• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 Abstract
 Introduction
 Literature review
 Field data collection
 Field data analysis
 Formulation of model equations
 Three dimensional numerical...
 Summary and conclusions
 Appendix A: Instrument calibra...
 Appendix B: Data plots
 Appendix C: Numerical solution...
 Bibliography






Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 118
Title: Circulation and transport within a system of shallow, interconnected barrier island lagoons
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00075476/00001
 Material Information
Title: Circulation and transport within a system of shallow, interconnected barrier island lagoons
Series Title: UFL-COEL-TR
Physical Description: xxiii, 302 p. : ill. ; 28 cm.
Language: English
Creator: Peene, Steven J., 1960-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1995
 Subjects
Subject: Tidal currents -- Mathematical models -- Florida -- Sarasota Bay   ( lcsh )
Coastal and Oceanographic Engineering thesis, Ph. D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1995.
Bibliography: Includes bibliographical references (p. 298-302).
Statement of Responsibility: by Steven J. Peene.
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.
 Record Information
Bibliographic ID: UF00075476
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 41567306

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement 1
        Acknowledgement 2
    Table of Contents
        Table of Contents 1
        Table of Contents 2
        Table of Contents 3
        Table of Contents 4
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
        List of Figures 4
        List of Figures 5
        List of Figures 6
        List of Figures 7
        List of Figures 8
        List of Figures 9
        List of Figures 10
    List of Tables
        List of Tables 1
        List of Tables 2
        List of Tables 3
        List of Tables 4
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
    Literature review
        Page 10
        Page 11
        Page 12
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    Field data collection
        Page 28
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    Field data analysis
        Page 41
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    Formulation of model equations
        Page 118
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    Three dimensional numerical modeling
        Page 137
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    Summary and conclusions
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    Appendix A: Instrument calibration
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    Appendix B: Data plots
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    Appendix C: Numerical solution of equations
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    Bibliography
        Page 298
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Full Text




UFL/COEL-TR/118


CIRCULATION AND TRANSPORT WITHIN A SYSTEM
OF SHALLOW, INTERCONNECTED BARRIER ISLAND
LAGOONS




by



Steven J. Peene


Dissertation


1995




















CIRCULATION AND TRANSPORT WITHIN A SYSTEM OF SHALLOW,
INTERCONNECTED BARRIER ISLAND LAGOONS



By

STEVEN J. PEENE


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


1995











ACKNOWLEDGEMENTS


I would like to express my gratitude to my advisor and supervisory committee

chairman, Dr. Y. Peter Sheng, for his guidance and support throughout my doctoral

program. The freedom he allowed me in the development of the field measurement

program provided an education I could not have gotten anywhere else. I would also

like to thank the members of my committee, Dr. Robert G. Dean, Dr. Max Sheppard,
Dr. Daniel Hanes and Dr. Clay Montague, for their advice and support.

I must thank everyone out at the Coastal Laboratory where I spent the best parts

of my years in the program. Special thanks to Vernon Sparkman and Jim Joiner who

not only provided most of the brain power for the field work but also friendship,

patience, guidance and fun. Special thanks also to Sidney Schoefield, Danny Brown,

Don Mueller, Mark Southerland, Chuck Broward, Vik Adams and George Chappel.

I will never forget volleyball the Cypress Lodge, redneck preppies, tower ramming,

gator skiing, mutiny on the Munson, the sinking of the Anna Capri and all my friends

at the lab.

As my time in the program was rather lengthy, I was fortunate to make many

good friends. I owe them a lot because they helped make my time at the University

fun. Thanks to Tom B., Rick, Victor, Yuming, Sam, Jeff, Barry, Gusty, Mike and

Sheila, Phil and Lynn, Becky and Terry, Sandra, Lucy, Laura, Paul, Jei Kok, Dave,

H.K. Lee, Phil H., Mark P., and Eduardo. A special thanks to all the members of

L.A.S. whom I will always count as my good friends.

Thanks to my parents for always believing in me and supporting me in whatever
endeavor I undertook. Also to my sister C.J. for her love and support through this






whole craziness.

Finally, my wife Christina, whom I met at the start of this program, fell in love

with and married as a doctoral candidate. She always stood by me and supported

me. She went through all the tough times and always told me I could make it. She

never lost faith in me.













TABLE OF CONTENTS


ACKNOWLEDGEMENTS . ...

LIST OF FIGURES ............

LIST OF TABLES .............

ABSTRACT ................

CHAPTERS
I TNTmThr~ThTTC TT T/Vl NT


SIN L U I N . . . . .

1.1 Barrier Island Lagoons ........................

1.2 General Circulation and Transport within Barrier Island Lagoons

1.3 Study Area Description ........................

1.4 Statement of Purpose ........................

1.5 Presentation Outline .........................

2 LITERATURE REVIEW .........................

2.1 Analyses of Field Measurements . . . . .

2.2 Simplified Analytic Solutions and Numerical Models . .

2.3 Multidimensional Modeling . . . . . .

2.4 Studies Relative to Sarasota Bay . . . . .

2.5 Chapter Summary ..........................

3 FIELD DATA COLLECTION ......................

3.1 Introduction . . . . . . . .

3.2 University of Florida Data Collection Stations . . .

3.2.1 Bay Stations . . . . .. .. .

3.2.2 Offshore Stations .......................


...........

...........

...........

...........


ii

viii

xviii

xxii



1

1

2

4

6

8

10

10

16

23

25

26

28

28

28

29

36







3.3 Tide and Discharge Measurements Taken by the USGS . .

3.3.1 Tidal Data... ............... ..........

3.3.2 Discharge Measurements . . . ... .

4 FIELD DATA ANALYSIS ...........................

4.1 Introduction ... .. ....... .... .. ..... ........ .

4.2 Decomposition of Water Surface Elevations, Currents and Wind .


4.2.1

4.2.2


Presentation and Discussion of Ra

Spectral Analysis of Tides, Curren


w Data . . .

ts and Wind . . .


4.2.3 Harmonic Analysis of Tides and Currents . . .

4.2.4 Analysis of Sub-Tidal Tides and Currents . . .

4.3 Discharge Measurements .........................

4.4 Freshwater Inflow Measurements . . . ..... ...

4.5 Salinities Measured at the UFL Bay Stations . . . .

4.6 Chapter Summary ............................

5 FORMULATION OF MODEL EQUATIONS . . .. . .

5.1 The Cartesian Equations of Motion and Transport . . .

5.2 General Cartesian Boundary Conditions . . . .


5.2.1 Free Surface Boundary Conditions

5.2.2 Bottom Boundary Conditions .

5.2.3 Lateral Boundary Conditions .

5.2.4 Initial Conditions .........

Vertically Integrated Equations . .

Sigma Stretching of Equations . .

Non-Dimensionalization of Equations .

Boundary Fitted Equations . .

5.6.1 Grid Generation ..........


. . . . 121

. . . . 122

. . . . 123

. . . . 124

. . . . 125

. . . . 126

. . . . 128

. . . . 129

. . . . 130


5.6.2 Transformation of the Equations of Motion and Transport


44

58

69

86

98

105

108

113

118

118

121







6 THREE DIMENSIONAL NUMERICAL MODELING ........

6.1 Numerical Grid and Bathymetry .................

6.2 Boundary Conditions ........................

6.2.1 Tidal Forcing ........................

6.2.2 W ind Forcing ........................

6.3 Quantifying Model Accuracy ................. ...


6.3.1 Calculation of the RMS Errors ..

6.3.2 Comparison of the Simulated and

6.3.3 Comparison of the Measured and

6.3.4 Comparison of the Measured and

6.3.5 Comparison of the Measured and

6.3.6 Comparison of the Measured and

6.4 Model Sensitivity .............

6.4.1 Bottom Friction ..........

6.4.2 Horizontal Diffusion . .

6.4.3 Vertical Turbulence . .

6.4.4 Bathymetric Conditions .....

6.4.5 Vertical Resolution . .


Measured Energies .... .156

Simulated Harmonics .. 162

Simulated Residuals. . 173

Simulated Discharges . 180

Simulated Salinities .... .186

. . . . 192

. . . . 193

. . . . 197

. . . . 200

. . . . 205

. . . . 206


6.4.6 Summary of Model Accuracy and Sensitivity . . .

6.5 The Relative Influence of the Model Forcing Mechanisms . .

6.5.1 Periodic/Short Term Forcings . . . . .

6.5.2 Residual Forcings .........................

7 SUMMARY AND CONCLUSIONS . . . . . .

APPENDICES

A INSTRUMENT CALIBRATION ....... .. ..............

B DATA PLOTS .................................


137

137

142

142

144

146


206

209

210

215

224






C NUMERICAL SOLUTION OF EQUATIONS ............... .282

C.1 Introduction .................... ........... 282

C.2 General Structure of Numerical Solution and Grid . . ... 282

C.3 Alternating Direction Implicit Solution for the External Mode .. 284

C.4 Internal Mode Solution .......................... 287

C.5 Calculation of Vertical Velocities . . . ..... 289

C.6 Finite Difference Solution of Advection-Diffusion Equations . 290

C.7 The Non-Dimensional Variables and Parameters . . ... 294

C.8 The Tensor Invarient Equations of Motion . . . ... 296

BIBLIOGRAPHY ................... ............. 298

BIOGRAPHICAL SKETCH ........................... 303











LIST OF FIGURES




1.1 A site map of the Sarasota Bay System and its location relative
to the State of Florida and the Gulf of Mexico . . 5

2.1 The idealized geometry for the canal/inlet system utilized in the
study by van de Kreeke, along with the variation in the net dis-
charge as a function of inlet depth, width and length (van de
Kreeke and Cotter, 1974) ...................... 18

2.2 The idealized channel geometry used in the solution of the 1-D
Equations of Momentum and Continuity (Speer and Aubrey, 1985) 21

3.1 The locations of the UFL and USGS data collection stations within
Anna Maria Sound and Big Sarasota Bay, 1991 deployment. 30

3.2 The locations of the UFL and USGS data collection stations in
Little Sarasota Bay and Blackburn Bay, 1991 deployment. . 31

3.3 A schematic of the University of Florida instrument platforms. .32

3.4 A schematic diagram of the offshore data collection stations 37

4.1 The measured water surface elevations from Julian Day 255 to 285,
1990. a) offshore; b) USGS-05 (Big Pass); c) USGS-04 (Roberts
Bay); d) USGS-06 (Little Sarasota Bay) . . .... 45

4.2 The measured water surface elevations from Julian Day 200 to 230,
1991. a) UFL-O1; b) USGS-05 (Big Pass); c) USGS-04 (Roberts
Bay); d) USGS-06 (Little Sarasota Bay). . . .... 46

4.3 A comparison of measured water surface elevations from Julian
Day 220 to 225, 1991 at USGS-05 (Big Pass) and USGS-06 (Little
Sarasota Bay) ..................... ....... 47

4.4 The bathymetric cross-section at station UFL-B1 . ... 48

4.5 The current vector components measured from Julian Day 200 to
230, 1991 at UFL-B1. a) Surface East-West Velocity; b) Surface
North-South Velocity; c) Bottom East-West Velocity; d) Bottom
North-South Velocity. ...................... 49







4.6 The current vector components measured from Julian Day 200 to
230, 1991 at UFL-B2. a) Surface East-West Velocity; b) Surface
North-South Velocity; c) Bottom East-West Velocity; d) Bottom
North-South Velocity. ........................ 51

4.7 The current vector components measured from Julian Day 200 to
230, 1991 at UFL-B3. a) Surface East-West Velocity; b) Surface
North-South Velocity; c) Bottom East-West Velocity; d) Bottom
North-South Velocity. ........................ 53

4.8 Idealized velocity profiles under laminar and turbulent boundary
layers ................ ....... ......... 54

4.9 The current vector components measured from Julian Day 200 to
230, 1991 at UFL-B4. a) Surface East-West Velocity; b) Surface
North-South Velocity; c) Bottom East-West Velocity; d) Bottom
North-South Velocity. .................... .... ..55

4.10 The wind velocity vector components. a) East-west component
measured at the Sunshine Skyway (Julian Day 280 to 310, 1990);
b) north-south component measured at the Sunshine Skyway (Ju-
lian Day 280 to 310, 1990); c) east-west component measured at
UFL-B3 (Julian Day 200 to 230, 1991); d) north-south component
measured at UFL-B3 (Julian Day 200 to 230, 1991). ...... 57

4.11 Spectral density of water surface elevations measured from Julian
Day 255 to 315, 1990. a) USGS-05; b) USGS-04; c) USGS-06 60

4.12 Spectral density of water surface elevations measured from Julian
Day 200 to 260, 1991. a) USGS-05; b) USGS-04; c) USGS-06 61

4.13 The spectral density of the measured surface north-south current
components measured from Julian Day 200 to 260, 1991. a) UFL-
Bl; b) UFL-B2; c) UFL-B3; d) UFL-B4. .............. 66

4.14 Spectral density of the measured wind speed components from
Julian Day 200 to 260, 1991 at UFL-B3. a) East-west component;
b) north-south component. . . . . . 68

4.15 The Overtide Ratios and Form Numbers calculated from the mea-
sured water surface elevations, a) Julian Day 255 to 315; b) Julian
Day 200 to 260 ......................... 74

4.16 The primary harmonic ellipses at UFL-B1 for Julian Day 200 to
260, 1991. a) Surface velocities; b) bottom velocities. ...... 77

4.17 The primary harmonic ellipses at UFL-B2 for Julian Day 200 to
260, 1991. a) Surface velocities; b) bottom velocities. ...... 80

4.18 The primary harmonic ellipses at UFL-B3 for Julian Day 200 to
260, 1991. a) Surface velocities; b) bottom velocities. ...... 82






4.19 The primary harmonic ellipses at UFL-B4 for Julian Day 200 to
260, 1991. a) Surface velocities; b) bottom velocities. . 84

4.20 The frequency response curve for the Chebychev II, 48 hour low
pass filter . . . . . . . 88

4.21 a) The filtered alongshore and cross-shore winds versus the filtered
water surface elevation at USGS-04 for Julian Day 255 to 285,
1990; b) The coherence between wind vector components spaced
at 30 degree increments and the filtered water surface elevation at
U SG S-04 .. . . . . . . . 90

4.22 a) The filtered alongshore and cross-shore winds versus the filtered
water surface elevation at USGS-06 for Julian Day 200 to 250,
1991. b) The coherence between wind vector components spaced
at 30 degree increments and the filtered water surface elevation at
U SG S-06 . . . . . . . 92

4.23 The filtered wind speed components compared to the current vec-
tor components at UFL-B1, Julian Day 200 to 260. a) North-south
wind component compared to the bottom and surface north-south
current component; b) east-west wind component compared to the
bottom and surface east-west current component. . ... 93

4.24 The coherence between the filtered bottom current vector compo-
nents and the filtered wind vector components at 30 degree spac-
ings from 190 to 340 degrees, UFL-B1, Julian Day 200 to 260. a)
north-south currents; b) east-west currents. . . ... 96

4.25 The coherence between the filtered surface current vector compo-
nents and the filtered wind vector components at 30 degree spac-
ings from 190 to 340 degrees, UFL-B1, Julian Day 200 to 260. a)
north-south currents; b) east-west currents. . . ... 97

4.26 The filtered wind speed components compared to the current vec-
tor components at UFL-B2, Julian Day 200 to 260. a) North-south
wind component compared to the bottom and surface north-south
current component; b) east-west wind component compared to the
bottom and surface east-west current component. . ... 98

4.27 The filtered wind speed components compared to the current vec-
tor components at UFL-B3, Julian Day 200 to 260. a) North-south
wind component compared to the bottom and surface north-south
current component; b) east-west wind component compared to the
bottom and surface east-west current component. . ... 99

4.28 The filtered wind speed components compared to the current vec-
tor components at UFL-B4, Julian Day 200 to 260. a) North-south
wind component compared to the bottom and surface north-south
current component; b) east-west wind component compared to the
bottom and surface east-west current component. . ... 100






4.29 The measured discharge compared with the measured water sur-
face elevation at Roberts Bay and Blackburn Bay (solid line is the
water surface elevation, broken lines are discharge). a) Julian Day
204 to 206, 1991; b) Julian Day 224 to 226, 1991. . ... 101

4.30 The measured discharge compared with the measured water sur-
face elevations, a) New Pass and Big Pass, Julian Day 148, 1992;
b) Longboat Pass and Anna Maria Sound, Julian Day 149, 1992. 103

4.31 The measured freshwater inflows to the Sarasota Bay System, Ju-
lian Day 200 to 260, 1991. a) Manatee River; b) Walker Creek. 107

4.32 a) The surface salinity at UFL-B1 from Julian Day 200 to 250,
1991; b) The bottom salinity at UFL-B1 from Julian Day 200 to
250, 1991; c) The surface minus bottom salinity at UFL-B1 from
Julian Day 200 to 250, 1991 ............ ..... 110

4.33 a) The surface salinity at UFL-B2 from Julian Day 200 to 250,
1991; b) The bottom salinity at UFL-B2 from Julian Day 200 to
250, 1991; c) The surface minus bottom salinity at UFL-B2 from
Julian Day 200 to 250, 1991 ................ ...... 111

4.34 a) The surface salinity at UFL-B3 from Julian Day 200 to 250,
1991; b) The bottom salinity at UFL-B3 from Julian Day 200 to
250, 1991; c) The surface minus bottom salinity at UFL-B3 from
Julian Day 200 to 250, 1991 . . . ..... 112

4.35 a) The surface salinity at UFL-B4 from Julian Day 200 to 250,
1991; b) The bottom salinity at UFL-B4 from Julian Day 200 to
250, 1991; c) The surface minus bottom salinity at UFL-B4 from
Julian Day 200 to 250, 1991 . . . .. 114

5.1 An idealized representation of the Sigma transformation . 126

5.2 An Idealized Boundary Fitted Transformation . ... 131

5.3 Cartesian vs. Curvilinear Coordinate Systems . . ... 132

6.1 The curvilinear grid utilized with the numerical model CH3D. 138

6.2 The model bathymetry within Anna Maria Sound, Sarasota Bay,
Roberts Bay and the northern offshore region. . ... 140

6.3 The model bathymetry within Little Sarasota Bay, Blackburn Bay
and the southern offshore region. . . . ... 141

6.4 A comparison of the measured wind speed components at UFL-
B1, UFL-B2, UFL-B3 and UFL-B4. a) East-west component; b)
north-south component. . . . . . 145

6.5 A comparison of the measured and simulated water surface eleva-
tions, Julian Day 200 to 230. 1991. a) USGS-04; b) USGS-05; c)
USGS-06; d) USGS-07 ..................... 149






6.6 A comparison of the measured and simulated current components
at station UFL-B1, Julian Day 200 to 230, 1991. a) Bottom
east-west; b) surface east-west; c) bottom north-south; d) surface
north-south ........................... 151

6.7 A comparison of the measured and simulated current components
at station UFL-B2, Julian Day 200 to 230, 1991. a) Bottom
east-west; b) surface east-west; c) bottom north-south; d) surface
north-south ........................... 154

6.8 A comparison of the measured and simulated current components
at station UFL-B3, Julian Day 200 to 230, 1991. a) Bottom
east-west; b) surface east-west; c) bottom north-south; d) surface
north-south .. .. ..... .. .... ... ........ 155

