Citation
Circulation and transport within a system of shallow, interconnected barrier island lagoons

Material Information

Title:
Circulation and transport within a system of shallow, interconnected barrier island lagoons
Series Title:
UFL-COEL-TR
Creator:
Peene, Steven J., 1960- ( Dissertant )
University of Florida -- Coastal and Oceanographic Engineering Dept
Sheng, Y. Peter ( Thesis advisor )
Dean, Robert G. ( Reviewer )
Sheppard, Max ( Reviewer )
Hanes, Daniel ( Reviewer )
Montague, Clay ( Reviewer )
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept., University of Florida
Publication Date:
Copyright Date:
1995
Language:
English
Physical Description:
xxiii, 302 p. : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Bays ( jstor )
Inlets ( jstor )
Lagoons ( jstor )
Modeling ( jstor )
Ocean tides ( jstor )
Salinity ( jstor )
Sensors ( jstor )
Simulations ( jstor )
Surface water ( jstor )
Velocity ( jstor )
Coastal and Oceanographic Engineering thesis, Ph. D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Tidal currents -- Mathematical models -- Florida -- Sarasota Bay ( lcsh )
Sarasota Bay ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )
Spatial Coverage:
United States -- Florida -- Sarasota Bay

Notes

Abstract:
Data of water surface elevations, currents, winds, discharge 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 distribution 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 with 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 recieve tidal forcing from opposite direction exhibit similar characteristics, such as increased residual flow energy, and equivalent distribution of energy between the semi-diurnal and diurnal. Regions which are forced more uni-directionally exhibit opposing characteristics. All regions no matter the depth exhibit some level of three-dimensionality in the currents, both in the short term and residual flows. Filtering of the winds, water levels, and current identified the driving mechanism for the residual fluctuation 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 band (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 characteristics 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.
Thesis:
Thesis (Ph. D.)--University of Florida, 1995.
Bibliography:
Includes bibliographical references (p. 298-302).
Funding:
This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
General Note:
Includes vita.
General Note:
UFL/COEL-TR/118
Statement of Responsibility:
by Steven J. Peene.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
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The University of Florida George A. Smathers Libraries respect the intellectual property rights of others and do not claim any copyright interest in this item. This item may be protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work have responsibility for determining copyright status prior to reusing, publishing or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. The Smathers Libraries would like to learn more about this item and invite individuals or organizations to contact Digital Services (UFDC@uflib.ufl.edu) with any additional information they can provide.
Resource Identifier:
41567306 ( OCLC )

Full Text
UFL/COEL-TR/118

CIRCULATION AND TRANSPORT WITHIN A SYSTEM OF SHALLOW, INTERCONNECTED BARRIER ISLAND LAGOONS
by
Steven J. Peene

Dissertation

1995




CIRCULATION AND TRANSPORT WITHIN A SYSTEM OF SHALLOW,
INTERCONNECTED BARRIER ISLAND LAGOONS
By
STEVEN J. PEENE

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

1995




ACKNOWLEDGEMENTS

I would like to express my gratitude to my advisor and supervisory committee chairman, Dr. Y. Peter Sheng, for his guidance and support throughout my doctoral program. The freedom he allowed me in the development of the field measurement program provided an education I could not have gotten anywhere else. I would also like to thank the members of my committee, Dr. Robert G. Dean, Dr. Max Sheppard, Dr. Daniel Hanes and Dr. Clay Montague, for their advice and support.
I must thank everyone out at the Coastal Laboratory where I spent the best parts of my years in the program. Special thanks to Vernon Sparkman and Jim Joiner who not only provided most of the brain power for the field work but also friendship, patience, guidance and fun. Special thanks also to Sidney Schoefield, Danny Brown, Don Mueller, Mark Southerland, Chuck Broward, Vik Adams and George Chappel. I will never forget volleyball the Cypress Lodge, redneck preppies, tower ramming, gator skiing, mutiny on the Munson, the sinking of the Anna Capri and all my friends at the lab.
As my time in the program was rather lengthy, I was fortunate to make many good friends. I owe them a lot because they helped make my time at the University fun. Thanks to Tom B., Rick, Victor, Yuming, Sam, Jeff, Barry, Gusty, Mike and Sheila, Phil and Lynn, Becky and Terry, Sandra, Lucy, Laura, Paul, Jei Kok, Dave, H.K. Lee, Phil H., Mark P., and Eduardo. A special thanks to all the members of L.A.S. whom I will always count as my good friends.
Thanks to my parents for always believing in me and supporting me in whatever endeavor I undertook. Also to my sister C.J. for her love and support through this




whole craziness.
Finally, my wife Christina, whom I met at the start of this program, fell in love with and married as a doctoral candidate. She always stood by me and supported me. She went through all the tough times and always told me I could make it. She never lost faith in me.




