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Subtidal Variability in Water Levels of the St. Johns River

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Title:
Subtidal Variability in Water Levels of the St. Johns River
Creator:
Henrie, Krista J
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (61 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Coastal and Oceanographic Engineering
Civil and Coastal Engineering
Committee Chair:
Valle-Levinson, Arnoldo
Committee Members:
Thieke, Robert J
Graduation Date:
5/5/2012

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Subjects / Keywords:
Amplitude ( jstor )
Basins ( jstor )
Bodies of water ( jstor )
Buffaloes ( jstor )
Estuaries ( jstor )
Modeling ( jstor )
River water ( jstor )
Rivers ( jstor )
Signals ( jstor )
Water filtration ( jstor )
Civil and Coastal Engineering -- Dissertations, Academic -- UF
subtidal
St. Johns River, FL ( local )
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Coastal and Oceanographic Engineering thesis, M.S.

Notes

Abstract:
Hourly water level data at 5 stations along the St. Johns River were compiled for the year of 2004 with the purpose of determining the propagation of subtidal pulses along the estuary. In order to identify these subtidal pulses, data were low-pass filtered at half-periods of 30 h. The subtidal water level records included a dominant seasonal signal that hindered the study of shorter term pulses. This seasonal oscillation was removed from the low-pass filtered records. The resulting signals were analyzed with Complex Empirical Orthogonal Functions (CEOF), through a Hilbert Transform, to discern the amplitude and phase of the subtidal pulses propagating throughout the estuary. The first CEOF mode explained 94% of the temporal variability and its spatial structure indicated an unusual distribution: attenuation in amplitude (11.4%) over the first 60 km, then amplification of 2.9% from 60 to 130 km, and attenuation of 8.9% for the remainder of the estuary. The phase of the first CEOF mode illustrated progressive wave behavior over the first 60 km of the estuary and quasi-standing wave behavior for the remaining 85 km. Additionally, the phase of the first mode suggested two separate locations for subtidal pulse forcing. An absolute minimum in phase at the estuary’s entrance demonstrated that the dominant forcing was from the coastal ocean. The phase also revealed a local minimum around Palatka, indicating that a second, weaker forcing occurred around 130 km into the estuary. Finally, an analytical model that describes the evolution of long waves through a channel with frictional damping was fit to the first mode of the statistical (CEOF) results. Solutions were obtained as a function of two parameters: kappa, a relative measure of the channel length to the wavelength, and delta, a relative measure of frictional damping to local acceleration. Although multiple combinations of kappa and delta with similar root mean square errors (RMSe) could be applied to describe the Lower St. Johns River, the best match (0.45% RMSe) with the CEOF results was produced with 0.6 for kappa, the geometric parameter and 1.6 for delta, the dynamic parameter. A value of kappa of 0.6 means that the basin length is roughly one tenth of the wavelength and a delta of 1.6 indicates the entire water column is influenced by friction. Subtidal pulses in this estuary, therefore, behave as damped waves that can be represented with simplified theoretical solutions. ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2012.
Local:
Adviser: Valle-Levinson, Arnoldo.
Statement of Responsibility:
by Krista J Henrie.

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Copyright Henrie, Krista J. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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1 SUBTIDAL VARIABILITY IN WATER LEVELS OF THE ST. JOHNS RIVER By KRISTA HENRIE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCI ENCE UNIVERSITY OF FLORIDA 2012

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2 2012 Krista Henrie

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3 To my sister, Kayla

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4 ACKNOWLEDGMENTS I thank my family for always providing me with love and support in all my endeavors. I also thank my advisor, Dr. Arnoldo Valle Levinson for his guid ance and patience throughout this project. Dr. Arnoldo Valle world of thanks for all of their encouragement and advice. I also thank Dr. Robert Thieke for his instruction and support

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF FIGURES ................................ ................................ ................................ .......... 6 LIST OF ABBREVIATIONS ................................ ................................ ............................. 8 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 12 Motivation ................................ ................................ ................................ ............... 12 Long Wave Propagation ................................ ................................ ......................... 1 2 Subtidal Variability ................................ ................................ ................................ .. 13 2 METHODS ................................ ................................ ................................ .............. 15 Study Area ................................ ................................ ................................ .............. 15 Data Collection ................................ ................................ ................................ ....... 17 Data Processing ................................ ................................ ................................ ..... 18 The Mod el ................................ ................................ ................................ ............... 19 3 RESULTS ................................ ................................ ................................ ............... 26 Subtidal Water Levels ................................ ................................ ............................. 26 Removal of the Seaso nal Signal ................................ ................................ ............. 26 Statistical Results ................................ ................................ ................................ ... 28 4 D ISCUSSION ................................ ................................ ................................ ......... 47 5 CONCLUSIO N ................................ ................................ ................................ ........ 56 APPENDIX : ANALYTICAL MODEL EQUATIONS ................................ ........................ 57 LIST OF REFERENCES ................................ ................................ ............................... 59 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 61