6.9 A comparison of the measured and simulated current components
at station UFL-B4, Julian Day 200 to 230, 1991. a) Bottom
east-west; b) surface east-west; c) bottom north-south; d) surface
north-south ........................... 157

6.10 A comparison of the measured and simulated form numbers and
overtime ratios for the tides at USGS-04, USGS-05, USGS-06 and
USGS-07, Julian Day 200 to 230, 1991 . . ..... 165

6.11 A comparison between the simulated and measured water surface
elevations, Julian Day 200 to 230, 1991. a) USGS-04; b) USGS-05;
c) USGS-06; d) USGS-07. ....................... 175

6.12 The residual velocity vectors near UFL-B1 predicted by the model,
Julian Day 200 to 230, 1991. a) Layer 1; b) layer 2; c) layer 3; d)
layer 4 . . . . . . . .. 178

6.13 The Long Frequency Variations in the simulated and Measured
Residual Current Vectors at UFL-B1, Julian Days 200 to 230,
1991. a) Bottom east-west component; b) bottom north-south
component; c) surface east-west component; d) surface north-
south component ........................ 179

6.14 The residual velocity vectors near UFL-B2 predicted by the model,
Julian Day 200 to 230, 1991. a) Layer 1; b) layer 2; c) layer 3; d)
layer 4. ........................... . . 181

6.15 The residual velocity vectors near UFL-B3 predicted by the model,
Julian Day 200 to 230, 1991. a) Layer 1; b) layer 2; c) layer 3; d)
layer 4 . . . . . . . . 182

6.16 The residual velocity vectors near UFL-B4 predicted by the model,
Julian Day 200 to 230, 1991. a) Layer 1; b) layer 2; c) layer 3; d)
layer 4. ......................... . . 183






6.17 Comparisons of the Measured and simulated Discharges. a) Black-
burn Bay, Julian Day 204 to 205, 1991; b) Roberts Bay, Julian Day
205 to 206, 1991; c) Blackburn Bay, Julian Day 224 to 225, 1991;
d) Roberts Bay, Julian Day 225 to 226, 1991. . . .... 185

6.18 The Freshwater Inflow Boundary Conditions Utilized in the Model;
a). Manatee River; b). Phillipee Creek; c). North Creek . 187

6.19 The Freshwater Inflow Boundary Conditions Utilized in the Model;
a). South Creek; b). Crane Creek; c). Hackett Creek .. ... 188

6.20 A Comparison Between the Measured and Simulated Salinities
at Stations UFL-B1 and UFL-B2; a) Bottom Salinity UFL-B1;
b). Surface Salinity UFL-B1; c). Bottom Salinity UFL-B2; d).
Surface Salinity UFL-B2 ...................... 190

6.21 A Comparison Between the Measured and Simulated Salinities
at Stations UFL-B3 and UFL-B4; a) Bottom Salinity UFL-B3;
b). Surface Salinity UFL-B3; c). Bottom Salinity UFL-B4; d).
Surface Salinity UFL-B4 ...................... 191

6.22 The Non-Dimensional Forcing Terms Within the Equations of Mo-
tion for the 30 Day No Wind Simulation in 1991 at UFL-B1; a).
Alongchannel Component, b). Crosschannel Component ..... 211

6.23 The Non-Dimensional Forcing Terms Within the Equations of Mo-
tion for the 30 Day No Wind Simulation in 1991 at UFL-B2; a).
Alongchannel Component, b). Crosschannel Component . 212

6.24 The Non-Dimensional Forcing Terms Within the Equations of Mo-
tion for the 30 Day No Wind Simulation in 1991 at UFL-B3; a).
Alongchannel Component, b). Crosschannel Component ..... 213

6.25 The Non-Dimensional Forcing Terms Within the Equations of Mo-
tion for the 30 Day No Wind Simulation in 1991 at UFL-B4; a).
Alongchannel Component, b). Crosschannel Component ..... 214

6.26 The Filtered Non-Dimensional Forcing Terms Within the Equa-
tions of Motion for the 30 Day Simulation in 1991 at UFL-B1; a).
Alongchannel Component, b). Crosschannel Component ..... .216

6.27 The Filtered Non-Dimensional Forcing Terms Within the Equa-
tions of Motion for the 30 Day No Wind Simulation in 1991 at
UFL-B1; a). Alongchannel Component, b). Crosschannel Com-
ponent .... ........................... 218

6.28 A Comparison Between the Simulated Residual Water Level Fluc-
tuations and the Simulated Alongchannel and Crosschannel Sur-
face Slope Terms for the 30 Day No Wind Run 1991 (dashed lines
are surface slope, solid line is water level) . . .... 219






6.29 The Filtered Non-Dimensional Forcing Terms Within the Equa-
tions of Motion for the 30 Day Simulation in 1991 at UFL-B2; a).
Alongchannel Component, b). Crosschannel Component ..... ..221

6.30 The Filtered Non-Dimensional Forcing Terms Within the Equa-
tions of Motion for the 30 Day Simulation in 1991 at UFL-B3; a).
Alongchannel Component, b). Crosschannel Component ..... ..222

6.31 The Filtered Non-Dimensional Forcing Terms Within the Equa-
tions of Motion for the 30 Day Simulation in 1991 at UFL-B4; a).
Alongchannel Component, b). Crosschannel Component . 223

A.1 The Residual Conductivity for Sensor 825 (Residual=Instrument
Conductivity Bath Conductivity), Bottom Sensor UFL-B1 235

A.2 The Residual Conductivity for Sensor 829 (Residual=Instrument
Conductivity Bath Conductivity), Top Sensor UFL-B1 . 235

A.3 The Residual Conductivity for Sensor 823 (Residual=Instrument
Conductivity Bath Conductivity), Bottom Sensor UFL-B2 236

A.4 The Residual Conductivity for Sensor 816 (Residual=Instrument
Conductivity Bath Conductivity), Top Sensor UFL-B2 . 236

A.5 The Residual Conductivity for Sensor 824 (Residual=Instrument
Conductivity Bath Conductivity), Bottom Sensor UFL-B3 237

A.6 The Residual Conductivity for Sensor 828 (Residual=Instrument
Conductivity Bath Conductivity), Top Sensor UFL-B3 . 237

A.7 The Residual Conductivity for Sensor 822 (Residual=Instrument
Conductivity Bath Conductivity), Bottom Sensor UFL-B4 238

A.8 The Residual Conductivity for Sensor 821 (Residual=Instrument
Conductivity Bath Conductivity), Top Sensor UFL-B4 . 238

A.9 The Residual Temperature for Sensor 1125 (Residual=Instrument
Temperature Bath Temperature), Bottom Sensor UFL-B1 239

A.10 The Residual Temperature for Sensor 1126 (Residual=Instrument
Temperature Bath Temperature), Top Sensor UFL-B1 . 239

A.11 The Residual Temperature for Sensor 1127 (Residual=Instrument
Temperature Bath Temperature), Bottom Sensor UFL-B2 240

A.12 The Residual Temperature for Sensor 1132 (Residual=Instrument
Temperature Bath Temperature), Top Sensor UFL-B2 . 240

A.13 The Residual Temperature for Sensor 1131 (Residual=Instrument
Temperature Bath Temperature), Bottom Sensor UFL-B3 241

A.14 The Residual Temperature for Sensor 1130 (Residual=Instrument
Temperature Bath Temperature), Top Sensor UFL-B3 . 241






A.15 The Residual Temperature for Sensor 1129 (Residual=Instrument
Temperature Bath Temperature), Bottom Sensor UFL-B4 242

A.16 The Residual Temperature for Sensor 1128 (Residual=Instrument
Temperature Bath Temperature), Top Sensor UFL-B4 . 242

A.17 The Calibration Curve for Wind Sensor 5202, Station UFL-B1 243

A.18 The Calibration Curve for Wind Sensor 5203, Station UFL-B2 244

A.19 The Calibration Curve for Wind Sensor 5200, Station UFL-B3 .245

A.20 The Calibration Curve for Wind Sensor 5199, Station UFL-B4 246

B.1 The Water Surface Elevation Measured at the Anna Maria Station
(USGS-01) from Julian Day 255, 1990 to Julian Day 50, 1991 and
Julian Day 250, 1991 to Julian Day 300, 1991 . . ... 248

B.2 The Water Surface Elevation Measured at the Anna Maria Station
(USGS-01) from Julian Day 300, 1991 to Julian Day 100, 1992 249

B.3 The Water Surface Elevation Measured at the Anna Maria Station
(USGS-01) from Julian Day 100, 1992 to Julian Day 300, 1992 250

B.4 The Water Surface Elevation Measured at the Sarasota Bay East
Station (USGS-02) from Julian Day 255, 1990 to Julian Day 50,
1991 and Julian Day 250, 1991 to Julian Day 300, 1991 . 251

B.5 The Water Surface Elevation Measured at the Sarasota Bay East
Station (USGS-02) from Julian Day 300, 1991 to Julian Day 100,
1992 . . . . . . . . .252

B.6 The Water Surface Elevation Measured at the Sarasota Bay East
Station (USGS-02) from Julian Day 100, 1992 to Julian Day 300,
1992 . . . . . . . . .253

B.7 The Water Surface Elevation Measured at the Sarasota Bay West
Station (USGS-03) from Julian Day 255, 1990 to Julian Day 50,
1991 and Julian Day 250, 1991 to Julian Day 300, 1991 . 254

B.8 The Water Surface Elevation Measured at the Sarasota Bay West
Station (USGS-03) from Julian Day 300, 1991 to Julian Day 100,
1992 . . . . . . . . .255

B.9 The Water Surface Elevation Measured at the Sarasota Bay West
Station (USGS-03) from Julian Day 100, 1992 to Julian Day 300,
1992 . . . . . . . . .256

B.10 The Water Surface Elevation Measured at the Roberts Bay Station
(USGS-04) from Julian Day 255, 1990 to Julian Day 100, 1991 257

B.11 The Water Surface Elevation Measured at the Roberts Bay Station
(USGS-04) from Julian Day 100, 1991 to Julian Day 300, 1991 258






B.12 The Water Surface Elevation Measured at the Big Pass Station
(USGS-05) from Julian Day 255, 1990 to Julian Day 100, 1991 259

B.13 The Water Surface Elevation Measured at the Big Pass Station
(USGS-05) from Julian Day 100, 1991 to Julian Day 300, 1991 260

B.14 The Water Surface Elevation Measured at the Big Pass Station
(USGS-05) from Julian Day 300, 1991 to Julian Day 100, 1992 261

B.15 The Water Surface Elevation Measured at the Big Pass Station
(USGS-05) from Julian Day 100, 1992 to Julian Day 300, 1992 262

B.16 The Water Surface Elevation Measured at the Little Sarasota Bay
Station (USGS-06) from Julian Day 255, 1990 to Julian Day 100,
1991 . . . . . . . . 263

B.17 The Water Surface Elevation Measured at the Little Sarasota Bay
Station (USGS-06) from Julian Day 100, 1991 to Julian Day 300,
1991 .... .. .. ....... .............. 264

B.18 The Water Surface Elevation Measured in Blackburn Bay (USGS-
07) from Julian Day 255, 1990 to Julian Day 100, 1991 . 265

B.19 The Water Surface Elevation Measured in Blackburn Bay (USGS-
07) from Julian Day 100, 1991 to Julian Day 300, 1991 . 266

B.20 The Bottom and Surface Water Velocities Measured at Station
UFL-B1 from Julian Day 230 to 260, 1991 . . ... 267

B.21 The Bottom and Surface Water Velocities Measured at Station
UFL-B2 from Julian Day 230 to 260, 1991 . . ... 268

B.22 The Bottom and Surface Water Velocities Measured at Station
UFL-B3 from Julian Day 230 to 260, 1991 . . ... 269

B.23 The Bottom and Surface Water Velocities Measured at Station
UFL-B4 from Julian Day 230 to 260, 1991 . . ... 270

B.24 The East-West and North-South Wind Speed Components Mea-
sured at Station UFL-B1 from Julian Day 200 to 260, 1991 271

B.25 The East-West and North-South Wind Speed Components Mea-
sured at Station UFL-B2 from Julian Day 200 to 260, 1991 272

B.26 The East-West and North-South Wind Speed Components Mea-
sured at Station UFL-B3 from Julian Day 200 to 260, 1991 .273

B.27 The East-West and North-South Wind Speed Components Mea-
sured at Station UFL-B4 from Julian Day 200 to 260, 1991 274






B.28 The Spectral Density versus Frequency for the Water Surface El-
evation Data Measured at the Roberts Bay (USGS-04), Big Pass
USGS-05), Little Sarasota Bay (USGS-06) and Blackburn Bay
USGS-07) Stations for Julian Days 200 to 260, 1991 ...... 275

B.29 The Spectral Density versus Frequency for the Surface and Bottom
Current Vector Components at the UFL-B1 Station for Julian
Days 200 to 260, 1991 ...................... 276

B.30 The Spectral Density versus Frequency for the Surface and Bottom
Current Vector Components at the UFL-B2 Station for Julian
Days 200 to 260, 1991 ........................ 277

B.31 The Spectral Density versus Frequency for the Surface and Bottom
Current Vector Components at the UFL-B3 Station for Julian
Days 200 to 260, 1991 ........................ 278

B.32 The Spectral Density versus Frequency for the Surface and Bottom
Current Vector Components at the UFL-B4 Station for Julian
Days 200 to 260, 1991 ........................ 279

B.33 The Spectral Density versus Frequency for the Wind Speed Com-
ponents at the UFL-B1 and UFL-B2 Stations for Julian Days 200
to 260, 1991 . . . . . . .. 280

B.34 The Spectral Density versus Frequency for the Wind Speed Com-
ponents at the UFL-B3 and UFL-B4 Stations for Julian Days 200
to 260, 1991 . . . . . . .. 281

C.1 An Idealized Representation of the Vertical and Horizontal Grid
Structure .. . .. .. ... .. .. . ...... 283


xvii











LIST OF TABLES


2.1 A Summary of Historic Studies of Tides and Currents within Shal-
low Barrier Island Lagoons ..................... 27

3.1 The locations and depths of the University of Florida Stations 33

3.2 Instrument elevations on the University of Florida platforms, 1991
deployment .............................. 33

3.3 The locations of the USGS tidal data stations. . ... 39

3.4 Benchmarks used to verify elevations of USGS tide gauges . 39

4.1 The distribution of tidal energy across the primary and secondary
frequency bands, 1990 data . . . . ... 63

4.2 The distribution of tidal energy across the primary and secondary
frequency bands, 1991 data ..................... 63

4.3 The distribution of current energy ((cm/sec)2- sec) across the pri-
mary and secondary frequency bands, 1991 data (values in paren-
thesis represent percentage) . . . . ... 67

4.4 A list of the harmonic constituents analyzed . . ... 70

4.5 The harmonic constituents calculated from the 1990 tidal data .71

4.6 The harmonic constituents, 1991 tidal data . . .... 72

4.7 The principal axes harmonic constituent amplitudes, phases and
axis directions for station UFL-B1, Julian Day 200 to 260 . 78

4.8 The principal axes harmonic constituent amplitudes, phases and
axis directions for Station UFL-B2, Julian Day 200 to 260 . 79

4.9 The principal axes harmonic constituent amplitudes, phases and
axis directions for Station UFL-B3, Julian Day 200 to 260 . 83

4.10 The principal axes harmonic constituent amplitudes, phases and
axis directions for station UFL-B4, Julian Day 200 to 260 . 85

4.11 The measured maximum discharges through Anna Maria Sound,
Longboat Pass, New Pass and Big Pass, Julian Days 148 to 150,
1992. . . . . . . . .. 104


xviii






4.12 The calculated discharges through Anna Maria Sound, Longboat
Pass, New Pass, Big Pass, Roberts Bay and Blackburn Bay, Julian
Day 149, 1992.. ......................... 105

6.1 The average wind speeds and wind stresses at the four UFL bay
stations . . .. . . . . .. 144

6.2 The RMS errors between the measured and simulated water sur-
face elevations, Julian Day 200 to 230, 1991 . . ... 150

6.3 The RMS errors between the measured and simulated bottom and
surface east-west and north-south current components, Julian Day
200 to 230, 1991 .. .. ......... .. ... ....... 152

6.4 A comparison of the measured and simulated total spectral energy
and the percent distribution of energy between the sub-tidal, diur-
nal, semi-diurnal and third-diurnal bands for the water surface el-
evations measured at stations USGS-04, USGS-05, USGS-06, and
USGS07, Julian Day 200 to 230, 1991 . . . ... 159

6.5 A comparison of the measured and simulated total spectral energy
and the percent distribution of energy between the sub-tidal, di-
urnal, semi-diurnal and third-diurnal bands for the July/August
1991 simulations at station UFL-B1 . . . ... 159

6.6 A comparison of the measured and simulated total spectral energy
and the percent distribution of energy between the sub-tidal, di-
urnal, semi-diurnal and third-diurnal bands for the July/August
1991 simulations at station UFL-B2 . . . ... 160

6.7 A comparison of the measured and simulated total spectral energy
and the percent distribution of energy between the sub-tidal, di-
urnal, semi-diurnal and third-diurnal bands for the July/August
1991 simulations at station UFL-B3 . . . ... 161

6.8 A comparison of the measured and simulated total spectral energy
and the percent distribution of energy between the sub-tidal, di-
urnal, semi-diurnal and third-diurnal bands for the July/August
1991 simulations at station UFL-B4 . ......... 161

6.9 A comparison between the measured and simulated harmonic tidal
constituents for the July/August 1991 data . . .... 163

6.10 A comparison between the measured and simulated harmonic cur-
rent constituents for the July/August 1991 data at UFL-B1 167

6.11 A comparison between the measured and simulated harmonic cur-
rent constituents for the July/August 1991 data at UFL-B2 169

6.12 A comparison between the measured and simulated harmonic cur-
rent constituents for the July/August 1991 data at UFL-B3 170







6.13 A comparison between the measured and simulated harmonic cur-
rent constituents for the July/August 1991 data at UFL-B4 172

6.14 The mean water surface elevation predicted by the model for Ju-
lian Day 200 to 230, 1991 ...................... 173

6.15 A comparison of the measured and simulated mean currents for
Julian Day 200 to 230, 1991 ..................... 176

6.16 A comparison of the percent of the total discharge through the
inlets to Sarasota Bay and Anna Maria Sound between the calcu-
lated discharges for 1992 and the simulated discharges for Julian
Days 200 to 230, 1991 ........................ 186

6.17 A Listing of the Critical Model Input Values used within the Sen-
sitivity Tests . . . .. . . .. 193

6.18 A Comparison of Tidal Harmonic Constituents Under Varying
Bottom Roughness Height, Base Value = 0.8 cm, Low Value =
0.02 cm, High Value = 2.0 cm (USGS-04, USGS-05, USGS-06) 195

6.19 A Comparison of the Principal Axis Current Harmonic Amplitudes
Under Varying Bottom Roughness Height, Base Value = 0.8 cm,
Low Value = 0.02 cm, High Value = 2.0 cm (UFL-B2, UFL-B3) 196

