Citation
Integrated modeling of the Tampa Bay estuarine system

Material Information

Title:
Integrated modeling of the Tampa Bay estuarine system
Series Title:
UFLCOEL-TR
Creator:
Yassuda, Eduardo Ayres, 1963- ( Dissertant )
University of Florida -- Coastal and Oceanographic Engineering Dept
Sheng, Peter ( Thesis advisor )
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Language:
English
Physical Description:
xxii, 395 p. : ill., maps ; 28 cm.

Subjects

Subjects / Keywords:
Modeling ( jstor )
Nitrogen ( jstor )
Nutrients ( jstor )
Oxygen ( jstor )
Salinity ( jstor )
Sediments ( jstor )
Shengs ( jstor )
Simulations ( jstor )
Velocity ( jstor )
Water quality ( jstor )
Coastal and Oceanographic Engineering thesis, Ph. D ( lcsh )
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF ( lcsh )
Estuarine plants -- Florida -- Tampa Bay ( lcsh )
Estuarine pollution -- Mathematical models -- Florida -- Tampa Bay ( lcsh )
Estuarine sediments -- Florida -- Tampa Bay ( lcsh )
Seagrasses -- Florida -- Tampa Bay ( lcsh )
Water quality -- Mathematical models -- Florida -- Tampa Bay ( lcsh )
Tampa Bay ( local )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )
Spatial Coverage:
United States -- Florida -- Tampa Bay

Notes

Abstract:
Integrated modeling of the Tampa Bay Estuarine System is conducted in an attempt to further the understanding of estuaries as integrated systems, and to provide quantitative assessment of various management practices. The primary objective is to use models and field data to produce a detailed characterization of the hydrodynamics and water quality dynamics within the system. To test the hypothesis that seagrass is a bioindicator of the overall health state of the estuarine system, a conceptual seagrass model is coupled to the hydrodynamics and water quality models. The integrated model is then used to study the effect of anthropogenic inputs to the estuarine system. this study combines the enhanced versions of a 3-D hydrodynamics model, a 3-D water quality model, and a seagrass model to simulate the circulation, transport, water quality, and seagrass dynamics in Tampa Bay. The hydrodynamics component of this integrated model has been successfully calibrated and verified using Tampa Bay data provided by the National Oceanic and Atmospheric Administration (NOAA) and the United States Geological Survey (USGS). The effects of hydrodynamics have been incorporated into the water quality model by using the same grid spacing and time step, hence eliminating the need for ad-hoc tuning of advective fluxes and dispersion coefficients. The water quality component has been tested using monthly water quality data provided by the Hillsborough County Environmental Protection Commission (EPC), although a more comprehensive data set is needed to fully validate the water quality model. Results of previous statistical and mass-balance models were used to determine the relevant biogeochemical processes, and to test causal relationships among state variables. These simple models also proved to be useful tools for calibration of the water quality model coefficients in the absence of process-specific data (e.g. remineralization, nitrification, denitrification). Incident-light data provided by USGS allowed the calibration of a light model of the MacPherson and Miller (1994) type. the seagrass model has been used to investigate the ecological relationships between nutrient loading, water quality dynamics, and the response of seagrass. Once validated, this integrated model can be used to determine nutrient loading reduction targets required to maintain and expand seagrass meadows in Tampa Bay. Simulated load reduction scenarios indicate that water quality can respond quickly (within 2 months), while seagrass responds more slowly (more than 6 months) to load reduction. Nevertheless, the results indicate that integrated modeling is a viable approach to provide quantitative assessment of various management practices for restoring estuarine systems.
Thesis:
Thesis (Ph. D.)--University of Florida, 1996.
Bibliography:
Includes bibliographical references (p. 377-393).
General Note:
Vita.
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
Statement of Responsibility:
by Eduardo Ayres Yassuda.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Eduardo Ayres Yassuda. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
36803763 ( OCLC )
002218224 ( aleph )

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UFL/COEL-TR/113


INTEGRATED MODELING OF THE TAMPA BAY
ESTUARINE SYSTEM







by




Eduardo Ayres Yassuda


Dissertation


1996















INTEGRATED MODELING OF THE TAMPA BAY ESTUARINE SYSTEM


By

EDUARDO AYRES YASSUDA

















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

UNIVERSITY OF FLORIDA


1996















ACKNOWLEDGMENTS


First, I would like to express my gratitude to the CNPq Conselho Nacional de

Desenvolvimento Cientifico e Tecnol6gico (Brazilian Research Council) for the financial

support during my graduate program at the University of Florida. Several University of

Florida research projects provided the opportunities for me to gain experience in

hydrodynamics and water quality modeling and field work. These projects include the Lake

Okeechobee Phosphorus Dynamics Study funded by the South Florida Water Management

District, the Sarasota Bay Field and Modeling Study funded by the Sarasota Bay National

Estuary Program and United States Geological Survey, the Tampa Bay Circulation Modeling

Study funded by the Tampa Bay National Estuary Program, the Roberts Bay Water Quality

Modeling Study funded by the Sarasota Bay National Estuary Program, and the Indian River

Hydrodynamics and Water Quality Modeling Study funded by the St. Johns River Water

Management District.

My appreciation is extended to my advisor and chairman of the supervisory

committee, Prof. Peter Sheng, for his guidance, financial support, and patience throughout

this study; to Prof. A. Mehta, and Prof. R. Thieke from the Coastal Engineering Department

for their comments and advice; to Prof. K.R. Reddy from the Soil and Water Science

Department for helping us bridge the gap between experimentalists and modelers; and to

Prof. C. Montague from the Environmental Engineering and Science Department, for his









unconditional support and high motivation. Two former students deserve special

acknowledgment: Steve Peene and Xinjian Chen.

I also want to thank my professors at the Oceanographic Institute of the University

of Sao Paulo, specially Prof. Joseph Harari, Prof. Luiz B. de Miranda, and Prof. Moyses

Tessler for their invaluable contributions to my career.

It would not be possible to complete this work if not for the technical guidance and

help of the following scientists and researchers: Mr. Richard Boler, Dr. Kate Bosley, Mr.

Michael DelCharco, Dr. Kent Fanning, Dr. Peggy Fong, Ms. Holly Greening, Dr. Kurt Hess,

Mr. Ronald Miller, Dr. Gerold Morrison, and Dr. David Tomasko.

Grateful thanks goes to my buddies in room 429, H.K. Lee, Yang, Justin, Liu, and

Kevin, in our quest for "bugs," and for reviewing the manuscript. I would like to express my

gratitude to Sidney Schofield, "Professor" Mark Gosselin, and "Wally" Yigong Li for bailing

me out in a great number of opportunities throughout this program. Life would not be the

same without the Coastal Lab and its staff. Acknowledgment goes to all of them. Deserving

special honors also are Subarna Malakar, Becky Hudson, Sandra Bivins, Lucy Hamm, Helen

Twedell, and John Davis.

My most sincere appreciation is extended to the DelCharco family, for adopting and

taking us as one of their own during all family occasions.

I would like to dedicate this dissertation to my parents, because only now, as Daniel's

father, do I realize how much effort they had to spend educating me.

Finally, I want to thank Monica for being there for me all the time, sharing the ups

and downs of this never-ending challenge.













TABLE OF CONTENTS

ACKNOWLEDGMENTS ............................................... iii

ABSTRACT .................................... .................... xxi

CHAPTERS

1 INTRODUCTION .................................................. 1

B background ....................................................... 1
Water Quality Modeling ..............................................2
Integrated Modeling Approach for Estuarine Systems ...................... 4
O objectives ........................................................7

2 TAMPA BAY CHARACTERIZATION ................................9

Climate ......................................................... 11
Tides ....................................................... 12
Salinity D distribution ............................................... 12
Rainfall ......................................................... 13
W ind ............. ....................... ..................... 13
B athym etry ...................................................... 16
Freshw ater Inflow .................................................16
Hillsborough River .......................................... 18
Alafia River ................................................... 19
Little Manatee River ........................................... 20
M anatee River ................................................. 21
Rocky Creek ................................................. 21
Lake Tarpon Canal ............................................ 22
Sweetwater Creek ............................................. 22
Non-Point Sources ............................................. 22
Nutrients Distribution and Loading ................ .................. 23
Sediment Type and Distribution ..................................... 26

3 THE CIRCULATION AND TRANSPORT MODEL ..................... 31

Previous W ork ................................................ 31
Circulation Model ................................................ 33
Continuity Equation ............................................ 33










X-component of Momentum Equation .............................. 34
Y-component of Momentum Equation ............................. 34
Hydrostatic Pressure Relation .................................... 34
Salinity Equation .............................................. 35
Equation of State ......................... ...................... 36
Conservative Species Equation .................................. 36
Sediment Transport Model ......................................... 37
Curvilinear Boundary-Fitted and Sigma Grid ............................ 38
Boundary and Initial Conditions ..................................... 40
Vertical Boundary Conditions .................................... 40
Lateral Boundary Conditions ..................................... 42

4 THE WATER QUALITY MODEL ................................. 45

Previous Work ................................................... 45
Development of the Numerical Model ................................. 50
Mathematical Formulation ......................................... 52
Nutrient Dynamics in Estuarine Systems .............................. 53
Ammonia Nitrogen ............................................ 55
Dissolved Ammonium Nitrogen ................................. 56
Nitrite+Nitrate Nitrogen ........................................ 58
Soluble Organic Nitrogen ....................................... 60
Particulate Organic Nitrogen ..................................... 61
Particulate Inorganic Nitrogen .................................... 61
Algal Nitrogen ................................................ 62
Zooplankton Nitrogen .......................................... 62
Sorption and Desorption Reactions .................................. 63
Phytoplankton Dynamics in Estuarine Systems .......................... 64
Oxygen Balance in Estuarine Systems ................................ 66
Light Attenuation in Estuarine Systems ................................ 69
Model Coefficients ............................................... 73

5 THE SEAGRASS MODEL ......................................... 79

Using Seagrass as a Bioindicator of the Estuarine System .................. 79
Seagrass Ecosystems .............................................. 80
Previous Work ................................................... 83
Development of the Numerical Model ............................... 85
Mathematical Formulation ......................................... 88
Light ....................................................... 88
Temperature .................................................. 89
Density-dependent Growth Rate ............... ................. 89
Growth Rate Dependence on Light ............................... 91









Growth Rate Dependence on Salinity ............................. 93
Growth Rate Dependence on Temperature ........................... 96
Growth Rate Dependence on Sediment Nutrients ...................... 98

6 APPLICATION OF THE CIRCULATION AND TRANSPORT MODEL ..... 99

Design ofTampa Bay Grid ......................................... 99
Forcing Mechanisms and Boundary Conditions ......................... 105
Modeling Strategy ............................................... 115
Results of the Barotropic Simulation ................................ 115
Results of the Baroclinic Simulation ..................................... 119
Tides ................................................... 121
Currents ................................................. 128
Salinity ... ................................................. 148
Validation of the Model ................ ......................... 156
Residual Circulation ............................................. 168
Results of the Suspended Sediment Simulation ......................... 177

7 CALIBRATION OF THE WATER QUALITY MODEL ................. 185

Initial and Boundary Conditions of the Water Quality Model .............. 188
Water Column ............................................... 188
Sediment Column ............................................ 201
Modeling Strategy ............................................ 212
Sensitivity Analysis ............................................ 212
Simulation of the Summer 1991 Condition ............................. 224
Dissolved Oxygen ............................................ 225
Phytoplankton ............................................. 238
Nitrogen Species ............................................. 250
Tidal Exchange ...............................................261
Nutrient Budget .............................................. 265
Load Reduction Simulations ......................................... 269
Comparison with AScI (1996) study ................ ................ 271
Comparison with Coastal Inc. (1995) study ............................ 274
Advantages and Limitations of this Integrated Modeling Approach .......... 275

8 CALIBRATION OF THE SEAGRASS MODEL ...................... 277

Initial Conditions ................................................ 280
Sensitivity Analysis .............................................. 282
Simulation of the Summer 1991 Condition ........................... 294
Load Reduction Simulation ......................................... 296










9 CONCLUSION AND RECOMMENDATIONS ........................ 303

APPENDICES

A NUMERICAL SOLUTION OF THE EQUATIONS .................... 309

B MODELING SEDIMENT DYNAMICS .................... .......... 329

C DISSOLVED OXYGEN SATURATION AND REAERATION
EQUATIONS .................................................. 339

D LIGHT MODEL EQUATIONS ................................... 341

E RESULTS OF THE SUMMER 1991 SIMULATION .................... 343

F SENSITIVITY TESTS OF THE SEAGRASS MODEL ................... 363

REFERENCES ..................................................... 377

BIOGRAPHICAL SKETCH ............................................ 395













LIST OF FIGURES


Figure page

2.1 Tampa Bay Estuarine System subdivisions as defined by
Lewis and Whitman (1985) (from Wolfe and Drew, 1990)................ 10

2.2 Monthly rainfall in Tampa Bay (Wooten, 1985). ........................ 14

2.3 Seasonal wind pattern in Florida (Echternacht, 1975) .................... 15

2.4 Tampa Bay watershed (Wolfe and Drew, 1990). ....................... 17

2.5 Surface Sediments in Tampa Bay (Goodell and Gorsline, 1961). .......... 28

2.6 Mud zone in Hillsborough Bay (Johansson and Squires, 1989). ........... 29

5.1 Seagrass species commonly found in west Florida
(from Phillips and Mefiez, 1987) .................................. 82

5.2 Structure and components of the numerical seagrass
model used for this study. ....................................... 86

5.3 Epiphytic algae model flow chart. ................................. 87

5.4 Seagrass model flow chart. ....................................... 87

5.5 Seagrass density-dependent maximum growth rate:
Thalassia (dotted line), Halodule (solid line),
and Syringodium (dash-dotted line). .............................. 90

5.6 Seagrass growth rate dependence on light: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line). ............... 92

5.7 Seagrass growth rate dependence on salinity: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line). ............... 95

5.8 Seagrass growth rate dependence on temperature: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line). ............... 97









6.1 NOAA's TOP station locations in Tampa Bay. ....................... 101

6.2 A boundary-fitted grid for the Tampa Bay Estuarine System. ............. 102

6.3 Tampa Bay bathymetric contours. ................. .............. 103

6.4 Bay segments (Sheng and Yassuda, 1995)............................. 104

6.5 Tidal forcing for the 1990 simulation .......................... .. .106

6.6 Tidal forcing for the 1991 simulation. .............................. 107

6.7 Initial salinity distribution (surface) for the 1990 simulation. ............. 108

6.8 Initial salinity distribution (surface) for the 1991 simulation. ............ 109

6.9 Rainfall data for the 1990 and 1991 simulations ....................... 111

6.10 River discharges for the 1990 and 1991 simulations ................... 112

6.11 Wind velocity for the 1990 simulation. ............................. 113

6.12 Wind velocity for the 1991 simulation. ............................ 114

6.13 Surface elevation at Egmont Key and St.Petersburg
(September 1990)............................................... 117

6.14 Surface elevation at Davis Island and Old Tampa Bay
(September 1990)............................................... 118

6.15 Spectra of water surface elevation for the 1990 simulation ............. 123

6.16 Simulated and measured bottom velocity at Egmont Channel -
September/1990. .............................................. 130

6.17 Simulated and measured surface velocity at Egmont Channel -
September/1990. .............................................. 131

6.18 Simulated and measured bottom velocity at Skyway Bridge -
September/1990. ................. ............................ 133

6.19 Simulated and measured mid-depth velocity at Skyway Bridge -
September/1990. .............................................. 134










6.20 Simulated and measured surface velocity at Skyway Bridge -
September/1990 ............................................135

6.21 Simulated and measured bottom velocity at Port of Manatee Channel -
September/1990. .............................................. 137

6.22 Simulated and measured surface velocity at Port of Manatee Channel -
September/1990. .............................................. 138

6.23 Simulated and measured bottom velocity at Port of Tampa Channel -
September/1990 ............................................ 139

6.24 Simulated and measured bottom velocity at Port of Tampa Channel -
September/1990. ........................................... .141

6.25 Energy density spectra of bottom currents at Skyway Bridge -
September/1990. ............................................... 144

6.26 Energy density spectra of surface currents at Skyway Bridge -
September/1990. .............................................. 145

6.27 Tidal current ellipses for the semi-diurnal components September/1990. 149

6.28 Tidal current ellipses for the diurnal components September/1990. ...... 150

6.29 Near-bottom salinity (solid line) and temperature (dashed line) at NOAA
station S-4 starting at Julian Day 150 in 1990. ...................... 151

6.30 Simulated and measured near-bottom salinity at NOAA
station C-21 September/1990 .................................153

6.31 Simulated and measured near-bottom salinity at C-23 -
September/1990 ............... ............................ 154

6.32 Simulated and measured near-bottom salinity at C-4 -
September/1990. .............................................. 155

6.33 Surface elevation at St.Petersburg and Davis Island -
"Marco" Storm October/1990. .................................157

6.34 Surface elevation at St.Petersburg and Davis Island July/1991........... 158










6.35 Simulated and measured bottom current at Skyway Bridge -
"Marco" Storm (October/1990) ....................................161

6.36 Simulated and measured surface current at Skyway Bridge -
"Marco" Storm (October/1990) ................................... 162

6.37 Simulated and measured near-bottom salinity at station S-4 -
(July/1991). .................................................. 163

6.38 Simulated and measured near-surface salinity at station S-4 -
(July/1991). ...................................................164

6.39 Relative flushing for several bay segments September/1990 ........... 167

6.40 Residual circulation after 30 days September/1990 .................. 169

6.41 Simulated velocity field representing maximum ebb currents -
September/29/1990 18:00. ..................................... 171

6.42 Simulated velocity field representing maximum flood currents -
September/29/1990 10:00. ..................................... 172

6.43 Velocity cross-section at Skyway Bridge looking up the Bay. Vertical
scale in meters, and horizontal scale in computational grid j-index ....... 174

6.44 Salinity cross-section at Skyway Bridge looking up the Bay. Vertical
scale in meters, and horizontal scale in computational grid j-index ........ 175

6.45 Longitudinal distribution of salinity along the navigation channel. Vertical
scale in meters, and horizontal scale in computational grid i-index. ....... 176

6.46 Location of the USGS station in Old Tampa Bay
(Schoellhammer, 1993). ........................................ 180

6.47 Wind speed and direction, and suspended sediment concentration at
USGS station during tropical storm "Marco" (Schoellhammer, 1993). ..... 181

6.48 Simulated significant wave height and period during tropical storm
"Marco" (October/1990). .......................................182

6.49 Simulated wave-induced bottom shear stress and suspended sediment
concentration at the USGS station for October 10 and 11, 1990. ......... 183









6.50 Simulated suspended sediment concentration at 6:00am -
October 11, 1990............................................... 184

7.1 Water quality monitoring stations of the Hillsborough County
Environmental Protection Commission (EPC) (Boler, 1992). ............ 189

7.2 Measured near-bottom dissolved oxygen concentration (mg/L) in
Tampa Bay (June 1991) ......................................... 190

7.3 Measured near-surface dissolved oxygen concentration (mg/L) in
Tampa Bay (June 1991). ........................................ 191

7.4 Measured organic nitrogen concentration (mg/L) in
TampaBay (June 1991) ........................................ 192

7.5 Measured dissolved ammonium-nitrogen concentration (mg/L) in
Tampa Bay (June 1991) ........................................ 193

7.6 Measured nitrite+nitrate concentration (mg/L) in
Tampa Bay (June 1991). ........................................ 194

7.7 Measured chlorophyll-a concentration (pg/L) in
Tampa Bay (June 1991). ......................................... 195

7.8 Measured color (Pt-Co) in Tampa Bay (June 1991). .................. 196

7.9 Measured turbidity (NTU) in Tampa Bay (June 1991). ................. 197

7.10 Water quality zones in Tampa Bay used in the model simulations of the
summer of 1991 conditions ..................................... 200

7.11 Total organic nitrogen (dry weight %) in the surface sediments of
Tampa Bay during 1963 (Taylor and Saloman, 1969) .................. 204

7.12 Total Kjeldahl nitrogen (dry weight %) in Tampa Bay sediments,
1982-86 (Brooks and Doyle, 1992) ................................ 205

7.13 Sedimentary nitrogen (dry weight %) in Hillsborough Bay
in 1986 (COT, 1988). .......................................... 206

7.14 Location of the NOAA sediment sampling stations in 1991 (phase 1) and
1992 (phase 2) (NOAA, 1994)..................................... 207










7.15 Total sediment nitrogen (dry weight %) obtained from NOAA
(1994) data. .................. ................................208

7.16 Dry density profile for water quality zone 1 in Tampa Bay
(Sheng et al., 1993). ................ ......................... 209

7.17 Water quality parameters after 30 days for a simulation using the lower
limit of the mineralization constant rate. ............................ 221

7.18 Water quality parameters after 30 days for a simulation using the higher
limit of the mineralization constant rate. ............................ 222

7.19 Near-bottom dissolved oxygen levels after 30 days for the mineralization
constant rate tests. ............................................. 223

7.20 Near-bottom dissolved oxygen concentration in Tampa Bay for
June 26, after 30 days of simulation. ............................. 226

7.21 Near-bottom dissolved oxygen concentration in Tampa Bay for
July 26, after 60 days of simulation. ............................. 227

7.22 Near-bottom dissolved oxygen concentration in Tampa Bay for
August 25, after 90 days of simulation. ............................ 228

7.23 Near-bottom dissolved oxygen concentration in Tampa Bay for
September 24, after 120 days of simulation ........................... 229

7.24 Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Hillsborough Bay. ................................... 231

7.25 Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Old Tampa Bay .................................... 232

7.26 Model results and measured data for near-bottom DO at
EPC stations 70 and 8. ......................................... 233

7.27 Model results and measured data for near-bottom DO at
EPC stations 73 and 80. ............... ........................ 234









7.28 Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Middle Tampa Bay. .................................. 236

7.29 Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Lower Tampa Bay .................................... 237

7.30 Near-surface chlorophyll-a concentration in Tampa Bay for
June 26, after 30 days .......................................... 240

7.31 Near-surface chlorophyll-a concentration in Tampa Bay for
July 26, after 60 days .... .............. ........................ 241

7.32 Near-surface chlorophyll-a concentration in Tampa Bay for
August 25, after 90 day ......................................... 242

7.33 Near-surface chlorophyll-a concentration in Tampa Bay for
September 24, after 120 ...................................... 243

7.34 Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Hillsborough Bay. .......................... 245

7.35 Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Old Tampa Bay ........................... 246

7.36 Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Middle Tampa Bay ......................... 248

7.37 Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Lower Tampa Bay.......................... 249

7.38 Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
June 26, after 30 days of simulation ............................... 251

7.39 Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
July 26, after 60 days of simulation .............................. 252

7.40 Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
August 25, after 90 days of simulation ............................ 253

7.41 Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
September 24, after 120 days of simulation .......................... 254











7.42 Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Hillsborough Bay.................. 256

7.43 Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Old Tampa Bay. ................. 257

7.44 Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Middle Tampa Bay. ............... 258

7.45 Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Lower Tampa Bay ................ 259

7.46 Measured and simulated transport across the mouth of Hillsborough Bay,
along with the Kjeldahl nitrogen concentration (mean and standard
deviation) presented by Rines (1991). ........................... 263

7.47 Measured and simulated transport across the entrance of Tampa Bay,
along with the Kjeldahl nitrogen concentration (mean and standard
deviation) presented by Rines (1991). ......................... 264

7.48 Simulated nitrogen cycle for the summer of 1991 conditions:
(a) Loading, (b) biogeochemical processes in the water column,
(c) biogeochemical processes in the sediment column. ................. 268

7.49 Near-bottom dissolved oxygen concentration in Tampa Bay, after
60 days of the load reduction simulation. ........................... 272

7.50 Near-surface chlorophyll-a concentration in Tampa Bay, after
60 days of the load reduction simulation. .......................... 273

8.1 Extent of seagrass meadows in Tampa Bay. (a) corresponding to 1943,
and (b) to 1983 (Lewis etal., 1985). .............................. 278

8.2 Initial seagrass distribution in the computational grid. Dark areas indicate
seagrass meadows (100 gdw/m2). ................................ 281

8.3 Simulated seagrass biomass in Tampa Bay. .......................... 283

8.4 Growth rate dependence on temperature ........................... 285

8.5 Growth rate dependence on light. ................................. 286









8.6 Growth rate dependence on salinity................................ 287

8.7 Growth rate dependence on sediment nutrient concentration. ............. 288

8.8 Simulated seasonal distribution of Thalassia. ........................ 290

8.9 Simulated Thalassia biomass in Tampa Bay for July 26,
after 60 days of simulation....................................... 297

8.10 Simulated Halodule biomass in Tampa Bay for July 26,
after 60 days of simulation....................................... 298

8.11 Simulated Syringodium biomass in Tampa Bay for July 26,
after 60 days of simulation...................... ................. 299

8.12 Near-bottom light levels in Tampa Bay for July 26,
after 60 days of simulation........................................ 300

8.13 Comparison between simulated light levels for the Present Condition
simulation (solid line) and the 100% Load Reduction (dashed line) ....... 301


xvii













LIST OF TABLES


Table page

2.1 Area of the subdivisions in Tampa Bay (Lewis and Whitman, 1985).......... 11

2.2 Surface water discharges to Tampa Bay (Lewis and Estevez, 1985). ........ 18

2.3 1991 annual average water quality of eight point sources discharging
into Tampa Bay (Boler, 1992) and (USGS, 1991) (mg/L). ............... 23

2.4 Mean annual total nitrogen loading into each segment of Tampa Bay
(Coastal, 1994) ................................................26

4.1 Description of the coefficients used in the water quality model ............ 74

4.2 Literature ranges and values of the coefficients used in the water
quality model. ................................................... 75

6.1 The rms error (Erms) between measured and simulated
water surface elevation September/90 ............................. 121

6.2 The distribution of tidal energy for water surface elevation -
September 1990. ............................................... 124

6.3 Major tidal constituents in Tampa Bay September/1990. ............... 127

6.4 The rms error between measured and simulated bottom (b) and
surface (s) currents September/1990 .............................. 142

6.5 The distribution of tidal energy for bottom (b) and surface (s) currents -
September 1990................................................. 146

6.6 The rms error between measured and simulated salinity -
September 1990................................................. 156

6.7 The rms error between measured and simulated water surface elevation
October/1990 and July/91. ........................................ 159


xviii









6.8 The rms error between measured and simulated bottom (b) and
surface (s) currents "Marco" Storm. .............................. 160

6.9 The rms error between measured and simulated salinity July/1991. ....... 165

7.1 Estimated total suspended solids concentration (TSS), and calculated
water column partition coefficients for particulate organic nitrogen
(pcon) and adsorbed ammonium (pcan). ............................ 201

7.2 Estimated dry density for the sandy zones of Tampa Bay ................ 210

7.3 Initial nitrogen concentration in the sediment (Ae) aerobic layer, and
(An) anaerobic layer for each water quality zone. (SON) soluble organic
nitrogen, (NH4) dissolved ammonium nitrogen, (N03) nitrite+nitrate. ..... 211

7.4 Model coefficients in the (W) water column, (Ae) aerobic layer, and
(An) anaerobic layer for each water quality zone. ...................... 211

7.5 Parameters, baseline values, and range used in the sensitivity analysis. ..... 214

7.6 Sensitivity tests description. ............ ........................... 215

7.7 Sensitivity analysis results............. ...... ..................... 217

7.8 Nitrogen budget between July 1 and August 31, 1991. .................. 267

8.1 Sensitivity tests description....................................... 291

8.2 Simulated and reported seagrass biomass in the Tampa Bay area. ......... 294















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

INTEGRATED MODELING OF THE TAMPA BAY ESTUARINE SYSTEM

By

Eduardo Ayres Yassuda

December 1996

Chairperson: Dr. Y. Peter Sheng
Major Department: Coastal and Oceanographic Engineering

Integrated modeling of the Tampa Bay Estuarine System is conducted in an attempt

to further the understanding of estuaries as integrated systems, and to provide quantitative

assessment of various management practices. The primary objective is to use models and

field data to produce a detailed characterization of the hydrodynamics and water quality

dynamics within the system. To test the hypothesis that seagrass is a bioindicator of the

overall health state of the estuarine system, a conceptual seagrass model is coupled to the

hydrodynamics and water quality models. The integrated model is then used to study the

effect of anthropogenic inputs to the estuarine system.

This study combines the enhanced versions of a 3-D hydrodynamics model (Sheng,

1989), a 3-D water quality model (Chen and Sheng, 1994), and a seagrass model (Fong and

Harwell, 1994) to simulate the circulation, transport, water quality, and seagrass dynamics

in Tampa Bay. The hydrodynamics component of this integrated model has been

successfully calibrated and verified using Tampa Bay data provided by the National Oceanic

xxi









and Atmospheric Administration (NOAA) and the United States Geological Survey (USGS).

The effects of hydrodynamics have been incorporated into the water quality model by using

the same grid spacing and time step, hence eliminating the need for ad-hoc tuning of

advective fluxes and dispersion coefficients. The water quality component has been tested

using monthly water quality data provided by the Hillsborough County Environmental

Protection Commission (EPC), although a more comprehensive data set is needed to fully

validate the water quality model. Results of previous statistical and mass-balance models

were used to determine the relevant biogeochemical processes, and to test causal

relationships among state variables. These simple models also proved to be useful tools for

calibration of the water quality model coefficients in the absence of process-specific data

(e.g., remineralization, nitrification, denitrification). Incident-light data provided by USGS

allowed the calibration of a light model of the MacPherson and Miller (1994) type. The

seagrass model has been used to investigate the ecological relationships between nutrient

loading, water quality dynamics, and the response of seagrass.

Once validated, this integrated model can be used to determine nutrient loading

reduction targets required to maintain and expand seagrass meadows in Tampa Bay.

Simulated load reduction scenarios indicate that water quality can respond quickly (within

2 months), while seagrass responds more slowly (more than 6 months) to load reduction.

Nevertheless, the results indicate that integrated modeling is a viable approach to provide

quantitative assessment of various management practices for restoring estuarine systems.


xxii














CHAPTER 1
INTRODUCTION



Background



Historically, an estuary has been defined as "a semi-enclosed coastal body of water

which has a free connection with the open sea and within which the sea water is measurably

diluted with fresh water derived from continental drainage" (Cameron and Pritchard, 1963 -

p. 306). In order to assess environmental problems along the entire coastal zone, the

classical definition of estuary was revised by the National Research Council (1977) to

include not only the estuary from the classical definition, but also all coastal environments

characterized as transitional zones. Following this new definition, an estuarine system

comprises bays, coastal lagoons, inlets, deltas, and salt marshes; all affected by different tidal

regimes and freshwater discharges.

In an estuarine system, the region characterized by accentuated gradients of some

specific properties is defined as the mixing zone (Harleman, 1971). It is usually located

between two stable zones, the freshwater and the oceanic ecosystems, wherein these

properties are treated as "reservoirs," with relative slower temporal variations.

Salinity is the primary physical property that presents a markedly longitudinal

gradient. Upstream from the tidal portion of the river, salinity is usually constant and nearly









2

equal to zero. In the coastal zone beyond the region of freshwater influence, salinity is equal

to the "oceanic reservoir" condition.

In a cross-section, the mixing zone reveals important vertical gradients. The most

evident is the intertidal zone, which is periodically flooded and exposed. In the intertidal

zone, there may be salt marshes, mangroves, beaches, and oyster banks. To overcome the

stresses originated by flood and dry conditions, organisms living in this zone have developed

special adaptations. Human presence is visible through structures like seawalls, piers, and

harbors.

According to Day et al. (1989), a second important vertical gradient is light

attenuation, going from a lighted, euphotic zone to a light depleted, aphotic zone. Where the

euphotic zone reaches the bottom, submerged aquatic vegetation like seagrasses is able to

thrive. Usually, water clarity also increases towards the ocean side. Another extremely

important gradient for biogeochemical processes is the redox potential in the sediment layer,

ranging from oxidized to reduced conditions. In a healthy estuarine system, the water

column is usually aerobic, but the bottom sediments become anaerobic in a very short

distance (order of few centimeters) from the water-sediment interface.


Water Ouality Modeling



The primary requirement in any estuarine water quality modeling is a thorough

understanding of the circulation and transport processes. Differently from freshwater

systems, where uni-directional flow and steady-state conditions may be applied in a variety









3

of cases, estuaries are complex systems where the circulation dynamics are driven by tides,

wind, river discharges, waves, Coriolis force, and density gradients, which give the estuarine

circulation an unsteady, multi-dimensional character. The baroclinic effect in estuarine

circulation has been studied by various investigators, including the classical works of

Pritchard (1956), Cameron and Pritchard (1963), and Hansen and Rattray (1965).

Weisberg and Williams (1991) demonstrated that horizontal salinity gradients in

Tampa Bay are capable of creating a density-driven circulation, through the generation of a

baroclinic forcing. Galperin et al. (1991) refuted the barotropic residual circulation pattern

obtained by Goodwin (1987) and Ross et al. (1984) in Tampa Bay, showing that when

baroclinic effects are included, the residual circulation changed substantially.

Models with a limited resolution (spatial and time scales) are useful tools to depict

a general trend in the overall circulation pattern or to study the response of the system to a

specific forcing mechanism. However, estuarine processes are not in steady state, and they

often present a three-dimensional distribution. Biogeochemical and ecological processes

occurring inside an estuarine system are primarily driven by physical factors with an

unsteady, multi-dimensional character. To implement an integrated hydrodynamics, water

quality and ecological model, it is essential to fully understand the coupling among the

hydrodynamics, water quality and ecological processes.









4

Integrated Modeling Approach for Estuarine Systems



Competitive demands for natural resources in estuarine systems can lead to a serious

deterioration of the environment. Solutions to environmental problems have been attempted

by resources management agencies to support a holistic approach to environmental

management. For example, the Florida Department of Environmental Protection has been

emphasizing that ecosystem management is an integrated, flexible approach to manage

Florida's biological and physical environment.

An efficient strategy to prevent or reverse the degradation of important estuarine

systems makes use of numerical models in conjunction with monitoring programs. Through

monitoring, not only the present state of the system can be obtained, but it is also possible

to evaluate the effectiveness of past management efforts.

Numerical models can be used to study management options and the corresponding

response of the system. In estuarine systems, numerical models can be applied to study the

hydrodynamics, sediment dynamics, water quality dynamics and system ecology.

Hydrodynamics and sediment dynamics models have been significantly advanced

during the past decade (e.g., Sheng, 1994). The developments in numerical techniques and

computer technology have been fully capitalized. Also, advancement in instrumentation and

basic understanding has led to the development of process-based models rather than

empirical lumped-process models.

On the other hand, applications of traditional water quality models (e.g., Ambrose et

al., 1994) are often based on coupling the hydrodynamics and water quality dynamics on an









5

intertidal basis (i.e., tidally averaged). This simplification was supported by high

computational cost of robust multi-dimensional models and the large time scale of the

kinetics in water quality models. But, by doing so, several hydrodynamic processes (e.g.,

wave actions) and sediment dynamics (e.g., resuspension, deposition) which can significantly

affect the water quality dynamics are not accurately represented. Chen and Sheng (1994)

developed a coupled hydrodynamics-sediment-water quality model and applied it to Lake

Okeechobee. A coupled hydrodynamics-water quality model has been used to study the

response of Chesapeake Bay to various loading scenarios (Chesapeake Bay Program, 1994).

The primary prerequisite in the implementation of a reliable water quality model is

the development of a budget for the specific pollutant of interest. In the case of Tampa Bay,

where eutrophication is one of the issues of greatest concern, nutrient loading levels have to

be defined. To develop a nutrient budget it is essential to quantify the sources of (Sheng et

al., 1993): (i) external nutrient loading from tributaries and non-point sources, (ii) nutrient

fluxes into and from the connecting ocean, and (iii) benthic nutrient fluxes. The most

difficult source to quantify is the benthic flux, due to measurement techniques, and the

competing influences of molecular diffusion, resuspension, and groundwater seepage.

Consequently, it is common to find nutrient budgets that consider the net benthic flux to be

simply the difference between the external loading and flux to the ocean. However, the

oceanic flux, induced primarily by tidal forcing is also difficult to estimate; hence,

subtracting tidally-averaged oceanic flux from the external loading may not give the correct

benthic flux. Results of McClelland (1984) nutrient box model of Tampa Bay shows that

nitrogen benthic flux can be as much as twice the external loading of point and non-point









6

sources. The author suggested that the supply of nitrogen through sediment resuspension and

biogeochemical reactions in the water column are likely important. Results of Johansson and

Squires (1989) nutrient budget for Tampa Bay suggest that the internal loading of nitrogen

associated with sediment resuspension events can be quite significant.

Ecological models are the primary tool in developing an overall picture of the system.

Using energy flow and Emergy concept (Odum, 1994), it is possible to identify the main

forcing functions that drive the system, and the causal relationships between state variables.

The conflicts between the "apparently" adversarial uses of an estuarine system can be better

mediated when they are evaluated on a common measure. System ecology models can be

used to connect environmental products with human use. The Emergy of the system

measures both the work of nature and that of humans in generating products and services.

By selecting choices that maximize Emergy production and use, policies and judgments can

favor those environmental alternatives that maximize real wealth, the whole economy, and

the public benefit (Odum, 1971).

In estuarine systems where seagrass has declined due to anthropogenic effects,

restoration of seagrass beds can be linked exclusively to environmental quality. In this sense,

seagrass provides a more direct assessment of the restoration processes (Dennison et al.,

1993). Seagrasses serve as habitat for fish and benthic invertebrates. Seagrass leaves provide

substrate for many epiphytic organisms. Herbivores such as manatees, fishes, sea turtles, and

sea urchins graze directly on seagrass blades. Dead leaves can constitute the majority of the

detritus pool. Seagrass also interacts with the physical components of the estuary by slowing

down the currents and enhancing the deposition of organic and inorganic material from the









7

water column. Their presence also inhibit the resuspension of sediments, which also affects

the nutrient cycles. Therefore, seagrass is a crucial indicator of the state of the estuary.



Objectives

Recognizing the important relationships among the various ecological components

(including hydrodynamics, sediment dynamics, water quality, aquatic vegetation, etc.), it is

now appropriate to take advantage of the advancement in computer resources and scientific

understanding to integrate models with multiple dimensions, more robust and coupled

processes. The purpose of this effort would be to further the understanding of estuaries as an

integrated system, and to provide a quantitative evaluation of various management practices.

The goals of this study are to develop a comprehensive model of the Tampa Bay

Estuarine System, and to produce a detailed characterization of the hydrodynamics and water

quality dynamics within the system. In order to test the hypothesis that seagrass is a

bioindicator of the overall health state of the Tampa Bay Estuarine System, a conceptual

seagrass model is coupled to the hydrodynamics and water quality models. This integrated

model will then be used to provide mechanisms for relating anthropogenic inputs to the

overall health of the estuary. The following questions have to be addressed in order to

accomplish these goals:

1) How important are the three-dimensional characteristics of the estuarine

circulation in the overall dynamics of the system?

2) What are the most important environmental parameters and biogeochemical

processes in the water quality dynamics of the estuarine system?

3) Can the integrated modeling provide a quantitative assessment of various

management practices for restoring the estuarine system?















CHAPTER 2
TAMPA BAY CHARACTERIZATION


Tampa Bay, classified as a subtropical estuarine system (Lewis and Estevez, 1988),

is the largest coastal plain estuary in the state of Florida. It is located on the west central part

of the Florida peninsula, between coordinates 270 30'and 280 02'N, and 820 20'and

820 50'W. The Y-shaped bay is approximately 60 km long, 15 km wide, covering

approximately 1,000 km2, and having a shoreline 1450 km long (Lewis and Whitman, 1985).

It is a highly complex system composed of numerous basins and subdivisions (Figure 2.1).

Some of them (e.g. Hillsborough Bay) are bordered by highly industrialized and urbanized

areas and others are bordered by mangroves, bayous, and seagrasses (e.g. Boca Ciega Bay).

Table 2.1 shows the morphometric features of each subdivision (Lewis and Whitman, 1985).

Major anthropogenic modifications that have altered the natural evolution of the system are

the four causeways (Sunshine Skyway Bridge, Courtney-Campbell Parkway, W. Howard

Frankland Bridge, and Gandy Bridge), an extensive network of dredged channels, turning

basins, and spoil islands.




















Mobbly


- 2D00'


City of
St. Petersburg


P9 ^?S LII Maote Rver
Cockroach &OaLI ~l --
Bay Subdivisions of Tampa Bay
( ---- Demarcation Line)
1. Old Tampa Bay
as 2. Hillsborough Bay
r3. Middle Tampa Bay
4. Lower Tampa Bay
5. Boca Clega Bay
6. Terra Cela Bay
S77. Manatee River
8. Anna Maria Sound

SManatee Re


Bradenton


- Tampa Bay Estuarine System subdivisions as defined by Lewis and Whitman
(1985) (from Wolfe and Drew, 1990).


S30
UZ 0U


Hillborough Rver


%0





a










- 2f 30'


Figure 2.1









11

Table 2.1 Area of the subdivisions in Tampa Bay (Lewis and Whitman, 1985).
Subdivision Area (km2)

Old Tampa Bay 201

Hillsborough Bay 105

Middle Tampa Bay 310

Lower Tampa Bay 247
Boca Ciega Bay 93

Terra Ceia Bay 21

Manatee River 55

Total 1032



Climate



The Tampa Bay Estuarine System is located in a zone of transition between a

temperate continental climate and a tropical Caribbean one (Lewis and Estevez, 1988). The

climate of the Tampa Bay area generally consists of a warm humid summer and a relatively

dry cool winter. Lewis and Estevez (1988) suggested three weather regimes for the Bay: the

warm, dry period between late April to mid-June, the warm, wet period during summer and

early fall, and the dry cold period between November to April. Based on four decades of

records, the mean annually averaged temperature in Tampa Bay is 22.3 C, with a low mean

of 16.0 Cin January and a high mean of 27.8 C in August (Lewis and Estevez, 1988).

Annual variation in water temperature ranges from 16 to 30 oC, with a vertical stratification

of no more than 2 C(Boler, 1992).









12

Tides



Tides and currents in the Gulf of Mexico are classified as mixed type, with K,, O1,

and P, the major diurnal and M2 and S2 the major semi-diurnal components. The strong

diurnal components are attributed to the interaction between co-oscillating tides propagating

from the Florida Straits and Yucatan Channel and the natural frequency of the Gulf of

Mexico basin. The average tidal range is 0.67 m, while typical current speeds range from

1.2 to 1.8 m/s at the entrance (Egmont Channel), to much smaller values in the upper reaches

of the Bay (NOAA, 1993). The tidal wave takes approximately three hours to travel from

the mouth to the upper reaches of Hillsborough Bay, and approximately 4 hours to upper Old

Tampa Bay. Harmonic analysis of year-long tidal records at St. Petersburg (NOAA, 1993)

yielded amplitudes of 37 constituents, which indicated that the shallow water components

are relatively small, and overtides are not significant in the overall circulation pattern of the

Bay.


Salinity Distribution



As in any other typical estuarine system, Tampa Bay generally exhibits significant

horizontal gradients in salinity. The higher salinity values in the adjacent Gulf of Mexico

fluctuate around 36 ppt, whereas the lowest salinity levels occur near the mouth of creeks and

rivers. Generally, the salinity distribution follows the annual precipitation pattern (Boler,

1992). Higher salinity tends to extend further up into the Bay during the dry winter and









13

spring, and the entire Bay becomes less saline, specially in the upper parts, during the wet

summer and fall. Vertically, salinity generally shows a homogeneous profile, with vertical

difference rarely exceeding 2 ppt.


Rainfall



Mean annual precipitation is approximately 140 cm (Heath and Connover, 1981),

which on an annual basis balances with evapotranspiration (Palmer, 1978). Dry season rains

vary from 5 to 6.5 cm per month. Wet season rainfall is much more variable, both

temporally and spatially, ranging from 13 to over 20 cm (Palmer, 1978). Figure 2.2

illustrates the monthly rainfall pattern for Tampa Bay.


Wind



The annual average wind speed is 3.9 m/s from the east. The four seasonal wind-field

patterns are shown in Figure 2.3. In the winter months, the easterly trade winds dominate

the region south of latitude 270 N, while the westerlies dominate the area north of latitude 29

N. Spring and Summer generally exhibit more southerly winds, and Fall is characterized by

easterly or northeasterly winds. Wind speed can exceed 10 m/s during the passage of winter

storms or during summer squalls, hurricanes and tornadoes (Wolfe and Drew, 1990).























Historical Monthly Rainfall in Tampa Bay


30



20 --


I

I\ I
I\ /

I \i




\I


/


--A-.--.. Minimun
- Average
---'-- Maximum










<^C-.


01 A A A A I I I I ,, A
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec


Figure 2.2 Monthly rainfall in Tampa Bay (Wooten, 1985).


E


r
















































Figure 2.3 Seasonal wind pattern in Florida (Echternacht, 1975).












Bathymetry



Tampa Bay is a relatively wide and shallow estuarine system, with an average depth

of 3.7 m (Goodwin, 1987). Depth generally does not exceed 10 m, except along the 96-km-

long navigational channel, which has been dredged to about 15 m. The navigational channel

extends parallel to the shorelines from the mouth to the upper reaches of Middle Tampa Bay,

where it splits into two branches, one connecting to the Port of Tampa in Old Tampa Bay,

and the other one entering Hillsborough Bay.


Freshwater Inflow



Unlike other well-studied estuarine systems in the U.S. (e.g. Chesapeake Bay,

Delaware Bay, etc.), Tampa Bay is not associated with any large river. All tributaries

flowing into Tampa Bay originate in the Florida peninsula, and therefore are relatively small

(Figure 2.4). The Bay receives drainage from a watershed that covers approximately 5700

km2, which delivers an average annual discharge of about 63 m 3/s (Lewis and Estevez,

1988). The analysis of existing and historical freshwater inflows to Tampa Bay (Coastal,

1994) demonstrated that inflows have not changed significantly in the past fifty years.

Table 2.2 shows the historical average discharge values for seven rivers or streams

flowing into Tampa Bay. The primary source of freshwater are the four major tributaries

(Hillsborough River, Alafia River, Little Manatee River, and Manatee River) which supply

about 70% of the total discharge. It has been estimated that Hillsborough Bay receives 63

to 77% of the total freshwater inflow to Tampa Bay (Lewis and Estevez, 1988).
























0
SO


Figure 2.4 Tampa Bay watershed (Wolfe and Drew, 1990).









18

Table 2.2 Surface water discharges to Tampa Bay (Lewis and Estevez, 1985).
.r Period of Record Average annual
(years) discharge (m3/s)
Hillsborough River 39 17.0
Alafia River 45 14.0
Little Manatee River 38 6.0
Manatee River 11 11.0
Rocky Creek 24 1.3
Lake Tarpon Canal 3 0.8
Sweetwater Creek 26 0.6
Others 12.3
Total 63.0



Hillsborough River


Draining a highly urbanized area, the Hillsborough River watershed collects the

discharge from most of Tampa, Temple Terrace, the eastern Interbay Peninsula, and Davis

Island. A dam constructed in 1945 (approximately 16 km from the mouth of the river in

Hillsborough Bay) separates two distinct water quality and hydrological environments:

upstream of the dam, the river is a freshwater reservoir, which provides freshwater to the

City of Tampa; and downstream of the river proper, which is tidal and brackish. Freshwater

discharges are controlled by the dam and range from 3.5 m 3/s in the dry season to 48 m /s

during the wet season, averaging 17 m 3/s (Dooris and Dooris, 1985). Tidal action can be

found at 16 km upstream the mouth (Wolfe and Drew, 1990). The salt wedge can penetrate

as far as 13 km into the river during low-flow conditions (< 3 m3/s), or it can be flushed

downstream to near 4 km from the mouth when the flow exceeds 25 m 3/s (Wolfe and Drew,









19

1990). Low flow rates and upstream salt wedge location seem to be well correlated with low

dissolved oxygen (DO) value and high nutrient concentrations inside the Hillsborough River.

A report from the Hillsborough County Environmental Protection Commission (EPC) (Boler,

1992) shows DO levels in the bottom saltier layer inside Hillsborough River below 4.0 mg/L,

with lowest values (< 2.0 mg/L) in May and June when flow is minimal. Surface values of

DO are generally above saturation (7.9 mg/L). BOD is reported to be less than 2.0 mg/L

throughout the year.

Ammonia and nitrate concentrations generally show a well mixed vertical distribution

upstream the salt wedge location, where the saltier water contains higher concentrations,

specially ammonia. Combined ammonia and nitrate values in the river range from 0 to 0.7

mg/L. In the dry season ammonia concentrations vary from 0.05 mg/L close to the dam to

0.2-0.3 mg/L towards the Bay. Nitrate concentrations vary from zero to 0.4 mg/L, and

organic nitrogen ranges from 0.38 to 5.60 mg/L (Wolfe and Drew, 1990).

Alafia River


The Alafia River watershed drains about 105 km2, south of the Hillsborough River

watershed. Flow in the Alafia River averages 14 m 3/s and ranges from 5.4 m 3/s in the dry

season to 28.3 m3/s during the wet season (Dooris and Dooris, 1985). Tidal action is

present up to 18 km upstream from the mouth. Johansson and Squires (1989) found that the

Alafia River, a major source of dissolved material to the Bay, can supply 51% of the Bay's

phosphate uptake for phytoplankton growth, and sediment flux rates are sufficient to meet

140% of the uptake. The authors attributed the high phosphate concentrations to leaching









20

of Florida's phosphate beds, fertilizer drainage from agricultural lands, and industrial and

sewage inputs. Phosphate concentration ranges from 4.8 mg/L in the upper reaches of the

river, decreasing to 1.2 mg/L near the Bay (Wolfe and Drew, 1990).

The salt wedge penetration depends on the river discharge and tidal regime, ranging

from 16 km during high tide and low flow condition to 4 km during low tide high flow

situation (Giovanelli, 1981).

Dissolved oxygen exhibits a vertical stratification near the mouth, ranging from

below 4.0 mg/L at middle and bottom layers to saturation levels (7.9 mg/L) at the surface

(Boler, 1992), where chlorophyll-a averages 24.1 pg/L.

The Alafia River tributaries exhibit high levels of nutrients. The poor water quality

in the North Prong is due to mining activities, and a greater number of phosphate and

chemical dischargers (Wolf and Drew, 1990). High levels of ammonia can reach as much

as 85-120 mg/L, and nitrate values as high as 3.0 mg/L. Dissolved oxygen remains below

5 mg/L 50% of the time.

Little Manatee River


The Little Manatee watershed is the least urbanized of the four major rivers, and it

generally exhibits the best water quality conditions (Flannery, 1989). Flow averages 6 m3/s

and ranges from 1.7 m3/s in the dry season to 17 m3/s during the wet season (Dooris and

Dooris, 1985). Tidal action is found up to 25 km upstream the mouth (Wolfe and Drew,

1990). Salinity close to the mouth averages 9.0 to 12.0 ppt (EPC, 1984). Flannery (1989)

presented some water quality data for a station 25 km upstream from the mouth, which









21

showed the following average concentrations: 0.63 mg/L of nitrate+nitrite, 0.09 mg/L of

ammonia, 1.3 mg/L of BOD, 0.60 mg/L of organic nitrogen, and 7.0 mg/L of DO.

Manatee River


The Manatee River is impounded 38 km upstream from the Bay. Downstream of the

dam, the Manatee River and its major tributary, the Braden River, collect drainage from the

cities of Palmetto and Bradenton before discharge into the Bay. Flow averages 11 m 3/s and

ranges from 1 m 3/s in the dry season to 25 m3/s during the wet season (Dooris and Dooris,

1985). Tidal action is present up to 31 km upstream from the mouth. Nutrient levels are

high and generally decrease from the dam to the river mouth (Wolfe and Drew, 1990).

Salinity ranges from 14 to 26 ppt in the dry season to 2 to 19 ppt during the wet season (Heyl,

1982). Close to the mouth, dissolved oxygen levels are low during summer months, ranging

from 2.0 to 4.0 mg/L. Concentrations of total nitrogen, mostly in the organic nitrogen form,

varies between 0.1 to 4.4 mg/L (Heyl, 1982).

Rocky Creek


The Rocky Creek drainage area is approximately 115 km2. The discharge 9.5 km

upstream from the river mouth averages 1.3m3/s, ranging from 6.9 (wet season) to

0.05 m 3/s (dry season) (USGS, 1991). In its upper reaches, water quality is generally good

with pockets of high concentrations of ammonia and total phosphorus (Wolfe and Drew,

1990). Dissolved oxygen is usually below saturation.











Lake Tarpon Canal


The Lake Tarpon Canal is a man-made canal which was completed in 1971 to control

flooding. A saltwater-barrier/flood-control structure is located midway between Lake Tarpon

and Old Tampa Bay. Discharges from the canal average 0.8 m 3/s, ranging from 22m3/s

in wet season to no flow in dry season (USGS, 1991). DO levels are usually high (7.0 to 8.0

mg/L) in the canal, pH is neutral (7.0), and nutrient concentrations are low (Dooris and

Dooris, 1985).

Sweetwater Creek


Sweetwater Creek is 17 km long and drains about 65 km2 of a primarily urban region.

The discharge at 6 km upstream from the river mouth averages 0.6m3/s, with a range

between 4.4 (wet season) to 0.03m3/s (dry season) (USGS, 1991). In the tidal portion of the

creek, DO (3.7 mg/L), BOD (6.0 mg/L), and nutrient concentrations (Ammonia

concentration ranging from 0.1 to 0.4 mg/L) indicate poor water quality (Wolfe and Drew,

1990).

Non-Point Sources


Coastal, Inc. (1994) developed a statistical model for the Tampa Bay National

Estuary Program (TBNEP) to support the preparation of the "Pollutant Load Reduction

Goals" (PLRG) for total nitrogen, total phosphorus, and total suspended solids for Tampa

Bay. They used measured data to develop regression relationships to describe the response

of the watershed to flow and loadings from non-point surface water sources, given a set of









23

rainfall and land use conditions. Results of that study indicate that non-point sources can

have a significant contribution to the total nutrient loading. Moreover, the study showed that

groundwater and nutrient inflow to Tampa Bay represent a smaller fraction of the total

loading. Table 2.3 summarizes the water quality of the seven point sources discharging into

Tampa Bay.



Table 2.3 1991 annual average water quality of seven point sources discharging into Tampa
Bay (Boler, 1992) and (USGS, 1991) (mg/L).
Near-Bottom Soluble Nitrate
Ammonium
River Dissolved Organic rogen +
Nitrogen
Oxygen Nitrogen Nitrite

Hillsborough River 5.0 0.66 0.07 0.04
Alafia River 4.3 0.68 0.06 0.36
Little Manatee River 5.3 0.75 0.05 0.11
Manatee River 7.1 0.52 0.01 0.08
Rocky Creek 3.0 0.93 0.07 0.02
Lake Tarpon Canal 4.4 0.89 0.10 0.04
Sweetwater Creek 4.7 0.85 0.14 0.35






Nutrients Distribution and Loading



Tampa Bay has high phosphate levels in both water column and sediment layer,

especially in Hillsborough Bay. Tiffany and Wilkinson (1989) reported that 20% of world's

phosphate production and 80% of all United States phosphate output take place in the area.

Approximately 50% of all tonnage leaving Tampa Bay is composed of phosphate related









24

products. The mean annual water column phosphate concentration in Hillsborough Bay can

be as high as 1.28 mg/L (Fanning and Bell, 1985).

Nitrogen, however, is probably the single most important macro nutrient that limits

primary production in Tampa Bay. Assuming that phytoplankton assimilates N and P in

proportion to the Redfield C:N:P atomic ratios of 106:16:1, if N:P is higher than 16, the

system is primarily phosphorus limited. Otherwise, the system is considered to be nitrogen

limited. Fanning and Bell (1985) reported that the N:P ratio in Tampa Bay ranged from 0.3

to 1.3 in 1981, and concluded that phytoplankton have been historically nitrogen limited.

According to Simon (1974), municipal sewage treatment plants are the primary

source of nitrogen to Tampa Bay. The Alafia River provides the highest annual loading of

nitrate to Tampa Bay (about 3.9 x 105 kg/yr), followed by the Manatee and Hillsborough

Rivers (each about 9.0x104 kg/yr). In terms of organic nitrogen, the Manatee and Alafia

Rivers have the highest loadings ( 2.5 x 105 kg/yr), followed by the Hillsborough River

with 2.0 x 105 kg/yr (Dooris and Dooris, 1985). High levels of organic nitrogen in the

Manatee River have been related to the Bradenton sewage treatment plant and pulp effluent

from citrus processing plant (DeGrove, 1984). McClelland (1984) reported municipal

sewage treatment plants elsewhere around the Bay as significant nitrogen sources. Goetz and

Goodwin (1980), summarizing data collected between 1972 to 1976, obtained a mean

organic nitrogen concentration ranging from 0.5-1.0 mg/L in Old Tampa Bay, around 0.5

mg/L in upper Tampa Bay, and the same level or below in the Lower Bay. In all three areas,

seasonal and year-to-year variation was low. On the other hand, mean organic nitrogen

concentration in Hillsborough Bay ranged from 0.75 to 1.25 mg/L, and temporal variation









25

was greater. Nitrite and nitrate concentrations were similarly low and steady everywhere in

the Bay, except in Hillsborough Bay. Ammonia levels were variable in all zones. Seasonal

minima were less than 0.1 mg/L in most places but more than 0.1 mg/L in Hillsborough Bay.

