Geomorphological and Meteorological Control of Estuarine Processes: a Three-Dimensional Modeling Analysis

Geomorphological and Meteorological Control of Estuarine Processes: A Three-Dimensional Modeling Analysis

Quamrul Ahsan, P.E., M.ASCE1; Alan F. Blumberg, M.ASCE2; Andrew J. Thuman, P.E., M.ASCE3; and Thomas W. Gallagher, P.E., M.ASCE4

Abstract: The proper timing, duration, and direction of wind events interacting with the geometry of an estuarine system can control the intensity of stratification. A three-dimensional, time-dependent hydrodynamic model was used to examine this process. Intense mixing is closely tied with wind-generated internal velocity shear. A south wind generates up-estuary directed surface currents, which eventually leads to downwelling movements of water. This downwelling process in the upper bay region accelerates the bottom current in a down-estuary direction. A vertical instability occurs, especially in the upper bay region, due to the generation of shear across the pycnocline, causing mixing sufficient to destratify the entire water column. On the other hand, strong stratification occurs when a north wind advects fresher upper bay surface water into the lower bay. A downwelling movement of water is produced, which in turn drives bottom saline water in the up-estuary direction. DOI: 10.1061/͑ASCE͒0733-9429͑2005͒131:4͑259͒ CE Database subject headings: Three-dimensional models; Hydrodynamics; Estuaries; Wind; Geometry; Stratification.

Introduction the tidal excursion to the distance between major bathymetric and shoreline features. They concluded that in estuaries where the Stratification in an estuarine environment is of significant impor- typical spacing of topographic features is less than the tidal ex- tance to phytoplankton populations, nutrient recycling, and dis- cursion, tidal dispersion may contribute significantly to the mix- solved oxygen distributions since they are strongly controlled by ing processes. In Chesapeake Bay, Blumberg and Goodrich the vertical structure of the water column. In a fully stratified ͑1990͒ have found that wind-driven internal shear is a more ef- estuarine system, such as Pensacola Bay, Fla., the presence of a fective mechanism of inducing destratification than turbulence strong pycnocline forms a barrier to the downward transport of generated at the surface. oxygen; this event is a dominant influence in causing hypoxia in The advective effects of wind forcing have been examined in the bottom layer. The amount of stratification also controls the many estuarine systems. Observations of local wind forcing in region’s physical characteristics, such as temperature, salinity, estuaries, especially in Chesapeake Bay, have shown that wind- and velocity structure. induced currents are typically larger than density-driven gravita- Astronomical tides have long been considered the major tional currents and can be of the same order as the tidal currents, source of mixing energy for the breakdown of stratification. especially during wind events ͑Goodrich 1985͒. Weisberg ͑1976͒ Stratification and destratification as a result of neap-spring tidal has found that wind-induced velocity fluctuations at a time scale mixing have been reported by Ruzecki and Evans ͑1985͒ in the between the steady-state gravitational circulation and tidal oscil- York River estuary. Geyer and Signell ͑1992͒ have argued that the lations are of equal or greater importance to the circulation phys- effectiveness of tidal dispersion depends on the relative scale of ics. Large variations in the salinity distributions associated with wind-driven velocity fluctuations were also observed in Chesa- 1PhD, Sr. Project Manager, HydroQual, Inc., 1200 McArthur Blvd., peake Bay by Wang ͑1979͒. Wang ͑1979͒ clearly demonstrated Mahwah, NJ 07430 ͑corresponding author͒. E-mail: qahsan@ that wind forcing has a twofold effect on the water column, pro- hydroqual.com 2 ducing wind-induced mixing and causing advective currents. PhD, George Meade Bond Professor of Ocean Engineering, Dept. of In general, wind-induced mixing tends to raise the potential Civil, Environmental and Ocean Engineering, Stevens Institute of energy of a water column by redistributing the salinity gradient Technology, Castle Point on Hudson, Hoboken, NJ 07030 and Consultant, HydroQual, Inc., 1200 McArthur Blvd, Mahwah, NJ 07430. over depth, thereby altering the horizontal pressure gradient. It is E-mail: [email protected] this gradient which essentially generates the gravitational flow. 3Associate, HydroQual, Inc., 1200 McArthur Blvd., Mahwah, NJ Several studies have demonstrated that a depth-dependent re- 07430. E-mail: [email protected] sponse to local wind forcing is a very effective mechanism in 4Principal Engineer, HydroQual, Inc., 1200 McArthur Blvd., maintaining stratification as well as leading to destratification. Mahwah, NJ 07430. E-mail: [email protected] Among these studies, work in Narragansett Bay by Weisberg Note. Discussion open until September 1, 2005. Separate discussions ͑1976͒ and in Chesapeake Bay by Wang ͑1979͒, Grano and Prit- must be submitted for individual papers. To extend the closing date by chard ͑1982͒, Goodrich ͑1985͒, Goodrich et al. ͑1987͒, and Blum- one month, a written request must be filed with the ASCE Managing ͑ ͒ Editor. The manuscript for this paper was submitted for review and pos- berg and Goodrich 1990 , and in Mobile Bay, by Noble et al. ͑ ͒ ͑ ͒ sible publication on January 5, 2004; approved on July 30, 2004. This 1996 and Schroeder et al. 1990 are notable. They suggest that paper is part of the Journal of Hydraulic Engineering, Vol. 131, No. 4, a down-estuary wind, which is frictionally coupled with the sur- April 1, 2005. ©ASCE, ISSN 0733-9429/2005/4-259–272/$25.00. face currents, tends to drive relatively fresh surface water in the