6.20 A Comparison of Mean Water Surface Elevation Under Varying
Bottom Roughness Height, Base Value = 0.8 cm, Low Value =
0.02 cm, High Value = 2.0 cm (USGS-04, USGS-05, USGS-06) 197

6.21 A Comparison of Residual Velocity Components Under Varying
Bottom Roughness Height, Base Value = 0.8 cm, Low Value =
0.02 cm, High Value = 2.0 cm (UFL-B2, UFL-B3) . ... 197

6.22 A Comparison of Tidal Harmonic Constituents Under Varying
Horizontal Eddy Coefficient Base Value = 50000 cm2 seccm,
Low Value = 5000 cm2 sec, High Value = 100000 cm2 sec
(USGS-04, USGS-05, USGS-06) . . . ..... 198

6.23 A Comparison of the Principal Axis Current Harmonic Amplitudes
Under Varying Horizontal Eddy Coefficient, Base Value = 50000
cm2 sec, Low Value = 5000 cm2 sec, High Value = 100000
cm2 sec (UFL-B2, UFL-B3) ................... 199

6.24 A Comparison of Mean Water Surface Elevation Under Varying
Bottom Roughness Height, Base Value = 50000 cm2 sec, Low
Value = 5000 cm2-sec, High Value = 100000 cm2-sec (USGS-04,
USGS-05, USGS-06) ......................... 200

6.25 A Comparison of Residual Velocity Components at Under Varying
Horizontal Eddy Coefficient, Base Value = 50000 cm2 sec, Low
Value = 5000 cm2- sec, High Value = 100000 cm2- sec (UFL-B2,
U FL-B3) . . . . . . .. 201







6.26 A Comparison of Tidal Harmonic Constituents using Constant
Vertical Eddy Viscosity (10 cm2 sec) versus a Second Order
Closure Model (USGS-04, USGS-05, USGS-06) . ... 202

6.27 A Comparison of the Principal Axis Current Harmonic Amplitudes
Using Constant Vertical Eddy Viscosity (10 cm2 sec) Versus a
Second Order Closure Model (UFL-B2, UFL-B3) . ... 203

6.28 A Comparison of Mean Water Surface Elevation Under Constant
Vertical Eddy Viscosity (10 2) versus a Second Order Closure
Model (USGS-04, USGS-05, USGS-06) . . ..... 204

6.29 A Comparison of Residual Velocity Components using Constant
Vertical Eddy Viscosity versus a Second Order Closure Model
(UFL-B2, UFL-B3) ......................... 204

6.30 A Comparison of the RMS Errors Between the Measured Tides
and Currents and Simulated Tides and Currents Using Four Ver-
tical Layers and Eight Vertical Layers. . . .... 207

A.1 Calibration runs for the Marsh-Mcbirney current sensors ..... 232

A.2 Calibration runs for the Marsh-Mcbirney current sensors ..... 233

A.3 Calibration coefficients for Marsh-Mcbirney current sensors 234











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

CIRCULATION AND TRANSPORT WITHIN A SYSTEM OF SHALLOW,
INTERCONNECTED BARRIER ISLAND LAGOONS

By

STEVEN J. PEENE

August 1995
Chairman: Dr. Y. Peter Sheng
Major Department: Coastal and Oceanographic Engineering

Data of water surface elevations, currents, winds, discharges and salinities collected

throughout a system of interconnected shallow barrier island lagoons are analyzed

to describe the circulation and transport processes. In addition, a three-dimensional

curvilinear model, representing the Sarasota Bay System, is calibrated to the data,

tested for sensitivity and used to isolate the forcing mechanisms driving the flow.

Spectral and harmonic analysis of the tides and currents quantified the distribu-

tion of energy across five frequency bands, the sub-tidal, diurnal, semi-diurnal, third

diurnal and fourth diurnal. The analyses showed that the inlets and constrictions act

as low pass filters for the tides reducing the semi-diurnal energies, while increasing

the semi-diurnal energy within the currents. The shift in current energy is driven by

the change from rotational flow within the Gulf to more unidirectional flow.

Currents within lagoons which receive tidal forcing from opposite directions ex-

hibit similar characteristics, such as increased residual flow energy, and equivalent

distribution of energy between the semi-diurnal and diurnal. Regions which are

forced more unidirectionally exhibit opposing characteristics. All regions no mat-

ter the depth exhibit some level of three-dimensionality in the currents, both in the

short term and residual flows.


xxii







Filtering of the winds, water levels and currents identified the driving mechanisms

for the residual fluctuations as Ekman Transport and local wind forcing. The Ekman

Transport acts within the lower frequency bands (7 to 10 days) while the local wind

forcing acts within higher bands (3 to 4 days).

The three-dimensional numerical model is calibrated to the collected data by

comparing the simulated energy distribution with those described above. The model

accurately simulates the short term tides and currents and captures the general char-

acteristics of the residual water level fluctuations and currents. The model is unable

to accurately simulate the absolute transport of salinity but succeeds in capturing

some of the general trends.

Finally, a term by term analysis of the equations of motion identified the primary

forcing mechanisms driving residual flow throughout the lagoons as wind and mean

water surface gradients.

The level of detail in the data analyses, the determination of the distribution of

energies and forcing mechanisms, as well as the quantification of the model accuracy

is largely unprecedented. This approach provides insight into the physics of the

overall circulation and transport within the shallow lagoons as well as quantifying

the capability of three-dimensional numerical models to simulate the complex flow

patterns.


'[vii











CHAPTER 1
INTRODUCTION


The study presented herein investigates the circulation and transport within a

multi-inlet barrier island lagoon system. The study focuses upon all aspects of the pro-

cesses which drive flow and transport utilizing collected data and a three-dimensional

numerical model.

1.1 Barrier Island Lagoons

Barrier islands and their associated lagoon systems can be found within coastal

plain environments throughout the world. They exist under varying morphologic con-

figurations along the east and west coasts of the United States, the northern coast of

Alaska, the Mediterranean Sea and even within the Great Lakes. The geologic forces

which created these protected lagoons have been the subject of debate within the

scientific community for many years. The first widely accepted theory was presented

by deBeaumont in 1845 (King, 1972) which stated that barrier islands (and therefore

the lagoons) were formed as offshore bar deposits which built up due to wave breaking

and eventually became islands trapping the waters behind them. In the early 1900's

this theory was tested and supported by Johnson (1919) and remained popular until

Hoyt (1967) proposed the idea that barrier lagoons were created by the most recent

sea level rise as lands behind former beach dunes and ridges were inundated.

Although the exact forces which created the lagoons remain in question, it is

generally accepted that barrier island lagoons exist within a wide range of tidal and

wave energy environments, and their morphology is highly dependent upon that en-

vironment. Hayes (1979) provides a generalized model of barrier islands and barrier

island lagoon morphology based upon the amount of hydrologic (tide and wave) en-





2
ergy expended upon a coastline. The classifications are; a macrotidal coast (tide range

greater than 4 meters), a mesotidal coast (tide range 2 4 meters), and a microtidal

coast (tide range less than 2 meters).

In general, barrier island lagoons do not exist along macrotidal coastlines. Bays

and estuaries along macrotidal coasts are instead dominated by wide openings and

broad expanses of salt marshes and mud flats. Lagoons along mesotidal coastlines

are characterized by tightly spaced multiple inlets due to the short stunted nature of

the barrier islands. Spacings between inlets within this environment are on the order

of 3 to 20 kilometers. Mesotidal lagoon formation and evolution are predominantly

driven by tidal forces which overshadow the effects of the waves. Microtidal lagoons

are generally very long and narrow with fewer inlet connections to the open ocean.

Spacings between inlets along microtidal coastlines are on the order of 30 to 100 kilo-

meters, and their formation and evolution are predominantly driven by wave forces.


1.2 General Circulation and Transport within Barrier Island Lagoons

As with morphology, the circulation and transport patterns observed within bar-

rier island lagoons are the product of the energy imparted by the forcing mechanisms

acting therein. These mechanisms include water surface gradients, wind stress, verti-

cal and horizontal density gradients and bottom friction. Acting in conjunction with

these forcing mechanisms, the multiple inlets, the varying bathymetry and geometry

all add to the overall complexity.

Generally the most visible forcing mechanism within barrier island lagoons is

the rise and fall of the water surface due to the tides. Tidal waves enter through the

multiple openings and create surface gradients which in turn drive flow. At first glance

tidal currents may appear to be symmetrical and a net transport nonexistent, but

tidal transport can be significant under the proper geometric conditions. Analytic and

numerical studies have shown this phenomena under idealized conditions (e.g., van






3
de Kreeke and Dean, 1975). Fisher (1979) defines two causes of net tidal transport,

"tidal pumping" and "tidal trapping." Tidal pumping occurs when the arrival of a

tidal wave to one opening proceeds the arrival at another within the same system.

The asymmetrical damping of the flow by bottom friction at high tide versus low

creates a net current from the leading inlet toward the lagging inlet. Tidal trapping

is a phenomenon which occurs due to the presence of side embayments and small

branching channels. During a flooding tide waters are trapped within these off-channel

features and separated from the main flow. Upon reversal of flow, the trapped waters

rejoin the flow in a new location and mixing occurs.

During normal weather conditions the magnitude of wind driven currents in bays

and estuaries are generally much smaller than their tidally driven counterparts, except

in locations which are far from an opening to the ocean. In contrast, the magnitude

of the wind driven residual currents can be of the same order of magnitude or greater

than the tidal residual. The application of winds over a water body can induce vertical

and horizontal circulation gyres. In the vertical, the wind stress acting at the surface

transports water in the direction of the wind creating a setup. To balance this force,

a return current which flows against the wind occurs along the bottom and a vertical

gyre is created. In a basin with a channel cut through the middle, the application

of wind stress upon the surface would create a horizontal gyre with flow traveling

with the wind along the shallow sides and return flow in the channel. Fischer (1979)

explains the physics behind this phenomena using a simplified estuary with a deep

channel running along one side. "The wind induces an approximately uniform stress

everywhere on the water surface. Therefore the line of action of the wind-induced

force is through the centroid of the water surface. The center of mass of the water in

the basin is displaced towards the deeper side, since there is more water there. Hence

the line of action of the force passes on the shallow side of the center of mass of the

water, and a torque is induced causing the water mass to rotate."3.






4
Density currents occur when waters of different temperature or salinity meet.

The gravitational force causes the higher density fluid to displace the other. The

classical circulation pattern occurs when higher density ocean waters move into a

drowned river valley and proceed upstream along the bottom as the fresher water

flows outward at the surface (Hansen and Rattray, 1967, van de Kreeke and Zimmer-

man, 1990). An excellent example of this situation exists within the Mississippi River

where it meets the Gulf of Mexico. Although in general vertical density gradients

are not primary forcing mechanisms within shallow barrier island lagoons, horizontal

density gradients may drive residual flows. This phenomena has been found to be

significant within Tampa Bay, a relatively shallow bay along the west coast of Florida.


1.3 Study Area Description

The focus of the studies presented herein is the circulation and transport within a

series of shallow interconnected barrier island lagoons situated along the western coast

of central Florida. Referred to for the purposes of this study as the "Sarasota Bay

System", the lagoons consist of Anna Maria Sound, Sarasota Bay, Roberts Bay, Little

Sarasota Bay and Blackburn Bay. Figure 1.1 presents a map showing the location of

the Sarasota Bay System relative to the State of Florida and the Gulf of Mexico.

The west coast of Florida has generally been classified as a mixed energy, wave

dominated environment, exhibiting an increased number of tidal inlets over classic

microtidal wave dominated systems (Hayes, 1979). For the Sarasota Bay System, five

barrier islands, totaling 54 kilometers in length, separate the interior lagoons from

the Gulf of Mexico. These are, from north to south, Anna Maria Island, Longboat

Key, Lido Key, Siesta Key and Casey Key. Examination of their shapes shows both

mesotidal (short stunted islands, Lido Key) and microtidal (long linear islands, Long-

boat Key) characteristics. The four inlets which connect the lagoons to the Gulf of

Mexico (Longboat Pass, New Pass, Big Pass and Venice Inlet) have spacings which




















































Figure 1.1: A site map of the Sarasota Bay System and its location relative to the
State of Florida and the Gulf of Mexico





6
range from less than 3 kilometers (New Pass to Big Pass) to more than 25 kilometers

(Big Pass to Venice Inlet). A fifth inlet (Midnight Pass) existed as recently as 1980

between Venice Inlet and Big Pass but it closed due to migration and infilling. An-

other tidal opening exists at the north end of the system where Anna Maria Sound

meets the southwest side of Tampa Bay.

The bathymetry within the Sarasota Bay System varies from lagoon to lagoon.

Anna Maria Sound is characterized by shallow waters and sea grass flats with average

depths ranging from 1 to 2 meters at mean water level. The deepest waters are found

within the Intracoastal Waterway (3 to 4 meters) and these must be maintained by

dredging.

The most open water body water is Sarasota Bay with an average width of 4

kilometers and depths ranging from 3 to 4 meters. Much of the shoreline has been

modified through the construction of seawalls, infilling of seagrass flats and excavation

of canals and channels. This is most pronounced immediately south of Sarasota Bay

where the islands of Bird Key and St. Armands were originally extensive seagrass

beds but were filled in for development purposes and their shorelines hardened.

South of Big Pass; Roberts Bay, Little Sarasota Bay and Blackburn Bay have

similar bathymetric and geometric features. All three lagoons are characterized by

very shallow tidal flats (0.5 to 1.5 meters at mean water level) and narrow widths

with the Intracoastal Waterway running longitudinally along their north-south axes.

These lagoons are in essence a self-contained system with only two tidal openings,

one at the north end which opens toward Big Pass, and one at the south end which

opens into the Gulf of Mexico.


1.4 Statement of Purpose

The Sarasota Bay System, as with many other coastal waters, has come under

increasing development pressure due to man's desire to live near or on the water.






7

As urbanization of the lands surrounding the lagoons increases, pollutant loadings

from residential, commercial and industrial runoff as well as sewage discharges from

the many package treatment plants, also increases. In the past it was assumed that

these systems were able to assimilate the waste loads without deterioration, but re-

cent studies have shown that water quality within the system is degrading with an

associated decline in fisheries and other habitats.

The first step in any study of water quality is the quantification of the circu-

lation and transport mechanisms. These determine the assimilative capacity of the

water body through flushing and transport of contaminants. Other aspects of the

water quality which are directly linked to the currents and tides include reaeration of

the water column, resuspension and deposition of bottom material, and many other

phenomena.

Since 1990, the Coastal and Oceanographic Engineering Department of the Uni-

versity of Florida, under the supervision of Dr. Y. Peter Sheng, embarked on a field

and modeling study of the circulation and transport in the Sarasota Bay system.

The study was supported by the Sarasota Bay National Estuary Program (SBNEP)

through the United States Geological Survey (USGS) (Sheng and Peene, 1992). The

purpose of the Sarasota Bay System Study included the general circulation, the effect

of opening Midnight Pass on the circulation and flushing of the southern lagoons and

the effect of freshwater inflow from the Manatee River on the circulation and trans-

port. The focus of this dissertation, which is part of the overall study, is a detailed

and comprehensive investigation of the tides and currents within the entire Sarasota

Bay System.

As was stated earlier, the water surface elevation fluctuations and the currents

within the Sarasota Bay System have multiple components which may be driven by

the actions of the tides, wind, density gradients and other forcing mechanisms. In

addition, each component is altered by the interaction of the flowing waters with the






8
complex geometry and bathymetry throughout the lagoons. These multiple compo-

nents superimpose upon one another to create the overall circulation and transport

patterns which are observed. The goal of this study, therefore, is to develop an im-

proved understanding of the overall circulation and transport within the Sarasota Bay

System through the quantification of these individual components and the determi-

nation of the relative influence of the forcing mechanisms defined above.

Field data and a numerical model are utilized to achieve this goal. An extensive

data set was collected by the Coastal and Oceanographic Engineering Department of

the University of Florida in 1991. Other data utilized for this study were collected by

USGS and the National Oceanographic and Atmospheric Administration (NOAA).

Chapter 3 presents a description of the data collected by UF and USGS. In Chapter

4 the data are systematically analyzed to isolate and quantify the relative impacts of

the individual forcing mechanisms.
The second tool is a three-dimensional numerical circulation and transport model

developed by Dr. Y. Peter Sheng. The model was modified and applied to the study

area described above. Once calibrated to the data, it allows a more spatially intensive

determination of the circulation and transport. In addition, the relative impacts of

the forcing mechanisms can be isolated and tested through iterative and sensitivity

runs of the model.


1.5 Presentation Outline

The following chapter highlights past efforts, both analytical and numerical, which

attempt to quantify the circulation and transport patterns within shallow barrier

island lagoons. Chapter 3 describes the data collection methodologies utilized by the

University of Florida and the United States Geological Survey. Chapter 4 presents

the analysis of the data. Chapter 5 presents a brief summary of the formulation of the

equations used in the model. Chapter 6 presents the calibration and sensitivity testing





9
of the numerical model along with applications of the model to define the overall

circulation patterns and the relative impacts of the individual forcing mechanisms.

Chapter 7 presents a summary of the work performed and conclusions drawn from

this study.











CHAPTER 2
LITERATURE REVIEW


A large body of literature exists concerning studies of circulation and transport

phenomena in estuarine systems, including drowned river valleys, fjords, lagoons and

bays in macro-, meso- or micro-tidal environments. These studies include the devel-

opment and application of numerical and analytical models as well as the collection

and analyses of field data of winds, tides, currents, temperature, salinity and other

physical parameters. In an effort to limit the review of literature, and to focus upon

those papers which relate directly to the work within this study, this review will

concentrate on research related to the physics of circulation and transport within

shallow, micro/mesotidal barrier island lagoons. Papers whose primary focus is the

development of numerical or analytical models, instead of quantification of the phys-

ical processes of circulation and transport, are not included.


2.1 Analyses of Field Measurements

Kjerfve (1975) studied the response of the water surface elevation within a Louisiana

bar-built estuary to tidal and fair weather wind inputs. Water levels were measured

at three stations, while winds were measured at a single station. The wind station

historically contained a six-level anemometer system which allowed detailed quantifi-

cation of the vertical wind profile. The initial study used the logarithmic law of the

wall to define the friction velocity at the water surface. The relationship between the

wind velocity at 6.77 meters and the friction velocity was developed through analysis

of 386 wind profiles. This relationship was used to quantify the wind stress due to

winds measured at 6.77 meters in the 1975 study. This later study found that tidal





11

dynamics dominate the flow for short term fluctuations, but for the sub-tidal varia-

tions it was found that the wind, through the creation of Ekman transport toward

the coastline, created water level variations on the order of 24 cm inside the estuary.

Smith (1979) measured and analyzed currents, water levels and winds in the

region of Aransas Pass, Texas, over a 45 day period to describe the tidal and low

frequency motions within the bay. The data showed that tides in that region are mixed

diurnal/semi-diurnal with dominance in the diurnal tides. The measured currents

showed a stronger diurnal signal in percentage than the measured tides. The data

were filtered using a low pass filter with a cutoff frequency equivalent to a 48-hour

period. The resulting long term fluctuations in water level showed a strong coherence

with cross-shore winds indicating the presence of wind set-up and set-down. Some

coherence between the alongshore winds and the fluctuations within the bay were

found but at very long time scales (greater than 10 days). This indicated portions

of the variations in mean tide were due to the propagation of low frequency waves

within the Gulf of Mexico driven by Ekman transport.