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6 LIST OF FIGURES Figure page 1 1 St. Johns River Estuary ................................ ................................ ...................... 14 2 1 5 NOAA stations along the St. Johns River ................................ ........................ 23 2 2 M 2 tidal amplitude ................................ ................................ ............................... 24 2 3 M 2 tidal phase ................................ ................................ ................................ ..... 25 3 1 Tidal and subtidal water levels at Mayport ................................ .......................... 30 3 2 Tidal and subtidal water levels at Main St. Bridge ................................ .............. 31 3 3 Tidal and subtidal water levels at I 295 Bridge ................................ ................... 32 3 4 Tidal and subtidal water levels at Palatka ................................ ........................... 33 3 5 Tida l and subtidal water levels at Buffalo Bluff ................................ ................... 34 3 6 Subtidal water levels in 2004 ................................ ................................ .............. 35 3 7 Least squares fit with 2 har monics to t he subtidal water level at Mayport .......... 36 3 8 Reconstruction of the subtidal water levels with the first mode from the EOFs .. 37 3 9 S easonal oscillation from the filtered first mode of the EOFs ............................. 38 3 10 Average seasonal cycle for Mayport ................................ ................................ ... 39 3 11 Subtidal water l evels minus the seasonal oscillation ................................ .......... 40 3 12 Temporal variability of dominant modes ................................ ............................. 41 3 13 Amplitude vs. distance along the est uary for modes 1 and 2 ............................. 42 3 14 Reconstruction of the subtidal record with mode 1 of the CEOFs ...................... 43 3 15 Reconstruction of the subt idal record with modes 1 and 2 of the CEOFs ........... 44 3 16 Phase vs. distance along the estuary for modes 1 and 2 ................................ ... 45 3 17 Phase vs. dis tance along the estuary for mode 1 ................................ ............... 46 4 1 Model bathymetry ................................ ................................ ............................... 50 4 2 RMSe as a function of and ................................ ................................ ............ 51

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7 4 3 Amplitude ................................ .......................... 52 4 4 ................................ ............................... 53 4 5 ...................... 54 4 6 ........................... 55

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8 LIST OF ABBREVIATION S Velocity gradient Local acceleration Water surface gradient A z Eddy viscosity B Half the b asin width (m) Wave celerity (m/s) CEOF Complex empirical o rthogonal f unctions EOF Em pirical orthogonal f unctions Coriolis Gravitational acceleration H Water depth (m) h Non dimensional cross waterway depth Length of basin (m) M 0 Complex function of and h N 0 Sea level NOAA National Oceanographic and Atmospheric Administra tion P 0 Complex function of and h Q 0 Complex function of and h Re[ ] Real part of the function RMSe Root mean square error t Time (s) u Velocity of flow u 0 Complex velocity amplitude

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9 U(z) Velocity of flow as a function of depth X Non dimensiona l distance along the basin y Non dimensional distance across the basin with the origin at the center of the basin z Non dimensional depth of the basin Aspect ratio of the basin Frictional paramter Water surface Geometric paramter Frictional p arameter Ratio of the amplitude of the tidal wave at the open end of the basin to the maximum depth

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10 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degr ee of Master of Science SUBTIDAL VARIABILITY IN WATER LEVEL S OF THE ST. JOHNS RIVER By Krista Henrie May 2012 Chair: Arnoldo Valle Levinson Major: Coastal and Oceanographic Engineering Hourly water level data at 5 stations along the St. Johns River we re compiled for the year of 2004 with the purpose of determining the propagation of subt idal pulses along the estuary. In order to identify these subtidal pulses, data were low pass filtered at half periods of 30 h The subtidal water level records include d a dominant seasonal signal that hindered the study of shorter term pulses. Th is seasonal oscillation was removed from the low pass filtered records The resulting signals were analyzed with Complex Empirical Orthogonal Functions (CEOF), through a Hilbert Transform, to discern the amplitude and phase of the subtidal pulses propagating through out the estuary The first CEOF mode explained 94% of the temporal variability and its spatial structure indicated an unusual distribution : attenua tion in amplitude (1 1.4%) over the first 60 km, then amplification of 2.9% from 60 to 130 km and attenuation of 8.9% for the remain der of the estuary The phas e of the first CEOF mode illustrat ed progressive wave behavior over the first 60 km of the estuary and quasi standin g wave behavior for the remaining 85 km. Additionally, the phase of the first mode suggested two separate locations for subtidal pulse forcing An absolute minimum in phase at the entrance demonstrated that the dominant forcing was from the coast al ocean. The

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11 phase also revealed a local minimum around Palatka, indicating that a second, weaker forcing occurred around 130 km into the estuary. Finally, an analytical model that describes the evolution of long waves through a channel with frictional da mping was fit to the first mode of the statistical (CEOF) results Solutions were obtained as a function of two parameters: a relative measure of the channel length to the wavelength, and a relative measure of frictional damping to local acceleration Although multiple combinations of a nd with similar root mean square errors (RMSe) could be applied to describe the Low er St. Johns River, the best match (0.45% RMSe) with the CEOF results was produced with 0.6 for the geometric parameter and 1.6 for the dynamic parameter A value of of 0.6 means that the basin length is roughly one tenth of the wavelength and a of 1.6 indicates the entire water column is influenced by friction Subtidal pulses in this estuary, therefore, behave as damped waves that can be represented with simplified theoretical solutions.

