soil: [C ] = kd[C p]
Material lost from foliage by decay: kd" ff C"P
Material lost from roots by decay: kd "fr C"'
Diffusion between CP and Cw : kdf([C P][CP )/df
Oxidation of organic soil: k "S"
Macrophyte lost be senescence: k"pCmP
Particulate organic lost by senescence: k PoC
Suspended organic material settled: k '[C P"]
Inorganic soil entrained into the water column: k o[S"]
Organic soil entrained into the water column: k 'o[Ss"]


1Arrows denote the transfer/transformation from originating store to destination store that the model process represents
2Abbreviated notation used in equations. Dimensions and units are [M L2 T1-] and g/m2/d, respectively








Appendixes 79


Table A2. Chemical and material components used in the model.


Mobile or
Symbol Description Location
slabile
Organic Material


Biofilm
Macrophytes
Phytoplankton (subset of particulate organic material)
Nonphytoplankton fraction of particulate organic material
Particulate organic material
Organic soil
Inorganic Material


Soil (upper surface)
Water column
Water column
Water column
Water column
Soil


Mobile
Mobile and/or stabile
Mobile
Mobile
Mobile
Stabile


C0 Particulate inorganic material
S' Inorganic soil

C Dissolved phosphorus in pore water
C P Dissolved phosphorus in surface water


Water column
Soil


Dissolved Solutes


Soil (water phase)
Water column


Particulate Solutes
C Phosphorus in particulate inorganic material
C Phosphorus in phytoplankton
C P Phosphorus in nonphytoplankton particulate organic material
C p Phosphorus in particulate organic material
Soil
S Phosphorus in inorganic soil
S o Phosphorus in organic soil
Biomass
C Phosphorus in biofilm
C P Phosphorus in macrophytes


Water column
Water column
Water column
Water column


Soil (solid phase)
Soil (solid phase)


Soil (upper surface)
Water column


Mobile
Stabile


Stabile
Mobile


Mobile
Mobile
Mobile
Mobile


Stabile
Stabile


Stabile
Mobile and/or stabile








80 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Table A3. Parameters used in the model.

[Abbreviations for stores defined by subscript and superscript are provided in table Al. SRP, soluble reactive phosphorus]

Symbol Description I Symbol Description


Soil parameters

Sorption distribution coefficient
Active soil depth
Soil porosity
Bioturbation factor, BF
Bulk density
Water-column parameters
Arrhenius constant
Molecular diffusion coefficient
Diffusion coefficient
Tortuosity
Incident light
Particle drag coefficient
Light extinction coefficient

Light extinction coefficient due to biomass

Sediment particle diameter
Temperature
Surface water velocity in x-direction
Surface water velocity in y-direction
Depth of diffusive exchange
Surface-water depth
Distance below water surface
Particle density
Density of water
Mass fractions of phosphorus
[dimensions, [MP MM ']; units, mg/kg (dry weight)]
Mass fraction of phosphorus in epiphitic
biofilm
Mass fraction of phosphorus in foliage

Mass fraction of phosphorus in organic soil

Mass fraction of phosphorus in particulate
organic
Mass fraction of phosphorus in roots


Rate constants
[Dimension, [T']; units, 1/d]
Cohesion rate coefficient
Foliage decay rate coefficient
Root decay rate coefficient
Foliage growth rate coefficient
Slough rate coefficient
Root growth rate coefficient
Organic soil oxidation rate


Particulate organic (plankton) growth rate coefficient


Particulate organic (plankton) senescence coefficient

Macrophyte senescence coefficient
Biofilm growth rate
Half saturation constants
[Dimension, [M L3]; units, g/m3]
Plankton half saturation constant
Biofilm half saturation constant
Foliage half saturation constant
Root half saturation constant
Soil and macrophyte fractions
Foliage fraction of macrophytes
Inorganic soil fraction
Organic soil fraction
Root fraction of macrophytes (1 -f )
Remaining mass flux quantities used in the model
[Dimension, [M L2 T1], units, g/m2/s]
Soluble reactive phosphorus deposited with rainfall (pre-
cipitation)
Material entrained from soil surface into water column
Atmospheric deposition of particulate inorganic phospho-
rus