During the 1980s Smith conducted a series of field studies to quantify the tides

and currents within Indian River Lagoon, which is a micro-tidal barrier island lagoon

along the east coast of Florida. Smith (1980) compared tides measured offshore to

tides measured just inside Fort Pierce Inlet. The data showed that as the tidal wave

propagates toward and through the inlet, the semi-diurnal harmonic constituent (M2)
is damped to a greater degree than the diurnal constituents (K1 and O1), i.e. the

inlet acts as a low pass filter for the tidal wave. Similar results were found in a study

of water level dynamics over a 25 year period at 23 stations along the Indian River

Lagoon (Smith, 1987). The results were presented in terms of the "form number"

at various locations within the lagoon. The form number represents the ratio of the

diurnal to semi-diurnal tidal amplitudes and was calculated using the formula,

01 + K1
F = (2.1)
M2 + S2





12

where Ox and K1 are the amplitudes of the principal diurnal harmonic constituents,

and M2 and S2 are the amplitudes of the principal semi-diurnal constituents. The

results showed that the semi-diurnal constituents were damped to a greater degree

and the form numbers increased as the tidal waves traveled through the inlets and

further into the lagoon.

In another study, Smith (1983) analyzed 32 days of current data from 4 stations

along the Intracoastal Waterway between Ft. Pierce Inlet and Sebastian Inlet. The

stations were spaced evenly 8 km apart. The current data, along with winds measured

at the Vero Beach Municipal Airport, were filtered using a low pass filter with a cutoff

frequency equivalent to a 48 hour period. The filtered currents showed significant

coherence with the along channel winds and Smith surmised that local wind forcing

was a significant transport mechanism within this portion of the Indian River lagoon.

Comparison of the percent sub-tidal (more than 48 hour period) energies from the

station nearest to Ft. Pierce Inlet with the station farthest interior to the bay showed

a percentage increase ranging from 1 to 27 percent.

A similar study was performed using data from a single current meter moored

within the Intracoastal Waterway between St. Lucie Inlet and Ft. Pierce Inlet (Smith,

1985). The station was 25 kilometers from the nearest inlet. The data were analyzed

using a harmonic analysis program and the purely tidal currents were subtracted

from the raw data to provide the wind driven currents. Additionally, the influence

of the tidal currents upon the wind stress (i.e. alterations in wind stress due to tidal

currents opposing or flowing with the winds) were removed along with the nonlinear

interactions due to bottom friction. The remaining currents were the pure nontidal

components. Comparison of data with a simple one-dimensional wind model produced

a correlation coefficient of 0.66. The results indicated that tidal forcing accounted for

45 percent of the total variance at the study site, while local wind forcing constituted

45 percent. The remaining energies were attributed to freshwater inflow and non-local







forcing mechanisms.

van de Kreeke and Wang (1984) analyzed data from 4 tide gages installed within

the northern portion of Biscayne Bay. The northern part of the bay is characterized

by shallow waters with the Intracoastal Waterway running longitudinally along its

axis. Multiple causeways cross the bay, effectively separating it into 5 water bodies

interconnected by narrow openings. Harmonic analyses of the tides were performed

and the results analyzed to define the relative contributions from the various harmonic

constituents. The data showed the M2 constituent to be the dominant harmonic

with some measured higher harmonic overtides at the M4 frequency. A net 3-4 cm

set-up was measured in the bay and this was attributed to interaction between the

incoming tidal wave and the reflected tidal wave from the northern end of the bay.

The correlation coefficient between the measured tides and the tides calculated from

the harmonic constituents indicated that the tidal harmonics account for 95 percent

of the tidal energy within the bay. The remaining 5 percent of the variations were

attributed to longer scale meteorological forcing.

In addition to the tidal measurements, currents were measured within Bakers

Haulover Inlet and Government Cut which connect Biscayne Bay to the Atlantic

Ocean. The conveyance factors (C) were calculated for each inlet based upon the

equations

Q = CRS (2.2)
A1
2gL
S 2L (2.3)
S 2fL + mR

where Q is the flow rate, AI is the cross-sectional area of the inlet, S is the hydraulic

gradient, R is the hydraulic radius, L is the inlet length, m is the entrance and exit

loss friction coefficient, and f is the friction factor

f = b (2.4)
pU2





14

where, rb is the bottom shear stress, U, is the cross-sectionally averaged velocity and

p is the fluid density. Based upon the magnitude of the conveyance factors it was

determined that tidal asymmetry existed at the two inlets. This asymmetry favored

a net flow from Bakers Haulover Inlet to Government Cut.

The tidal amplitude to depth ratio has been found to be a critical parameter

determining the significance of non-linear interactions for tides and currents (Aubrey

and Speer, 1985, Aubrey and Friedrichs, 1988). In lagoons where this ratio is relatively

large, the non-linearity created through bottom friction, inertial forcing and other

sources can become significant. A number of field studies (Aubrey and Speer, 1985,

Aubrey and Friedrichs, 1988) have been conducted to determine the significance of

non-linear interactions upon the tides and currents within micro/mesotidal barrier

island lagoons. The following presents results from those studies.

Harmonic analysis of tides and currents collected at multiple stations within the

Nauset Harbor Estuary system in Massachusetts (Aubrey and Speer, 1985) was per-

formed to determine the spatial variations in the M4/M2 amplitude ratio and the

(2M2-M4) phase relation. Along coastlines where the dominant tidal constituent is

the semi-diurnal M2 component, the predominant overtime or higher harmonic is the

M4 constituent. Consequently the M4/M2 ratio is an indication of the level of non-

linearity or asymmetry. The 2M2-M4 phase relation in this case indicates the sense of

the asymmetry. For 2M2-M4 between 0 degrees and 180 degrees, the falling or ebbing

tide is longer than the rising or flood tide. For a phase relationship between 180

degrees and 360 degrees, the rising or flood tide is longer than the ebb. Considering

an inlet, if the ebb tide lasts longer the flooding tide will have stronger velocities in

order to maintain continuity; this situation is termed flood dominance. The opposite

situation is termed ebb dominance.

Analyses of the tides and currents within Nauset Harbor indicated flood domi-

nance throughout the entire system. This flood dominance is phase locked in that the





15

2M2-M4 phase relationship remains constant at 60-70 degrees throughout the system.

Additionally, Speer and Aubrey found a fortnightly tidal component MSf with a 10

cm amplitude. This component created lower mean water levels during neap tide as

versus spring tide. It was surmised that this variation in water level will impact the

degree of non-linearity as the depth to tidal amplitude ratio (a/h) will change.

Boon (1988) utilized complex demodulation of predicted and measured tides at

Wachapreague, Virginia, to determine the temporal variations in the amplitudes of

the tidal asymmetries (M4/M2 ratio) and the phase relationships (2M2-M4). The

predicted tidal signals were generated from harmonic constituents calculated from

the measured data. The amplitude ratio was shown to have a significant seasonal

variation with a range of values from 0.02 to 0.08. The phase relationships did not,

however, show significant temporal variations. The demodulation showed that the

amplitude of the quarter-diurnal tide (M4) varies as the square of the amplitude of

the semi-diurnal tide (M2).

Aubrey and Friedrichs (1988) used recorded sea level data over a 16 month period

at Murrells, South Carolina along with a simple one-dimensional numerical model
to study the changes in tidal asymmetry due to variations in mean sea level and

tidal amplitudes of the primary harmonic constituents. Analyses of the data showed

that as the tidal amplitude to depth ratio increased, as the result of increased tidal

amplitude, the tidal distortion became more flood dominant. For long term sea level

fluctuations they showed that the tidal asymmetry changes were highly dependent

upon the extent of tidal flats adjacent to the channel. In areas with extensive tidal

flats, as a/h decreased, the tidal asymmetry or flood dominant nature of the system

increased. In areas with small tidal flats, as a/h increased, the flood dominance

increased.

Seim and Sneed (1988) performed harmonic analysis of current and tidal data

collected within the Mississippi Sound and the adjacent continental shelf from 1980





16
to 1981. They computed the form numbers using equation 2.1, and calculated the
ratios of the form numbers for the tides and currents measured on the continental
shelf with those measured inside the inlets. The ratios for the currents were as low as

0.5, i.e., the inlets showed a much higher predominance of semi-diurnal tidal energy
in the currents. The tides showed little change from offshore to the inlets. Inside of
the bay the form number ratio for the currents increased back toward that found from
the offshore data. This phenomenon was examined through theoretical derivations of

the form numbers derived for Sverdrup waves and uniform flow through an inlet. The
theoretically derived form numbers indicated that maintaining continuity through the
inlet caused the semi-diurnal currents to increase relative to the diurnal as the tidal
wave progressed from a 2-D rotational region to a 1-D unidirectional region. The
authors speculated that this phenomenon will occur in all regions with narrow inlets
and mixed offshore tides.


2.2 Simplified Analytic Solutions and Numerical Models

A series of studies conducted in the 1970s (van de Kreeke 1971, Cotter 1974,
van de Kreeke and Cotter 1974, van de Kreeke and Dean 1975) quantified the net
discharge in a simplified canal open to tidal forcing at two ends; the tides at the two
ends were forced through idealized inlets. The canal/inlets are a representation of
the many multiple inlet lagoon systems throughout the State of Florida. Figure 2.1
presents the geometry of the idealized system. The basic equations solved for in the
canal are the simplified one-dimensional equations of motion and transport

( 8aQ
b + = 0 (2.5)
at ax
aQ + ( 1 aQ2 -fQQb
+ gA + (2.6)
aOt Ox A- ax A

where b is the width of the lagoon, C is the water surface elevation, Q is the discharge,
g is the acceleration due to gravity, AI is the cross-sectional area b(h + (), h is the







depth, and f is the friction factor.

Within the inlets the equation used to describe the flow is the semi-empirical

equation

a( -f1QQb
gA x A (2.7)

where, fi is the friction coefficient for the inlet and accounts for lateral and bottom

friction as well as the entrance and exit losses.

In each of the studies listed above, the equations were solved numerically using

finite difference techniques for the net discharge, Q., through the canal such that

1/
Q. = Qdx (2.8)
T o

The forcing of the tides occurs at the ocean side of the idealized inlets and is

defined as

C( = alcos(at + 6) (2.9)

(4 = a4cos(at) (2.10)

where ( is the water surface elevation, a- is the frequency of the forcing tide (generally

12.42 hours, M2), a is the amplitude of the forcing tide and 5 is a phase lag in degrees.

To determine the impacts of various geometric conditions on the net discharge,

specific parameters were varied while all others were held constant. Figure 2.1 presents

the results for varying relative depth, width and length of the two inlets. The plots

show that transport occurs toward the inlet with the lesser depth, the lesser width

and longer length. For a phase lag between the two inlets the transport is toward

the lagging inlet. The tide induced transport is shown to be proportional to (a2/h2),

therefore a significant net transport will only occur for a large tidal amplitude to

depth ratio, i.e. in shallow lagoons.

In order to allow for analytic solutions of these simplified equations, the friction

term is linearized. Comparison of the analytic solutions to the numerical solutions
























LAGOON


200.
10 .


I
I


I I


INLET IT


- DEPTH OF INLET =( CFT.)


300


20I

Ioo I

DT C
| I WIDTH OP INL.LT X rPT)


100 1


-Z=03


oo600 loOQ 16oo Oo


FOR. CONFIGURATION OF LA0GON- INLLT
a SYSTEM W. FIGURl. I
FOR. NUMEARJCAL VALUES USiE IN
THE. COMPUTATIONS S.E. ABLE. I


Figure 2.1: The idealized geometry for the canal/inlet system utilized in the study
by van de Kreeke, along with the variation in the net discharge as a function of inlet
depth, width and length (van de Kreeke and Cotter, 1974)


INLET I


I


1 I


II


I


1


L~u


I-U





19

indicates that while the results maintain the same general form, linearization of the

friction terms introduces significant error in systems with large amplitude to depth

ratios (a/h much greater than 0).

Johnson and Lee (1977) investigated the influence of horizontal density gradi-

ents on residual velocities and flushing within Biscayne Bay and Card Sound. They

solved simplified versions of the momentum, continuity and conservation of density

equations within an idealized representation of the two water bodies. The results

indicated that residence times for density induced motion was on the order of 20 to

1000 years. Comparison with residence times calculated from wind and tide induced

flow (3 months) showed that density induced motion plays a very small part in the

flushing of Biscayne Bay.

Dronkers (1978) studied the longitudinal dispersion created by the filling and

draining of tidal flats alongside of dredged navigation channels. He found that in

estuaries which have significant tidal flats the dispersion is the result of three phe-

nomena. The first is mixing of waters propagating over the shallow tidal flat areas.

The geometric variability, presence of sea grasses and marsh grass, and bottom fric-

tion combine to create significant mixing. The second phenomenon is the exchange

of water between the tidal flats and the channel due to means other than the rise

and fall of the tides, i.e. density currents and horizontal eddies. The third and final

method is due to a phase shift between the tides and the currents; this causes the

channel to flow out prior to drainage of the tidal flats, which creates mixing similar

to the "trapping" phenomena presented in Chapter 1.

Moody (1988) integrated a simplified form of the 1-D equation of motion ignoring

the inertial terms. He defined an equation which relates the square of the ratio of the

bay amplitude to the ocean amplitude to a dimensionless number


L2 = CQI


(2.11)







where

L = -b (2.12)

is termed the amplitude response; it relates the bay amplitude ((b) to the ocean
amplitude (,,), and

QI= (2g ) (AI2 (2.13)
QW2 JAb

is a dimensionless parameter in which A, is the inlet cross-sectional area, Ab is the
surface area of the bay, and w is the frequency of the tidal wave. The author calculated
the value of QI for six inlets on or near Cape Cod, Massachusetts, and for 12 tidal
constituents (01,K1,N2,M2,S2,MK3, MN4,M4,MS4MK4,M6,M 8) and fit the results
by linear regression to the equation:

ln(L2) = ln(cQm) (2.14)

Three separate linear regressions were performed. The first only included the diurnal
and semi-diurnal constituents, which gave a value of m = 0.59 and c = 0.11, with a
correlation coefficient of 0.808. The second was for all of the constituents, which gave
a value of m = 0.92 and c = 0.09 with a correlation coefficient of 0.839. The third
was made excluding overtides within inlets which had an excessive area of tidal flats,
which gave a value of m = 0.72 and c = 0.07. The study concluded that small-scale
inlets act as amplitude and frequency dependent tidal filters and the bay response
can be closely simulated by a simple quadratic response function.
Speer and Aubrey (1985), Aubrey and Friedrichs (1988), Friedrichs and Aubrey
(1988), and Speer, Aubrey and Friedrichs (1991) examined the tidal asymmetry in
shallow inlet/bay systems using numerical solutions of the simplified 1-D equations of
continuity and momentum. The equations include flooding and drying of tidal flats
and are of the form
aU, a U2 7b p
S+ U gA P (2.15)
at xO At ox p
























Figure 2.2: The idealized channel geometry used in the solution of the 1-D Equations
of Momentum and Continuity (Speer and Aubrey, 1985)

9( 1 a9U
-t-+ =b x 0 (2.16)
at b Bz

where ( is the sea surface elevation, g is the acceleration of gravity, b is the channel
width, U, is the cross-sectional flux, rb is the average shear stress on the boundaries,

P is the wetted channel perimeter, A is the channel cross-sectional area and p is the

water density. The bottom friction, Tb, is calculated using the quadratic stress law

b = pUU (2.17)

where, f is a dimensionless friction factor. Figure 2.2 shows the idealized channel

used in the solutions.

Speer and Aubrey (1985) found that for a/h less than 0.3 all systems were flood

dominant. For a/h = 0.1 to 0.2 the systems were flood dominant if tidal flats were

not extensive. The addition of tidal flats to the system when a/h = 0.1 to 0.2 brought

the system from flood dominance to ebb dominance.

Friedrichs and Aubrey (1988) analyzed the estuary length, depth, ocean M2 am-

plitude, a/h and marsh storage volume to channel volume ratio (V,/Ve) for 26 separate

systems and applied the one-dimensional numerical solution. Based upon these solu-





22
tions, the authors determined that a/h is the primary determining factor in the type

of estuary (flood or ebb dominant), i.e. for a/h less than 0.2 it is an ebb dominant

system, for a/h greater than 0.2 and a/h less than 0.3 the type of system can be

determined by the channel volume to marsh storage volume ratio, for a/h greater

than 0.3 the systems are flood dominant.

Speer, Aubrey and Friedrichs (1991) extended the application of the simplified 1-

D equations to a special class of flood-dominant estuaries in which estuarine channels

shoal over short distances to depths less than the offshore tidal amplitude. The tidal

asymmetry within these types of systems exhibit high M4/M2 ratios (0.3 to 0.4) and

low M2 to M4 relative phases (5 to 35 degrees).

Friedrichs and Madsen (1992) solved the equations of motion and continuity as-

suming the non-linear terms are negligible. They utilized a channel similar to that

shown in Figure 2.2. Solving for the velocity within the simplified momentum equa-

tion, and inserting it into the continuity equation, gave a non-linear diffusion equation

of the form

9( 1 9 bh 9(
t n =0 (2.18)

where n is Manning's friction coefficient and be is the channel width. The term within

the parenthesis and to the left of the spatial derivative is comparable to the diffusion

coefficient seen in the standard equations of motion. This equation was solved analyt-

ically and numerically and compared with numerical solutions of the 1-D continuity

and momentum equations. The first-order solutions to the equation were obtained

by assuming a constant diffusion coefficient. The second order solution was obtained

by assuming that the diffusion coefficient is variable in time but constant in space.

Comparison of the analytic solutions of the zero-inertia equations of motion with nu-

merical solutions of the full 1-D equations showed that this equation reproduced the

main features of the nonlinear tidal signal observed in shallow lagoons.






23
Sheng, Peene and Liu (1991) applied a one-dimensional numerical model over

the entire Indian River Lagoon to determine the tide and wind driven circulation.

The model was forced through the multiple inlets within the system and defined the

currents under the conditions of no wind and along channel wind forcing.

2.3 Multidimensional Modeling

Wang and Swakon (1977) applied a 2-D finite element model in the study of

tides and currents within the southern portion of Biscayne Bay. The model utilized

tidal and wind forcing to drive the simulations. The model was used to study the

advective transport within the bay. The results indicated that, although tides define

the primary transport mechanisms for short term fluctuations, the wind is the primary

driving mechanism in the long term transport and therefore the flushing of the system.