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 259 Fig. 1. Geographic and bathymetric features of Pensacola Bay system. Field observation stations are marked; these data were used for model calibration purposes seaward direction, and subsequently a compensating more-saline water level measurements. Favorable comparison of the model- bottom water movement can occur in the up-estuary direction. computed salinity distribution against the observed data provides This kind of response to the wind is more pronounced both in a firm basis for believing that the model-computed circulation is space and time if the coastline of the estuary changes direction an accurate representation of the bay circulation. near its confluence with the ocean, for example, the Gulf Breeze Peninsula in Pensacola Bay ͑Fig. 1͒. On the other hand, destratification may occur due to an up-estuary wind. Goodrich ͑1985͒ Physical Characteristics of Pensacola Bay suggested that this depth-dependent response to wind is an effective mechanism for generating vertical shear which, in turn, produces significant vertical mixing to destratify the entire water The general morphological features of the Pensacola Bay system ͑ ͒ ͑ column. Fig. 1 are well documented USDI, FWPCA 1970; Wolfe et al. ͒ A three-dimensional hydrodynamic model was used to simu- 1988; NOAA 1993 . The present hydrodynamic study focuses on late the physics of the bay in response to various forcing mecha- the processes governing stratification and destratification in nisms, including tides, fresh water inflow, and atmospheric and Pensacola Bay and their connection in controlling water quality meteorological conditions. The modeling analysis was directed at processes such as the vertical dissolved oxygen distribution and examining both the mechanism of mixing and the temporal and phytoplankton growth. These physical processes are dependent on spatial distribution of salinity in the bay. Model calibration was the geomorphology, freshwater discharge, tidal energy dissipa- performed through comparison of the model results against ob- tion, and atmospheric and meteorological conditions in the sys- served data. The observed data include salinity, temperature, and tem.