Fanning and Bell (1985) reported a mean ratio of ammonia to inorganic nitrogen of 0.84

(ranging from 0.54 to 0.99) in Hillsborough Bay. Seasonality was evident for total inorganic

nitrogen, which decreases substantially after rainy seasons, without an apparent reason

(Lewis and Estevez, 1988).

In a preliminary nitrogen budget for Tampa Bay, Ross et al. (1984) suggested a

nitrogen storage of 3.87 x 107kg, an input from rainfall and anthropogenic sources of

21,470 kg/day, and a benthic release of 55,750 kg/day. Exports would occur in tidal

exchange (16,100 kg/day), biological losses (8,140 kg/day), and benthic uptake (53,000

kg/day). Fanning and Bell (1985) estimated a turnover rate for nitrate and nitrite of 42 days,

due to runoff, and that benthic releases of ammonia could replace the overlying ammonia in

14 days.

Coastal, Inc. (1994) developed estimates of total nitrogen, total phosphorus, and total

suspended solids loading, as well as total freshwater inflow, to Tampa Bay. Two scenarios

(existing and "benchmark" conditions) were presented for the major seven segments of the

Bay. In order to account for ungaged areas, the Coastal, Inc. study used a statistical model

that related watershed characteristics to streamflow. Table 2.4 summarizes the mean annual

total nitrogen loading into each segment of Tampa Bay.









26

Table 2.4 Mean annual total nitrogen loading into each segment of Tampa Bay (Coastal,
1994).
Bay Segment Loading (tons/year)
Old Tampa Bay 600

Hillsborough Bay 2100

Middle Tampa Bay 1100

Lower Tampa Bay 500

Boca Ciega Bay 300

Terra Ceia Bay 80

Manatee River 600





Sediment Type and Distribution



Goodell and Gorsline (1961) studied the surface sediments composition and

distribution from all major areas of the Bay. They reported that Tampa Bay sediments are a

mixture of eroded quartz sands from Pleistocene terrace deposits and carbonates from shell

fragments produced within the system. The present sediment distribution is related to tide

generated currents, while sedimentary types correspond with bathymetric features. In sand

and grass flats less than 2 m deep, mean grain size was determined as 0.132 mm and

sediment was 2.7% carbonate. In deeper natural channels (> 6 m), mean grain size was 0.241

mm and sediment was 25.2% carbonate, whereas mangrove areas contained no carbonate.

Mean grain size decreased from 0.218 mm at the mouth to 0.109 mm at the upper reaches

of the Bay. Mean carbonate content decreased from 16% to 2% over the same distance.









27

Figure 2.5 shows the surface sediment distribution for Tampa Bay. According to Johansson

and Squires (1989), the descriptive work of Goodell and Gorsline (1961), conducted thirty

five years ago, did not intend to map fine grained sediments specifically, so the areal

coverage of these sediments was not well defined as the mud zone delineated in later studies.

Figure 2.6 shows the mud zones in Hillsborough Bay delineated by the Bay Study Group of

the City of Tampa Sanitary Sewer Department in 1986.

















- 28oo00 City of
Tampa






Pinellas inter- NaR Rier
Peninsula Bay
Peninsula


City of
St. Petersburg








O




0 0



Maatge Rier






[ Very coarse-coarse sand Fine sand Silt
Medium sand Very fire sand
Figure 2.5 Surface Sediments in Tampa Bay (Goodell and Gorsline, 1961).
















































Figure 2.6 Mud zone in Hillsborough Bay (Johansson and Squires, 1989).















CHAPTER 3
THE CIRCULATION AND TRANSPORT MODEL



Previous Work



Circulation and sediment transport models for estuaries have been significantly

advanced during the past 30 years. Sheng (1994) provided a comprehensive review on

circulation models for shallow waters. Sheng (1986) and Sheng et al. (1991) presented

comprehensive reviews of sediment transport models for estuaries and lakes.

Circulation in Tampa Bay has previously been modeled by Ross et al. (1984),

Goodwin (1987), Galperin et al. (1991), Sheng and Peene (1992), Peene et al. (1992), and

Hess (1994). The Ross et al. (1984) modeling system consisted of an integrated set of a 2-D

vertically-averaged circulation model, and box models for water quality and particulate

transport. Goodwin (1987) used a 2-D vertically-averaged model to study the effects of the

dredged navigation channel and dredged disposal sites on the circulation of Tampa Bay. The

residual circulation obtained from both studies (Ross et al., 1984 and Goodwin, 1987)

showed a complex pattern of numerous gyres, that were assumed to be responsible for poor

flushing conditions. Galperin et al. (1991) demonstrated that the barotropic residual

circulation pattern, obtained by Ross et al. (1984) and Goodwin (1987) in Tampa Bay, can

be completely overwhelmed by baroclinic effects. The baroclinic residual circulation









32

obtained by Galperin et al. (1991) exhibited a classical two-layer flow, with the surface layer

flowing out of the Bay and the saltier bottom layer flowing into the Bay. Sheng and Peene

(1992), studying the circulation and transport in Sarasota Bay, used a coarse grid (grid

spacing on the order of 1 to 2 km) to describe the circulation in Tampa Bay. Tampa Bay was

added to the Sarasota Bay grid of that study to evaluate the importance of Manatee River

discharge on the residual circulation of Anna Maria Sound. Peene et al. (1992) simulated

the tide- and wind-driven circulation in the Sarasota and Tampa Bay system during the

passage of Tropical Storm Marco in October 1990 using an earlier version of the three-

dimensional boundary-fitted grid model used in this study. Hess (1994) developed a three-

dimensional orthogonal curvilinear model with seven sigma grid layers for Tampa Bay,

based on the Princeton University ocean model (Blumberg and Mellor, 1987). The main

goals of Hess (1994) were to update the NOAA tidal current atlas for Tampa Bay, and to

synthesize the extensive observational data set obtained during the survey performed by

NOAA in 1990-91.

The three-dimensional hydrodynamics model CH3D (Sheng, 1989) forms the basis

of the numerical simulations in this study. The model framework has been improved and

modified from earlier versions (e.g., Sheng, 1989; Sheng et al., 1991; Sheng and Peene,

1992) in order to develop an integrated model that couples hydrodynamics, sediment and

water quality dynamics. The application (model setup, calibration, and validation) of the

circulation and transport model to produce a detailed characterization of the hydrodynamics

within system constituted the most important step in the development of the integrated model

of the Tampa Bay Estuarine System. Within the scope of this dissertation, the complete









33

details of model equations in the curvilinear boundary-fitted and sigma coordinates are of

secondary interest, and are therefore presented in Appendix A.


Circulation Model



The governing equations that describe the velocity and surface elevation fields in

shallow water are derived from the Navier-Stokes equations. In general, four simplifying

approximations are applied. First, it is assumed that the water is incompressible, which

results in a simplified continuity equation. Second, based on the fact that the characteristic

vertical length scale is much smaller than the horizontal counterpart, i.e., H/L << 1, the

vertical velocity is small and the vertical acceleration may be neglected. Hence, the vertical

momentum equation is reduced to the hydrostatic pressure relation. Third, with the

Boussinesq approximation, an average density can be used in the equations except in the

buoyancy term. Finally, the eddy-viscosity concept, which assumes that the turbulent

Reynolds stresses are the product of mean velocity gradients and "eddy viscosities", is

employed. In the transport equation, this concept means that the turbulent mass fluxes are

the product of mean concentration gradients and "eddy diffusivities".

With the above assumptions, the basic equations of motion in a right-handed

Cartesian coordinate system (x, y, z) are as follows:

Continuity Equation


au av aw
+- + = (3.1)
ax ay az











X-component of Momentum Equation


au + uu uv + uw 1 ap A u
-+- + -+ -- = fv +- A
at ax ay az p, ax ax ax
(3.2)
+ AH + A u
ay ( ay z az)


Y-component of Momentum Equation


av + uv + avv vw f 1 p +a AH v
-+- + -+-= -fu +- AH
at ax 9y az p, ay ax ax
(3.3)
a av ( av
+ ( AH (+ A
ay ay 9z 9z


Hydrostatic Pressure Relation


9p
ap pg (3.4)
az

where (u, v, w) are mean fluid velocities in the (x, y, z) directions, p is pressure, g is the

Earth's gravitational acceleration, po is a reference fluid density, p(x,y,z) is the fluid density,

and f is the Coriolis parameter. AH and A, are the horizontal and vertical turbulent eddy

viscosity coefficients, respectively.











Salinity Equation


In Cartesian coordinates, the conservation of salt can be written as:

as a(us) + a(vs) a(wS)
at ax ay az
(3.5)
a as a as a v as) (3
ax i ax) ay ay) az( Va


where S is the salinity, DH and D, are the horizontal and vertical turbulent eddy diffusivity

coefficients, respectively.

Since the length scales of horizontal motion in estuarine systems are much greater

than those of vertical motion, it is common to treat the vertical turbulence and horizontal

turbulence separately. It has been shown (e.g. Sheng et al., 1995) that in shallow estuaries,

the effect of the horizontal eddy viscosities on circulation is much smaller than the effect of

the vertical one. In the model, the horizontal turbulent mixing, which describes the effect

of sub-grid scale motion, is represented by a constant diffusion coefficient.

Vertical turbulent mixing is an important process which can significantly affect the

circulation and transport in an estuary. Since turbulence is a property of the flow instead of

the fluid, it is essential to use a robust turbulence model to parameterize the vertical turbulent

mixing. In this study, the vertical eddy coefficients (Av and Dv ) are computed from a

simplified second-order closure model developed by Sheng and Chiu (1986) and Sheng and

Villaret (1989).











Equation of State



P = p (T,S) (3.6)

where p is density, T is temperature.

Various forms of the equation of state can be used. In the present model, the equation

given by Eckert (1958) is used:

p = P/(a + 0.698P)

P = 5890 + 38T 0.375T2 + 3S (3.7)

a = 1779.5 + 11.25T 0.0745T2 (3.8 + 0.10T)S

where T is in C, S is in ppt and p is in g/cm3.

Conservative Species Equation


Flushing and residence time studies in an estuarine system can be carried out by

solving the conservation equation for a conservative species, cs:

ac + (uc,) (vc ) a (wc,)
at ax ay az
(3.8)

ax ax ay' Hay) az[ az )


First, the estuarine system needs to be divided into segments with similar circulation

characteristics. To study the tidal flushing, a uniform concentration is released into all the

cells of a specific segment, while the concentration in the other ones are given zero values.

As the simulation proceeds, the remaining mass of the conservative species in each segment









37

is calculated as a fraction of the original mass. The flushing capacity of each segment is then

defined in terms of the reduction in the relative mass (Sheng et al., 1996).


Sediment Transport Model



An integrated model of the Tampa Bay Estuarine System must contain a sediment

transport model that can be used to address environmental problems related to dredging

operations in the navigation channels, and especially, the ecological problems related to the

adsorptive capacity of fine sediments to carry particulate forms of nutrients, heavy metals,

PCB's, and other organic pollutants.

The suspended sediment model includes the advection-diffusion processes, which

are computed by the hydrodynamics model, as well as such processes as erosion, deposition,

flocculation, settling, consolidation, and entrainment (Sheng, 1986; Mehta, 1986).

The governing equation that represents the transport of suspended sediments is given

by:


c uc+ avc + a(w-w)c
at ax ay az
(3.9)
a a Dac a H ac
ax ax) ay9 ay) az z )


where c is the suspended sediment concentration, w, is the settling velocity of suspended

sediment particles (positive downward), DH is the horizontal turbulent eddy diffusivity, and Dv

is the vertical turbulent eddy diffusivity.









38

Three simplifying approximations are implied in Equation (3.9). First, the concept

of eddy diffusivity is valid for the turbulent mixing of suspended sediments. Second, the

suspended sediment dynamics are represented by the concentration of a single particle size

group, assuming a homogeneous distribution of sediment particles size. Third, the

suspended sediment concentration is sufficiently low ( 1000 mg/L) such that non-

Newtonian behavior can be neglected.

In this study, the determination of settling, flocculation, deposition, erosion,

fluidization, and consolidation processes is based on the previous work of Sheng and Lick

(1979), Sheng(1986), Hwang and Mehta (1989), Sheng et al. (1991), and Chen and

Sheng(1994), and is described in Appendix B.


Model Equations in Curvilinear Boundary-Fitted and Sigma Grid



In three-dimensional modeling, complex bottom topographies can be better

represented with the application of a-stretching (Sheng, 1983), since it is possible to obtain

the same vertical resolution for the shallow coastal areas and the deeper navigation channels.

The vertical coordinate z is transformed into a new coordinate a by (Phillips, 1957):

z ((x,y,t)
a = (3.10)
h(x,y) + (x,y,t)

where is the surface elevation, and h is the mean water depth.

With this transformation, the numerical grid in the computational plane becomes

constant in space and time. However, in the physical plane, since the water surface is

constantly changing in time due to dynamic forcing conditions, the sigma grid is time









39

dependent. A a-grid formulation is suitable for simulating flow and salinity transport in

regions of gradual bathymetric variations and gives a more accurate estimation of bottom

stress than a z-grid model, which resolves the depth with "stair-step" grids. Nevertheless,

recent studies (Sheng et al., 1989a; Haney, 1991) showed that a a-grid model is accurate only

when there are sufficient grid points across regions of sharp bathymetric gradients. In the

case of insufficient grid points, Sheng et al. (1989a) suggested a direct evaluation of the

horizontal density gradient terms along constant z-plane, and avoiding higher-order advective

schemes along the sharp bathymetric variation, to reduce numerical error.

Using non-orthogonal boundary-fitted horizontal grid, it is possible to better represent

the circulation and transport processes in estuarine systems with complex geometries.

Thompson (1983) developed a method to generate 2-D boundary-fitted grids in complex

domain by solving a set of elliptic equations. These equations relate the generally non-

orthogonal curvilinear coordinates in the physical plane x and y with the uniformly-spaced

coordinates in the transformed plane, and il.

The spatial coordinates in the physical plane, (x, y, z), have dimensions of length,

while the coordinate system in the computational plane, ( Cr,, a), is dimensionless. In this

new coordinate system ( et, a), the velocity vector are expressed in terms of contravariant

components, with dimension of [t'] (Sheng, 1989). The equations of motion in the ( 77, a)

coordinates are shown in Appendix A.









40

Boundary and Initial Conditions



In order to numerically solve the set of equations presented, boundary conditions are

required for the dependent variables.

Vertical Boundary Conditions


The boundary conditions for Equations (3.1), (3.2), (3.3), (3.5), and (3.9) at the free

surface ( a = 0) are:

P, Av u v' \

SS
0 (3.11)


+=0
a c

az



At the free surface, wind velocity is converted to stress by:


(s s) Pa Cds. + (u+ V)2 V) (3.12)


where sx, and cy are the components of the wind stress, p. is the air density

(0.0012 g/cm3), uw and vw are the components of wind speed measured at some height

above the sea level. C,, the drag coefficient, is given as a function of the wind speed

measured at 10 meters above the water surface by (Garrat, 1977):

Cds = (0.075 + 0.067 W) 0.001 (3.13)


where Ws is the wind speed magnitude in m/s.









41

The vertical velocity is obtained from the kinematic boundary condition imposed at

the surface:


w + u + (3.14)
at ax ay



The boundary conditions for Equations (3.1), (3.2), (3.3), (3.5), and (3.9) at the

bottom

(a = -1) are:


p. Av a aV = (vbx 'by
az az ) 'by

= Cdb 2 V2 1/2 (U1,V
as (3.15)
a S
-0
ao

S(w + wc + D, = Vd c E


where vd is the deposition velocity, E is the rate of erosion, Av, and Dv are vertical turbulent

eddy coefficients. Cdb is the bottom friction coefficient, and u,, v, represent the velocity

components at the first grid point above the bottom. Taking z, as half of the bottom layer

thickness (which starts at the bottom roughness height, z,), Cdb, for a hydraulic rough flow,

is given by (Sheng, 1983):


2iI ZI 1-2
Cdb = K2 In (3.16)
zo


where Kis the von Karman constant.












Lateral Boundary Conditions


Along the shoreline where river inflow or outflow may occur, the conditions are

generally:


u = u(x,y,z,t)


v = v(x,y,z,t) (3.17)


w = 0

Along a solid boundary, the normal velocity component is zero. In addition, the

normal derivatives of salinity and suspended sediment concentration are assumed to be zero.

Along an open boundary, the surface elevation, ;, is given by either a time series of

measured data or specified through harmonic constituents using the following equation:


"max 2 r t
C = (x,y,t) = Ancos + d)n (3.18)
n=1 Tn


where An, T and (n are the amplitude, period, and phase angle of the astronomical tidal


constituents.

When open boundary conditions are given in terms of ;, the normal velocity

component is assumed to be of zero slope while the tangential velocity component may be

either zero, of zero slope, or computed from the momentum equations.

The salinity and suspended sediment concentration along an open boundary or river

entrance is computed from a 1-D advection equation during the outflow. During the inflow,

the concentration takes on a prescribed value.









43

Contravariant velocity components provide lateral boundary conditions similar to

those in the (x, y) system. Along solid boundaries, the normal velocity is zero. When flow

is specified at the open boundary, the normal velocity component is prescribed.

To initiate a simulation, the initial spatial distributions of C, u, v, S and c need to

be specified. When initial data are unknown, the simulation starts with zero initial fields.

When initial data are known at a limited number of locations, an initial field can be

interpolated. For salinity simulations, the "spin-up" time is longer and sufficient time should

be allowed in model simulations.


















CHAPTER 4
THE WATER QUALITY MODEL



Previous Work



Considerable effort has been expended in the past 20 years to develop water quality

models for freshwater and marine systems. In freshwater systems, Streeter and Phelps (1925)

were the first researchers to introduce a set of equations for predicting the biochemical

oxygen demand (BOD) and dissolved oxygen (DO) concentrations. Since then, simple zero-

and first-order exponential decay, dilution and sedimentation terms have been added to

predict other conservative and non-conservative species. Sheng (1994) provided a

comprehensive review on water quality models for shallow waters. Jorgensen et al. (1996)

provided the most recent review of environmental models developed in the last two decades.

Water quality models can be classified in terms of the approach undertaken for

solution and analysis. Steady-state models are usually simpler and require less computational

effort than dynamic models. On the other hand, multi-dimension, robust models can provide

more detailed and comprehensive information on the water quality. Stochastic models

require more data for calibration and validation than deterministic models. Water quality

parameters simulated by deterministic models are expressed in terms of expected values,

while simulations performed by stochastic models explicitly take into account the uncertainty









46

of physical and biogeochemical processes. Validation of stochastic models is particularly

difficult due to the quantity of observational data required to compare probability

distributions of variables rather than just their expected or mean values (Loucks, 1981).

Moreover, it is more meaningful, in terms of interpretation, to estimate biogeochemical

parameters like growth and nitrification rates than empirical parameters like autoregressive

and moving average coefficients (Solow, 1995).

Until recently, water quality models, originally developed for rivers and stream flows,

were indiscriminately used in estuarine systems. The assumption of steady or quasi-steady

state of the hydrodynamics processes justified the use of coarse grids, and models were either

uncoupled or loosely coupled with hydrodynamics models. However, even in freshwater

systems, there is increasing evidence that hydrodynamics processes have very significant

effects on water quality and ecological processes. Chen and Sheng (1994) found that the

internal loading of nutrients from bottom sediments in Lake Okeechobee could not be

accurately calculated by a water quality model using a large time step of 6 hours. During one

time step, the internal loading of nutrients from bottom sediments calculated by a

conventional water quality model may be zero, because of the zero average net flux from the

bottom sediments in this 6-hour period. In reality, the resuspension and deposition processes

can significantly affect internal loading through sorption/desorption processes. Model

simulations which include such effects produced results that agree well with field data

(Sheng et al., 1993). The water quality model developed by Chen and Sheng (1994) forms

the basis of the water quality model of the present study, although their model did not include

the dissolved oxygen balance and was limited to rectangular grid system.









47

In estuarine systems, the necessity to accurately represent hydrodynamics and

biogeochemical processes is even more relevant. Estuarine systems are physically dominated

ecosystems, where the action of the sun, tides, wind, atmospheric disturbances, river

discharges, and complex geomorphometric features interact. It is the balance of these

physical forces acting as subsidies and stresses that will dictate the water quality dynamics

of each estuarine system.

In traditional water quality box models like WASP (Ambrose et al., 1994), salinity

data is used to obtain the so-called dispersivee coefficients" during model calibration. This

salinity calibration consists of first averaging the flows over the calibration period and then

estimating tidal dispersion coefficients, assuming steady-state conditions (AScI, 1996). In

an estuarine environment, this approach is questionable since salinity is an active species.

Its concentration and gradients affect the temporal and spatial distribution of the density

field, driving baroclinic forces that completely change the hydrodynamic characteristics of

the flow.

AScI (1996) has applied WASP4 in Tampa Bay aiming at the development of a

"broad-based, management-oriented model". The primary objective of the AScI study is to

provide the Southwest Florida Water Management District (SWFWMD) with a modeling

tool to define eutrophication management strategies. The rationale of this approach was that

the hydrodynamic and water quality data gathered in Tampa Bay, from 1985 to 1991, was

sufficient for the determination of the dispersive and the other "ad-hoc" coefficients of the

model. In addition to the 28 model coefficients, sediment oxygen demand and benthic fluxes

were also determined for specific Bay segments during the calibration process. Another


I









48

limitation of the AScI study is the time scale (time step of one month), which prevents the

model from capturing episodic events. Schoellhammer (1993) showed that resuspension in

Old Tampa Bay is closely related to storm systems and local wind-generated waves. Sheng

et al. (1993) showed that the contribution of resuspension flux to the internal loading during

episodic events can be orders of magnitude greater than the normal diffusive benthic flux.

Coastal, Inc. (1995) developed a statistical model to investigate the relationships

among nutrient loading, water quality parameters (chlorophyll-a), and light attenuation

coefficients. Like the AScI (1996) study, the rationale supporting this simple approach was

the large amount of data gathered between 1985 and 1991. It was thought that if the

available water quality data were sufficient to calibrate and validate this empirically-based

model, it would serve as a management tool to determine external nitrogen loadings

consistent with seagrass light requirements. Using regression analysis, Coastal, Inc.

determined the relationships between total nitrogen loading, chlorophyll-a, turbidity and light

attenuation coefficients in the four major Bay segments (Old Tampa Bay, Hillsborough Bay,

Middle Tampa Bay, and Lower Tampa Bay). The conclusions of the Coastal, Inc. study was

that no reduction in annual average nitrogen loading and chlorophyll a concentration would

be required for the 20% near-bottom light level target for the four major Bay segments.

However, a substantial reduction in nitrogen loads would be required in order to achieve the

25% light level target.

The limitations of the Coastal, Inc. study are related to the fact that the simplifying

assumptions applied (linear correlation between cause and effect) proved deficient to explain

any correlation between external loading and nitrogen and chlorophyll-a concentrations


I









49

inside the Bay (Coastal, 1995). This limitation suggests that the internal loading has a

significant role in the nutrient budget, and consequently should be considered in the

strategies to control the eutrophication process. Furthermore, another uncertainty of the

Coastal analysis was originated from their conclusion that a three month cumulative lag

period for nitrogen loads could explain the variation in the chlorophyll-a data. Johansson

(1991), using a similar statistical approach presented evidences for a three-year lag between

external nitrogen loading and chlorophyll-a response. Again, different rates of internal

nitrogen loading may explained the lag difference between Coastal, Inc. (1995) and

Johansson (1991) studies.

These previous modeling efforts on Tampa Bay provided useful foundation for this

more comprehensive modeling study. Despite their simplified approach, these studies were

able to isolate relevant processes and determine some specific model coefficients. At the end

of this chapter, Table 4.2 presents the model coefficients used in this study, the range of each

coefficient found in the literature, and the values used by AScI (1996). In order to account

for both point and non-point sources of nitrogen loading into the Bay, the water quality

species concentration along model boundaries were determined from the nutrient loadings

presented by Coastal, Inc. (1994). Total nitrogen loadings were converted to concentrations

and used along with river discharges.

The water quality component of this integrated model for Tampa Bay focuses on the

interactions between oxygen balance, nutrient dynamics, light attenuation, phytoplankton and

zooplankton dynamics. To develop the water quality model, the mass conservation principle

can be applied to each water quality parameter related to the phytoplankton and zooplankton


I









50

dynamics, phosphorus cycle, nitrogen cycle, and oxygen balance. With regard to nutrients,

the nitrogen cycle is more important than the phosphorus cycle since nitrogen has been the

macro-nutrient limiting phytoplankton growth in Tampa Bay (FWCA,1969; Lewis and

Estevez, 1988; Johansson, 1991; Coastal, 1995; AScI, 1996). Hence phosphorus cycle is not

included as part of the water quality model for Tampa Bay.


Development of the Numerical Model



The nitrogen cycle in Tampa Bay is modeled through a series of first-order kinetics,

which start with the biogeochemical process controlling nitrogen fixation. Phytoplankton

growth controls ammonia and nitrate uptake. The uptake rate for each species is proportional

to its concentration relative to the total inorganic nitrogen content, and a preferential factor

for ammonia uptake. Nitrogen returns from the planktonic biomass pool as dissolved and

particulate organic nitrogen and as dissolved inorganic nitrogen through endogenous

respiration and non-predatory mortality. Organic nitrogen is converted to ammonia

mineralizationn) at a temperature-dependent rate, and ammonia is then converted to nitrate

(nitrification) in a temperature and oxygen-dependent rate. The stability of the dissolved

form of ammonium in water is pH dependent. It can exist in its ionic form, ammonium

(NH1,) or as ammonia (NH3), with the latter being lost from the system through

volatilization. Low levels of dissolved oxygen may induce a bacterial-mediated

transformation of nitrate into nitrogen gas (denitrification) at a temperature-dependent rate.









51

The oxygen balance couples dissolved oxygen to the other state variables. Reaeration

through the atmosphere-water interface, and phytoplankton production during photosynthesis

are the main sources for oxygen. Oxidation of organic matter and carbonaceous material,

respiration by zoo and phytoplankton, and oxygen consumption during the nitrification

process are collectively grouped into the CBOD (carbonaceous-biochemical oxygen demand)

variable, which is a sink for dissolved oxygen (Ambrose et al., 1994).

The light penetration inside water can be determined through measurements of

turbidity, color, and light penetration (Kirk, 1994). In the integrated model for Tampa Bay,

the primary concern is the availability of photosynthetically active radiation (PAR), which

is influenced by the intensity of incident solar radiation, solar elevation angle, weather

conditions, water depth, tidal range, concentrations of sediments, detritus and phytoplankton

(Miller and McPherson, 1995).

Phytoplankton kinetics is the central part of this water quality model, since the

primary water quality issue in the Tampa Bay Estuarine System is eutrophication (Boler et

al., 1991). Phytoplankton population is a complex variable to obtain in the field. For single

species, a direct measurement of the population size is the number of cells per unit of

volume. However, in natural multi-species environment, it is difficult to distinguish viable

and non-viable cells and, for species that tend to colonize, counting requires an extra effort

to separate individual cells because the size of the colonies are quite variable (Ambrose et

al., 1994). An alternate solution is to measure phytoplankton population through chlorophyll

analysis, although this is not an absolute indicator of planktonic biomass. Some species do

not contain chlorophyll and when chloroplasts (chlorophyll-containing structures found in









52

algal and green plant cells) are present, they vary in number, size and pigment content per

cell (Boler et al., 1991). The conversion to phytoplankton dry weight or carbon involves

further species-dependent constants that depend on nutrient and light levels.

The rationale behind this water quality modeling effort is that planktonic organisms

have a fast response to environmental conditions. In other words, by combining chlorophyll

with nutrient levels, dissolved oxygen balance, and light attenuation, it is possible to evaluate

and quantify short and long term water quality processes such as hypoxia and eutrophication.


Mathematical Formulation



In this study, the water quality equations are derived from an Eulerian approach,

using a control volume formulation. In this method, the time rate of change of the

concentration of any substance within this control volume is the net result of (i)

concentration fluxes through the sides of the control volume, and (ii) production and sink

inside the control volume. The conservation equation for each of the water quality

parameters is given by:

+ V-((ii) = V-[D V(() )] + Q
a t (4.1)

(i) (ii) (iii) (iv)

where (i) is the evolution term (rate of change of concentration in the control volume), (ii)

is the advection term (fluxes into/out of the control volume due to advection of the flow

field), (iii) is the dispersion term (fluxes into/out of the control volume due to turbulent









53

diffusion of the flow field), and (iv) is the sink/source term, representing the kinetics and

transformations due to sorption/desorption, oxidation, excretion, decay, growth,

biodegradation, etc. The water quality equations in the curvilinear non-orthogonal boundary-

fitted system (T, rl, o) is given by:

1 aHd 1 a (Dado
H -t H2 ao v" 9a
1 [_/(r-Hudo)\+9 I (-oHV,)] 1 9 Hodo
ao (FHu + Hdo H (4.2)
H- g, aE an

+ DH [g11 a2 +2g 12 2 + g222 ]
Wa2 2~rl ar|2


where d represents any water quality parameter, (g,) is the Jacobian of horizontal

transformation, (g g 12, g 22) are the metric coefficients of coordinate transformation, and

Q represents the biogeochemical processes.

In the following sections, the biogeochemical processes controlling the sink/source

term of Equation (4.2) will be discussed in detail for the nutrient dynamics, zooplankton and

phytoplankton dynamics, and oxygen balance in estuarine systems.


Nutrient Dynamics in Estuarine Systems



As explained earlier, the nutrient dynamics will be centered in the nitrogen cycle,

assuming it is the macro-nutrient that limits phytoplankton growth. For the present study,

the basic transformation processes for the nitrogen cycle are similar to those described in

Chen and Sheng (1994).


I









54

Nitrogen comprises 78% of the atmosphere, mostly molecular N2 This form is

biologically unavailable except for fixation by procaryotic organisms containing the enzyme

nitrogenase. Considering the kinetic pathway organic nitrogen -*ammonia -4 nitrate -+N2,

fixed forms of nitrogen such as nitrate, ammonium, and organic nitrogen would gradually

be depleted from the biosphere if not for nitrogen fixation.

Nitrogen inputs to estuarine systems are related to point and non-point sources from

land, atmospheric deposition, and fixation. Additionally, internal loadings such as from

resuspended sediments containing inorganic and organic forms are also important. The

specification and quantification of each of these contributions is the first step towards the

determination of nitrogen budget in an estuarine system.

As shown in Equation (4.2), the nitrogen cycle is highly dependent on the

hydrodynamics and sediment dynamics of the estuarine system. Resuspension events,

combined with desorption processes can significantly change the input and budget of

nitrogen in the system. On the other hand, deposition and sorption may contribute to major

losses of nitrogen from the water column. The hydrodynamics not only drive the sediment

processes, but also affect the sorption/desorption reactions, through turbulent mixing.

The processes simulated in this study include:

a) Mineralization of organic nitrogen

b) Nitrification of ammonium

c) Volatilization of ammonia

d) Denitrification of nitrate

e) Uptake of ammonia and nitrate by phytoplankton









55

f) Conversion of algal-nitrogen into zooplankton-nitrogen through grazing

g) Excretion by algae and zooplankton

For the purpose of studying its cycle, the nitrogen species are first divided into

dissolved and particulate groups. This division is usually established in the laboratory using

filtering techniques. In the dissolved group, this study will consider nitrogen as ammonia

nitrogen, represented by the state variable NH3; dissolved ammonium nitrogen, represented

by the state variable NH4; nitrate+nitrite nitrogen, represented by the state variable N03; and

dissolved or soluble organic nitrogen (SON). Particulate nitrogen includes: particulate

inorganic nitrogen (PIN), and particulate organic nitrogen (PON). Zooplankton nitrogen

(ZOON), and algal nitrogen (ALGN) relate biomass to nitrogen concentration through fixed

stoichiometric ratios: zooplankton nitrogen to carbon ratio (zNc ), and algal nitrogen to

carbon ratio (ad).

In order to couple the water quality model with hydrodynamics and sediment

dynamics, Equation (4.2) needs to be modified for the particulate forms of nitrogen, so that

it includes a settling velocity. For the inorganic species, it is reasonable to assume the same

settling velocity of the suspended sediment particles. For phytoplankton, literature values

of algae settling velocity, which accounts for the limited vertical motion of these organisms

will be used.

Ammonia Nitrogen


Ammonia volatilization is a physico-chemical process where ammonium N is in

equilibrium between its gaseous and hydroxyl form:


I I












NH3(aq) + H2O NH4' + OH- (4.3)



As stated, the process is pH dependent, with an alkaline environment driving the

reaction to the left, i.e. favoring the aqueous form. Since the concentration of ammonia in

the atmosphere is very low, the partial pressure difference may produce a sink for nitrogen

in the system, according to Henry's law. The kinetic pathway for ammonia nitrogen (state

variable NH3) is represented in the sink term of Equation (4.2) as:


Q = KA pH *NH4 K l[hv'NH3 (NH3),] (4.4)
Hi + pH



where KAI is the ammonia conversion rate constant, and H, is the half-saturation constant

for ammonia conversion. KvoLis the volatilization rate constant, hV is Henry's constant, and (NH3)a.

is the ammonia concentration in the air.

Dissolved Ammonium Nitrogen


Nitrogen fixation is a biogeochemical process mediated by a variety of autotrophic

and heterotrophic bacteria, by which nitrogen gas is reduced to ammonium:


N2(g) + 8H' + 6e- 2NH4' (4.5)


In aquatic systems, this reaction is only possible in very reduced environments

(Snoeyink and Jenkins, 1980). Such an environment exists inside photosynthetic cells of

blue-green algae, and in the symbiotic association in root nodules between bacteria of the

genus Rhizobium and certain plants. It has been reported that cyanobacteria are responsible


I









57

for most planktonic fixation in aquatic environments, with a high correlation between

fixation rates and cyanobacteria biomass (Howarth et al., 1988). In most estuaries, the

biomass of these nitrogen-fixing species of cyanobacteria usually makes up a very small

percentage of the phytoplanktonic biomass (< 1%), suggesting insignificant amount of

nitrogen fixation (Howarth et al., 1988). Johansson et al. (1985) showed that, prior to 1984,

planktonic filamentous blue-green algae (Schizothrix calcicola sensu Drouet) dominated the

phytoplankton population in Tampa Bay from early summer to early winter. However,

Johansson (1991) stated that there was no information to support that this blue-green algae

is responsible for nitrogen fixation in Tampa Bay. Actually, it has been estimated that

nitrogen fixation should account for no more than 5% of the total nitrogen budget in the Bay

(Johansson, personal communication). These evidences support the hypothesis generally

accepted that many estuaries are nitrogen limited in part due to the low rates of nitrogen

fixation. Hence, nitrogen fixation was not considered in this study.

The biogeochemical transformation of organic nitrogen to ammonium is defined as

ammonification. Another source for dissolved ammonium is the release of NH4 during

mortality and excretion of algae and zooplankton, and the sorption/desorption reaction with

sediment particles. The kinetic pathway of ammonium nitrogen (state variable NH4) is

represented in the source term of Equation (4.2) by a first-order reaction (Rao et al., 1984),

and a partitioning between particulate and dissolved form regulated by the

sorption/desorption kinetics (Chen and Sheng, 1994):












DO
Q = K SON K O NH4
NM SON NN Hnit + DO

+ da(PIN pn-c-NH4)
(4.6)
Pnpa-ALGN + KC-ALGN + KZ-ZOON


K pH -NH4
SH. + pH



whereKoNu the rate of organic nitrogen mineralization is a function of water temperature,

pH, and the C/N ratio of the residue (Reddy and Patrick, 1984). KN is the nitrification rate

constant, DO is the dissolved oxygen concentration, Hkit is the half saturation constant for

oxygen limitation. d, is the desorption rate of NH4 from sediment particles, p, is the

partition coefficient between NH4 and PIN, and c is the suspend sediment concentration. P,


is the ammonium preference factor for algae uptake, Pa is the algae growth rate,

K and K, are the algae and zooplankton excretion rate constants, respectively. All

coefficients related to zoo and phytoplankton dynamics will be discussed later in this

Chapter.

Nitrite+Nitrate Nitrogen


In an aerobic environment, the mineralization of organic nitrogen proceeds with a

bacterial-mediated transformation of ammonium into nitrate. The nitrification process is a

two step process, in which the chemoautotrophic bacteria of the genera Nitrosomonas

mediate the formation of nitrite, and bacteria of the genera Nitrobacter the formation of

nitrate:












NH4' + 1.5 02 NO2- + 2H' + H20
(4.7)
NO2- + 0.5 02 NO3


Nitrification is a strictly aerobic process, occurring only in the water column and in

the aerobic layer of the sediment column. Equation (4.7) shows that the nitrification process

is a sink for dissolved oxygen in the system.

Denitrification is defined as the biogeochemical transformation of nitrate N to

gaseous end products such as molecular nitrogen or nitrous oxide (Reddy and Patrick, 1984).

Like volatilization, denitrification represents a sink for nitrogen in the system. Under

anaerobic conditions and in the presence of available organic substrate, denitrifying bacteria

(e.g. Pseudomonas denitrificans) can use nitrate as an electron acceptor during anaerobic

respiration. As an example, the oxidation of a carbohydrate substrate to CO2 and HO using

nitrate instead of oxygen can be given as:


5(CH20) + 4NO3- + 4H' 5CO2 + 2N2 + 7H20 (4.8)


This irreversible reaction is actually a two-step process in which nitrate is reduced

to nitrous oxide before being converted into molecular nitrogen. Nitrous oxide has been

related to the Earth's "greenhouse" effect because N20 reacts and breaks down atmospheric

ozone (McElroy et al., 1978). Reddy et al. (1978) showed that under carbon-limiting

conditions, the denitrification process described in Equation (4.8) can be represented by a

first-order reaction.









60

In this study, the kinetic pathway of nitrite+nitrate (state variable NO3) is

represented in the source term of Equation (4.2) as a sequence of first-order reactions, limited

by the dissolved oxygen concentration:


S Hit+DO Hno3+DO



where KD is the denitrification rate constant, and HN3 is the half saturation constant for

denitrification, which can be calibrated to only allow the denitrification process to occur

under low dissolved oxygen conditions (Ambrose et al., 1994).

Soluble Organic Nitrogen


Besides N2 the largest pool of nitrogen in estuarine systems are dissolved and

particulate organic nitrogen. The kinetic pathway of dissolved or soluble organic nitrogen

is the convention of SONtoNH4 during ammonification, and the sorption/desorption reaction

with sediment particles. For soluble organic nitrogen (state variable SON), the source term

of Equation (4.2) can be represented by:

Q = KON SON + d,, (PON Pn, c SON) (4.10)


where dn is the desorption rate of SON from the sediment particles, and pn,, is the partition

coefficient between SON and PON.











Particulate Organic Nitrogen


The kinetic pathway of particulate organic nitrogen is the release of PON during

mortality and excretion of algae and zooplankton, and the sorption/desorption reaction with

sediment particles. In estuarine systems with organic-rich sediments, benthic mineralization

of detritus can be a major recycling pathway, and account for a significant fraction of the

nutrient requirements of primary producers in overlying water column (Klump and Martens,

1981). For particulate organic nitrogen (state variable PON), the source term of Equation

(4.2) can be represented as:

Q = K ALGN + K, ZOON do (PON P c SON) (4.11)


where K is the mortality rate of zooplankton.

Particulate Inorganic Nitrogen


Sources of PIN are related to nitrogen contained in the suspended particulate matter

derived from landward and seaward origin (Keefe, 1994). There have been several studies,

at various spatial and temporal scales, of particulate nitrogen distribution in estuarine systems

(Sharp et al., 1982; Edmond et al., 1985; Wafar et al., 1989). Nevertheless, little insight is

available concerning the partitioning between the inorganic and organic fraction of these

materials (Froelich, 1988). The kinetic pathway of particulate inorganic nitrogen (state

variable PIN) is related to the sorption/desorption reaction with sediment particles, and the

source term of Equation (4.2) can be written as:


Q = -d, (PIN Pan c NH4)


(4.12)












Algal Nitrogen


Through uptake of inorganic nitrogen, algae assimilates nitrogen in proportion to its

growth rate. The particulate nitrogen recycles to the inorganic pool by means of excretion

and non-predatory mortality. Inasmuch as there is no data on excretion of zoo and

phytoplankton under field conditions, most of water quality models consider constant

excretion and mortality rates proportional to the biomass (Jorgensen, 1983; Najarian et al.,

1984; Ambrose et al., 1994; Chen and Sheng, 1994). Another sink for ALGN is due to

grazing by zooplankton, at a rate proportional to the zooplankton growth rate. Growth rates

for phytoplankton and zooplankton in estuarine systems are complex functions of the species

present, and they will be discussed later in this Chapter.

The algal nitrogen (state variable ALGN) is represented in this model by a fixed

stoichiometric ratio relating algal biomass and nitrogen concentration as:

ALGN = aN (Algal Biomass) (4.13)


where a is the algal nitrogen to carbon constant ratio.

Zooplankton Nitrogen


Similar to ALGN, the kinetic pathway of particulate zooplankton nitrogen depends

on growth, excretion, and mortality rates. In this case, the zooplankton nitrogen (state

variable ZOON) is given by:

ZOON = ZNC (Zooplankton Biomass)


where zNC is the zooplankton nitrogen to carbon constant ratio.












Sorption and Desorption Reactions



In the nitrogen cycle, sorption processes refer to the conversion from soluble to solid

phase of inorganic and organic species, while desorption reactions describe the inverse

process. Sorption/desorption processes, combined with resuspension events can significantly

alter the nitrogen cycle in the system.

The kinetics of sorption/desorption reactions are dependent on each nitrogen species

characteristics, sediment properties, pH, temperature, and dissolved oxygen concentration

(Simon, 1989). Some studies have shown that sorption/desorption processes can be more

important in marine environment than in freshwater. The primary reason has been attributed

to a six times higher adsorptive capacity of clays for organic matter in seawater than in

freshwater, due to salinity effects (Pocklington, 1977; Martinova, 1993).

The most commonly used mathematical representation of sorption/desorption

processes is the linear, reversible, isotherm (Berkheiser et al., 1980; Reddy et al., 1988):


N -Dr N, + Sr N (4.15)
at


where Dr is the desorption rate constant, Sr is the sorption rate constant, N. is the adsorbed

nitrogen concentration, and N, is the dissolved nitrogen concentration.

Equation (4.15) can be reformulated, considering that at equilibrium, the ratio

between the desorption and sorption rates gives the partition coefficient between dissolved

and particulate forms:












aN
S-Dr(Nd p N) (4.16)



where Pc is the partition coefficient.


Phytoplankton Dynamics in Estuarine Systems



The overall water quality in the Tampa Bay Estuarine System is markedly influenced

by the dynamics of the zoo and phytoplankton communities (Lewis and Estevez, 1988; Boler

et al., 1991; AScI, 1996). In a review of the phytoplankton in Tampa Bay, Steidinger and

Gardiner (1985) reported the dominance of nannoplankton (less than 20 Pm), with a head to

mouth gradient, following the salinity distribution. The authors also reported that Tampa

Bay presents more than 250 species of phytoplankton, with diatoms making up the bulk of

the distribution. However, the lack of data on each specific species prevented a more

detailed characterization, and the entire phytoplanktonic community is represented in this

study by a single state variable.

In this study, a quantitative model of phytoplankton population dynamics also uses

the conservation of mass principle, in which hydrodynamics transport plays a major role.

Phytoplankton growth is represented by a temperature-dependent maximum growth rate that

is limited by nutrient availability and light. Light limitation is formulated according to the

equation first proposed by Steele (1965). The nutrient limitation is represented by a modified

version of the Michaelis-Menton formulation. Some researchers (e.g. Jorgensen, 1976)

suggest that the nutrient-limited growth rate of phytoplankton is a function of the internal









65

nutrient content. According to this approach, external nutrients are taken up by

phytoplankton and stored. Ensuing growth would then be related to this internal nutrient

content. Assuming a dynamic state of equilibrium between the external concentration and

internal content (Di Toro, 1980), it is possible to represent the nutrient limitation according

to the formulation suggested by Riley and Stefan (1988).

In this study, the phytoplankton growth rate is represented by:


S oT-20 I I NH4 + N03
o = a exp 1 ( 4.17)
Ia = (a)m 2ax I e p( H+ NH4 + N03 (4.17)



where (a)max is the algae maximum growth rate, 0 is the temperature correction factor, I is

the light intensity, I is the optimum light intensity for algal growth, Hn is the half saturation

constant for algal growth.

The phytoplankton kinetics are represented by growth, respiration, non-predatory

mortality, grazing by zooplankton, and a settling term which accounts for the limited vertical

motion. The source term of Equation (4.2) can be written as:


Q = (WSge -PHY) + (p,,- K) PHY z,' ZOO (4.18)


where wSigae is the phytoplankton settling velocity. Chen and Sheng (1994) reviewed

algal settling rate measured in eutrophic water bodies, and showed that it is not only species

dependent, but it also a function of flocculation and senescence.

Zooplankton are the lower-trophic level consumers that constitute the primary

herbivorous component of an estuarine ecosystem (Kennish, 1990). In this study,









66

phytoplankton are the object of concern, therefore, no attempt is made to investigate the

details of the zooplankton dynamics. Zooplankton is only considered as the predators of

phytoplankton, utilizing their available biomass as food supply.

Zooplankton growth is represented by a temperature-dependent maximum growth

rate, that is limited by phytoplankton availability:


z = )mx T-20. PHY
Hphy + PHY (4.19)



where (z)max is the maximum growth rate for zooplankton, 6z is the temperature limiting

function for zooplankton, and Hphy is the half saturation constant for phytoplankton uptake.

The zooplankton kinetics, influenced by growth, respiration, and mortality, is

represented in the source term of Equation (4.2) by:

Q = (Fz Kzx-K )ZOO (4.20)



Oxygen Balance in Estuarine Systems



Dissolved oxygen dynamics in aquatic systems have been extensively studied

(Streeter and Phelps, 1925; O'Connor and Thomann, 1972; Orlob, 1983; Ambrose et al.,

1994). Dissolved oxygen evolution depends on the balance between photosynthetic

production, total respiration, and exchanges with the atmosphere. Oxygen, as a byproduct

of photosynthesis, increases as a result of autotrophs' growth. Dissolved oxygen saturation

in seawater is determined as function of temperature and salinity (APHA, 1985). For









67

dissolved oxygen levels below saturation, DO diffuses into surface waters. When the water

is super-saturated, mainly as a result of primary production, oxygen will be diffused out to

the atmosphere. As any other water quality parameter, dissolved oxygen is also subject to

advective transport in the estuarine system.

In this study, the formulation of the oxygen balance is based on that in the WASPS

model, with some modifications. The rate of dissolved oxygen production is assumed to be

proportional to the growth rate of the phytoplankton in a fixed stoichiometry reaction. For

each milligram of phytoplankton carbon produced by growth using nitrate, a fixed amount

of phytoplankton nitrogen (ALGN) is reduced, and (48/14) a, (phytoplankton

nitrogen/carbon ratio) mg of 02 is produced. The dissolved oxygen fluxes on the air-water

interface are determined as a product of a reaeration coefficient multiplied by the difference

between dissolved oxygen saturation and the dissolved oxygen concentration at the surface

layer. The reaeration coefficient is assumed to be proportional to the water velocity, depth,

and wind speed (Thomann and Fitzpatrick, 1982). Details of the dissolved oxygen saturation

and reaeration coefficient calculations are presented in Appendix C.

In this model, there are two options for the kinetic pathway of DO. The first one,

describing the oxygen balance through a full non-linear equation is represented in the source

term of Equation (4.2) as:













A 12 14 12

32 DO
3-K a *PHY K --DO *CBOD
12 c D Hbod + DO (4.21)

64K DO NH4
14 NN Hit + DO




where DO, is the saturation value for dissolved oxygen concentration, KA is the reaeration

coefficient, and ao is the constant oxygen to carbon ratio for phytoplankton respiration (gO2

/ gC).

In order to minimize "spin-up" time due to the non-linear character of Equation

(4.21), a second option describes the oxygen balance through a linear equation where the

source term of Equation (4.2) is given as (Ambrose et al. 1994):


Q = KA(DO, DO)+ 2[P -(K +K)] PHY

(4.22)
64
-K,-CBOD K NH4
14


The use of carbonaceous oxygen demand (CBOD) as a measure of the oxygen-

demanding processes simplifies modeling efforts by aggregating their potential effects

(Ambrose et al. 1994). Oxidation organic matter, nitrification, non-predatory mortality and

respiration by zoo and phytoplankton are nitrogenous-carbonaceous-oxygen-demand,

collectively combined into the state variable CBOD.









69

The kinetic pathway of CBOD is represented in the source term of Equation (4.2) as:


Q [WSCBOD.(1 -fdcBOD) CBOD]

DO
KD CBOD
Hbod + DO
(4.23)
5 32 Kno3
.. .K NO3
4 14 DN H + DO

+ K*-ALGN + K ZOON


where fdcBoD corresponds to the fraction of the dissolved CBOD, and wscBOD is the

settling velocity for the particulate fraction of CBOD. fdcBOD and WSCBOD are empirically-

based coefficients that represent the fact that under quiescent flow conditions, the particulate

fraction of CBOD can settle through the water column, and eventually deposit on the bottom

(Ambrose et al. 1994). The determination of both coefficients should proceed in terms of

the best fit between measured and modeled data (J0rgensen and Gromiec, 1989).


Light Attenuation in Estuarine Systems



The solar radiation that reaches the ocean's surface includes the ultraviolet range

(290-380 nm), the visible range (380-760 nm), and the infra-red (760-3000 nm). As to

primary production in estuarine systems, ecologists are normally concerned with light in the

range of wavelengths from 400-700 nm. Defined as "Photosynthetically Active Radiation"

(PAR), this range of irradiance provides the predominant source of energy for autotrophic

organisms (Day et al., 1989). Moreover, instead of measuring PAR in terms of energy,









70

commercially available quantum meters record the number of quanta (or photons, in the

visible range) received per unit area per unit time. The unit of this photon flux density is

micro Einstein per squared meter per second ( E m -2 s -1).

The incident light can be reflected, absorbed, and refracted by dissolved and

suspended substances in the water and by the water itself. The Beer-Lambert law can be used

to describe the light distribution with depth (Day et al., 1989):


I = e-Koz (4.24)

where Io is light intensity at the water surface, I is light intensity at depth z, z is the depth

in meters, and Ko is the vertical light attenuation coefficient in m-.

For long term simulations, the seasonal variation of surface irradiance in Tampa Bay

can be represented by a sine curve:


1 = 1800 + 400 -sin( 3 +2 ( 2j)) (4.25)
O 2 365) (4.25)

corresponding to an average solar radiation of 1800 pE/m2 s. Monthly variations range from

1600 in January to 2200 jE m -2 s-1 in mid July.

Some studies reported higher values in middle to late spring rather than summer

because of increased precipitation and cloud cover associated with the rainy season (Wolfe

and Drew, 1990). For this study, real data of surface irradiance, obtained by USGS (Tampa

Bay) between June 1990 and September 1991, was used.

McPherson and Miller (1994) and Miller and McPherson (1995) developed a model

by partially adjusting the attenuation coefficient in Tampa Bay for changing solar elevation,









71

and used multiple regression analysis to partition the coefficient into the relative contribution

of seawater, water color, chlorophyll and non-chlorophyll suspended matter.

A simplified geometric description of the incident direct solar beam and diffuse

skylight is used to describe the effects of solar elevation angle and cloudiness on the amount

of PAR that passes through the air-sea interface. Since so far, there is no process-based

model that relates optical characteristics of the water to mass (or concentration) of

constituents inside the water column, a large data set which covers a wide range of

conditions is required to determine statistical correlations. In their work, Miller and

McPherson (1995) used 16083 observations (255 days between 6/02/90 and 9/29/91) of

scalar PAR, measured in air and at two depths in the water column, to evaluate irradiance that

entered the water and subsequent attenuation.

The attenuation coefficient is obtained as the product of the partitioned coefficient

and a correction term that accounts for the geometry of the incident irradiance:


K, = [lwtd Kadj (4.26)

where pwtd is the correction factor (weighted average cosine), andKad is the partitioned

attenuation coefficient. The formulation for the correction factor, pwtd, developed in Miller

and McPherson (1995) is presented in Appendix D.

Lorenzen (1970) showed that the vertical attenuation of PAR can be linearly

partitioned into a set of partial attenuation coefficients:


K4 = K, + + Kd + K42


(4.27)









72

where K, is the attenuation coefficient due to water, Kc is due to the presence of chlorophyll

a, K, is due to dissolved substances, and K is due to non-algal particulate matter.

Nevertheless, other researchers have shown that the partitioning of the components of light

attenuation into an empirical model using standard water quality parameters is not precise

(e.g. Mote Marine Lab, 1995).

According to Kirk (1994), the inherent properties of the water can be determined by

linear superposition of the partial contributions (e.g. color, chlorophyll, etc.). However, the

vertical attenuation coefficient is an "apparent" optical property of the water (Kirk, 1994),

and it is not only a function of the inherent properties of absorption and scatter, but also the

angular and spectral distribution of the incident light.

Originally, McPherson and Miller (1994) partitioned the attenuation coefficient into

a set of partial attenuation coefficients:

K, = k + E2C2 + E3 C3 + E4 C4 (4.28)


where k, is the PAR-waveband average attenuation coefficient of seawater, 0.0384 m7'

(Lorenzen, 1972); E2 is the attenuation coefficient of dissolved matter, in (m Pt-Co units)';

C2 is the water color, in Pt-Co units; E3 is the attenuation coefficient of chlorophyll and other

matter associated with chlorophyll a, in m2 mg-1; C3 is the concentration of chlorophyll a, in

mg m-3; E4 is the attenuation coefficient of nonchlorophyll suspended matter (NSM), which

includes inorganic and organic particulate not directly associated with color or chlorophyll

a, in m2 mg-'; and C4 is the concentration of NSM, in mg m3.









73

The lack of good measurements of NSM (in terms of total suspended solids and

turbidity) constrained the determination of the "E4 C4" term, and the equation was modified

to (McPherson and Miller, 1994):

K = 0.014C2 + 0.062- (turbidity) + 0.049 C3 +0.30 (4.29)


with the coefficients E2 and E3determined from Tampa Bay and Charlotte Harbor data. In

this study, the adjusted attenuation coefficient is determined from Equation (4.29), with C2

representing the average water color, in Pt-Co units; C3 is the chlorophyll a concentration

in mg/m3; and turbidity is given in NTU. Data of water color and turbidity for each

segment of the Bay was obtained from the EPC reports (Boler, 1992). Chlorophyll-a

concentration is determined from the water quality portion of the model.

After determining the correction factor (wtd ), and the partitioned attenuation

coefficient (Kad ), the attenuation coefficient (Ko ) is obtained from Equation (4.26).


Model Coefficients



The model parameters required to simulate the water quality dynamics in the Tampa

Bay Estuarine System, are described in Table 4.1. During the implementation phase, model

coefficients were determined by isolating specific processes in a test grid with a similar

spatial scale as Tampa Bay, and initial values were obtained from literature and previous

modeling studies (e.g. AScI, 1996). The value of the coefficients used in this study are

presented in Table 4.2.