Atmospheric deposition of particulate organic phosphorus

Loss of soil to deep burial


J p J Coprecipitation of SRP with particulate inorganics








Appendixes 81


Appendix 2. Model Parameter Values for Levels 1,2, and 3


[Unit abbreviations: cm2/s, square centimeter per second; i -, cubic meter per gram; g/m3, gram per cubic meter; m/s, meter per second; m, meter. Acronyms
and other annotations: EAA, Everglades Agricultural Area; SAV, submerged aquatic vegetation; SFWMD, South Florida Water Management District; STA-1W,
Stormwater Treatment Area 1 West; WCA; water conservation area; --, unknown or not applicable]


Parameter Units Values Conditions Reference

Newman and others (2005); Moore and
7.91 x 106 Assumed tortuosity = 1
others (1991)
7.34 x 106 HPO42 Li and Gregory (1974)
kd cm2/s 8.46 x 10 6 H,PO4 Li and Gregory (1974)
4.0 x 105 _Fisher and Reddy (2001)
.7 x 105 1.5 x 10-5 Sweerts and others (1991)
3.53 x 106 3.33 x 106 Calculated for 0= 0.7 0.98
.0016 Bog Bridgham and others (1998)
.0014 Acidic fen Bridgham and others (1998)
.0011 Intermediate fen Bridgham and others (1998)
.0019 Cedar swamp Bridgham and others (1998)
k I/day
.0013 Tamarack swamp Bridgham and others (1998)
.0019 Meadow Bridgham and others (1998)
.00027 Fens and bogs Bauer (2004)
.00093 Fens and bogs Bauer (2004)
.0008 .0025 Soil and sediments Daroub and others (2002)
.0009 .0025 Canal sediments in EAA Daroub and others (2002)
.0003 Dairy farm** Reddy and others (1999)
.001 Chandler slough Reddy and others (1999)
X P %/100 .00074 Lake sediment microcosm Song and others (2004)
.00063 .0013 STA-1W DB Environmental, Inc. (2002b)
.00058 STA-1W cell 4 outflow DB Environmental, Inc. (2002b)
.0013 STA-1W cell 5 inflow DB Environmental, Inc. (2002b)
.00049 .00053 STA-1W DB Environmental, Inc. (2002a)
8.0 x 106 11.0 x 106 Everglades soils Richardson and Vaithiyanathan (1995)
2.20 x 105 Houghton fen peat Richardson (1985)
5.0 x 10 6 Pocosin bog peat (Dare) Richardson (1985)
3 x 106 Pocosin bog peat (Ponzer) Richardson (1985)
9 x 106 Pocosin bog mineral-peat (Arapahoe) Richardson (1985)
k, m3/g 81 x 10 6 Swamp forest mineral-peat Richardson (1985)
600 x 10 6 Colorado River sediments Mayer and Gloss (1980)
300 x 106 Mississippi River floodplain sediments Wauchope and McDowell (1984)
25 x 106 35 x 106 Lake sediments Li and others (1972)
50 x 106 3750 x 106 Estuarine sediments Krom and Berner (1980)
7 x 106- 436 x 106 Marine sediments Slomp and VanRaaphorst (1993)








82 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)