TABLE OF CONTENTS

ACKNOWLEDGEMENTS .. .. .. .. LIST OF FIGURES... .. .. .. .. ..
LIST OF TABLES.. .. .. .. .. .. ..
ABSTRACT... .. .. .. .. .. .. .. .
CHAPTERS

I IiN I kiL)JJ U I WiN .. .... ...... ... ........... .
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 Sumnmary.... .. .. .. .. .. .. .. .. .. .. .. ...
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
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 Wind 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
CA1 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 discharge 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 (Julian 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) UFLBi; 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 measured 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 11, 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
USGS-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
USGS-06 .. .. .. .. .. ... .... ... .... ... ... ...92
4.23 The filtered wind speed components compared to the current vector 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 components and the filtered wind vector components at 30 degree spacings from 190 to 340 degrees, UFL-B31, Julian Day 200 to 260. a)
north-south currents; b) east-west currents .. .. .. .. ... ....96
4.25 The coherence between the filtered surface current vector components and the filtered wind vector components at 30 degree spacings from 190 to 340 degrees, UFL-B31, 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 vector 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 vector 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 vector components at UFL-B34, 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 surface 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, Julian 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 UFLB1, 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 elevations, 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
overtide 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 northsouth 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) Blackburn 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 Motion 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 Motion 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 Motion 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 Motion 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 Equations 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 Equations of Motion for the 30 Day No Wind Simulation in 1991 at UFL-B1; a). Alongchannel Component, b). Crosschannel Component . . . . 218
6.28 A Comparison Between the Simulated Residual Water Level Fluctuations and the Simulated Alongchannel and Crosschannel Surface 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 Equations 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 Equations 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 Equations 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 (USGS07) from Julian Day 255, 1990 to Julian Day 100, 1991 ...... ..265
B.19 The Water Surface Elevation Measured in Blackburn Bay (USGS07) 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 Measured at Station UFL-B1 from Julian Day 200 to 260, 1991 271
B.25 The East-West and North-South Wind Speed Components Measured at Station UFL-B2 from Julian Day 200 to 260, 1991 272
B.26 The East-West and North-South Wind Speed Components Measured at Station UFL-B3 from Julian Day 200 to 260, 1991 273
B.27 The East-West and North-South Wind Speed Components Measured at Station UFL-B4 from Julian Day 200 to 260, 1991 274




B.28 The Spectral Density versus Frequency for the Water Surface Elevation 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 Components 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 Components 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 Shallow 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/s eC)2 -sec) across the primary and secondary frequency bands, 1991 data (values in parenthesis 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-B31, Julian Day 200 to 260 78
4.8 The principal axes harmonic constituent amplitudes, phases and
axis directions for Station UFL-B32, Julian Day 200 to 260 79
4.9 The principal axes harmonic constituent amplitudes, phases and
axis directions for Station UFL-B33, 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 surface 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, diurnal, semi-diurnal and third-diurnal bands for the water surface elevations measured at stations USGS-04, USGS-OS, USGS-06, and
USGSO7, 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, diurnal, semi-diurnal and third-diurnal bands for the July/August
1991 simulations at station UFL-B .. .. ... ... ... ...159
6.6 A comparison of the measured and simulated total spectral energy
and the percent distribution of energy between the sub-tidal, diurnal, 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, diurnal, 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, diurnal, 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 current constituents for the July/August 1991 data at UFL-B1 167
6.11 A comparison between the measured and simulated harmonic current constituents for the July/August 1991 data at UFL-B2 169
6.12 A comparison between the measured and simulated harmonic current constituents for the July/August 1991 data at UFL-B3 170




6.13 A comparison between the measured and simulated harmonic current constituents for the July/August 1991 data at UFL-B4 172
6.14 The mean water surface elevation predicted by the model for Julian 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 calculated 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 Sensitivity 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 see, Low Value = 5000 cm2 sec, High Value = 100000 cm2 sec (UFL-B2,
UFL-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
Vericl EdyVisosty(10 2:
Vertical Eddy Viscosity (10 ) 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 Vertical 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 distribution 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 exhibit 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 matter 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 characteristics 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.




CHAPTER
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 processes 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 configurations 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 environment. 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 kilometers, 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 barrier island lagoons are the product of the energy imparted by the forcing mechanisms acting therein. These mechanisms include water surface gradients, wind stress, vertical 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
35
water, and a torque is induced causing the water mass to rotate."