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12 CHAPTER 1 INTRODUCTION Motivation As sea level rises ove r the next century, estuaries around the world will be threatened by increased salt intrusion. At present, salt intrudes into estuaries in subtidal pulses that propagate up estuary Understanding how such subtidal pulses behave inside the estuary will even tually illuminate the effects to be expected from sea level rise First, investigating the subtidal water level behavior will help elucidate how far upstream the forcing from the ocean will be felt inside the estuary Second, the linkage between this ocean pulse and the length of salt intrusion could be assessed This study investigates the first step, understanding th e subtidal wave propagation and its associated lowest order physics in the St. Johns River Estuary (Fig ure 1 1 ) Long Wave Propagation Studie s on long wave propagation in estuaries includin g Wong et al. (2009), Wong (1986 ), and Snedden et al. (2007) have found frequency dependent reductions in wave amplitude W ong et al. (2009) and Wong (1986 ) found that in a coastal lagoon and a microtidal est uary, the semidiurnal tidal amplitude experienced nearly a half reduction However, at lower (subtidal) frequencies, the sea level experienced no attenuation over the same stretch In contrast, Snedden et al. (2007) found that a Louisiana deltaic estuary e xperienced amplitude reductions into the subtidal frequency spectrum Other studies on long waves i ncluding Waterhouse et al. (2011 ) illustrated that tides behave more like diffusive processes in highly frictional environments rather than propagating wa ves confirming earlier works by LeBlond (1978) and Frederichs and Madsen (1992) These results a nd theoretical findings (Winant 2007 ) suggest that the frequency

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13 dependent wave propagation in estuaries depends on the geometry and the frictional character of t he system. Subtidal Variability Subtidal variability of water levels and their effects on salinity intrusion in the St. Johns River, in particular, have been studied with numerical models ( Sucsy and Morris 2002 ) The purpose of these studies was to determi ne potential uses of the river water for domestic purposes Sucsy and Morris (2002) found that subtidal pulses initiated at Mayport, the estuary mouth, were transmitted upstream from the ocean with relatively little attenuation throughout the lower river a nd were primarily responsible for reversing the river flow Our results, anchored by observations, supplement and challenge those results This study investigates the subtidal water level variability in the Lower St. Johns River by using statistical analy sis and a theoretical (analytical) model Statistical analysis consists of Complex Empirical Orthogonal Functions (CEOFs) that show the progression of the subtidal waves as they travel through the estuary An analytical model (Winant 2007) is compared to t he statistical results (spatial structure of the CEOF dominant mode) to determine the dominant dynamics of the system.

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14 Figure 1 1. St. Johns River Estuary

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15 CHAPTER 2 METHODS Study Area ted in the northeast co rner of Florida (Figure 1 1) The St. Johns River is unusual in that it flows from south to north, originating near Vero Beach and discharging to the ocean near Jacksonville This elongated estuary is characterized by a bottom slope of ~1.210 6 (0.12 cm/km ) (Toth 1993) The Lower St. Johns River refers to the area from the inlet at May port to Lake George, roughly 175 km upstream (Figure 1 1) Near the inlet, the river is narrow and deep to accommodate the large ship traffic from the port of Jacksonville (JAXPORT) About 40 km from the estuary mouth, the deep draft vessel traffic ceases and the river widens and shoals from a dredged depth of 15 m to a natural depth of approximately 6 m g estuary stretch from Jacksonville to Green Cove Springs, reaching a maximum breadth of 5 km The 0.3 km at Buffalo Bluff, 145 km from the inlet (Figure 1 1). The chan nel geometry induces variations in tidal amplitude along the estuary Tidal amplitude is maximum (~0.67 m) upon entering the inlet at Mayport Seventy five kilometers upstream, the tidal amplitude decreases to a minimum (~0.11 m) at Green Cove Springs Ups tream of Green Cove Springs, tidal amplitude increases to a local maximum of 0.17 m at Palatka (~130 km from Mayport) Ninety eight percent of the tidal water level variability is a result of five harmonic constituents: M 2 N 2 S 2 O 1 and K 1 with periods of 12.42, 12. 67, 12.00, 25.82, and 23.93 h respectively M 2 is the dominant tidal freque ncy, accounting for 90.5% of the tidal variability in the system Strong

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16 frictional damping causes an 80% reduction in the M 2 tidal amplitude in the first 50 km (Fig u re 2 2 ) The next stretch of approximately 90 km shows an amplitude change of only about 0.05 m Similar to the total tidal amplitude, that of the M 2 also features a local maximum at Palatka, 127 km upstream of the inlet High and low tides can occur simul taneously at different points in the estuary, owing to the 220 phase difference (Fig ure 2 3 ) between Mayport and Buffalo Bluff (Sucsy and Morris 2002) Bacopoulos et al. (2009) found through numerical models that meteorological forcing was greater than or equal to the tidal forcing in the St. Johns River during the s ummer of 2005 L ocal winds as well as those from the deep ocean have been shown to impact the water levels in the estuary (Bacopoulos et al. 2009) Local w inds affecting the estuary have an ave rage monthly speed of 2.8 4.4 m/s, with the greatest speeds occurring in winter The N S component of the wind exhibits a strong seasonal variability, in contrast to the lack of seasonality in the E W component Northerly winds dominate from September thro ugh January, while southerly winds dominate from February through August (Bergman 1992) The average river outflow for the St. Johns is 223 m 3 /s (Suscy, et al. 2010) Seasonal rain patterns cause high flows in late summer to early fall and low flows are f ound in the winter (NOAA 1985) On average, tributaries downstream of Buffalo Bluff contribute 38% of the total discharge entering the estuary Flow reversals occur ~ 37 km from the inlet at Acosta Bridge 3.3 times per month and reach as far upstream as Buf falo Bluff (~145 km) 1.6 times per month Ninety percent of these flow reversals last for 3 days or less (Sucsy and Morris 2002) and are linked to the subtidal water level variability