Parameter Units Values Conditions Reference

.02 2- Sand-Jensen and Borum (1991)
.1-5.65 Extensive review Jorgensen and others (1991)
1-2.5 Total phytoplankton (20 ) Chen and Wells (1976)
1.5 Total phytoplankton (20 ) Grenney and Kraszewski (1981)
1-2.7 Total phytoplankton (Tp ) Scavia and Park (1976)
kf' 1/day 1.5 Total phytoplankton (20) Nyholm (1978)
1.8-2.53 Total phytoplankton (T1,) Jorgensen and others (1978)
.2-8 Calibrated Baca and Arnett (1976)
.2-8 Calibrated Grenney and Kraszewski (1981)
.58-3 Comprehensive review Jorgensen (1976)
.406 STA-1W CH2M HILL (2002); SFWMD (2003)
.0006-1.27 Freshwater phytoplankton Borchardt (1996)
.06 Periphyton Dodds (2003)
.0001-.0283 Shallow subtropical lake Hwang and others (1998)
.002-.035 Comprehensive review Jorgensen and others (1991)
.05-.5 Phytoplankton Chen and Wells (1976)
0-4 Phytoplankton Bowie and others (1985)
kpl m/s
.05-.2 Phytoplankton Thomann and others (1974)
0-.9 Turbulent conditions Ruiz and others (2004)
.04-.6 Phytoplankton Jorgensen (1976)
.01-4 Calibrated Baca and Arnett (1976)
0-2 Calibrated Smith (1978)
k p m/s
.15-2 Calibrated Roesner and others (1981)
0-30 Comprehensive review Jorgensen and others (1991)
.1 From Kadlec and Knight (1995) R.A. Smith and Associates (1994)
.009-.015 Total phytoplankton Daroub and others (2002)
.015 Total phytoplankton Chen and Wells (1976)
.0088 Total phytoplankton Jorgensen (1976)
XP %/100
p1 .01-.012 Total phytoplankton Smith (1978)
.016-.05 Calibrated Baca and Arnett (1976)
.0008-.0117 Comprehensive review Jorgensen and others (1991)
P.004-.17 In Appalachian rivers Rodgers and others (1983)
k "P 1/day
k .015 Calibrated for submerged aquatic vegetation DB Environmental, Inc. (2002b)
.005 Calibrated Collins and Wlosinski (1989)
k,"P g/m3 .0047 Field data Wright and McDonnel (1986a)
.025 Calibrated for submerged aquatic vegetation. DB Environmental, Inc. (2002b)
.03 Maximum Collins and Wlosinski (1998)
k "P 1/day 0-.045 Calibrated Wright and McDonnel (1986b)
.05 Maximum Wright and McDonnel (1986b)
.003-.005 g/g Canal vegetation Daroub and others (2002)
X p %/100 .00017 .00258 Cattail and sawgrass Heilman (1995)
.0008-.002 SAV STA-1W cell 4 DB Environmental, Inc. (2002a)
.88 Lake sediment microcosm Song and others (2004)
.8 Wetlands in general Mitsch and Gosselink (2000)
0 nitless .93 Everglades Harvey and others (2004)
U n ities s------------------------------------
.98 Everglades Harvey and others (2004)
.91-.94 Peat soil Comas and others (2004)








Appendixes 83


Parameter Units Values Conditions Reference

.25 Lake sediment microcosm Song and others (2004)
.09 Everglades Judson and others (2004)
.049 .070 WCA-2A Fisher and Reddy (2001)
.051 Bog Bridgham and others (1998)
.019 Acidic fen Bridgham and others (1998)
p Unitless
b.088 Intermediate fen Bridgham and others (1998)
.118 Cedar swamp Bridgham and others (1998)
.103 Tamarack swamp Bridgham and others (1998)
.224 Meadow Bridgham and others (1998)
.095-.13 STA-1W DB Environmental, Inc. (2002b)
260 Based on Pe#: Cattaillopen water Kadlec (1994)
250 Based on Pe#: Cattail Stairs (1993)
120 Based on Pe#: Cattail Kadlec and Knight (1996)
, m 70 Based on Pe#: Cattail Herskowitz (1986)
270 Based on Pe#: Open water Bavor and others (1988)
150 Based on Pe#: Myriophyllum Fisher (1990)
70 Based on Pe#: Sawgrass Rosendahl (1981)
260 Assumed 21 = 1 Kadlec (1994)
250 Assumed 21 = 1, Stairs (1993)
120 Assumed 2 = A1 Kadlec and Knight (1996)
1 m 70 Assumed 21 = 21 Herskowitz (1986)
270 Assumed 21 = A1 Bavor and others (1988)
150 Assumed 2 = A1 Fisher (1990)
70 Assumed 21 = 1 Rosendahl (1981)
'The values were not available at the time of initiating the sensitivity analysis.






