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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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