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17 The Lower St. Johns River exhibits a mean annual rainfall of 1.32 m (B ergman 1992) Summer showers and tropical storms in June through October constitute roughly (Sucsy and Morris 2002) Typically, the dry season is from November through April, but occasional winter fronts can generate lar ge storms that persist for days and drive up the flow in the river Prolonged droughts are also common in summer months (Bergman 1992) Annual mean evaporation in the Lower St. Johns River is 1.22 m Net precipitation (rainfall minus evaporation) results i n two wet and two dry periods per year Convective activity in July through September drives the largest net precipitation of +150 mm In December through February, winter storms create a second wet season, generating +63 mm Dry periods of net precipitati on include March through June and October through November, with 44 mm and 2 mm, respectively Although December through February is included in the dry season for rainfall, low evaporation results in positive net precipitation values (Sucsy and Morris 2 002) Wind forcing and freshwater input to the St Johns affect subtidal variability of water levels as indicated by the data described here. Data Collection Hourly water level data were compiled from 5 tide gauge stations maintained by the Center for Opera tional Oceanographic Products and Services of the National Ocean Service in the National Oceanic and Atmospheric Administration (NOAA) Data were obtained from the website tidesandcurrents.noaa.gov for the entire year of 2004 Although 3 hurricanes genera ted unusually large discharge events in the St. Johns River watershed during 2004, this year provided continuous water level measurements with the best coverage of the estuarine area The five stations ranging included ( fro m

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18 mouth to head of the estuary ) ( Figure 2 1): Mayport (station 8720218 ), Main Street Bridge (87020226), I 295 B ridge (8720357), Palatka (8720774), and Buffalo Bluff (8720767) All data were selected relative to mean sea level and Greenwich Mean Time. Data Processing Water level data from all stations were low pass filtered with a Lan czos window centered at 30 h to eliminate the variance associated with tidal and in ertial frequencies A seasonal signal associated with wet and dry seasons affects the estuary throughout its reach (N OAA 2012) This seasonal signal coincided with the first mode of empirical orthogonal fu nctions (EOFs) that were obtained from the entire data set of 5 subtidal records The EOFs are obtained from solving the eigenfunctions related to the covariance matrix of the data set To remove the seasonal oscillation from all 5 records and isolate indi vidual subtidal pulses, the low pass filtered (half period = 45 days) version of the first EOF mode was subtracted from each of the filtered water level data (half period = 30 h ). After the subtidal pulses were isolated by subtracting the seasonal signal a Hilbert transform was applied to convert each signal to a time series of complex numbers in which the real part is the original signal and the complex part is also the original signal but shifted 90 The result of the Hilbert transformed times series is that the real part is independent (orthogonal) from the imaginary part. Hilbert transformation was done to extract phase propagation information from one station to the other using Complex Empirical Orthogonal Functions (CEOFs) This is the same as solvin g the eigenvalue problem related to the covariance of the complex, Hilbert transformed, matrix of data.

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19 The CEOF functions provided information on the spatial structure (along estuary distribution) of the subtidal pulses, as well as their associated phase propagation and temporal variability throughout the St. Johns River The application of CEOFs yields information on the predominant structure of the subtidal pulses, but sheds little light onto their dynamics. The Model In order to study the lowest order d ynamics of the subtidal pulses, an analytical model that depicts the behavior of a frictional (attenuated) long wave was implemented to the St. Johns River The analytical model, proposed by Winant (2007), assumes linear motion associated with a long wave m oving in a homogeneous fluid Those assumptions yield the continuity equation (Eq. 2 1) and the mom entum balance in Equations 2 2 and 2 3 In order to solve Equations 2 1 through 2 3, non dimensional variables [Winant 2007; Eq. 2 4 through 2 15] were deve loped. (2 1) (2 2) (2 3) (2 4) (2 5) (2 6) (2 7) (2 8)

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20 (2 9) (2 10) (2 11) (2 12) (2 13) (2 14) (2 15) The variable is Coriolis pa rameter, is the motion frequency, is the basin length, 2 is the maximum basin width, is the maximum basin depth, A z is the eddy viscosity, is the free surface elevation, and is the wave celerity Notable non dimensional parameters include : = (Winant 2007) the ratio of the tidal wave amplitude at the open end to the maximum depth the geometric para meter the frictional parameter, and the aspect ratio Substituting the non dimensional variables [Winant 2007; Eq. 2 4 t hrough 2 15 ] into Equations 2 1 through 2 3 yields the non dimensional mom entum balance and continuity equation shown in Eq uations 2 16 through 2 18 (Winant 2007). (2 1 6 ) (2 17 ) (2 1 8 )