Sheng (1983) used a three-dimensional numerical model to study the tidal and
wind-driven circulation and sediment transport in Mississippi Sound, a shallow barrier

island lagoon along the Mississippi coast of the Gulf of Mexico. The model domain

included an area approximately 220 kilometers by 120 kilometers. To produce the

open boundary condition for the circulation model, Sheng used the tidal constituents

simulated by Reid and Whittaker's (1981) Gulf tide model along the deep offshore

water which is 60 kilometers offshore of the barrier islands. The model was able

to accurately simulate the measured dynamics of the water level and currents in

the Mississippi Sound. Significant currents inside the tidal inlets were found to be

sufficient to cause sediment erosion and resuspension.

van de Kreeke and Wang (1984, 1986) investigated the flow within the north-

ern portion of Biscayne Bay using a nested 1-D/2-D numerical model. The one-

dimensional model was applied over the entire bay, while the two-dimensional model

was applied to the individual bodies of water connected through the causeways. The

one-dimensional model was used to develop tidal forcing at the causeway openings

for the two-dimensional model while maintaining conservation of energy and mass





24
throughout the system. The model results verified the existence of a net residual flow

from Bakers Haulover Inlet toward Government Cut as discussed in the earlier field

measurement section. The residual was attributed to phase and amplitude differences

between the two inlets. Flushing of the various interconnected water bodies was cal-

culated using the model. The results indicated an exchange period of 1-2 weeks which

is highly dependent upon local wind forcing, i.e. whether or not the winds oppose or

enhance the residual flow.

Smith (1990a) studied the residual flow in the Indian River Lagoon utilizing a

two-dimensional laterally averaged numerical model. The model contained four layers

within the Intracoastal Waterway and communicated with two-layer zones along the

tidal flats on either side. Simulations were conducted for a 161 day period in 1983.

The model results indicated cumulative transport within the shallow regions in the

direction of net winds while the bottom layers within the Intracoastal Waterway show

return flow.

A two-dimensional, four-layer numerical model of tidally induced residual flow was

applied and calibrated to a 65 day data set of tides and currents from the summer of

1991 within the Indian River Lagoon (Smith, 1990b). Water depths and surface slopes

at the approximate midpoint between Ft. Pierce and St. Lucie inlet were calculated

by assuming that the tide inside the lagoon is the superposition of exponentially

damped sine waves representing six tidal constituents. The tidal wave moving south

from Ft. Pierce Inlet was modified by a tidal wave of the same six constituents

moving north from St. Lucie Inlet. The net slope as the two waves passed through

one another defined the barotropic pressure gradient and the net tidal residual flow.

The results showed a depth averaged tidally induced residual flow of 0.8 cm/sec at

the point where measured data were available. The residual flow varied from 0.1 to

1.2 cm/sec over a synodic lunar month. Examination of the mechanisms driving the

residual flow indicated that just under two-thirds of the total is explained by Stokes





25
transport, with the remainder attributed to Eulerian mass transport.

Sheng et al. (1993) used a one-dimensional model and a three-dimensional model

to simulate the circulation and flushing in Indian River Lagoon under the forcing of

tide, wind, and density gradients.

2.4 Studies Relative to Sarasota Bay

Although much research within the Sarasota Bay system has been conducted

relative to water. quality and ecology, few studies have focused upon the circulation

and transport processes. The following describes all studies found which relate to the

hydrodynamic processes within the entire Sarasota Bay system.

A simplified analytic model was applied to the Big Sarasota Bay system in order

to define the residence times and flushing characteristics (Chiu, T.Y., J. van de Kreeke

and R.G. Dean, 1970). The model considered the forcing from Longboat Pass, New

Pass and Big Pass. The results were inconclusive relative to the flushing within the

system as residual velocities predicted were very low.

A link-node model was applied to Little Sarasota Bay and Blackburn Bay in order

to quantify the impacts of the closure of Midnight Pass on the circulation and flushing

characteristics within that system (Dendrou, S.A., C.I. Moore and R. Walton, 1983).

The model defined the tidal currents and predicted the flushing times within Little

Sarasota Bay under the conditions of Midnight Pass open and closed. The model was

forced at the north end of Little Sarasota Bay and the south end of Blackburn Bay.


A number of publications related to Sarasota Bay circulation proceeded the pub-

lication of this report. Sheng and Peene (1991) presented some data and simulation

of tidal circulation inside Big Sarasota Bay. The simulations were conducted without

including Little Sarasota Bay and Tampa Bay. Peene, Sheng and Houston (1991)

simulated the circulation in Sarasota Bay and Tampa Bay during the passage of a

tropical storm in 1990. Sheng and Peene (1992) presented a study on the flushing in-





26
side the Sarasota Bay system. Sheng and Peene (1993) presented a preliminary study

on the residual circulation in Sarasota Bay. This report presents the results of an

enhanced and more comprehensive study on Sarasota Bay Circulation by performing

a more quantitative analysis of data and more detailed model simulations.

2.5 Chapter Summary

The studies presented herein, focused predominantly upon simplified one-dimensional

solutions pertaining to individual characteristics of circulation and transport. Al-

though these simplified studies were able to quantify some of the mechanisms driving

the flow, few addressed the complete circulation and the relative influences of one

mechanism versus another. Those studies which did address the multidimensional

nature of the flow focus primarily upon the verification of the numerical models ap-

plied therein, and did not present a comprehensive analysis of the physics of the

circulation.

The studies presented relative to Sarasota Bay provided little or no knowledge

of the physics of the circulation and the interactions between the multiple lagoons

and inlets. Additionally, the spatial distribution of net transport, and the relative

influence of the forcing mechanisms of wind, tides and density gradients have not

been thoroughly investigated.

Table 2.1 presents a summary of the investigations presented herein highlighting

the type of study (data analysis, model simulation) along with the forcing mechanisms

considered. No study presented examines all the forcing mechanisms and their rela-

tive influence utilizing both measured data and multidimensional modeling. In the

subsequent chapters, an attempt is made to further the understanding of the physics

of circulation within the Sarasota Bay System through data analysis and multidi-

mensional modeling. The study considers all of the forcing mechanisms listed within

Table 2.1 and the relative influence each has upon the short term periodic, and long

term residual, tides and currents.













Table 2.1: A Summary of Historic Studies of Tides and Currents within Shallow
Barrier Island Lagoons


Study Method Tidal Wind Residual Non-Linear Density
Forcing Forcing Transport Forcing Grad.
Kjerfve (1975) Data yes yes yes no no
Smith (1979) Data yes yes yes no no
Smith (1980) Data yes no no no no
Smith (1983) Data no yes yes no no
Smith (1985) Data, yes yes yes no no
1-D Model
van de Kreeke Data yes no no yes no
and Wang(1984) 2-D Model
Speer, Aubrey Data yes no no yes no
Friedrichs 1-D Model
(1985-1992)
Boon (1988) Data yes no no yes no
Seim and Sneed Data yes no no yes no
(1988)
van de Kreeke 1-D Model yes no yes yes no
Dean, Cotter
(1971-1975)
Johnson, Lee 1-D Model yes yes yes no yes
(1977)
Dronkers (1978) 1-D Model yes no no yes no
Moody (1988) 1-D Model yes no no yes no
Wang, Swakon 2-D Model yes yes yes no no
(1977)
Smith (1990a,b) 2-D Model yes yes yes no no
Sheng (1983) 3-D Model yes yes no yes no
Sheng (1993) 3-D Model yes yes yes yes yes











CHAPTER 3
FIELD DATA COLLECTION


3.1 Introduction

As part of a cooperative agreement, the Coastal and Oceanographic Engineering

Department of the University of Florida (UFL) and the Water Resources Division of

the United States Geologic Survey (USGS) collected hydrodynamic data throughout

the Sarasota Bay system during the years 1990 to 1992. The data collection effort

involved 13 locations at which tides, currents, salinity, temperature and wind speed

were measured (not all were measured at each station). In conjunction, intra-tidal

discharge measurements were taken at critical cross sections within the lagoons and

across the inlets connecting the lagoons to the Gulf of Mexico. This chapter de-

scribes the locations where the data were collected, the periods over which the data

were collected, the types of instruments used and their relative accuracy, the instru-

ment maintenance and any possible instrument errors.


3.2 University of Florida Data Collection Stations

The Coastal and Oceanographic Engineering Department of the University of

Florida deployed a total of six sets of instruments in Anna Maria Sound, Sarasota

Bay, Little Sarasota Bay, Blackburn Bay and offshore in the Gulf of Mexico. Figures

3.1 and 3.2 show the locations.

The UFL stations are defined in two categories, bay stations and offshore stations.

On Figures 3.1 and 3.2 the offshore stations are prefixed by an "0" and the bay

stations prefixed by a "B". The offshore stations were installed to obtain data on the





29

tidal and salinity conditions in the Gulf of Mexico. These data are used to produce

boundary conditions for the circulation and transport model the results of which are

presented in Chapter 6. In addition, these data are analyzed in Chapter 4 to compare

the nature of the offshore tides with those measured inside the lagoons and how the

offshore forcing impact the interior circulation.

The bay stations were installed to measure currents, water surface elevation, con-

ductivity, water temperature and wind at discrete positions throughout the interior

lagoons. These data are first analyzed in Chapter 4 to provide some insight into the

physics of the circulation and transport, and later used to calibrate and verify the

numerical model.


3.2.1 Bay Stations

At the bay stations, UFL-B1, UFL-B2, UFL-B3, and UFL-B4 the instruments

were mounted on surface piercing platforms. A schematic of the platforms is shown

in Figure 3.3.

Platform Design and Installation

The platforms were designed and constructed at the University of Florida Coastal

and Oceanographic Engineering Department. They are made of lightweight alu-

minum; a 4 meter high platform weighs approximately 125 kg without instrumen-

tation. The platforms were designed such that they could be broken apart and trans-

ported as joints and connecting pipes. The corner joints for each platform are the

same and the height is determined by varying the lengths of the connecting pipes.

This allowed for deployment over a range of depths, and allowed the sizes to be altered

simply by cutting new connecting pipes. The conning tower, where the data logger

and power supply were mounted, is the same for each platform.

The deployment procedure consisted of the following. The platforms were assem-

bled at a dockside location without the instrumentation. A transport saddle, which





30


PASSAGE KEY ... '. .........
INLET TAMPA BAY::: :::: ::::::::



ANNA
USGS-O1 MARS
ANNA MARIA OUND

.0 PALMA .
SOLA
UFL-B1. .......... .....
. ..:: .::: : : .:.: .:: : : : .. .: . ..: ..::: : : .: : .:I:.:::: .:::::



LONGBOAT ...---. ..02.::...
PASS .. ....... ...SARASOTA BAY EAST::::



USGS-03
SARASOTA BAY WEST




UFL-01 =::-: ..^ = ==: == =
l,* UFL-B2.7 OUSGS-04
So, U FL-B2 :.::.ROBERTS:
.vc v:v: BAY.;.;:::::
GULF OF MEXICO



NEW PASS....


O 2.000 4.000 USGS-05
I ////// BIG PASS B 3 .
SCALE IN METERS
1" = 4,000 m


Figure 3.1: The locations of the UFL and USGS data collection stations within Anna
Maria Sound and Big Sarasota Bay, 1991 deployment.



















JFL- B........



















.BLACKBU .RN...: .- .. ..
V A G" :::::::::::::::::::: ::::::::::::::::::: :: : '
2 5 ::..7 ^ .....:::::..:;. .........:::::::::::. .:::.::::.:.......










































USGS-07
BLACKBURN SARASOTA BAY:BAY:::::::::::::::::::
VENICE INLETF OF MEX


02. FL-.B4v..v .v ...........v.v.. v...
2.000 m \ ..... . .. .. .' ...
.. .. .. .. .. .. .. ** .. *

































BLACKBURN BAY. ..
VENICE INTTLET SARASOTA BAY.......
.. .. .. .. .. .. . .. .. .. .. .
........ .................. ........................ ......." '' '
. .. . .. . .. . .. . .
. . . .. .. . . . . . . . .
.......... ....................................... .....' `' '

.. .. .. .. .. .. .. .. .. .. .. .. .
........ ....... ....... ........ ....... ....... .......
.. .. .. .. .... .. .. ..... .. .. .. .. ... .. .. .. .. .. ... .. '
.. . .. . .. . . . .
.. .. ...... .. .. .. ... ... .. ... ... ... .. .. ... .. ..' "
a .......................................................
... .. ... ... ... ... .. ... ... ... ... ... ... ..
.. .. .. .. .. .. .. .. .. .
F O F M E X C O ...... .......................
. . . . . . . . . . . .
. .. . . .. . . .. .
.. .. .. .. .. . .. .
. . .. . . . . .
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .
.. .. . .. .. .. .. .. .


Figure 3.2: The locations of the UFL and USGS data collection stations in Little
Sarasota Bay and Blackburn Bay, 1991 deployment.


UFL-



GUL


0 11
I F///CA
SCALE IN
1. .


_ ___ _1


e-:












Logger


Temperature and
Conductivity Sensors


Pressure
Sensor'


Figure 3.3: A schematic of the University of Florida instrument platforms.

was designed and constructed for this project, was mounted on the Coastal Vessel

Munson and allowed the platforms to be transported to their predetermined loca-

tions and easily lowered into the water. The stations were secured to the bay bottom

by jetting in pipes at the three corners of the base and clamping the corner joints

to the jet pipes. The instruments were then mounted onto the frame along with the

data logging system and the power supply. The complete installation procedure for

each station lasted approximately 6 hours. The station locations in latitude and lon-

gitude, the water depth at mean sea level, and the deployment durations are given

.in Table 3.1. The station locations were determined by triangulation to known land

references.








Table 3.1: The locations and depths of the University of Florida Stations

Station I.D. Latitude Longitude Depth(cm) Duration
UFL-B1 27 28.50 82 41.80 240.0 07/18/91 09/23/91
UFL-B2 27 21.00 82 33.50 330.0 07/17/91 09/23/91
UFL-B3 27 14.20 82 31.15 210.0 07/19/91 09/23/91
UFL-B4 27 09.30 82 28.92 210.0 07/20/91 09/23/91
UFL-O1 27 12.63 82 33.02 900.0 07/15/91 09/14/91
UFL-02 27 22.57 82 42.52 900.0 07/15/91 09/14/91


Instruments

Each station had instruments mounted at two elevations below the low water mark

on arms which extended toward the center of the frame (see Figure 3.3). This was

done to prevent snagging on the anchor lines of boats mooring near the platforms.

The platforms were designed such that the diameter of the connecting pipes was

as small as possible (2 inches), this reduced any possible wake interference on the

current readings. In addition, where possible, the platforms were oriented such that

no support pipes were directly upstream or downstream of the current sensors.

Table 3.2: Instrument elevations on the University of Florida platforms, 1991 deploy-
ment


Station Arm Number Current Conductivity Temperature
UFL-B1 1 25 cm 55 cm 55 cm
2 145 cm 175 cm 175 cm
UFL-B2 1 55 cm 85 cm 85 cm
2 225 cm 255 cm 255 cm
UFL-B3 1 25 cm 55 cm 55 cm
2 115 cm 145 cm 145 cm
UFL-B4 1 25 cm 55 cm 55 cm
2 115 cm 145 cm 145 cm


Each instrument arm had an electromagnetic current sensor, a conductivity sensor

and a temperature sensor. In addition, each platform had a wind sensor mounted

approximately 4 feet above the top of the conning tower and a pressure sensor mounted





34
below the lower low water datum. The instrument elevations for each platform are

given in Table 3.2.

The electromagnetic current sensors utilize Faraday's principle which states that

any conductor passing through a magnetic field will produce a voltage, and the volt-

age is proportional to the speed at which the conductor passes. To make use of this

principle, the current sensors have an electromagnet inside their head which produces

a magnetic field. As water (a conductor) moves past the head, a voltage is induced

within the field which is sensed by elements on the outside of the sensor. The magni-

tude of the voltage measured, along with the polarity, determines the velocity vector

components. The sensing elements are positioned along orthogonal axes of a plane

radiating outward from the sensor, therefore only two-dimensions of the velocity field

can be measured. In our case these were the horizontal velocity vector components.

Electromagnetic current sensors have a good tilt response factor, i.e. the measure-

ments of the horizontal vector components are not contaminated by vertical velocity

fluctuations which may be present. They are also accurate sensors, capable of measur-

ing velocities as low as 1-2 cm/sec. This was important in this study as the amplitude

of the tidal currents at some of the stations were as low as 5 to 10 cm/sec.

One disadvantage of these instruments is that the current sensing elements can

be prone to fouling. The head has an antifoulant coating everywhere except at the

tips of the sensing elements. This means that frequent cleaning, on the order of a

week, were required to prevent inaccurate readings. The other disadvantage is that

the sensors can drift, i.e. the voltage which corresponds to zero current can change

slowly over time. To monitor this problem the sensors have a setting (calibrate) which

corresponds to a specific voltage and can be scanned to spot any drift. The calibrate

voltage was scanned on a weekly basis throughout the deployment.

The current sensors were calibrated prior to deployment in the USGS flow tank

at the Stennis Space Center in Slidel, Louisiana. The calibrations are presented and







discussed in Appendix A.

The conductivity and temperature sensors were manufactured by Sea Bird Tech-

nologies. They were designed to be used to measure vertical profiles of conductivity

and temperature in the open ocean and are accurate enough to resolve minor changes.

The temperature probes are accurate to within .002 Degrees C. The conductivity sen-

sors are accurate to within .0002 siemens/meter. The calibrations of these sensors

were conducted by the manufacturer and the sensors were deployed for the first time

on this project. The manufacturers calibrations are presented in Appendix A.

The temperature sensors were unaffected by fouling, while the conductivity sen-

sors were susceptible to fouling. The three electrodes used in the conductivity probes

are housed in a Plexiglas tube which allows the sea water to pass through it. In

order to prevent growth within this tube, antifoulant sleeves were place on both ends.

These sleeves, which allowed seawater to pass through, were lined with tributyl-tin

which dissolved slowly throughout the deployment. They effectively prevented growth

within the tubes and eliminated all fouling due to algal and barnacle growth. The

only fouling which occurred was caused by fine silty material settling inside the tubes

at stations with low velocities. Pre and post cleaning readings showed the error, after

conversion to salinity, to be at most 0.2 parts per thousand (ppt).

The wind sensors were R.M. Young anemometers which measured speed and di-

rection. The speed is measured as a voltage induced by a spinning propeller and the

direction is measured by a potentiometer as the sensor moves to face the wind direc-

tion. The wind sensors were calibrated prior to the deployment in a wind tunnel at

the Aerospace Engineering Department of the University of Florida. The calibration

curves for the wind sensors are included in Appendix A.

The pressure sensors were deployed to measure the water surface elevation at the

stations. The pressure transducers were purchased from Transmetrics Corporation

and placed in a housing designed and manufactured at the Coastal and Oceanographic





36
Engineering Laboratory of the University of Florida. The sensing element sits in a

pool of oil and is separated from the water by a diaphragm which is free to transfer

any pressure changes through the oil.

All data collected were recorded using Onset Tattletale data loggers. These log-

gers are programmed in BASIC to allow the sampling to be tailored to the users needs.

For this deployment the loggers were programmed to record ten minute averages of

data taken at a 1 hertz rate on the quarter hour. All data were collected with time

set to Eastern Standard Time. This standard was maintained for all data collected

either by the University of Florida or the United States Geological Survey.

Overall the data loggers operated well. Stations UFL-B1, UFL-B2 and UFL-B4

had short periods of down time in the data logging system, station UFL-B3 operated

continuously throughout the study. Station UFL-B4 had the longest periods of down

time as the result of battery failures. Stations UFL-B1 and UFL-B2 only had short

periods of down time.