84 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)

Appendix 3. Equations and XML Input Files for Complexity Levels 1, 2, and 3
The equations and XML input files for complexity levels 1, 2, and 3 are presented in this appendix. The sources used for
all three complexity levels include surface-water soluble reactive phosphorus (SRP), pore-water SRP, organic soil, and sorbed
inorganic phosphorus. In addition to these souces, level 2 includes plankton biomass and level 3 includes plankton biomass and
macrophyte biomass. Finally, two input files, Regional Simulation Model/Water Quality Model (RSM/WQ) XML equation file
and RSM/WQ parameter definition files, are presented herein for each complexity level.

[Symbols are defined in appendixes 1 and 2]

Level-1 Equations
Surface-water SRP: Mobile [grams per cubic meter]


dt dt Id Zwdf Za 0 "
dftso]I


Units check:


[ p 1 1 [, 1 3Mp I Ap
LTj [T LL LLL3 1? 1?)J


Coded form:


d(SRP _sw) (k df)(SRP pw) )
dt [ (depth)(z df )(active soil depth) (soil porosity )

Pore-water SRP: Stabile [grams per square meter]


dC,
dt


dC' P dCj' da'
dt d t dt o
S diffusion \ oxidaton sorption


(k df)(SRP _sw)
(depth)(z _df )


kdf Cj C +X k k0ko'
zdf Z 0 as0


Units check:


_ [I(MH I MP A Mp)] M IM] [1 MAL34 3 M] +[ MP
LT T LL3 L3 )J[ AMTL2 T L3 M L3 L2 J LT A


Coded form:


d(SRP pw) [
dt (z_


(k_ df)(SRP_pw)


df)(active soil depth) (soil porosity)


(k _df)(SRP s)_
(z d_ f)


+ [(chi org soil)(k ox)(org soil)]


[ (k l)(bulk density)(k d)(SRP pw)ol p
(o+ p iy)-- p + (k 1)(soil inorg P)
I (soil porosity) I






Appendixes 85


Organic soil: Stabile [grams per square meter]


dS' dSo 1 kS'
d -koxSo
dt oxidaton


Units check:


LT[ TL]J


Coded form:


d(orgsoil)
d(orgsoi) = [-(k_ox)(org_soil)]
dt


Sorbed inorganic phosphorus: Stabile [grams per square meter]

dS,- dS p k k P kS
S-klpk I kSj)
dt Idt
\ S orptionfl


Units check


LTJ TL L L3 L ,[T L2 TJ


Coded form:


d(inorg soil _P)
dt


(k 1) (bulk density)(k d)(SRP pw (l)(
- (soi oi _(k 1) (soil org P)
S(0soil porosity) I









86 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)



RSM/WQXML Equation File (eqs_one.xml)






SRP sw


SRP_pw
k df
z df
soilporosity
activesoil_depth
depth


SRP sw
k df
z df
depth




SRP_pw


SRP_pw
k df
z df
soilporosity
activesoil_depth

SRP sw
k df
z df


org soil
k ox
chiorgsoil


SRP_pw
k l
bulkdensity
k d
soilporosity


soil_inorg_p
k l




orgsoil


org soil
k ox




soil_inorg_p











Appendixes 87


SRP_pw
k 1
bulkdensity
k d
soil_porosity


soil_inorg_p
k l






RSM/WQ Parameter Definition File (level_one_wq.xml)




tslen="30"
tstype="minute"
use operator splitting="true"
postprocess="true"
linear solver type="gmres"
linear_preconditioner_type="ilu"
chemistry_solver_type="gmres"
chemistry_preconditioner_type="ilu"
equation filename="eqsone.xml"
fixed velocity="true"
x vel="0.00579"
y_vel="0.0"
depth="l.0">



SRPsw



SRP_pw





0.05




0.071


org soil
30000


soil_inorg_p
0.027






k df
parl


k ox
par2


chi_org_soil
par3


kd
par4


k 1


distribution>




distribution>


distribution>




distribution>




distribution>




distribution>









88 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


1


zdf
0.04


soil_porosity
par5




surface_porosity
1


activesoil_depth
C


fraction organicsoil
C


fraction inorganicsoil
0.


bulk density
par6


longdisp
par7


transdisp
par8



SRP sw
0.05





-.0




.1




).95




02


initial distribution>




initial distribution>




initial distribution>




"robin nodes.dat">



SRP sw
orgsoil
SRP_pw
soil_inorg_p
time_format="no_timeprinted"
every="-l"
spatial format="indexed">./output/tp finaloutput.dat