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21 Periodic solutions are a pproximated usi ng complex amplitudes [Winant 2007; Eq. 2 19 through 2 22 ] of U V and W along estuary cross estuary and vertical velocity amplitudes, respectively; N is the water level amplitude (2 1 9 ) (2 20 ) (2 2 1 ) (2 2 2 ) For the purposes of this study, the relevant variable is the subtidal water level 0 which is solved along the estuary Assuming that depth only varies across the estuary (with y ), the lowest order closed form sol ution is given by Equation (2 23 ) (Winant 2007). At the entrance (x=0), the subtidal water level amplitude N is assumed to be 1 At the head of the estuary, there is assumed to be no transport and no a long estuary gradient of N ( N x =0). (2 23 ) (2 24 ) (2 25 ) T he parameter [Winant 2007; Eq. 2 24] represents frictional effects and depends on the lateral average of M 0 [Winant 2007; Eq. 2 25] M 0 is obtained from [ f 2 Q 0 2 /P 0 ] P 0 (Winant 2007) where Q 0 and P 0 are also frictional parameters shown in Appendix A. The solution, N (0) [Winant 2007; Eq. 2 23] describes an attenuated long wave in a basin and its along estuary behavior that depends on two m ajor parameters, and The geometric parameter compares the length of the basin to the wavelength and a

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22 dynamical parameter compares frictional effects to the frequency of forcing The ratio that defines [Winant 2007; Eq. 2 15] resembles the Froude number a re lative measure of the ambient velocity to the long wave speed. The parameter [Winant 2007; Eq. 2 9], sometimes referred to as the Stokes number (Huijts et al. 2009) is analogous to the inverse of the Reynolds number T he parameter can be regarded as a measure of the dynamical depth of a system: the larger the more frictional or dynamically shallow the basin. When is zero, the wave is frictionless and under no rotation, the momentum equation and its solution portray a plane wave (a sinusoid undist urbed in space and time) The amplitude and phase of the subtidal pulses as indicated by the spatial structure from the CEOF analysis were compared to the analytical solution The best fit between CEOF spatial structure and analytical results was obtained through an iterative approach that minimized the difference between CEOF and analytical distributions, using and as free parameters

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23 Figure 2 1. 5 NOAA stations along the St. Johns River

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24 Figure 2 2 M 2 tidal amplitude

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25 Figure 2 3 M 2 tidal phase

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26 CHAPTER 3 RESULTS Subtidal Water Levels The raw water level data along with the filtered dat a (half period = 30 h ), for each station are shown in Figures 3 1 to 3 5 These figures clearly illustrate the landward attenuation and then amplification, at Palatka, of tidal oscillations The subtidal (filtered) water level records from each station (Fi g ure 3 6 ) displayed two main types of oscillations: short term subtidal pulses and a long term seasonal modulation The seasonal oscillation was in part due to the large discharge events associated with several hurricanes that impacted the northeast coast of Florida in 2004 Other factors included seasonal rain patterns, steric water level changes, atmospheric pressure, ocean currents, and fluctuations in salinity ( NOAA 2012 ) The combination of these effects caused the subtidal water level at Mayport to be greatest from mid April to August and least from mid August to December (Figure 3 6 ). Removal of the Seasonal Signal The seasonal signal distorted the behavior of the shorter term subtidal pulses and thus had to be removed in order to determine the wave propagation associated with those shorter pulses Two options were explored to remove the seasonal signal: harmonic analysis and EOFs A harmonic analysis with a semi annual and an annual signal ( Figure 3 7 ) produced less than desirable results A Least Sq uares Fit (LSF) with two harmonics was performed on the subtidal records from each station The LSF captured the general trend, but as shown in the r epresentative station (Figure 3 7 ), it was not centered in the data Moreover, the concave down nature of t he data at the beginning of the year was escaped by the LSF method and using it to subtract the

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27 seasonal signal would have inco rporated a new signal. The second method tested to extract the seasonal signal was EOFs The first mode ( Figure 3 8 ) captured 97 % of the temporal variability and the seasonal signal To remove the shorter term variability and isolate the seasonal signal found in the first mode, a filter with a half pe riod of 45 days was applied Figure 3 9 displays the filtered (half period = 45 day s) first mode that proved to be the better method to isolate the seasonal signal found in the 2004 subtidal records. The seasonal modulation from the filtered first mode of 2004 was compared to the average seasonal cycle for Mayport ( Figure 3 10 NOAA 2012 ) Reasonable agreement was shown overall but slight differences included lower water levels in the spring and early summer months and higher water levels during the hurricane season of 2004 The year of 2004 displayed a water level that was about 0.17 m b elow t he typical seasonal water level f or the spring and summer months and 0.07 m above the average during the hurricane season. I n order to eliminate the overpowering seasonal signal that hindered the examination of the shorter term individual pulse beha vior t he filtered fir st mode (half period = 45 days) ( Figure 3 9 ) was subtracted from the subtidal water level records ( Figure 3 6 ) The subtidal water levels that resulted ( Figure 3 11 ) were ce ntered at zero with the maxima primarily at Mayport. These da ta included only the shorter term pulses with periods less than 30 days and were used in all further analysis to determine subtidal wave propagation information both from a statistical perspective and from the lowest order dynamics of the system.