Table 4.1 Description of the coefficients used in the water quality model.
Coefficient Description Units


(OA D )T-20
(ea)T-20


(OAI)T-20

(OBOD)T-20

(OD N )T-20

(6,O )T-20

(0 D T-20

(OQNM)T20
(0RESP)T-20
(0z)T-20


(Pa)max

(Pz)max
(NH3)air

achla

an

ao0

dan

do n

dmol

E2

E,

E4

fdCBOD

Hai

Hbod


temperature coefficient for NH4 desorption

temperature coefficient for algae growth

temperature coefficient for ammonium instability

temperature coefficient for CBOD oxidation

temperature coefficient for denitrification

temperature coefficient for nitrification

temperature coefficient for SON desorption

temperature coefficient for mineralization

temperature coefficient for algae respiration

temperature coefficient for zooplankton growth

algae maximum growth rate

zooplankton maximum growth rate

ammonia concentration in the air

algal carbon-chlorophyll-a ratio

algal nitrogen-carbon ratio

algal oxygen-carbon ratio

desorption rate of adsorbed ammonium nitrogen

desorption rate of adsorbed organic nitrogen

molecular diffusion coefficient for dissolved species

light attenuation coefficient due to dissolved matter

light attenuation coefficient due to chlorophyll a

light attenuation coefficient due to NSM

fraction of dissolved CBOD

half-saturation constant for ammonia conversion

half-saturation constant for CBOD oxidation


I/day

I/day

pg/L
mg C / mg Chl-a

mg N / mg C

mg 0O / mg C
I/day

I/day

cm2/s

l/(m Pt-Co)

1/(m pg/L)

l/(m mg/L)


(pH unit)

mg O2











Table 4.1 continued.
Coefficient Description Units

H, half-saturation constant for algae uptake mg/L
Hnit half-saturation constant for nitrification mg 02

Hno3 half-saturation constant for denitrification mg 02
h, Henry's constant mg/L-atm

I, optimum light intensity for algal growth pE / m2 / s
Ka x excretion rate by algae I/day
Kas mortality rate of algae I/day

KAE reaeration rate constant l/day
KAI ammonia conversion rate constant l/day
KDN denitrification rate constant I/day


Table 4.2 Literature ranges and values of the coefficients used in the water quality model.
Coefficient Literature Range Tampa Bay Source

(A D)T-20 1.08 1.08 Assumption
(6a)T-20 1.01-1.2 1.08 Di Toro & Connoly(1980);AScI(1996)
(AI)T-20 1.08 1.08 Assumption

(OBOD)T-20 1.02-1.15 1.08 Bowie et al. (1980); AScI (1996)
(ODN)T-20 1.02-1.09 1.08 Baca & Arnett (1976); AScI (1996)
(ONN)T20 1.02-1.08 1.08 Bowie et al. (1980); AScI (1996)
(O) D)T'20 1.08 1.08 Assumption
(o0NM )T-20 1.02-1.09 1.08 Baca & Arnett (1976); AScI (1996)
(0RESP)T20 1.045 1.05 Ambrose et al. (1994); AScI (1996)
(0z)T-20 1.01-1.2 1.08 Di Toro & Connoly (1980)

(Pa)max 0.2-8. 1.47 Baca & Arnett (1976); AScI (1996)












Table 4.2 continued.
Coefficient Literature Range Tampa Bay Source


0.15-0.5

0.1

10-112

0.05-0.43

2.67


([z)max
(NH3)air

iacha
an c

aoc

da n

do n
dmol

E2

E3

E4

fdcBoD

Hai
Hbod

Hn

Hnit

Hno3

h,

Is

Ka x

Kas
KAE

KAI

KD

KDN


0.5

0.1

112

0.15

2.67

4.0

4.0

1.E-5

0.014

0.062

0.30

0.7

9.0

0.18

0.05

2.0

0.1

43.8

200.

0.15

0.08


0.003

0.15

0.90


J0rgensen (1976)

Freney et al. (1981)

J0rgensen (1976);AScI (1996)

J0rgensen (1976); AScI (1996)

Ambrose et al. (1994); AScI (1996)

Simon (1989)

Assumption
Rao et al.(1984);Krom & Berner (1980)

Miller & McPherson (1995)

Miller & McPherson (1995)

Miller & McPherson (1995)

Assumption

Freney et al. (1981)

AScI (1996)

AScI (1996)

Ambrose et al. (1994); AScI (1996)

Ambrose et al. (1994); AScI (1996)

Sawyer & McCarty (1978)

Di Toro & Connoly(1980);AScI(1996)

J0rgensen (1976); AScI (1996)

J0rgensen (1976); AScI (1996)

see Appendix C

Reddy et al.(1990)

Bowie et al. (1980); AScI (1996)

Baca & Arnett (1976); Assumption


4.E-6-1.E-5








9.0

0.02-5.6

0.0015-0.4

0.1-2.0

0.1

43.8

300-350

0.05-0.2

0.01-0.1


0.003-0.008

0.02-0.6

0.02-1.0












Table 4.2 continued.
Coefficient Literature Range Tampa Bay Source


0.001-0.6

0.01-0.4

3.5-9.0

0.05-0.3

0.03-0.075

0.5E-7-1.0E-5

1.0E-5


0.0-30.


0.08

0.1

7.0

0.05

0.05

1.0E-5

1.0E-5

5.0


AScI (1996); Reddy et al.(1990)

Di Toro & Connoly(1980);AScI(1996)

Fillery and DeDatta (1986)

Baca & Arnett (1976)

J0rgensen (1976)

Simon (1989)

Simon (1989)

Assumption

J0rgensen (1976)


KNN

KONM
KVOL

Kzs

Kz.


Pan

Pon

WSCBOD

ws algae







Full Text
UFL/ COEL-TR/113
INTEGRATED MODELING OF THE TAMPA BAY
ESTUARINE SYSTEM
Eduardo Ayres Yassuda
Dissertation
1996

INTEGRATED MODELING OF THE TAMPA BAY ESTUARINE SYSTEM
By
EDUARDO AYRES YASSUDA
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1996

ACKNOWLEDGMENTS
First, I would like to express my gratitude to the CNPq - Conselho Nacional de
Desenvolvimento Científico e Tecnológico (Brazilian Research Council) for the financial
support during my graduate program at the University of Florida. Several University of
Florida research projects provided the opportunities for me to gain experience in
hydrodynamics and water quality modeling and field work. These projects include the Lake
Okeechobee Phosphorus Dynamics Study funded by the South Florida Water Management
District, the Sarasota Bay Field and Modeling Study funded by the Sarasota Bay National
Estuary Program and United States Geological Survey, the Tampa Bay Circulation Modeling
Study funded by the Tampa Bay National Estuary Program, the Roberts Bay Water Quality
Modeling Study funded by the Sarasota Bay National Estuary Program, and the Indian River
Hydrodynamics and Water Quality Modeling Study funded by the St. Johns River Water
Management District.
My appreciation is extended to my advisor and chairman of the supervisory
committee, Prof. Peter Sheng, for his guidance, financial support, and patience throughout
this study; to Prof. A. Mehta, and Prof. R. Thieke from the Coastal Engineering Department
for their comments and advice; to Prof. K.R. Reddy from the Soil and Water Science
Department for helping us bridge the gap between experimentalists and modelers; and to
Prof. C. Montague from the Environmental Engineering and Science Department, for his
m

unconditional support and high motivation. Two former students deserve special
acknowledgment: Steve Peene and Xinjian Chen.
I also want to thank my professors at the Oceanographic Institute of the University
of Sao Paulo, specially Prof. Joseph Harari, Prof. Luiz B. de Miranda, and Prof. Moyses
Tessler for their invaluable contributions to my career.
It would not be possible to complete this work if not for the technical guidance and
help of the following scientists and researchers: Mr. Richard Boler, Dr. Kate Bosley, Mr.
Michael DelCharco, Dr. Kent Fanning, Dr. Peggy Fong, Ms. Holly Greening, Dr. Kurt Hess,
Mr. Ronald Miller, Dr. Gerold Morrison, and Dr. David Tomasko.
Grateful thanks goes to my buddies in room 429, H.K. Lee, Yang, Justin, Liu, and
Kevin, in our quest for “bugs,” and for reviewing the manuscript. I would like to express my
gratitude to Sidney Schofield, “Professor” Mark Gosselin, and “Wally” Yigong Li for bailing
me out in a great number of opportunities throughout this program. Life would not be the
same without the Coastal Lab and its staff. Acknowledgment goes to all of them. Deserving
special honors also are Subama Malakar, Becky Hudson, Sandra Bivins, Lucy Hamm, Helen
Twedell, and John Davis.
My most sincere appreciation is extended to the DelCharco family, for adopting and
taking us as one of their own during all family occasions.
I would like to dedicate this dissertation to my parents, because only now, as Daniel’s
father, do I realize how much effort they had to spend educating me.
Finally, I want to thank Monica for being there for me all the time, sharing the ups
and downs of this never-ending challenge.
IV

TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
ABSTRACT . xxi
CHAPTERS
1 INTRODUCTION 1
Background 1
Water Quality Modeling 2
Integrated Modeling Approach for Estuarine Systems 4
Objectives 7
2 TAMPA BAY CHARACTERIZATION 9
Climate 11
Tides 12
Salinity Distribution 12
Rainfall 13
Wind 13
Bathymetry 16
Freshwater Inflow 16
Hillsborough River 18
Alafia River 19
Little Manatee River 20
Manatee River 21
Rocky Creek 21
Lake Tarpon Canal 22
Sweetwater Creek 22
Non-Point Sources 22
Nutrients Distribution and Loading 23
Sediment Type and Distribution 26
3 THE CIRCULATION AND TRANSPORT MODEL 31
Previous Work 31
Circulation Model 33
Continuity Equation 33
v

X-component of Momentum Equation 34
Y-component of Momentum Equation 34
Hydrostatic Pressure Relation 34
Salinity Equation 35
Equation of State 36
Conservative Species Equation 36
Sediment Transport Model 37
Curvilinear Boundary-Fitted and Sigma Grid 38
Boundary and Initial Conditions 40
Vertical Boundary Conditions 40
Lateral Boundary Conditions 42
4 THE WATER QUALITY MODEL 45
Previous Work 45
Development of the Numerical Model 50
Mathematical Formulation 52
Nutrient Dynamics in Estuarine Systems 53
Ammonia Nitrogen 55
Dissolved Ammonium Nitrogen 56
Nitrite+Nitrate Nitrogen 58
Soluble Organic Nitrogen 60
Particulate Organic Nitrogen 61
Particulate Inorganic Nitrogen 61
Algal Nitrogen 62
Zooplankton Nitrogen 62
Sorption and Desorption Reactions 63
Phytoplankton Dynamics in Estuarine Systems 64
Oxygen Balance in Estuarine Systems 66
Light Attenuation in Estuarine Systems 69
Model Coefficients 73
5 THE SEAGRASS MODEL 79
Using Seagrass as a Bioindicator of the Estuarine System 79
Seagrass Ecosystems 80
Previous Work 83
Development of the Numerical Model 85
Mathematical Formulation 88
Light 88
Temperature 89
Density-dependent Growth Rate 89
Growth Rate Dependence on Light 91
vi

Growth Rate Dependence on Salinity 93
Growth Rate Dependence on Temperature 96
Growth Rate Dependence on Sediment Nutrients 98
6 APPLICATION OF THE CIRCULATION AND TRANSPORT MODEL 99
Design of Tampa Bay Grid 99
Forcing Mechanisms and Boundary Conditions 105
Modeling Strategy 115
Results of the Barotropic Simulation 115
Results of the Baroclinic Simulation 119
Tides 121
Currents 128
Salinity 148
Validation of the Model 156
Residual Circulation 168
Results of the Suspended Sediment Simulation 177
7 CALIBRATION OF THE WATER QUALITY MODEL 185
Initial and Boundary Conditions of the Water Quality Model 188
Water Column 188
Sediment Column 201
Modeling Strategy 212
Sensitivity Analysis 212
Simulation of the Summer 1991 Condition 224
Dissolved Oxygen 225
Phytoplankton 238
Nitrogen Species 250
Tidal Exchange 261
Nutrient Budget 265
Load Reduction Simulations 269
Comparison with AScI (1996) study 271
Comparison with Coastal Inc. (1995) study 274
Advantages and Limitations of this Integrated Modeling Approach 275
8 CALIBRATION OF THE SEAGRASS MODEL 277
Initial Conditions 280
Sensitivity Analysis 282
Simulation of the Summer 1991 Condition 294
Load Reduction Simulation 296
vii

9 CONCLUSION AND RECOMMENDATIONS 303
APPENDICES
A NUMERICAL SOLUTION OF THE EQUATIONS 309
B MODELING SEDIMENT DYNAMICS 329
C DISSOLVED OXYGEN SATURATION AND REAERATION
EQUATIONS 339
D LIGHT MODEL EQUATIONS 341
E RESULTS OF THE SUMMER 1991 SIMULATION 343
F SENSITIVITY TESTS OF THE SEAGRASS MODEL 363
REFERENCES 377
BIOGRAPHICAL SKETCH 395
viii

LIST OF FIGURES
Figure page
2.1- Tampa Bay Estuarine System subdivisions as defined by
Lewis and Whitman (1985) (from Wolfe and Drew, 1990) 10
2.2 - Monthly rainfall in Tampa Bay (Wooten, 1985) 14
2.3 - Seasonal wind pattern in Florida (Echtemacht, 1975) 15
2.4 - Tampa Bay watershed (Wolfe and Drew, 1990) 17
2.5 - Surface Sediments in Tampa Bay (Goodell and Gorsline, 1961) 28
2.6 - Mud zone in Hillsborough Bay (Johansson and Squires, 1989) 29
5.1- Seagrass species commonly found in west Florida
(from Phillips and Mefiez, 1987) 82
5.2 - Structure and components of the numerical seagrass
model used for this study 86
5.3 - Epiphytic algae model flow chart 87
5.4 - Seagrass model flow chart 87
5.5 - Seagrass density-dependent maximum growth rate:
Thalassia (dotted line), Halodule (solid line),
and Syringodium (dash-dotted line) 90
5.6 - Seagrass growth rate dependence on light: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line) 92
5.7 - Seagrass growth rate dependence on salinity: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line) 95
5.8 - Seagrass growth rate dependence on temperature: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line) 97
IX

6.1- NOAA’s TOP station locations in Tampa Bay 101
6.2 - A boundary-fitted grid for the Tampa Bay Estuarine System 102
6.3 - Tampa Bay bathymetric contours 103
6.4 - Bay segments (Sheng and Yassuda, 1995) 104
6.5 - Tidal forcing for the 1990 simulation 106
6.6 - Tidal forcing for the 1991 simulation 107
6.7 - Initial salinity distribution (surface) for the 1990 simulation 108
6.8 - Initial salinity distribution (surface) for the 1991 simulation 109
6.9 - Rainfall data for the 1990 and 1991 simulations Ill
6.10 - River discharges for the 1990 and 1991 simulations 112
6.11 - Wind velocity for the 1990 simulation 113
6.12 - Wind velocity for the 1991 simulation 114
6.13 - Surface elevation at Egmont Key and St.Petersburg
(September 1990) 117
6.14 - Surface elevation at Davis Island and Old Tampa Bay
(September 1990) 118
6.15 - Spectra of water surface elevation for the 1990 simulation 123
6.16 - Simulated and measured bottom velocity at Egmont Channel -
September/1990 130
6.17 - Simulated and measured surface velocity at Egmont Channel -
September/1990 131
6.18 - Simulated and measured bottom velocity at Skyway Bridge -
September/1990 133
6.19 - Simulated and measured mid-depth velocity at Skyway Bridge -
September/1990 134
x

6.20 - Simulated and measured surface velocity at Skyway Bridge -
September/1990 135
6.21 - Simulated and measured bottom velocity at Port of Manatee Channel -
September/1990 137
6.22 - Simulated and measured surface velocity at Port of Manatee Channel -
September/1990 138
6.23 - Simulated and measured bottom velocity at Port of Tampa Channel -
September/1990 139
6.24 - Simulated and measured bottom velocity at Port of Tampa Channel -
September/1990 141
6.25 - Energy density spectra of bottom currents at Skyway Bridge -
September/1990 144
6.26 - Energy density spectra of surface currents at Skyway Bridge -
September/1990 145
6.27 - Tidal current ellipses for the semi-diurnal components - September/1990. . 149
6.28 - Tidal current ellipses for the diurnal components - September/1990 150
6.29 - Near-bottom salinity (solid line) and temperature (dashed line) at NOAA
station S-4 starting at Julian Day 150 in 1990 151
6.30 - Simulated and measured near-bottom salinity at NOAA
station C-21 - September/1990 153
6.31 - Simulated and measured near-bottom salinity at C-23 -
September/1990 154
6.32 - Simulated and measured near-bottom salinity at C-4 -
September/1990 155
6.33 - Surface elevation at St.Petersburg and Davis Island -
“Marco” Storm - October/1990 157
6.34 - Surface elevation at St.Petersburg and Davis Island - July/1991 158
xi

6.35 - Simulated and measured bottom current at Skyway Bridge -
“Marco” Storm (October/1990) 161
6.36 - Simulated and measured surface current at Skyway Bridge -
“Marco” Storm (October/1990) 162
6.37 - Simulated and measured near-bottom salinity at station S-4 -
(July/1991) 163
6.38 - Simulated and measured near-surface salinity at station S-4 -
(July/1991)...... 164
6.39 - Relative flushing for several bay segments - September/1990 167
6.40 - Residual circulation after 30 days - September/1990 169
6.41 - Simulated velocity field representing maximum ebb currents -
September/29/1990 - 18:00 171
6.42 - Simulated velocity field representing maximum flood currents -
September/29/1990 - 10:00 172
6.43 - Velocity cross-section at Skyway Bridge looking up the Bay. Vertical
scale in meters, and horizontal scale in computational grid j-index 174
6.44 - Salinity cross-section at Skyway Bridge looking up the Bay. Vertical
scale in meters, and horizontal scale in computational grid j-index 175
6.45 - Longitudinal distribution of salinity along the navigation channel. Vertical
scale in meters, and horizontal scale in computational grid i-index 176
6.46 - Location of the USGS station in Old Tampa Bay
(Schoellhammer, 1993) 180
6.47 - Wind speed and direction, and suspended sediment concentration at
USGS station during tropical storm “Marco” (Schoellhammer, 1993) 181
6.48 - Simulated significant wave height and period during tropical storm
“Marco” (October/1990) 182
6.49 - Simulated wave-induced bottom shear stress and suspended sediment
concentration at the USGS station for October 10 and 11, 1990 183
xii

6.50 - Simulated suspended sediment concentration at 6:00am -
October 11, 1990 184
7.1 - Water quality monitoring stations of the Hillsborough County
Environmental Protection Commission (EPC) (Boler, 1992) 189
7.2 - Measured near-bottom dissolved oxygen concentration (mg/L) in
Tampa Bay (June 1991) 190
7.3 - Measured near-surface dissolved oxygen concentration (mg/L) in
Tampa Bay (June 1991) 191
7.4 - Measured organic nitrogen concentration (mg/L) in
Tampa Bay (June 1991) 192
7.5 - Measured dissolved ammonium-nitrogen concentration (mg/L) in
Tampa Bay (June 1991) 193
7.6 - Measured nitrite+nitrate concentration (mg/L) in
Tampa Bay (June 1991) 194
7.7 - Measured chlorophyll-a concentration (pg/L) in
Tampa Bay (June 1991) 195
7.8 - Measured color (Pt-Co) in Tampa Bay (June 1991) 196
7.9 - Measured turbidity (NTU) in Tampa Bay (June 1991) 197
7.10 - Water quality zones in Tampa Bay used in the model simulations of the
summer of 1991 conditions 200
7.11 - Total organic nitrogen (dry weight %) in the surface sediments of
Tampa Bay during 1963 (Taylor and Saloman, 1969) 204
7.12 - Total Kjeldahl nitrogen (dry weight %) in Tampa Bay sediments,
1982-86 (Brooks and Doyle, 1992) 205
7.13 - Sedimentary nitrogen (dry weight %) in Hillsborough Bay
in 1986 (COT, 1988) 206
7.14 - Location of the NO A A sediment sampling stations in 1991 (phase 1) and
1992 (phase 2) (NOAA, 1994) 207
xm

7.15 - Total sediment nitrogen (dry weight %) obtained from NOAA
(1994) data. 208
7.16 - Dry density profile for water quality zone 1 in Tampa Bay
(Sheng etal., 1993). 209
7.17 - Water quality parameters after 30 days for a simulation using the lower
limit of the mineralization constant rate 221
7.18 - Water quality parameters after 30 days for a simulation using the higher
limit of the mineralization constant rate 222
7.19 - Near-bottom dissolved oxygen levels after 30 days for the mineralization
constant rate tests 223
7.20 - Near-bottom dissolved oxygen concentration in Tampa Bay for
June 26, after 30 days of simulation 226
7.21 - Near-bottom dissolved oxygen concentration in Tampa Bay for
July 26, after 60 days of simulation 227
7.22 - Near-bottom dissolved oxygen concentration in Tampa Bay for
August 25, after 90 days of simulation 228
7.23 - Near-bottom dissolved oxygen concentration in Tampa Bay for
September 24, after 120 days of simulation 229
7.24 - Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Hillsborough Bay 231
7.25 - Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Old Tampa Bay 232
7.26 - Model results and measured data for near-bottom DO at
EPC stations 70 and 8 233
7.27 - Model results and measured data for near-bottom DO at
EPC stations 73 and 80 234
xiv

7.28 - Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Middle Tampa Bay 236
7.29 - Model results for segment-averaged near-bottom DO (solid line),
segment maximum and minimum (dashed line), and the EPC
data inside Lower Tampa Bay 237
7.30 - Near-surface chlorophyll-a concentration in Tampa Bay for
June 26, after 30 days 240
7.31 - Near-surface chlorophyll-a concentration in Tampa Bay for
July 26, after 60 days 241
7.32 - Near-surface chlorophyll-a concentration in Tampa Bay for
August 25, after 90 day 242
7.33 - Near-surface chlorophyll-a concentration in Tampa Bay for
September 24, after 120 243
7.34 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Hillsborough Bay 245
7.35 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Old Tampa Bay 246
7.36 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Middle Tampa Bay 248
7.37 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Lower Tampa Bay 249
7.38 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
June 26, after 30 days of simulation 251
7.39 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
July 26, after 60 days of simulation 252
7.40 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
August 25, after 90 days of simulation 253
7.41 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay for
September 24, after 120 days of simulation 254
xv

7.42 - Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Hillsborough Bay 256
7.43 - Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Old Tampa Bay 257
7.44 - Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Middle Tampa Bay 258
7.45 - Model results for near-bottom segment-averaged Kjeldahl nitrogen
(solid line) and the EPC data inside Lower Tampa Bay 259
7.46 - Measured and simulated transport across the mouth of Hillsborough Bay,
along with the Kjeldahl nitrogen concentration (mean and standard
deviation) presented by Riñes (1991) 263
7.47 - Measured and simulated transport across the entrance of Tampa Bay,
along with the Kjeldahl nitrogen concentration (mean and standard
deviation) presented by Riñes (1991) 264
7.48 - Simulated nitrogen cycle for the summer of 1991 conditions:
(a) Loading, (b) biogeochemical processes in the water column,
(c) biogeochemical processes in the sediment column 268
7.49 - Near-bottom dissolved oxygen concentration in Tampa Bay, after
60 days of the load reduction simulation 272
7.50 - Near-surface chlorophyll-a concentration in Tampa Bay, after
60 days of the load reduction simulation 273
8.1 - Extent of seagrass meadows in Tampa Bay. (a) corresponding to 1943,
and (b) to 1983 (Lewis etal., 1985) 278
8.2 - Initial seagrass distribution in the computational grid. Dark areas indicate
seagrass meadows (100 gdw/m2) 281
8.3 - Simulated seagrass biomass in Tampa Bay 283
8.4 - Growth rate dependence on temperature 285
8.5 - Growth rate dependence on light 286
xvi

8.6 - Growth rate dependence on salinity 287
8.7 - Growth rate dependence on sediment nutrient concentration 288
8.8 - Simulated seasonal distribution of Thalassia 290
8.9 - Simulated Thalassia biomass in Tampa Bay for July 26,
after 60 days of simulation 297
8.10 - Simulated Halodule biomass in Tampa Bay for July 26,
after 60 days of simulation 298
8.11 - Simulated Syringodium biomass in Tampa Bay for July 26,
after 60 days of simulation 299
8.12 - Near-bottom light levels in Tampa Bay for July 26,
after 60 days of simulation 300
8.13 - Comparison between simulated light levels for the Present Condition
simulation (solid line) and the 100% Load Reduction (dashed line) 301
xvii

LIST OF TABLES
Table page
2.1 - Area of the subdivisions in Tampa Bay (Lewis and Whitman, 1985) 11
2.2 - Surface water discharges to Tampa Bay (Lewis and Estevez, 1985) 18
2.3 - 1991 annual average water quality of eight point sources discharging
into Tampa Bay (Boler, 1992) and (USGS, 1991) (mg/L) 23
2.4 - Mean annual total nitrogen loading into each segment of Tampa Bay
(Coastal, 1994) 26
4.1 - Description of the coefficients used in the water quality model 74
4.2 - Literature ranges and values of the coefficients used in the water
quality model 75
6.1 - The rms error (Erms) between measured and simulated
water surface elevation - September/90 121
6.2 - The distribution of tidal energy for water surface elevation -
September 1990 124
6.3 - Major tidal constituents in Tampa Bay - September/1990 127
6.4 - The rms error between measured and simulated bottom (b) and
surface (s) currents - September/1990 142
6.5 - The distribution of tidal energy for bottom (b) and surface (s) currents -
September 1990 146
6.6 - The rms error between measured and simulated salinity -
September 1990 156
6.7 - The rms error between measured and simulated water surface elevation
October/1990 and July/91 159
xviii

6.8 - The rms error between measured and simulated bottom (b) and
surface (s) currents - “Marco” Storm. 160
6.9 - The rms error between measured and simulated salinity - July/1991 165
7.1 - Estimated total suspended solids concentration (TSS), and calculated
water column partition coefficients for particulate organic nitrogen
(peon) and adsorbed ammonium (pean) 201
7.2 - Estimated dry density for the sandy zones of Tampa Bay 210
7.3 - Initial nitrogen concentration in the sediment (Ae) aerobic layer, and
(An) anaerobic layer for each water quality zone. (SON) soluble organic
nitrogen, (NH4) dissolved ammonium nitrogen, (N03) nitrite+nitrate 211
7.4 - Model coefficients in the (W) water column, (Ae) aerobic layer, and
(An) anaerobic layer for each water quality zone 211
7.5 - Parameters, baseline values, and range used in the sensitivity analysis 214
7.6 - Sensitivity tests description 215
7.7 - Sensitivity analysis results 217
7.8 - Nitrogen budget between July 1 and August 31, 1991 267
8.1 - Sensitivity tests description 291
8.2 - Simulated and reported seagrass biomass in the Tampa Bay area 294
xix


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
INTEGRATED MODELING OF THE TAMPA BAY ESTUARINE SYSTEM
By
Eduardo Ayres Yassuda
December 1996
Chairperson: Dr. Y. Peter Sheng
Major Department: Coastal and Oceanographic Engineering
Integrated modeling of the Tampa Bay Estuarine System is conducted in an attempt
to further the understanding of estuaries as integrated systems, and to provide quantitative
assessment of various management practices. The primary objective is to use models and
field data to produce a detailed characterization of the hydrodynamics and water quality
dynamics within the system. To test the hypothesis that seagrass is a bioindicator of the
overall health state of the estuarine system, a conceptual seagrass model is coupled to the
hydrodynamics and water quality models. The integrated model is then used to study the
effect of anthropogenic inputs to the estuarine system.
This study combines the enhanced versions of a 3-D hydrodynamics model (Sheng,
1989), a 3-D water quality model (Chen and Sheng, 1994), and a seagrass model (Fong and
Harwell, 1994) to simulate the circulation, transport, water quality, and seagrass dynamics
in Tampa Bay. The hydrodynamics component of this integrated model has been
successfully calibrated and verified using Tampa Bay data provided by the National Oceanic
xxi

and Atmospheric Administration (NOAA) and the United States Geological Survey (USGS).
The effects of hydrodynamics have been incorporated into the water quality model by using
the same grid spacing and time step, hence eliminating the need for ad-hoc tuning of
advective fluxes and dispersion coefficients. The water quality component has been tested
using monthly water quality data provided by the Hillsborough County Environmental
Protection Commission (EPC), although a more comprehensive data set is needed to fully
validate the water quality model. Results of previous statistical and mass-balance models
were used to determine the relevant biogeochemical processes, and to test causal
relationships among state variables. These simple models also proved to be useful tools for
calibration of the water quality model coefficients in the absence of process-specific data
(e.g., remineralization, nitrification, denitrification). Incident-light data provided by USGS
allowed the calibration of a light model of the MacPherson and Miller (1994) type. The
seagrass model has been used to investigate the ecological relationships between nutrient
loading, water quality dynamics, and the response of seagrass.
Once validated, this integrated model can be used to determine nutrient loading
reduction targets required to maintain and expand seagrass meadows in Tampa Bay.
Simulated load reduction scenarios indicate that water quality can respond quickly (within
2 months), while seagrass responds more slowly (more than 6 months) to load reduction.
Nevertheless, the results indicate that integrated modeling is a viable approach to provide
quantitative assessment of various management practices for restoring estuarine systems.
XXII

CHAPTER 1
INTRODUCTION
Background
Historically, an estuary has been defined as “a semi-enclosed coastal body of water
which has a free connection with the open sea and within which the sea water is measurably
diluted with fresh water derived from continental drainage” (Cameron and Pritchard, 1963 -
p. 306). In order to assess environmental problems along the entire coastal zone, the
classical definition of estuary was revised by the National Research Council (1977) to
include not only the estuary from the classical definition, but also all coastal environments
characterized as transitional zones. Following this new definition, an estuarine system
comprises bays, coastal lagoons, inlets, deltas, and salt marshes; all affected by different tidal
regimes and freshwater discharges.
In an estuarine system, the region characterized by accentuated gradients of some
specific properties is defined as the mixing zone (Harleman, 1971). It is usually located
between two stable zones, the freshwater and the oceanic ecosystems, wherein these
properties are treated as “reservoirs,” with relative slower temporal variations.
Salinity is the primary physical property that presents a markedly longitudinal
gradient. Upstream from the tidal portion of the river, salinity is usually constant and nearly
1

2
equal to zero. In the coastal zone beyond the region of freshwater influence, salinity is equal
to the “oceanic reservoir” condition.
In a cross-section, the mixing zone reveals important vertical gradients. The most
evident is the intertidal zone, which is periodically flooded and exposed. In the intertidal
zone, there may be salt marshes, mangroves, beaches, and oyster banks. To overcome the
stresses originated by flood and dry conditions, organisms living in this zone have developed
special adaptations. Human presence is visible through structures like seawalls, piers, and
harbors.
According to Day et al. (1989), a second important vertical gradient is light
attenuation, going from a lighted, euphotic zone to a light depleted, aphotic zone. Where the
euphotic zone reaches the bottom, submerged aquatic vegetation like seagrasses is able to
thrive. Usually, water clarity also increases towards the ocean side. Another extremely
important gradient for biogeochemical processes is the redox potential in the sediment layer,
ranging from oxidized to reduced conditions. In a healthy estuarine system, the water
column is usually aerobic, but the bottom sediments become anaerobic in a very short
distance (order of few centimeters) from the water-sediment interface.
Water Quality Modeling
The primary requirement in any estuarine water quality modeling is a thorough
understanding of the circulation and transport processes. Differently from freshwater
systems, where uni-directional flow and steady-state conditions may be applied in a variety

3
of cases, estuaries are complex systems where the circulation dynamics are driven by tides,
wind, river discharges, waves, Coriolis force, and density gradients, which give the estuarine
circulation an unsteady, multi-dimensional character. The baroclinic effect in estuarine
circulation has been studied by various investigators, including the classical works of
Pritchard (1956), Cameron and Pritchard (1963), and Hansen and Rattray (1965).
Weisberg and Williams (1991) demonstrated that horizontal salinity gradients in
Tampa Bay are capable of creating a density-driven circulation, through the generation of a
baroclinic forcing. Galperin et al. (1991) refuted the barotropic residual circulation pattern
obtained by Goodwin (1987) and Ross et al. (1984) in Tampa Bay, showing that when
baroclinic effects are included, the residual circulation changed substantially.
Models with a limited resolution (spatial and time scales) are useful tools to depict
a general trend in the overall circulation pattern or to study the response of the system to a
specific forcing mechanism. However, estuarine processes are not in steady state, and they
often present a three-dimensional distribution. Biogeochemical and ecological processes
occurring inside an estuarine system are primarily driven by physical factors with an
unsteady, multi-dimensional character. To implement an integrated hydrodynamics, water
quality and ecological model, it is essential to fully understand the coupling among the
hydrodynamics, water quality and ecological processes.

4
Integrated Modeling Approach for Estuarine Systems
Competitive demands for natural resources in estuarine systems can lead to a serious
deterioration of the environment. Solutions to environmental problems have been attempted
by resources management agencies to support a holistic approach to environmental
management. For example, the Florida Department of Environmental Protection has been
emphasizing that ecosystem management is an integrated, flexible approach to manage
Florida's biological and physical environment.
An efficient strategy to prevent or reverse the degradation of important estuarine
systems makes use of numerical models in conjunction with monitoring programs. Through
monitoring, not only the present state of the system can be obtained, but it is also possible
to evaluate the effectiveness of past management efforts.
Numerical models can be used to study management options and the corresponding
response of the system. In estuarine systems, numerical models can be applied to study the
hydrodynamics, sediment dynamics, water quality dynamics and system ecology.
Hydrodynamics and sediment dynamics models have been significantly advanced
during the past decade (e.g., Sheng, 1994). The developments in numerical techniques and
computer technology have been fully capitalized. Also, advancement in instrumentation and
basic understanding has led to the development of process-based models rather than
empirical lumped-process models.
On the other hand, applications of traditional water quality models (e.g., Ambrose et
al., 1994) are often based on coupling the hydrodynamics and water quality dynamics on an

5
intertidal basis (Le., tidally averaged). This simplification was supported by high
computational cost of robust multi-dimensional models and the large time scale of the
kinetics in water quality models. But, by doing so, several hydrodynamic processes (e.g.,
wave actions) and sediment dynamics (e.g., resuspension, deposition) which can significantly
affect the water quality dynamics are not accurately represented. Chen and Sheng (1994)
developed a coupled hydrodynamics-sediment-water quality model and applied it to Lake
Okeechobee. A coupled hydrodynamics-water quality model has been used to study the
response of Chesapeake Bay to various loading scenarios (Chesapeake Bay Program, 1994).
The primary prerequisite in the implementation of a reliable water quality model is
the development of a budget for the specific pollutant of interest. In the case of Tampa Bay,
where eutrophication is one of the issues of greatest concern, nutrient loading levels have to
be defined. To develop a nutrient budget it is essential to quantify the sources of (Sheng et
al, 1993): (i) external nutrient loading from tributaries and non-point sources, (ii) nutrient
fluxes into and from the connecting ocean, and (iii) benthic nutrient fluxes. The most
difficult source to quantify is the benthic flux, due to measurement techniques, and the
competing influences of molecular diffusion, resuspension, and groundwater seepage.
Consequently, it is common to find nutrient budgets that consider the net benthic flux to be
simply the difference between the external loading and flux to the ocean. However, the
oceanic flux, induced primarily by tidal forcing is also difficult to estimate; hence,
subtracting tidally-averaged oceanic flux from the external loading may not give the correct
benthic flux. Results of McClelland (1984) nutrient box model of Tampa Bay shows that
nitrogen benthic flux can be as much as twice the external loading of point and non-point

6
sources. The author suggested that the supply of nitrogen through sediment resuspension and
biogeochemical reactions in the water column are likely important. Results of Johansson and
Squires (1989) nutrient budget for Tampa Bay suggest that the internal loading of nitrogen
associated with sediment resuspension events can be quite significant.
Ecological models are the primary tool in developing an overall picture of the system.
Using energy flow and Emergy concept (Odum, 1994), it is possible to identify the main
forcing functions that drive the system, and the causal relationships between state variables.
The conflicts between the “apparently” adversarial uses of an estuarine system can be better
mediated when they are evaluated on a common measure. System ecology models can be
used to connect environmental products with human use. The Emergy of the system
measures both the work of nature and that of humans in generating products and services.
By selecting choices that maximize Emergy production and use, policies and judgments can
favor those environmental alternatives that maximize real wealth, the whole economy, and
the public benefit (Odum, 1971).
In estuarine systems where seagrass has declined due to anthropogenic effects,
restoration of seagrass beds can be linked exclusively to environmental quality. In this sense,
seagrass provides a more direct assessment of the restoration processes (Dennison et al.,
1993). Seagrasses serve as habitat for fish and benthic invertebrates. Seagrass leaves provide
substrate for many epiphytic organisms. Herbivores such as manatees, fishes, sea turtles, and
sea urchins graze directly on seagrass blades. Dead leaves can constitute the majority of the
detritus pool. Seagrass also interacts with the physical components of the estuary by slowing
down the currents and enhancing the deposition of organic and inorganic material from the

7
water column. Their presence also inhibit the resuspension of sediments, which also affects
the nutrient cycles. Therefore, seagrass is a crucial indicator of the state of the estuary.
Objectives
Recognizing the important relationships among the various ecological components
(including hydrodynamics, sediment dynamics, water quality, aquatic vegetation, etc.), it is
now appropriate to take advantage of the advancement in computer resources and scientific
understanding to integrate models with multiple dimensions, more robust and coupled
processes. The purpose of this effort would be to further the understanding of estuaries as an
integrated system, and to provide a quantitative evaluation of various management practices.
The goals of this study are to develop a comprehensive model of the Tampa Bay
Estuarine System, and to produce a detailed characterization of the hydrodynamics and water
quality dynamics within the system. In order to test the hypothesis that seagrass is a
bioindicator of the overall health state of the Tampa Bay Estuarine System, a conceptual
seagrass model is coupled to the hydrodynamics and water quality models. This integrated
model will then be used to provide mechanisms for relating anthropogenic inputs to the
overall health of the estuary. The following questions have to be addressed in order to
accomplish these goals:
1) How important are the three-dimensional characteristics of the estuarine
circulation in the overall dynamics of the system?
2) What are the most important environmental parameters and biogeochemical
processes in the water quality dynamics of the estuarine system?
3) Can the integrated modeling provide a quantitative assessment of various
management practices for restoring the estuarine system?


CHAPTER 2
TAMPA BAY CHARACTERIZATION
Tampa Bay, classified as a subtropical estuarine system (Lewis and Estevez, 1988),
is the largest coastal plain estuary in the state of Florida. It is located on the west central part
of the Florida peninsula, between coordinates 27° 30'and 28" 02'N, and 82" 20'and
82" 50'W. The Y-shaped bay is approximately 60 km long, 15 km wide, covering
approximately 1,000 km2, and having a shoreline 1450 km long (Lewis and Whitman, 1985).
It is a highly complex system composed of numerous basins and subdivisions (Figure 2.1).
Some of them (e.g. Hillsborough Bay) are bordered by highly industrialized and urbanized
areas and others are bordered by mangroves, bayous, and seagrasses (e.g. Boca Ciega Bay).
Table 2.1 shows the morphometric features of each subdivision (Lewis and Whitman, 1985).
Major anthropogenic modifications that have altered the natural evolution of the system are
the four causeways (Sunshine Skyway Bridge, Courtney-Campbell Parkway, W. Howard
Frankland Bridge, and Gandy Bridge), an extensive network of dredged channels, turning
basins, and spoil islands.
9

10
Mobbly
Bay
Hillsborough River
Safety]
Harbor
Courtney
j City of
Clearwater
) Inter- J
bay (,
Peninsula
Alalia River
The It Narrows
City of
St. Petersburg
) < Dredged
¡I Channels
II M
// 7
Cockroach
Bay
Egmont
Key
Manatee River
AnriaV
Maria \
Island
City of
Bradenton
City of
Tampa
McKay Bay
East Bay
Little Manatee River
Subdivisions of Tampa Bay
( •— Demarcation Line)
1. Old Tampa Bay
2. Hillsborough Bay
3. Middle Tampa Bay
4. Lower Tampa Bay
5. Boca Ciega Bay
6. Terra Ceia Bay
7. Manatee River
8. Anna Maria Sound
Bishops
Harbor
Figure 2.1 - Tampa Bay Estuarine System subdivisions as defined by Lewis and Whitman
(1985) (from Wolfe and Drew, 1990).

11
Subdivision
Area (km2)
Old Tampa Bay
201
Hillsborough Bay
105
Middle Tampa Bay
310
Lower Tampa Bay
247
Boca Ciega Bay
93
Terra Ceia Bay
21
Manatee River
55
Total
1032
Climate
The Tampa Bay Estuarine System is located in a zone of transition between a
temperate continental climate and a tropical Caribbean one (Lewis and Estevez, 1988). The
climate of the Tampa Bay area generally consists of a warm humid summer and a relatively
dry cool winter. Lewis and Estevez (1988) suggested three weather regimes for the Bay: the
warm, dry period between late April to mid-June, the warm, wet period during summer and
early fall, and the dry cold period between November to April. Based on four decades of
records, the mean annually averaged temperature in Tampa Bay is 22.3 °C, with a low mean
of 16.0 °Cin January and a high mean of 27.8 °C in August (Lewis and Estevez, 1988).
Annual variation in water temperature ranges from 16 to 30 °C, with a vertical stratification
of no more than 2 °C(Boler, 1992).

12
Tides
Tides and currents in the Gulf of Mexico are classified as mixed type, with K,, Oj,
and P, the major diurnal and M2 and S2 the major semi-diurnal components. The strong
diurnal components are attributed to the interaction between co-oscillating tides propagating
from the Florida Straits and Yucatan Channel and the natural frequency of the Gulf of
Mexico basin. The average tidal range is 0.67 m, while typical current speeds range from
1.2 to 1.8 m/s at the entrance (Egmont Channel), to much smaller values in the upper reaches
of the Bay (NOAA, 1993). The tidal wave takes approximately three hours to travel from
the mouth to the upper reaches of Hillsborough Bay, and approximately 4 hours to upper Old
Tampa Bay. Harmonic analysis of year-long tidal records at St. Petersburg (NOAA, 1993)
yielded amplitudes of 37 constituents, which indicated that the shallow water components
are relatively small, and overtides are not significant in the overall circulation pattern of the
Bay.
Salinity Distribution
As in any other typical estuarine system, Tampa Bay generally exhibits significant
horizontal gradients in salinity. The higher salinity values in the adjacent Gulf of Mexico
fluctuate around 36 ppt, whereas the lowest salinity levels occur near the mouth of creeks and
rivers. Generally, the salinity distribution follows the annual precipitation pattern (Boler,
1992). Higher salinity tends to extend further up into the Bay during the dry winter and

13
spring, and the entire Bay becomes less saline, specially in the upper parts, during the wet
summer and fall. Vertically, salinity generally shows a homogeneous profile, with vertical
difference rarely exceeding 2 ppt.
Rainfall
Mean annual precipitation is approximately 140 cm (Heath and Connover, 1981),
which on an annual basis balances with evapotranspiration (Palmer, 1978). Dry season rains
vary from 5 to 6.5 cm per month. Wet season rainfall is much more variable, both
temporally and spatially, ranging from 13 to over 20 cm (Palmer, 1978). Figure 2.2
illustrates the monthly rainfall pattern for Tampa Bay.
Wind
The annual average wind speed is 3.9 m/s from the east. The four seasonal wind-field
patterns are shown in Figure 2.3. In the winter months, the easterly trade winds dominate
the region south of latitude 27° N, while the westerlies dominate the area north of latitude 290
N. Spring and Summer generally exhibit more southerly winds, and Fall is characterized by
easterly or northeasterly winds. Wind speed can exceed 10 m/s during the passage of winter
storms or during summer squalls, hurricanes and tornadoes (Wolfe and Drew, 1990).

14
Historical Monthly Rainfall in Tampa Bay
Figure 2.2 - Monthly rainfall in Tampa Bay (Wooten, 1985).

15

16
Bathymetry
Tampa Bay is a relatively wide and shallow estuarine system, with an average depth
of 3.7 m (Goodwin, 1987). Depth generally does not exceed 10 m, except along the 96-km-
long navigational channel, which has been dredged to about 15 m. The navigational channel
extends parallel to the shorelines from the mouth to the upper reaches of Middle Tampa Bay,
where it splits into two branches, one connecting to the Port of Tampa in Old Tampa Bay,
and the other one entering Hillsborough Bay.
Freshwater Inflow
Unlike other well-studied estuarine systems in the U.S. (e.g. Chesapeake Bay,
Delaware Bay, etc.), Tampa Bay is not associated with any large river. All tributaries
flowing into Tampa Bay originate in the Florida peninsula, and therefore are relatively small
(Figure 2.4). The Bay receives drainage from a watershed that covers approximately 5700
km2, which delivers an average annual discharge of about 63 m3/s (Lewis and Estevez,
1988). The analysis of existing and historical freshwater inflows to Tampa Bay (Coastal,
1994) demonstrated that inflows have not changed significantly in the past fifty years.
Table 2.2 shows the historical average discharge values for seven rivers or streams
flowing into Tampa Bay. The primary source of freshwater are the four major tributaries
(Hillsborough River, Alafia River, Little Manatee River, and Manatee River) which supply
about 70% of the total discharge. It has been estimated that Hillsborough Bay receives 63
to 77% of the total freshwater inflow to Tampa Bay (Lewis and Estevez, 1988).

17
Figure 2.4 - Tampa Bay watershed (Wolfe and Drew, 1990).

18
Table 2.2 - Surface water discharges to Tampa Bay (Lewis and Estevez, 1985)
River
Period of Record
(years)
Average annual
discharge (m3/s)
Hillsborough River
39
17.0
Alafia River
45
14.0
Little Manatee River
38
6.0
Manatee River
11
11.0
Rocky Creek
24
1.3
Lake Tarpon Canal
3
0.8
Sweetwater Creek
26
0.6
Others
-
12.3
Total
63.0
Hillsborough River
Draining a highly urbanized area, the Hillsborough River watershed collects the
discharge from most of Tampa, Temple Terrace, the eastern Interbay Peninsula, and Davis
Island. A dam constructed in 1945 (approximately 16 km from the mouth of the river in
Hillsborough Bay) separates two distinct water quality and hydrological environments:
upstream of the dam, the river is a freshwater reservoir, which provides freshwater to the
City of Tampa; and downstream of the river proper, which is tidal and brackish. Freshwater
discharges are controlled by the dam and range from 3.5 m 3/s in the dry season to 48 m 3/s
during the wet season, averaging 17 m3/s (Dooris and Dooris, 1985). Tidal action can be
found at 16 km upstream the mouth (Wolfe and Drew, 1990). The salt wedge can penetrate
as far as 13 km into the river during low-flow conditions (< 3 m3/s), or it can be flushed
downstream to near 4 km from the mouth when the flow exceeds 25 m 3/s (Wolfe and Drew,

19
1990). Low flow rates and upstream salt wedge location seem to be well correlated with low
dissolved oxygen (DO) value and high nutrient concentrations inside the Hillsborough River.
A report from the Hillsborough County Environmental Protection Commission (EPC) (Boler,
1992) shows DO levels in the bottom saltier layer inside Hillsborough River below 4.0 mg/L,
with lowest values (< 2.0 mg/L) in May and June when flow is minimal. Surface values of
DO are generally above saturation (7.9 mg/L). BOD is reported to be less than 2.0 mg/L
throughout the year.
Ammonia and nitrate concentrations generally show a well mixed vertical distribution
upstream the salt wedge location, where the saltier water contains higher concentrations,
specially ammonia. Combined ammonia and nitrate values in the river range from 0 to 0.7
mg/L. In the dry season ammonia concentrations vary from 0.05 mg/L close to the dam to
0.2-0.3 mg/L towards the Bay. Nitrate concentrations vary from zero to 0.4 mg/L, and
organic nitrogen ranges from 0.38 to 5.60 mg/L (Wolfe and Drew, 1990).
Alafia River
The Alafia River watershed drains about 105 km2, south of the Hillsborough River
watershed. Flow in the Alafia River averages 14 m 3/s and ranges from 5.4 m 3/s in the dry
season to 28.3 m3/s during the wet season (Dooris and Dooris, 1985). Tidal action is
present up to 18 km upstream from the mouth. Johansson and Squires (1989) found that the
Alafia River, a major source of dissolved material to the Bay, can supply 51% of the Bay’s
phosphate uptake for phytoplankton growth, and sediment flux rates are sufficient to meet
140% of the uptake. The authors attributed the high phosphate concentrations to leaching

20
of Florida’s phosphate beds, fertilizer drainage from agricultural lands, and industrial and
sewage inputs. Phosphate concentration ranges from 4.8 mg/L in the upper reaches of the
river, decreasing to 1.2 mg/L near the Bay (Wolfe and Drew, 1990).
The salt wedge penetration depends on the river discharge and tidal regime, ranging
from 16 km during high tide and low flow condition to 4 km during low tide high flow
situation (Giovanelli, 1981).
Dissolved oxygen exhibits a vertical stratification near the mouth, ranging from
below 4.0 mg/L at middle and bottom layers to saturation levels (7.9 mg/L) at the surface
(Boler, 1992), where chlorophyll-a averages 24.1 pg/L.
The Alafia River tributaries exhibit high levels of nutrients. The poor water quality
in the North Prong is due to mining activities, and a greater number of phosphate and
chemical dischargers (Wolf and Drew, 1990). High levels of ammonia can reach as much
as 85-120 mg/L, and nitrate values as high as 3.0 mg/L. Dissolved oxygen remains below
5 mg/L 50% of the time.
Little Manatee River
The Little Manatee watershed is the least urbanized of the four major rivers, and it
generally exhibits the best water quality conditions (Flannery, 1989). Flow averages 6 m Vs
and ranges from 1.7 m Vs in the dry season to 17 m Vs during the wet season (Dooris and
Dooris, 1985). Tidal action is found up to 25 km upstream the mouth (Wolfe and Drew,
1990). Salinity close to the mouth averages 9.0 to 12.0 ppt (EPC, 1984). Flannery (1989)
presented some water quality data for a station 25 km upstream from the mouth, which

21
showed the following average concentrations: 0.63 mg/L of nitrate+nitrite, 0.09 mg/L of
ammonia, 1.3 mg/L of BOD, 0.60 mg/L of organic nitrogen, and 7.0 mg/L of DO.
Manatee River
The Manatee River is impounded 38 km upstream from the Bay. Downstream of the
dam, the Manatee River and its major tributary, the Braden River, collect drainage from the
cities of Palmetto and Bradenton before discharge into the Bay. Flow averages 11 m 3/s and
ranges from 1 m 3/s in the dry season to 25 m 3/s during the wet season (Dooris and Dooris,
1985). Tidal action is present up to 31 km upstream from the mouth. Nutrient levels are
high and generally decrease from the dam to the river mouth (Wolfe and Drew, 1990).
Salinity ranges from 14 to 26 ppt in the dry season to 2 to 19 ppt during the wet season (Heyl,
1982). Close to the mouth, dissolved oxygen levels are low during summer months, ranging
from 2.0 to 4.0 mg/L. Concentrations of total nitrogen, mostly in the organic nitrogen form,
varies between 0.1 to 4.4 mg/L (Heyl, 1982).
Rockv Creek
The Rocky Creek drainage area is approximately 115 km2. The discharge 9.5 km
upstream from the river mouth averages 1.3m3/s, ranging from 6.9 (wet season) to
0.05m3/s (dry season) (USGS, 1991). In its upper reaches, water quality is generally good
with pockets of high concentrations of ammonia and total phosphorus (Wolfe and Drew,
1990). Dissolved oxygen is usually below saturation.

22
Lake Tarpon Canal
The Lake Tarpon Canal is a man-made canal which was completed in 1971 to control
flooding. A saltwater-barrier/flood-control structure is located midway between Lake Tarpon
and Old Tampa Bay. Discharges from the canal average 0.8m3/s, ranging from 22m3/s
in wet season to no flow in dry season (USGS, 1991). DO levels are usually high (7.0 to 8.0
mg/L) in the canal, pH is neutral (7.0), and nutrient concentrations are low (Dooris and
Dooris, 1985).
Sweetwater Creek
Sweetwater Creek is 17 km long and drains about 65 km2 of a primarily urban region.
The discharge at 6 km upstream from the river mouth averages 0.6m3/s, with a range
between 4.4 (wet season) to 0.03 m 3/s (dry season) (USGS, 1991). In the tidal portion of the
creek, DO (3.7 mg/L), BOD (6.0 mg/L), and nutrient concentrations (Ammonia
concentration ranging from 0.1 to 0.4 mg/L) indicate poor water quality (Wolfe and Drew,
1990).
Non-Point Sources
Coastal, Inc. (1994) developed a statistical model for the Tampa Bay National
Estuary Program (TBNEP) to support the preparation of the “Pollutant Load Reduction
Goals” (PLRG) for total nitrogen, total phosphorus, and total suspended solids for Tampa
Bay. They used measured data to develop regression relationships to describe the response
of the watershed to flow and loadings from non-point surface water sources, given a set of

23
rainfall and land use conditions. Results of that study indicate that non-point sources can
have a significant contribution to the total nutrient loading. Moreover, the study showed that
groundwater and nutrient inflow to Tampa Bay represent a smaller fraction of the total
loading. Table 2.3 summarizes the water quality of the seven point sources discharging into
Tampa Bay.
Table 2.3 -1991 annual average water quality of seven point sources discharging into Tampa
Bay (Boler, 1992) and (USGS, 1991) (mg/L).
River
Near-Bottom
Dissolved
Oxygen
Soluble
Organic
Nitrogen
Ammonium
Nitrogen
Nitrate
+
Nitrite
Hillsborough River
5.0
0.66
0.07
0.04
Alafia River
4.3
0.68
0.06
0.36
Little Manatee River
5.3
0.75
0.05
0.11
Manatee River
7.1
0.52
0.01
0.08
Rocky Creek
3.0
0.93
0.07
0.02
Lake Tarpon Canal
4.4
0.89
0.10
0.04
Sweetwater Creek
4.7
0.85
0.14
0.35
Nutrients Distribution and Loading
Tampa Bay has high phosphate levels in both water column and sediment layer,
especially in Hillsborough Bay. Tiffany and Wilkinson (1989) reported that 20% of world’s
phosphate production and 80% of all United States phosphate output take place in the area.
Approximately 50% of all tonnage leaving Tampa Bay is composed of phosphate related

24
products. The mean annual water column phosphate concentration in Hillsborough Bay can
be as high as 1.28 mg/L (Fanning and Bell, 1985).
Nitrogen, however, is probably the single most important macro nutrient that limits
primary production in Tampa Bay. Assuming that phytoplankton assimilates N and P in
proportion to the Redfield C:N:P atomic ratios of 106:16:1, if N:P is higher than 16, the
system is primarily phosphorus limited. Otherwise, the system is considered to be nitrogen
limited. Fanning and Bell (1985) reported that the N:P ratio in Tampa Bay ranged from 0.3
to 1.3 in 1981, and concluded that phytoplankton have been historically nitrogen limited.
According to Simon (1974), municipal sewage treatment plants are the primary
source of nitrogen to Tampa Bay. The Alafia River provides the highest annual loading of
nitrate to Tampa Bay (about 3.9 x 105 kg/yr), followed by the Manatee and Hillsborough
Rivers (each about 9.0xl04 kg/yr). In terms of organic nitrogen, the Manatee and Alafia
Rivers have the highest loadings ( 2.5 x 105 kg/yr), followed by the Hillsborough River
with 2.0 x 105 kg/yr (Dooris and Dooris, 1985). High levels of organic nitrogen in the
Manatee River have been related to the Bradenton sewage treatment plant and pulp effluent
from citrus processing plant (DeGrove, 1984). McClelland (1984) reported municipal
sewage treatment plants elsewhere around the Bay as significant nitrogen sources. Goetz and
Goodwin (1980), summarizing data collected between 1972 to 1976, obtained a mean
organic nitrogen concentration ranging from 0.5-1.0 mg/L in Old Tampa Bay, around 0.5
mg/L in upper Tampa Bay, and the same level or below in the Lower Bay. In all three areas,
seasonal and year-to-year variation was low. On the other hand, mean organic nitrogen
concentration in Hillsborough Bay ranged from 0.75 to 1.25 mg/L, and temporal variation

25
was greater. Nitrite and nitrate concentrations were similarly low and steady everywhere in
the Bay, except in Hillsborough Bay. Ammonia levels were variable in all zones. Seasonal
minima were less than 0.1 mg/L in most places but more than 0.1 mg/L in Hillsborough Bay.
Fanning and Bell (1985) reported a mean ratio of ammonia to inorganic nitrogen of 0.84
(ranging from 0.54 to 0.99) in Hillsborough Bay. Seasonality was evident for total inorganic
nitrogen, which decreases substantially after rainy seasons, without an apparent reason
(Lewis and Estevez, 1988).
In a preliminary nitrogen budget for Tampa Bay, Ross et al. (1984) suggested a
nitrogen storage of 3.87 x 107kg, an input from rainfall and anthropogenic sources of
21,470 kg/day, and a benthic release of 55,750 kg/day. Exports would occur in tidal
exchange (16,100 kg/day), biological losses (8,140 kg/day), and benthic uptake (53,000
kg/day). Fanning and Bell (1985) estimated a turnover rate for nitrate and nitrite of 42 days,
due to runoff, and that benthic releases of ammonia could replace the overlying ammonia in
14 days.
Coastal, Inc. (1994) developed estimates of total nitrogen, total phosphorus, and total
suspended solids loading, as well as total freshwater inflow, to Tampa Bay. Two scenarios
(existing and “benchmark” conditions) were presented for the major seven segments of the
Bay. In order to account for ungaged areas, the Coastal, Inc. study used a statistical model
that related watershed characteristics to streamflow. Table 2.4 summarizes the mean annual
total nitrogen loading into each segment of Tampa Bay.