All the individual instruments except the pressure transducers performed well

throughout the study. Barnacle growth on the rubber diaphragm created false pres-

sure readings. The barnacles were frequently cleaned off but their rapid regrowth

created contamination of the data which was unresolvable. Given the number and

spacing of the USGS tide stations, the loss of this data was not deemed critical. A

description of the tidal data collected by the USGS is presented in section 3.3.


3.2.2 Offshore Stations

Stations UFL-01 and UFL-02 were deployed approximately 4 kilometers offshore

in the Gulf of Mexico. The instruments consisted of a bottom mounted Sea Data

Package which recorded pressure, and two conductivity sensors mounted on a buoy

tether. Figure 3.4 presents a schematic of the offshore data stations. Table 3.1 lists

the lengths of time that data were collected at the offshore stations, the water depth







-,? 1'


Buoy


Conductivity
/ Sensors


Sea-Data Package
S/ with Pressure
?^- Transducer


Figure 3.4: A schematic diagram of the offshore data collection stations

at mean tide and the station locations in latitude and longitude. The station locations

were chosen to be evenly spaced across the offshore open boundary to the model.

The Sea Data Loggers were programmed to perform 5 minute averages of the

pressure every 10 minutes and store the results. The pressure was then transformed

into water surface elevation using the hydrostatic equations. Given that the Sea Data

Instruments were bottom mounted, in a depth of 10 meters, it was impossible to refer-

ence the tidal fluctuations to a specific datum. Therefore, these data were demeaned

and detrended prior to use. The Sea Data packages operated properly throughout

the study period and provided a continuous record of offshore tidal fluctuations.

The conductivity sensors along with separate data loggers were deployed by USGS


4
9





38
at two levels along the buoy tether at each of the stations. The gages were installed

to measure conductivity and temperature throughout the study. The data logging

systems on both stations did not operate properly and no reliable data were obtained

from these gages.


3.3 Tide and Discharge Measurements Taken by the USGS

3.3.1 Tidal Data

The Water Resources Division of the USGS established 7 stations throughout the

project area, Table 3.3 gives the latitudes and longitudes. Each station consisted of

a data logger in an aluminum shelter over a PVC stilling well attached to a dock.

Pressure sensors measured the changes in water level and the data were stored on the

logger. The data consisted of instantaneous pressure readings taken every 15 minutes.

The pressure was converted into water surface elevation using hydrostatic equations.

The stations were established on August 2nd and 3rd, 1990 and maintained on an

intermittent basis until October 1992. The station at Big Sarasota Pass (USGS-05)

was maintained for the entire period. The stations at Roberts Bay (USGS-4), Little

Sarasota Bay (USGS-06) and Blackburn Bay (USGS-07) were maintained from Au-

gust 1990 to January 1992. The stations at Anna Maria Sound (USGS-01), Sarasota

Bay East (USGS-02) and Sarasota Bay West (USGS-03) were maintained from Au-

gust 1990 to January 1991 and from January 1992 to October 1992. Periodic power

failures and instrument malfunctions created gaps in the data.

Initial elevations on the instruments were established using a Trimble Global

Positioning System (GPS). The datum corrections to NGVD, determined from the

GPS system, are listed in Table 3.3 under "GPS". Examination of the data indicated

some possible errors in the initial survey work. As a check, 4 of the 7 stations were

releveled using standard techniques tied to existing benchmarks. The revised datum

corrections are listed under "Level". Table 3.4 lists the reference benchmarks used to







Table 3.3: The locations of the USGS tidal data stations.

Location Latitude Longitude GPS Level Settling
(feet) (feet) (feet)
Anna Maria Sound (USGS-01) 27 30.08 82 42.60 -5.181 -5.280 .02
Sarasota Bay East (USGS-02) 27 24.13 82 43.32 -6.610 -6.311 .02
Sarasota Bay West (USGS-03) 27 23.25 82 38.28 -6.640 -6.252 .01
Roberts Bay (USGS-04) 27 18.00 82 32.65 -5.416 None .02
Big Sarasota Pass (USGS-05) 27 17.22 82 33.78 -7.745 -7.279 .00
Little Sarasota Bay (USGS-06) 27 11.73 82 29.60 -5.745 None .03
Blackburn Bay (USGS-07) 27 07.50 82 28.13 -5.465 None .03


establish the revised datum for each station.

The releveling indicated that the error is different for each of the stations and for

the purposes of analysis the datum established by the standard methods was used.

Based upon this, the corrections to NGVD established for the Roberts Bay, Little

Sarasota Bay and Blackburn Bay stations are not reliable.

As well as setting the elevations for each station, USGS periodically ran optic

levels from the established reference marks to the instrument. This was done to de-
termine the amount of settling of the stilling well over the study period. The amount

of settling for each station is listed in Table 3.3.


Table 3.4: Benchmarks used to verify


elevations of USGS tide gauges


Station Benchmark (BM)
Anna Maria Sound (USGS-01) USCGS N-254, 1965
DNR 13 85 A15
DOT 13 85 A15 REF
Sarasota Bay East (USGS-02) Manatee County BM
FEMA BM
Sarasota Bay West (USGS-03) Sarasota County BM R-2, 1985
17-84 A02
Big Sarasota Pass (USGS-05) DNR R-44A (reset 1985)







3.3.2 Discharge Measurements

Measurements of discharge were taken by USGS at critical cross sections within

the lagoon system and at the inlets. In 1991 the discharge at the Siesta Bridge in

Roberts Bay and the Nokomis Bridge in Blackburn Bay were measured (see figures

3.1 and 3.2). These two cross sections are the only two entrances to the Roberts

Bay/Little Sarasota Bay/Blackburn Bay system. The purpose was to quantify the

relative flow from the north and south into Little Sarasota Bay and Blackburn Bay.

The discharge was measured at both stations over an ebb as well as a flood tide.

The method utilized to measure the flows was as follows. The cross-section di-

rectly below the bridge was divided into sections of even area. Current meters were

lowered from the bridge and measurements were taken at 20 and 80 percent of the

depth at the centerline of each section. Where the depth was too shallow, readings

were taken at 60 percent of the depth only. The measurements were taken over the

entire cross section as rapidly as possible to obtain instantaneous discharges. The

longest time for the completion of one cycle was 30 minutes, while the average time

was approximately 15 minutes. The discharge was then calculated by multiplying the

average velocity within each section by the area and summing over the cross section.

Results presented later show the measurements as instantaneous readings.

In 1992 an Acoustic Doppler Current Profiler (ADCP) was made available to

USGS to perform the discharge measurements. This instrument allowed measure-

ments to be taken from a boat. The profiler was mounted off of the boat and pulled

across the cross section. The time to profile in this manner was much quicker than

the 1991 method and the results represent a more instantaneous measurement. The

1992 discharge measurements were taken across the inlets connecting the lagoons to

the Gulf of Mexico. Data were collected at Big Pass, New Pass, Longboat Pass, Anna

Maria Sound and Roberts Bay.











CHAPTER 4
FIELD DATA ANALYSIS


4.1 Introduction

In Chapter 2, studies were presented which isolated the response of shallow barrier

island lagoons to the forcing by the tides, wind and density gradients. In conjuction,

the studies examined how the varying bathymetry and geometry within the lagoons

modified their response. Within this chapter, the response of the Sarasota Bay System

to these "forcing mechanisms" is examined through analysis of the data set described

in Chapter 3.

The first part of this chapter includes spectral analysis, filtering, and harmonic

analysis of the data of water surface elevation, current and wind. The continuous

signals are decomposed into sub-components and separated into portions driven by

single forcing mechanisms. These separated signals are analyzed comparatively to

define the relative energy in each, and correlated to one another to isolate and identify

the forcing.

The second part of this chapter presents the results from the discharge measure-

ments conducted by the USGS in 1991 and 1992. The discharges are analyzed to

quantify the relative flows through each of the multiple inlets connecting the lagoons

with the Gulf of Mexico, as well as defining the flows through critical cross sections

separating sub-bays within the system.

The final section presents the salinity measurements taken at the University of

Florida bay stations along with representative measurements of freshwater inflow to

the system. These data are analyzed to define the levels and variations in salinity

under the inflow of freshwater from the tributaries. These data provide a qualitative





42
evaluation of transport and the level of flushing within the individual lagoons. Ad-

ditionally, these data provide information on the spatial and temporal variations of

stratification.

The data collection effort spanned two years, from 1990 to 1992. From this data

set two 60 day periods are focused upon. The first period coincides with the time

when the University of Florida deployed its platforms (July 17, 1991 to September

15, 1991). This period reflects summer conditions with its associated localized thun-

derstorms and low overall wind energy. The second period (September 15, 1990 to

November 15, 1990) reflects fall to winter conditions with higher sustained wind en-

ergy. As the University of Florida platforms, which contained the current meters and

salinity sensors, were not deployed during 1990, the available tide and wind data are

analyzed in order to compare and quantify the effects of the differing weather patterns

on the circulation throughout the system.


4.2 Decomposition of Water Surface Elevations, Currents and Wind

The water surface elevations and the currents can each be represented in equation

form as (Pugh, 1987),

X(t) = Zo(t) + T(t) + S(t) (4.1)

where X(t) is either the measured water surface elevation or current, Zo(t) is the

slowly varying mean water level or mean current, T(t) is the short term tidally driven

portion of the signal and S(t) is the short term portion of the signal driven by the

meteorological forcing.

Within the terms on the right hand side of the equation, various sub-components

exist. For instance, the tidally driven portion of the signal is actually the superposition

of a number of harmonic constituents each with its own amplitude and period. These

include the semi-diurnal (M2 and N2) the diurnal (K1 and O1) and other higher and

lower frequency harmonics. These variations, which are associated with the pull of





43
the sun and moon, are termed gravitational tides or currents.

The short term meteorological variations are normally associated with wind stress

acting upon the water surface creating surge and flow. These forcing may occur

locally or may, as in the case of a lagoon connected to the ocean, occur in a larger

body of water and propagate into the lagoon through the inlets. Certain periodic

constituents, such as the S2 harmonic, may be partially driven by meteorological

forcing, i.e. the effects of the sea breeze. When meteorological forcing result in

periodic fluctuations, they are termed radiational tides or currents.

The long-term variations in the mean water level may contain both gravitational

and radiational forcing. The S, harmonic constituent for instance is the annual

variation in mean water level due to the relative positions of the sun and moon. The

long period gravitational forcing in general are small in relation to the long term

variations in water level associated with meteorological forcing.

Inside of a lagoon or bay, gravitational tides are considered to be remotely forced,

i.e. the variations occur in larger bodies of water such as the Gulf of Mexico and

propagate into the bay through the inlets. The currents are then locally driven by

water surface elevation gradients. Radiational tides or currents may be either locally

(i.e. wind driven currents or surge) or remotely forced, i.e. due to Ekman transport

propagating in from the offshore.

All of the mechanisms described above act simultaneously to produce the mea-

sured tidal and current fluctuations. In the following sections the relative energies

imparted by these mechanisms will be examined through decomposition of the raw

data signals and comparison and correlation between the measured water surface el-

evations, currents and winds. Prior to decomposition, the raw data will be presented

and discussed relative to the bathymetry and geometry of the lagoons.





44
4.2.1 Presentation and Discussion of Raw Data

Water Surface Elevation Data

Figures 4.1 and 4.2 present example data of water surface elevation measured

from Julian day 255 to 285 in 1990 and from Julian day 200 to 230 in 1991. On both

figures the data are presented with the offshore stations in the top plot progressing

farther interior to the lagoons going down. The complete water surface elevation data

sets for the seven USGS stations are plotted in Appendix B.

The plots demonstrate the mixed semi-diurnal/diurnal tides characteristic of the

Gulf of Mexico. These mixed tides create an irregular pattern in the amplitudes and

periods. The damping of the tidal wave can be seen by comparing the offshore tides

(UFL-01, NOAA-01) with the Little Sarasota Bay tides (USGS-06). The effects of

the wind, as shown by the short term fluctuations in the water level data (day 270

to 272 in Figure 4.1), are less pronounced at the more interior stations. Additionally

there is an increase in the non-linearity of the wave. Figure 4.3 presents a comparison

between tides measured at USGS-05 (Big Pass) and USGS-06 (Little Sarasota Bay)

over a five day period. The tidal wave at the interior station (USGS-06) has a more

peaked non-linear shape. Although the data indicate a super elevation at the interior

stations, errors associated with the leveling of the tide gages, described in Chapter 3,

make any conclusions unreliable.

Current Data

This section will present the north-south and east-west velocity vector components

measured from Julian Day 200 to 230 in 1991. Plots of the remaining data set (beyond

Julian Day 230) for the four University of Florida stations are included in Appendix

B.

Visual examination of the plots is the first step towards an understanding of the

circulation patterns within the bay. As the geometry and bathymetry of a lagoon or

estuary can have a significant influence on the circulation and transport patterns, a













80
60
E 40
20
2 0
-20
-40
-60


Julian Day (1990)


100
-80
E 60
40
o 20

--20
-40
-40


Julian Day (1990)


Julian Day (1990)


USGS-06 (Little Sarasota Bay)


270
Julian Day (1990)


Figure 4.1: The measured water surface elevations from Julian Day 255 to 285, 1990.

a) offshore; b) USGS-05 (Big Pass); c) USGS-04 (Roberts Bay); d) USGS-06 (Little

Sarasota Bay).


100
80
E 60
40
. 20
C0
-2-20
-40


100
80
E 60



at
.2 20
5o
- -20
Ul
-40
-SrI


260


265












Offshore (UFL-O1)


80
S60
E 40
o
20
o 0
S-20
2-40
-60
-8 $C


210


215
Julian Day (1991)


220


Julian Day (1991)


USGS-04 (Roberts Bay)


30 205 210 215 220 225 23
Julian Day (1991)



USGS-06 (Little Sarasota Bay)


210


215
Julian Day (1991)


220


225


i!iln41IIV\h~V
jilvi


230


Figure 4.2: The measured water surface elevations from Julian Day 200 to 230, 1991.
a) UFL-O1; b) USGS-05 (Big Pass); c) USGS-04 (Roberts Bay); d) USGS-06 (Little
Sarasota Bay).


205


100
-.80
E 60
40
.2 20
0
-20
-40


100
80
E 60
o
40
.2 20
Jo o
C0
-20
LU
-40
-602





100
S80
E 60
40
r-
.2 20
-20
LU
-40
-6%


f!ii


B


(a)










10




(b)









0




(C)









0


_


0


0













120
100
E 80
60
40
0
S20
> 0
w -20
-40


Julian Day (1991)


Figure 4.3: A comparison of measured water surface elevations from Julian Day 220
to 225, 1991 at USGS-05 (Big Pass) and USGS-06 (Little Sarasota Bay)


discussion of the geometry and bathymetry surrounding each station is included.

Station UFL-B1

Station UFL-B1 is located within a constriction which connects Anna Maria

Sound and Palma Sola Bay with the northern end of Sarasota Bay and Longboat

Pass (see Figure 3.1). This constriction is approximately 700 meters wide and is

oriented at 330 degrees. The nearest inlet is Longboat Pass which is 3 kilometers to

the south. Anna Maria Sound opens into the southwest corner of Tampa Bay which

immediately opens out to the Gulf of Mexico through Passage Key Inlet.

The bathymetry near UFL-B1 is characterized by shallow flats (1 to 2 meters)

intersected longitudinally by the Intracoastal Waterway and other maintained chan-

nels. Looking from east to west across the constriction where UFL-B1 was located,

the cross-section goes from deep water on the eastern side of the channel (3 to 4 me-

ters) sloping upward to the west with a 300 meter wide shallow region (approximately

1 meter) on the western side (Figure 4.4). The instrument platform was located in

the transition region between the deep and shallow waters, the station depth at mean

water level was presented in Table 3.1.








100 "* .

me0 n wir levl (MLW)
-J
-lo UFL-B1 Platform



ca
.o0 -200

U.J
.300


-400 t . I I I i .
0 100 200 300 400 500 600 700
Distance From Cortez (m)


Figure 4.4: The bathymetric cross-section at station UFL-B1


The measured currents (Figure 4.5) show a distinct SSE directed residual. Taking

the means from each of the signals gives residual current magnitudes of 3.0 and 4.4

cm/sec for the bottom and surface east-west velocity components respectively, and

-6.0 and -8.5 cm/sec for the bottom and surface north-south velocity components

respectively. The resultant vectors are a 6.7 cm/sec residual oriented at 154 degrees

near the bottom, and a 9.6 cm/sec residual oriented at 153 degrees near the surface.

Some simplified analyses were described in Chapter 2 which defined the net trans-

port between two inlets in a multi-inlet lagoon system (van de Kreeke 1971, Cotter

1974, van de Kreeke and Cotter 1974, van de Kreeke and Dean 1975). As UFL-B1 is

essentially between two inlet openings, Tampa Bay (Passage Key Inlet) and Longboat

Pass, it is possible to explain qualitatively some possible driving mechanisms for this

residual. Figure 2.1 presented the net flow for the simplified geometry under varying

inlet widths, depths and amplitudes of the tidal forcing. The results showed that

net flow is toward the inlet which is narrower, shallower and has the smaller tidal

amplitude. Examining each of these characteristics in relation to the two openings,

Longboat Pass is narrower and shallower than the openings to Tampa Bay. Addi-














Surface East-West Velocity, Station 1


210


215
Julian Day


220


Julian Day


Bottom East-West Velocity, Station 1


21U


Julan Day
Julian Day


Bottom North-South Velocity, Station 1





-AW V^'W^^


210


215
Julian Day


Figure 4.5: The current vector components measured from Julian Day 200 to 230,

1991 at UFL-B1. a) Surface East-West Velocity; b) Surface North-South Velocity; c)

Bottom East-West Velocity; d) Bottom North-South Velocity.


~4


205


S50
o

- 25
E
0

0
-25
e


,50
so
a
u
"- 25
E


0
-25


,50
o
O
a'
S25
E
0


0-
O

o -25
e,


.sfl -L--~


9C)'~":% ~,,i;~~~~


I


--UOO


50

-25
E
0


-25
o -2


"200


205


-5n -


~'~mjr~h~N7~'~r~;l~h~E~\~


N'~ErStU~/"~,"~~u'~?,


2U2


eeLa


22U


225


23U





50
tionally, it will be shown later that the tidal amplitude in the offshore regions is

reduced moving from north to south, and therefore the tidal amplitude at Longboat

Pass may be lower than that entering Tampa Bay. Each of these characteristics sup-

ports a residual flow from north to south across UFL-B1. These explanations will

be examined in later parts of this chapter and through application of the numerical

model.

Station UFL-B2

Station UFL-B2 is located on the southern end of Sarasota Bay. Sarasota Bay

is the most open body of water within the system and is approximately 5 kilometers

wide and 15 kilometers long. The depths are relatively uniform and range from 8.0

feet to 13.0 feet, the deepest portions are at the center. Tidal velocities at this station

are driven by the wave propagating through New Pass and Big Pass (see Figure 3.1).