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 Zimmerman, 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, Longboat 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. Another tidal openning 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, infiuling 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 recent 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 circulation 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 colun, resuspension and deposition of bottom material, and many other phenomena.
Since 1990, the Coastal and Oceanographic Engineering Department of the University 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 openning 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 transport. 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,7 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 components 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 improved understanding of the overall circulation and transport within the Sarasota Bay System through the quantification of these individual components and the determination 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 development 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 physical 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 quantification 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 variations 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 01), 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, 0, + K, (2.1)
M2 + S2




12
where 01 and K, 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-diumal 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 Itiver 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 I 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 forcings.
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
A, C-VRS(2.2)
2gL(23
2 fL + mR(23
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 = Tb(2.4)
pU.,




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 performed 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 overtide or higher harmonic is the M4 constituent. Consequently the M4/M2 ratio is an indication of the level of nonlinearity 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 dominance 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 bL +a 0 (2.5)
a9t a9x
aQ+A ( + I aQ2 _-fQQb (2.6)
at a9x AI 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
gAvI = -(2.7)
Ox2
where, fr 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
Q IT]QdX (2.8)
The forcing of the tides occurs at the ocean side of the idealized inlets and is defined as
(i = alcos(at+6) (2.9)
(4= a4COS(o't) (2.10)
where C is the water surface elevation, o- 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 (a2/1h 2), 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

4oo. 1000.

/ /
I
I
I
I

I I

INLET I

- DEPTH OF INLET = ( FT)

300
IO
10 I iool
I =
I
~ I wIoTH OF INL.LT X (PT)

10oo

-Z=1

Soo00 7 1Q00o 2.000ZO

FORn CONFIGURATION OF LAG0ON- INLLT SYSTEM WFL FIGURE I FOp. NUME.RJAL VAL.UJLS .5 IN THE. C .MPUTATIONS .E. TABLE 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

1 I

m

1

L




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 gradients 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.
Drinkers (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 phenomena. 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 friction 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 I-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

L' = CQi

(2.11)




where
L= -(b (2.12)
is termed the amplitude response; it relates the bay amplitude ((b) to the ocean amplitude ((,), and
=( 2g ) (AI 2 (2.13)
QI (W2 JK4A
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,MS4,MK4,M6,M) 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
U: OU gAp (2.15)
at O A, ox p




Figure 2.2: The idealized channel geometry used in the solution of the l-D Equations of Momentum and Continuity (Speer and Aubrey, 1985) ,9( 1 a-t-b +b ax 0 (2.16)
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 UU (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 amplitude, a/h and marsh storage volume to channel volume ratio (V/V) 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 1D 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 M41M2 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 assuming 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 equation, and inserting it into the continuity equation, gave a non-linear diffusion equation of the form
at b~ ni~j) =0(2.18) where n is Manning's friction coefficient and b, 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 analytically 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 numerical 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 northern portion of Biscayne Bay using a nested 1-D/2-D numerical model. The onedimensional 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 forcings 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 calculated 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 forcings 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 preceeded the publication 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. Although 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 applied 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 relative 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 multidimensional 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
S 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 describes 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 instrument 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 forcings impact the interior circulation.
The bay stations were installed to measure currents, water surface elevation, conductivity, 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-B31, 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 aluminum; a 4 meter high platform weighs approximately 125 kg without instrumentation. The platforms were designed such that they could be broken apart and transported 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 assembled at a dockside location without the instrumentation. A transport saddle, which




30
INE TAMPA BAY
.. ..L. .. .. .
. ..o. . .
.. ...NN A. .. .. .
U SG S-al .........A.. ................
ANNA MARIA...... ..............N.......
. . . .
.... ... ...A.. .... ... ... ... ...
PASS.................. ... RA ....T. BAY... EAST.. ...
U S. .. .. .. ..-. ..0.. .. .
SARAOTA AYNWES
U S S 0 A I .... .. .I. . .. . ..+. .
SCA AREINMTR
. 4.0 0 . ..m. . . .
Figur 3.1 The. loaton of.. the...... ..L.an.USGSdata.ollecion.sation.withn.Ann
Maria Sund an Big SrasotaBay,.191.depoyment




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1P ....................... ................ ......
In
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v ............. U S G S 0 6 ..............................
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. ...................................................
...................................................
.. ............ ............ .... ......... I ...... ........
. ...................................................
. .........................................
. ........................
..................
....................................
FL-84.
..****'* .......................................
..............................................
..............................................
............................................
...................
....................................
....... ...............
':' BLACKSURN'o' ...............
... ... ...........................
.. .... ............... *** ..
...... M Y .................................
......................................
.....................................
.....................................
....................................
.....................................
....................................
..........................
....................................
. ............................
. . . .
. . . .
. . . .
000 2.000
. . . .
................ .
4 M ETERS .. ........ .................
....... ....
Z.000 M
USGS-07
BLACKBURN BAY
VENICE INLET

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 1. SCALE I~




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 locations 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 Iongitude, 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.