26
Table 2.4 - Mean annual total nitrogen loading into each segment of Tampa Bay (Coastal,
1994).
Bay Segment
Loading (tons/year)
Old Tampa Bay
600
Hillsborough Bay
2100
Middle Tampa Bay
1100
Lower Tampa Bay
500
Boca Ciega Bay
300
Terra Ceia Bay
80
Manatee River
600
Sediment Type and Distribution
Goodell and Gorsline (1961) studied the surface sediments composition and
distribution from all major areas of the Bay. They reported that Tampa Bay sediments are a
mixture of eroded quartz sands from Pleistocene terrace deposits and carbonates from shell
fragments produced within the system. The present sediment distribution is related to tide
generated currents, while sedimentary types correspond with bathymetric features. In sand
and grass flats less than 2 m deep, mean grain size was determined as 0.132 mm and
sediment was 2.7% carbonate. In deeper natural channels (> 6 m), mean grain size was 0.241
mm and sediment was 25.2% carbonate, whereas mangrove areas contained no carbonate.
Mean grain size decreased from 0.218 mm at the mouth to 0.109 mm at the upper reaches
of the Bay. Mean carbonate content decreased from 16% to 2% over the same distance.

27
Figure 2.5 shows the surface sediment distribution for Tampa Bay. According to Johansson
and Squires (1989), the descriptive work of Goodell and Gorsline (1961), conducted thirty
five years ago, did not intend to map fine grained sediments specifically, so the areal
coverage of these sediments was not well defined as the mud zone delineated in later studies.
Figure 2.6 shows the mud zones in Hillsborough Bay delineated by the Bay Study Group of
the City of Tampa Sanitary Sewer Department in 1986.

GuH oi Mexico
28
I
82P 30'
Hillsborough River
City of
Tampa
P Inter- ¿,
Bay \
Peninsula
Pinellas
Peninsula
Alafia River
City of
St. Petersburg
Uttfe Manatee River
Manatee River
28° 00
27° 30
Very coarse-coarse sand MHU
Fine sand
mm Medium sand
Very fine sand
Figure 2.5 - Surface Sediments in Tampa Bay (Goodell and Gorsline, 1961).

29


CHAPTER 3
THE CIRCULATION AND TRANSPORT MODEL
Previous Work
Circulation and sediment transport models for estuaries have been significantly
advanced during the past 30 years. Sheng (1994) provided a comprehensive review on
circulation models for shallow waters. Sheng (1986) and Sheng et al. (1991) presented
comprehensive reviews of sediment transport models for estuaries and lakes.
Circulation in Tampa Bay has previously been modeled by Ross et al. (1984),
Goodwin (1987), Galperin et al. (1991), Sheng and Peene (1992), Peene et al. (1992), and
Hess (1994). The Ross et al. (1984) modeling system consisted of an integrated set of a 2-D
vertically-averaged circulation model, and box models for water quality and particulate
transport. Goodwin (1987) used a 2-D vertically-averaged model to study the effects of the
dredged navigation channel and dredged disposal sites on the circulation of Tampa Bay. The
residual circulation obtained from both studies (Ross et al., 1984 and Goodwin, 1987)
showed a complex pattern of numerous gyres, that were assumed to be responsible for poor
flushing conditions. Galperin et al. (1991) demonstrated that the barotropic residual
circulation pattern, obtained by Ross et al. (1984) and Goodwin (1987) in Tampa Bay, can
be completely overwhelmed by baroclinic effects. The baroclinic residual circulation
31

32
obtained by Galperin et al. (1991) exhibited a classical two-layer flow, with the surface layer
flowing out of the Bay and the saltier bottom layer flowing into the Bay. Sheng and Peene
(1992), studying the circulation and transport in Sarasota Bay, used a coarse grid (grid
spacing on the order of 1 to 2 km) to describe the circulation in Tampa Bay. Tampa Bay was
added to the Sarasota Bay grid of that study to evaluate the importance of Manatee River
discharge on the residual circulation of Anna Maria Sound. Peene et al. (1992) simulated
the tide- and wind-driven circulation in the Sarasota and Tampa Bay system during the
passage of Tropical Storm Marco in October 1990 using an earlier version of the three-
dimensional boundary-fitted grid model used in this study. Hess (1994) developed a three-
dimensional orthogonal curvilinear model with seven sigma grid layers for Tampa Bay,
based on the Princeton University ocean model (Blumberg and Mellor, 1987). The main
goals of Hess (1994) were to update the NOAA tidal current atlas for Tampa Bay, and to
synthesize the extensive observational data set obtained during the survey performed by
NOAA in 1990-91.
The three-dimensional hydrodynamics model CH3D (Sheng, 1989) forms the basis
of the numerical simulations in this study. The model framework has been improved and
modified from earlier versions (e.g., Sheng, 1989; Sheng et al., 1991; Sheng and Peene,
1992) in order to develop an integrated model that couples hydrodynamics, sediment and
water quality dynamics. The application (model setup, calibration, and validation) of the
circulation and transport model to produce a detailed characterization of the hydrodynamics
within system constituted the most important step in the development of the integrated model
of the Tampa Bay Estuarine System. Within the scope of this dissertation, the complete

33
details of model equations in the curvilinear boundary-fitted and sigma coordinates are of
secondary interest, and are therefore presented in Appendix A.
Circulation Model
The governing equations that describe the velocity and surface elevation fields in
shallow water are derived from the Navier-Stokes equations. In general, four simplifying
approximations are applied. First, it is assumed that the water is incompressible, which
results in a simplified continuity equation. Second, based on the fact that the characteristic
vertical length scale is much smaller than the horizontal counterpart, i.e., H /L « 1, the
vertical velocity is small and the vertical acceleration may be neglected. Hence, the vertical
momentum equation is reduced to the hydrostatic pressure relation. Third, with the
Boussinesq approximation, an average density can be used in the equations except in the
buoyancy term. Finally, the eddy-viscosity concept, which assumes that the turbulent
Reynolds stresses are the product of mean velocity gradients and “eddy viscosities”, is
employed. In the transport equation, this concept means that the turbulent mass fluxes are
the product of mean concentration gradients and “eddy diffusivities”.
With the above assumptions, the basic equations of motion in a right-handed
Cartesian coordinate system (x, y, z) are as follows:
Continuity Equation
du + dv + dw
dx dy dz
(3.1)

34
X-component of Momentum Equation
du
dt
+
+
duv duw r 1 dp
+ = fv — +
By dz p0 dx
_a_
' du'
d
4-
A —
dy
' ay J
dz
V A,
( dz /
(3.2)
Y-component of Momentum Equation
dv
dt
+
+
dvv <3vw r 1 dp
+ = -fu —
dy dz p„ dy
d
L *}
d
4.
( 3 \
A §V
dy
{' "Syl
dz
( dz /
dx
dv
dx
(3.3)
Hydrostatic Pressure Relation
(3.4)
where (u, v, w) are mean fluid velocities in the (x, y, z) directions, p is pressure, g is the
Earth’s gravitational acceleration, po is a reference fluid density, p(x,y,z) is the fluid density,
and/is the Coriolis parameter. AH and Av are the horizontal and vertical turbulent eddy
viscosity coefficients, respectively.

35
Salinity Equation
In Cartesian coordinates, the conservation of salt can be written as:
dS | d(uS) + d(vS) + d(wS)
dt dx dy dz
D
H
35
dx
d ( t, ds)
+ d ( n ds)
+ — Dv —
V dz j
(3.5)
where 5 is the salinity, DH and Dy are the horizontal and vertical turbulent eddy diffusivity
coefficients, respectively.
Since the length scales of horizontal motion in estuarine systems are much greater
than those of vertical motion, it is common to treat the vertical turbulence and horizontal
turbulence separately. It has been shown (e.g. Sheng et al, 1995) that in shallow estuaries,
the effect of the horizontal eddy viscosities on circulation is much smaller than the effect of
the vertical one. In the model, the horizontal turbulent mixing, which describes the effect
of sub-grid scale motion, is represented by a constant diffusion coefficient.
Vertical turbulent mixing is an important process which can significantly affect the
circulation and transport in an estuary. Since turbulence is a property of the flow instead of
the fluid, it is essential to use a robust turbulence model to parameterize the vertical turbulent
mixing. In this study, the vertical eddy coefficients (Av and Dv ) are computed from a
simplified second-order closure model developed by Sheng and Chiu (1986) and Sheng and
Villaret (1989).

36
Equation of State
P = P (T,S)
(3.6)
where p is density, T is temperature.
Various forms of the equation of state can be used. In the present model, the equation
given by Eckert (1958) is used:
p = P/( a + 0.698P)
P = 5890 + 3ST - 0.375 T2 + 35 (3.7)
a = 1779.5 + 11.25T - 0.0745r2 - (3.8 + 0.10T)5
where Tis in °C, 5 is in ppt and p is in g/cm3.
Conservative Species Equation
Flushing and residence time studies in an estuarine system can be carried out by
solving the conservation equation for a conservative species, c :
dcs , d(ucs) „ a(vc*) , d(WCs)
dt
dx
dx
d c
D
dy
\
H
dx t
dy
dz
d c
D, 4
(3.8)
H
\
dy
dz
D ^
v dz)
First, the estuarine system needs to be divided into segments with similar circulation
characteristics. To study the tidal flushing, a uniform concentration is released into all the
cells of a specific segment, while the concentration in the other ones are given zero values.
As the simulation proceeds, the remaining mass of the conservative species in each segment

37
is calculated as a fraction of the original mass. The flushing capacity of each segment is then
defined in terms of the reduction in the relative mass (Sheng et al, 1996).
Sediment Transport Model
An integrated model of the Tampa Bay Estuarine System must contain a sediment
transport model that can be used to address environmental problems related to dredging
operations in the navigation channels, and especially, the ecological problems related to the
adsorptive capacity of fine sediments to carry particulate forms of nutrients, heavy metals,
PCB’s, and other organic pollutants.
The suspended sediment model includes the advection-diffusion processes, which
are computed by the hydrodynamics model, as well as such processes as erosion, deposition,
flocculation, settling, consolidation, and entrainment (Sheng, 1986; Mehta, 1986).
The governing equation that represents the transport of suspended sediments is given
by:
dt dx dy dz
(3.9)
~ oc d ~ oc a ~ a c
+ — D„— +— D„— +— Dv —
H dx) dy\ H dy v dz,
where c is the suspended sediment concentration, w„ is the settling velocity of suspended
sediment particles (positive downward), DH is the horizontal turbulent eddy diffusivity, and Dv
is the vertical turbulent eddy diffusivity.

38
Three simplifying approximations are implied in Equation (3.9). First, the concept
of eddy diffusivity is valid for the turbulent mixing of suspended sediments. Second, the
suspended sediment dynamics are represented by the concentration of a single particle size
group, assuming a homogeneous distribution of sediment particles size. Third, the
suspended sediment concentration is sufficiently low (< 1000 mg/L) such that non-
Newtonian behavior can be neglected.
In this study, the determination of settling, flocculation, deposition, erosion,
fluidization, and consolidation processes is based on the previous work of Sheng and Lick
(1979), Sheng(1986), Hwang and Mehta (1989), Sheng et al. (1991), and Chen and
Sheng(1994), and is described in Appendix B.
Model Equations in Curvilinear Boundary-Fitted and Sigma Grid
In three-dimensional modeling, complex bottom topographies can be better
represented with the application of a-stretching (Sheng, 1983), since it is possible to obtain
the same vertical resolution for the shallow coastal areas and the deeper navigation channels.
The vertical coordinate z is transformed into a new coordinate o by (Phillips, 1957):
z ~ C(x,y,t)
h(x,y) + C (x,y,t)
(3.10)
where cis the surface elevation, and h is the mean water depth.
With this transformation, the numerical grid in the computational plane becomes
constant in space and time. However, in the physical plane, since the water surface is
constantly changing in time due to dynamic forcing conditions, the sigma grid is time

39
dependent. A o-grid formulation is suitable for simulating flow and salinity transport in
regions of gradual bathymetric variations and gives a more accurate estimation of bottom
stress than a z-grid model, which resolves the depth with “stair-step” grids. Nevertheless,
recent studies (Sheng et al, 1989a; Haney, 1991) showed that a a-grid model is accurate only
when there are sufficient grid points across regions of sharp bathymetric gradients. In the
case of insufficient grid points, Sheng et al. (1989a) suggested a direct evaluation of the
horizontal density gradient terms along constant z-plane, and avoiding higher-order advective
schemes along the sharp bathymetric variation, to reduce numerical error.
Using non-orthogonal boundary-fitted horizontal grid, it is possible to better represent
the circulation and transport processes in estuarine systems with complex geometries.
Thompson (1983) developed a method to generate 2-D boundary-fitted grids in complex
domain by solving a set of elliptic equations. These equations relate the generally non-
orthogonal curvilinear coordinates in the physical plane x and y with the uniformly-spaced
coordinates in the transformed plane, £ and q.
The spatial coordinates in the physical plane, (x, y, z), have dimensions of length,
while the coordinate system in the computational plane, ( £ r], o), is dimensionless. In this
new coordinate system (£,r¡, a), the velocity vector are expressed in terms of contravariant
components, with dimension of [r;] (Sheng, 1989). The equations of motion in the {£ij,d)
coordinates are shown in Appendix A.

40
Boundary and Initial Conditions
In order to numerically solve the set of equations presented, boundary conditions are
required for the dependent variables.
Vertical Boundary Conditions
The boundary conditions for Equations (3.1), (3.2), (3.3), (3.5), and (3.9) at the free
surface ( a = 0) are:
(3.11)
do
(w +w)c + Dv— = 0
1 s) Vdz
At the free surface, wind velocity is converted to stress by:
(3.12)
where tw, and t are the components of the wind stress, pa is the air density
(0.0012 g/cm3), uw and are the components of wind speed measured at some height
above the sea level. Cds, the drag coefficient, is given as a function of the wind speed
measured at 10 meters above the water surface by (Garrat, 1977):
Cds = (0.075 + 0.0671^)0.001
(3.13)
where W5 is the wind speed magnitude in m/s.

41
The vertical velocity is obtained from the kinematic boundary condition imposed at
the surface:
+ u
H
dx
(3.14)
The boundary conditions for Equations (3.1), (3.2), (3.3), (3.5), and (3.9) at the
bottom
(a = -1) are:
P,A
' du dv
dz ’ dz
(Tto ’ Xby)
= Cdb (ui + vi )m(u¡'vi)
-(
w + w
\ r, dc
)c tDvdz =
Vdc - E
(3.15)
where vd is the deposition velocity, E is the rate of erosion, Av, and Dv are vertical turbulent
eddy coefficients. Cdb is the bottom friction coefficient, and u¡, v¡ represent the velocity
components at the first grid point above the bottom. Taking z, as half of the bottom layer
thickness (which starts at the bottom roughness height, z„), Cdb, for a hydraulic rough flow,
is given by (Sheng, 1983):
-2
(3.16)
( \
K2
In
h.
, Zo ,
where /ris the von Karman constant.

42
Lateral Boundary Conditions
Along the shoreline where river inflow or outflow may occur, the conditions are
generally:
u = u(x,y,z,t)
v = v(x,y,z,t) (3.17)
w =
0
Along a solid boundary, the normal velocity component is zero. In addition, the
normal derivatives of salinity and suspended sediment concentration are assumed to be zero.
Along an open boundary, the surface elevation, c, is given by either a time series of
measured data or specified through harmonic constituents using the following equation:
C = C(x,y,t) = £ Ancos
n=1
2tc t
+ „
(3.18)
where An,Tn, and (¡)n are the amplitude, period, and phase angle of the astronomical tidal
constituents.
When open boundary conditions are given in terms of the normal velocity
component is assumed to be of zero slope while the tangential velocity component may be
either zero, of zero slope, or computed from the momentum equations.
The salinity and suspended sediment concentration along an open boundary or river
entrance is computed from a 1-D advection equation during the outflow. During the inflow,
the concentration takes on a prescribed value.

43
Contravariant velocity components provide lateral boundary conditions similar to
those in the (x,y) system. Along solid boundaries, the normal velocity is zero. When flow
is specified at the open boundary, the normal velocity component is prescribed.
To initiate a simulation, the initial spatial distributions of C,u,v,S and c need to
be specified. When initial data are unknown, the simulation starts with zero initial fields.
When initial data are known at a limited number of locations, an initial field can be
interpolated. For salinity simulations, the “spin-up” time is longer and sufficient time should
be allowed in model simulations.


CHAPTER 4
THE WATER QUALITY MODEL
Previous Work
Considerable effort has been expended in the past 20 years to develop water quality
models for freshwater and marine systems. In freshwater systems, Streeter and Phelps (1925)
were the first researchers to introduce a set of equations for predicting the biochemical
oxygen demand (BOD) and dissolved oxygen (DO) concentrations. Since then, simple zero-
and first-order exponential decay, dilution and sedimentation terms have been added to
predict other conservative and non-conservative species. Sheng (1994) provided a
comprehensive review on water quality models for shallow waters. Jprgensen et al. (1996)
provided the most recent review of environmental models developed in the last two decades.
Water quality models can be classified in terms of the approach undertaken for
solution and analysis. Steady-state models are usually simpler and require less computational
effort than dynamic models. On the other hand, multi-dimension, robust models can provide
more detailed and comprehensive information on the water quality. Stochastic models
require more data for calibration and validation than deterministic models. Water quality
parameters simulated by deterministic models are expressed in terms of expected values,
while simulations performed by stochastic models explicitly take into account the uncertainty
45

46
of physical and biogeochemical processes. Validation of stochastic models is particularly
difficult due to the quantity of observational data required to compare probability
distributions of variables rather than just their expected or mean values (Loucks, 1981).
Moreover, it is more meaningful, in terms of interpretation, to estimate biogeochemical
parameters like growth and nitrification rates than empirical parameters like autoregressive
and moving average coefficients (Solow, 1995).
Until recently, water quality models, originally developed for rivers and stream flows,
were indiscriminately used in estuarine systems. The assumption of steady or quasi-steady
state of the hydrodynamics processes justified the use of coarse grids, and models were either
uncoupled or loosely coupled with hydrodynamics models. However, even in freshwater
systems, there is increasing evidence that hydrodynamics processes have very significant
effects on water quality and ecological processes. Chen and Sheng (1994) found that the
internal loading of nutrients from bottom sediments in Lake Okeechobee could not be
accurately calculated by a water quality model using a large time step of 6 hours. During one
time step, the internal loading of nutrients from bottom sediments calculated by a
conventional water quality model may be zero, because of the zero average net flux from the
bottom sediments in this 6-hour period. In reality, the resuspension and deposition processes
can significantly affect internal loading through sorption/desorption processes. Model
simulations which include such effects produced results that agree well with field data
(Sheng etal., 1993). The water quality model developed by Chen and Sheng (1994) forms
the basis of the water quality model of the present study, although their model did not include
the dissolved oxygen balance and was limited to rectangular grid system.

47
In estuarine systems, the necessity to accurately represent hydrodynamics and
biogeochemical processes is even more relevant. Estuarine systems are physically dominated
ecosystems, where the action of the sun, tides, wind, atmospheric disturbances, river
discharges, and complex geomorphometric features interact. It is the balance of these
physical forces acting as subsidies and stresses that will dictate the water quality dynamics
of each estuarine system.
In traditional water quality box models like WASP (Ambrose et al, 1994), salinity
data is used to obtain the so-called “dispersive coefficients” during model calibration. This
salinity calibration consists of first averaging the flows over the calibration period and then
estimating tidal dispersion coefficients, assuming steady-state conditions (AScI, 1996). In
an estuarine environment, this approach is questionable since salinity is an active species.
Its concentration and gradients affect the temporal and spatial distribution of the density
field, driving baroclinic forces that completely change the hydrodynamic characteristics of
the flow.
AScI (1996) has applied WASP4 in Tampa Bay aiming at the development of a
“broad-based, management-oriented model”. The primary objective of the AScI study is to
provide the Southwest Florida Water Management District (SWFWMD) with a modeling
tool to define eutrophication management strategies. The rationale of this approach was that
the hydrodynamic and water quality data gathered in Tampa Bay, from 1985 to 1991, was
sufficient for the determination of the dispersive and the other “ad-hoc” coefficients of the
model. In addition to the 28 model coefficients, sediment oxygen demand and benthic fluxes
were also determined for specific Bay segments during the calibration process. Another

48
limitation of the AScI study is the time scale (time step of one month), which prevents the
model from capturing episodic events. Schoellhammer (1993) showed that resuspension in
Old Tampa Bay is closely related to storm systems and local wind-generated waves. Sheng
et al. (1993) showed that the contribution of resuspension flux to the internal loading during
episodic events can be orders of magnitude greater than the normal diffusive benthic flux.
Coastal, Inc. (1995) developed a statistical model to investigate the relationships
among nutrient loading, water quality parameters (chlorophyll-a), and light attenuation
coefficients. Like the AScI (1996) study, the rationale supporting this simple approach was
the large amount of data gathered between 1985 and 1991. It was thought that if the
available water quality data were sufficient to calibrate and validate this empirically-based
model, it would serve as a management tool to determine external nitrogen loadings
consistent with seagrass light requirements. Using regression analysis, Coastal, Inc.
determined the relationships between total nitrogen loading, chlorophyll-a, turbidity and light
attenuation coefficients in the four major Bay segments (Old Tampa Bay, Hillsborough Bay,
Middle Tampa Bay, and Lower Tampa Bay). The conclusions of the Coastal, Inc. study was
that no reduction in annual average nitrogen loading and chlorophyll a concentration would
be required for the 20% near-bottom light level target for the four major Bay segments.
However, a substantial reduction in nitrogen loads would be required in order to achieve the
25% light level target.
The limitations of the Coastal, Inc. study are related to the fact that the simplifying
assumptions applied (linear correlation between cause and effect) proved deficient to explain
any correlation between external loading and nitrogen and chlorophyll-a concentrations

49
inside the Bay (Coastal, 1995). This limitation suggests that the internal loading has a
significant role in the nutrient budget, and consequently should be considered in the
strategies to control the eutrophication process. Furthermore, another uncertainty of the
Coastal analysis was originated from their conclusion that a three month cumulative lag
period for nitrogen loads could explain the variation in the chlorophyll-a data. Johansson
(1991), using a similar statistical approach presented evidences for a three-year lag between
external nitrogen loading and chlorophyll-a response. Again, different rates of internal
nitrogen loading may explained the lag difference between Coastal, Inc. (1995) and
Johansson (1991) studies.
These previous modeling efforts on Tampa Bay provided useful foundation for this
more comprehensive modeling study. Despite their simplified approach, these studies were
able to isolate relevant processes and determine some specific model coefficients. At the end
of this chapter, Table 4.2 presents the model coefficients used in this study, the range of each
coefficient found in the literature, and the values used by AScI (1996). In order to account
for both point and non-point sources of nitrogen loading into the Bay, the water quality
species concentration along model boundaries were determined from the nutrient loadings
presented by Coastal, Inc. (1994). Total nitrogen loadings were converted to concentrations
and used along with river discharges.
The water quality component of this integrated model for Tampa Bay focuses on the
interactions between oxygen balance, nutrient dynamics, light attenuation, phytoplankton and
zooplankton dynamics. To develop the water quality model, the mass conservation principle
can be applied to each water quality parameter related to the phytoplankton and zooplankton

50
dynamics, phosphorus cycle, nitrogen cycle, and oxygen balance. With regard to nutrients,
the nitrogen cycle is more important than the phosphorus cycle since nitrogen has been the
macro-nutrient limiting phytoplankton growth in Tampa Bay (FWCA,1969; Lewis and
Estevez, 1988; Johansson, 1991; Coastal, 1995; AScI, 1996). Hence phosphorus cycle is not
included as part of the water quality model for Tampa Bay.
Development of the Numerical Model
The nitrogen cycle in Tampa Bay is modeled through a series of first-order kinetics,
which start with the biogeochemical process controlling nitrogen fixation. Phytoplankton
growth controls ammonia and nitrate uptake. The uptake rate for each species is proportional
to its concentration relative to the total inorganic nitrogen content, and a preferential factor
for ammonia uptake. Nitrogen returns from the planktonic biomass pool as dissolved and
particulate organic nitrogen and as dissolved inorganic nitrogen through endogenous
respiration and non-predatory mortality. Organic nitrogen is converted to ammonia
(mineralization) at a temperature-dependent rate, and ammonia is then converted to nitrate
(nitrification) in a temperature and oxygen-dependent rate. The stability of the dissolved
form of ammonium in water is pH dependent. It can exist in its ionic form, ammonium
(NHX + ) or as ammonia (NHJ, with the latter being lost from the system through
volatilization. Low levels of dissolved oxygen may induce a bacterial-mediated
transformation of nitrate into nitrogen gas (denitrification) at a temperature-dependent rate.

51
The oxygen balance couples dissolved oxygen to the other state variables. Reaeration
through the atmosphere-water interface, and phytoplankton production during photosynthesis
are the main sources for oxygen. Oxidation of organic matter and carbonaceous material,
respiration by zoo and phytoplankton, and oxygen consumption during the nitrification
process are collectively grouped into the CBOD (carbonaceous-biochemical oxygen demand)
variable, which is a sink for dissolved oxygen (Ambrose et al., 1994).
The light penetration inside water can be determined through measurements of
turbidity, color, and light penetration (Kirk, 1994). In the integrated model for Tampa Bay,
the primary concern is the availability of photosynthetically active radiation (PAR), which
is influenced by the intensity of incident solar radiation, solar elevation angle, weather
conditions, water depth, tidal range, concentrations of sediments, detritus and phytoplankton
(Miller and McPherson, 1995).
Phytoplankton kinetics is the central part of this water quality model, since the
primary water quality issue in the Tampa Bay Estuarine System is eutrophication (Boler et
al., 1991). Phytoplankton population is a complex variable to obtain in the field. For single
species, a direct measurement of the population size is the number of cells per unit of
volume. However, in natural multi-species environment, it is difficult to distinguish viable
and non-viable cells and, for species that tend to colonize, counting requires an extra effort
to separate individual cells because the size of the colonies are quite variable (Ambrose et
al., 1994). An alternate solution is to measure phytoplankton population through chlorophyll
analysis, although this is not an absolute indicator of planktonic biomass. Some species do
not contain chlorophyll and when chloroplasts (chlorophyll-containing structures found in

52
algal and green plant cells) are present, they vary in number, size and pigment content per
cell (Boler et al., 1991). The conversion to phytoplankton dry weight or carbon involves
further species-dependent constants that depend on nutrient and light levels.
The rationale behind this water quality modeling effort is that planktonic organisms
have a fast response to environmental conditions. In other words, by combining chlorophyll
with nutrient levels, dissolved oxygen balance, and light attenuation, it is possible to evaluate
and quantify short and long term water quality processes such as hypoxia and eutrophication.
Mathematical Formulation
In this study, the water quality equations are derived from an Eulerian approach,
using a control volume formulation. In this method, the time rate of change of the
concentration of any substance within this control volume is the net result of (i)
concentration fluxes through the sides of the control volume, and (ii) production and sink
inside the control volume. The conservation equation for each of the water quality
parameters is given by:
54 + V-(«) = V-[D v(i»)] + Q
dt (4.1)
(0 (¿0 (Hi) (iv)
where (i) is the evolution term (rate of change of concentration in the control volume), (ii)
is the advection term (fluxes into/out of the control volume due to advection of the flow
field), (Hi) is the dispersion term (fluxes into/out of the control volume due to turbulent

53
diffusion of the flow field), and (iv) is the sink/source term, representing the kinetics and
transformations due to sorption/desorption, oxidation, excretion, decay, growth,
biodegradation, etc. The water quality equations in the curvilinear non-orthogonal boundary-
fitted system (£, , o) is given by:
1 dH$ = J_J_
H dt hz da
1
D.
v ao,
Ufa
+ D
* JL(faHv4>)
i a//(j(j)
H da
(4.2)
H
gil 1A + 2g12 9 ^ + g2ld ae
a^ari
arp
+ Q
where (J) represents any water quality parameter, \J(ga) is the Jacobian of horizontal
transformation, (g11, g12 ,gzz) are the metric coefficients of coordinate transformation, and
Q represents the biogeochemical processes.
In the following sections, the biogeochemical processes controlling the sink/source
term of Equation (4.2) will be discussed in detail for the nutrient dynamics, zooplankton and
phytoplankton dynamics, and oxygen balance in estuarine systems.
Nutrient Dynamics in Estuarine Systems
As explained earlier, the nutrient dynamics will be centered in the nitrogen cycle,
assuming it is the macro-nutrient that limits phytoplankton growth. For the present study,
the basic transformation processes for the nitrogen cycle are similar to those described in
Chen and Sheng (1994).

54
Nitrogen comprises 78% of the atmosphere, mostly molecular N2. This form is
biologically unavailable except for fixation by procaryotic organisms containing the enzyme
nitrogenase. Considering the kinetic pathway organic nitrogen —►ammonia —► nitrate —*N2,
fixed forms of nitrogen such as nitrate, ammonium, and organic nitrogen would gradually
be depleted from the biosphere if not for nitrogen fixation.
Nitrogen inputs to estuarine systems are related to point and non-point sources from
land, atmospheric deposition, and fixation. Additionally, internal loadings such as from
resuspended sediments containing inorganic and organic forms are also important. The
specification and quantification of each of these contributions is the first step towards the
determination of nitrogen budget in an estuarine system.
As shown in Equation (4.2), the nitrogen cycle is highly dependent on the
hydrodynamics and sediment dynamics of the estuarine system. Resuspension events,
combined with desorption processes can significantly change the input and budget of
nitrogen in the system. On the other hand, deposition and sorption may contribute to major
losses of nitrogen from the water column. The hydrodynamics not only drive the sediment
processes, but also affect the sorption/desorption reactions, through turbulent mixing.
The processes simulated in this study include:
a) Mineralization of organic nitrogen
b) Nitrification of ammonium
c) Volatilization of ammonia
d) Denitrification of nitrate
e) Uptake of ammonia and nitrate by phytoplankton

55
f) Conversion of algal-nitrogen into zooplankton-nitrogen through grazing
g) Excretion by algae and zooplankton
For the purpose of studying its cycle, the nitrogen species are first divided into
dissolved and particulate groups. This division is usually established in the laboratory using
filtering techniques. In the dissolved group, this study will consider nitrogen as ammonia
nitrogen, represented by the state variable NH3; dissolved ammonium nitrogen, represented
by the state variable NH4; nitrate+nitrite nitrogen, represented by the state variable N03; and
dissolved or soluble organic nitrogen (SON). Particulate nitrogen includes: particulate
inorganic nitrogen (PIN), and particulate organic nitrogen (PON). Zooplankton nitrogen
(ZOON), and algal nitrogen (ALGN) relate biomass to nitrogen concentration through fixed
stoichiometric ratios: zooplankton nitrogen to carbon ratio {zNC ), and algal nitrogen to
carbon ratio (aNC).
In order to couple the water quality model with hydrodynamics and sediment
dynamics, Equation (4.2) needs to be modified for the particulate forms of nitrogen, so that
it includes a settling velocity. For the inorganic species, it is reasonable to assume the same
settling velocity of the suspended sediment particles. For phytoplankton, literature values
of algae settling velocity, which accounts for the limited vertical motion of these organisms
will be used.
Ammonia Nitrogen
Ammonia volatilization is a physico-chemical process where ammonium N is in
equilibrium between its gaseous and hydroxyl form:

56
NH3{aq) + H20 - NH4+ + OH
(4.3)
As stated, the process is pH dependent, with an alkaline environment driving the
reaction to the left, i.e. favoring the aqueous form. Since the concentration of ammonia in
the atmosphere is very low, the partial pressure difference may produce a sink for nitrogen
in the system, according to Henry’s law. The kinetic pathway for ammonia nitrogen (state
variable NH3) is represented in the sink term of Equation (4.2) as:
(4.4)
where KA, is the ammonia conversion rate constant, and is the half-saturation constant
for ammonia conversion. KV0Lis the volatilization rate constant, hv is Hemy’s constant, and (NH3)atm
is the ammonia concentration in the air.
Dissolved Ammonium Nitrogen
Nitrogen fixation is a biogeochemical process mediated by a variety of autotrophic
and heterotrophic bacteria, by which nitrogen gas is reduced to ammonium:
N2(g) + 8/T + 6e~ - 2NH4
(4.5)
In aquatic systems, this reaction is only possible in very reduced environments
(Snoeyink and Jenkins, 1980). Such an environment exists inside photosynthetic cells of
blue-green algae, and in the symbiotic association in root nodules between bacteria of the
genus Rhizobium and certain plants. It has been reported that cyanobacteria are responsible

57
for most planktonic fixation in aquatic environments, with a high correlation between
fixation rates and cyanobacteria biomass (Howarth et al., 1988). In most estuaries, the
biomass of these nitrogen-fixing species of cyanobacteria usually makes up a very small
percentage of the phytoplanktonic biomass (< 1%), suggesting insignificant amount of
nitrogen fixation (Howarth etal., 1988). Johansson etal. (1985) showed that, prior to 1984,
planktonic filamentous blue-green algae (Schizothrix caldcóla sensu Drouet) dominated the
phytoplankton population in Tampa Bay from early summer to early winter. However,
Johansson (1991) stated that there was no information to support that this blue-green algae
is responsible for nitrogen fixation in Tampa Bay. Actually, it has been estimated that
nitrogen fixation should account for no more than 5% of the total nitrogen budget in the Bay
(Johansson, personal communication). These evidences support the hypothesis generally
accepted that many estuaries are nitrogen limited in part due to the low rates of nitrogen
fixation. Hence, nitrogen fixation was not considered in this study.
The biogeochemical transformation of organic nitrogen to ammonium is defined as
ammonification. Another source for dissolved ammonium is the release of NH4 during
mortality and excretion of algae and zooplankton, and the sorption/desorption reaction with
sediment particles. The kinetic pathway of ammonium nitrogen (state variable NH4) is
represented in the source term of Equation (4.2) by a first-order reaction (Rao et al., 1984),
and a partitioning between particulate and dissolved form regulated by the
sorption/desorption kinetics (Chen and Sheng, 1994):

58
Q - Kom-SON - K,
DO
NN
+ D0
â–  NH4
+ dm(PIN - Pan-c-NH4)
- Pu-ALGN + K-ALGN + K-ZOON
ft It mA
pH
(4.6)
- K
A!
H* - PH
•NH4
whereKom , the rate of organic nitrogen mineralization is a function of water temperature,
pH, and the C/N ratio of the residue (Reddy and Patrick, 1984). KNN is the nitrification rate
constant, DO is the dissolved oxygen concentration, Hn-t is the half saturation constant for
oxygen limitation. dan is the desorption rate of NH4 from sediment particles, pm is the
partition coefficient between NH4 and PIN, and c is the suspend sediment concentration. Pn
is the ammonium preference factor for algae uptake, p<( is the algae growth rate,
Kand Kzx are the algae and zooplankton excretion rate constants, respectively. All
coefficients related to zoo and phytoplankton dynamics will be discussed later in this
Chapter.
Nitrite+Nitrate Nitrogen
In an aerobic environment, the mineralization of organic nitrogen proceeds with a
bacterial-mediated transformation of ammonium into nitrate. The nitrification process is a
two step process, in which the chemoautotrophic bacteria of the genera Nitrosomonas
mediate the formation of nitrite, and bacteria of the genera Nitrobacter the formation of
nitrate:

59
NH/ + 1.5 02 - N0{ + 2H* + H20
N0{ + 0.5 02 - NO{
(4.7)
Nitrification is a strictly aerobic process, occurring only in the water column and in
the aerobic layer of the sediment column. Equation (4.7) shows that the nitrification process
is a sink for dissolved oxygen in the system.
Denitrification is defined as the biogeochemical transformation of nitrate N to
gaseous end products such as molecular nitrogen or nitrous oxide (Reddy and Patrick, 1984).
Like volatilization, denitrification represents a sink for nitrogen in the system. Under
anaerobic conditions and in the presence of available organic substrate, denitrifying bacteria
(e.g. Pseudomonas denitrificans) can use nitrate as an electron acceptor during anaerobic
respiration. As an example, the oxidation of a carbohydrate substrate to C02 and H20 using
nitrate instead of oxygen can be given as:
5 [CH20) + ANO{ + 4 H* -5 C02 + 2 N2 + 7 H20 (4.8)
This irreversible reaction is actually a two-step process in which nitrate is reduced
to nitrous oxide before being converted into molecular nitrogen. Nitrous oxide has been
related to the Earth’s “greenhouse” effect because N20 reacts and breaks down atmospheric
ozone (McElroy et al., 1978). Reddy et al. (1978) showed that under carbon-limiting
conditions, the denitrification process described in Equation (4.8) can be represented by a
first-order reaction.

60
In this study, the kinetic pathway of nitrite+nitrate (state variable N03) is
represented in the source term of Equation (4.2) as a sequence of first-order reactions, limited
by the dissolved oxygen concentration:
Q =K,
DO
AW
tfnit +DO
â– NH4-K,
H.
no3
DN
»„03 +DO
â– N03-(\-Pn\Va-ALGN (4.9)
where KDN is the denitrification rate constant, and Hm} is the half saturation constant for
denitrification, which can be calibrated to only allow the denitrification process to occur
under low dissolved oxygen conditions (Ambrose et al., 1994).
Soluble Organic Nitrogen
Besides N2 , the largest pool of nitrogen in estuarine systems are dissolved and
particulate organic nitrogen. The kinetic pathway of dissolved or soluble organic nitrogen
is the convertion of SON to NH4 during ammonification, and the sorption/desorption reaction
with sediment particles. For soluble organic nitrogen (state variable SON), the source term
of Equation (4.2) can be represented by:
Q - -K„u-SON * dm-(PON - Pm-C-S0N) (4.10)
where d(m is the desorption rate of SON from the sediment particles, and pm is the partition
coefficient between SON and PON.

61
Particulate Organic Nitrogen
The kinetic pathway of particulate organic nitrogen is the release of PON during
mortality and excretion of algae and zooplankton, and the sorption/desorption reaction with
sediment particles. In estuarine systems with organic-rich sediments, benthic mineralization
of detritus can be a major recycling pathway, and account for a significant fraction of the
nutrient requirements of primary producers in overlying water column (Klump and Martens,
1981). For particulate organic nitrogen (state variable PON), the source term of Equation
(4.2) can be represented as:
Q = K^-ALGN * K^-ZOON - dm-[PON - pm -c-SON) (4.11)
where is the mortality rate of zooplankton.
Particulate Inorganic Nitrogen
Sources of PIN are related to nitrogen contained in the suspended particulate matter
derived from landward and seaward origin (Keefe, 1994). There have been several studies,
at various spatial and temporal scales, of particulate nitrogen distribution in estuarine systems
(Sharp et al., 1982; Edmond et ah, 1985; Wafar et ah, 1989). Nevertheless, little insight is
available concerning the partitioning between the inorganic and organic fraction of these
materials (Froelich, 1988). The kinetic pathway of particulate inorganic nitrogen (state
variable PIN) is related to the sorption/desorption reaction with sediment particles, and the
source term of Equation (4.2) can be written as:
Q = ~ dan â–  [PIN - pm' c- NH4)
(4.12)

62
Algal Nitrogen
Through uptake of inorganic nitrogen, algae assimilates nitrogen in proportion to its
growth rate. The particulate nitrogen recycles to the inorganic pool by means of excretion
and non-predatory mortality. Inasmuch as there is no data on excretion of zoo and
phytoplankton under field conditions, most of water quality models consider constant
excretion and mortality rates proportional to the biomass (Jprgensen, 1983; Najarían et al.,
1984; Ambrose et al., 1994; Chen and Sheng, 1994). Another sink for ALGN is due to
grazing by zooplankton, at a rate proportional to the zooplankton growth rate. Growth rates
for phytoplankton and zooplankton in estuarine systems are complex functions of the species
present, and they will be discussed later in this Chapter.
The algal nitrogen (state variable ALGN) is represented in this model by a fixed
stoichiometric ratio relating algal biomass and nitrogen concentration as:
ALGN = aNC • (Algal Biomass) (4.13)
where aNC is the algal nitrogen to carbon constant ratio.
Zooplankton Nitrogen
Similar to ALGN, the kinetic pathway of particulate zooplankton nitrogen depends
on growth, excretion, and mortality rates. In this case, the zooplankton nitrogen (state
variable ZOON) is given by:
ZOON - ZNC • (Zooplankton Biomass)
where zNC is the zooplankton nitrogen to carbon constant ratio.

63
Sorption and Desorption Reactions
In the nitrogen cycle, sorption processes refer to the conversion from soluble to solid
phase of inorganic and organic species, while desorption reactions describe the inverse
process. Sorption/desorption processes, combined with resuspension events can significantly
alter the nitrogen cycle in the system.
The kinetics of sorption/desorption reactions are dependent on each nitrogen species
characteristics, sediment properties, pH, temperature, and dissolved oxygen concentration
(Simon, 1989). Some studies have shown that sorption/desorption processes can be more
important in marine environment than in freshwater. The primary reason has been attributed
to a six times higher adsorptive capacity of clays for organic matter in seawater than in
freshwater, due to salinity effects (Pocklington, 1977; Martinova, 1993).
The most commonly used mathematical representation of sorption/desorption
processes is the linear, reversible, isotherm (Berkheiser etal., 1980; Reddy etal., 1988):
dN.
= ~DrNai + SrN, (4.15)
where Dr is the desorption rate constant, Sr is the sorption rate constant, is the adsorbed
nitrogen concentration, and Ns is the dissolved nitrogen concentration.
Equation (4.15) can be reformulated, considering that at equilibrium, the ratio
between the desorption and sorption rates gives the partition coefficient between dissolved
and particulate forms:

where pc is the partition coefficient.
Phytoplankton Dynamics in Estuarine Systems
The overall water quality in the Tampa Bay Estuarine System is markedly influenced
by the dynamics of the zoo and phytoplankton communities (Lewis and Estevez, 1988; Boler
et al, 1991; AScI, 1996). In a review of the phytoplankton in Tampa Bay, Steidinger and
Gardiner (1985) reported the dominance of nannoplankton (less than 20 pm), with a head to
mouth gradient, following the salinity distribution. The authors also reported that Tampa
Bay presents more than 250 species of phytoplankton, with diatoms making up the bulk of
the distribution. However, the lack of data on each specific species prevented a more
detailed characterization, and the entire phytoplanktonic community is represented in this
study by a single state variable.
In this study, a quantitative model of phytoplankton population dynamics also uses
the conservation of mass principle, in which hydrodynamics transport plays a major role.
Phytoplankton growth is represented by a temperature-dependent maximum growth rate that
is limited by nutrient availability and light. Light limitation is formulated according to the
equation first proposed by Steele (1965). The nutrient limitation is represented by a modified
version of the Michaelis-Menton formulation. Some researchers (e.g. Jprgensen, 1976)
suggest that the nutrient-limited growth rate of phytoplankton is a function of the internal

65
nutrient content. According to this approach, external nutrients are taken up by
phytoplankton and stored. Ensuing growth would then be related to this internal nutrient
content. Assuming a dynamic state of equilibrium between the external concentration and
internal content (Di Toro, 1980), it is possible to represent the nutrient limitation according
to the formulation suggested by Riley and Stefan (1988).
In this study, the phytoplankton growth rate is represented by:
I \ aT-20 I
M, =KL'0. -exp
1 -
s J
NH4 + NQ3
+ NH4 + NO 3
(4.17)
where (u ) is the algae maximum growth rate, 0 is the temperature correction factor, I is
' "/max
the light intensity, / is the optimum light intensity for algal growth, Hn is the half saturation
constant for algal growth.
The phytoplankton kinetics are represented by growth, respiration, non-predatory
mortality, grazing by zooplankton, and a settling term which accounts for the limited vertical
motion. The source term of Equation (4.2) can be written as:
2 - yz(â„¢^.-pHY) * (h.-k^-k^-phy - M* * ZOO (4.18)
where ws^ is the phytoplankton settling velocity. Chen and Sheng (1994) reviewed
algal settling rate measured in eutrophic water bodies, and showed that it is not only species
dependent, but it also a function of flocculation and senescence.
Zooplankton are the lower-trophic level consumers that constitute the primary
herbivorous component of an estuarine ecosystem (Kennish, 1990). In this study,

66
phytoplankton are the object of concern, therefore, no attempt is made to investigate the
details of the zooplankton dynamics. Zooplankton is only considered as the predators of
phytoplankton, utilizing their available biomass as food supply.
Zooplankton growth is represented by a temperature-dependent maximum growth
rate, that is limited by phytoplankton availability:
DUV
(4.19)
where (u ) is the maximum growth rate for zooplankton, 0 is the temperature limiting
V ’/max ^
function for zooplankton, and Hphy is the half saturation constant for phytoplankton uptake.
The zooplankton kinetics, influenced by growth, respiration, and mortality, is
represented in the source term of Equation (4.2) by:
(4.20)
Oxygen Balance in Estuarine Systems
Dissolved oxygen dynamics in aquatic systems have been extensively studied
(Streeter and Phelps, 1925; O’Connor and Thomann, 1972; Orlob, 1983; Ambrose et al.,
1994). Dissolved oxygen evolution depends on the balance between photosynthetic
production, total respiration, and exchanges with the atmosphere. Oxygen, as a byproduct
of photosynthesis, increases as a result of autotrophs’ growth. Dissolved oxygen saturation
in seawater is determined as function of temperature and salinity (APHA, 1985). For

67
dissolved oxygen levels below saturation, DO diffuses into surface waters. When the water
is super-saturated, mainly as a result of primary production, oxygen will be diffused out to
the atmosphere. As any other water quality parameter, dissolved oxygen is also subject to
advective transport in the estuarine system.
In this study, the formulation of the oxygen balance is based on that in the WASP5
model, with some modifications. The rate of dissolved oxygen production is assumed to be
proportional to the growth rate of the phytoplankton in a fixed stoichiometry reaction. For
each milligram of phytoplankton carbon produced by growth using nitrate, a fixed amount
of phytoplankton nitrogen (ALGN) is reduced, and (48/14) aNC (phytoplankton
nitrogen/carbon ratio) mg of 02 is produced. The dissolved oxygen fluxes on the air-water
interface are determined as a product of a reaeration coefficient multiplied by the difference
between dissolved oxygen saturation and the dissolved oxygen concentration at the surface
layer. The reaeration coefficient is assumed to be proportional to the water velocity, depth,
and wind speed (Thomann and Fitzpatrick, 1982). Details of the dissolved oxygen saturation
and reaeration coefficient calculations are presented in Appendix C.
In this model, there are two options for the kinetic pathway of DO. The first one,
describing the oxygen balance through a full non-linear equation is represented in the source
term of Equation (4.2) as:

68
Q - MD0> - D0) *
32
32 + 48 J4
12 + 14 12
— Kox'aoc'PHY ~ Kd — ■
12 “* "c D Hbod + DO
f1 ~Pn)
CBOD
â– ALGN
(4.21)
-«I
DO
14
AW
^nit +
â–  NH4
where DOs is the saturation value for dissolved oxygen concentration, KAE is the reaeration
coefficient, and aoc is the constant oxygen to carbon ratio for phytoplankton respiration (g02
/gC).
In order to minimize “spin-up” time due to the non-linear character of Equation
(4.21), a second option describes the oxygen balance through a linear equation where the
source term of Equation (4.2) is given as (Ambrose et al. 1994):
a - Kts-(DO, - DO) + || [m,-K*Kj\-PHY
- Kd-CBOD - ^Km-NH4
(4.22)
The use of carbonaceous oxygen demand (CBOD) as a measure of the oxygen¬
demanding processes simplifies modeling efforts by aggregating their potential effects
(Ambrose et al. 1994). Oxidation organic matter, nitrification, non-predatory mortality and
respiration by zoo and phytoplankton are nitrogenous-carbonaceous-oxygen-demand,
collectively combined into the state variable CBOD.

69
The kinetic pathway of CBOD is represented in the source term of Equation (4.2) as:
Q =
d_
dz
Kn
[ WSCBOD ' ( 1 fácBOD ) ' CBOD j
DO
tfbod + DO
CBOD
5_ 32
4 14
K,
K.
no 3
DN
^no3 + DO
N03
+ Kax • ALGN + K^-ZOON
(4.23)
where fdCB0D corresponds to the fraction of the dissolved CBOD, and wsCBOD is the
settling velocity for the particulate fraction of CBOD. fdCB0D and wsCB0D are empirically-
based coefficients that represent the fact that under quiescent flow conditions, the particulate
fraction of CBOD can settle through the water column, and eventually deposit on the bottom
(Ambrose et al. 1994). The determination of both coefficients should proceed in terms of
the best fit between measured and modeled data (Jprgensen and Gromiec, 1989).
Light Attenuation in Estuarine Systems
The solar radiation that reaches the ocean’s surface includes the ultraviolet range
(290-380 nm), the visible range (380-760 nm), and the infra-red (760-3000 nm). As to
primary production in estuarine systems, ecologists are normally concerned with light in the
range of wavelengths from 400-700 nm. Defined as “Photosynthetically Active Radiation”
(PAR), this range of irradiance provides the predominant source of energy for autotrophic
organisms (Day et al., 1989). Moreover, instead of measuring PAR in terms of energy,

70
commercially available quantum meters record the number of quanta (or photons, in the
visible range) received per unit area per unit time. The unit of this photon flux density is
micro Einstein per squared meter per second ( \iEm ~2 s_1).
The incident light can be reflected, absorbed, and refracted by dissolved and
suspended substances in the water and by the water itself. The Beer-Lambert law can be used
to describe the light distribution with depth (Day et al., 1989):
(4.24)
where Io is light intensity at the water surface, / is light intensity at depth z, z is the depth
in meters, and Ko is the vertical light attenuation coefficient in m'1.
For long term simulations, the seasonal variation of surface irradiance in Tampa Bay
can be represented by a sine curve:
(4.25)
corresponding to an average solar radiation of 1800 pE/m2 s. Monthly variations range from
1600 in January to 2200 p E m “2 s_1 in mid July.
Some studies reported higher values in middle to late spring rather than summer
because of increased precipitation and cloud cover associated with the rainy season (Wolfe
and Drew, 1990). For this study, real data of surface irradiance, obtained by USGS (Tampa
Bay) between June 1990 and September 1991, was used.
McPherson and Miller (1994) and Miller and McPherson (1995) developed a model
by partially adjusting the attenuation coefficient in Tampa Bay for changing solar elevation,

71
and used multiple regression analysis to partition the coefficient into the relative contribution
of seawater, water color, chlorophyll and non-chlorophyll suspended matter.
A simplified geometric description of the incident direct solar beam and diffuse
skylight is used to describe the effects of solar elevation angle and cloudiness on the amount
of PAR that passes through the air-sea interface. Since so far, there is no process-based
model that relates optical characteristics of the water to mass (or concentration) of
constituents inside the water column, a large data set which covers a wide range of
conditions is required to determine statistical correlations. In their work, Miller and
McPherson (1995) used 16083 observations (255 days between 6/02/90 and 9/29/91) of
scalar PAR, measured in air and at two depths in the water column, to evaluate irradiance that
entered the water and subsequent attenuation.
The attenuation coefficient is obtained as the product of the partitioned coefficient
and a correction term that accounts for the geometry of the incident irradiance:
Ko = Ktd'Kadj (4.26)
where \xwtd is the correction factor (weighted average cosine), and Kadj is the partitioned
attenuation coefficient. The formulation for the correction factor,\*-wtd, developed in Miller
and McPherson (1995) is presented in Appendix D.
Lorenzen (1970) showed that the vertical attenuation of PAR can be linearly
partitioned into a set of partial attenuation coefficients:
Kadj = K + Kc + Kd + Kp
(4.27)

72
where Kw is the attenuation coefficient due to water, Kc is due to the presence of chlorophyll
a, Kd is due to dissolved substances, and K is due to non-algal particulate matter.
Nevertheless, other researchers have shown that the partitioning of the components of light
attenuation into an empirical model using standard water quality parameters is not precise
(e.g. Mote Marine Lab, 1995).
According to Kirk (1994), the inherent properties of the water can be determined by
linear superposition of the partial contributions (e.g. color, chlorophyll, etc.). However, the
vertical attenuation coefficient is an “apparent” optical property of the water (Kirk, 1994),
and it is not only a function of the inherent properties of absorption and scatter, but also the
angular and spectral distribution of the incident light.
Originally, McPherson and Miller (1994) partitioned the attenuation coefficient into
a set of partial attenuation coefficients:
Kadj = K+E2C2+E3C3+E4C4 (4.28)
where kw is the PAR-waveband average attenuation coefficient of seawater, 0.0384 m'1
(Lorenzen, 1972); E2 is the attenuation coefficient of dissolved matter, in (m Pt-Co units)'1;
C2 is the water color, in Pt-Co units; E3is the attenuation coefficient of chlorophyll and other
matter associated with chlorophyll a, in m2 mg'1; C3 is the concentration of chlorophyll a, in
mg m'3; E4 is the attenuation coefficient of nonchlorophyll suspended matter (NSM), which
includes inorganic and organic particulate not directly associated with color or chlorophyll
a, in m2 mg'1; and C4 is the concentration of NSM, in mg m'3.

73
The lack of good measurements of NSM (in terms of total suspended solids and
turbidity) constrained the determination of the líE4-C¡' term, and the equation was modified
to (McPherson and Miller, 1994):
Kadj = 0.014-C2 + 0.062- (turbidity) + 0.049-C3 + 0.30 (4.29)
with the coefficients E2 and E3 determined from Tampa Bay and Charlotte Harbor data. In
this study, the adjusted attenuation coefficient is determined from Equation (4.29), with C2
representing the average water color, in Pt-Co units; C3 is the chlorophyll a concentration
in mg/m3; and turbidity is given in NTU. Data of water color and turbidity for each
segment of the Bay was obtained from the EPC reports (Boler, 1992). Chlorophyll-a
concentration is determined from the water quality portion of the model.
After determining the correction factor {\xwtd ), and the partitioned attenuation
coefficient (Kadj), the attenuation coefficient (K0 ) is obtained from Equation (4.26).
Model Coefficients
The model parameters required to simulate the water quality dynamics in the Tampa
Bay Estuarine System, are described in Table 4.1. During the implementation phase, model
coefficients were determined by isolating specific processes in a test grid with a similar
spatial scale as Tampa Bay, and initial values were obtained from literature and previous
modeling studies (e.g. AScI, 1996). The value of the coefficients used in this study are
presented in Table 4.2.