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28 Statistic al Results A Hilbert Transform was applied to the subtidal water levels less the seasonal signal (Fig ure 3 11 ) to transform all sea level signals to the complex plane CEOFs were applied to garner wave propagation information Results from the CEOFs (Fig ur e 3 12 ) showed that the first mode described 94 % of the temporal variability of the subtidal pulses and the second mode described only 4% The periods of most influence for the second mode included mid March, late September, and November through December However, even when the amplitude of the second mode was at its largest, the amplitude of first mode was customarily much greater in magnitude The amplitude of the pulse with respect to distance from the inlet for the first and second modes of the CEOFs i s shown in Figure 3 13 The first mode, denoted by the blue line, illustrated an 11.4% reduction in amplitude in the first 60 km followed by a slight amplification of 2.9% from about 60 km to 130 km into the lower river A second stretch of attenuation, wi th stronger frictional damping than the first, resulted in an 8.9% reduction in amplitude from about 130 km to 145 km into the estuary Although the first mode described 94 % of the temporal variability, it could not explain the along estuary wave attenuat ion found in the data The lack of attenuation is illustrated in the reconstructed subtidal records with only the first mode (Figure 3 14 ) In some periods such as June July, the attenuation from Mayport to Buffalo Bluff was underestimated by 48% wh en comp ared with the data ( Figure 3 11 ) The addition of the second mode produced a much better picture of the frictional damping t hat occurred in the basin (Figure 3 15 ) The other component from the CEOF analysis was the phase (Fi gure 3 16 ) Minima in phase in dicated the location of the forcing mechanisms in the estuary The

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29 CEOF results displayed two minima : an absolute minimum at Mayport, indicating the dominant forcing originated from the coastal ocean, and a local minimum at Palatka, suggesting that a secon d, smaller forcing mechanism occurred 130 km into the estuary The phase lag between stations illustrated the travel time of the wave For example, the phase difference of 0.34 rad ians from Mayport to Main St. Bridge for the first mode translated into a 6. 4 h travel time for a typical subtidal pulse with a period of 5 days Considering the more drastic phase change of 0.85 rad ians for the second mode over the same distance resulted in a travel time of 16.2 h Finally, the slope of the phase versus distance lines yielded information of the type of subtidal wave behavior in the estuary Lines with relatively large positive slopes in Figure 3 16 indicated progressive wave behavior and nearly horizontal lines indicated quasi standing wave behavior The phase of the first and second modes featured relatively large increases from Mayport to I 295 Bridge, 0.43 and 3.4 radians, respectively, suggesting progressive wave behavior The small phase change of 0.045 radians in the first mode and 0.34 radians in the second mode illustrate d quasi standing wave behavior from 55.4 km to 144 km (I 295 Bridge to Buffalo Bluff).

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30 Figure 3 1 Tidal and subtidal water levels at Mayport

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31 Figure 3 2 Tidal and subtidal water levels at Main St. Bridge

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32 Figure 3 3 Tidal and subtidal water levels at I 295 Bridge

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3 3 Figure 3 4 Tidal and subtidal water levels at Palatka

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34 Figure 3 5 Tidal and subtidal water levels at Buffalo Bluff

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35 Figure 3 6 Subtidal water levels in 2004

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36 Figure 3 7 Least squares fit with 2 harmonics (semi annual and annual) to the subtidal water level at Mayport

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37 Figure 3 8 Reconstruction of the subtidal water levels with the first mode from the EOFs

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38 Figure 3 9 Seasonal oscillation from the filtered (half period = 45 days) first mode of the EOFs

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39 Figure 3 10 Average seasonal cycle for Mayport [Adapted from NOAA, cited 2012 : Average Seasonal Cycle 8720218 Mayport Florida. (Available online at http://tidesandcurrents.noaa.gov/sltrends/seasonal.shtml ?stnid=8720218 &name=Mayport&state=Florida.)]

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40 Figure 3 11 Subtidal water levels minus the seasonal oscillation

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41 Figure 3 12 Temporal variability of dominant modes

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42 Figure 3 13 Amplitude vs. distance along the estuary for modes 1 and 2

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43 Figure 3 14 Reconstruction of the subtidal record with mode 1 of the CEOFs

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44 Figure 3 15 Reconstruction of th e subtidal record with modes 1 and 2 of the CEOFs

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45 Figure 3 16 Phase vs. distance along the estu ary for modes 1 and 2

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46 Figure 3 17 Phase vs. dist ance along the estuary for mode 1

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47 CHAPTER 4 DISCUSSION The dynamics of the St. Johns River Estuary were explored by reproducing the amplitude and phase of the dominant mode from the CEOFs with an analytical model The model, developed by Winant (2007), describes an evolution of long waves in a channel through a balance of pressure gradient and frictional damping The model solution for the non dimensional water surface elevation (Eq 2 22 ) depends on the free parameters (Eq. 2 15 ) and (Eq. 2 9 ) Given that both and depend on and H a relationship between and can be derived ( Eq. 4 1) (4 1) Reasonable values of and were established for the St. Johns River Estuary using a constant length of 175 km (the distance from Mayport to Lake George) and a constant maximum depth of 5 m The non dimensional cr oss waterway depth was given by Equation 4 2, where y varied from 1 to 1 along the channel (Fig ure 4 1 ). (4 2) The period w as varied from 2 to 8 days and the eddy v iscosity was varied from 0.0005 to 0.002 (m 2 /s) A plot of RMSe (Fig ure 4 2 ) was constructed to illustrate the range of and that were best suited for the subtidal water levels i n the St. Johns River Estuary. Pos sible values ranged from 0.2 to 0.9 and values from 1 to 4, indicating that in all these scenarios, the full water column would be under the influence of friction. Multiple combinations of and (Figure 4 2 ) yielded similar results for RMSe in a comp arison of model versus the dom inant first mode of the CEOFs. The best results ( RMSe of 3% or less for the amplitude) were produced using ranging from 2 to 3 and