Logger

Temperature and Conductivity Sensors




Table 3.1: The locations and depths of the University of Florida Stations
Station I.D. Latitude I 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 deployment

Station Arm Number] Current Conductivity I 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 voltage 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 magnitude 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 measurements of the horizontal vector components are not contaminated by vertical velocity fluctuations which may be present. They are also accurate sensors, capable of measuring 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 cleanings, 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 Technologies. 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 sensors 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 sensors 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 direction. 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 direction. 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 pooi 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 loggers 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-Bl1, UFL-B32 and UFL-B34 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-B31 and UFL-B32 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 pressure 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




Buoy
Conductivity Sensors
Sea-Data Package
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 reference 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




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 August 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 August 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 determine 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 directly 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 measurements 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 measurements 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
devaluation of transport and the level of flushing within the individual lagoons. Additionally, 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 thunderstorms and low overall wind energy. The second period (September 15, 1990 to November 15, 1990) reflects fall to winter conditions with higher sustained wind energy. 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 (M!2 and AN2) the diurnal (K1 and 01) 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 forcings 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 forcings 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 forcings. 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 forcings in general are small in relation to the long term variations in water level associated with meteorological forcings.
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 measured 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 elevations, 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-O1) 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-O5 (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




8o
60 E 40 20 0
-20 0-40
.60

Julian Day (1990)

100 A80 EE 60
40 o 20
.2-20
L-4
-40

Julian Day (1990)

Julian Day (1990)

USGS-06 (Little Sarasota Bay)

27O
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 .2 20 C0
-2 -20
w
-40

100
80 E 60 C.)
40 20 C)
- -20
LI
-40
.SrI

260

265




Offshore (UFL-O1)

80 S60 E 40 p.
20 2 0
>-20
--40
-60
-8 $C

215
Julian Day (1991)

220

Julian Day (1991)

USGS-04 (Roberts Bay)

0 205 210 215 220 225 23
Julian Day (1991)
USGS-06 (Little Sarasota Bay)

210

215
Julian Day (1991)

220

225

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).

210

100
_ 80 E 60
40 .0 20
0
-220
-40

205

100
80 E 60
p
40
-G
o. 20
0
.220
a
-& -20
LM
-40
-602
100
- 80 E 60
40
.2 20 C0 .2.20
-40
.6%2

!vv~~ ~ 1,4 vvvvv vvij lV

(a)
30
(b)
0
(c)
0

0i

0




120 100
-E80
--60
g 40
" 20 > 0
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 channels. 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 meters) 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 .
mrn, wmie eval (MLW)
0
100 fUFL-B1 Platform
o0 -200
ca
.300
-400 t . . .
0 100 200 300 400 600 600 700
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 transport 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-




49
Surface East-West Velocity, Station 1

210

25
0
0 0
o 25
O 2
E C)
0
-25
E
0 25 0D

220

Surface North-South Velocity, Station 1

21U

Jul
Julian Day

Bottom East-West Velocity, Station 1

21U

Julian Day

Bottom North-South Velocity, Station 1

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

215
Julian Day

205

-200

205

- 0
- 25
E
0
0
-25

9~

I

~flI

- -ZOO

50
0
0 c.
-'- 25
E
0
C0
0 25
S

-200

205

.R -- .. .^^ t

1 1% mo,

220U

225

220

ee;a

220

225:

ejU




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 supports 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 current 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 4-4 -.. ... ..

21i
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
"- 20
E
0
-20
S

.. 40
0
S
c- 20
E
0
20 o-20

0
C
E
0 0>
0
o

C
E
0
0
o.
C)

205




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-bottomn 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
DO 205 210 215 220 225 2
Julian Day
Bottom East-West Velocity, Station 3

DO205 210 215 220 225 23
Julian Day
Bottom North-South Velocity, Station 3

210

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
20
0
0

~2O0

- 40
20
E
0 0-2
C)
0
0
_ 40
0
0
-0
-20
E
-0
0




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 eastwest 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

__ 40
"- 20
E
0
20
52

-4 0200 205 210 215 220 225 230
Julian Day Bottom North-South Velocity, Station 4 40
20
"-0
-20
-ArLu

--Zo0

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
0
- 20
0
-20
-402C

-_ 40 20
E
20
20 S.20

205

Ca
5.
0
0
S

220U

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 between 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 9 220 225 230
Julian Day (1991)
Station UFL-B3 (North-South Wind) I

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 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).