74
Table 4.1 - Description of the coefficients used in the water quality model.
Coefficient
Description
Units
(SAD)â„¢
temperature coefficient for NH4 desorption
-
O/-20
temperature coefficient for algae growth
-
(0a.)T-20
temperature coefficient for ammonium instability
-
(0bod)T-20
temperature coefficient for CBOD oxidation
-
(0dn)T-20
temperature coefficient for denitrification
-
(0nn)T-20
temperature coefficient for nitrification
-
(0od)T-20
temperature coefficient for SON desorption
-
(0onm)T-20
temperature coefficient for mineralization
-
(0Resp)T-20
temperature coefficient for algae respiration
-
(0Z)T-20
temperature coefficient for zooplankton growth
-
(Pa)max
algae maximum growth rate
1/day
(^z)max
zooplankton maximum growth rate
1/day
(NH3)air
ammonia concentration in the air
Mg/L
achla
algal carbon-chlorophyll-a ratio
mg C / mg Chl-a
c
algal nitrogen-carbon ratio
mg N / mg C
aOC
algal oxygen-carbon ratio
mg 02 / mg C
n
desorption rate of adsorbed ammonium nitrogen
1/day
0o n
desorption rate of adsorbed organic nitrogen
1/day
o!
molecular diffusion coefficient for dissolved species
cm2/s
e2
light attenuation coefficient due to dissolved matter
l/(m Pt-Co)
e3
light attenuation coefficient due to chlorophyll a
l/(m pg/L)
e4
light attenuation coefficient due to NSM
l/(m mg/L)
E^cbod
fraction of dissolved CBOD
-
Hai
half-saturation constant for ammonia conversion
(pH unit)
od
half-saturation constant for CBOD oxidation
mg 02

75
Table 4.1 - continued.
Coefficient
Description
Units
H„
half-saturation constant for algae uptake
mg/L
H„it
half-saturation constant for nitrification
mg02
H„ o 3
half-saturation constant for denitrification
mg02
hv
Henry’s constant
mg/L-atm
Is
optimum light intensity for algal growth
pE / m2 / s
Kax
excretion rate by algae
1/day
Kas
mortality rate of algae
1/day
KAE
reaeration rate constant
1/day
ka1
ammonia conversion rate constant
1/day
Kdn
denitrification rate constant
1/day
Table 4.2 - Literature ranges and values of the coefl
icients used in the water quality model.
Coefficient
Literature Range
Tampa Bay
Source
(0ad)T-2°
1.08
1.08
Assumption
(0a)T-20
1.01-1.2
1.08
Di Toro & Connoly( 1980);AScI( 1996)
(0m)T-20
1.08
1.08
Assumption
(0bod)T-20
1.02-1.15
1.08
Bowie et al (1980); AScI (1996)
(0dn)T-20
1.02-1.09
1.08
Baca & Arnett (1976); AScI (1996)
(0nn)T-20
1.02-1.08
1.08
Bowie et al. (1980); AScI (1996)
(0od)T-20
1.08
1.08
Assumption
rfi \T-2°
1.02-1.09
1.08
Baca & Arnett (1976); AScI (1996)
(0REsr)T'20
1.045
1.05
Ambrose etal. (1994); AScI (1996)
(0Z)T-20
1.01-1.2
1.08
Di Toro & Connoly (1980)
(Ma)max
0.2-8.
1.47
Baca & Arnett (1976); AScI (1996)

76
Table 4.2 - continued.
Coefficient
Literature Range
Tampa Bay
Source
(Pz)max
0.15-0.5
0.5
Jprgensen (1976)
(NH3)air
0.1
0.1
Freney etal. (1981)
h 1 a
10-112
112
Jprgensen (1976);AScI (1996)
anc
0.05-0.43
0.15
Jprgensen (1976); AScI (1996)
aoc
2.67
2.67
Ambrose et al. (1994); AScI (1996)
n
-
4.0
Simon (1989)
d0„
-
4.0
Assumption
o 1
4.E-6-1.E-5
l.E-5
Rao et a/.(1984);Krom & Bemer (1980)
e2
-
0.014
Miller & McPherson (1995)
E,
-
0.062
Miller & McPherson (1995)
e4
-
0.30
Miller & McPherson (1995)
fdcBOD
-
0.7
Assumption
Hai
9.0
9.0
Freney etal. (1981)
Hb Q
0.02-5.6
0.18
AScI (1996)
Hn
0.0015-0.4
0.05
AScI (1996)
H„it
0.1-2.0
2.0
Ambrose et al. (1994); AScI (1996)
Hno3
0.1
0.1
Ambrose et al. (1994); AScI (1996)
hv
43.8
43.8
Sawyer & McCarty (1978)
Is
300-350
200.
Di Toro & Connoly(1980);AScI(1996)
Kax
0.05-0.2
0.15
Jprgensen (1976); AScI (1996)
Kas
0.01-0.1
0.08
Jprgensen (1976); AScI (1996)
kae
-
-
see Appendix C
kai
0.003-0.008
0.003
Reddy et al. (1990)
kd
0.02-0.6
0.15
Bowie etal. (1980); AScI (1996)
K-dn
0.02-1.0
0.90
Baca & Arnett (1976); Assumption

77
Table 4.2 - continued.
Coefficient
Literature Range
Tampa Bay
Source
Knn
0.001-0.6
0.08
AScI (1996); Reddy et a/.(1990)
Konm
0.01-0.4
0.1
Di Toro & Connoly(1980);AScI(1996)
K-vol
3.5-9.0
7.0
Fillery and DeDatta (1986)
Kzs
0.05-0.3
0.05
Baca & Arnett (1976)
K..
0.03-0.075
0.05
Jprgensen (1976)
Pan
0.5E-7-1.0E-5
1.0E-5
Simon (1989)
Pon
1.0E-5
1.0E-5
Simon (1989)
WSCBOD
-
5.0
Assumption
WSalgae
0.0-30.
5.0
Jprgensen (1976)


CHAPTER 5
THE SEAGRASS MODEL
Using Seagrass as a Bioindicator of the Estuarine System
Seagrasses have an important role in the ecology of estuarine systems where they are
present (e.g. Culter, 1992; Tomasko et al., 1996; Phillips and Meñez, 1988; Short, 1980).
They serve as habitat for fish and benthic invertebrates. Seagrass leaves provide substrate
for many epiphytic organisms. Herbivores such as manatees, fishes, sea turtles, and sea
urchins graze directly on seagrass blades. Dead leaves constitute the majority of the detritus
pool in seagrass beds. Seagrass also interacts with the physical components of the estuary
by slowing down the currents (Fonseca et al., 1982). Their presence also inhibits the
resuspension of sediments, which also affects nutrient cycles by reinforcing the deposition
of organic and inorganic material from the water column (Bartleson, 1988).
Since each species of seagrass has its own particular response to physical and
oceanographical factors, one species is usually dominant in any given area (Dawes et al.,
1985; Williams, 1990; Short et al, 1989). Some studies even suggest that succession or
replacement can be attributed to the water quality and trophic state of the system (Tomasko
et al., 1996). According to the authors, Thalassia can be characterized as a truly
oligotrophic species, which cannot prevail in areas of elevated nutrient loading.
79

80
Therefore, in estuarine systems where seagrass has declined due to anthropogenic
effects, restoration of seagrass beds can be linked exclusively to environmental quality. In
this sense, seagrass provides a direct assessment of the success of the restoration processes
(Dennison etal., 1993).
Seagrass Ecosystems
Seagrasses are unique for the marine environment as they are the only flowering
plants that have totally returned to the sea (Zieman, 1982). Florida enjoys one the largest
seagrass resources on Earth. Of the 10,000 km2 of seagrass bed in the Gulf of Mexico, over
8,500 km2 are in Florida waters, primarily in the southern end of the peninsula. Physical and
oceanographical factors drastically reduce the amount of seagrass bed north of Florida Bay,
on both coasts. Along the Atlantic coast, a wave dominated environment with a relatively
unstable substrate, seagrass beds are confined to inlets and lagoons. On the Gulf of Mexico
coast, seagrass beds diminish due to the high-turbidity waters and reduced salinity coming
from land drainage. North of this area, several bays, including Tampa Bay and Boca Ciega
Bay, formerly possessed extensive seagrass coverage, but anthropogenic perturbations have
greatly reduced the extent of these beds (Zieman, 1982).
According to den Hartog (1970), marine aquatic angiosperms referred to as
seagrasses include approximately 49 species in 12 genera. The three dominant species of the
west coast of Florida are Thalassia testudinum, Halodule wrightii, and Syringodium filiforme
(Zieman and Zieman, 1989). A detailed description of physiology and production ecology
of seagrasses can be found in McRoy and Helfferich (1977), Phillips and McRoy (1980),

81
Zieman (1982), and Phillips and Meñez (1987). The following is a brief description of each
species reproduced from Zieman (1982). Figure 5.1 shows a schematic picture of the three
species.
Thalassia testudinum (turtle grass) is the largest and most vigorous of the southwest
Florida seagrasses. Leaves are ribbon-like, typically 4 to 12 mm wide with rounded tips and
are 10 to 35 cm in length. There are commonly two to five leaves per turion. Rhizomes are
typically 3 to 5 mm wide and may be found as deep as 25 cm in the sediment. Turtle grass
forms extensive meadows throughout most of its range.
Halodule wrightii (shoal grass) is an early colonizer of disturbed areas. It is found
primarily in disturbed areas where Thalassia or Syringodium are excluded because of
prevailing conditions such as repeated exposure to air. Leaves are flat, typically 1 to 3 mm
wide and 10 to 20 cm long, and arise from erect shoots. The tips of the leaves are not
rounded, but have two or three points, an important recognition character. Shoal grass has
been reported to be the most tolerant of all seagrasses to variations in salinity, and exposure
to air (e.g., McMillan, 1974). However, recent low salinity and seagrass distributions in
Florida Bay may suggest that Thalassia could be more tolerant to prolonged lower salinity
levels (Montague, person, comm.).
Syringodium fdiforme (manatee grass) is distinctive in having cylindrical leaves.
There are commonly two to four leaves per turion, and these are 1.0 to 1.5 mm in diameter.
Length is highly variable, but can exceed 50 cm. The rhizome is less robust than that of
Thalassia and more surficially rooted. Manatee grass is commonly mixed with the other
seagrasses, or in small, dense, monospecific patches.

82
Figure 5.1 -
Seagrass species
Meñez, 1987).
commonlyfoundinwest
Florida (from Phillips and

83
Previous Work
The development of a numerical model of the seagrass community may provide a
mechanism for synthesizing all the dynamic functions (hydrodynamics, water quality,
primary production, etc.) of an estuarine ecosystem. Short (1980), using energy flow
diagrams (Odum, 1971), developed a seagrass community model to investigate the
mechanisms of temperate seagrass (eelgrass) production. Results of that study predicted an
average production rate for Charlestown Pond (Rhode Island) that was comparable to
observed rates.
Bach (1993) extended a general eutrophication model for the Denmark coastal area
to include the seasonal variations in growth of seagrass. Coupling between the eutrophication
and seagrass models was performed by seagrass nutrient uptake and detritus. Hydrodynamics
effects were coupled to the model simulation through a hydrodynamics box model.
Fears (1993) used a numerical model developed by Dr. C. Montague (unpublished
manuscript) to study the salinity fluctuations effects on seagrass distribution, abundance, and
species composition. The salinity fluctuations were represented in the model by step
functions, single short-lived pulses, or sinusoidal functions. For each seagrass species,
literature and experimental values were assigned for maximum growth rate, optimal salinity,
range of salinity tolerance, and death rate. Model sensitivity analysis showed maximum
growth rate and minimum death rate as the crucial parameters of the model. Optimal salinity

84
coefficient and tolerance range were key parameters in determining the cause/effect
relationship between salinity fluctuations and seagrass response.
Fong and Harwell (1994) developed a STELLA model to predict changes in the
biomass of five components (three species of tropical seagrass, epiphytic algae, and
macroalgae) of the seagrass community of Florida Bay. Environmental parameters (light,
temperature, salinity, sediment nutrients, water column nutrients) were represented by
literature values or sinusoidal functions, with no coupling with hydrodynamics. The most
important model parameters were productivity/biomass relationships, differential tolerances
to extreme salinity, and P/I curves. An important characteristic of Fong and Harwell’s model
is the feedback loop between the abundance of epiphytes and the amount of light reaching
the seagrass blades, leading to a competition type of relationship.
Erftemeijer and Middelburg (1995) studied the nutrient cycling in tropical seagrass
using a simple mass balance model. Model simulations used measured data on nutrient
availability, seagrass primary production, community oxygen metabolism, seagrass tissue
nutrient contents, and sediment-water nutrient exchange rates from South Sulawesi
(Indonesia). Results of that study, showed that the ratio between leaf vs. root nutrient uptake
depend on internal nutrient recycling (translocation from old plant parts to new growing
parts), with higher internal recycling increasing the importance of leaf uptake. Throughout
the internal recycling range (from 0 to 50%), the model showed that nutrient is
predominantly uptaken by the root-system.
Sheng et al. (1995) developed a coupled 2-D hydrodynamics-water quality-light-
seagrass model to quantify the impact of reduced nutrient loading on the water quality and

85
light/seagrass dynamics in Roberts Bay, Florida. The results of that study showed that
reduced nutrient loading led to increased DO and light, and reduced phytoplankton, CBOD,
dissolved organic nitrogen and ammonium nitrogen. However, there was no noticeable
increase in seagrass biomass, since sediment nutrient concentration, which controlled the
seagrass growth in the model, was still saturated. With a 100% load reduction, the study
showed a more pronounced impact for such parameters as nitrogen and phytoplankton, but
not significantly different for light and seagrass, again due to saturated nutrient concentration
in the sediment column.
Development of the Numerical Model
The conceptual model used in this study was originally developed by Fong and
Harwell (1994), and was shown to be able to describe some dynamic interactions of the
seagrass community structure in the Florida Keys. In this study, the conceptual model is
improved to: (a) adapt the model to the Tampa Bay conditions; (b) give the model a spatial
dimension; (c) add a more realistic mathematical description of the available light to the
seagrass bed; and (d) incorporate the three-dimensional structure of the hydrodynamics,
sediment and water quality dynamics model into the simulations.
This seagrass model consists of four biotic variables, including three species of
seagrass found in Tampa Bay, Thalassia testudinum, Halodule wrightii, and Syringodium
filiforme, and a functional form of epiphytic algae on seagrass (Figure 5.2). In the model the
epiphytic algae is controlled by light, temperature, water-column nutrient concentration, and

86
available substrate (seagrass density) (Figure 5.3). The abundance of each species of
seagrass is controlled by available light, temperature, salinity, sediment nutrient
concentration, and physical disturbance through bottom shear stress (Figure 5.4).
Figure 5.2 - Structure and components of the numerical seagrass model used for this
study.

87
Figure 5.3 - Epiphytic algae model flow chart.
Figure 5.4 - Seagrass model flow chart,

88
Mathematical Formulation
For each species of seagrass, literature values of maximum growth rates and biomass
are obtained, and incorporated to a density-dependent growth function. Subsequently,
environmental variability in light, temperature, salinity, and sediment nutrient concentration
would result in stresses to the growth rate, reducing the maximum growth rate according to
species-specific sensitivity. Death rates are accelerated when extreme values of salinity and
temperature are endured for an extended period of time. Next, the mathematical formulation
describing environmental factors that affect the seagrass community will be presented,
followed by the relationships controlling seagrass productivity.
Light
Light regime is the primary environmental factor influencing photosynthesis, growth
and depth distribution of seagrasses (Dennison, 1987). Light availability is often the primary
limiting factor for seagrass growth (e.g. Wetzel and Penhale, 1983; Dennison and Alberte,
1985). Studies showing the decline of seagrass due to increases in water turbidity
demonstrate the crucial role of light in determining seagrass distribution (Orth and Moore,
1983; Cambridge and McComb, 1984). Therefore, the determination of the relationship
between available light and seagrass growth and distribution is of extreme importance in a
modeling effort. The amount of photosynthetically active radiance (PAR) reaching the
seagrass bed is obtained from the water quality component of this integrated model.

89
Temperature
The seasonal variation of water temperature is represented in the model by a sine
curve:
(5.1)
corresponding to an annual average of 23 °C, higher temperature levels during summer
(maximum of 30 °C) and the lowest levels during winter (minimum of 16 °C) (Zieman and
Zieman, 1989).
Salinity
Montague and Ley (1993) reviewed previous studies on salinity tolerance of major
species of seagrass, and discussed possible effects of salinity fluctuation on seagrass
abundance in Northeastern Florida Bay. Their study showed that salinity changes could
cause changes in both the distribution and total abundance of benthic vegetation.
Salinity is a state variable of the circulation and transport model, and its distribution
is obtained from the hydrodynamics component of this integrated model.
Density-Dependent Growth Rate
For Thalassia, Williams (1988) found maximum growth rates up to 27 g dry wt
m ~2 day "’in pristine areas of the Virgin Islands, and Fourqurean and Zieman (1991) found
maximum biomass to be 470 g dry wt m ~2 in Florida Bay. Powell et al. (1989) found that
Halodule in Florida Bay can grow as fast as 16 g dry wt m”2 day"1, and a maximum
biomass of 150 g dry wt m "2. For Syringodium, Short et al. (1985) reported a maximum

90
growth rate of 6.3 g dry wt m ~2 day , in the Bahamas, and a maximum biomass of 190
g dry wt m '2. Thus, the hierarchy for growth rates is Thalassia > Halodule > Syringodium
and for maximum biomass is Thalassia > Halodule ~ Syringodium, resulting in a density-
dependent growth curve that favors Thalassia throughout the range of densities (Figure 5.5).
These growth rates correspond to “optimal” environmental conditions, therefore, each
maximum growth rate is further modified by light, temperature, salinity, and sediment
nutrient concentration, resulting in a possible alteration in the growth-rate hierarchy.
Density-dependent Growth Rate
Figure 5.5 - Seagrass density-dependent maximum growth rate: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line).

91
Growth Rate Dependence on Light
Most studies on seagrass distribution and growth reveal that light is an important
factor controlling seagrass distribution (e.g. Williams, 1987; Dawes and Tomasko, 1988;
Dunton, 1990). Fourqurean and Zieman (1991) established the relationship between light
and photosynthesis for Thalassia, specifying Pmaxof 200 pg 02- g_1 • min'1. In this model,
we assumed saturation occurring at 425 \xE m ~2 s_1, and no photoinhibtion at high light
levels; the compensation point is approximately 15.1-15.7 \xEm "2 s_1. Williams (1987)
found that light saturation levels for Halodule and Syringodium were similar. Fong and
Harwell (1994) assumed that Halodule may require less light than the other species for
maximum productivity, so in the model the saturation point for Halodule is 300 \xEm ~2 s l.
In other words, Fong and Harwell (1994) postulates that growth of Thalassia and
Syringodium is reduced when available light is less than 425 \iE m '2 s ~l, while growth
remains maximum for Halodule until light is below 300 \xE m ~2 s_1 .
The mathematical formulation of the growth rate dependence on light is given by
(Fig. 5.6):
j _ e -0.013-avll
l. -e (5.2)
j _ g -0.040-avll
T
1 light
Hlight
Slight
where avll represents the available light at the seagrass bed.

Light Limitation Factor
92
Light Dependence
Figure 5.6 - Seagrass growth rate dependence on light: Thalassia (dotted line), Halodule
(solid line), and Syringodium (dash-dotted line).

93
Growth Rate Dependence on Salinity
There are few studies that directly test the effect of altered salinity on seagrasses. We
performed a laboratory experiment to study the response of three species of tropical
seagrasses to salinity fluctuations (Yassuda et al, 1996 - manuscr. in preparation), and
preliminary results demonstrate that tolerance is species-specific, with Halodule being the
most tolerant to salinity variations, and Syringodium being the least tolerant. This results
agree with literature and the hypothesis of the original model (Fong and Harwell, 1994).
The seagrass growth-salinity relationship specific for each species shows that
Halodule has the widest salinity optimal, with growth being reduced for salinity below 30
and above 45 ppt.
The mathematical formulation of the growth rate dependence on salinity is given by
(Figure 5.7):
For Thalassia
salinity < 31.67
Tsal = 0.00035 -e025-sal
31.67 < sal < 35.0
Tsai = 0.009 -sal +0.685
35.0 < sal < 41.67
Lai = I’»
41.67 < sal < 45.0
Tsai = -0.003 â–  sal + 1.125
(5.3)

94
For Halodule
salinity < 18.0
Hsal = 0.006’sal - 0.0751
18.0 < sal < 28.0
Hsal = -0.0109-sal2 + 0.5963-sal - 7.2
28.0 < sal < 32.0
Hsal = 0.0165’sal + 0.4785
32.0 < sal < 35.0
Hsal = 1-0
35.0 < sal < 38.0
Hsal = -0.3003 • sal + 11.5105
sal > 38.0
(5.4)
For Syringodium
salinity < 18.0
Ssal = 0.0
18.0 < sal < 32.0
SsaI = 0.0065-sal2 - 0.2551 -sal + 2.5037
32.0 < sal < 38.0
Ssal = -0.0056-sal2 + 0.3885-sal - 5.74
38.0 < sal < 52.0
Ssal = 0.0065-5fl/2 -0.6533-ia/ + 3.35
sal > 52.0
(5.5)

95
Salinity Dependence
Figure 5.7 - Seagrass growth rate dependence on salinity: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line).

96
Growth Rate Dependence on Temperature
Tomasko and Dawes (1990) reported some seasonal trends in the growth rate of
Sarasota Bay seagrasses. To be consistent with the hypothesis that Halodule is an
opportunistic species that often dominates in transition areas, the model specifies a broader
range of optimal temperature for Halodule, followed by Thalassia, and assigns to
Syringodium the least temperature variation tolerance. Optimum growth for all three species
of seagrass occurs at 26 °C, and growth rate decreases at higher or lower temperatures.
The mathematical formulation of the growth rate dependence on temperature is given
by (Figure 5.8):
For Thalassia
Ttemp = -0.0059-temp2 + 0.329-temp - 3.5862 (5.4)
For Halodule:
temp < 23.0
Htemp = -0.0123’temp2 +0.6029'temp - 6.3436
23.0 < temp < 26.0
Htemp = 1.0
26.0 < temp < 52.0
Htemp - “0.0123 • temp 2 + 0.6029 • temp - 6.3436
temp > 52.0
H
temp
0.0
(5.3)

97
For Syringodium
temp < 18.0
^ = o-o
18.0 < temp < 32.0
temp
-0.0203-temp2 + 1.021 'temp - 11.83
(5.3)
temp > 32.0
Stemp = 0-0
Temperature Dependence
Figure 5.8 - Seagrass growth rate dependence on temperature: Thalassia (dotted line),
Halodule (solid line), and Syringodium (dash-dotted line).

98
Growth Rate Dependence on Sediment Nutrients
According to the characterization presented in Chapter 2, Tampa Bay sediments are
rich in phosphorus. If sediment nutrients limit seagrass production, it is most likely
nitrogen. Seagrass takes up most of its nitrogen requirements as ammonium from the
sediment via its root-rhizome system (Short and McRoy, 1984; Erftemeijer and Middelburg,
1995). In this study, the nitrogen uptake is proportional to a fixed internal concentration that
is assumed to be 2% of the seagrass dry weight (Zimmerman et al., 1987; Pellikaan and
Nienhuis, 1988). Using a formulation similar to the one describing phytoplankton nutrient
uptake, sediment nitrogen levels below 0.95% of the seagrass internal content is assumed to
inhibit growth (Short, 1987; Pregnall etal., 1987; Zimmerman etal., 1987).
Theoretically, specific sediment nutrient relationships should be formulated to
describe species differentiation. Like for the physical parameters, Halodule would be
favored in more extreme conditions of a eutrophic organic-rich sediment (Tomasko et al.,
1996). Syringodium would prevail in low suspended sediment concentration, since its
distribution is restricted to more oceanic environments. Thalassia would present a wide
range of sediment nutrient concentration tolerance, but could not survive in anaerobic
conditions that commonly occur in nutrient-rich sediments (Tomasko et al., 1996). The lack
of literature data on tropical seagrasses and nitrogen uptake prevented a further refinement
of the model formulation, and reveals the need for more experimental research in this area.

CHAPTER 6
APPLICATION OF THE CIRCULATION AND TRANSPORT MODEL
Design of Tampa Bav Grid
Previous hydrodynamic studies (Goodwin, 1987; Galperin etal. 1991; Hess, 1994;
Sheng and Yassuda, 1995) demonstrated that complex geometrical and bathymetrical
features in the Tampa Bay Estuarine System (Figure 2.1) have a profound influence on the
circulation and transport within the Bay. Thus, to successfully apply an integrated model to
Tampa Bay, it is essential to design a numerical grid which preserves the dominant
geometrical/bathymetrical features. Using a boundary-fitted curvilinear grid, it is possible
to design grid lines which coincide with shoreline, causeways, bridges, and the navigation
channels. Sheng and Peene (1992), Peene (1995), and Sheng et al. (1995) used a relatively
coarse boundary-fitted grid for Tampa Bay (15 x 51 horizontal cells and 4 vertical layers) in
their studies of the entire Sarasota and Tampa Bay Systems (189 x 51 horizontal cells and
4 vertical layers). Preliminary studies of the navigation channel influence on the
hydrodynamics (Yassuda etal., 1992) demonstrate the importance of accurate representation
of navigation channel in simulating the circulation pattern in Tampa Bay. Sheng and
Yassuda (1995) refined the grid to 39 x 62 horizontal cells and 4 vertical layers in order to
simulate residual flow and salinity field under four different forcing conditions. Their results
suggest that simulation results could be improved by refining the horizontal grid along the
East side of the Bay, where most of the freshwater inflow occurs. Model tests with 4, 8, and
99

100
15 vertical layers were performed and the optimal balance between computational cost and
accuracy was obtained with 8 layers. Furthermore, the grid was extended offshore so that
the ocean boundary coincided with the NOAA C-l station, where tidal data was obtained for
the period of August 1990 to September 1991. Figure 6.1 shows the location of the NOAA’s
“Tampa Bay Oceanographic Project” stations, where “C” stands for current meters, “M” for
meteorological, “T” for tidal gages, and “S” for salinity.
The computational grid used for the integrated model of the Tampa Bay Estuarine
System is shown in Figure 6.2. It contains 45 by 85 horizontal cells and 8 vertical layers,
with a total of 30600 grid cells. Grid spacing varies from 100 to 1500 meters. This grid was
generated using a grid generation program originally developed by Thompson (1985), and
digitized Florida coastline data.
The depth information was based on the raw data obtained from NOAA’s National
Geophysical Data Center. Inasmuch as these data sets were obtained from surveys done
during the 1960's and 1970's, they lack a good representation of the navigation channel.
Hess(1994), during the calibration process of the NOAA/Princeton model of Tampa Bay,
reported that the best result was obtained by multiplying the original cell depth by spatially
varying constants. In an attempt to improve model results, the raw bathymetric data was
modified by “dredging” the navigation channel up to the depth recorded by NOAA’s
instruments in 1991 (NOAA, 1994), and then smoothing the bathymetry along the cross-
section. The bathymetric contours used in this study are plotted in Figure 6.3.
Causeways, small spoil islands, and any other sub-grid scale features are represented
as bars in the computational grid. Flow and transport are not allowed to go through the bars.
For the purpose of studying advective fluxes throughout the Bay, Sheng and Yassuda
(1995) further divided the computational grid of Figure 6.2 into 14 Bay segments,

101
approximately corresponding to the WASP segments of AScI (1996) study. This
segmentation, shown in Figure 6.4, will be used in this study to evaluate the flushing
characteristics of each Bay segment.
NOAA’s Tampa Bay Oceanographic Project Stations
Figure 6.1 - NOAA’s TOP station locations in Tampa Bay.

Gulf of Mexico
102
N
TAMPA BAY
Computational Grid - 45 x 85 cells
ii ssrvfc»
Figure 6.2 - A boundary-fitted grid for the Tampa Bay Estuarine System.

Gulf of Mexico
103
TAMPA BAY
Bathymetry
Figure 6.3 - Tampa Bay bathymetric contours

104
Figure 6.4 - Bay segments (Sheng and Yassuda, 1995).

105
Forcing Mechanisms and Boundary Conditions
The tidal forcing along the Gulf of Mexico boundary was prescribed by real data
obtained at the NOAA C-l station (Figure 6.5 and 6.6). The time series were obtained from
a pressure transducer fixed to a bottom-mounted ADCP (Acoustic Doppler Current Profiler)
unit positioned approximately 8 km west of the mouth of the Bay. The tidal spectrum clearly
shows the diurnal and semidiurnal frequency dominance. From these figures, it is possible
to classify the incident tide as mixed, mainly semidiurnal, which is in accordance with the
results obtained by NOAA (1993) using the Defant (1961) criteria .
The baroclinic simulation requires a realistic initial salinity field in order to minimize
effects of the initial conditions on the solution, and to avoid longer “spin-up” time.
Seasonal-averages of the salinity distribution in Tampa Bay (Boler, 1992) were used to
determine an initial salinity at each grid cell. Since the data portrayed vertically averaged
conditions, a 1 ppt difference was assumed between the bottom and the top layer in Lower
and Middle Tampa Bay. For Hillsborough Bay and Old Tampa Bay, a 2 ppt vertical
stratification was assumed. Figure 6.7 shows the initial salinity field (surface layer) used in
the 1990 simulation, and Figure 6.8 shows the initial salinity field (surface layer) used in the
1991 simulation.
The offshore salinity boundary condition was determined from a 1 -D advection for
the ebb flow, and a prescribed value during the inflow. Based on NOAA’s data (NOAA,
1993), the salinity in the Gulf of Mexico next to Tampa Bay is approximately constant,
around 36 ppt. Hence, salinity value of 36 ppt was assigned as the prescribed boundary
condition.

power spectrum density (cm2 - day) Surface Elevation (cm)
106
Tidal Forcing -1990
50
0
-50
_-|0Q 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
230 240 250 260 270 280 290
Julian Day (1990)
Spectra of Tidal Forcing
cycles/day (cpd)
Figure 6.5 - Tidal forcing for the 1990 simulation.

power spectrum density (cm2 - day) Surface Elevation (cm)
107
cycles / day (cpd)
Figure 6.6 - Tidal forcing for the 1991 simulation.

108
Initial Salinity Distribution - Sep/1990
Surface
Salinity
36
32
28
23
19
15
Figure 6.7 - Initial salinity distribution (surface) for the 1990 simulation

109
Initial Salinity Distribution - Jul/1991
Surface
Salinity
36
32
28
23
19
15
Figure 6.8 - Initial salinity distribution (surface) for the 1991 simulation

110
River discharge and rainfall are the two principal sources of freshwater into the
system. Hourly rainfall data were obtained from NOAA’s National Climate Data Center
(NCDC) at three stations (Tampa Bay Inti. Airport, St. Petersburg, and Parrish) (NOAA,
1991). Figure 6.9 shows the rainfall data for September to November of 1990 (dry-period),
and July to August of 1991 (wet-period). The rainfall data were interpolated into the
computational grid, with the weighting function inversely proportional to the distance to each
of the three stations.
Daily river discharge for the Hillsborough River, Alafia River, Little Manatee River,
Rocky Creek, and Sweetwater Creek were obtained from USGS (1991, 1992). Since these
publications only report discharges upstream the Manatee River dam, and there was no
record for Lake Tarpon Canal, historical values were used for these two rivers (Figure 6.10).
At each river boundary, salinity was prescribed as constant based on seasonal values (Wolfe
and Drew, 1990; Boler, 1992).
During the simulations, wind stress is applied at all surface cells. For the 1990
simulation, the wind field (velocity and direction) from two stations (Tampa Bay Inti. Airport
and NOAA’s station M-2) was obtained with a three-hour interval. For the 1991 simulation,
data from four stations (Tampa Bay Inti. Airport and NOAA’s stations M-2, M-3, and M-4)
were used. Wind speed is transformed to wind stress using Garrat’s formula (Garrat, 1977),
and interpolated into the computational grid according to the same procedure used for
rainfall. Figure 6.11 and 6.12 show stick diagrams of the wind velocities for September to
November 1990, and July to August 1991, respectively.

Rainfall (cm)
111
Rainfall Data
Julian Day (1990)
Figure 6.9 - Rainfall data for the 1990 and 1991 simulations.

Discharge (m3/s) Discharge (m3/s)
112
1990 Simulation - River Discharges
1991 Simulation - River Discharges
120 I-
100
— Hillsborough
- Alafia
Little Manatee
Rocky
Sweetwater
Manatee
Lake Tarpon Canal
190 200 210 220
Julian Day (1991)
230
240
Figure 6.10 - River discharges for the 1990 and 1991 simulations.

113
Station M-2
Tampa Inti. Airport
10 m/s
240
245
250
255
260
265
270
275
280
Julian Day (1990)
Figure 6.11 - Wind velocity for the 1990 simulation.

114
Station M-1
180”“ * * 190 ‘ ‘ 200 * ‘ 210 * 220 * ‘ 230 ‘ * 240 250
Julian Day (1991)
Station M-3
180 190 200 210 220 230 240 250
Julian Day (1991)
Station M-4
10 m/s
180"“ ' ' 190 ' ' 200 ' ' 210 220 230 ' 240 “"250
Julian Day (1991)
Figure 6.12 - Wind velocity for the 1991 simulation.

115
Modeling Strategy
During the calibration process, the model was adjusted to simulate a particular
condition where enough data enabled tuning of model coefficients and inputs. For this
purpose, September 1990 was selected because the “Tampa Bay Oceanographic Project”
(NOAA, 1993) provided data for tidal stage, currents, and salinity at several locations
throughout the Bay. As to validation, model coefficients were held fixed at the calibration
values, and the hydrodynamic component of the model was tested using July and August
1991 data. The model’s ability to reproduce episodic events was assessed by means of the
simulation of the tropical storm “Marco” in October 1990.
Results of the Barotropic Simulation
Several simulations were performed in order to test the grid configuration, bottom
roughness, horizontal diffusion constant, and bathymetry. The results evidenced that the
model is particularly sensitive to water depth. Unfortunately, the “Tampa Bay
Oceanographic Project” conducted by NOAA did not make any attempt to improve the
bathymetric data of the Bay, which correspond to surveys done prior to major dredging.
Initial results showed that tidal amplitude and phase in the upper reaches of the Bay
could be calibrated through bottom friction, although the corresponding bottom roughness
height (0.01 cm) was an order of magnitude smaller than usual values reported in the
literature (0.1 to 1.0 cm). Furthermore, a comparison between data and model results at the
Sunshine Skyway Bridge revealed an offset in the vertical profile of the longitudinal residual

116
currents. This difference suggests that on an intertidal basis, more water should be entering
the Bay. By dredging the navigation channel up to the depth reported by the instruments
deployed in 1990 by NOAA, a better agreement was obtained between data and model
results.
Figure 6.13 shows the comparison between measured and simulated surface elevation
for Egmont Key, close to the mouth of the Bay, and St. Petersburg, in Middle Tampa Bay.
Figure 6.14 shows data and model results for Davis Island in the upper reaches of
Hillsborough Bay, and Bay Aristocrat Village in the upper reaches of Old Tampa Bay. In
order to avoid offsets due to original leveling of the gages, the measured data sets were
demeaned prior to comparison with model results. The plots show a good agreement
between data and model results, both in amplitude and phase. From these figures, it can be
seen that tidal range increases about 31% from the mouth to the upper reaches of the Bay.
Also, the tidal wave takes about four to five hours to reach the head of Old Tampa Bay, and
about three to four hours to reach the head of Hillsborough Bay.
Overall, the model is able to simulate surface elevation within 10%. This indicates
that the propagation of the tidal wave can be accurately simulated with the barotropic model,
and bathymetry, horizontal diffusion, and bottom roughness constant are reasonably
calibrated.
Summing up, grid resolution and bathymetry are the most sensitive inputs to the
model, with increased resolution improving model accuracy. Changes in bathymetry are
usually directly related to changes in tidal amplitude. Bottom friction is inversely
proportional to tidal amplitude, especially in the upper reaches of the Bay. Increasing bottom
friction also reduces amplitude of currents, and increase the time lag of the tidal wave.

Surface Elevation (cm) Surface Elevation (cm)
117
Surface Elevation
Figure 6.13 - Surface elevation at Egmont Key and St.Petersburg (September 1990).

Surface Elevation (cm) Surface Elevation (cm)
118
Surface Elevation
Figure 6.14 - Surface elevation at Davis Island and Old Tampa Bay (September 1990).

119
Results of the Baroclinic Simulation
Following the barotropic simulation with tidal forcing only, the model calibration
proceeded with baroclinic and wind-driven circulation as well. The baroclinic simulation
starts with a “spin-up” run which is summarized below:
• A initial salinity field (Figure 6.6), typical of dry-season conditions was generated
based on available data collected by EPC throughout the Bay (Boler, 1992). As described
in the “Forcing Mechanisms and Boundary Conditions” section, data from different stations
were interpolated into the computational grid, using a weighting function inversely
proportional to the distance from the three closest stations.
• Starting with a zero velocity field, and without any barotropic forcing mechanisms
(tides, river discharges, and wind), a steady-state condition, representing the balance between
the initial salinity distribution (that remained unchanged), the velocity field, and surface
elevation was achieved in 5 days. The results showed that the horizontal salinity gradient
between the Gulf of Mexico and the upper reaches of Bay is balanced by a setup of 4 cm
towards the head of the Bay. This superelevation, as defined by Mehta (1990), is in
agreement with the results of the conceptual model developed by Weisberg and Williams
(1991) in a study of the role of buoyancy in driving a non-tidal circulation in Tampa Bay.
• After this period, tides (represented by the four major tidal constituents - M2, S 2,
O j, and K,), and river discharges (averaged values for September 1990) were turned on

120
and the simulation continued for 90 days. This 90-day spin-up time was sufficient to allow
the salinity field to reach a dynamic steady-state throughout the computational grid.
Using the results of the spin-up run (surface elevation, velocity, and salinity) as the
initial condition, Tampa Bay circulation during September 1990 was simulated with real data
of tidal forcing, river discharges, rainfall, and wind field.
To quantify the model’s performance, time series statistics are presented in terms of
the root-mean-square error (Erms) and the normalized rms error, defined as the ratio between
the rms error to the observed range. The normalized rms error gives a more meaningful
indication on model’s ability to reproduce the tidal signal at each station.
The rms error is calculated according to:
(6.1)
where N is the total number of signal pairs, r\model is the model result, and r\data is the tidal
data at each NOAA station.
Since tidal constituents do not vary significantly over the year inside Tampa Bay
(NOAA, 1993), it is worthwhile to evaluate the model’s ability to simulate measured tidal
characteristics by using the method of harmonic analysis i.e., comparing simulated and
measured tidal constituents at a few selected stations.
First, a Fourier analysis was performed to determine the spectral density of both
measured and simulated data. Inasmuch as the area under the spectral density curve
(variance) is proportional to the total energy of the signal, the breakdown of the spectral
density in specific frequency-bands defines the relative energies within each band.

121
Subsequently, a least-squares harmonic analysis was performed. Simulated and measured
data were compared in terms of the amplitude and phase of the four major tidal components
(M2, S2, Oj, and K,).
The spectral analysis was performed using specific subroutines (power spectrum
density - psd) of the data analysis program MATLAB. In calculating the spectral density,
MATLAB utilizes Welch’s method which performs an FFT transformation over a series of
overlapping or non-overlapping data sets. Due to normalization done internally in the
program, the energies calculated by MATLAB were utilized in a relative sense to determine
the distribution of spectral densities, and to perform comparative analysis.
Tides
Table 6.1 presents the maximum measured tidal range, the rms error, and the
normalized rms error percentile for Egmont Key, close to the mouth of the Bay, St.
Petersburg, in Middle Tampa Bay, Davis Island in the upper reaches of Hillsborough Bay,
and Bay Aristocrat Village in the upper reaches of Old Tampa Bay.
Table 6.1- The rms error (Erms) between measured and simulated water surface elevation -
September/90.
Station
Measured Tidal
Range (cm)
Erms
(cm)
Normalized
Erms (%)
Egmont Key
86.57
4.02
4.6
Mullet Key
82.16
3.77
4.5
Desoto Point
86.71
4.63
5.3
St.Petersburg
87.79
6.59
7.5
Davis Island
106.28
7.95
7.5
Old Tampa Bay
99.15
5.90
5.9

122
The normalized errors are low, demonstrating the model’s ability to accurately
reproduce surface elevation in Tampa Bay. The highest errors presented in St. Petersburg
and Davis Island can be attributed to the horizontal grid configuration, since the
computational grid does not have a high resolution close to the area where the gages were
located.
Figure 6.15 shows the spectra of water surface elevation (data and model results) for
the same stations. These spectral curves reveal major energy bands centered around three
frequencies: the subtidal band (up to 0.5 cycles per day); the diurnal band (between 0.8 to 1.2
cycles per day); and the semi-diurnal band (1.8 to 2.2 cycles per day). The three bands
combined, represent the tides propagating from the Gulf of Mexico into the Bay. Secondary
energy bands, representing non-linear interactions between diurnal and semi-diurnal tides
with complex geometries and bathymetric features inside the Bay, are represented by the
relatively small third and fourth diurnal peaks. As indicated by NOAA (1993), these
overtides are not significant in the overall circulation pattern of the Bay. Model results agree
quite well with data in terms of total spectral energies as well as in the representation of the
major frequency bands. The diurnal band is particularly well represented by the model, from
the entrance of the Bay up to the head of Hillsborough Bay and Old Tampa Bay. In St.
Petersburg, model results show a broader spectrum in the semi-diurnal band than the one
from measured data. Particularities of the location of the tidal gage, not resolved in the
model could be causing that.

TC
a
power spectrum density
(cm2 - day)
power spectrum density
(cm2 - day)
Davis Island
power spectrum density power spectrum density
(cm2 - day) (cm2 - day)
tsJ
OJ

124
Table 6.2 presents the distribution of energies for water surface elevation in terms of
the total energy (area under the spectral density curve), the percent energies within each
frequency bands, and the total energy represented by these four bands. It should be pointed
out that energies associated with each frequency band include not only tidal components but
also those related to the wind field. As an example, the diurnal pattern of the seabreeze is
incorporated into the diurnal band, and meteorological fronts can be associated to subtidal
fluctuations (Peene, 1995).
Station
Total
Energy
(cm2 - day)
Sub
Tidal
(%)
Diurnal
(%)
Semi
Diurnal
(%)
Overtide
(%)
Percent
Total
Egmont Key
Data
4.7E5
1.7
59.2
37.4
0.8
99.2
Model
5.2E5
1.0
55.7
42.1
0.6
99.4
St.Petersburg
Data
5.9E5
3.5
55.4
39.5
0.4
98.8
Model
5.7E5
1.2
55.2
42.9
0.2
99.5
Davis Island
Data
6.5E5
2.7
53.2
42.4
0.5
99.0
Model
7.4E5
1.7
47.4
49.1
1.0
99.2
Old Tampa
Data
7.4E5
1.6
52.9
43.9
0.9
99.2
Bay
Model
6.9E5
1.2
52.7
44.2
1.3
99.3
In terms of total energy, the model overpredicts surface elevation in Egmont Key and
Davis Island, while underpredicting it in St. Petersburg and Old Tampa Bay, with no clear
pattern of inconsistency. The simulated and measured subtidal band are in the same order
of magnitude, with the model constantly underpredicting subtidal energy. The greatest
difference occurs in St. Petersburg. As part of the conclusions of the NOAA’s “Tampa Bay
Oceanographic Project” (NOAA, 1993), it was found that water level fluctuations at

125
Clearwater Beach were coherent with longshore winds over the continental shelf, and also
that subtidal fluctuations in Clearwater and St. Petersburg were highly coherent. This
phenomenon suggested that transport perpendicular to the coast would affect water levels in
Clearwater, penetrate Tampa Bay through Boca Ciega Bay and Egmont Channel, and cause
subtidal fluctuations in St. Petersburg. Peene (1995) also found that the measured residual
currents in Anna Maria Sound could only be reproduced in the model if a longitudinal setup
was imposed in the oceanic boundary condition. In his conclusions, he attributed this
mechanisms to Ekman transport generated by alongshore winds in the Gulf of Mexico. In
the computational grid of the integrated model of the Tampa Bay Estuarine System only a
small portion of the Gulf of Mexico is represented, therefore large scale circulation features
cannot be resolved, and some of them will appear as subtidal fluctuations.
The simulated and measured energy within the diurnal band were very similar.
However, the agreement in the semi-diurnal band is not as good, and the model consistently
overpredicts water level fluctuations. The major discrepancy occurs in Hillsborough Bay,
where the data shows a clear diurnal dominance, while the energies in the model are equally
split, with a small dominance of the semi-diurnal band. In the secondary energy band, the
model is able to capture the general trend, presenting not only the same order of magnitude
of overtides energy, but also the same distribution inside this band (Figure 6.15).
Unlike Sarasota Bay, where inlets and restrictions act as low pass filters (Peene,
1995), Tampa Bay does not exhibit any damping in the higher frequencies as the tidal wave
propagates from the mouth (Egmont Key) to the head (Hillsborough Bay and Old Tampa
Bay). The total energy at the upper reaches of Old Tampa Bay and Hillsborough Bay is

126
almost 60% and 40% greater than the total energy at Egmont Key, respectively. This
amplification suggests that the tidal wave gradually changes from a progressive wave
entering from the Gulf of Mexico to a partially standing wave at the upper reaches of the
Bay. Numerical experiments using a 5 by 10 horizontal grid were able to reproduce this
amplification, when the longitudinal dimension of the basin became closer to a quarter of the
tidal wave length. Considering the idealized simulation of a closed-end frictionless tidal
basin, the ratio between the surface displacement at the head of the basin to the incident tide
tends to infinity when the longitudinal length approaches a quarter of the tidal wave length
(Ippen, 1966).
The results of the harmonic analysis revealed that the major tidal constituents are: the
lunar (M2, N2) and solar (S2) semi-diurnal constituents; and the lunar (O,) and solar (K])
diurnal constituents. Table 6.3 presents comparisons between measured and simulated tidal
harmonic constituents (amplitudes and phases) for the water surface elevation at Egmont Key
(entrance of the Bay), St. Petersburg (Middle Tampa Bay), Davis Island (head of
Hillsborough Bay), and Bay Aristocrat Village (head of Old Tampa Bay). The forcing tide
at the offshore boundary is also presented. The phases are relative to the first observation
(Julian Day 250 at 01:00), and phase differences are presented in hours in order to allow
comparison between constituents of different period.
Throughout the Bay, the model simulates the data with a satisfactory degree of
accuracy. Like in the barotropic simulation, the errors were greater in St. Petersburg and
Davis Island. The model consistently over-predicts amplitude and the simulated tidal wave
is always ahead in phase, which would indicate that bottom friction is not satisfactorily

127
damping the tidal wave as it propagates through the estuarine system. But, as it will be seen
from the analysis of currents, simulated velocity profiles at the Sunshine Skyway Bridge
present lower magnitudes, indicating a need for decreasing friction. A plausible explanation
would be that bathymetry is not well represented, and the mean water depth should be greater
up to Middle Tampa Bay, and shallower thereafter.
Overall, the model is able to better simulate the diurnal components than semi¬
diurnal. The greatest difference in Davis Island suggests that the lateral boundaries of the Bay
(e.g. bayous, mangroves, and wetlands) not represented in the model could help damping the
semidiurnal tidal wave that in the model is amplified due to the approximately quarter wave
length dimension of the Bay.
Table 6.3 -
Major tidal constituents in
Tampa Bay -
September/1990.
Station
Constituent
Amplitude
Data
(cm)
Amplitude
Model
(cm)
Error
(cm)
Phase
Data
(degrees)
Phase
Model
(degrees)
Error
(hours)
M2
18.0
18.0
-
221.7
221.7
-
Offshore
S2
11.0
11.0
-
317.8
317.8
-
Tide
N2
4.0
4.0
“
97.3
97.3
-
01
16.0
16.0
-
90.1
90.1
-
K1
10.0
10.0
-
39.5
39.5
-
M2
17.0
18.0
-1.0
248.0
229.6
0.63
S2
9.0
11.0
-2.0
347.8
326.0
0.72
Egmont
Key
N2
3.0
4.0
-1.0
120.7
104.9
0.55
Ol
16.0
16.0
0.0
103.0
92.4
0.76
K1
10.0
10.0
0.0
50.0
41.7
0.55

128
Table 6.3 - continued.
Station
Constituent
Amplitude
Amplitude
Error
Phase
Phase
Error
Data
Model
(cm)
Data
Model
(hours)
(cm)
(cm)
(degrees)
(degrees)
M2
20.0
20.0
0.0
316.8
286.0
1.06
S2
9.0
11.0
-2.0
61.7
25.9
1.19
St.
Petersburg
N2
4.0
4.0
0.0
196.5
166.7
1.04
01
17.0
16.0
1.0
127.6
117.1
0.75
K1
11.0
11.0
0.0
77.8
67.0
0.71
M2
21.0
24.0
-3.0
321.1
292.6
0.98
S2
11.0
13.0
-2.0
63.9
34.6
0.97
Davis
Island
N2
4.0
5.0
-1.0
201.3
174.9
0.92
Ol
17.0
17.0
0.0
130.4
119.4
0.78
K1
11.0
11.0
0.0
80.6
69.5
0.73
M2
23.0
22.0
1.0
354.5
333.6
0.72
Old
S2
11.0
12.0
-1.0
98.9
78.2
0.69
Tampa
N2
4.0
4.0
0.0
246.1
220.0
0.91
Bay
01
18.0
18.0
0.0
144.1
139.2
0.35
K1
13.0
12.0
1.0
91.3
88.6
0.17
Currents
For the purpose of assessing the model’s ability to reproduce the velocity field in the
Tampa Bay Estuarine System, time series of bottom and surface currents are compared in
terms of rms error, spectrum, and harmonic analysis.

129
In the deeper parts of the Bay, NOAA collected water velocity data using an ADCP.
The instruments were deployed on the bottom looking upward, with the velocity profile
obtained from measurements every meter from the bottom up to the surface.
Figure 6.16 shows the simulated and measured bottom velocity components at
NOAA’ station C-2 in the Egmont Channel (entrance of the Bay). The model underpredicts
the magnitude of bottom currents throughout the simulation period, which would indicate
an overestimation of bottom stress. However, as discussed in the surface elevation analysis,
forcing bottom stress to be smaller through adjustment of coefficients would make the tidal
ranges in the upper reaches of the Bay unrealistically bigger than measured data. A plausible
reason for the discrepancy between simulated and measured data could be attributed to
particularities in bottom topography not resolved by the computational grid, as well as the
precise location of the sensor not coinciding with model output. Nevertheless, the model
appears to simulate the general characteristics of the flow, both in the East-West and North-
South directions.
Figure 6.17 shows the simulated and measured surface velocity components at
NOAA’ station C-2 in the Egmont Channel (entrance of the Bay). The magnitude of the
surface currents are well simulated, both in East-West and North-South directions. This
indicates that the model is able to capture the details of the local circulation, marked by a
complex pattern of unidirectional (along channel axis) flow.

North-South Velocity (cm/s) East-West Velocity (cm/s)
130
Egmont Channel (22,12)
Bottom North-South Velocity
Figure 6.16 - Simulated and measured bottom velocity at Egmont Channel -
September 1990.

North-South Velocity (cm/s) East-West Velocity (cm/s)
131
Egmont Channel (22,12)
245
Surface North-South Velocity
i
250
255
260
Julian Day (1990)
265
270
Model
Data
275
Figure 6.17 - Simulated and measured surface velocity at Egmont Channel -
September 1990.

132
Figure 6.18 shows the simulated and measured bottom velocity components at the
Sunshine Skyway Bridge. This station, located inside the navigation channel at about Middle
Tampa Bay, presents high velocities in the along-channel direction, and a low across-channel
component. Since the navigation channel axis lies between 60 °T and 70 °T, the East-West
component is much greater than the North-South counterpart. The model appears to
accurately simulate the ebb flow, while systematically underpredicting flood flow.
Moreover, the along-channel currents are better represented than the across-channel ones.
Figure 6.19 shows the simulated and measured mid-depth velocity components at the
Sunshine Skyway Bridge. Likewise bottom currents, the model is able to reproduce the
overall circulation at mid-depth, corresponding to the ADCP signal at about 7 meters from
the bottom.
Figure 6.20 shows the simulated and measured surface velocity components at the
Sunshine Skyway Bridge. The comparison is made through the model results at the second
layer (from the surface) and the ADCP signal at about 13 meters from the bottom. Similar
to the bottom and mid-depth results, the model seems to accurately simulate the tidal flow
characteristics, despite of underpredicting currents during flood tide.
Comparing Figures 6.17 and 6.20 it is reasonable to argue that during flood tide, the
currents are well represented up to Egmont Channel, and somehow the model is
misrepresenting the flood flow thereafter. Due to small scale morphological features (e.g.
Cabbage Key, Mullet Key, and the Pinellas Bayway connecting them) and the shallowness
of the region, the computational grid developed in this study does not resolve the connection

North-South Velocity (cm/s) East-West Velocity (cm/s)
133
Skyway Bridge (23,36)
Model
Figure 6.18 - Simulated and measured bottom velocity at Skyway Bridge - September 1990.

North-South Velocity (cm/s) East-West Velocity (cm/s)
134
Skyway Bridge (23,36)
Model
Figure 6.19 - Simulated and measured mid-depth velocity at Skyway Bridge -
September 1990.

North-South Velocity (cm/s) East-West Velocity (cm/s)
135
Skyway Bridge (23,36)
Julian Day (1990)
Model
Figure 6.20 - Simulated and measured surface velocity at Skyway Bridge - September 1990.

136
between Boca Ciega Bay and the Gulf of Mexico. Hence, it is possible that the solid
boundary imposed in this region is causing this problem.
Figure 6.21 shows the simulated and measured bottom velocity components, and
Figure 6.22 shows the simulated and measured surface velocity components at NOAA’s
station C-4 in the Port of Manatee Channel. Among all the stations analyzed, C-4 shows the
poorest agreement between measured data and model results. Bottom currents are
underpredicted by the model, both during ebb and flood, although the phase appears to be
well represented. As to the surface flow, the model seems to better represent flood then ebb
flows, with the model not capturing a localized event that occurred around Julian Day 261
to 265. During this period, ebb flow velocities were much higher than usual values, with no
apparent correlation with other stations or with the wind field.
The Port Manatee Channel, dredged in the early 80's to a nominal depth of 10 meters
and width of about 150 m, is surrounded by underwater spoil areas and bathymetrical
features that may originate localized currents that are highly variable in space and time.
Therefore, it would be expected that any inaccuracy on matching the exact sensor location
would produce such results. So long as the model can reproduce the general characteristics
of the East-West and North-South surface and bottom velocities around the region, it will be
termed satisfactorily calibrated.
Figure 6.23 shows the simulated and measured bottom velocity components at
NOAA’s station C-5 in the Port of Tampa Channel. Located next to the “Cut K Channel”
(which runs along 15 °T), this station presents a much stronger North-South velocity
component than the East-West velocity. The model appears to slightly underpredict the

North-South Velocity (cm/s) East-West Velocity (cm/s)
137
100
Port Manatee Channel (24,42)
Bottom East-West Velocity
Model
Data
Figure 6.21 - Simulated and measured bottom velocity at Port of Manatee Channel
September/1990.

North-South Velocity (cm/s) East-West Velocity (cm/s)
138
Port Manatee Channel (24,42)
Model
Surface North-South Velocity
Model
Data
Figure 6.22 - Simulated and measured surface velocity at Port of Manatee Channel
September 1990.

North-South Velocity (cm/s) East-West Velocity (cm/s)
139
Port of Tampa (10,61)
Model
30
20
10
0
-10
-20
-30
Bottom East-West Velocity
Data
ii
nmiMn i
245
250
255
260
Julian Day (1990)
265
270
275
Bottom North-South Velocity
Model
Data
Figure 6.23 - Simulated and measured bottom velocity at Port of Tampa Channel
September 1990.

140
North-South component (along-channel). The East-West component is not only under
predict, but there is also a phase shift between measured and simulated results. Bottom
topography and lack of horizontal resolution in defining the navigation channel can be
attributed as the primary causes for inaccuracies.
Figure 6.24 shows the simulated and measured surface velocity components at
NOAA’s station C-5 in the Port of Tampa Channel. The model seems to accurately simulate
the North-South currents (along-channel), while presenting an offset towards East in the
across-channel currents (East-West). In the southwest comer of the Interbay Peninsula there
is a small spoil area running parallel to the channel in a “spit” like formation that is not
represented in the computational grid, and possibly causing a small change in the flow
direction.
Table 6.4 shows the rms errors for the surface and bottom velocity vector components
along with measured data range and the normalized percent error (as defined for the surface
elevation comparisons).
Velocities inside the Egmont Channel present the highest ranges in Tampa Bay, and
the model appears to simulate both East-West and North-South component within 10%
accuracy. The across-channel surface velocity present the highest error, which would
indicate a small deviation in the orientation of the channel axis.
The errors for the Skyway Bridge station were also around 10%, with the greatest
magnitude presented in the surface along-channel direction. As shown in Figure 6.20, the
model appears to have a problem in simulating the flood flow at this station.

North-South Velocity (cm/s) East-West Velocity (cm/s)
141
Port of Tampa (10,61)
Model
30
20
10
0
-10
-20
-30.
Surface East-West Velocity
Data
245
250
255
260 265
Julian Day (1990)
270
275
Surface North-South Velocity
Kiu.l.t ¡I
III!
I!
Model
Data
245
250
255
260
Julian Day (1990)
265
270
275
Figure 6.24 - Simulated and measured surface velocity at Port of Tampa Channel -
September 1990.

142
Table 6.4 - The rms error between measured and simulated bottom (b) and surface (s)
currents - September/1990.
Station
Component
Velocity
Range (cm)
Erms
(cm)
Normalized
Erms (%)
(E-W)b
174.15
14.25
8.2
(N-S)b
123.66
11.53
9.3
Egmont Channel (C-2)
(E-W)s
226.18
20.32
9.0
(N-S)s
147.79
15.18
10.3
(E-W)b
146.08
11.74
8.0
(N-S)b
98.44
7.55
7.7
Skyway Bridge
(E-W)s
173.41
17.46
10.1
(N-S)s
105.00
5.99
5.7
(E-W)b
81.16
8.99
11.1
(N-S)b
102.34
10.4
11.5
Port Manatee Channel (C-4)
(E-W)s
124.33
13.9
11.6
(N-S)s
126.05
12.47
11.1
(E-W)b
41.65
6.56
15.7
(N-S)b
139.15
14.03
10.1
Port of Tampa (C-5)
(E-W)s
43.92
7.26
16.5
(N-S)s
152.22
16.1
10.6
The normalized rms errors for the Port Manatee Channel were uniformly distributed
around 11%. Although differences in magnitude appears to be significant (Figures 6.21 and
6.22), the good agreement in phases helped keeping the errors in an acceptable range.
On the other hand, graphical comparisons between model results and measured data
for the Port of Tampa station (Figures 6.23 and 6.24) showed a good agreement in

143
magnitude, but a shift in phase. Since the model currents peak ahead of the measured data,
this shift produces error in the rms calculations even though the magnitudes are well
represented. The highest percent error is presented in the across-channel direction, once
again revealing that the channel orientation and the grid resolution can be improved if the
details of the circulation and transport in that area need to be resolved.
Figure 6.25 shows the energy density spectra for simulated and measured bottom
velocities and Figure 6.26 shows the energy density spectra for simulated and measured
surface velocities at the Sunshine Skyway Bridge. These figures demonstrate the dominance
of the tidal oscillation, with the semi-diurnal signal being the strongest one. Like the
spectral density curve for surface elevation, the area under the spectrum is proportional to
the total energy (square of the amplitude) of the signal. Therefore, performing a spectral
analysis of the currents at specific stations throughout the Bay, it is possible to make
comparisons between modeled and measured energy distribution of the velocity components.
Table 6.5 presents comparisons between the simulated and measured current spectral
energy within the sub-tidal, diurnal, and semi-diurnal frequency bands (as defined for surface
elevation) for the September 1990 simulation. The table shows the total energy over the
entire frequency range, and the percent of the total energy located within each primary sub¬
band.

spectral density (cm2 - day) spectral density (cm2 - day)
144
Energy Density Spectra of Currents at Skyway Bridge
Data
Model
Figure 6.25 - Energy density spectra of bottom currents at Skyway Bridge - September 1990.

spectral density (cm2 - day) spectral density (cm2 - day)
145
Energy Density Spectra of Currents at Skyway Bridge
Data
Model
Figure 6.26 - Energy density spectra of surface currents at Skyway Bridge - September 1990.