The measured currents (Figure 4.6) exhibit primarily north-south flow. The cur-

rent magnitudes range from 30 cm/sec during spring tides to 15 cm/sec during neap

tides. Current magnitudes are highest during flood tide which occurs over a shorter

duration. Using terminology introduced in Chapter 2, this type of system would be

termed flood dominant as transport would be greater during flood tide. The flood

tides at this station may also be stronger due to the nature of the flood and ebb

patterns near an inlet. The flooding currents enter the bay through New Pass and

Big Pass as a jet and reach farther in than the ebbing currents which tend to flow

from all directions.

Taking the mean values for each component gives 2.7 cm/sec and 1.1 cm/sec for

the bottom and surface east-west residual velocities and 2.2 cm/sec and 2.8 cm/sec

for the bottom and surface north-south residual velocities. The resultant vectors are

a 3.4 cm/sec residual at an angle of 51 degrees on the bottom and a 3.0 cm/sec

residual at an angle of 21 degrees on the surface. The residual currents exhibit a

counterclockwise rotation from the bottom to the surface.















Surface East-West Velocity, Station 2


Julian Day


Surface North-South Velocity, Station 2


Julian Day


Bottom East-West Velocity, Station 2


40

20




-20


" 00 205 210 215 220 225 231
Julian Day


Bottom North-South Velocity, Station 2
40






20
-20


.4(L ^^


5l
Julian Day


Figure 4.6: The current vector components measured from Julian Day 200 to 230,

1991 at UFL-B2. a) Surface East-West Velocity; b) Surface North-South Velocity; c)

Bottom East-West Velocity; d) Bottom North-South Velocity.


- 40
0

E
0
O
-20
0,


, 40
a
- 20
E
0

20
-20
os-2


-..

E
O




0
0


C,

E
-a



0
0
-s
9,


ZU05







Station UFL-B3

Station UFL-B3 is located in the northern end of Little Sarasota Bay. Little

Sarasota Bay is a narrow lagoon approximately 20 kilometers long with numerous

constrictions. The average width is 1000 to 1500 meters. The bathymetry within

Little Sarasota Bay is shallow with an average depth of 1 to 2 meters at low water.

The Intracoastal Waterway runs down the center of the bay and is an artificially

maintained channel 70 to 100 meters wide and 3 meters deep. The connections from

Little Sarasota Bay to the Gulf of Mexico are narrow and highly restrictive. To the

north, the tidal wave propagates through Roberts Bay and then through a long narrow

artificial channel which at some points reduces to less than 100 meters in width. To

the south the wave enters through Venice Inlet and propagates through the narrow

passage from Venice Inlet into Blackburn Bay and finally to Little Sarasota Bay.

The instrument platform was located approximately 100 meters to the west of the

Intracoastal Waterway in approximately 2 meters or water. This station was located

the greatest distance from any opening to the Gulf of Mexico, the nearest inlet was

Big Pass 16 kilometers to the north.

The velocities presented in Figure 4.7 reflect the distance to the Gulf of Mexico and

the restricted flow into Little Sarasota Bay. The highest recorded current magnitudes

were near 15 cm/sec flowing predominantly to the north-south. Although the two

current sensors were only one meter apart in the vertical, there was a more significant

top-to-bottom reduction in the current magnitudes in comparison with the other

stations. One explanation for this increased damping is that the bottom boundary

layer within this region may be laminar, whereas at the other stations it may be

turbulent. Figure 4.8 shows a comparison between two ideal velocity profiles under

laminar and turbulent flow. The thickness of the boundary layer under laminar flow

is greater and therefore there is a larger top-to-bottom velocity gradient.

Calculation of the mean velocities gives -1.2 cm/sec and -3.7 cm/sec in the bottom














Surface East-West Velocity, Station 3


205


210


215
Julian Day


220


225


Surface North-South Velocity, Station 3










00 205 210 215 220 225 23
Julian Day

Bottom East-West Velocity, Station 3


oo 205 210 215 220 225 23
Julian Day

Bottom North-South Velocity, Station 3


21U


215
Julian Day


Figure 4.7: The current vector components measured from Julian Day 200 to 230,

1991 at UFL-B3. a) Surface East-West Velocity; b) Surface North-South Velocity; c)
Bottom East-West Velocity; d) Bottom North-South Velocity.


-40
O
0

E
O
0
O
S-20
o


'200


- 40



0
0-
- 20
E



02
20




-40

-... 40
0
I-4


0
- 20
E

O









o
- 20




0




E

. 0

S-20
C


- I A '


-~ciI~r,"2s~,n~,~pl~,n~~itil~''~.~M






























Figure 4.8: Idealized velocity profiles under laminar and turbulent boundary layers

east-west and north-south velocities respectively, and -1.9 and -1.3 in the surface east-

west and north-south velocities respectively. The resultant vectors are a 3.4 cm/sec

residual at 198 degrees on the bottom, and a 2.3 cm/sec residual at 235 degrees at

the surface. The residual velocities show a 37 degree clockwise rotation from top to

bottom.

Station UFL-B4

Station UFL-B4 was located in the northern end of Blackburn Bay. Blackburn

Bay is a narrow lagoon oriented predominantly north-south. The bathymetry is

similar to UFL-B3, i.e. shallow with depths from 1 to 2 meters with the Intracoastal

Waterway running longitudinally along its axis. The instrument platform was located

75 meters to the west of the Intracoastal Waterway in approximately 2 meters of

water. The nearest opening to the Intracoastal Waterway is through Venice Inlet 8

kilometers to the south.














Surface East-West Velocity, Station 4


210


215
Julian Day


Surface North-South Velocity, Station 4


Julian Day


Bottom East-West Velocity, Station 4





i-^yltr
uF l'' ~~ru y yl i II ~'I V I P 0 r" AYi YYIY


. 40

-- 20

0
o
o20
E
0



>
*,


.4 00 205 210 215 220 225 230
Julian Day

Bottom North-South Velocity, Station 4
40

20




-20

-A --


2-o 0


205


210


215
Julian Day


Figure 4.9: The current vector components measured from Julian Day 200 to 230,

1991 at UFL-B4. a) Surface East-West Velocity; b) Surface North-South Velocity; c)

Bottom East-West Velocity; d) Bottom North-South Velocity.


-.40

20
E




20

-4Q02


..40
20

E
0


0
S.


205


Ca
E


0
0


1 h
jlSIi~jnni~2


z220


225





56
The velocity components presented in Figure 4.9 show the influence of Venice

Inlet on the flows. Current magnitudes are as high as 25 to 30 cm/sec during neap

conditions. The residual velocities in the surface meter are not considered reliable

due to a calibration problem with the surface north-south component on the sensor.

The residual velocities measured at the bottom show -1.8 cm/sec in the east-west and

2.2 cm/sec in the north-south. The resultant vector is a 2.8 cm/sec residual at 319

degrees.

Although Stations UFL-B3 and UFL-B4 were in nearly identical bathymetric

conditions, and sensor elevations were identical, the vertical variations in velocity

were different. Visual comparison of the surface and bottom velocity components for

both stations indicates that UFL-B4 does not have as high a vertical velocity gradient.

This supports the assertion made earlier that the bottom boundary layer at Station

UFL-B3 may be laminar (due to the low velocity conditions) as versus turbulent at

UFL-B4. A more quantitative analysis of this phenomena will be made in Section

4.2.3 entitled "Harmonic Analysis of the Intertidal and Intratidal Frequency Bands".

Wind Data

Figure 4.10 presents the measured east-west and north-south components of the

wind speed for the 1990 and 1991 data periods. The 1990 data were obtained from a

permanent weather station positioned atop the Sunshine Skyway Bridge in the middle

of Tampa Bay. This station is maintained by NOAA. The University of Florida

stations were not installed during this period and therefore no wind measurements

were available for Sarasota Bay. The 1991 data were taken from the winds measured

at UFL-B3. The measured winds from UFL-B1, UFL-B2, and UFL-B4 are presented

in Appendix B.

Visual examination of the plots shows the difference in the wind conditions be-

tween the summer months and the fall. During the summer (bottom plots) the winds

are dominated by the sea breeze which is caused by the relative heating of the land











Sunshine Skyway (East-West Wind)


285


290


295
Julian Day (1990)


300


305


Sunshine Skyway (North-South Wind)


285


290


295
Julian Day (1990)


300


305


Station UFL-B3 (East-West Wind)


(a)









0



(b)


00 205 210 215 220 225 230
Julian Day (1991)

Station UFL-B3 (North-South Wind) i





,iv i1.U iih mii*nWk'b


205


210


215
Julian Day (1991)


220


225


230


Figure 4.10: The wind velocity vector components. a) East-west component measured
at the Sunshine Skyway (Julian Day 280 to 310, 1990); b) north-south component
measured at the Sunshine Skyway (Julian Day 280 to 310, 1990); c) east-west compo-
nent measured at UFL-B3 (Julian Day 200 to 230, 1991); d) north-south component
measured at UFL-B3 (Julian Day 200 to 230, 1991).


V p\^AYw
i: ft\j


E 10
-o

cn
S-10
00
Q.
U)
T-10


-Z80


E lO
-0
Q.
a)
CO

-10


--80


E 10
-0
0
a) 0
CO
C-10
i


-24


E 10


U)
-10
n (
0
Q.


~1"V~"~''-"i~MN


--UOO


-2(1L


-2nL-


C





58
mass versus the waters of the Gulf. The shoreline along Sarasota Bay is oriented

nearly north-south therefore the sea breezes are most pronounced in the east-west

wind components. Typical conditions during the summer have the wind coming out

of the east during the late evening and early morning hours, switching over to the west

during the daytime. The fall season (top plots) also shows sea breezes, but superim-

posed upon this are the effects of frontal systems. As fronts begin to propagate as far

south as Sarasota, the wind becomes dominated by these systems creating sustained

wind from one direction over several days.

Around day 284 in 1990, tropical storm Marco passed by Sarasota and Tampa

Bays. The storm moved into the Gulf of Mexico and ran along the coastline just

offshore over a period of 8 to 10 hours. The eye of the storm remained just offshore as

the storm passed, and the resulting winds are clearly seen in the 1990 measurements

taken at the Skyway Bridge.


4.2.2 Spectral Analysis of Tides, Currents and Wind

The first step in the decomposition of the water surface elevations and the currents

is to define where the energy within each of the signals resides. This is accomplished

through spectral analysis. The spectral density is a measure of the energy of a given

signal within a specific frequency band.

Analysis Method

Fourier Analysis was performed upon the water surface elevation, current, and

wind data to determine the variance or spectral density. The total variance (area

under the spectral density curve) represents the total energy of the signal. Therefore

the breakdown of the spectral density as a function of frequency will define the relative

energies within each frequency band.

The basic idea of Fourier analysis is that any function may be represented as the

sum of a series of sines and cosines of frequencies which are multiples of a fundamental






59
frequency o = (2r/MAt). The series can be expressed in equation form as;
M/2 M/2
X(t) = Zo + E Acos(mact) + E Bsin(mot) (4.2)
m=1 m=1
where, Am and Bm may be determined by evaluating M values of X(t) sampled at a

constant interval At. Once these values are determined the variance can be calculated

for each frequency band.

The data analysis program MATLAB was utilized to develop the power spectra or

spectral density curves. For this application the data consisted of 60 days of measure-

ments taken at 15 minute intervals, therefore each data set contained 5760 discrete

samples. 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 (Krauss, Shure and Little, 1993). For this study, it was desired to resolve the

spectral densities at frequencies as low as 0.1 cycles per day (10 day period). To

accomplish this, data sets of 2048 points were analyzed with sufficient overlap to

cover the entire 60 days of data. The data sets were demeaned and broken into 3

statistically independent sets of 2048 each. The sets overlapped each other by 200

data points. This methodology was utilized in all the subsequent spectral analyses.

One note on the use of the MATLAB spectral analysis subroutines is that due

to internal non-dimensionalization, which occurs within the MATLAB subroutines,

the absolute energy levels are not calculated. These can be corrected, but for this

study the energies were only utilized in a relative sense to determine the distribution

of the spectral energies. Therefore so long as the data sets compared are at identical

sampling intervals and durations the non-dimensionalization may be ignored when

performing comparative analyses.

Spectral Analysis of Water Surface Elevation Data

Figures 4.11 and 4.12 present plots of the spectral density function for three

of the USGS tidal stations during the 1990 and 1991 data periods. The stations

plotted represent a transition from conditions at an inlet (USGS-05) to a station well











Big Pass (USGS-05)


-- 10
E

10



Q 10
010
0z
ol
S10
U)








E
o


10'



CO
Q.
U)
10I






E
o
.104


S10'

Q.
10
) l


Frequency (cycles/day)


Frequency (cycles/day)


Figure 4.11: Spectral density of water surface elevations measured from Julian Day
255 to 315, 1990. a) USGS-05; b) USGS-04; c) USGS-06


Frequency (cycles/day)

Roberts Bay (USGS-04)







61




Big Pass (USGS-05)


E
o

10

10

( 0
o 10
0.
3)


Frequency (cycles/day)


Frequency (cycles/day)


Figure 4.12: Spectral density of water surface elevations
200 to 260, 1991. a) USGS-05; b) USGS-04; c) USGS-06


measured from Julian Day


1 2 3 4
Frequency (cycles/day)

Roberts Bay (USGS-04)


- 10
E

10
o

>104
Q
10 a


0 10s
Q.
u)
10'






4- 10'






102

CD
0.
C,
101






62
inside the system far from any inlet (USGS-06). The Roberts Bay station (USGS-04)

represents the transition region. The spectral density functions for all other stations

are presented in Appendix B.

The data exhibit three primary energy bands and three secondary energy bands.

The primary bands occur below 0.5 cycles per day (greater than 2 day period), 1 cycle

per day (1 day period) and 2 cycles per day (12 hour period). The term subtidal will

be applied to those frequencies below 0.5 cycles per day (Wong and Garvine, 1984)

as these are outside of the classic diurnal/semi-diurnal tidal periods. The other two

primary energy bands surround the diurnal and semi-diurnal harmonic constituents,

these are termed intertidal frequencies. The three bands are primary because they

are not generated locally (for the most part) but propagate into the system from the

Gulf of Mexico.

The secondary bands occur around 3 cycles per day (8 hour period) and 4 cycles

per day (6 hour period), and are termed respectively the third and fourth-diurnal.

These higher frequency signals are weak in the offshore but increase in magnitude

traveling into the lagoons. They are generated by the non-linear interaction between

the primary harmonic constituents (Pugh, 1987). These "intratidal" frequency bands

or "overtides" are generated locally and do not propagate in through the inlets.

The area under the spectral density curve represents the total energy within the

signal. Concurrently, the area under the curve within the individual energy bands

represents the energy within that particular range. Utilizing the range of frequencies

over which the harmonic constituents within a particular band are found to define the

frequency ranges (Pugh, 1987), the relative energy within the primary and secondary

bands are determined. The subtidal band is defined as ranging from 0 to 0.5 cycles

per day, the diurnal band is defined from 0.8 to 1.2, the semi-diurnal from 1.8 to 2.2,

the third-diurnal from 2.8 to 3.2 and the fourth-diurnal from 3.8 to 4.2.

Tables 4.1 and 4.2 present the distribution of energy found in the 1990 and 1991







Table 4.1: The distribution of tidal energy across the primary and secondary frequency
bands, 1990 data

Station Total Sub Diurnal Semi Third/Fourth Percent
Energy Tidal Diurnal Diurnal Total
cm2 s percent percent percent percent
USGS-01 26941.5 3.0 22.6 72.6 1.0 99.2
USGS-02 23432.9 4.4 24.0 69.5 .8 98.8
USGS-03 23677.4 3.3 24.1 70.4 1.1 98.9
USGS-04 19533.1 4.7 26.9 66.5 .5 98.6
USGS-05 25398.8 3.2 23.7 71.4 .6 98.9
USGS-06 13481.7 6.3 31.4 60.0 .8 98.5
USGS-07 12996.1 5.6 31.6 60.9 1.0 99.1



Table 4.2: The distribution of tidal energy across the primary and secondary frequency
bands, 1991 data

Station Total Sub Diurnal Semi Third/Fourth Percent
Energy Tidal Diurnal Diurnal Total
cm2 s percent percent percent percent
NOAA-O1 50578.0 .8 52.2 46.1 .5 99.6
UFL-O1 48090.5 .9 53.8 44.2 .5 99.5
UFL-02 42795.8 .8 54.3 43.6 .6 99.3
USGS-04 28392.2 2.5 56.8 39.4 .4 99.1
USGS-05 35738.2 1.8 51.3 45.6 .3 99.0
USGS-06 20825.6 3.2 64.0 30.9 1.3 99.3
USGS-07 19870.0 3.0 60.5 35.3 .3 99.1


water surface elevations. The tables list the station locations, the total energy (area

under the spectral density curve) and the percent energies within each of the frequency

bands. The final number is the percent of the total energy accounted for by adding

the sub-tidal, diurnal, semi-diurnal and the third/fourth diurnal energy percentages.

It is important to note that although the frequency bands are defined based upon

the tidal harmonics (i.e. gravitational forcing) all of the energy within the band may

not be forced by gravity. Meteorological forcing with associated frequencies may


contribute to the energy.





64
Within the Primary Bands, damping of the tidal wave as it propagates from the

offshore into the lagoons is highly dependent upon the associated frequency. Smith

(1980) showed that tidal inlets act as low pass filters. This can be carried one step

further and shown that restrictions within the lagoons also act as low pass filters,

and as the wave moves further into the lagoons the energies in the higher frequencies

are damped. This trend can be seen from the spectral analysis of the 1990 and the

1991 tidal data (Tables 4.1 and 4.2). The data show a decrease in the semi-diurnal

percentages going from USGS-05 to USGS-04 as well as from USGS-04 to USGS-06.

Coincident with this decrease in the semi-diurnal energy is an increase in the diurnal

and sub-tidal energy percentages. Going from USGS-05 to USGS-04 to USGS-06

represents movement from within an inlet further into the lagoons.

Comparison of the 1991 offshore data indicates that the tidal energy lessens from

north to south with the Tampa station showing the highest energy. This will affect the

interior stations as each is influenced by different inlets along the barrier islands. For

instance, the total energy at Blackburn Bay (USGS-07) is lower than the total energy

at Little Sarasota Bay (USGS-06). This result is unexpected based upon the location

of the two stations relative to their nearest forcing. The most likely explanation is

that the wave propagating in through Venice Inlet has less energy than that passing

through Big Pass. As these two waves combine to create the tides at Little Sarasota

Bay, the tides at Little Sarasota Bay are higher. Additionally, the total energy at the

station inside of Anna Maria Sound which is forced from Longboat Pass and Tampa

Bay is higher than that found within Big Pass. Were the offshore forcing constant,

this result would not be expected due to damping of the wave prior to reaching Anna

Maria Sound.

The energy residing in the secondary bands (Third/Fourth Diurnal) were com-

bined as they are relatively insignificant in comparison to the energies in the primary

bands. The data do indicate an increase within those bands at the more interior sta-





65
tions as compared with offshore and at the inlets. A more in-depth analysis of these

components will occur in the section entitled "Harmonic Analysis of the Intertidal

and Intratidal Frequency Bands".