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48 ranging from 0.3 to 0.5 The along estuary amplitude was constructed with the analytical mo del using sample values of of 2, 2.5, and 3 and of 0.46, 0.35, and 0. 28 Comparing the model results with the amplitude from the first CEOF mode illustrated the best fit in the first 60 km of the estuary, from Mayport to I 295 Bridge (Figure 4 3 ) T he model produced less than desirable results when it encountered the amplification at Palatka and rapid attenuation from Palatka to Buffalo Bluff Similarly, the phase comparison ( Figure 4 4) between the model and the first mode showed th e best fit up to 60 km (I 195) A divergence occu r r ed in the region from I 295 Bridge to Buffalo Bluff (Figure 4 4) where the analytical model predicted progressive wave behavior, but the statistical analysis evidenc ed quasi standing wave behavior One explanation for the discrepancy between the model and the CEOF results in this area of the estuary is the possible second forcing mechanism indicated by the local minimum in the phase (Figure (3 17) at Palatka The analytical model (Winant 2007) was d esigned to illustrate the evolution of a single long wave in an estuary If another pulse was in fact generated near Palatka as the phase of the CEOFs indicates then the model would have to account for the effects of multiple pulses, a scenario that was n ot Disparity between the model and the statistics was further aggravated by non uniform frictional effects along the St. Johns River E stuary Extreme coastline convergence and shoaling from Palatka to Buffalo Bluff ca used increased friction that was not accommodated by the model which prescribes uniform friction throughout the domain In order to eliminate the area of increased fric t i onal influence a second estimate for RMSe was conducted using only the stations fro m Mayport to Palatka The

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49 amplitude comparison resulted in a much better agreement in which several combinations of and yielded a RMSe < 1% Removing the last station (Buffalo Bluff) shifted the best fit ranges of and to 1.3 2.3 and 0.25 0.7 respe ctively M odel solutions (Figure 4 5 ) w ere produced using value s of 1.4, 1.6, and 1.8 and their corresponding value s of 0.70, 0.59, and 0.51 which all yielded a RMSe of 1% or less. The best fit (RMSe 0.45%) was obtained with a of 1.6 and a of 0.59 Physically this implies that the basin is roughly one tenth of the subtidal wavelength and that the entire water column is influenced by friction. Although removing the region of increased dissipation improved the model prediction of the amplitude, the m odel phase (Figure 4 6) still diverged around Palatka due to the change of physics associated with the possible second forcing mechanism.

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50 Figure 4 1 Model bathy metry

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51 Figure 4 2 RMSe as a function of and

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52 Figure 4 3 Amplitude comparison for various and with a RMSe of less than 3%

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53 Figure 4 4 Phase comparison for various and with a RMSe of less than 3%

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54 Figure 4 5 Amplitude comparison for various and with a RMSe of le ss than 1% or less for Mayport to Palatka

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55 Figure 4 6 Phase comparison for various and with a RMSe of less than 1% for Mayport to Palatka

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56 CHAPTER 5 CONCLUSION The subtidal waves generated from the coastal ocean propagated all the way to Buffalo Bluff, 145 km upstream of the inlet The dominant mode of behavior for the subtidal waves of 2004 exhibited a 10% attenuation over the first 30 km to Main St. Bridge The second 30 km to I 295 Bridge, yielded a lesser attenuation of only 1.1% From I 295 Bridge to Palatka, a distance of approximately 70 km the amplitude amplified by 2 .9% Increased fric tion caused by the narrowing and shoaling from Palatka to Buffalo Bluff yielded an 8.9% attenuation over just 15 km The dominant behavior of the subtidal wave propagation from Mayport to I 295 was modeled through a temporally varying balance between pressure gradient and friction In the first 60 km, the subtidal pulse behaved like a damped, progressive wave The along estuary amplitude was also modeled acc urately ( RMSe of less than 1%) using the same momentum balance for a distance of 130 km However, the second forcing mechanism near Palatka changed the physics in that region so the phase could not be represented equally as well The p rop osition of the se cond pulse at Palatka requires further investigation with increased spatial resolution of data in the region betwe en I 295 Bridge and Palatka The study would also benefit from an increased period of data collection to determine whether the second pulse wa s a byproduct of the unique signatures in the data for 2004, such as multiple hurricanes or whether the s ubtidal dynamics illustrated in this study are typical for the St. Johns River Estuary The dominant mode of the CEOF analysis illustrated two types o f subtidal wave behavior in the estuary: damped progressive wave behavior from Mayport to I 295 Bridge and quasi standing wave behavior from I 295 Bridge to Buffalo Bluff.