146
Table 6.5 - The distribution of tidal energy for bottom (b) and surface (s) currents -
September 1990.
Station Component Source Total Sub-tidal Diurnal Semi¬
energy diurnal
(cm/s-day)2 (%)(%)(%)
Egmont
Channel (C-2)
data 1.8E6 0.2 34.1 63.6
(E-W)b
model 1.6E6 0.7 26.7 71.4
data 9.1E5 0.1 37.2 59.5
(N-S)b
model 8.9E5 0.8 30.3 67.2
data 2.7E6 2.9 39.8 53.9
(E-W)s
model 2.5E6 0.3 26.4 72.1
data 9.3E5 5.1 33.0 52.0
(N-S)s
model 8.3E5 1.3 23.0 72.3
Skyway Bridge
data 1.4E6 0.4 31.3 67.2
(E-W)b
model 1.4E6 1.5 27.3 69.5
data 5.5E5 0.1 36.6 60.6
(N-S)b
model 4.5E5 0.1 23.9 75.1
data 2.0E6 0.01 33.9 64.3
(E-W)s
model 1.9E6 0.3 26.4 72.5
data 6.9E5 0.9 30.2 66.2
(N-S)s
model 7.2E5 1.5 27.0 69.6
Port Manatee
Channel (C-4)
data 4.4E5 0.6 36.1 61.3
(E-W)b
model 2.2E5 2.7 22.0 73.6
data 6.8E5 0.3 33.2 64.7
(N-S)b
model 3.2E5 0.2 24.0 74.6
data 7.9E5 4.9 34.1 56.2
(E-W)s
model 4.2E5 1.1 24.3 72.7
data 9.3E5 1.5 34.4 58.9
(N’S)S model 5.1E5 1.6 22.0 74.8

147
Table 6.5 - continued.
Station Component
Source
Total
Sub-tidal
Diurnal
Semi-
energy
diurnal
(cm/s-day)2
(%)
(%)
(%)
(E-W)b
data
1.0E5
0.6
24.7
70.3
model
1.1E5
0.4
15.7
79.0
(N-S)b
data
1.6E6
0.1
27.4
69.6
Port of Tampa
(C-5)
model
1.3E6
0.1
17.1
78.8
(E-W)s
data
1.3E5
1.7E5
0.3
25.2
70.6
model
2.1
12.4
80.0
(N-S)s
data
1.8E6
0.1
27.3
69.7
model
2.2E6
0.3
17.6
78.5
From the simulated and measured “Total Energy” information (which is actually
proportional to the total energy), it can be concluded that the model captures the
characteristics of the circulation throughout the Bay. The highest discrepancy is found in the
Port of Manatee Channel (C-4), because of grid resolution and localized bathymetrical
features not represented in the model. Nonetheless, the model was able to simulate the
diurnal and semi-diurnal distribution, reproducing the semi-diurnal dominance of the
currents. The total energy represented by these four sub-bands accounted for more than 90%
of the signal at all stations.
Results of the harmonic analysis help determine the character of the tidal currents.
Where they are rectilinear, the tidal ellipses present a much smaller minor axis, relative to
the magnitude of the major axis. Furthermore, the ellipses for different components are
nearly aligned. Where the tidal currents are rotary, the ellipses are not necessarily aligned,

148
and there is a more even distribution between the minor and major axis. Figure 6.27 shows
the simulated and measured tidal ellipses for the semi-diurnal components, and Figure 6.28
shows the simulated and measured tidal ellipses for the diurnal components of the surface
velocity for the Skyway Bridge station. From these figures, it can be seen that, first the semi¬
diurnal components are much greater. Second, the orientation of the navigation channel is
well represented in the model, and the simulated results slightly underpredicts the measured
components.
Salinity
Salinity and temperature present significant annual variations in the Tampa Bay
Estuarine System. Figure 6.29, from NOAA (1994), shows near-bottom salinity and
temperature for the station S-4 at the entrance of Hillsborough Bay. Since the simulations
in this study focus on specific periods (Julian Days 244 to 274 in 1990) when temperature
is uniform (around 30 °C), temperature fluctuations are not taken into consideration.
In order to isolate the sub-tidal salinity fluctuations from the signal, a low pass filter
was designed. Using the data analysis program MATLAB, a chebychev-H filter with a 24-
hour cutoff period was designed to remove all tidal components while minimizing the noise
within the cutoff frequency band, and producing the steepest possible response curve.

(cm/s) (cm/s)
149
Tidal Current Elipses - M2
Data
Model
Tidal Current Elipses - S2
Figure 6.27 - Tidal current ellipses for the semi-diurnal
components - September 1990.
Data
Model

(cm/s) (cm/s)
150
Tidal Current Elipses - 01
Data
Model
Tidal Current Elipses - K1
Data
Model
Figure 6.28 - Tidal current ellipses for the diurnal
components - September 1990.

SALINITY (PSU) AND TEMPERATURE 1C)
14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 34.0 36.0 38.0
151
Figure 6.29 - Near-bottom salinity (solid line) and temperature (dashed line) at NOAA
station S-4 starting at Julian Day 150 in 1990 (from Hess, 1994).

152
Figure 6.30 compares simulated and measured mid-depth salinity at station C-21 in
the entrance of the Bay. The model appears to represent the general characteristics of the
salinity distribution, with the difference between filtered simulated and measured salinities
not exceeding 1 ppt. During ebb tide, the model overpredicts the drop in salinity. This error
is probably caused by the geographical position of the station, and an artificial boundary
imposed in the computational grid. This station is located next to Anna Maria Sound, in the
south part of the Bay’s entrance. Since the model does not resolve the connection between
Tampa and Sarasota Bay, all the discharge of the Manatee River is forced outside Tampa
Bay. Sheng et al. (1995) suggested that a southerly residual current in Anna Maria Sound
is caused among other factors by the discharge of the Manatee River.
Figure 6.31 shows the near-bottom simulated and measured salinity at NOAA station
C-23. Similar to station C-21, the difference between filtered simulated and measured
salinities did not exceed 1 ppt. In this station, the model appears to better simulate ebb than
flood tide. During ebb tide, simulated and measured salinities agree well, but during flood
the model overpredicts the rise in salinity. The most likely cause of the discrepancy is Boca
Ciega Bay not being resolved in the computational grid. In the case of salinity, it becomes
clear that the source of error comes from the transport during flood, because it is only in this
upwind condition that the model is lacking accuracy.
Figure 6.32 shows the near-bottom simulated and measured salinity at NOAA station
C-4, in the Port Manatee Channel. Once again the model is able to capture the general
dynamics of the salinity distribution. Since salinity is highly influenced by hydrodynamic
transport, discrepancies in the velocity field will be translated to differences between
simulated and measured salinities.

Salinity (ppt) Salinity (ppt)
153
NOAA Station C-21 (34,10)
Figure 6.30- Simulated and measured near-bottom salinity at NOAA station C-21
September/1990.

Salinity (ppt) Salinity (ppt)
154
NOAA Station C-23 (23,26)

Salinity (ppt) Salinity (ppt)
155
NOAA Station C-4 (24,42)

156
Table 6.6 shows the rms errors for the near-bottom salinity along with measured data
range and the normalized percent error (as defined for the surface elevation comparisons).
Table 6.6 - The rms error between measured and simulated salinity - September 1990.
Station
Measured Salinity
Erms
Normalized
Range(ppt)
(PPO
Erms (%)
NO A A C-21
2.41
0.53
22.1
NO A A C-23
3.28
0.53
16.1
NOAA C-4
3.82
0.39
10.3
The results show the model’s ability to simulate salinity within 25% accuracy. So,
even though comparisons between filtered salinity indicate that differences are below 1 ppt
most of the time, the range of salinity fluctuations are also quite small.
Validation of the Model
Based on the results presented, the model was considered calibrated, and two
additional simulations were performed to validate the model. First, a short-term simulation
was performed around Julian Day 284 (October 11, 1990), when the tropical storm “Marco”
passed just West of the Bay. Additionally, the wet-season conditions of July 1991, when
river discharges and rainfall were above historical averages, were simulated.
Figure 6.33 shows the simulated and measured surface elevation for the tropical
storm “Marco” simulation, and Figure 6.34 shows the simulated and measured surface
elevation for the July 1991 simulation at St. Petersburg and Davis Island. These two stations
presented the greatest normalized rms errors during calibration. The model constantly
overpredicts surface elevation at these stations. A probable source of error could be the
bathymetry, indicating that the computational grid is deeper than reality. Once again, it has

Surface Elevation (cm) Surface Elevation (cm)
157
1990).

Surface Elevation (cm) Surface Elevation (cm)
158
Figure 6.34 - Surface elevation at St.Petersburg and Davis Island - July 1991.

159
been demonstrated the sensitivity of the model to bathymetry, and the necessity of accurate
bathymetric data to avoid uncertainties. Figure 6.33 demonstrates the model’s ability to
simulate episodic events. In both stations, model results for Julian Day 284 show the change
in surface elevation, going from a predominantly tidally-driven pattern towards a more wind-
driven one, with the storm surge well represented. In Davis Island, the data shows that the
water level remained higher than model results during the ebb flows of the storm. It is
possible that the runoff in Hillsborough Bay, which is not represented in the model, became
strong enough to be responsible for that.
Table 6.7 presents the maximum measured tidal range, the rms error, and the
normalized rms error percentile for St. Petersburg, in Middle Tampa Bay, and Davis Island
in the upper reaches of Hillsborough Bay.
Table 6.7 - The rms error between measured and simulated water surface elevation
October/1990 and July/91.
Station
Simulation
Tidal
Erms
Normalized
Period
Range (cm)
(cm)
Erms (%)
St.Petersburg
Oct/90
101.79
18.73
18.5
Jul/91
112.22
12.56
11.2
Davis Island
Oct/90
105.46
12.84
12.2
Jul/91
128.63
15.41
11.9
The normalized errors are comparable to those of the calibration simulation (Table
6.1). Only in St. Petersburg the error seems to be excessively higher; however, as it is shown
in Figure 6.33, the source of error is more related to a phase difference, with the amplitude
being well represented.

160
Figure 6.35 shows the simulated and measured bottom velocity components and
Figure 6.36 shows the simulated and measured surface velocity components at the Sunshine
Skyway Bridge, during the tropical storm “Marco” simulation. The model seems to
accurately simulate the tidal flow characteristics, despite of underpredicting currents during
flood tide.
Table 6.8 shows the rms errors for the surface and bottom velocity vector components
along with measured data range and the normalized percent error.
Table 6.8 - The rms error between measured and simulated bottom (b) and surface (s)
currents - “Marco” Storm.
Station
Component
Velocity
Range (cm)
Erms
(cm)
Normalized
Erms (%)
(E-W)b
151.94
14.65
9.6
Skyway Bridge
(N-S)b
92.89
8.71
9.4
(E-W)s
164.55
18.62
11.3
(N-S)s
106.48
6.74
6.3
The model is able to simulate both East-West and North-South component within
15% accuracy. Likewise the calibration simulation, the model appears simulates the ebb
better than the flood flow, and the reasons have been discussed along with Figure 6.18
through Figure 6.20.
Figures 6.37 and 6.38 show the near-bottom and near-surface simulated and measured
salinity at NOAA station S-4, near the entrance of Hillsborough Bay, during July of 1991.
Similar to the calibration simulation, the difference between filtered simulated and measured
salinities did not exceed 1 ppt. The model is able to capture the general dynamics of the
salinity distribution. Hess (1993) reports likely errors in the data, since the top sensor

East-West Velocity (cm/s)
161
Figure 6.35 - Simulated and measured bottom
(October/1990).
current at Skyway Bridge - “Marco” Storm

North-South Velocity (cm/s) East-West Velocity (cm/s)
162
Figure 6.36 - Simulated and measured surface current at Skyway Bridge - “Marco” Storm
(October/1990).

salinity (ppt) salinity (ppt)
163
NOAA Station S-4 (29,59)
Julian Day (1991)
Figure 6.37 - Simulated and measured near-bottom salinity at station S-4 - (July/1991).

salinity (ppt) salinity (ppt)
164
NOAA Station S-4 (29,59)
Near-Surface Filtered Salinity
Figure 6.38 - Simulated and measured near-surface salinity at station S-4 - (July/1991).

165
constantly presents higher salinity than the bottom sensor. Since model results show no
apparent reason for this vertical instability, the agreement between the model and measured
data is better for the bottom layer.
Table 6.9 shows the rms errors for the near-bottom and surface salinity along with
measured data range and the normalized percent error (as defined for the surface elevation
comparisons).
Table 6.9 - The rms error between measured and simulated salinity - July/1991.
Station
Layer
Salinity
Erms
Normalized
Range(ppt)
(Ppt)
Erms (%)
S-4
Bottom
6.62
0.84
12.7
Surface
10.40
1.43
13.3
Likewise the calibration simulation, the results show the model’s ability to simulate
salinity within 15%.
Flushing Characteristics of Bay Segments
An important management issues to be addressed by an integrated model, intended
to support ecosystem management, deals with the relative flushing characteristics of the
various segments defined in the Bay (Sheng and Yassuda, 1995).
In order to calculate the flushing rates for each specific segment in the Bay, the model
simulates the transport of a conservative species (i.e., without considering any
biogeochemical transformation). Initially, one segment is filled with a uniform
concentration, while remaining zero everywhere else in the Bay. After a certain amount of
time, the conservative species is transported by advection and dispersion due to the flow

166
field. The flushing rate is then determined by the fraction of mass flushed out of the segment
over that period of time. The relative flushing rates for various segments of the Bay were
calculated by independently repeating this procedure over a 10-day period simulation. Figure
6.39 shows the time-varying relative flushing for segments 2 (upper reaches of Old Tampa
Bay), segment 4 (entrance of Old Tampa Bay), segment 5 (upper reaches of Hillsborough
Bay), segment 6 (entrance of Hillsborough Bay), segment 9 (Middle Tampa Bay), and
segment 11 (entrance of Tampa Bay). As expected, the results show the lowest flushing rate
for the upper reaches of Old Tampa Bay, where 40% of the conservative species mass was
flushed out of the segment. In the upper reaches of Hillsborough Bay, about 55% of the
initial mass was flushed out. The difference between Old Tampa Bay and Hillsborough Bay
flushing rates can be attributed to higher freshwater discharges in the latter. The segment
located at the entrance of Old Tampa Bay presented a high flushing rate due to the strong
velocities field that develops along the Port of Tampa navigation channel. Approximately
75% of the initial mass was flushed out of the segment 4 in the 10-day period simulation.
Segment 6, at the entrance of Hillsborough Bay was able to flush about 70% of the initial
mass. The segments in Middle Tampa Bay and Lower Tampa Bay presented similar flushing
characteristics, flushing out between 80 to 90% of the initial mass.

Percentage of Mass Remaining Percentage of Mass Remain'rg Percentage of Mass Remaining
167
23fl 239 240 241 242 243 244
Julian Day (1990)
Figure 6.39 - Relative flushing for several bay segments - September/1990.

168
Residual Circulation
In order to be an effective tool to support ecosystem management, the integrated
model of the Tampa Bay Estuarine System needs to be able to address issues with time scales
greater then a few tidal cycles. The concept of residual circulation and transport has been
referred to filtering or averaging out the intratidal fluctuations. Two methodologies can be
applied in determining these residuals. The Eulerian residual circulation and transport is
obtained by simply averaging variables over several tidal cycles (e.g., usually a period of the
order of a month). While, the Lagrangian residual circulation and transport are related to the
Lagrangian mean velocities, which are defined as the net displacement of a specific particle
over a tidal cycle, divided by the displacement time (Cheng and Casulli, 1982). The first-
order Lagrangian residual circulation and transport is the sum of the Eulerian residual and
the Stoke’s drift.
The analysis of surface elevation and currents showed that it is reasonable to assume
the Tampa Bay Estuarine System as a relatively weak non-linear system; therefore, only the
Eulerian residual circulation and transport will be assessed.
Figure 6.40 shows the residual circulation and salinity distribution for September
1990. The residual circulation generated a two-layer velocity field, with a seaward surface
flow, and a landward bottom layer flow. During this period (characterized as dry-season),
the saltier waters of the Gulf of Mexico penetrate the Bay along the bottom-layer of the
navigation channel, up to the head of Hillsborough Bay. Model results show that along the
shallow sides of the Bay the residual flow is seaward over the entire water column, which

169
Residual Circulation - Sep/1990 J
Salinity
Figure 6.40 - Residual circulation after 30 days - September/1990.

170
agrees with the findings of Weisberg and Williams (1991). Galperin et al. (1992) presented
a residual circulation suggesting a much strong stratification, with the entire bottom layer
flowing landward, and a seaward flow in the surface layer. Their results may be explained
by historical-averages river discharge used as well as a zero salinity used for the river
boundaries. In their study, they also refuted the “residual gyres” described by the barotropic
two-dimensional models of Ross (1973) and Goodwin (1987), by concluding that the
barotropic residual circulation is overwhelmed by the baroclinic counterpart. Figure 6.40
shows that the complex shoreline and bathymetrical features of the Bay are also important
components in generating residual circulation and transport. Numerous gyres were formed
next to the causeways, specially in the bottom layer. The greater depths in the upper reaches
of Middle Tampa Bay induce a large scale counter-clock gyre that forces the flow from
Hillsborough Bay to the west side of Middle Tampa Bay, towards St. Petersburg. This
feature may help to explain the lower salinities presented in the west side, compared to the
east side, where most of the freshwater inflow occurs, and where one would expect to find
the lower salinity levels.
In a intertidal basis, the flow is spatially uniform, as shown in Figure 6.41 for the ebb
flow, and Figure 6.42 for the flood flow. These figures show that the greatest velocities are
found in the Egmont Channel and in the entrance of Old Tampa Bay, which is in agreement
with the findings of the NOAA’s “Tampa Bay Oceanographic Project” (NOAA, 1993).

171
Surface
Surface
Figure 6.41 - Simulated velocity field representing maximum ebb currents -
September/29/1990 - 18:00.

172
Figure 6.42 - Simulated velocity field representing maximum flood currents -
September/29/1990 - 10:00.

173
Figure 6.43 shows the velocity cross-section simulated along the Sunshine Skyway
Bridge. The ebb flow of September, 29 1990 (14:00) presents a typical estuarine circulation,
with stronger ebb velocities concentrated in the center of the surface layer. The magnitude
of the flood velocities are smaller, and dispersed throughout the cross-section. This ebb-
flood pattern can be explained by the fact that the period of ebb flow is shorter than the flood
period. The residual cross-section shows a landward flow restricted to the bottom layer of
the navigation channel and the shallow sides of the Bay, and a seaward flow in the surface
layer.
Figure 6.44 shows the salinity cross-section simulated along the Sunshine Skyway
Bridge. As a consequence of the circulation pattern, higher salinities are confined to the
deeper parts of the navigation channel, with lower salinities along the shallow sides of the
Bay.
Figure 6.45 shows the longitudinal salinity distribution along the navigation channel,
from the Gulf of Mexico to Hillsborough River. There is a mild vertical stratification, with
surface to bottom salinities differences never exceeding 2 ppt. However, it is interesting to
notice the roughness in the 32 ppt contour line during ebb flow. Apparently, the lower-
salinity water mass flowing seaward is trying to overcome a higher-salinity water mass
flowing landward, generating a small front like feature in Lower Tampa Bay.

174
Ebb Tide
Velocity Cross-Section at Sunshine Skyway Bridge - Sep/29/1990 -14:00
Flood Tide
Velocity Cross-Section at Sunshine Skyway Bridge - Sep/29/1990 - 21:00
Residual Circulation
Cross-Section at Sunshine Skyway Bridge
Figure 6.43 - Velocity cross-section at Skyway Bridge looking up the
Bay. Vertical scale in meters, and horizontal scale in
computational grid j-index.

175
Ebb Tide
Salinity Cross-Section at Sunshine Skyway Bridge - Sep/29/1990 -14:00
Cross-Section at Sunshine Skyway Bridge
Salinity
34
33.25
32.5
31.75
31
Salinity
Figure 6.44 - Salinity cross-section at Skyway Bridge looking up the
Bay. Vertical scale in meters, and horizontal scale in
computational gridj-index.

176
Ebb Tide
Salinity Along the Navigation Channel - Sep/29/1990 -14:00
Flood Tide
Salinity Along the Navigation Channel - Sep/29/1990 - 21:00
Residual Salinity
Along the Navigation Channel
Figure 6.45 - Longitudinal distribution of salinity along the
navigation channel. Vertical scale in meters,
and horizontal scale in computational grid i-index.

177
Summing up, currents inside Tampa Bay are distinctly tidal oscillations, with the
mixed tide signal presenting a strong dominance of the semi-diurnal component. Throughout
the Bay, the tidal ellipses reflect an uni-directional flow aligned with the navigation channel.
Filtering the tidally driven flow, a baroclinic circulation is revealed, with a two-layer pattern
flowing landward in the bottom layers, and seaward along the surface. The salinity
distribution closely follows the circulation pattern. The model reveals a low-salinity
distribution along the western side of the Bay, originated from the freshwater discharge in
Hillsborough Bay, and transported there through “topographical” residual currents.
Results of the Suspended Sediment Simulation
The role of suspended sediments in the integrated model of an estuarine system can
be demonstrated by the importance of its concentration in determining light availability,
supply of water column nutrients, and fate of sorbed pollutants.
Erosion rates, critical shear stress, settling velocities and other model parameters
were determined by previous studies in Tampa Bay (Ross, 1988; Sheng et al., 1992 and
1993; and Schoellhammer, 1993). The bottom shear stress due to the combined action of
waves and currents was calculated in the hydrodynamics component of this integrated model,
and then used to determine the erosion and deposition rates.
Schoellhammer (1993) showed that net sediment resuspension in Old Tampa Bay is
primarily driven by strong and sustained winds associated with episodic events. In order to
test the sediment component of this integrated model, results of a 10 days simulation and

178
data are compared. The simulation comprises the period when the tropical storm “Marco”
moved northward along the Gulf coast on October 11, 1990, and suspended sediment
concentration data were collected at the USGS platform (Schoellhammer, 1993). Figure 6.46
shows the location of the USGS platform in Old Tampa Bay. During the storm, the wind
shifted from easterly (at about 5 m/s) in the afternoon of October 10 to southerly (at about
15 m/s) during the morning of October 11 (Figure 6.47). The wind magnitude returned to
normal in the afternoon of October 11. Suspended sediment concentration was measured at
two vertical levels (24 cm and 183 cm above the bed), although near-bottom data stopped
at 1200 hours on October 11. Figure 6.48 shows the simulated significant wave height and
period, suggesting a transition from deep water wave condition (40 cm wave height, 2
seconds period in a 4.5 m water depth) to a shallow water wave condition during the passage
of the storm (Shore Protection Manual, 1984). Figure 6.49 shows the simulated wave-
induced bottom shear stress and the suspended sediment concentration at the USGS station
for October 10 and 11, 1990. Prior to the storm, the bottom shear stress fluctuates around
the Shields critical stress, calculated to be around 1.6 dyne/cm2 . During the storm, the
significant wave height basically doubled, hence, the bottom shear stress, which is
proportional to the square of the wave height (Kajiura, 1968), increased to about four times
the original value. Both measured data (Figure 6.47) and simulated results (Figure 6.49)
show that the near-bottom suspended sediment concentration increased to about 200-300
mg/L during the peak of the storm. It is interesting to notice the prompt response of the Bay
to the wind action. The maximum concentration correspond to the maximum southerly
wind, and it decreased as wind velocities decreases during the afternoon. Figure 6.50 shows

179
a contour plot of the suspended sediment distribution at 6:00 am of October 11. The lack of
suspended sediment data throughout the Bay during the event prevents further comparisons.
Although wind-generated waves are represented by the simple SMB model (which
consist of a single wave amplitude and wave period), whereas episodic events are
characterized by many wave amplitudes and frequencies, the model appears to reproduce the
general trend of the event, which is probably due to an accurate representation of the bottom
shear stress.
The suspended sediment simulations were carried out using the settling velocity
proposed by Ross (1973) (Equation B-4) for the mud region, and constant settling velocity
for the sandy bottom, with the values obtained from Schoellhammer (1993). The
resuspension rates were calculated using the Power Law (Equation B-5) with Td = 1 and
p = 1. The critical shear stress utilized in this simulation was xcr = 1.6 dyne/cm2 for the
sandy region and xcr = 1.2 dyne/cm2 for the mud region. The deposition velocity was
assumed to be equal to the settling velocity at the bottom layer, which corresponds to a
Krone’s probability of deposition p= 1.
The suspended sediment dynamics in Tampa Bay are primarily driven by episodic
events, when short period waves are responsible for resuspension, while strong currents are
responsible for the vertical mixing. Model results showed that current-induced bottom stress
have negligible effects on the resuspension flux of sediments, however, the combined action
of waves and currents can be responsible for high levels of suspended sediments during
episodic events.

180
Figure 6.46 - Location of the USGS station in Old Tampa Bay (Schoellhammer,
1993).

SUSPENDED-SOLIDS WIND VECTOR AZIMUTH. WIND SPEED,
CONCENTRATION. IN MG/L IN DEGREES IN METERS PER SECOND
181
360
270 -c
• 0 „o
° * OOO
°o°ooO
180 -
80 -
-J L.
««.». «
. -o o
10
OCTOBER
1990
11
Figure 6.47 - Wind speed and direction, and suspended
sediment concentration at USGS station
during tropical storm “Marco”
(Schoellhammer, 1993).

Wave Period (sec) Wave Height (cm)
182
283.0 283.5 284.0 284.5 285.0 285.5 286.0
Julian Day (1990)
Figure 6.48 - Simulated significant wave height and period during tropical storm
“Marco” (October/1990).

183
Simulated Bottom Shear Stress
Suspended Sediment Concentration
Julian Day (1990)
Figure 6.49 - Simulated wave-induced bottom shear stress and
suspended sediment concentration at the USGS station
for October 10 and 11, 1990.

184
Near-Bottom Suspended Sediment Concentration
October/11/1990 - 06:00am
BOT
Figure 6.50 - Simulated suspended sediment concentration at 6:00am - October 11,
1990.
mg/L

CHAPTER 7
CALIBRATION OF THE WATER QUALITY MODEL
The primary goal of this integrated modeling effort is to develop a water quality
model that is fully coupled with the three-dimensional hydrodynamics model for Tampa Bay.
In other words, a water quality model that runs simultaneously with the same time step and
computational grid, hence eliminating the need for ad-hoc tuning of advective fluxes and
dispersion coefficients.
The model which includes the processes described in Chapters 3,4, and 5 can be used
to study Tampa Bay as an integrated system, and provide a detailed characterization of the
hydrodynamics and water quality dynamics within the system. At this stage of development,
the model can assist ecosystem managers in determining which water quality data need to
be obtained, and the processes to be further investigated in order to solve for the uncertainty
of model coefficients. A preliminary nutrient budget, accounting for external loading,
benthic fluxes, and exchange with the Gulf of Mexico can be obtained. Model results can
also be used to maximize management efforts by determining the best location of sampling
stations in order to be representative of each of the Bay sub-divisions. A subsequent
refinement of the model can be used to address such ecosystem management issues as
controlling estuarine eutrophication and determining allowable external nutrient loading
levels to restore seagrass to a target level throughout the Bay.
185

186
This chapter describes the calibration of the water quality model for the Tampa Bay
Estuarine System. The major objective of model calibration is to synthesize some available
Tampa Bay water quality data with the water quality model described in Chapter 4. Of
particular interest is the summer of 1991 data which showed a decline in water quality,
especially in the upper reaches of Hillsborough Bay, as measured by the Hillsborough
County Environmental Protection Commission (EPC) water quality index. An attempt will
be made to simulate the summer 1991 condition by determining the proper combination of
model coefficients. In this regard, model calibration can help to identify specific processes
for which basic research is needed, and the type and amount of additional data required.
Due to the vast spatial and temporal variability in hydrodynamics and water quality
dynamics, it is impossible to rely only on field and laboratory experiments to develop a
system-wide understanding of the Bay. To understand the water quality dynamics in Tampa
Bay, model must be used to synthesize field and laboratory data. As noted in previous
studies (e.g., Fanning and Bell, 1985; Spaulding etal., 1989), the lack of a well coordinated
and long-term water quality data collection efforts for determining process rates and
boundary/initial conditions impose a major challenge towards the development of a
predictive water quality model for the Tampa Bay Estuarine System. Water quality data were
collected in various parts of Tampa Bay at different times. Therefore, a major task of the
present water quality modeling effort of the Tampa Bay Estuarine System is the synthesis and
integration of available data, and the calibration of the model, prior to any attempt of model
prediction. Using the process-based modeling system described in previous chapters, it is
possible to synthesize the data collected from various parts of the Bay at different times, so

187
long as one takes into consideration the uncertainty of model coefficients. Typical laboratory
studies on rate constant and model coefficients determine the constant/coefficient at one or
two ambient conditions only, and hence do not adequately describe the natural variability of
the processes. As a result, model can be used to bridge the gap of data. For example, model
sensitivity studies can be conducted to investigate the relative importance of various
processes and coefficients. Chen and Sheng (1994) used a process-based hydrodynamics-
water quality model to investigate the phosphorus transport and to demonstrate the effects
of DO and pH on desorption of dissolved inorganic phosphorus in Lake Okeechobee.
An exception to the available Tampa Bay data is the water quality data provided by
the EPC since 1972 (Boler, 1992). With monthly sampling at 52 Bay stations and 40
tributary stations, the EPC water quality data enabled a preliminary evaluation of the present
water quality model. Data during the month of June 1991 were selected to determine the
initial condition of water quality model for two reasons: they reflect the water quality
characteristics of the Bay prior to the wet season, and because the EPC water quality index
(Boler, 1992) for Hillsborough Bay in June 1991 was relatively higher compared to the July
and August values. From July to September, several water quality parameters like
chlorophyll-a, color, and total Kjeldahl nitrogen showed a marked increase. The EPC water
quality index for October recovered to a value comparable to the June level, hence showing
the effects of rainfall and increased freshwater discharge during the wet season. One of the
goals of this study is to simulate this dynamic response of the Bay to increased freshwater
discharge and loading during June to September 1991.

188
Initial and Boundary Conditions of the Water Quality Model
For the model simulation of Summer 1991, initial and boundary conditions must be
developed from available data. As described earlier, this is not an easy task. Available
synoptic data were not collected simultaneously and data are inadequate, particularly in the
sediment column. The following discussions are given in terms of the water column data
first, and then sediment column data.
Water Column
The water column initial concentrations of several water quality parameters were
determined from the EPC data of June 1991. Figure 7.1 shows the locations of the EPC
water quality monitoring stations in Tampa Bay. The water quality data at the sampling
stations were interpolated to each curvilinear grid cell by using the data at the closest three
EPC stations, with a weighting function inversely proportional to the distance to each of the
three stations. Since the water quality data were collected at only mid-depth, it is reasonable
to assume a vertically uniform nutrient distribution as the initial condition for water quality
simulation. Dissolved oxygen concentrations were measured at three vertical levels, hence
the near-bottom concentration was assigned to the first two sigma-grid levels near the
bottom, the mid-depth concentration to the intermediate three sigma levels, and the near¬
surface concentration to the top three sigma levels. Figures 7.2 to 7.9 show the resulting
initial concentration fields for dissolved oxygen at the bottom sigma level, dissolved oxygen
at the top sigma level, organic nitrogen, ammonium, nitrate+nitrite, chlorophyll-a, color, and

189
Figure 7.1 - Water quality monitoring stations of the Hillsborough County Environmental
Protection Commission (EPC) (Boler, 1992).

190
TAMPA BAY
Near-Bottom Dissolved Oxygen
June -1991
Figure 7.2 - Measured near-bottom dissolved oxygen concentration (mg/L) in Tampa Bay
(June 1991).

191
N
L
TAMPA BAY
Near-Surface Dissolved Oxygen
June -1991
DOT
8.0
7.2
6.4
5.6
4.8
4.0
Figure 7.3 - Measured near-surface dissolved oxygen concentration (mg/L) in Tampa Bay
(June 1991).
mg/L

Gulf of Mexico
192
N
L
TAMPA BAY
Organic Nitrogen Concentration
June -1991
1.0
0.8
0.6 ^
0.4 S’
0.2
0.0
Figure 7.4 - Measured organic nitrogen concentration (mg/L) in Tampa Bay (June 1991).

193
N
L
TAMPA BAY
Ammonium-Nitrogen Concentration
June -1991
8
'8
5
o
"5
C3
Alafia River
Little Manatee
River
Manatee River
10 km
0.25
0.20
0.15
0.10
0.05
0.00
Figure 7.5 - Measured dissolved ammonium-nitrogen concentration (mg/L) in Tampa Bay
(June 1991).
mg/L

Gulf of Mexico
194
TAMPA BAY
Nitrite+ Nitrate Concentration
June -1991
Figure 7.6 - Measured nitrite+nitrate concentration (mg/L) in Tampa Bay (June 1991).

195
N
i
TAMPA BAY
Chlorophyll-a Concentration
June -1991
C3
Hillsborough River
Alafia River
Little Manatee
River
Chla
20.0
16.0
12.0
8.0
4.0
0.0
Figure 7.7 - Measured chlorophyll-a concentration (pg/L) in Tampa Bay (June 1991).
-]/6H

Gulf of Mexico
196
N
L
TAMPA BAY
Water Color
June -1991
If \ \ i VflK
Figure 7.8 - Measured color (Pt-Co) in Tampa Bay (June 1991).

197
TAMPA BAY
Turbidity
June -1991
Figure 7.9 - Measured turbidity (NTU) in Tampa Bay (June 1991).
NTU

198
turbidity. These figures do not represent exact snapshots of the Bay conditions, since the
data were not collected simultaneously at all 52 stations, but were collected from June 4 to
19, between 9:00am and 3:00pm. The organic nitrogen data exhibit the overall trend of
higher concentrations in Hillsborough Bay and the upper reaches of Old Tampa Bay, and a
rapid decrease in concentration towards the mouth of the Bay. An isolated low organic
nitrogen concentration was noticed around St. Petersburg area. In Middle and Lower Tampa
Bay, the nitrite+nitrate and dissolved ammonium data show uniformly low level (around 0.01
mg/L) throughout the Bay. Since the EPC data for tributaries show discharges into the Bay
of an order of magnitude higher (0.1 to 0.3 mg/L) than the Bay values, it is reasonable to
assume that dissolved inorganic nitrogen was readily uptaken by phytoplankton, which is
consistent with the hypothesis that phytoplankton growth in Tampa Bay is limited by
nitrogen. Another possibility for lower dissolved ammonium and nitrite+nitrate may be the
loss of nitrogen through high nitrification and denitrification rates, as found by Nixon (1981)
in Narragansett Bay, Rhode Island.
Riverine boundary conditions required for the model simulations were determined
from the nutrient loading study of Coastal, Inc. (1994), which provided estimated monthly
nitrogen loading in terms of total nitrogen (TN). In order to divide it among the nitrogen
species considered in this study, some assumptions had to be made. The data at the EPC
tributary stations were analyzed for total nitrogen partitioning. Based on the averaged ratios,
the total nitrogen (TN) provided by Coastal, Inc. (1994) was divided into organic nitrogen
(corresponding to 60% of TN), nitrate+nitrite (consisting of 28% of TN), and ammonium

199
nitrogen (consisting of 12% of TN). This same partitioning procedure was adopted by AScI
(1996) to determine the external loading input for their box model of Tampa Bay.
In model simulations, water quality parameters along the oceanic boundary are
computed similarly to the salinity simulation. During the outflow, open boundary
concentrations are computed from a 1-D advection equation. During the inflow, the open
boundary concentrations take on the value of the previous time step, which corresponds to
assume the estuarine system as an exporter of nutrients. Although this assumption is
generally correct, it may be questionable for some nitrogen species like nitrate, which can
be actually imported to the estuary during tidal inflow (Vargo, 1996, pers. comm.).
However, since nitrate values in the Gulf of Mexico region adjacent to Tampa Bay during
summer 1991 were not available, the exporting assumption will be used in the water quality
simulations.
For the present water quality modeling, most model coefficients were initially set to
values used by AScI (1996) in their Tampa Bay modeling study, and literature values of
coefficients were used for those processes not included in the AScI study, e.g., zooplankton,
benthic processes, volatilization. Based on the EPC water quality data shown in Figures 7.2
to 7.9, and the surface sediment composition in Figures 2.5 and 2.6, Tampa Bay was divided
into four different zones with distinct sediment types. Zone 1 corresponds to the fine silt and
clay sediments of Hillsborough Bay and the upper reaches of Old Tampa Bay. Zone 2
corresponds to the fine sand of the upper reaches of Middle Tampa Bay. Zone 4 corresponds
to the coarser sediments of Lower Tampa Bay and adjacent Gulf of Mexico, and Zone 3
corresponds to a transition zone between zones 2 and 4. Figure 7.10 shows the water quality

200
zonation in the curvilinear grid used in this study. For each of the four zones, model
coefficients were then selected and calibrated according to its distinct biogeochemical
characteristics.
For the mud zone in Hillsborough Bay, the partition coefficients and desorption
constant rates in the water column were determined from the resuspension study of Sheng
et al. (1993). For the sandy regions, the water column partition coefficients were estimated
based on data. Total suspended solids, dissolved and particulate Kjeldahl nitrogen, dissolved
ammonium, and nitrate data from Riñes (1991), and the EPC water quality data were used
Water Quality Zones
Figure 7.10 - Water quality zones in Tampa Bay used in the model simulations of the
summer of 1991 conditions.

201
to determine the fraction of dissolved and particulate forms of organic and inorganic nitrogen
in the water column. Table 7.1 shows the estimated total suspended solids concentration,
and the calculated water column partition coefficients for particulate organic nitrogen and
particulate inorganic nitrogen (adsorbed ammonium) used in the simulations.
Table 7.1 - Estimated total suspended solids concentration (TSS), and calculated water
column partition coefficients for particulate organic nitrogen (peon) and adsorbed
ammonium (pean).
Zone
TSS (mg/L)
peon (L/mg)
pean (L/mg)
1
22.0
1.0E-5
5.0E-7
2
15.0
7.5E-6
7.5E-8
3
12.5
5.E-6
5.0E-8
4
10.0
1.0E-6
1.0E-8
Sediment Column
Studies on sediment nitrogen (dissolved and particulate species) in the top 2 cm of
Tampa Bay sediment were performed in 1963 (Taylor and Saloman, 1969), 1985-1986
(COT, 1986; FDER, 1988, Brooks and Doyle, 1992), and 1991-1992 (NOAA, 1994). A
literature review showed that studies by Taylor and Saloman (1963), COT (1986), and
Brooks and Doyle (1992) used the same sampling methodology (grab samplers), and the
results were presented on the same dry-weight basis.

202
In 1991 and 1992, as part of the National Status and Trends Program for Marine
Environmental Quality, NOAA (1994) performed a survey of the sediment toxicity in Tampa
Bay, with total sediment nitrogen being part of the sediment chemistry analysis. Sediment
samples were collected aboard a research vessel with a van Veen grab sampler, and all
chemical analyses were performed by the Skidway Institute of Oceanography, Savannah,
Georgia.
No core samples were taken in all the data mentioned above. The data did not
include complete fractionation of all nitrogen and phosphorus species, particularly the
refractory and non-labile fractions of nitrogen and phosphorus. Nevertheless, useful insight
can be developed from these data, and reasonable sediment nutrient distributions can be
constructed by making use of all available data from the sediment and water columns.
Assuming the sediment composition presented in these studies is relative to the same
dry-weight basis, the following nitrogen enrichment hypothesis may be postulated. Using the
sedimentary nitrogen concentration of the 60's as the background sediment composition
(Figure 7.11), one can state that the upper reaches of the Bay were heavily stressed during
the 70's and early 80's (Figure 7.12). External loadings of organic and inorganic nitrogen
exceeded limits that could be naturally recycled or flushed, and led to accumulation in the
sediment layer. Brooks and Doyle (1992) reported that this nutrient enrichment occurred
mainly in Hillsborough Bay, with the rest of the Bay showing a negligible change in
sediment nutrient composition between 1963 and the mid-80's. The primary source of
contaminants in Hillsborough Bay during this period was the discharge of the Hooker’s Point
Wastewater Treatment Plant, which achieved advanced waste treatment (AWT) standards
only after 1979 (Boler, 1992). Starting in the 80's, a steady improvement in the water quality
of Hillsborough Bay, due primarily to a reduction in phosphorus and nitrogen loading (Boler,

203
1992), apparently reversed the process of sediment nutrient enrichment. The 1991 study by
NOAA (1994) showed that levels of nitrogen species in the surface sediments are returning
to levels comparable to the early 60's. As shown in Figure 7.11, the total organic nitrogen
in 1963 was between 0.05 to 0.1% of the sediment, Figure 7.12 shows a partial map of the
total Kjeldahl nitrogen in Tampa Bay sediments during 1982-1986 with values between 0.1
and 0.2%, and Figure 7.13 shows the sediment nitrogen in 1986, with values as high as 0.3%
throughout Hillsborough Bay.
Figure 7.14 shows the location of the NOAA’s sediment sampling stations in 1991
(phase 1) and 1992 (phase 2). Figure 7.15 shows the total nitrogen concentration in the
sediment layer obtained from the surveys, and interpolated into the curvilinear grid using the
same procedure used for the water column data. The contour values of TN in Figure 7.15
appear to have returned to the 1963's values shown in Figure 7.11.
The initial condition of sediment nitrogen concentrations for the simulations
performed in this study is based on the total nitrogen data provided by NOAA (1994). In
order to fractionate the total nitrogen into the organic and inorganic forms required by the
model, the following assumptions were made. First, the nitrogen dry weight percentage in
the surface sediments (NOAA, 1994) was converted to concentration using the sediment dry
density. For the mud zone in Hillsborough Bay, the dry density was determined by Sheng
et al. (1993), with a vertical profile showing a density which increases with depth (Figure
7.16). For the sand region, literature values relating sediment size and porosity were used
to determined the dry density (Lambe and Whitman, 1969). Table 7.2 shows the dry density
for each of the three sandy zones, along with the mean sediment size.

204
Figure 7.11 - Total organic nitrogen (dry weight %) in the surface sediments of
Tampa Bay during 1963 (Taylor and Saloman, 1969).

205
Figure 7.12 - Total Kjeldahl nitrogen (dry weight %) in Tampa Bay sediments,
1982-86 (Brooks and Doyle, 1992).

206
Figure 7.13 - Sedimentary nitrogen (dry weight %) in Hillsborough Bay
in 1986 (COT, 1988).

207
17 0
Old Tampa Bay
r, 16
v Hillsborough
\ Bay £• '
7
Sites ?"*:
S
J
â–  â–  .
! Smacks Bayou
A JL -Í.
oca Coffeepot Bayou
St. Petersburg
5 „Bayboro Harbor
Bi9.
Middle Tampa Bay
.Cockroach Bay
-fTv». '*J£SÍa-'» • ' ' J
Terra Ciea Bay
Manatee River
Bradenton
Survey sites-phase 1
o J
twl’x •
••
Gulf of Mexico
^ Lower Tampa
Bay
Figure 7.14 - Location of the NOAA sediment sampling stations in 1991 (phase 1) and
1992 (phase 2) (NOAA, 1994).

Gulf of Mexico
208
TAMPA BAY
Total Nitrogen in the Sediment Layer -1991
Contours in dry weight %
Figure 7.15 - Total sediment nitrogen (dry weight %) obtained from NOAA (1994) data.

209
Sediment Dry Density Profile in Hillsborough Bay
Figure 7.16 - Dry density profile for water quality zone 1 in Tampa Bay (Sheng et al.,
1993).

210
Table 7.2 - Estimated dry density for the
sandy zones
of Tampa Bay.
Zone
d50 (mm)
Dry density (g/cm3)
2
0.090
1.40
3
0.125
1.44
4
0.210
1.48
The various particulate and dissolved nitrogen species in the sediment column were
calculated using the sediment dry density and the same composition obtained by Simon
(1989) for the Potomac Estuary. The results show that the total sedimentary nitrogen is
divided into organic (90% of total nitrogen) and inorganic (10% of total nitrogen) forms.
The same procedure for fractionating the particulate and dissolved nitrogen forms in the
water column was applied to the sediment column. In agreement with Simon (1989) results,
the adsorbed ammonium averaged approximately 8% of the total sedimentary nitrogen.
The vertical profiles of nitrogen sediment are expected to contain spatial and
temporal variations, due to changes in redox potential and aerobic and anaerobic conditions.
In the absence of information on vertical profiles of 1991 sediment nutrient data, initially
uniform vertical profiles were assumed for the anaerobic and aerobic sediment layers. For
modeling purposes, the thickness of the aerobic layer was set to 1 cm (Fanning, 1996, pers.
comm.). The initial nutrient concentrations in the aerobic and anaerobic sediment layers are
presented in Table 7.3.
Table 7.4 summarizes the final selection of model coefficients for the biogeochemical
processes in four lateral water quality regions and three different vertical layers (water
column, aerobic, and anaerobic sediment layers).

211
Table 7.3 - Initial nitrogen concentration in the sediment (Ae) aerobic layer, and (An)
anaerobic layer for each water quality zone. (SON) soluble organic nitrogen, (NH4) dissolved
ammonium nitrogen, (NQ3) nitrite+nitrate.
Zone 1
(mg/L)
Zone 2
(mg/L)
Zone 3
(mg/L)
Zone 4
(mg/L)
Ae
40.0
30.0
20.0
10.0
SON
An
80.0
60.0
40.0
20.0
Ae
4.5
4.2
2.8
1.5
NH4
An
8.5
6.0
3.0
1.5
Ae
0.6
0.5
0.4
0.4
N03
An
0.01
0.01
0.01
0.01
Table 7.4 - Model coefficients in the (W) water column, (Ae) aerobic layer, and (An)
anaerobic layer for each water quality zone.
W
Zone 1
Ae
An
W
Zone 2
Ae
An
W
Zone 3
Ae
An
w
Zone 4
Ae
An
^an
36
4
4
36
4
4
36
4
4
36
4
4
n
36
4
4
36
4
4
36
4
4
36
4
4
o 1
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
IE-5
kd
0.25
0.03
0.01
0.20
0.02
0.01
0.15
0.01
0.01
0.05
0.01
0.01
^DN
0.05
0.10
1.50
0.05
0.10
1.20
0.04
0.10
1.00
0.04
0.08
1.00
Knn
0.06
0.10
0.00
0.05
0.10
0.00
0.06
0.10
0.00
0.06
0.10
0.00
Kqnm
0.08
0.02
0.01
0.10
0.05
0.01
0.10
0.05
0.01
0.10
0.10
0.05

212
Modeling Strategy
The model simulations to be presented consist of (1) a model sensitivity analysis
which was designed to test the sensitivity of model results in an idealized Tampa Bay to such
parameters as molecular diffusion coefficients for the sediment layer, thickness of aerobic
layer, desorption rates and partition coefficients, mineralization rates, nitrification,
denitrification, algae growth, death, and excretion rates; (2) model simulations of the summer
1991 condition in Tampa Bay using the nutrient loading provided by Coastal, Inc. (1994),
which defines the present condition of the Bay; and (3) two loading reduction cases (100%
and 40% loading reduction) to study the response of the Bay to improvements in point-source
discharges into the system.
Sensitivity Analysis
The sensitivity analysis refers to a study of the sensitivity of model results (measured
as the percent variation in model results vs. the baseline simulation results) given a range of
possible variation for each of several model parameters. A thorough sensitivity analysis for
all model coefficients and input parameters is prohibitively time-consuming. Therefore, a
set of sensitivity tests were performed to identify the most important model coefficients and
input parameters. Through this sensitivity analysis, it is also possible to identify the type and
amount of additional data required. In this study, the sensitivity analysis was conducted for
such model coefficients and input parameters as molecular diffusion coefficient, thickness

213
of sediment aerobic layer, partition coefficients between dissolved and particulate nitrogen
species, nitrification rate, denitrification rate, mineralization rate for organic nitrogen,
maximum algal growth, half saturation constant for algal uptake, algal nitrogen to carbon
ratio, deoxygenation rate, CBOD settling velocity, sediment composition, erosion rates, and
linear oxygen balance.
In order to test the model response to variation of these specific parameters, the
sensitivity tests were conducted in an idealized rectangular basin, with dimensions similar
to Tampa Bay. Like Tampa Bay, the test basin was divided in four water quality zones, and
initial condition for water quality parameters were set to average values of the same zones
in Tampa Bay. During 30-day simulations, no external forcing (e.g., tide, wind, and river
discharge) were applied, so that variations in nutrient composition could be directly related
to biogeochemical processes. The tests were performed by varying each parameter within
“reasonable” ranges. Table 7.5 shows the parameters considered in the sensitivity analysis,
the baseline value used in the simulations, and the range of variation tested. Table 7.6
describes each sensitivity test, and specifies a test identification code that will be used during
analysis of results. The baseline simulation corresponds to the configuration of model
parameters and coefficients used in the Tampa Bay simulations.

214
Table 7.5 - Parameters, baseline values, and range used in the sensitivity analysis.
Parameter
Literature
Range
Tampa Bay
Test Range
Molecular Diffusion
Coefficient (cm2 / s)
l.E-2 ~ l.E-6
l.E-5
l.E-4- l.E-6
Thickness of Sediment
Aerobic Layer (cm)
0.0 ~ 5.0
1.0
0.5 - 2.0
Partition Coefficient (L/mg)
5.E-7 ~ l.E-5
5.E-7- l.E-5
5.E-8 - l.E-4
Nitrification Constant Rate
(day -1)
0.001 ~ 0.6
0.2
0.02 - 2.0
Denitrification Constant Rate
(day -1)
0.02-1.0
0.9
0.09-1.5
Mineralization Constant Rate
(day -1)
0.01 - 0.4
0.1
0.01 - 0.4
Maximum Algal Growth
(mg/L/day)
0.2 - 8.0
1.4
0.7 - 2.8
Half Saturation Constant for
Uptake (mg/L)
0.0015-0.4
0.05
0.01-0.1
Algal Nitrogen to Carbon
Ratio
0.05 -0.43
0.15
0.07 - 0.25
Deoxygenation Constant Rate
(day -1)
0.02 - 0.6
0.2
0.02 - 2.0
Fraction of dissolved CBOD
(%)
0-100
50-85
1-99
Particulate CBOD Settling
Velocity (m/day)
-
ws/2.
ws/10. - ws
Sediment Composition
-
Bulk Density
(Pb)
0.5 pB - 1.5 pB

215
Table 7.6 - Sensitivity tests description.
Description
Range
Test#
Baseline
-
T1
Baseline * 10.
T2.1
Molecular Diffusion Coefficient
Baseline * 0.1
T2.2
Thickness of Sediment Aerobic Layer
0.5 cm
T3.1
2 cm
T3.2
Baseline * 10.
T4.1
Partition Coefficient
Baseline * 0.1
T4.2
Baseline * 10.
T5.1
Nitrification Constant Rate
Baseline * 0.1
T5.2
Baseline * 10.
T6.1
Denitrification Constant Rate
Baseline * 0.1
T6.2
Baseline * 4.0
T7.1
Mineralization Constant Rate
Baseline * 0.1
T7.2
Maximum Algal Growth
Baseline * 2.0
T8.1
Baseline * 0.5
T8.2
Half Saturation Constant for Uptake
Baseline * 2.0
Baseline * 0.5
T9.1
T9.2
Algal Nitrogen to Carbon Ratio
Baseline * 2.0
Baseline * 0.5
T10.1
T10.2
Non-linear Oxygen Balance
-
Tll.l
Deoxygenation Constant Rate
Baseline * 10.
Baseline * 0.1
T12.1
T12.2
Baseline * 10.
T13.1
Fraction of Dissolved CBOD
Baseline * 0.1
T13.2

216
Table 7.6 - continued
Description
Range
Test#
Baseline * 10.
T14.1
CBOD Settling Velocity
Baseline * 0.1
T14.2
Bulk density* 1.2
T15.1
Sediment Composition
Bulk density*0.7
T15.2
The tests were conducted by varying each coefficient between the extreme values
within literature range. Table 7.7 shows the partition between water column soluble organic
nitrogen, ammonium, nitrite+nitrate, and phytoplankton concentration for the baseline run,
the total percent of the water column nitrogen accounted in these three species, and the
dissolved oxygen concentration at the bottom layer. The results of the sensitivity tests for
the nitrogen species are presented in terms of percent variation from the baseline run.
Positive values corresponding to an increase percent in concentration, relative to the baseline
run, and negative values corresponding to a decrease. The non-linear oxygen balance test
(T11.1) was conducted to evaluate the amount of “spin-up” time required by a fully non¬
linear equation, and the sensitivity of model results to linear and fully non-linear options.
The results of the tests showed mineralization constant rate as the most sensitive
parameter in the water quality model. Increasing mineralization (T7.1) is more influential
on phytoplankton than decreasing it (T7.2). Results of test T7.1 show that soluble organic
nitrogen (SON) is rapidly mineralized to ammonium nitrogen (NH4). Nitrite+nitrate (N03)

217
Table 7.7 - Sensitivity analysis results.
Test
SON
NH4
N03
ALGN
TN
DOB
(%)
(%)
(%)
(%)
(%)
(mg/L)
T1
57.5
6.2
0.5
35.0
99.2
6.4
T2.1
<0.01
<0.01
<0.01
<0.01
99.2
6.4
T2.2
<0.01
<0.01
<0.01
<0.01
99.2
6.4
T3.1
0.6
-0.5
-0.1
-1.04
99.2
6.4
T3.2
-0.6
0.5
0.1
1.1
99.2
6.4
T4.1
-5.0
-0.2
1.5
4.2
97.8
6.3
T4.2
0.7
0.2
0.5
-0.6
99.4
6.4
T5.1
-0.2
-44.3
543.6
0.2
99.3
5.8
T5.2
-0.1
7.6
-89.5
0.04
99.2
6.4
T6.1
1.1
1.2
-41.4
-1.4
99.2
6.4
T6.2
<0.01
<0.01
<0.01
<0.01
96.4
6.5
T7.1
-55.5
81.0
109.5
74.2
98.8
6.3
T7.2
55.1
-62.6
-22.8
-77.9
99.6
6.1
T8.1
3.9
-51.3
-73.7
4.3
99.3
6.6
T8.2
-11.5
152.0
540.3
-17.5
98.8
6.2
T9.1
-5.3
68.0
189.3
-6.9
99.0
6.3
T9.2
3.0
-39.6
-62.0
3.4
99.3
6.5
T10.1
1.6
-21.8
-40.5
2.3
99.3
6.4
T10.2
-4.1
52.3
153.7
-6.0
98.8
6.2
Tll.l
0.01
0.09
-0.5
O
O
i
96.4
4.1
T12.1
<0.01
<0.01
<0.01
<0.01
96.4
5.8
T12.2
<0.01
<0.01
<0.01
<0.01
96.4
7.5
T13.1
<0.01
<0.01
<0.01
<0.01
99.2
1.9
T13.2
<0.01
<0.01
<0.01
<0.01
99.2
6.5
T14.1
-0.6
-0.5
0.1
1.1
99.2
6.9
T14.2
-0.6
-0.5
0.1
1.1
99.2
3.1

218
Table 7.7 - continued
Test
SON
NH4
N03
ALGN
TN
DOB
(%)
(%)
(%)
(%)
(%)
(mg/L)
T15.1
-1.1
-1.1
-2.8
2.1
99.2
6.4
T15.2
0.1
0.4
5.2
0.3
99.2
6.4
levels also increased due to nitrification. Since more inorganic nutrients were available, an
expected increase in uptake resulted in a noticeable increase in phytoplankton nitrogen
(ALGN). On the other hand, decreasing mineralization promoted an increase in SON, and
decrease in NH4, N03, and ALGN.
The second most important parameter revealed by the sensitivity tests is maximum
algal growth (T8.1 and T8.2), followed by the half saturation constant for uptake (T9.1 and
T9.2). These two parameters are related and their major impact should be detected in the
phytoplankton biomass. However, the ALGN seems to be more sensitive to mineralization
than maximum growth or half saturation, which reveals the extension of nitrogen limitation
to phytoplankton growth. Moreover, the effect of reducing maximum growth rate (T8.2) is
more pronounced in ALGN than increasing it (T8.1). Inorganic nitrogen, both NH4 and
N03, are more sensitive to variations of these parameters. Test T8.2 showed that maximum
growth rate is the most sensitive parameter for ammonium nitrogen. As to N03, the
maximum growth rate is the second most sensitive coefficient, right after nitrification rate
constant. Inorganic nitrogen species are more sensitive to a decrease in maximum growth
rate (T8.2) and increase in half saturation constant (T9.1), than to the opposite (T8.1 and
T9.2), which reinforces the evidence of nitrogen limitation.