SRP sw
orgsoil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescelll.dat



SRP sw
orgsoil
SRP_pw









Appendixes 89


soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescell41.dat



SRP sw
org soil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescell81.dat



SRP sw
org soil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescelll21.dat



SRP sw
org soil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescell40.dat



SRP sw
org soil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescell80.dat



SRP sw
org soil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescelll20.dat



SRP sw
org soil
SRP_pw
soil_inorg_p
time format="%Y-%B-%d %H:%M"
every="l"
spatial format="indexed">./output/timeseriescelll60.dat










90 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)


Level-2 Equations
Surface-water SRP: Mobile [grams per cubic meter]


dC0
dt


+dC so dC2 = /kd ( P P Pk cP( --P XP'
t d ,t,o. \ plank ,oton growth ) + K )


Units check:


S3
E MT L L M L 1? 1 ? MA, M T M _ 3
FTJ [TLL~ 3 P L ,)J [ TLMpK M+ E1


Coded form:


d(SRP sw)
dt


(k _df )(SRP _pw) i (kdf )(SRP w)
(depth) (z df)(active soil depth) (soil_ porosity)) (depth) (z df )


[((chi _pl)(k pl growth) (plankton)(SRP _sw)1
S (SRP sw)+ (k halfsat pl)

Pore-water SRP: Stabile [grams per square meter]


SdC- dtC P dC on
dt / dt or dt
S dffuston/ \ oxdation sorption


kf CL P+ Xs Pk SO k Pbkd CS + kS,
Zdf Z- I j k j is,


Units check:


E l1M, 1 [M MP,>1, [MPM1 !M M, 1[M1
L[T\] _= T L_ L 3 IJ[(,1 [_+A T LAM M L3 L32 IJ [
P T TL L s L3 1 3) -- s 3 3 1? +L,- /


Coded form:


d(SRP _pw) _[(k df)(SRP _pw)
dt (z df)(active _soil depth)(soil_ porosity)


(k _df)(SRP sw)
(z_ df)


+ [(chi org soil)(k ox)(org _soil)]

S(k )(bulk density)(k_ d)(SRP pw) ol y
+ -- -- ) +(k 1) (soil inorg P)
I_ (soil porosity) I


dC
dt






Appendixes 91


Organic soil: Stabile [grams per square meter]


dt dS ox,idation + d plankton settling

Units check:


[A I A - L A -
PT T T \ -T T 3P

Coded form:

d(orgsoil) (k ox)(org soil)+ [(k pl settle)(plankton)]


Sorbed inorganic phosphorus: Stabile [grams per square meter]

dSP, d ,s, k pbk klS,
on+k Cr s -k,
dt dt 0

Units check:
[r] = [l]^ L3 IM a, .[
PLTM 1 A M L M L LT rJ

Coded form:

d(inorg _soil _P) (k _1) (bulk _density)(k d)(SRP _pw) ( (o o
dt ([ soil porosity) (k ) oilnorg P)j

Plankton biomass: Mobile [grams per cubic meter]

dC____ dCw_ dC, CI k k
dt dt dt IC + k,, z
plankton growth plankton _senescence

Units check


AL I A, _L1,
/T 3 /A A, //L Lr Z ZI A
T T 3 TL3


Coded form:

d(plankton) (k p growth)(plankton) (SRP sw) (k _pl settle)(plankton)
dt (SRP sw+(k _pl half (depth)









92 Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TARSE)



RSM/WQXML Equation File (eqs_two.xml)






SRP sw


SRP_pw
k df
z df
soilporosity
activesoil_depth
depth


SRP sw
k df
z df
depth


plankton
SRP sw
k_halfsat_pl
chi_pl
k_pl_growth




SRP_pw


SRP_pw
k df
z df
soilporosity
active soil depth


SRP sw
k df
z df


orgsoil
k ox
chi org soil


SRP_pw
k l
bulk density
k d
soilporosity


soil_inorg_p
k l




orgsoil


orq soil




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