V ~ pf~J~~/t

E 10
-o
0
0.
U)
"_0

-Z5O

E 10
0
CO
-10
0

- 280

E 10 "0
00
0
C-10

-2%

E 10 (D0
0 U)
-10

MN

--UU

-2n-




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 sununer 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 superimposed 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(mcrt) + E B,,sin(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 measurements 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)

- 10s
E
a10
o 0z
10'
C
-0-.10s
E
os
10'
0 101
10
0.
u)
loll
10s
E
o
N 10
1 10
104
Ca
C
3
0
C.) lo

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)

-- 10
2
10
10
o 102 O102
0.
43)

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
10
Q 10
o 2
S10
101
4- 10'
E
0
1>.i04
C
01 Cu
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 overridess" 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
.____1cm2-_ 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
UJSGS-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
cm 2_sprtpercent percent percent ___NOAA-01 50578.0 .8 52.2 46.1 .5 99.6
UFL-01 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-O5 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,7 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 forcings 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 sem-i-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 forcings. 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 forcings 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 combined 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 quantities 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 highest 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 exception 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 semidiurnal, 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-B 1 (Surface North-South Velocity)
o1 2 3 4 5
Frequency (cycles/day)
Station UFL-B2 (Surface North-South Velocity)
//
0/
o i 2 3 '44 5
Frequency (cycles/day)
Station UFL-B3 (Surface North-South Velocity)
o i2 34
Frequency (cycles/day)
Station UFL-B4 (Surface North-South Velocity)
2 3 4 5
Frequency (cycles/day)

Figure 4.13: The spectral density of the measured surface north-south current components 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. UFLB2 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 forcings. 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 UFLB3, 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 U FL-B3 (East-West Wind)

CD10
C 10 1 0 3 4
Frequency (cycles/day)
Station UFL-B3 (North-South Wind) (b)
E
>,104
0
CL
J 101 /
C) I I23 45
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 bottom 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 components 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,, = Hcos(at &) (4.3)
where, H.,, is the amplitude, & is the phase lag of the tide referenced to a specific time datum (usually Greenwich) and o- 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 o,,, 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 constituents separated by at least a complete period from their neighboring constituents,




Table 4.4: A list of the harmonic constituents analyzed
Constituent I Period(hours) ]Origin M2_____ 12.42 Principal Lunar (Semi-Diurnal)
S2_____ 12.00 Principal Solar (Semni-Diurnal)
N2 12.65 Larger Elliptical Lunar
K, 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 (Ml2, K1)
M46.21 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: No. of days = 1. 24.0 = l4.7days (4.4)
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
M03 .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, UFL02, 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
If 16.5 16.6 15.7 13.7 15.4 12.0 12.3
01 15.4 15.1 14.2 14.5 14.6 13.5 12.3
M03 .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
IfK1 -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
M03 -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 distribution 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 overtide 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 overtide 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 M2/1M4 ratio in other studies (Boon, 1988).
Examining the trends in the form number plots versus the trends in the overtide ratio plots provides insight into the mechanisms altering the tidal wave. The over-




1991 Data Period

0.06 0.04
0.02 -

0 N 1 NOAA-O1

UFL-01 UFL-02

USGS-05 USGS-07 USGS-04 USGS-0

Il Overtide Ratio + Form Number

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 a
0.08 1.8
- 1.6
0.06
o
0.04
- 1.2
'(D0.04 z
-3 1.2 E > LL
0.02 1
0 N S U 0.8
NOAA-01 USGS-05 USGS-07 USGS-01 USGS-04 USGS-02 USGS-03 USGS-06

ig Overtide Ratio Form Number I

1.8 1.6
E 1.4 z
It..
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 restrictions 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 overtide ratio while USGS-02 and USGS-03 have high overtide 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-01 is located approximately 5 kilometers offshore between Longboat Pass and New Pass, Station UFL-02 is located south of UFL-01 approximately 4 kilometers offshore between Venice Inlet and Big Pass. Station NOAA-01 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-01 and nearly simultaneously at the two outer stations, UFL-02 and NOAA-O1. This phase distribution does not support the residual flow measured at UFL-B31. 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-B31, 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-B31. 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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