219
The partition coefficients are not the most sensitive parameters in this water quality
model. Tests T4.1 and T4.2 demonstrated that increasing the partition coefficient (T4.1) has
more effect than decreasing it (T4.2). The variation of partition coefficients regulate not
only the relative composition between species, but also the availability of inorganic nutrients
for algal uptake. An increase in the partition coefficient corresponds to a decrease in
available inorganic nutrients, hence limiting phytoplankton uptake.
The thickness of the aerobic layer (T3) did not show a major impact in the
distribution of nitrogen species. Water colum soluble organic nitrogen, ammonium,
nitrate+nitrite, and algal nitrogen do not seem to be sensitive to this parameter.
Results of the non-linear oxygen balance test (T 11.1) showed that it does not affect
the relative composition of the nitrogen species in the water column. However, since a
longer “spin-up” time is required by the fully non-linear option, the near-bottom dissolved
oxygen value after 30 days was different from the baseline run. The other tests (T12 to T14)
that were designed to evaluate the oxygen balance equations, revealed that fraction of
dissolved CBOD is the most sensitive parameter, followed by particulate CBOD settling
velocity and deoxygenation coefficient. Actually, these three parameters are closely
correlated. It is the nature of the organic matter present in the water column and the ability
of the micro-organisms to utilize it that will dictate the fraction of dissolved CBOD, the
CBOD settling velocity, and the rate of biochemical oxidation (Sawyer and McCarty, 1978).
In order to improve the model, not only DO and BOD have to be measured, but also the
nature of the organic matter has to be known, so that laboratory experiments can be
performed to determine fCB0D, wsCB0D, and KD (Equation 4.23).

220
The sediment composition tests (T15) showed that, in a 30-day simulation, variations
in the bulk density have a minimal effect on the water column nutrient distribution.
In order to show the effects of the sensitivity tests in Tampa Bay, two simulations
using the lower and upper limits of the mineralization coefficients were performed. Figure
7.17 shows the soluble organic nitrogen, chlorophyll-a, ammonium nitrogen, and
nitrite+nitrate contours after 30 days of simulation using the lower limit of the mineralization
constant rate. As it would be expected, there is an accumulation of soluble organic nitrogen
throughout the Bay. Consequently, ammonium nitrogen is not readily formed, thus limiting
phytoplankton growth and nitrification. Figure 7.18 shows the soluble organic nitrogen,
chlorophyll-a, ammonium nitrogen, and nitrite+nitrate contours after a 30-day simulation
using the upper limit of the mineralization constant rate. In contrast with the previous case,
the results of the higher mineralization constant rate showed low concentration of organic
nitrogen throughout the Bay, and an increase in phytoplankton concentration. Due to an
increase in respiration, decomposition, and nitrification, dissolved oxygen levels decreased
mainly in Hillsborough Bay as shown in Figure 7.19.
The information obtained from the sensitivity tests enabled a fine tunning of the
model coefficients, using the EPC monthly data. The final values for mineralization constant
rate, phytoplankton maximum growth rate, and half saturation constant were determined
from phytoplankton, dissolved oxygen, and soluble organic nitrogen measured
concentrations.

221
Soluble Organic Nitrogen
1000
BOO
600
400
200
0
í>
it
Chlorophyll-a
Ammonium Nitrogen
100
80
60
40
20
0
=t
Nitrite-f Nitrate
Figure 7.17 - Water quality parameters after 30 days for a simulation using the lower limit
of the mineralization constant rate.

222
Soluble Organic Nitrogen
Chlorophyll-a
Figure 7.18 - Water quality parameters after 30 days for a simulation using the higher limit
of the mineralization constant rate.
1000
800
600
400
200
0
100
80
60
40
20
0
Nitrite+Nitrate
Ammonium Nitrogen

223
Low Mineralization Constant Rate
High Mineralization Constant Rate
Figure 7.19 - Near-bottom dissolved oxygen
levels after 30 days for the mineralization
constant rate tests.

224
Simulation of the Summer 1991 Condition
The integrated model of the Tampa Bay Estuarine System was used to perform a
four-month simulation of the hydrodynamics and water quality dynamics during the summer
of 1991. Using the salinity distribution of the hydrodynamics simulation described in
Chapter 6 as initial condition, the water quality dynamics in Tampa Bay was simulated with
real data of tidal forcing, river discharges, rainfall, and wind field. The initial conditions for
the water quality parameters were described in the “Initial and Boundary Conditions of the
Water Quality Model” section.
The calibration of model coefficients and water quality zonation were performed
using the monthly water column data provided by the EPC. The assumption implicit in this
methodology is that the EPC stations inside each of the four major sub-basins (Hillsborough
Bay, Old Tampa Bay, Middle Tampa Bay, and Lower Tampa Bay) are representative of the
whole area. In the following, model results will be presented for dissolved oxygen,
phytoplankton, and nitrogen species in terms of time series at specific grid cells that coincide
with EPC stations, contour plots that give a snapshot of the Bay in each month (June to
September of 1991), the simulated fluxes across the mouth of the Bay (upstream Egmont
Key), entrance to Hillsborough Bay, and the benthic fluxes for organic and inorganic
nitrogen species.

225
Dissolved Oxygen
The dissolved oxygen balance is the most important process in any aquatic
environment, because living organisms depend on oxygen in one form or another to maintain
their metabolic processes. In the model, dissolved oxygen is a function of photosynthesis
and respiration by planktonic organisms, reaeration, nitrification and denitrification,
decomposition of organic matter, tidal and wind mixing, and loading. In this sense, the
model’s accuracy to simulate the dynamics of DO can be linked to the overall ability of the
model to synthesize the water quality dynamics within the system.
Figures 7.20 to 7.23 show the evolution of DO concentration through the summer
months. Figure 7.20 shows a snapshot of the near-bottom DO distribution in Tampa Bay for
June 26, after 30 days of simulation. Figure 7.21 shows the snapshot for July 26, after 60
days of simulation, Figure 7.22 shows the snapshot for August 25, after 90 days of
simulation, and Figure 7.23 shows the snapshot for September 24, after 120 days of
simulation.
Due to its shallowness, wind, and tidal mixing, Tampa Bay generally exhibits a
vertically well-mixed distribution of DO. In Hillsborough Bay, which usually presents the
lowest levels of DO, some stratification may occur due to high consumption near the bottom
and super-saturation near the surface. High oscillations in DO concentration that are
commonly seen in Hillsborough Bay are characteristic of an eutrophic water body. The
upper reaches of Old Tampa Bay also exhibited some low levels of DO (between 5 and 6
mg/L), but Figures 7.20 to 7.23 show that it does not seem to evolve throughout the summer.
Model results showed that DO variations in Middle and Lower Tampa Bay are mild, without
a distinct trend from June to September of 1991.

226
Near-Bottom Dissolved Oxygen
After 30 days (June 26,1991)
10 km
Figure 7.20 - Near-bottom dissolved oxygen concentration in Tampa Bay for
June 26, after 30 days of simulation.

227
Near-Bottom Dissolved Oxygen
After 60 days (July 26,1991)
Figure 7.21 - Near-bottom dissolved oxygen concentration in Tampa Bay for
July 26, after 60 days of simulation.
mg/L

228
Near-Bottom Dissolved Oxygen
After 90 days (August 25,1991)
10 km
Figure 7.22 - Near-bottom dissolved oxygen concentration in Tampa Bay for
August 25, after 90 days of simulation.

229
Near-Bottom Dissolved Oxygen
After 120 days (September 24,1991)
Figure 7.23 - Near-bottom dissolved oxygen concentration in Tampa Bay for
September 24, after 120 days of simulation.
mg/L

230
Assuming that the EPC data are representative of the Bay conditions, model results
were plotted along with the measured data for comparison. Figures 7.24 shows the time
series of model results for the segment-averaged DO (near-bottom) and the EPC data inside
Hillsborough Bay. The model results for the segment-averaged DO appears to reproduce the
EPC averages, as well as the maximum and minimum peaks. Figure 7.25 shows the model
results for the segment-averaged DO (near-bottom) and the EPC data inside Old Tampa Bay.
Like in Hillsborough Bay, the model seems to accurately reproduce the overall trend in DO,
expressed in terms of the EPC averages and the model results for segment-averaged DO.
The maximum and minimum values obtained from model simulations are within the range
of the measured data. Comparing Figures 7.24 and 7.25, it is possible to visualize the
differences between these two water bodies. Both Bays exhibit minimum DO concentrations
that are comparable to hypoxic or even anoxic conditions. It appears that organic matter
decomposition and nitrification/denitrification processes are the major sinks for DO in the
bottom layers of these Bays. As to the maximum peaks, Old Tampa Bay presents an almost
flat curve, close to saturation levels of DO. On the other hand, Hillsborough Bay exhibits
a very dynamic maximum fluctuation, with the above saturation levels suggesting high
phytoplankton activity, typical of eutrophic conditions.
A more direct assessment of model’s accuracy was performed by comparing model
results at specific grid cells, corresponding to the location of the EPC stations. Figures 7.26
and 7.27 show the model results and measured data for near-bottom dissolved oxygen at EPC
stations 8, 70, 73, and 80, in Hillsborough Bay. These figures show that the model was able

231
Near-Bottom Dissolved Oxygen - Hillsborough Bay
Julian Day (1991)
Model
EPC avg
Station 6
Station 7
Station 8
Station 44
Station 52
Station 54
Station 55
Station 58
Station 70
Station 71
Station 73
Station 80
Figure 7.24 - Model results for segment-averaged near-bottom DO (solid line), segment
maximum and minimum (dashed line), and the EPC data inside Hillsborough
Bay.

232
Near-Bottom Dissolved Oxygen - Old Tampa Bay
Julian Day (1991)
Model
EPC avg
Station 36
Station 38
Station 40
Station 41
Station 46
Station 47
Station 50
Station 51
Station 60
Station 61
Station 62
Station 63
Station 64
Station 65
Station 66
Station 67
Station 68
Figure 7.25 - Model results for segment-averaged near-bottom DO (solid line), segment
maximum and minimum (dashed line), and the EPC data inside Old Tampa
Bay.

Concentration (mg/L) Concentration (mg/L)
233
Near-Bottom Dissolved Oxygen
Model
Station 70
Model
Station 8
Figure 7.26 - Model results and measured data for near-bottom DO at EPC stations 70 and
8.

Concentration (mg/L) Concentration (mg/L)
234
Near-Bottom Dissolved Oxygen
Model
Station 73
Model Results x EPC Station 80
Model
Station 80
Figure 7.27 - Model results and measured data for near-bottom DO at EPC stations 73 and
80.

235
to capture the different dynamics of the dissolved oxygen balance occurring on specific
areas in Hillsborough Bay. The near-bottom dissolved oxygen balance in the upper reaches
of Hillsborough Bay (Figure 7.26) shows a very dynamic environment, with concentrations
varying from super-saturation values to hypoxic conditions. On the other hand, Figure 7.27
shows that, close to the mouth of Hillsborough Bay, the near-bottom dissolved oxygen
exhibits a more stable balance, similar to the average conditions found in the other parts of
Tampa Bay. Moreover, these figures show the importance of using a three-dimensional fine-
resolution model to fully understand the water quality dynamics in Hillsborough Bay.
Figure 7.28 and 7.29 show the model results for the segment-averaged DO (near¬
bottom) and the EPC data inside Middle and Lower Tampa Bay, respectively. Simulated DO
for Middle and Lower Tampa Bay was not able to accurately reproduce the EPC data,
although the segment-averaged DO was within the data range. Both Middle and Lower
Tampa Bay EPC-average showed a sharp decrease in DO during August that was not
captured by the model. Possible reasons for this discrepancy are two-fold: the phytoplankton
dynamics, and the offshore boundary conditions. In the first one, the phytoplankton
simulations could not be reflecting the dynamics of the system, with an unbalanced
relationship between photosynthesis and respiration in late summer causing the drop in the
DO levels. Tests with different phytoplankton/zooplankton relationships were able to shift
the segment-averaged DO curve up and down, but were not capable of reproducing the
dynamics shown in the EPC data. The second reason could be the offshore boundary
condition. The EPC data at the most offshore station (station 94) present one of the lowest

236
Near-Bottom Dissolved Oxygen - Middle Tampa Bay
Model
EPC avg
Station 11
Station 13
Station 14
Station 16
Station 19
Station 28
Station 32
Station 33
Station 81
Station 82
Station 84
Julian Day (1991)
Figure 7.28 - Model results for segment-averaged near-bottom DO (solid line), segment
maximum and minimum (dashed line), and the EPC data inside Middle
Tampa Bay.

237
Near-Bottom Dissolved Oxygen - Lower Tampa Bay
Model
EPC average
Station 21
Station 23
Station 24
Station 25
Station 90
Station 91
Station 92
Station 93
Station 94
Station 95
Station 96
Figure 7.29 - Model results for segment-averaged near-bottom DO (solid line), segment
maximum and minimum (dashed line), and the EPC data inside Lower Tampa
Bay.

238
levels of DO (Figure 7.29), and it seems to be driving the trend of low DO during July and
August. If that is the case, the boundary condition used by the model, which does not
account for disturbances originated in the Gulf of Mexico, may be compromising the results.
Phytoplankton
The phytoplankton dynamics is also one of the most important processes simulated
in this study. It is closely related to the nutrient recycling through uptake during growth, and
excretion/decay during respiration and senescence. The diurnal variations exhibited by the
dissolved oxygen cycle is a result of photosynthetic oxygen production during daylight
combined with consumption during the night. As one of the dominant components of the
primary producers in Tampa Bay (Pomeroy, 1960), phytoplankton forms the basis of the food
chain, affecting the dynamics of all successive trophic levels (Steidinger and Gardiner, 1985).
Phytoplankton also presents an important feedback to the circulation and water quality
models through its contribution to total suspended solids and light attenuation simulations.
In this integrated model of the Tampa Bay Estuarine System, the phytoplankton
community is aggregated into a single constituent, and simulated in a mass per volume basis.
In order to make comparisons with the data obtained by EPC, the conversion of model results
to chlorophyll-a had to be made. Although a rigorous stoichiometric conversion considers
the variability due to species composition, cell size, physiological conditions, and
environmental parameters (external nutrient concentration, light, and temperature), most
water quality models (e.g., Di Toro etal., 1971; Najarían, 1984; Ambrose etal., 1991, Chen
and Sheng, 1994) consider a fixed carbon to chlorophyll-a ratio in the absence of specific
data.

239
Figures 7.30 to 7.33 show the evolution of chlorophyll-a concentration through the
summer months. Figure 7.30 shows a snapshot of the near-surface chlorophyll-a distribution
in Tampa Bay for June 26, after 30 days of simulation. Figure 7.31 shows the snapshot for
July 26, after 60 days of simulation, Figure 7.32 shows the snapshot for August 25, after 90
days of simulation, and Figure 7.33 shows the snapshot for September 24, after 120 days of
simulation. From the initial condition (Figure 7.7) to the end of June snap-shot (Figure 7.30)
it is possible to conceive of the development of high planktonic activity as summer
progresses. Only a few spots in upper Hillsborough Bay exhibit chlorophyll-a concentrations
above 20 pg/L, and they seem to originate from Hillsborough River and Alafia River
discharges. Old Tampa Bay, which started with chlorophyll-a levels comparable to
Hillsborough Bay, does not seem to develop high concentrations towards the summer
months. Middle and Lower Tampa Bay showed uniformly low concentrations, with a small
increase towards the shallow areas, on both sides of the Bay.
After 60 days (Figure 7.31), the model results showed that Hillsborough Bay
maintains the highest concentrations of chlorophyll-a, with most of the upper reaches of the
Bay exhibiting chlorophyll-a concentrations of 20 pg/L or higher. The highest concentrations
of chlorophyll-a found in the upper Hillsborough Bay can be attributed to high nutrient
concentration and poor flushing, an ideal combination for the development of algae blooms.
Algal blooms are always related to high turbidity, odors, depletion of dissolved oxygen, and
sometimes associated with extensive fish kills. According to the EPC report (Boler, 1992),
the tributaries of the upper Hillsborough Bay have been the source of many complaints from
residents concerned with algal blooms and fish kills.

240
Chlorophyll-a Concentration
After 30 days (June 26,1991)
Figure 7.30 - Near-surface chlorophyll-a concentration in Tampa Bay for
June 26, after 30 days of simulation.

241
Chlorophyll-a Concentration
After 60 days (July 26,1991)
Figure 7.31 - Near-surface chlorophyll-a concentration in Tampa Bay for
July 26, after 60 days of simulation.

242
Chlorophyll-a Concentration
After 90 days (August 25,1991)
Figure 7.32 - Near-surface chlorophyll-a concentration in Tampa Bay for
August 25, after 90 days of simulation.

243
Chlorophyll-a Concentration
After 120 days (September 24,1991)
Figure 7.33 - Near-surface chlorophyll-a concentration in Tampa Bay for
September 24, after 120 days of simulation.

244
Figure 7.34 shows the time series of model results for the segment-averaged
chlorophyll-a and the EPC data in Hillsborough Bay. After the first 30 days, model results
and data were within the same range (Julian Day 163). Model results show a steady curve
for phytoplankton dynamics up to the beginning of July (Julian Day 182), when chlorophyll-a
levels start to increase. The maximum peak of 27 pg/L occurs around Julian Day 204, after
which the chlorophyll-a levels decrease. A closer look to the rainfall (Figure 6.9) and river
discharge (Figure 6.10) data suggests that the high rainfall between Julian Days 192 and 196,
leading to an abnormal river discharge into Hillsborough Bay, especially from Alafia River,
may have triggered this event.
Figure 7.35 shows the time series of model results for the segment-averaged
chlorophyll-a and the EPC data in Old Tampa Bay. The model was able to capture the
general trend described by the EPC averages, although the small increase of the August EPC-
average (Julian Day 219) was not shown in the model results. It is clear that the outlier
represented by the EPC station 62 (represented by the symbol “B” in Figure 7.35) is pulling
the average upward. EPC station 62 is located at the mouth of Sweetwater Creek, whose
discharge does not show any particular increase during this period. In the model, the
concentration for each water quality parameter is fixed, and linked to the total loading
through the river discharge. Therefore, the difference between the EPC data and model
results could be attributed to a localized change in environmental conditions, that was not
captured by the fixed riverine boundary condition of the model.

245
*d
O)
=1
c
o
2
c
CD
o
c
o
o
Segment Averaged Chlorophyll-a - Hillsborough Bay
1 (78.8)
A (53.7)
t
L 3(67.3)
30
25
20
15
10
5
B 3
Model
0 EPCavg
t Station 6
2 Station 7
3 Station 8
4 Station 44
5 Station 52
6 Station 54
7 Station 55
8 Station 58
9 Station 70
A Station 71
B Station 73
C Station 80
Q fl i, I i i i i I i i i—i—I—i—i—i—i—I—i—i—i—i—I—L
160 180 200 220 240
i
260
Julian Day (1991)
Figure 7.34 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Hillsborough Bay.

246
Depth Averaged Chlorophyll-a - Old Tampa Bay
Model
EPC average
Station 36
Station 38
Station 40
Station 41
Station 46
Station 47
Station 50
Station 51
Station 60
Station 61
Station 62
Station 63
Station 64
Station 65
Station 66
Station 67
Station 68
Figure 7.35 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Old Tampa Bay.

247
Figure 7.36 shows the time series of model results for the segment-averaged
chlorophyll-a and the EPC data in Middle Tampa Bay. For this particular subdivision of
Tampa Bay, the data is so scattered, with both spatial and temporal variations, that it is
difficult to draw any conclusion. After the first 30 days, the model is over predicting the
EPC average, with only a few stations showing chlorophyll-a levels higher than the model
segment-average. For the August data (between Julian Days 219 and 233), an excessive high
concentration in EPC station 32 (represented by the symbol “7” in Figure 7.36) shifts the
EPC averages upward, and causes an under prediction by the model results.
Figure 7.37 shows the time series of model results for the segment-averaged
chlorophyll-a and the EPC data in Lower Tampa Bay. As discussed for dissolved oxygen,
model results for segment-averaged chlorophyll-a are within the data range, although they
did not reflect the dynamics of the phytoplankton in Lower Tampa Bay. For the first 30 and
60 days, the model over predicts chlorophyll-a in Lower Tampa Bay, and it appears that the
low average levels are driven by the most offshore stations (EPC stations 93 and 94). In
August (Julian Day 236), all the EPC stations showed an increase in chlorophyll-a
concentration, with the EPC station 94 presenting the highest relative increase.
The analysis of the dissolved oxygen and chlorophyll-a concentrations in Lower
Tampa Bay suggests the necessity of specific data for the oceanic boundary condition.
During flood flow, the model should use a prescribed value obtained from temporal
interpolation of measured data. During ebb flow, the water quality parameters would be
computed internally. Therefore, disturbances originated in the Gulf of Mexico could be
captured by model simulations. Thomman et al. (1994) reported the use of an ocean
boundary sub-model to specifically study the effects of the coastal zone as part of the
Integrated Chesapeake Bay Models.

248
Segment Averaged Chlorophyll-a - Middle Tampa Bay
Model
EPC avg
Station 11
Station 13
Station 14
Station 16
Station 19
Station 28
Station 32
Station 33
Station 81
Station 82
Station 84
Figure 7.36 - Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Middle Tampa Bay.

249
10
9
8
7
2
1
0
Figure 7.37
Depth Averaged Chlorophyll-a - Lower Tampa Bay
4
1
§
A
B
I l I I I â–  .In. â–  1 ... â–  â–  I I I I 1 I 1 lilt l I 1 I I i I I I I l 1 L
160 180 200 220 240 260
Julian Day (1991)
Model
EPC avg
Station 21
Station 23
Station 24
Station 25
Station 90
Station 91
Station 92
Station 93
Station 94
Station 95
Station 96
- Model results for segment-averaged near-surface chlorophyll-a (solid line)
and the EPC data inside Lower Tampa Bay.

250
Nitrogen Species
In order to compare the nitrogen cycle simulations with the nitrogen species data
presented by EPC, simulated soluble organic nitrogen, dissolved ammonium and ammonia
nitrogen concentrations were combined and compared with the EPC total Kjeldahl nitrogen.
Since most organic compounds containing nitrogen are derivatives of ammonia, the Kjeldahl
method employs sulfuric acid to oxidize the organic portion of the molecules and release the
nitrogen as ammonia, which is then measured by standard laboratory procedures. The EPC
total Kjeldahl nitrogen included nitrogen from ammonia, amino acids, polypeptides and
proteins, mostly of biological origin (Boler, 1992). It can be anticipated that model results
are going to under predict the Kjeldahl nitrogen data due to the fact that the methodology
applied by the EPC makes use of unfiltered samples, therefore, including some particulate
species (Boler, 1996 - pers. comm.).
Figures 7.38 to 7.41 show the evolution of near-bottom Kjeldahl nitrogen
concentration through the summer months. Figure 7.38 shows a snapshot of the near-bottom
Kjeldahl nitrogen distribution in Tampa Bay for June 26, after 30 days of simulation. Figure
7.39 shows the snapshot for July 26, after 60 days of simulation, Figure 7.40 shows the
snapshot for August 25, after 90 days of simulation, and Figure 7.41 shows the snapshot for
September 24, after 120 days of simulation. Following the same pattern of the phytoplankton
distribution, the Kjeldahl nitrogen exhibits higher concentrations in Hillsborough Bay, with
a sharp decrease towards the mouth of Tampa Bay. This same spatial gradient was kept
throughout the summer months. According to model results, Lower and Middle Tampa Bay

251
Kjeidahl Nitrogen
After 30 days (June 26,1991)
Figure 7.38 - Near-surface Kjeidahl nitrogen concentration in Tampa Bay
for June 26, after 30 days of simulation.
mg/L

252
Kjeldahl Nitrogen
After 60 days (July 26,1991)
Figure 7.39 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay
for July 26, after 60 days of simulation.
mg/L

253
Kjeldahl Nitrogen
After 90 days (August 25,1991)
Figure 7.40 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay
for August 25, after 90 days of simulation.
mg/L

254
Kjeldahl Nitrogen
After 120 days (September 24,1991)
Figure 7.41 - Near-surface Kjeldahl nitrogen concentration in Tampa Bay
for September 24, after 120 days of simulation.

255
were not significantly affected by summer conditions, maintaining low concentration on the
order of 0.10 to 0.2 mg/L. Figure 7.39 shows that in late summer, Kjeldahl nitrogen
concentrations can rise up to 0.70 mg/L in upper Hillsborough Bay. The source of these high
concentrations can be attributed to high phytoplankton activity and loading, but the fate of
this nutrient enriched waters needs further investigation. As discussed in Chapter 6, the ebb
currents flowing out of the Hillsborough Bay may take the direction parallel to the Interbay
Peninsula shoreline towards Old Tampa Bay, causing an advective flux of nutrient enriched
waters from Hillsborough Bay to the entrance of Old Tampa Bay. To answer specific
management questions regarding the effects of Hillsborough Bay nutrients in Old Tampa
Bay, a more intensive numerical study could be performed using particle trajectory
simulations.
Figure 7.42 shows the time series of model results for the segment-averaged Kjeldahl
nitrogen and the EPC data in Hillsborough Bay. Model results seems to capture the overall
trend of the EPC data. The July (around Julian Day 200) peak in concentration was captured
by model results, which follows a similar pattern to the chlorophyll-a distribution (Figure
7.34). Figure 7.43 shows the time series of model results for the segment-averaged Kjeldahl
nitrogen and the EPC data in Old Tampa Bay. Model results under predict Kjeldahl nitrogen
throughout the summer months. As explained for the chlorophyll-a distribution, it seems that
the outlier of station 62 (represented by the symbol “B” in Figure 7.43) is forcing the average
upward. Both data and model results showed that Kjeldahl nitrogen in Old Tampa Bay does
not seem to show any particular dynamics during the summer months of 1991. Figure 7.44
shows the time series of model results for the segment-averaged Kjeldahl nitrogen and the

Concentration (mg/L)
256
2.0
1.5
1.0
0.5
0.0 h
Figure 7.42
Segment Averaged Kjeldahl Nitrogen - Hillsborough Bay
3
5
A
Model
O EPCavg
1 Station 6
2 Station 7
3 Station 8
4 Station 44
5 Station 52
6 Station 54
7 Station 55
8 Station 58
9 Station 70
A Station 71
B Station 73
C Station 80
160 180 200 220 240 260
Julian Day (1991)
- Model results for near-bottom segment-averaged Kjeldahl nitrogen (solid line)
and the EPC data inside Hillsborough Bay.

Concentration (mg/L)
257
Segment Averaged Kjeldahl Nitrogen - Old Tampa Bay
Model
EPC avg
Station 36
Station 38
Station 40
Station 41
Station 46
Station 47
Station 50
Station 51
Station 60
Station 61
Station 62
Station 63
Station 64
Station 65
Station 66
Station 67
Station 68
Figure 7.43 - Model results for near-bottom segment-averaged Kjeldahl nitrogen (solid line)
and the EPC data inside Old Tampa Bay.

Concentration (mg/L)
258
Segment Averaged Kjeldahl Nitrogen - Middle Tampa Bay
Model
EPC avg
Station 9
Station 11
Station 13
Station 14
Station 16
Station 19
Station 28
Station 32
Station 33
Station 81
Station 82
Station 84
Figure 7.44 - Model results for near-bottom segment-averaged Kjeldahl nitrogen (solid line)
and the EPC data inside Middle Tampa Bay.

259
EPC data in Middle Tampa Bay. Once more, model results under predict Kjeldahl nitrogen
throughout the summer months, with both model and data showing no particular event during
the summer months of 1991. Figure 7.45 shows the time series of model results for the
segment-averaged Kjeldahl nitrogen and the EPC data in Lower Tampa Bay. Although
model results under predict the Kjeldahl nitrogen throughout the simulation, the difference
between model and data appears to be smaller for Lower Tampa Bay. Unlike model results
for chlorophyll-a, the simulated Kjeldahl nitrogen does not seem to be affected by the
oceanic boundary condition. Actually, all the measured data exhibit a narrow range of
variation, suggesting a uniform distribution of Kjeldahl nitrogen in Lower Tampa Bay, that
is maintained throughout the summer of 1991.
From the modeling point of view, it is difficult to compare the EPC unfiltered
samples with model results. The fraction of particulate organic nitrogen, particulate
inorganic nitrogen and even phytoplankton cells accounted in the samples is not well defined
and prevent a more rigorous comparison. Nevertheless, the constant pattern of model under
predicting Kjeldahl nitrogen was maintained for all the sub-divisions of Tampa Bay (Figures
7.42 to 7.45). Numerically, the difference could be improved by changing the algal nitrogen
to carbon ratio (anc). Like the carbon to chlorophyll-a ratio, anc can vary with species
composition, cell size, and physiological conditions. The sensitivity test T10 showed that
decreasing anc would cause an increase in inorganic nitrogen, with a proportional decrease
in algal nitrogen. Since the model results for phytoplankton are in good agreement with the
EPC data in the upper reaches of the Bay, a spatially variant coefficient would be required.

Concentration (mg/L)
260
Segment Averaged Kjeldahl Nitrogen - Lower Tampa Bay
Model
EPC avg
Station 21
Station 23
Station 24
Station 25
Station 90
Station 91
Station 92
Station 93
Station 94
Station 95
Station 96
Figure 7.45 - Model results for near-bottom segment-averaged Kjeldahl nitrogen (solid line)
and the EPC data inside Lower Tampa Bay.

261
Without specific data on the composition of the phytoplankton community, arbitrary tuning
of model coefficients can be dangerous, and compromise the model’s credibility.
Model results for nitrate+nitrite and ammonium nitrogen are presented in Appendix
E in terms of contour plots that give a snapshot of the Bay in each of the summer months
(June to September of 1991). Also presented in Appendix E are time series for dissolved
oxygen, chlorophyll-a, and TKN at specific grid cells that coincide with EPC stations.
Tidal Exchange
During August 25-30,1991, NOAA used a remote acoustic Doppler sensor (RADS)
mounted in a downward-looking mode to measure current profiles along three transects in
Tampa Bay. Volumetric flow rates were calculated from the RADS data in four steps: (1)
computing the eastward and northward components of flow rate per unit width at each RADS
station; (2) multiplying the normal component by the horizontal distance between stations
to get flow rate per segment; (3) summing all segment flow rates to get a total for the pass;
and (4) estimating the flow rate in the parts of the cross-section that were not measured. The
detailed description of the methodology for volumetric flow calculation is presented in Hess
(1991). Riñes (1991) presented the results of a nutrient sampling survey, which coincides
with the NOAA transect across the mouth of Hillsborough Bay and the entrance to Tampa
Bay. Along the transect, three stations were sampled, at two to four depths, every three hours
over a 24-hour cycle, for a total of eight sampling events. Figure 7.46 shows the measured
and simulated transport across the mouth of Hillsborough Bay, along with the Kjeldahl
nitrogen concentration (mean and standard deviation) presented by Riñes (1991). In the top

262
figure, model results and the flow rate calculated from RADS data showed reasonable
agreement, both in magnitude and phase. It is noteworthy that model results were obtained
after 94 days of simulation. Also, the top figure shows the simulated Kjeldahl nitrogen flux
across the mouth of Hillsborough Bay. It appears that the inflow and outflow of Kjeldahl
nitrogen are in balance, for this particular period. The Kjeldahl nitrogen concentration was
calculated from the simulated tidal flow and Kjeldahl nitrogen flux. Figure 7.46 (bottom)
shows the simulated Kjeldahl nitrogen concentration along with the calculated averages and
standard deviations presented by Riñes (1991). According to the analysis presented by Riñes
(1991), a variety of parameters may influence the analysis of the results. The sampling
station location, depth, and tidal cycle accounted for a significant variability in the
calculation of the mean and standard deviation presented.
Figure 7.47 shows the measured and simulated transport across the mouth of
Tampa Bay (upstream Egmont Key), along with the Kjeldahl nitrogen concentration (mean
and standard deviation) presented by Riñes (1991). In the top figure, the flow rate calculated
from RADS data and the model results are in reasonable agreement, both in magnitude and
phase. Again, model results were obtained after 90 days of simulation. The simulated
Kjeldahl nitrogen flux across the mouth of Tampa Bay is also presented in the top figure.
It appears that the inflow and outflow of Kjeldahl nitrogen are in balance, for this particular
period. The Kjeldahl nitrogen concentration was also obtained from the simulated tidal flow
and Kjeldahl nitrogen flux. Figure 7.47 (bottom) shows the simulated Kjeldahl nitrogen
concentration along with the calculated averages and standard deviations presented by Riñes
(1991).

Concentration (mg/L) Flow Rate (m3/s) x 10:
263
Tidal Exchange - Hillsborough Bay
Transect-averaged Kjeldahl Nitrogen
Figure 7.46 - Measured and simulated transport across the mouth of Hillsborough
Bay, along with the Kjeldahl nitrogen concentration (mean and
standard deviation) presented by Riñes (1991).
Kjeldahl Nitrogen Flux (ton/day)

Concentration (mg/L) Flow Rate (m3/s) x 10'
264
Tidal Exchange - Entrance to Tampa Bay
Transect-averaged Kjeldahl Nitrogen
Model
average
maxima
minima
Figure 7.47 - Measured and simulated transport across the entrance of Tampa Bay,
along with the Kjeldahl nitrogen concentration (mean and standard
deviation) presented by Riñes (1991).
Simulated Total Kjeldahl Flux (tons/day)

265
Nutrient Budget
Another application of this integrated model of the Tampa Bay Estuarine System that
can support ecosystem management is the determination of a nutrient budget for the Bay.
Model results were used to compute the net amount of soluble organic nitrogen, ammonium
nitrogen, and nitrite+nitrate entering the Bay through point-source loading, benthic fluxes,
and exchange with the Gulf of Mexico. The total point-source loading is an input parameter
of the model, and it is calculated through a constant concentration multiplied by real data of
river discharges.
The subject of benthic fluxes have been discussed by Berner (1971), and applied in
a variety of water bodies (e.g., Fanning, 1992; Sheng, 1993). The simplified solution of the
diffusion equation gives:
-dmoi$•
(
\
(7.1)
where, is the flux of species i in mass per unit area of sediment and time, dmol is the
molecular diffusion coefficient, in the sediment layer, Cz0 is the concentration of i at a depth zO in the sediment or water
column layer, and Z is the shallow depth within the linear gradient (taken as the mid-point
between zO and zl). In the model, the molecular diffusion coefficient is a constant set to
1.0je 10'5 cm2s-1. The resuspension flux, as defined by Sheng (1993), can be used to
calculate the amount of nutrients released by sediments in the case of sediment resuspension
events. The analysis of the sediment net resuspension (erosion - deposition) throughout

266
Tampa Bay showed that no major resuspension event occurred during the summer of 1991,
resulting in a net depositional flux. The net resuspension and depositional fluxes of
particulate nitrogen species were calculated in the model according to:
Net Flux(PON, PIN) = D-{PON,PIN)
-E-(PON, PIN)
bottom layer of water column
top layer of sediment column
(7.2)
where D is the deposition rate, and E is the erosion rate.
The tidal exchange with the Gulf of Mexico was computed similarly to the transect
calculations at the entrance to Tampa Bay (Figure 7.47). At each vertical grid cell, the
velocity normal to the direction of the mouth of the Bay was multiplied by the vertical cross-
sectional area of the grid cell and the nutrient concentration. The values were accumulated
during a 24-hour period, giving the net exchange per day. Since the tidal period contains
diurnal and semi-diurnal information, model results were averaged over a two-month period
in order to provide a better estimation of the nutrient exchange with the Gulf of Mexico.
Table 7.8 summarizes the nutrient budget between July 1 and August 31, 1991. The total
nitrogen represents the sum of soluble organic nitrogen, ammonium nitrogen, ammonia,
nitrite+nitrate, algal and zooplankton nitrogen, particulate organic and inorganic nitrogen,
obtained from the summer of 1991 simulation.

267
Table 7.8 - Nitrogen budget between July 1 and August 31,1991.
Total Nitrogen (kg)
Initial Mass (July 1,1991)
1.351
X
106
Loading
1.640
X
106
Exported to the Gulf of Mexico
2.313
X
106
Benthic Flux (into the water column)
0.733
X
106
Final Mass (August 31, 1991)
1.411
X
106
Results of the simulation of the summer of 1991 conditions suggested a conceptual
model for the water quality dynamics in the Tampa Bay Estuarine System that is summarized
in Figure 7.48. Just for illustrative purposes, the nitrogen cycle was divided in three separate
steps, corresponding to (a) loading, (b) water-column-related biogeochemical processes, and
(c) sediment-column-related biogeochemical processes. For the loading step, Figure 7.48(a)
shows organic and inorganic nitrogen species and phytoplankton been released into the Bay
through point sources, non-point sources, and atmospheric deposition (collectively combined
into point discharges during model simulations). The net results of the water-column-related
biogeochemical processes shown in Figure 7.48(b) demonstrated the central role played by
soluble organic nitrogen. The rate at which it is mineralized dictates both the formation of
nitrite+nitrate, through nitrification, and the availability of dissolved inorganic nitrogen to
phytoplankton uptake. The high levels of soluble organic nitrogen and phytoplankton inside
the Bay produce a net export of these water quality parameters to the Gulf of Mexico. On
the other hand, the nitrogen limiting condition of the Bay causes a depletion of dissolved
inorganic nitrogen species, and the net transport generated is from the Gulf of Mexico into

268
(a)
Gulf of Mexico
water
sediment
zoo
I PON |-
| PIN [-
(b)
Figure 7.48 - Simulated nitrogen cycle for the summer of
1991 conditions: (a) Loading, (b) biogeochemical
processes in the water column, (c) biogeochemical
processes in the sediment column.

269
the Bay. Figure 7.48(c) shows that particulate organic and inorganic nitrogen have a net
depositional flux. Two sources were considered in the simulations: the settling and
deposition of particulate species, following the suspended sediment dynamics, and the burial
of algal cells from the first vertical layer next to the bottom. Particulate inorganic nitrogen
(adsorbed ammonium nitrogen) and interstitial ammonium interchange according to the
sorption/ desorption reaction. Particulate organic nitrogen is converted to soluble organic
nitrogen at a constant hydrolysis rate. Since both organic an inorganic dissolved species
exhibit higher concentrations in the sediment layer than in the water column, the net
diffusive flux is from the sediment into the water column.
Load Reduction Simulations
One of the primary objectives of this integrated model of the Tampa Bay Estuarine
System is to provide a tool to study management options and the corresponding response of
the system. At this point of development, the model has been tested using monthly water
quality data provided by the Hillsborough County Environmental Protection Commission
(EPC), and a more comprehensive data set is needed to fully validate the water quality
model. Nevertheless, a preliminary analysis of the potential impact of reduced nutrient
loadings to the system was carried out by model simulations using 100% and 40% nutrient
load reduction.
The 100% load reduction simulation was performed with all the nitrogen species,
chlorophyll-a, and CBOD concentrations set to 0 mg/L at the river boundaries. Dissolved
oxygen concentration at river boundaries were set to saturation values. In the 40% load

270
reduction simulation, water quality parameters were set to 40% of the summer of 1991
condition. Figure 7.49 shows the predicted response of the near-bottom dissolved oxygen,
after 60 days of the load reduction simulations. As expected, the upper reaches of
Hillsborough Bay, which receives most of the freshwater inflow, is the most sensitive
segment of the Bay to load reduction. With 40% load reduction, no hypoxic events were
found during the simulations, and with 100% load reduction the dissolved oxygen
distribution exhibit minimal vertical stratification, with concentration values fluctuating
around saturation. In upper Old Tampa Bay (between Courtney Campbell Parkway and W.
Howard Frankland Bridge), some localized low levels of near-bottom dissolved oxygen were
maintained even during the 100% load reduction scenario. Since there is only one EPC
monitoring station (station 65) in the area, model results can be used to recommend a
refinement of the monitoring network in order to provide a better representation of the entire
Old Tampa Bay. In Middle and Lower Tampa Bay, the effects of the 60-day load reduction
simulation seems to be restricted to the vicinity of the mouth of rivers (Little Manatee and
Manatee).
Figure 7.50 shows the predicted response of the near-surface chlorophyll-a, after 60
days of the load reduction simulations. The 100% load reduction simulation demonstrated
the importance of loading to the system. With no external source of inorganic nitrogen and
phytoplankton, the initial phytoplankton distribution was flushed out of Hillsborough Bay,
and after 60 days of simulation, the chlorophyll-a concentration was around 5pg/L
throughout Hillsborough Bay. In agreement with the analysis of Figures 7.30 to 7.33 and the
segment-averaged time series (Figures 7.34 to 7.37), the other sub-divisions of the Bay (Old

271
Tampa Bay, Middle Tampa Bay, and Lower Tampa Bay) did not exhibit major dynamic
events during the summer months of 1991. Therefore, the effects of load reduction in a 60-
day simulation were not significant for these Bay sub-divisions.
Comparison with AScI 119961 study
The box model utilized by the AScI (1996) study solves a mass balance equation for
8 state variables (ammonia, nitrate, dissolved inorganic phosphorus, phytoplankton biomass,
CBOD, dissolved oxygen, organic nitrogen, and organic phosphorus). The biogeochemical
processes simulated include four interacting systems: phytoplankton kinetics, the phosphorus
cycle, the nitrogen cycle, and the dissolved oxygen balance. Apparently, the strongest
advantage of the AScI box model is related to its ability to perform long term simulations,
however, the monthly time scale utilized was exceedingly large. Water quality issues related
to eutrophication processes and hypoxia events cannot be addressed at this level of
resolution. Furthermore, the main limitation of the model was the descriptive hydrodynamics
approach, in which circulation and transport were represented by prescribed values for
advective and diffusive fluxes. First, the dynamic circulation generated by tides, wind, and
baroclinic forcing were all averaged and combined into an advective flux. Next, the
simulated salinity was adjusted to segment- and monthly-averaged salinity data through
tunning of the so-called dispersive flux. Results of the summer of 1991 simulation presented
in this study demonstrated that the water quality dynamics within each segment of the Bay
is highly variable (e.g., Figures 7.26 and 7.27) both in time and space, and could not be fully

272
Near-Bottom Dissolved Oxygen
After 60 days (July 26, 1991)
100% Load Reduction
40% Load Reduction
Figure 7.49 - Near-bottom dissolved oxygen concentration in Tampa Bay, after 60 days of
the load reduction simulation.
mg/L

273
Near-Surface Chlorophyll-a
After 60 days (July 26,1991)
100% Load Reduction 40% Load Reduction
Figure 7.50 - Near-surface chlorophyll-a concentration in Tampa Bay, after 60 days of
the load reduction simulation.
T/fiTi

274
captured by a box model using monthly-averaged exchange between segments. Therefore,
the segmentation scheme used by AScI (1996) (only 13 segments, with one vertical layer)
could not solve for the horizontal and vertical gradients, characteristics of this estuarine
system.
The WASP box modeling framework has proven to be an excellent water quality
model for riverine systems, where the steady state assumption is applicable. In addition, this
simple box model can be successfully used to perform numerical experiments like the
sensitivity tests described in this chapter, or “what if’ simulations using segment-averaged
output from more robust models. However, in marine environments, it should not be used
without the proper linkage with three-dimensional hydrodynamics and sediment models,
because tide, wind and baroclinic forcing interact in an unsteady balance.
Comparison with Coastal Inc. (19951 study
The Coastal, Inc. (1995) study was based on regression models developed to
investigate the relationships among loadings, water quality, and light levels at the seagrass
bed. The complex process of validation of such stochastic models was performed using the
extensive data set available from the EPC monitoring network. The available data were
considered sufficient to define external nutrient loading levels that were consistent with the
light requirements of existing seagrass meadows in Tampa Bay. The Tampa Bay National
Estuary Program (TBNEP) has established a range of target light requirements between 20%

275
and 25% of incident light. This range corresponds to the average light conditions historically
observed along the deep edge of the seagrass beds (around 2 meters) in Lower Tampa Bay.
The relationship between nitrogen loading and light attenuation was obtained through
a two-step modeling approach. First, the response of chlorophyll-a to nitrogen loading was
assumed to be linear, and the relationship was obtained by fitting a regression equation to the
chlorophyll-a concentration response to total nitrogen loads. Second, the response of diffuse
light attenuation to chlorophyll-a and turbidity was assumed to be linear, and the relationship
was obtained by fitting a regression equation to the light attenuation coefficient response to
the additive effects of chlorophyll-a concentration and turbidity.
The determination of nutrient load management targets based on the results obtained
by Coastal, Inc. (1995) must take into account that the dynamic response of the Bay to
different loading scenarios was not considered. The simple linear approach could not explain
the relationships between nitrogen loading and ambient nitrogen concentrations, which
strongly suggest that internal sources of nitrogen (e.g., phytoplankton kinetics, and exchange
with the sediment layer) and the exchange with the Gulf of Mexico play a major role in the
water quality dynamics of the Tampa Bay Estuarine System.
Advantages and Limitations of this Integrated Modeling Approach
Due to the vast spatial and temporal variability in hydrodynamics and water quality
dynamics, a system-wide understanding of the Tampa Bay Estuarine System cannot be
achieved if studies rely only on field monitoring and laboratory experiments. Using the

276
process-based modeling system developed in this study, it is possible to synthesize the data
collected from various parts of Tampa Bay at different times, taking into account the
uncertainty of model coefficients. Presently, basic research is needed to reduce the range of
model coefficients to specific conditions of Tampa Bay, especially the parameters related to
the sediment layer, the water-sediment interface, and the oceanic boundary condition.
Research to improve this integrated modeling approach would certainly enhance our
understanding of the relationships between nutrient loading, water quality conditions, and
the response of seagrass. Moreover, this modeling approach would benefit management
resources agencies that want to develop a management tool, built on process-based
understanding rather than regression coefficients. Subsequent refinement of this integrated
model can be used to address ecosystem management issues such as controlling estuarine
eutrophication and determining allowable external nutrient loading levels to restore seagrass
throughout the Bay.

CHAPTER 8
CALIBRATION OF THE SEAGRASS MODEL
Several studies focusing on Florida seagrass beds and associated communities (e.g.,
Lewis etal., 1985; Zieman and Zieman, 1989; Haddad, 1989; Lewis et al., 1991;Tomasko
et al., 1996) have demonstrated the ecological and economical value of seagrass to estuarine
systems. In Tampa Bay, the reduction of seagrass meadows can be directly correlated to the
extended period of increasingly poor water quality and destruction of habitats experienced
throughout the Bay until the early 80's (Coastal Inc., 1995). Taylor and Saloman (1969)
estimated that the dredging operations in Boca Ciega Bay resulted in an annual monetary loss
of 1.4 million dollars in fishery activities due to the destruction of the seagrass habitat. In
a review of the seagrass meadows of Tampa Bay, Lewis et al. (1985) found that areal
coverage of seagrass beds has been reduced in about 80% from its historical coverage (Figure
8.1). These past studies arrived at a common conclusion that the loss of seagrass habitats is
related more to anthropogenic effects than to natural causes. Moreover, these studies
suggested that the consequences of this destruction would bounce back, decreasing landings
of fishery products, promoting more erosion along the shoreline, and reducing the aesthetic
value of the Bay. Fortunately, water quality within the Tampa Bay Estuarine System has
been improving since the late 80's (Boler, 1992). As a result, seagrass meadows are
expanding in Tampa Bay (Coastal Inc., 1995).
277

278
Figure 8.1 - Extent of seagrass meadows in Tampa
Bay. (a) corresponding to 1943, and (b)
to 1983 (Lewis et al., 1985).

279
Tomasko et al. (1996) studied the effects of anthropogenic nutrient enrichment on
Thalassia testudinum in Sarasota Bay (Florida). The authors concluded that traditional water
quality monitoring programs, based on sparse sampling stations, may fail to detect
differences between locations where high gradients of anthropogenic nutrient enrichment
exist. They suggested that well-coordinated water quality monitoring programs, in areas with
extensive seagrass beds, should incorporate the status of seagrass habitats (e.g., biomass,
productivity, species diversity, etc).
This integrated model utilizes seagrass as a bioindicator of the environmental quality
of the Tampa Bay Estuarine System. In other words, the basic hypothesis of this integrated
modeling study is that the Tampa Bay seagrass community can be used as a bioindicator
capable of synthesizing all the dynamic functions (hydrodynamics, water quality, primary
production, etc.) of the system. This chapter describes the calibration of the seagrass model.
The major objectives of model calibration are: (1) to test the sensitivity of the seagrass model
described in Chapter 5 to such model assumptions as density-dependent growth rate, growth
rate dependence on temperature, salinity, light, and sediment nutrient concentration; and (2)
to simulate the response of the Bay to the dynamics of the summer of 1991 conditions.
The above-ground biomass of three tropical seagrass species (Thalassia, Halodule,
Syringodium) was simulated based on their specific relationships with physical and
biogeochemical parameters. The seagrass component of this integrated model can run
simultaneously with the hydrodynamics and water quality components, or it can use average
conditions to run long term simulations (order of years).

280
Initial Conditions
The initial distribution of seagrass in Tampa Bay was determined based on literature
data presented in Lewis et al. (1985), Zieman and Zieman (1989), Haddad (1989), Lewis et
al. (1991). Lewis and Phillips (1980) reported the results of 226 samples collected
seasonally throughout the Bay, and determined a percent species occurrence in which
Thalassia comprises 42.5%, Halodule 40.7%, and Syringodium 19.0% of the sampling
distribution. Figure 8.2 shows the initial seagrass distribution used in the simulations, along
with the location of grid cells that will be used for time series analysis. In addition to the
information obtained from Figure 8.1, the occurrence of seagrass meadows in the
computational grid was restricted to a maximum depth of 2.0 meters. This depth limit
correspond to 20% of incident light penetration, historically observed in Lower Tampa Bay
(Coastal Inc., 1995). In the beginning of the simulation, the same initial biomass (100 grams
of dry weight per square meter - gdw/m 2) was given to all three species of seagrass studied
(Thalassia, Halodule, and Syringodium). Based on different responses to environmental
conditions, each species of seagrass should prevail in regions where they are able to thrive
close to their specific optimum growth.

281
Initial Seagrass Distribution
Figure 8.2 - Initial seagrass distribution in the computational grid. Dark
areas indicate seagrass meadows (100 gdw/m2).

282
Sensitivity Analysis
In order to test the seagrass relationships described in Chapter 5, the sensitivity
analysis was conducted for such model formulations as density-dependent growth rate,
growth rate dependence on temperature, salinity, light, and sediment nutrient concentration.
The baseline consisted of a two-year simulation using the relationships described in Chapter
5, average conditions for the water quality parameters (nutrient concentrations, color,
turbidity), and a seasonal variation for water temperature, salinity, and incident light. The
lack of specific data on epiphytic algae prevent the use of this component on the simulations.
Temperature is not dynamically simulated in this integrated model, and its seasonal variation
is described by Equation (5.1). In order to give a more realistic representation of the
temperature distribution with depth, a linear decrease of two degrees Celsius between the
surface and 3-meter depth was assumed.
Figure 8.3 shows the time series of seagrass biomass for the baseline simulation, at
three grid cells located in the shallow area close to Sunshine Skyway Bridge (top), in the
deep edge of the seagrass bed, outside Mullet Key (middle), and in a shallow area located in
the upper reaches of Middle Tampa Bay, close to Apollo Beach (bottom). In 30 days, the
species-specific response to environmental conditions was already determining the seagrass
distribution. Hence, demonstrating that the initial condition (same initial biomass for all three
species) had a minor effect on the results of the simulation. In all three places, Thalassia

Biomass (gdw / mz) Biomass {gdw / m2) Biomass (gdw / m2)
283
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Days
Figure 8.3 - Simulated seagrass biomass in Tampa Bay.
600

284
is the dominant species, with the shallow areas exhibiting a maximum biomass of 230
gdw/m2 during the summer months. The seasonal fluctuation in biomass for the two cells
located in Lower Tampa Bay (Figure 8.3 - top and middle) seems to be driven only by
temperature variations and the density-dependent growth rate. During summer, when
temperature is close to its optimum conditions, Thalassia dominates the distribution.
Syringodium, which has been hypothesized as sensitive to both low and high temperatures,
exhibits the lowest biomass throughout the year. The deep edge of the seagrass bed also
showed a clear dominance of Thalassia, although the maximum biomass during mid-summer
was smaller than the one occurring in the shallow area. Since Thalassia and Halodule have
similar growth dependence on temperature and salinity, the density-dependent growth
rate that favors Thalassia is the probable cause for its dominance. In the upper reaches of
the Bay, a mid-summer decrease in biomass can be attributed to salinity levels below optimal
conditions.
Figures 8.4 to 8.7 show the relationships controlling the seagrass dynamics in the
baseline simulation. Figure 8.4 (top and bottom) shows the growth rate dependence on
temperature for grid cells (16, 33) and (33,55), located in shallow areas. The negative effect
of low temperatures on the Tampa Bay seagrass is revealed by the sharp decrease during the
winter months. On the other hand, Thalassia, Halodule, and Syringodium seem to tolerate
the water temperature commonly found during the summer. Figure 8.4 (middle) shows the
growth rate dependence on temperature for the grid cell (19,34), located in the deep edge of
the seagrass bed outside Mullet Key. According to model assumptions, temperature is the
environmental parameter limiting seagrass growth during winter, with the reduction factor

Limiting Factor Limiting Factor Limiting Factor
285
Growth Rate Dependence on Temperature
Tarpón Key (16,33) _
Ttemp
Htemp
Stemp
Outside Mullet Key (19,34)
Apollo Beach (33,55)
Figure 8.4 - Growth rate dependence on temperature (baseline simulation).

Limiting Factor Limiting Factor Limiting Factor
286
Growth Rate Dependence on Light
Tarpon Key (16,33)
Tlight
Hlight
Slight
-J . . i I i i i L_
100 200 300
Days
Outside Mullet Key (19,34)
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
00 —*—1—*—•—1—*—‘—‘—■—I———*—'—1—‘—*—*—‘—1—‘—1—‘—*—1—*—‘—1—1—1—*—‘—*—1—*—
0 50 100 150 200 250 300 350
Days
Figure 8.5 - Growth rate dependence on light (baseline simulation).
Apollo Beach (33,55)
1.0 ;
0.8 -
0.6 -
0.4 -
0.2 -
0.0 -
0
i.o r

Limiting Factor Limiting Factor Limiting Factor
287
Growth Rate Dependence on Salinity
Tarpon Key (16,33)
1.0
0.8 -
0.6 -
0.4 -
0.2 -
_i 1 1 1 1—
100 200 300
0.0 L
0
Tsai
Hsal
Ssal
Days
Outside Mullet Key (19,34)
vo
0.8 -
0.6 -
0.4 -
0.2 -
0.0 L_.—■—I—.—I—I—.—I—.—I—I—I—1—.—I—I—i—■—I—I—1—I . . 1—1—■—■—■—■—I—*—I—‘—■—I—
0 50 100 150 200 250 300 350
Days
Apollo Beach (33,55)
Figure 8.6 - Growth rate dependence on salinity (baseline simulation).

Limiting Factor Limiting Factor Limiting Factor
288
Growth Rate Dependence on Substrate
Tarpon Key (16,33)
Tnut
Hnut
Snut
Days
Outside Mullet Key (19,34)
1.0 -
0.8 -
0.6 -
0.4 -
0.2 -
0.0 -
0
1.0 r
0.8 -
0.6 -
0.4 -
0.2 -
0.0 I I . , , , I .
0 50 100 150 200 250 300 350
Days
Figure 8.7 - Growth rate dependence on sediment nutrient concentration
(baseline simulation).
50
100
150
200
250
300
350
Days
Apollo Beach (33,55)

289
reaching zero value for all three species during the coldest period of the year (mid-December
to mid-February). Lewis et al. (1985) presented a comprehensive review of the seagrass
meadows of Tampa Bay, and postulated that the seagrass distribution is largely controlled
by water temperature. Figure 8.5 (top and bottom) shows the growth rate dependence on
light for grid cells (16, 33) and (33,55), located in shallow areas. As expected, the shallow
areas do not exhibit any light limitation throughout the year. Along the deep edge of the
seagrass bed (Figure 8.5 - middle), the available light seems to limit seagrass growth.
According to the model assumptions, the light limiting effects are more sensitive in Halodule
and Thalassia. Figure 8.6 shows the growth rate dependence on salinity. As expected, the
seasonal fluctuation of salinity in Lower Tampa Bay is within the optimum range for all three
species simulated, therefore, the seagrass beds of Lower Tampa Bay are not limited by
salinity. In the upper reaches of the Bay, where salinity levels decrease to less than 20 ppt
during the summer months, the seagrass growth is noticeably influenced by salinity,
especially Syringodium. Figure 8.7 shows the growth rate dependence on sediment nutrient
concentration. In all three sites, shallow and deep areas of Tampa Bay, sediment nutrient
concentration values are within the optimum range for all three species, and it does not limit
seagrass growth throughout the year.
Also for the baseline simulation, Figure 8.8 shows the contour plots of Thalassia for
mid-summer and winter conditions. During the summer months, the biomass of Thalassia
reach as much as 300 gdw/m 2 in the border with Boca Ciega Bay, Anna Maria Sound, and
Terra Ceia Bay. During the winter, the biomass decreases, reaching its minimum level in
mid-January as shown in Figures 8.3 and 8.8.