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57 APPENDIX ANALYTICAL MODEL EQU ATIONS Substituting the complex amplitudes [Winant 20 07; Eq. 2 19 through 2 22] into Equation s 2 16 to 2 18 (Winant 2007) yields the continuity equation in form of Equation A 3 (Winant 2007) and the momentum equations in the form of Equations A 1 and A 2 (Winant 2007) The denote the vertically integrat ed quantities (A 1 ) (A 2 ) (A 3 ) The solutions to the momentum equations [Winant 2007; Eq. A 1 through A 2] are given by Equations A 4 and A 5 (Winant 2007) (A 4 ) (A 5 ) (A 6 ) (A 7 ) Substituting the depth integrated form of Equations A 4 and A 5 (Winan t 2007) into the continuity equation [Winant 2007; Eq. A 3] and multiplying by 2 2 produces an equation in the form of Equation A 8 (Winant 2007). The capital P 0 [Winant 2007; Eq. A 7] and Q 0 [Winant 2007; Eq. A 6] represent the vertically integrated fo rm of p 0 and q 0 (A 8 ) The sea level N is specified at the entrance of the basin (at x=0) and t he transport vanishes at the closed boundaries (at y=1 and x=1 ) Under these conditions, the order

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58 9 (Winant 2007) Integrating t he order 2 problem [Winant 2007; Eq. A 10] across the width of the basin and applying the boundary condition [Winant 2007; Eq. A 12] at y=0 yield s an ordinary differential equation for N (0) [Winant 2007; Eq. A 13] (A 9) (A 10) (A 11 ) (A 12 ) (A 1 3 ) As before, denotes the lateral average of a quantity [Winant 2007; Eq. 2 25] When is a complex constant, the closed form solution is given by Equation 2 23 (Winant 2007)

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59 LIST OF REFERENCES Bacopoulos, P., Y. Funakoshi, S. C. Hagen, A. T. Cox, and V. J. Cardone, 2009: The role of meteorological forcing on the St. Johns River (Northeastern Florida). J. Hydrol 36 9 55 70. Bergman, M. J. 1992: Volume 2 of the Lower St. Johns River Basin r econnaissance : S urface water hydrology SJRWMD Tech. Rep. SJ92 1, 145. Friedr ichs, C., and O. Madsen 1992: Nonlinear diffusion of the tidal signal in frictionally dominate d embayments. J. Geophys. Res., 97 (C4), 5637 5650. Huijts K. M. H ., H. M. Schuttelaars, H. E. De Swart, C. T. Friedrichs 2009: Analytical study of the transverse distribution of along channel and transverse residual flows in tidal estuaries. Cont Shelf Res ., 29 1, 89 100. LeBlond, P.H., 1978: On tidal propagation in shallow rivers. J. Geophys. Res., 83 (C9), 4717 4721. NOAA, 1985: National estuarine inventory, data atlas. Volume 1: Physical and hydrologic characteristics. NOS Tech. Rep. Rockville, MD. cited 2012: Average Seasonal Cycle 8720218 Mayport, Florida [Available online at h ttp://tidesandcurrents.noaa.gov/sltrends/seasonal.shtml?stnid=8720218 &name=Mayport&state=Florida .] Snedden, G. A., J. E. Cable, and W. J. Wiseman Jr. 2007: Subtidal sea level variability in a shallow Mississippi River deltaic estuary, Lousiana. Estuaries Coasts ., 30 5, 802 812 Suscy, P., G. Belaineh, K. Park D. Christian Y. Zhang E. Carte, J. Martin, S. Rouhani, L. Motz, S. Peene, M. Good rich, and D. Summer, 2010: Hydrodynamics of the Lower and Middle St. Johns River. 4 th NRC Meeting St. Augu stine, FL, SJRWMD and F.W. Morris, 2002: Calibration of a three dimensional circulation and mixing model of the Lower St. Johns River. SJRWMD Tech. Rep., 212. Toth, D. J. 1993 : Volume 1 of the Lower St. Johns River Basin r econnaissance : H ydrogeology SJRWMD Tech. Rep. SJ93 7, 58. Waterhouse, A.F., A. Valle Levinson, and C.D. Winant, 2011: Tides in a System of Connected Estuaries. J. Phys. Oceanogr ., 41 946 959. Winant, C.D., 2007: Three dimensional tidal flow in an elongated, rotating basin. J. Phys. Oceanogr ., 37 2345 2362

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60 Wong, K.C., B. Dzwonkowski, and W.J. Ullman 2009: Temporal and spatial variability of sea level and volume flux in the Murderkill Estuary. Estuarine, Coastal, Shelf Sci., 84 440 446. 1986: Sea level fluctuations in a coastal lagoon. Estuarine, Coastal, Shelf Sci., 22 739 752.

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61 BIOGRAPHICAL SKETCH In the fall of 2006, Krista Henrie left her home in Niceville, Florida to pursue an education in coastal engineering at th e University of Florida During her un dergraduate program, Krista studied civil engineering and became act ive ly involved in the American Society of Civil Engineers Student Chapter Krista also serv ed as a teaching assistant for H ydrodynamics In 2010 Krista graduated with her Bachelor of Sci ence in Civil Engineering Upon graduat ion, s he immediately beg an graduate study in coastal engineering Krista obtained a Master of Science in Coastal and Oceanographic Engineering from the University of Florida in May 2012