Spectral Analysis of Current Data

Spectral analysis of the currents presents more difficulty as they are vector quan-

tities and contain direction as well as magnitude. For the purpose of the analyses, the

velocity vectors were broken into their east-west and north-south components. For

comparison Figure 4.13 presents the spectral density plots for the surface north-south

components at each of the four UFL stations. These components contained the high-

est level of energy at all four stations. The remaining spectral plots are included in

Appendix B.

The currents show energies in similar frequency bands as the tides with the ex-

ception of the subtidal component. All of the stations show energies in the secondary

bands as well as the primary bands. As energy is a scalar quantity, it is possible to

total the east-west and north-south components in order to define the total at each

station. Table 4.3 lists the total energy for both the bottom and surface currents,

along with the percent contained within each frequency band and the percent of the

total energy captured in the five frequency bands.

Looking first at the primary bands, two of the stations exhibit higher percent

energies in the sub-tidal than the other two. Stations UFL-B1 and UFL-B3 show

from 2 to 8 percent sub-tidal energy, while UFL-B2 and UFL-B4 exhibit less than 1

percent sub-tidal in all of the components. These similarities between stations extend

also to the distribution of the diurnal and semi-diurnal energies. Stations UFL-B1

and UFL-B3 show a more even distribution of energy between the diurnal and semi-

diurnal, while UFL-B2 and UFL-B4 show a much higher percent energy within the

semi-diurnal.

In Chapter 2, results from a study by Seim and Sneed (1988) were discussed










Station UFL-B1 (Surface North-South Velocity)








0 1 2 3 4 5
Frequency (cycles/day)

Station UFL-B2 (Surface North-South Velocity)




/ A




Frequency (cycles/day)

Station UFL-B3 (Surface North-South Velocity)








o 1 2 3 4 5
Frequency (cycles/day)

Station UFL-B4 (Surface North-South Velocity)





/ ,^, -,. \ f ,


0 1 2 3 4 5
Frequency (cycles/day)


Figure 4.13: The spectral density of the measured surface north-south current com-
ponents measured from Julian Day 200 to 260, 1991. a) UFL-B1; b) UFL-B2; c)
UFL-B3; d) UFL-B4.







Table 4.3: The distribution of current energy ((cm/sec)2-sec) across the primary and
secondary frequency bands, 1991 data (values in parenthesis represent percentage)

Station Sensor Total Sub Diurnal Semi 3rd/4th Percent
Height Energy Tidal Diurnal Diurnal Total
UFL-B1 Bottom 6726.3 2.4 37.0 40.6 11.5 91.5
Surface 11900.1 2.0 37.2 42.4 8.7 90.2
UFL-B2 Bottom 7042.4 .8 18.9 66.6 8.3 94.6
Surface 13679.3 .5 23.3 65.7 4.9 94.5
UFL-B3 Bottom 750.1 6.6 25.1 25.9 13.7 71.3
Surface 2174.5 7.7 33.1 34.5 6.4 81.8
UFL-B4 Bottom 2683.6 .8 21.5 53.6 16.8 92.8
Surface 7254.2 .7 32.2 51.8 7.2 92.0


which showed that inlets act to increase the semi-diurnal nature of currents entering

barrier island lagoons due to a transformation from a 2-D rotational flow (offshore) to

a 1-D unidirectional flow (within an inlet). The two stations which show the highest

percent of semi-diurnal energy (UFL-B2 and UFL-B4) share one common feature the

other two do not, the forcing for these come primarily from a single direction. UFL-

B2 from New Pass and Big Pass to the south and UFL-B4 from Venice Inlet to the

south. Additionally, UFL-B2 and UFL-B4 are closer to the inlet forcing. The high

percent energies in the semi-diurnal may be a residual influence from the passing of

the flow through the inlets. Seim and Sneed also showed that traveling further into

the lagoon the energy distribution begins to shift back toward the diurnal. This along

with the damping may explain the energies found at UFL-B1 and UFL-B3.

UFL-B2 and UFL-B4 share one other common characteristic, their percent total

energies contained within the four frequency bands are higher than UFL-B1 and UFL-

B3, with UFL-B3 (the most interior station) showing the lowest total percentage.

The results for the secondary bands show that the currents experience greater

influence from the non-linear interactions than seen in the tides. Percentages range

from 4.9 to 16.8 in contrast to 0.1 to 1.3 for the tides. Examination of the vertical

distribution of the energy shows that for all of the stations the percent energy in the










Station UFL-B3 (East-West Wind)


S101



Station UFL-B3 (North-South Wind) (b)




Q 10'
0 (O
CL
(j 10 1 / -
0 2 3 4 5
Frequency (cycles/day)

Figure 4.14: Spectral density of the measured wind speed components from Julian
Day 200 to 260, 1991 at UFL-B3. a) East-west component; b) north-south component.


secondary bands is highest for the currents nearer to the bottom. Studies presented

in Chapter 2 described the primary mechanism driving non-linear interaction as bot-

tom friction (Speer and Aubrey, 1985, Aubrey and Friedrichs, 1988, Freidrichs and

Aubrey, 1988, Speer, Aubrey and Friedrichs, 1991). The higher percentages in the

bottom measurements support this assertion.



Spectral Analysis of Wind Data

Figure 4.14 presents the spectral density functions for the measured wind compo-

nents at Station UFL-B3. The data from all four of the UFL Stations showed similar

spectrums with only minor differences. The east-west winds reflect the sea-breeze

with a peak in the spectral density at 1 cycle per day. The sub-tidal portion exhibits

a peak similar to that found in the tidal data and indicates some possible correlations.

The wind energy and its correlation to the currents and tides will be examined further





69

in the section 4.2.4 entitled "Analysis of Sub-Tidal Tides and Currents".


4.2.3 Harmonic Analysis of Tides and Currents

In the proceeding section the distribution of energy between the sub-tidal, diurnal,

semi-diurnal and the third/fourth diurnal were determined. In this section harmonic

analysis will be performed upon the water surface elevation and current data to

isolate the gravitational portion of the diurnal, semi-diurnal and third/fourth diurnal

frequency bands.

Harmonic analysis is the process of representing the gravitational portion of a

signal using a finite number of N terms of the form;

T, = Hgcos(aot S,) (4.3)

where, H, is the amplitude, ,, is the phase lag of the tide referenced to a specific

time datum (usually Greenwich) and a is the angular frequency of the harmonic.

An inherent assumption in harmonic analysis is that the mechanisms (or planetary

interactions) which create each component are known prior to the analysis, and the

task is to isolate chosen components from the signal.

A harmonic analysis program which utilizes least squares fitting was applied to

the data. The program creates a fit between the measured data and equation 4.3

with H,, g, and ao as the unknowns. The least squares fitting is adjusted so that

the square of the difference between the observed and computed tide levels, when

summed over all the observed values, has its minimum value. In all of the cases the

data are demeaned and detrended over the period of record prior to analysis.

The number of harmonic constituents to be analyzed is dependent upon the length

of the data record. In general, the longer the data record, the greater the number of

constituents which may be independently determined. A criteria for determining the

amount of data required to resolve two harmonic constituents states that, only con-

stituents separated by at least a complete period from their neighboring constituents,







Table 4.4: A list of the harmonic constituents analyzed

Constituent Period(hours) Origin
M2 12.42 Principal Lunar (Semi-Diurnal)
S2 12.00 Principal Solar (Semi-Diurnal)
N2 12.65 Larger Elliptical Lunar
K1 23.93 Principal Solar/Lunar (Diurnal)
01 25.82 Principal Lunar (Diurnal)
M03 8.39 Non-linear Interaction (M2, 01)
MK3 8.18 Non-linear Interaction (M2, K1)
M4 6.21 Non-linear Interaction (M2)


over the length of data, should be analyzed (Pugh, 1987). For example, in order to

determine the M2 and S2 tides independently, the number of days of data required is:

1.0
No. of days = 1 1.0 24.0 = 14.7days (4.4)
12.42- 12.00
The list of potential harmonic constituents is lengthy and contains over 1000

possibilities. These range from the solar annual with a period of 364.96 days to the

shallow water harmonic constituents which are generated by the non-linear interaction

of the primary harmonics. Applying Equation 4.4, a list of six primary constituents

and three secondary constituents was determined (Table 4.4). The list is relatively

short due to the length of the data record (60 days). Tidal data were available to

allow a greater number to be analyzed, but the current data were limiting and test

runs indicated that the components listed in Table 4.4 contained over 98 percent of

the energy.

Harmonic Analysis of the Water Surface Elevation Data

Tables 4.5 and 4.6 present the harmonic constituent amplitudes and phase lags

for the 1990 and 1991 tidal data. The harmonic analyses were performed on 60 days

of data starting Julian Day 255 in 1990 and Julian Day 200 in 1991. In the calculation

of the phase lags for both the 1990 and 1991 data, time zero was 00:00:00 EST in

1990.








Table 4.5: The harmonic constituents calculated from the 1990 tidal data

Amp. USGS USGS USGS USGS USGS USGS USGS
(cm) 01 02 03 04 05 06 07
M2 16.9 15.3 15.5 13.7 16.3 10.8 11.1
S2 8.0 7.0 7.1 6.1 7.6 4.9 5.0
N2 3.4 3.4 3.3 3.3 3.6 2.1 2.2
K1 9.9 9.3 9.9 9.2 9.4 8.6 8.3
01 15.9 14.8 15.0 14.3 15.5 13.1 13.3
MO3 .8 1.6 1.9 1.1 .4 1.4 .4
MK3 .3 .8 .8 .6 .3 .7 .2
M4 .7 .3 .6 .1 .4 .2 .4
Phase
Lag
(deg)
M2 79.4 96.5 97.7 93.9 60.6 135.6 83.5
S2 22.2 38.1 39.6 37.2 .6 78.3 24.6
N2 -.9 24.5 22.8 11.7 -21.6 66.3 4.8
K1 -55.5 -45.0 -43.5 -48.0 -65.1 -22.7 -48.7
01 29.1 41.3 41.1 38.9 21.5 62.6 36.9
M03 -43.8 30.0 31.8 39.9 -73.4 90.1 -93.2
MK3 -166.9 -96.0 -82.8 -92.5 147.9 -5.3 129.4
M4 -13.3 102.0 90.4 112.5 -102.6 -167.5 -43.5


Examination of the tidal constituent amplitudes provides further support to the

findings made in the previous section. First, the 1991 offshore data (NOAA-01, UFL-

02, UFL-03) show a reduction in the tidal amplitudes traveling north to south. There

is an 8 to 12 percent reduction in the semi-diurnal amplitudes and a 3 to 5 percent

reduction in the diurnal amplitudes. This offshore variation manifests itself in the

interior stations. For example, the tides at Anna Maria Sound show higher amplitudes

than Big Pass which should be more reflective of offshore conditions. The tides at

Blackburn Bay, which is just inside Venice inlet, show nearly identical amplitudes

compared to Little Sarasota Bay which is much further inside.

Secondly, the spectral analysis showed that the inlets and the lagoons act as low

pass filters by damping the higher frequency primary constituents. The results of the







The harmonic constituents, 1991


Amp. NOAA UFL UFL USGS USGS USGS USGS
(cm) 01 01 02 04 05 06 07
M2 19.0 18.0 16.8 13.7 16.3 10.5 11.0
S2 8.8 8.3 7.9 5.9 6.6 5.0 4.2
N2 4.4 4.3 4.1 3.1 3.8 2.5 2.5
KI 16.5 16.6 15.7 13.7 15.4 12.0 12.3
O1 15.4 15.1 14.2 14.5 14.6 13.5 12.3
MO3 .7 .9 .9 .7 .4 1.2 .6
MK3 .2 .3 .2 .9 .3 1.3 .1
M4 .5 .5 .5 .3 .1 .4 .2
Phase
Lag
(deg)
M2 25.3 16.8 25.2 57.7 29.3 107.5 53.9
S2 -8.4 -18.6 -10.5 39.0 -.9 98.7 27.3
N2 -77.7 -86.2 -76.2 -41.5 -72.8 6.8 -48.1
Kf1 -59.8 -63.8 -59.7 -39.1 -57.9 -9.5 -41.4
01 2.9 -1.7 1.7 23.0 4.6 54.2 25.2
MO3 -174.4 -177.7 -169.1 -23.2 -161.8 59.2 -169.1
MK3 175.9 -174.3 -166.9 -25.5 -37.9 34.3 105.7
M4 -119.4 -129.8 -107.2 63 .2 -140.9 155.9 -82.3


harmonic analyses allow further quantification of that damping through comparison

of the form numbers (equation 2.1). As stated in Chapter 2, the form number is

the ratio of the amplitudes of the two primary diurnal constituents (K1 and 01)

to the two primary semi-diurnal constituents (M2 and S2). An increase in the form

number indicates a shift in the energy distribution from the semi-diurnal to the diurnal

constituents.

Figure 4.15 present the form numbers plotted for each station for the 1990 and

1991 data periods. The stations are ordered on the x-axes such that they become

more interior (i.e. further from an inlet) moving from left to right. For the 1990 data,

the values range from 0.92 offshore up to 1.38 within Little Sarasota Bay, while for

the 1991 data they range from 1.15 in the offshore up to 1.68 within Little Sarasota


Table 4.6:


tidal data





73
Bay. The filtering of the tidal wave is clearly evident in the plots; there is a shift from

0.92 to 1.04 from the offshore to Big Pass in 1990 and from 1.15 to 1.31 in 1991.

The higher magnitudes of the form numbers in the 1991 data period reflect the

long term variations in the gravitational forcing mechanisms driving the tides within

the Gulf of Mexico. These variations impact the percent shift in the energy distribu-

tion between the diurnal and semi-diurnal constituents. Comparison of the change

in the form numbers between Big Pass and Little Sarasota Bay shows a 26 percent

shift for the 1991 data and a 34 percent shift for 1990. When the higher frequency

components represent a larger portion of the signal (as in the 1990 data period) the

shift in the energy distribution is greater.

Harmonic analysis provides further quantification of the overtides through the

calculation of the amplitudes of the non-linear constituents. Along coastlines where

the primary harmonic is the M2 tide, a measure of the degree of non-linear interaction

is the M4/M2 amplitude ratio. Consequently, along a coastline which has mixed tides,

such as the Gulf of Mexico, a similar ratio can be defined which compares the third

diurnal components with the three primary components which interact to create them.

An override ratio can be defined as;

(MO3 + MK3) (4.5)
(M2 + 01 + K1)

The third diurnal components are combined in order to eliminate any errors due to

leakage during the harmonic analysis. Leakage is where a portion of the energy which

exists in one component is mistakenly transferred to another with nearly the same

frequency.

Figure 4.15 presents plots of the overtime ratios for the 1990 and 1991 data. The

calculated ratios range from 0.01 at Big Pass to 0.08 in Little Sarasota Bay. These

are similar to values calculated for the M2/M4 ratio in other studies (Boon, 1988).

Examining the trends in the form number plots versus the trends in the overtime

ratio plots provides insight into the mechanisms altering the tidal wave. The over-








































1991 Data Period


0.06 -


0.04 -


0.02 -


0 -1
NOAA-O1


UFL-01 UFL-02


USGS-05 USGS-07 USGS-04 USGS-0


l Overtide Ratio + Form Number I


Figure 4.15: The Overtide Ratios and Form Numbers calculated from the measured
water surface elevations, a) Julian Day 255 to 315; b) Julian Day 200 to 260.


1990 Data Period I

0.08 1.8


1.6
0.06 -
o
1.4
D 0.04 -
'- 1.2
> LL
0.02 1


0 ,- 0.8
NOAA-01 USGS-05 USGS-07 USGS-01 USGS-04 USGS-02 USGS-03 USGS-06


i Overtide Ratio *. Form Number


1.8


1.6

E
1.4 z

t..
1.2


1
6





75
tide ratios for both the 1990 and 1991 data show similar trends. The ratios decrease

initially moving from the offshore through the inlets. The ratios begin to increase as

the wave propagates further into the system with the maximum values at the most

interior stations. The form numbers on the other hand appear to respond to restric-

tions within the system. Although the values increase moving further into the bay

this increase appears to be due to the wave encountering additional restrictions. This

phenomena is best illustrated by comparing station USGS-07 with stations USGS-02

and USGS-03. Station USGS-07 is near an opening to the Gulf of Mexico (Venice

Inlet) but there are narrow restrictions leading to the station. USGS-02 and USGS-03

on the other hand are more interior but only the passes restrict the wave, the stations

are in open water regions. USGS-07 has a high form number but a low overtime ratio

while USGS-02 and USGS-03 have high overtime ratios but low form numbers.

The harmonic phases allow the determination of the travel time of the tidal wave.

They also provide information on phase lags which may exist between the relative

openings to the bay. This is important in the determination of residual flow patterns.

In bodies of water with multiple inlets, a phase lag of the tidal wave arriving at one

inlet relative to another can create a net flow. In Chapter 2, studies were presented

which showed that within idealized multiple inlet systems a phase lag between the

arrival of the tidal wave from one inlet to the other can create a net flow toward the

lagging inlet (van de Kreeke and Dean, 1975, Fisher, 1979).

Comparing the phases of the two University of Florida offshore stations and the

NOAA offshore station defines the progression of the tidal wave as it propagates

within the Gulf of Mexico. Examination of Figure 3.1 shows that station UFL-O1 is

located approximately 5 kilometers offshore between Longboat Pass and New Pass,

Station UFL-02 is located south of UFL-O1 approximately 4 kilometers offshore

between Venice Inlet and Big Pass. Station NOAA-O1 is not shown on Figure 3.1

but is located approximately 10 kilometers off of the entrance to Tampa Bay north







of UFL-O1.

The data show that the tidal wave arrives first at Station UFL-O1 and nearly

simultaneously at the two outer stations, UFL-02 and NOAA-O1. This phase dis-

tribution does not support the residual flow measured at UFL-B1. Based upon the

idealized studies presented in Chapter 2 (van de Kreeke and Dean, 1975) if a phase

lag exists between two inlets a residual flow will develop toward the lagging inlet.

Based upon the offshore phase distribution, the tides within Tampa Bay should lag

behind Longboat Pass with an associated residual from Longboat toward Tampa Bay.

It is difficult to directly connect this phase distribution with the residual flow because

tide measurements were not taken directly north and south of UFL-B1, therefore the

exact phase distribution on either side is unknown.

Harmonic Analysis of Current Data

Harmonic analysis of the currents presents more difficulty as they are vector

quantities. In order to examine the tidal current harmonics it is standard practice

to evaluate the harmonic ellipses. For an idealized current, taking the position of

the head of the velocity vector and tracking throughout the tidal cycle with the base

remaining in a constant position gives an ellipse. Harmonic analysis of the currents

provides the magnitude of the principal major and minor axis lengths along with the

orientation of the major axis for each harmonic constituent. From this data ellipses

can be drawn which provide a visual representation of the characteristics of each

current component. The following describes the results of the harmonic analysis of

the currents for each station.

Station UFL-B1

Table 4.7 presents the harmonic ellipse components for Station UFL-B1. Figure

4.16 presents plots of the two primary semi-diurnal (M2, S2) and two primary diurnal

(K1 and 01) harmonic ellipses for the surface and bottom currents.

Using the principal axis amplitudes for these constituents, a form number can be




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