290
Winter
Summer
Figure 8.8 - Simulated seasonal distribution of Thalassia.
gdw/m¡

291
During the sensitivity tests, one-year simulations were performed with no external
forcing (e.g. tide, wind, and river discharge). Therefore, variations in seagrass distribution
could be directly related to the assumptions of the seagrass model. Table 8.1 describes each
sensitivity test, and specifies a test identification code that will be used during analysis of
results.
Table 8.1 - Sensitivity tests description.
Description
Range
Test#
Constant maximum growth rate
Sl.l
Density-dependent growth rate
Constant growth rate
S1.2
Broadest range for all three species
S2.1
Growth rate dependence on
Narrowest range for all three species
S2.2
temperature
No temperature dependence
S2.3
Broadest range for all three species
S3.1
Growth rate dependence on
Narrowest range for all three species
S3.2
salinity
No salinity dependence
S3.3
Growth rate dependence on
Broadest range for all three species
S4.1
light
Narrowest range for all three species
S4.2
Growth rate dependence on
10% of seagrass biomass
S5.1
sediment nutrient concentration
0.1 % of seagrass biomass
S5.2

292
Tests Sl.l and S1.2 were designed to assess the sensitivity of the model to the
density-dependent maximum growth rate. For test Sl.l, the maximum growth rate was set
to values obtained from the literature (Pomeroy, 1960 and Heffeman and Gibson, 1985), and
maintaining the effects of environmental variability in light, temperature, salinity, and
sediment nutrient concentration as described in Chapter 5. Test S 1.2 used the growth rates
of test S1.1 as a constant growth rate, without considering the effects of light, temperature,
salinity, and sediment nutrient concentration. Tests S2.1, S2.2, and S2.3 were designed to
assess the sensitivity of the model to the formulation of the species-specific growth rate
dependence on temperature. Test S2.1 used the growth rate dependence on temperature,
formulated for Thalassia, in all three species, while test S2.2 used the growth rate
dependence on temperature formulated for Syringodium. In test S2.3, it was assumed that
temperature does not affect seagrass growth rate, hence the values for the temperature
limiting factors were set to unity. Tests S3.1, S3.2, and S3.3 were designed to assess the
sensitivity of the model to the formulation of the species-specific growth rate dependence on
salinity. Test S3.1 used the growth rate dependence on salinity, formulated for Halodule, in
all three species, while test S3.2 used the growth rate dependence on salinity formulated for
Syringodium. In test S3.3, it was assumed that salinity does not affect seagrass growth rate,
hence the values for the salinity limiting factors were set to unity. Tests S4.1, and S4.2 were
designed to assess the sensitivity of the model to the formulation of the species-specific
growth rate dependence on light. Test S4.1 used the growth rate dependence on light,
formulated for Syringodium, in all three species, while test S4.2 used the growth rate
dependence on light formulated for Halodule. Tests S5.1, and S5.2 were designed to assess

293
the sensitivity of the model to the formulation of the species-specific growth rate dependence
on sediment nutrient concentration. For test S5.1, it was assumed that the nitrogen uptake
was proportional to 10% of the seagrass biomass, while test S4.2 assumed that the nitrogen
uptake was proportional to 0.1% of the seagrass biomass. The results of the simulated
biomass for tests S 1.1 to S5.2 are presented in Appendix F.
The sensitivity analysis revealed the density-dependent maximum growth rate as the
most important parameter in the seagrass model, determining not only the maximum seagrass
biomass, but also the Thalassia dominance when the environmental conditions are within
the optimum range for all three species. Previously reported from field studies (e.g., Lewis
et ai, 1985), the seagrass distribution in this subtropical estuarine system is largely
controlled by water temperature, and the growth rate dependence on temperature is also an
important parameter of the model. Changing from the broadest to the narrowest range did
not show as much effect as setting the temperature limiting factor to unity. In this latest case
(test S2.3), the seagrass biomass was almost constant throughout the year, with minor
fluctuations due to light and salinity variations. These two parameters, density-dependent
growth rate and temperature limiting factor have their influence extended over the entire Bay,
and they dictate the overall distribution and composition of the seagrass beds in Tampa Bay.
In addition, salinity and available light were responsible for two distinct limiting conditions
also found in the Bay. Along the bathymetric gradient, the deep edge of the seagrass bed is
determined by the available light. From the mouth of the Bay to its upper reaches, salinity
level (or its lower limit) dictates the seagrass distribution and composition, although seagrass
species tolerant to low salinity levels (e.g., Ruppia marítima) were not simulated.

294
Simulation of the Summer 1991 Condition
The integrated model of the Tampa Bay Estuarine System was used to study the
seagrass dynamics of the summer of 1991 conditions. The primary objective was to further
the understanding of the relationships between circulation and transport, nutrient loading,
biogeochemical transformations and the response of the of the seagrass community in Tampa
Bay. A four-month simulation was performed using the results of the baseline simulation
as initial condition for seagrass, and the initial conditions described in Chapter 6 and 7 for
the hydrodynamics and water quality parameters.
Model results showed that during the four-month simulation the seagrass distribution
did not vary significantly, with its biomass close to the maximum values obtained from the
baseline simulation. Table 8.2 shows the simulated biomass along with some available
literature data for the Tampa Bay region (Lewis et al., 1985).
Table 8.2 - Simulated and reported seagrass biomass in the Tampa Bay area.
Location
Biomass (gdw/m2)
Above-ground Below-ground
Reference
Thalassia testudinum
Simulated
(summer 1991)
190 - 230
-
Boca Ciega Bay
32.4
48.6
Pomeroy (1960)
Tampa Bay
0.41 - 52.7
-
Heffeman and Gibson (1982)
Tampa Bay
25 - 180
600 - 900
Lewis and Phillips (1980)

295
Table 8.2 - continued.
Location
Biomass (gdw/m2)
Above-ground Below-ground
Reference
Halodule wrightii
Simulated
(summer 1991)
60-80
Tampa Bay
4-27
Heffernan and Gibson (1982)
Tampa Bay
38 - 50 60 - 140
Lewis and Phillips (1980)
Syringodium filiforme
Simulated
(summer 1991)
5-25
Tampa Bay
5-11
Heffernan and Gibson (1982)
Tampa Bay
50- 170 160-400
Lewis and Phillips (1980)
Model results seem to be in accordance with field investigations, determining
Thalassia as the dominant species in Tampa Bay. Considering the summer months as the
maximum biomass period, the spatial distribution of seagrass in Tampa Bay is dictated by
two environmental parameters: available light and salinity. Described in the sensitivity tests,
light attenuation determines the maximum depth seagrass can grow, and the species
composition at low light levels. The head to mouth salinity gradient, highly accentuated
during summer, is also responsible for the species zonation and maximum biomass, specially
in the upper reaches of the Bay. Historically, human developments in the Tampa Bay
Estuarine System have caused great impact and disturbance on these two environmental
parameters. Changes in freshwater discharges, flushing rates, and anthropogenic nutrient
enrichment have been directly related to the reduction of the seagrass meadows in the system.

296
Figures 8.9 to 8.11 show the contour plots for Thalassia, Halodule, and Syringodium
biomass in July 26, after 60 days of simulation. Figure 8.12 shows the available light at the
first sigma level, near the bottom. Model results seem to describe the general characteristics
of the spatial and temporal seagrass composition and distribution in Tampa Bay. Thalassia
exhibits its annual-maximum biomass throughout the seagrass beds (Figure 8.9), except
along the deep edges, which allows Syringodium to achieve its maximum biomass (Figure
8.11). Halodule is also seen throughout the seagrass beds (Figure 8.10), mixed with
Thalassia and Syringodium. A much finer grid resolution would be required to show that
close to the shore, Halodule would be the prevailing species.
Since reducing nutrient loading is expected to have a greater impact on the light
levels reaching the bottom of the Bay, comparisons with subsequent load reduction
simulations were made in terms of improvement in available light at the seagrass beds.
Load Reduction Simulations
The results of the water quality simulations suggested that nutrient load reduction is
expected to lower the concentration of dissolved inorganic nitrogen, and phytoplankton in
the water column. These changes are expected to increase the available light for seagrass and
hence, increase the maximum depth of seagrass bed.
Figure 8.13 shows the comparison between the Present Condition and the 100% Load
Reduction simulations. The response of available light was not noticed in the first 60 days

297
Thalassia Biomass
After 60 Days (July 26,1991)
Í
Thalassia
300
225 "e
150 ^
75
0
5
â– a
03
Figure 8.9 - Simulated Thalassia biomass in Tampa Bay for July 26, after 60 days of
simulation.

298
Halodule Biomass
After 60 Days (July 26, 1991)
Figure 8.10 - Simulated Halodule biomass in Tampa Bay for July 26, after 60 days of
simulation.
gdw / m'

299
Syringodium Biomass
After 60 Days (July 26,1991)
20
10
0
$
â– o
CD
Figure 8.11 - Simulated Syringodium biomass in Tampa Bay for July 26, after 60 days
of simulation.

300
Available Light
After 60 Days (July 26, 1991)
Figure 8.12 - Near-bottom light levels in Tampa Bay for July 26, after 60 days of
simulation.

PAR (jiE/m2/s) PAR(nE/m2/s) PAR(|iE/ma/s)
301
Available Light at the Seagrass Bed
Figure 8.13 - Comparison between simulated light levels for the Present Condition
simulation (solid line) and the 100% Load Reduction (dashed line).

302
of simulation, and the four-month simulation was not long enough to produce any
improvement in the seagrass biomass. Figure 8.13 (bottom) shows that the upper reaches of
the Bay are more sensitive to load reduction, due to its proximity to the freshwater
discharges. However, as discussed in the sensitivity analysis, light limitation is more likely
to influence the deep edge of the seagrass bed, determining the depth at which seagrass can
grow.
Summing up, the sensitivity analysis revealed the seagrass model inputs and
parameters that are most sensitive to variations. These include: density-dependent growth
rate, growth rate dependence on temperature, light, salinity, and a detailed mapping of
species distribution. Field and mesocosms experiments designed to determine these model
inputs for Tampa Bay would provide this integrated model with the realism required for
predictive simulations. Existing monitoring programs (e.g., EPC monthly monitoring) could
be redesign to include stations in areas covered by seagrass, where ongoing management
agencies (e.g., Department of Environmental Protection) or university (e.g., University of
South Florida) projects could measure seagrass parameters (e.g., biomass, productivity, leaf
length and color, species diversity, etc). In the long term, this coordinated programs would
not only enhance our understanding of the ecological relationships between environmental
conditions and the seagrass community, but would also provide important inputs for a model
that can be used to evaluate management alternatives for seagrass restoration.

CHAPTER 9
CONCLUSION AND RECOMMENDATIONS
An integrated model, combining the enhanced versions of a 3-D hydrodynamics
model (Sheng, 1989), a 3-D water quality model (Chen and Sheng, 1994), and a seagrass
model (Fong and Harwell, 1994), has been developed for the Tampa Bay Estuarine System.
Major conclusions of the study are summarized in the following:
1) A fine-resolution and smooth numerical grid which accurately represents the
complex geometrical and bathymetrical features in Tampa Bay was generated. Circulation
patterns produced by the hydrodynamic model revealed flow features which agree well with
existing information on Tampa Bay circulation, available from past modeling and field
studies. How and salinity features, which were not reported previously, were identified. The
normalized rms error analysis demonstrated the model’s ability to simulate surface elevation,
currents, and salinity within 7.5%, 20%, and 25% accuracy, respectively.
The residual advective fluxes and salinity distributions present a distinctive annual
variability. Wet season results indicate much stronger horizontal and vertical salinity
gradients than the dry season results. Rainfall has a significant effect on the salinity
distribution, but not on the velocity field.
A two-layer flow stmcture was found in the residual flows for all the
hydrodynamics simulations. This suggests the importance of considering vertical structure
in any modeling study of hydrodynamics and water quality dynamics of the Bay.
303

304
2) Because it incorporated increased understanding of the complex relationships
among hydrodynamics, sediment dynamics, nutrients, phytoplankton, light, and seagrass, the
integrated modeling allowed a direct coupling between all the components. The same time
step and spatial grid were used, and the effects of hydrodynamics were incorporated into the
water quality model without any ad-hoc tuning of advective fluxes and dispersion
coefficients.
Simple water quality models such as regression model and WASP5 model are
important first steps towards the development of a comprehensive “broad-based” model of
the entire Tampa Bay Estuarine System. They can be used in preliminary steps to help the
determination of relevant processes, and test causal relationships between state variables.
They are a powerful tool for calibration of water quality model coefficients in the absence
of process-specific data (e.g., nitrification, denitrification, etc). However, in marine
environments, where tide, wind and baroclinic forcing interact in an unsteady balance, their
predictive capability is limited.
The summer of 1991 simulation demonstrated the central role that organic nitrogen
and mineralization of organic matter have on the water quality dynamics of the Tampa Bay
Estuarine System. Simulation results showed that high levels of water column soluble
organic nitrogen and phytoplankton inside the Bay produce a net export of these water
quality parameters to the Gulf of Mexico. On the other hand, the nitrogen limiting condition
of the Bay cause a depletion of dissolved inorganic nitrogen species, and the net transport
generated is from the Gulf of Mexico into the Bay. Model results also showed that during
the summer of 1991, particulate organic and inorganic nitrogen have a net depositional flux.
Since both organic an inorganic dissolved species exhibited higher concentrations in the

305
sediment layer than in the water column, the net diffusive flux was from the sediment into
the water column.
Hillsborough Bay has the poorest water quality in the Bay. Although the EPC
water quality index has consistently increased since 1987 (Boler, 1992), eutrophic conditions
and hypoxia events still occur in the upper reaches of the Bay. Model results demonstrated
that external loading, nutrient-enriched sediments, and limited flushing capacity are the
primary causes of these characteristics.
Load reduction simulations demonstrated that loading has a direct effect on
nutrient concentration, phytoplankton production, and light attenuation. Model results
showed that water quality can respond quickly (within 2 months) to changes in load
reduction. This time scale is in agreement with Coastal’s (1995) estimation of 3-month
response time, but much less than Johansson’s (1991) estimate of 3-year response time.
3) The seagrass model has been used to investigate the ecological relationships
between nutrient loading, water quality dynamics, and the response of seagrass. Model
results showed that the seagrass distribution in Tampa Bay is largely controlled by seasonal
water temperature. Simulated growth rate is completely inhibited for all three species during
the coldest period of the year (mid-December to mid-February).
The second most important environmental parameters in the seagrass model are
light attenuation and salinity. Light attenuation determines the maximum depth seagrass can
grow, and the species composition at low light levels. The head to mouth salinity gradient,
highly accentuated during summer, is also responsible for the species zonation and maximum
biomass, specially in the upper reaches of the Bay.

306
Considering that light attenuation and salinity distribution have been highly altered
due to anthropogenic effects, restoration of seagrass beds can be linked to changes in
freshwater-discharge regime, flushing rates in each specific segment of the Bay, total
suspended solids concentration, and external nutrient loading.
The model presented in this study is still far from being a comprehensive model
that would explain all the processes occurring in the Tampa Bay Estuarine System and be
used as a predictive tool. Nevertheless, it is a model that integrates the major components
(hydrodynamics, sediment dynamics, water quality, and seagrass) that drive the system, and
it establishes a framework for future developments to answer specific management questions.
The dynamic response of the estuarine system to different load reduction levels
cannot be directly observed in the Bay, and can only be predicted by a reliable model. Using
the process-based and integrated modeling approach described in this study, it is possible to
synthesize field and laboratory data collected from various parts of the Bay. Model
simulation could then be performed to predict the Bay’s response to various management
practices. Once fully validated, this integrated model can be used to address such ecosystem
management issues as controlling estuarine eutrophication and determining allowable
external nutrient loading levels to restore seagrass in the Bay.
Future developments that are necessary to allow this integrated model to perform
predictive simulations are described in the following:
• Basic research is needed to reduce the range of the water quality model coefficients
to specific conditions of Tampa Bay, especially the parameters related to the sediment layer,
the water-sediment interface, and the oceanic boundary condition.
• With the grid resolution used in this study, the model cannot solve for the dynamics

307
of the shallow regions of the Bay (below lm deep), where wave interactions become an
important issue. More field data and modeling effort should be focused on the shallow
regions.
• During episodic events, resuspension of sediments can release as much as three
orders of magnitude more nutrients than diffusive fluxes (Sheng et al., 1993). In this case,
sediment model parameters (e.g., erosion and deposition rates) should be determined
througout the Bay. Again, field and modeling experiments are needed to further quantify the
resuspension and deposition fluxes.
• The seagrass model can be improved by field and mesocosms experiments designed
to determine the relationships between environmental parameters and seagrass for Tampa
Bay.
• Long-term (1-5 years) field data need to be collected to allow long-term calibration
and validation of the integrated model. This exercise will also allow us to quantitatively
compare the performance of the integrated model vs. simpler models in making long-term
predictions.
Data collection programs in Florida estuarine systems in the past have generally
focused only on a limited number of parameters. In view of the complex relationships
among the various components of the ecosystem and the site-specific nature of the estuarine
environment, it is prudent to design monitoring programs which will collect all essential
parameters at the same locations over long periods to augment the typical monthly or
quarterly synoptic surveys. It is also recommended that such monitoring programs be
designed with participation of modelers, to ensure that the data could be directly used for
trend analysis and model development.


APPENDIX A
NUMERICAL SOLUTION OF THE INTEGRATED MODEL
Governing Equations in the q-grid Coordinate System
The transformation from the Cartesian grid (x, y, z, t) to the vertically-stretched grid
(x’, y\ a, t’) was defined in Chapter 3 as
oír V 7 t) = z-t{x,y,t)
h{x,y) + C{x,y,t)
(A.l)
where h is the water depth relative to the mean sea level, and <; is the free surface elevation,
a is the transformed vertical coordinate such that o = 0 at the free surface and a = -1 at the
bottom.
Using the chain rule, the first-order differential operators in the (x, y, z, t) are related
to those in the (x’> y’, a,t") coordinate system through:
309

310
_a = + 9o._9_
8t 8t 3? 8t 8a
8 _ do d _ 18
dz
dz
do
H do
d
dx'
d dy1 8
• + J •
- +
do
d_
dx
dx
dx1
dy dy
/
dx
do
do
8
f*-c)
z
dH
_ 1
,3C
_ c
dH
dx
dx
l H j
H2
dx
H
dx
H:
dx
z
- C dH
_ 1
.SC
o
dH
1 #
dC
H2 dx
H
dx
H
dx
H
dx
d
d
1 ,
8Í. 8
o
dH
o
dx
dx'
H
dx do
H
dx
do
(A.2)
Similarly,
_8_ = 8 1 , 8C. 8 _ a _ 8// a
8y H dy do H dy do
In the a-grid, the hydrostatic relation is transformed to:
dp = ~ pgdz = ~ pgdo (A.3)
which, integrated from some depth a to the surface (a = 0) gives,
P(°) = Pa ~ gf P Hdo
(A.4)
where pa is the atmospheric pressure.
The x-derivative in the transformed coordinate system is given by:
dp dp Cu dp i dH cm,
= -~ ' g -do + g -op + g—f
9x rlyf J r)y' dx <3 v '
K
dx1
(A.5)

311
Using the flux conservative for the non-linear advective terms, and neglecting the
atmospheric pressure gradient term, the Equations (3.1), (3.2), (3.3), and (3.5) can be re¬
written, dropping the primes.
Continuity Equation
d( dHu dHv u do) „
dt dx dy do
(A.6)
X-Component of Momentum Equation
H
dHu dHuu dHuv ^ d
dt
dx
dy
?M(0
do
fv -g
K
dx
H i
0
'o
fpdo + op
J dx dx
O
J
\ o )
+ x
Po
d I . du ) d ( , du
i d
(
H2 do\ vdo
du
(H.O.T)
(A.7)
Y-Component of Momentum Equation
H
dHv dHv dHvv
+ +
dt
dx
dy
dvut r dC
+ — = ~fu~ 8^
do dy
g_
Po
o
dp
dH
H f — do
J dy dy
jpdo + a p
\ °
d f , dv^ d ( . dv
+ dx( h dx J + "dy,
1 d
H2 do
A —
v do
(H.O.T)
(A.8)

312
where the vertical velocity, co, is given by:
w 1 \ dt
— - —(1 + o)—2-
H H dt
Yxu ~ Yyv
(A.9)
The transformation of the diffusion terms produces some higher order terms which
are considered to be negligible when compared to the first order terms, and therefore ignored
in the computational solution. The higher order terms (H.O.T)x, and (H.O.T)y are:
1
( dt dH
— +o
’ d
< a 'i
ah—
d
( a
a du
Atj
H
^ dx dx ,
do
[ dx)
dx
l dx)
- A
H
du
do
( d2t d2H
—- + a
1
( dt dH) dH
— + o
H
v dx2 dx2 t
H2
K dx dx ) dx
1
, dt dH
+ — — + a
H2 l dx dx
2 d
(a
1 °
("O
v H do,
(A.10)
1
(dt dH)
— + a
’ a
Í ^ ^
+ a
iA«-)
H
1 dy dy j
do
l Hdy}
dy
l Hdy)\
A* —
H do
1
1
( d2t d2H
—- + a
i ( dt , ga//'| dH
H
l dy2 dy2 )
H2 [ dy dy ) dy
, dt dH
+ — —— + a
H2 { dy dy
2 a
( a A
A —
J do
l d°J
(A.11)
The Transport Equation
The transformation of the transport equation in the (x’,y o, t’) system can be shown
in terms of the salinity equation:

313
ds (o +1) de es | d(uS) _ i ac d(us) a bh d(uS)
dt' H dt do dx' H dx da Hdx do
| d(vS) 1 aC d(vS) a dH d(vS)
dy1 H dy da H dy da
i d
H da
tj c [ cdh cdh cd( c3C cd£
HwS + a| uS— + vS— + S— + uS— + vS-
dx dy dt dx
QdC, cd£ cd£
+ S— +uS— +vS-
dt
dx , dy
dy
Diffusion Terms
dy,
(A.12)
Re-arranging and canceling the proper terms,
+ SinS) + 3(v£) + . Diffusion Tems
dt' dx‘ dy' H da
(A.13)
tt • tu y t f f q , QdH QdHu „dHv QdHoi
Using the continuity equation times S ->• S + S + S + S ,
dt' dx' dy' da
the salinity equation can be written in a conservative form as:
H
dHS dHuS dHvS dHwS
+ + +
dt' dx'
dy1
da
= Diffusion Terms
(A.14)

314
The diffusion terms are obtained through the second-order derivatives, expressed as:
d 1 ac d a dH d
dx' H dx do H dx do
D
H
( dS 1 d( ds a dH dsx
dx' H dx do H dx do
/ J
(A.15)
3
\d„ dS)
a
' DHdC as'
a
' Dh° dH as'
dx'
l dx')
dx'
k H dx do t
dx'
k H dx do t
j_ac_a_
H dx do
o dH d
(
D
H
H dx do
D
H
ds
dx'
ds
dx1
\
H dx do
o dH d
D
H
ac ds
H dx do
H dx do
dh ac dS
H dx do
j_ac_a_
H dx do
o dH a
H dx do
Dh° dH dS
H dx do t
f
Dh° dH dS
H dx do
for the horizontal diffusion, x-direction (with similar development for the ^-direction). The
vertical diffusion term is given by:
1 a ( Fis\
(A.16)
1
±i
D 1
as\
i
—Í
D
H
do'
VH
do J
H2
do\
°V do)
The salinity equation in the sigma grid system can be written as (dropping the
primes):
1
H
dHS dHuS dHvS dHuS
+ + +
dt
+
dy
D
dx
dHS
dy
H
i a
aa
/
H
dy )\ H2 do
Dâ„¢
V
da
_a_ dHS_
ax( H dx
(h.o.t)s
\
(A.17)
where (H.O.T)s is given by:

315
(ho.t), = 1
1
d
( r, )
Dh dC dHS
a
Dh° dH dHS'
H
dx
k H dx do ,
dx
k H dx do /
j_ ac _a_
H dx do
JL ac _a_
H dx do
dx J
Dh d( dHS
H dx do
j_ ac J_
H dx do
o dH dHS
H dx do
o dH d
( „ dHS)
o dH a
Dh d( dHS'
H dx do
l a* )
H dx do
k H dx do ,
o dH d
H dx do
(
o dH dHS
\ H dx do
dy
\
Dh d( dHS
\ H dy do /
_a_
dy
Dh° dH dHS
H dy do
i ac a
( dHS)
. i ac a
' DH ac dHS'
H dy do
1 " Sy J
H dy do
K H dy do t
i ac a
( o dH dHS)
o dH d (
H dy do
K H dy do J
H dy do \
D
H
dHS
dy
(A.18)
o dH d
f DH ac dHs'
a dH d
( o dH dHS\
H dy do
^ H dy do ,
+ H dy do
v H dy do j
Time Scales and Dimensionless Equations
In order to reveal the relative importance of each term in the governing equations,
Sheng (1983) examined the characteristic time scales associated with various physical
processes in lakes and estuaries (Table A.l), and presented the above system of equations in
a dimensionless form.

316
Table A.l - Characteristic time scales of physical processes in estuaries (Sheng, 1983).
Physical Process Time Scale Order of Magnitude
Periodic Function
Advection
Inertia Oscillation
Vertical Turbulent
Diffusion
Horizontal Turbulent
Diffusion
Gravity Wave
Internal Gravity Wave
First, the following reference scales are introduced: Xr and Zr as the reference
lengths in the vertical and horizontal directions, Ur as the reference velocity, pr and A p as
the reference density and density gradient in a stratified flow, (A^ ,(Av) , ¡D^ , and (Dv}
as the reference eddy coefficients. Therefore, each term in the dimensionless equations is
composed of two parts: the dimensionless variable of the order unity, and the part containing
the dimensionless number, indicating the order of magnitude of the term.
Dimensionless Variables
(x *,y*,z*) = (u,v,wXrlZr)/ Ur
(u\v*,w*) = (x,y,zXr/Zr)/Xr
co* = oiXr/Ur
t * = tf
t.
i
tvdm ’ ^vds
1/(0
xr/ur
1//
Zr2/A , ZlID
r vr ’ r vr
lhdm ’ lhds
ge
gt
X'lJgZ'LpIp,
(A.19)

317
(vx*) - (<,Ty) / (p0fZrUr) = / Tr
Í* = sC/(fUrXr) = f/Sr
P* = (p-pj/fp.-pj
A//* = AH/AHr
Av* = VAv,
ZV = DH!DHr
Dimensionless Parameters
Rossby Number:
K
ur
(f*r)
A
Froude Number:
p
Ur
A
r r
1
Densimetric Froude Number:
F n
Fr
t .It
rD
fe
gl c
Vertical Ekman Number:
n
k. TTT'
^ ^
II
fi! Kdm
Horizontal Ekman Number:
Eh
A*r
^ tfidm
Vertical Schmidt Number:
1!
II
\'ds ^ tydm
Horizontal Schmidt Number:
SCH
vr
Kr
DHr
hids ! thdm
e
P
(Pr - Po)
Po
= gZr =lR IF )2 =
f2x;1
(A«)2

318
Dimensionless Equations
Utilizing the dimensionless variables and parameters defined above, the governing
equations become:
dC a dHu n dHv
— + p + p
dt dx dy
+ p#— - 0
da
(A.20)
1 dHu
H dt
dC + Ev d a du 'j
+ v
H
-Eh
dHuu dHvu dH(x>u
â–  â–  â–  + +
^ dx dy do ,
d ( . du
d
Í . d )
+ ^y
l Hdyj
dp , dH
— do +
dx dx
\
(A.21)
J dHv
h dt
ac +_5l J_(a iz
dy H2 do{ v do ,
E0 ( dHuv dHvv dHtov
H
dx
dy
da
+ E
H
dx
( a >
* dv
d
CD
Ah —
{ dx)
+3y
AH 3
l dy)
1
rD
H
0 3 iTji 0
f — do + fpdo +
J dv dvJ
\
op
/
(A.22)

319
ScvH2 da[ v do)
(A.23)
p = p(J\s)
(A.24)
Dimensionless Equations in Boundary-Fitted Coordinates
For most estuarine systems, not only the bathymetry but the geometry is also quite
complex and irregular. In order to accurately represents the hydrodynamic and water quality
processes, a curvilinear non-orthogonal boundary-fitted grid that conforms to complex
shorelines is necessary.
In CH3D, the independent variables (x,y) are transformed into a dimensionless
system (£ rf), and the velocities are expressed in terms of contravariant fluxes derived from
tensor analysis (Sheng, 1986). The contravariant and physical velocity components are
locally orthogonal to the grid line, whereas the covariant components generally are not. The
three components are identical in a Cartesian coordinate system. In a curvilinear non-
orthogonal boundary-fitted grid system, the relationship between the physical velocity and
the contravariant velocity is given by (Sheng, 1986):
(A.25)
with no summation on /.

320
The metric relationships required to transform the contravariant velocity components
to the same dimension of the physical velocity are defined as:
' dx)2 ( dy)2
Ud + Ud
dx
dr)
'ay)2
l ari J
Horizontal measures of lengths
dx dx + dy dy
(A.26)
dx dy'
dq dE, t
2
Jacobian of horizontal transformation
The Jacobian of horizontal transformation is used to obtain the surface area within
a grid cell, and to scale the contravariant velocity to a physical flow (per unit depth)
according to (Sheng, 1986):
Area = Jg~o-dZ-di\
= (A.27)
In the boundary-fitted curvilinear grid system shown in Figure 6.1, the three-
dimensional equations of motion written in terms of contravariant velocity components in
the transformed coordinates (^, rj, a) are (Sheng, 1987, 1989):

321
ac
dt
= 0
(A.28)
1 dHu
H dt
' ii 3C i2 3f
8 +S
\ 3£ 3r|
) S12 222
+ — u + — V
So ys0
g H I 11
as
+yr\s[SoHuV)
3r|
(y^\fioHuv +yn\fioHvv)
[xi^[i0Huu +\Jg¡Huv)
as
+ A^^“v+jc,'^JTvv^
So-
dHuo)
da
+ ÍJLÍ a lü
#2 3ol V0CT
/?
ii°
J pda + op
n a/f 12 a//
s11-^ +g12 —
as a rj
EhAh (Horizontal Diffusion)
(A.29)
An equation similar to (A.29) can be derived for v. The following equation is for (J),
which can be either salinity S or water quality species (if a reaction term is added):

322
H dt H2 do K
1 dmj) _ l d '
1 d#(j(j)
H do (A.30)
Turbulence Parameterization
One of the most important features in numerical circulation and transport models is
the parameterization of turbulence. Since the spatial scale of horizontal motion in an
estuarine system is typically 2-3 orders of magnitude larger than that of the vertical motion,
it is common to treat the vertical and horizontal turbulence separately (Sheng, 1983).
Vertical turbulent mixing is a very important process which can significantly affect the
circulation and transport in an estuarine system (Sheng et al., 1995). Since turbulence is a
property of the flow rather than the fluid, it is essential to make use of a robust turbulence
model to parameterize the vertical turbulent mixing. In this study, the vertical turbulent eddy
coefficients are obtained from a simplified second-order closure model of Sheng (1982) and
Sheng (1989).
A Simplified Second-Order Closure Model - Equilibrium Closure
Second-order closure models resolve the dynamics of turbulence by including the
differential transport equations for the turbulence variables, i.e., the second-order correlations

323
e.g., - u-uj , -uts' , and p/p/j. The equilibrium closure model solves for the following
algebraic equations, in addition to the mean flow equations:
0
uiuk
1 dui
dx.
Ujuk
1 dui
dx,
Si
/ /
UJ P
Po
Si
I /
ui p
o r\ I I - r\ ! '
2 eikl ^k Ul Uj ejlk Q Uk ui
I
JL
A
\
ll * q
Ui UJ "VJ
4"
11 12A
(A.31)
0
/ / dp
Uj Uj —
9Xj
77/ dui
p'p1
«y P — - g¡
ox. p
7 vo
/ /
2eijkQjukP - 0.75 q
ut p
A
(A.32)
0 - 2u/p'^- +0.45
dXj
A
(A.33)
where the subscripts i,j, k can take on the values of 1, 2, or 3. x. are the coordinate axis,
(uj, Uj, Ujlj are the mean velocity components, (u/, uj , w/j are the fluctuating velocity
components, po, and p; are the mean and fluctuating water density, eijk is the alternating
tensor, Q is the earth rotation, and 6^. is the Kronecker delta . A is the turbulence
macroscale, and ¡777 \'2 is the total rms fluctuating velocity. The above equations
q yu¡ u¡ j
contains a total of five model coefficients. These coefficients were determined from
laboratory experiments, and remain “invariants” in applications of the equilibrium closure
model.

324
As shown in Sheng et al. (1989), q2 can be determined from the following
dimensional equations when the mean flow variables are known:
3A2b2sQ4 + A[(bs + 3b +lb2s)Ri - Abs{ 1 -2b)]Q2
+ b{s + 3 +4bs)Ri2 + {bs-A){ 1 -2 b)Ri = 0 (A’34)
where A, b, andare model constants, Ri is the Richardson number, and
q = QA
\
du
dz
(A.35)
Once q2 is computed, the vertical eddy coefficients can be computed from
. A +ww/wl *
A = A q
A -wq
(A.36)
„ bs w'w' K
D = r Aq
v (bs - w)A q2
(A.37)
where
w = RH(AQ2)
w = w/(l - w/bs)
(A.38)
ii 1 _ 2.b 2
w w = — -rq
3(1 -2 w)
In a complete Reynolds stress model, a differential transport equation for the
turbulent macroscale A is usually derived. However, the A equation contains four model

325
coefficients that must be calibrated with experimental data. For ease of application, the
turbulent macroscale A is often assumed to satisfy a number of integral constraints. First of
all, A is assumed to be a linear function of the vertical distance immediately above the
bottom or below the free surface. In addition, the turbulent macroscale A must satisfy the
dA „ ,c
dz
(A.39)
following relationships:
A < Cx-H
(A.40)
A i C,-Hp
(A.41)
A <; C9• 8,
l q
(A.42)
VI
<
(A.43)
where Cx is a number usually within the range of 0.1 to 0.25, H is the total depth,H is the
depth of the pycnocline, C2, ranging from 0.1 and 0.25, is the fractional cut-off limitation of
turbulent macroscale based on bq2, the spread of the turbulence determined from the
turbulent kinetic energy ( q2) profile, and Ais the Brunt-Vaisala frequency, defined as:
at = f _ £ sp V'2
{ p dz)
(A.44)

326
Although the simplified second-order closure model is strictly valid when the
turbulent time scale ( A/q ) is much smaller than the mean flow time scale and when
turbulence does not change rapidly over A, it has been found to be quite successful in
simulating vertical flow structures in estuarine and coastal waters (Sheng et ah, 1989a; Sheng
etal., 1989b; Sheng etal., 1993; Sheng etal., 1995).
Solution Technique for the Water Quality Model
In the finite difference solution of the water quality model, the advection and
horizontal diffusion terms are treated explicitly, whereas the vertical diffusion and
biogeochemical transformations are treated implicitly. Following Chen (1994), a fractional
step method, which guarantees numerical stability and prevents negative concentrations is
applied in the numerical solution. First, the horizontal advection and diffusion, and the
vertical advection terms are calculated. Second, the numerical solution proceeds with the
calculation of the vertical diffusion and the transformation reactions that do not involve
sorption/desorption. Finally, the species that are coupled through dissolved and particulated
forms are solved simultaneously. Equations (A.45) shows a schematic of the numerical
solution algorithm method used in this study.

327
N*1 - Nn
At
N*2 - AT1
At
Nn+1 - iv*2
At
[Horiz. Advection + Horiz. Diffusion + Vertical Advection]"
[Vertical Diffusion]*2 + [Q]*2
[Sorption]"*1 + [Desorption]"*1
(A.45)
The coupling between the suspended sediment and water quality models takes place
during the solution of the sorption/desorption reactions. Assuming that any particulate
species (P) can be given in terms of mass per unit mass of sediment (p):
P = p-c (A.46)
where c represents the suspended sediment concentration. The solution of the second step
of the fractional method (*2) (Equation A.45) gives:
d pc d
dt dz
which can be expanded into:
dc dp d
p — + c—— - —
dt dt dz
Using the vertical one-dimensional suspended sediment equation:
i a \
„ dc
wc+ £> —
S V 3
dz
/ .
+ Q
(A.48)
wspc+Dv
dpc
r) 7
+ Q
(A.47)

328
de
dt
n de
w' c + Z) —
5 v dZi
(A.49)
Equation (A.48) becomes:
c^-
dp_
wc+D —1
+ -i
]
dt
dz \
' Vdz)
’ Sz J
(A.50)
At the sediment water interface, Equation (A.51) uses the balance between erosion
and deposition, and calculates the net flux of the particulate species coming out of the
sorption/desorption processes:
dp
dz
(D -E)
(
dz
n dp
D c——
V dz)
+ Q
\
(A.51)

APPENDIX B
MODELING SEDIMENT DYNAMICS
Equation (3.10) in Chapter 3 represents the governing equation for modeling
sediment dynamics in Estuarine Systems. The lateral boundary conditions along open and
river boundaries are applied similarly to the salinity equation. The vertical boundary
condition impose a zero flux at the free-surface, and a net flux determined by the balance
between erosion and deposition at the bottom (Figure B.l). Therefore, three important
processes need to be evaluated in the sediment model: settling, erosion, and deposition.
329

330
Settling Velocity
Due to its higher density, sediment particles tend to sink to the bottom, through a
process called settling. In this study, four options were used to determine the settling
velocity, depending on sediment characteristics.
Constant Settling
A constant settling velocity, determined from laboratory or field experiments can be
used in the sediment model:
ws = constant
(B.l)
Schoellhammer and Sheng (1993) studying resuspension events of non-cohesive sediments
in Old Tampa Bay used a constant settling velocity of 0.021 cm/s. In their study, the mean
particle diameter, d50 = 127 pm, and the density of bottom sediment, pf = 2.68 g/cm3.
Stokes’ Formula
For individual grain of fixed density ( pt), diameter (d), and fluid kinematic viscosity
(v), the terminal settling velocity is given by:
w
1 (P,~P w)sd2
(B.2)
S
18 v

331
Hwang & Mehta
Based on a laboratory experiment, Hwang and Mehta (1989) parameterize the effects
of flocculation and hindered settling on the settling velocity using:
w.
a c
(c2 + b2)n
(B.3)
where a, b, m, and n are empirical constants to be determined from laboratory experiments.
The shape of ws as function of c is shown in Figure B.2 for sediments from a site in Lake
Okeechobee, Florida (Hwang and Mehta, 1989). At low concentration ( c < 100 mg/L), w
is constant and can be described by Stoke’s law. At higher concentration (100 < c < 1000
mg/L), flocculation occurs as the result of increased collision among particles, resulting in
a higher settling velocity. As c exceeds 3000 mg/L, ws starts to decrease due to hindered
settling, i.e., interference on settling due to the presence of other particles.
Ross’ Formula
Settling velocity variation with concentration for the cohesive mud of Hillsborough
Bay was determined in a laboratory experiment by Ross (1988), according to a power law
(Figure B.3). For lower concentrations, more likely to occur in the field ( c < 1000 mg/L),
the settling velocity is given by:
ws = 0.11 c1-6
(B.4)

SETTLING VELOCITY, Ws(mms
332
Figure B.2 - Settling velocity as a function of concentration
(Hwang & Mehta, 1989).
Figure B.3 - Settling velocity as a function of concentration
(Ross, 1988).
SETTLING FLUX, Fsigm'V1)

333
Erosion
Erosion, defined as the process by which sediment is resuspended to the water
column due to bottom shear stress, is one of the primary links between the hydrodynamics
and sediment components of this integrated model. The erosion and ensuing resuspension
of bottom sediments depends on the bed structure and the characteristics of the flow just
above the bed. For non-cohesive sediments, erosion starts when the lift force acting on a
grain is larger than the downward force. For cohesive sediments, fluidization of the cohesive
bed and entrainment of fluid mud due to hydrodynamic forcing are considered erosional
processes, and thus, need to be assessed (Mehta, 1989).
Currently, three options for calculating erosion rates based on critical shear stress are
available in the model.
Power Law
(B.5)
where e'0 is the erosion rate constant per unit stress (i.e., it has the same units as E divided
by stress), xb is the bottom shear stress, t is the critical shear stress for erosion, p is an
empirical constant, and Td is a dimensionless erosion time constant. Non-
dimensionalization of the erosion time constant is obtained through Td = Tdl Tdo , where Td
is the dimensional time constant for erosion, and Tdo is the amount of time the sediment bed

334
has been lying undisturbed. Typically, Tdo is about one day, so the units of Tdo and Td are
days. Eo , Td , x , and p are empirical constants which must be determined from
laboratory or field experiments (Sheng and Chen, 1992).
hi Schoellhammer and Sheng (1993) study, a general erosion equation was applied
by setting the erosion rate equal to a power of the bottom shear stress:
E = a | xb p (B.6)
where the coefficients a = 4.08x 10~6 g/cm2s, and r| = 1.6 were determined during the
calibration process.
Exponential Law
Parchure and Mehta (1985) pointed out that the “Power Law” is pertinent to a dense
bed in which properties are vertically uniform. For a partially consolidated bed, both the
density and the bed strength increase with depth, and the erosion rate is better represented
by an exponential equation:
Bottom Shear Stress
Sediments from the bottom are resuspended into the water column by the combine
action of waves and currents. The sediment component of this integrated model utilizes the
Sverdrup-Munk-Bretschneider (SMB) model (U.S.Army Coastal Engineering Research

335
Center, 1984) to determine the characteristics of the wave field which induces bottom shear
stress. The wave-induced bottom shear stress is then calculated using the relationship
develop by Kajiura (1964, 1968). The primary assumption of the SMB model is that the
wind has been blowing long enough in one direction so that the wave field had time to come
into an equilibrium with the wind. Consequently, the wind input to the SMB model is
averaged over one-hour intervals. Details of the SMB model can be found in the Shore
Protection Manual (U.S.Army Corps of Engineers, 1984), Ahn (1989), and Sheng and Chen
(1992).
Deposition
Deposition and consolidation (in the case of cohesive sediments) are the processes
responsible for removal of sediment particles from the water column. The deposition
velocity can be defined in terms of the rate at which particles are removed from the water
column. The deposition in estuarine systems can be determined by the settling velocity,
shear strength, and concentration of depositing aggregates (Sheng, 1986; Chen, 1994), or it
can be assumed as the same as the settling velocity closed to the sediment bed
(Schoellhammer and Sheng, 1993). Krone (1993) defining deposition as a stochastic
process, introduced a probability function for deposition:
/
\
1
1
xb | i xb
2
Xcd Xcd J
(B.8)

336
where p is the probability of deposition, xb is the bottom shear stress, andx..(/ is the critical
shear stress for deposition. Equation (B.8) shows that when xb = 0, the probability of
deposition is 1, and when xb > xcd, there is no deposition. The probability of deposition of
sediment particles inversely proportional to the bottom shear stress.
Sheng’s Model
Sheng (1986) and Chen (1994) considered the flow over a surface covered with
several layers with the possible presence of vegetation, by expressing the deposition velocity
as:
P
W1 + (v*)-1 + (vr1
(B.9)
where -[w'c1) represents the depositional flux at the bed, cl is the suspended sediment
concentration at the first grid point above the bottom. vdh , vds , and vdc, representing the
deposition velocity within the hydrodynamic logarithmic layer, the viscous sublayer, and the
canopy layer, respectively, are given by:
K ll
v dh
.75 ln(z, / za)
(B.10)
vds
ill
0.3
í D 1
0.7
2
u.
3j
K V ,
Ul
2 2
+ 0.1 — -4-1
ul v
1 - exp(-0.08qzxrlvjj + xrg
(B.ll)

337
1 + LAI
>. = v,
dc ds 1 + D I Df
p f
(B.12)
where zx is the distance of the first grid point above the bottom, DB = 2.176x 1(T9 / rp is
the Brownian diffusion coefficient, v is fluid kinematic viscosity, ut = ^xb / pw is the
friction velocity, xb is the bottom shear stress, u¡ = [ut / k) ln(z5/zo) is the fluid velocity
outside the laminar sublayer, zb = 10zlu* is the height of the viscous sublayer.
xr = w / g is the relaxation time of sediment particles, q = (32)1/4 u t is the total turbulent
fluctuating velocity, LAI is the leaf area index (total wetted leaf area per unit bottom area).
In the absence of a vegetation canopy, vdc = 0.
The derivation of Sheng’s deposition model is based on fundamental consideration
of fluid dynamics principles and the fact that the inverse of vd express the “resistance”,
which is additive through the various layers. The advantage of Sheng’s model is that vd can
be explicitly computed if the turbulence and sediment parameters are known. The
disadvantage, however, is that it is difficult to obtain the field data required to validate the
model.
Solution Technique
Like the hydrodynamics component of the model, the sediment dynamics is
discretized using a finite difference formulation. Details of the numerical solution
algorithms used in this study are documented in Sheng and Chen (1992) and Sheng et al.

338
(1993). For completeness, a brief description of the finite difference formulation for the
vertical component is presented below.
.-,71+1 _ ti
Ck Ck
At
1
A Z,
Wsk+l-C";! + Dvk
+1 __ x'fW + 1
1
K‘ /
,,71 + 1 ,-,71 + 1
^•cr1 - ^
AZ,.
K¿ / J
(B.13)
,71 + 1
for k = 1
- r"
At
A Z,_
^+1-C-i + Dv,
^—T 71 + 1 _ >-,71 + 1
L'k+1
AZ
L V
- [D - E)
for k = km
v—r 71 + 1 ,-,71
At
AZ.
0 -
wvcr1 + ^
.-,71 + 1 _ , 71 + 1
C¿-1
AZ
/ J
where the superscript indicates time level, the subscript indicates vertical layer, C is the
suspended sediment concentration, D is the deposition rate, E is the erosion rate, Ws is the
settling velocity, At is the time step, Dv is the vertical diffusivity coefficient, and
AZk, AZtó, and AZkt are the vertical grid spacing as shown in Figure B.4.
Figure B.4 - Vertical grid spacing.

APPENDIX C
DISSOLVED OXYGEN SATURATION AND REAERATION EQUATIONS
Following APHA (1985), the concentration of dissolved oxygen in water (at different
temperatures and salinity) at equilibrium with water saturated air can be calculated as:
InDOs = -139.34 +(1.5757* 105/r)
-Í6.6423jcl07/r2) + (l.2438jcl010/T3)
(C.l)
-(8.6219jcl011/r4) - 0.5535•5,,[(3.1929xl0'2)
-(1.5428*10/7) + (3.8673* 103/r2)]
where DOs is the dissolved oxygen saturation, in mg/L; and T is the temperature, in degrees
K.
The reaeration rate constant, KAE is calculated in the model using the formula
proposed by Thomann and Fitzpatrick (1982) for the Potomac Estuary. This method
calculates reaeration as a function of velocity, depth, and wind speed as:
KAF = — + (0.728 w0-5 - 0.371 W + 0.0372 W2) (C.2)
AE h15 H
where Uavg is the depth average velocity, in fps; H is the local water ft, in meters; and W is
the wind speed, in m/s.
339


APPENDIX D
LIGHT MODEL EQUATIONS
Miller and McPherson (1995), developed a model that uses simple geometry to
compute the significant loss of scalar irradiance at the air-sea interface and to compute the
average angle of the light path just beneath the water surface.
During model simulations, the solar elevation angle is computed at each time step
from the date and time for the average latitude and longitude of Tampa Bay area, according
to:
Y = (d-iy
360
365-242
(D.l)
6 = 12.0 + 0.1236 sin(Y) - 0.0043 cos(Y)
+ 0.1538 sin(2 Y) + 0.0608 cos(2Y)
(D.2)
T = 15.0(t-8)-A
(D.3)
o = 279.9348 + Y + 1.9148 sin(Y) - 0.0795 cos(Y)
+ 0.0199 sin(2Y) - 0.0016 cos(2Y)
(D.4)
k = arcsin(0.39785077-sin(a))
sin(p) = sin(y)-sin(K) + cos(y)-cos(k)-cos(T)
(D.5)
(D.6)
341

342
where Y is the angular fraction of the year, in degrees; d is the Julian date; 6 is the true solar
noon, in hours; T is the solar hour angle, in degrees; t is the Greenwich Mean Time, in
hours; A is the local longitude, in degrees; a is an estimate of the true longitude of the sun,
in degrees; k is the solar declination, in degrees; y is the local latitude, in degrees; and P is
the solar elevation angle, in degrees.
The average zenith angle (0) of the refracted direct solar beam in water is computed
from the solar elevation angle by using Snell’s law and the assumption that the effects of the
wave action average to the refracted angle of a calm sea surface by:
0 = arcsin[sin(90° - P)/1.33] (D.7)
PAR data obtained from Tampa Bay were used to develop a cubic polynomial that
describes the upper limit of the averages as a function of the solar elevation angles on very
clear days in the Bay:
£,(max) = 216.47456 + 125.22091 -p - 1.8501726-p2 + 0.0093917741 *p3 (D.8)
The weighted average cosine, pwtí, for all refracted PAR is then calculated by:
[£o(max)]
} + cos(0) b2 sin(P) \Eo(I)!Eo{max)
vM
E0(I)/Eo( max)
+ &2sin(P) [Eo(7)/£o(max)
where bQ, bx, and b2 are regression coefficients determined from Tampa Bay data, and
Eo(I) is the irradiance data from the in-air sensor.

APPENDIX E
CONTOUR PLOTS FOR THE SUMMER OF 1991 SIMULATION
343

344
Ammonium Nitrogen
After 30 days (June 26,1991)
Figure E.l - Near-bottom ammonium nitrogen distribution in Tampa Bay
for June 26, after 30 days of simulation.

345
Ammonium Nitrogen
After 60 days (July 26, 1991)
Figure E.2 - Near-bottom ammonium nitrogen distribution in Tampa Bay
for July 26, after 60 days of simulation.
pg/L

346
Ammonium Nitrogen
After 90 days (August 25,1991)
Figure E.3 - Near-bottom ammonium nitrogen distribution in Tampa Bay
for August 25, after 90 days of simulation.

347
Ammonium Nitrogen
After 120 days (September 24,1991)
Figure E.4 - Near-bottom ammonium nitrogen distribution in Tampa Bay
for September 24, after 120 days of simulation.

348
Nitrate+Nitrite
After 30 days (June 26,1991)
Figure E.5 - Near-bottom nitrate+nitrite distribution in Tampa Bay for June
26, after 30 days of simulation.

349
Nitrate+Nitrite
After 60 days (July 26, 1991)
Figure E.6 - Near-bottom nitrate+nitrite distribution in Tampa Bay for July
26, after 60 days of simulation.

350
Nitrate+Nitrite
After 90 days (August 25, 1991)
Figure E.7 - Near-bottom nitrate+nitrite distribution in Tampa Bay for
August 25, after 90 days of simulation.

351
Nitrate+Nitrite
After 120 days (September 24,1991)
Figure E.8 - Near-bottom nitrate+nitrite distribution in Tampa Bay for
September 24, after 120 days of simulation.
M-g/L

Concentration (mg/L) Concentration (mg/L)
352
Near-Bottom Dissolved Oxygen
Model
Station 38
Model Results x EPC Station 36
Model
Station 36
Figure E.9 - Model results and measured data for near-bottom dissolved oxygen
at EPC stations 36 and 38.

Concentration (mg/L) Concentration (mg/L)
353
Near-Bottom Dissolved Oxygen
Model
Station 13
Model Results x EPC Station 14
Model
Station 14
Figure E.10 - Model results and measured data for near-bottom dissolved oxygen
at EPC stations 13 and 14.

Concentration (mg/L) Concentration (mg/L)
354
Near-Bottom Dissolved Oxygen
Model
Station 91
Model Results x EPC Station 24
Figure E.ll - Model results and measured data for near-bottom dissolved oxygen
at EPC stations 91 and 24.

Concentration (¡jg/L) Concentration (ng/L)
355
Near-Surface Chlorophyll-a
Model
Station 70
Model
Station 80
Figure E.12 - Model results and measured data for near-surface chlorophyll-a
concentration at EPC station 70 and 8.

Concentration (ng/L) Concentration (pg/L)
356
Near-Surface Chlorophyll-a
Model
Station 47
Model
Station 65
Figure E.13 - Model results and measured data for near-surface chlorophyll-a
concentration at EPC station 47 and 65.

Concentration (ng/L) Concentration (ng/L)
357
Near-Surface Chlorophyll-a
Model
Station 13
Model
Station 14
Figure E.14 - Model results and measured data for near-surface chlorophyll-a
concentration atEPC station 13 and 14.

Concentration (ng/L) Concentration (|ig/L)
358
Near-Surface Chlorophyll-a
Figure E.15 - Model results and measured data for near-surface chlorophyll-a
concentration at EPC station 91 and 23.

Concentration (mg/L) Concentration (mg/L)
359
Near-Bottom Kjeldahl Nitrogen
Model
Station 70
Model Results x EPC Station 80
Model
Station 8
Figure E.16 - Model results and measured data for near-bottom Kjeldahl nitrogen
concentration at EPC station 70 and 8.

Concentration (mg/L) Concentration (mg/L)
360
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Near-Bottom Kjeldahl Nitrogen
Model Results x EPC Station 38
Model
• Station 38
200 220
Julian Day (1991)
240
260
Model Results x EPC Station 36
Model
Station 36
Figure E.17 - Model results and measured data for near-bottom Kjeldahl nitrogen
concentration at EPC station 36 and 38.

Concentration (mg/L) Concentration (mg/L)
361
Near-Bottom Kjeldahl Nitrogen
Model
Station 13
Model Results x EPC Station 14
0.8
0.7
0.6
0.4 -
0.0
Model
Station 14
200 220
Julian Day (1991)
Figure E.18 - Model results and measured data for near-bottom Kjeldahl nitrogen
concentration at EPC station 13 and 14.

Concentration (mg/L) Concentration (mg/L)
362
Near-Bottom Kjeldahl Nitrogen
Model
Station 91
Model Results x EPC Station 23
Model
Station 23
Figure E.19 - Model results and measured data for near-bottom Kjeldahl nitrogen
concentration at EPC station 91 and 23.

APPENDIX F
SENSITIVITY TESTS OF THE SEAGRASS MODEL
363

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
364
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.l - Simulated seagrass biomass for test Sl.l.

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
365
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.2 - Simulated seagrass biomass for test S1.2.

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
366
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.3 - Simulated seagrass biomass for test S2.1.
300
350

367
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
368
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.5 - Simulated seagrass biomass for test S2.3.

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
369
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.6 - Simulated seagrass biomass for test S3.1.
300
350

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
370
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.7 - Simulated seagrass biomass for test S3.2.
300
350

371
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.8 - Simulated seagrass biomass for test S3.3.
350

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
372
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.9 - Simulated seagrass biomass for test S4.1.
300
350

373
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
300
350

Biomass (gdw / m2) Biomass (gdw / mz) Biomass (gdw / m2)
374
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.ll - Simulated seagrass biomass for test S5.1.
350

Biomass (gdw / m2) Biomass (gdw / m2) Biomass (gdw / m2)
375
Seagrass Biomass
Tarpon Key (16,33)
Mullet Key (19,34)
Apollo Beach (33,55)
Figure F.12 - Simulated seagrass biomass for test S5.2.
300
350


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BIOGRAPHICAL SKETCH
Eduardo Ayres Yassuda was born in Sao Paulo, Brazil, on July 26, 1963. He received
a Bachelor of Science degree in mechanical engineering at the Mackenzie University (Sao
Paulo, Brazil) in 1986. After working for a couple of years, he started his graduate program
at the Oceanographic Institute of the University of Sao Paulo, where he earned a Master of
Science degree in physical oceanography in 1991. In order to integrate his engineering
background with his passion for estuarine systems, he came to the U.S. to pursue a Ph.D. in
coastal and oceanographic engineering with a minor in the Environmental Engineering and
Science Department. Almost 5 years have gone by, and life has been very generous to him
and his wife (Monica). They are going back to Brazil with not only their diplomas, but with
Daniel, a three-year old wishful buddy, and another little one that up to this moment is
growing up in mammy’s belly.
395



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