260 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 The morphology tends to divide the entire study area in to two in the Blackwater Bay and East Bay areas, where modeling re- major estuarine systems; the Pensacola-Escambia Bay and East sults are of lesser interest. This variable grid spacing allows for Bay-Blackwater Bay systems. Unlike most estuarine systems, this the design of computationally efficient and time-effective model- estuary is physically separated from the coastal water ͑Gulf of ing system. Mexico͒ by a strip of land mass, the Gulf Breeze Peninsula ͑Fig. The modeling framework is configured such that it can accom- 1͒. The system however is dynamically connected to the Gulf of modate time dependent river flows, and water level, temperature, Mexico through the Pensacola Inlet. The Gulf Breeze Peninsula, and salinity along its open coastal boundaries and wind stress on which provides a physical barrier between these two systems, the water surface. River flows along with their temperature and estuary. The degree of stratification and destratification in the bay, salinity are used for Escambia, Blackwater, Yellow and East Bay accentuated by the oppositely directed near surface and near bot- Rivers, and Mulatto Bayou and Bayou Texar ͑see Fig. 1 for geo- tom currents, is substantially affected by the presence of the Gulf graphic locations of these rivers͒. Freshwater flows are obtained Breeze Peninsula. A detailed analysis of this process is provided from USGS maintained gages. The Pensacola Bay Bridge area is in this paper. where we have placed our open boundary. Through the specifica- The main freshwater source to Escambia and Pensacola Bay is tion of water levels, salinity and temperature at this boundary, the the Escambia River which provides approximately 65% of the large-scale circulation from the Gulf of Mexico is brought into the total freshwater discharge to the entire estuarine system. The Yel- modeled region. In addition, the hydrodynamic model requires low and Blackwater Rivers are major contributors to Blackwater the input of wind speed and direction, air temperature, relative and East Bay with a combined discharge of approximately half humidity, and short-wave solar radiation. This information was the Escambia River discharge ͑NOAA 1993͒. The average depth obtained from the continuous meteorological observations at a of the study area is about 3.15 m at low-low water. While this station 10 m above the I-10 bridge in the middle of Escambia Bay depth is quite shallow, top to bottom salinity variations of 15 ppt and also from the Pensacola Airport station. A uniform but time are commonly observed. Navigational channels exceeding 11 m varying wind field is used over the model domain. exist throughout lower Pensacola Bay and the Pensacola Inner Harbor ͑NOAA 1993͒. A deep channel within Pensacola- Escambia Bay and lower Escambia River ͑3–6 m͒ provides a Characteristics of Forcing Mechanisms conduit for saline water intrusion into the Escambia River. An extensive data set was gathered for the study to specify conditions at the model boundaries and to calibrate and validate the Hydrodynamic Modeling Framework model results. The period, September through October 1997, was the focus of the analysis of this study. Hydrographic casts were The hydrodynamic model used in this study is a three- taken at locations shown in Fig. 1 by URS Greiner Woodward dimensional, time-dependent, estuarine and coastal circulation Clyde of Tallahassee, Fla. ͑Niedoroda, personal communication model developed by Blumberg and Mellor ͑1987͒. The model 1999͒. These data consist of biweekly vertical profiles of tempera- incorporates the Mellor and Yamada ͑1982͒ level 2-1/2 turbulent ture, salinity, and dissolved oxygen at C1A, C2A, and C4A ͑see closure model to provide for a realistic parameterization of verti- Fig. 1 for locations͒. Time series of these same parameters are cal mixing. A system of curvilinear coordinates is used in the also obtained at the I-10 bridge station in the middle of the bay horizontal direction, which allows for a smooth and accurate rep- and at BAY1 near the Bay Bridge ͑see Fig. 1͒. The various forc- resentation of variable shoreline geometry. In the vertical scale, ing functions used in the present modeling analysis are shown in the model uses a transformed coordinate system known as the ␴ Fig. 3. Freshwater flows from the Escambia, Blackwater, and Yel- coordinate transformation to permit better representation of bot- low Rivers are shown in Fig. 3͑a͒. Blackwater River and Yellow tom topography and flow near the bottom. Water surface eleva- River flows were adjusted to account for the ungaged drainage tion, water velocity ͑in three dimensions͒, temperature, and salin- areas in these basins, located between the model boundary and ity, and water turbulence are calculated in response to weather river gage. Since there are no flow gages on East Bay River, conditions ͑wind and incident solar radiation͒, freshwater inflows, Mulatto Bayou, and Bayou Texar, these flows were estimated and tides, temperature, and salinity in open boundaries connected based on the drainage areas for each discharge. The study period to the coastal waters.The model solves a coupled system of dif- coincided with a time of relatively constant, low flow particularly ferential, prognostic equations describing the conservation of in the Escambia River, which experienced sustained low flows of mass, momentum, temperature, salinity, turbulence energy, and approximately 51 m3 s−1. However, in the Blackwater and Yellow turbulence macroscale. Detailed solution techniques are described Rivers, increased flows were observed during late September and in Blumberg and Mellor ͑1987͒ and Blumberg et al. ͑1999͒, and a late October and also in Escambia River in late October. The brief description of the model is given in the Appendix. 2 month average freshwater flows in Escambia, Blackwater, and Yellow Rivers were 51, 22, and 10 m3 s−1, respectively. The water level data measured at the Pensacola Bay Bridge Model Configuration station ͑BAY1͒ during the study period are shown in Fig. 3͑b͒. Note the significant nontidal events in the record in late Septem- The orthogonal, curvilinear grid system used in the present study ber and beginning October. Tidal variation is found to have mod- is shown in Fig. 2. The grid system consists of a 42ϫ87 segment est importance within the estuarine system ͑NOAA 1993͒. A har- grid in the horizontal plane and 11 equally spaced ␴ levels in the monic analysis of tidal elevation data measured at Pensacola Bay vertical plane. It should be noted that this curvilinear grid system Bridge station ͑BAY-1͒ suggests that the diurnal constituents ͑O1 allows for much finer grid resolution near areas of interest, such and K1͒ dominate the system. A spectral analysis of the tidal as the upper Escambia Bay and the Escambia River systems. A elevations also indicated that maximum variance occurred at an minimum grid size of 20ϫ154 m is used there. A coarser grid interval of approximately 25.8 h, suggesting a dominant diurnal system is adopted, with a maximum grid size of 2,020ϫ540 m, tidal signal. The resultant tidal harmonic constituents are provided

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 261 Fig. 2. Orthogonal curvilinear grid of Pensacola Bay. Grid system consists of 42ϫ87 computational cells in horizontal plane and 11 equally spaced ␴ levels in vertical plane in Table 1. These constituents lead to a spring-neap type of beat- with several factors. First, an increase in freshwater flow from the ing with a period of approximately 13.5 days. Blackwater and Yellow Rivers occurred during the same period. Surface and bottom salinity and temperature measured at sta- Second, this pattern is substantially accentuated by a strong north tion BAY1 during the study period are shown in Fig. 3͑c͒. High- wind which persisted between September 23 and 30 forcing fresh- frequency diurnal signals are present in both the salinity and tem- water in the down-estuary direction. A significant drop in water perature data. The surface temperature and salinity show more level was also observed during the same period as presented in diurnal variability than the bottom data, which may be due to Fig. 3͑b͒. day-and-night heating and cooling of the water surface and diur- Wind speed and direction measured at a meteorological station nal tide-and-wind action, respectively. Overall, the temperature installed on the top of the I-10 bridge ͑near the I-10 station shown remained relatively constant until the end of September when it in Fig. 1͒ during the study period are shown in Fig. 3͑d͒. Wind cooled by a couple of degrees Celsius ͑°C͒. A significant decline speeds were generally not large during the study period, typically in temperature occurred in the middle of October, when the cool- ranging from 2 to 8 m s−1. During the beginning of the study pe- ing season started. It is important to note that the bottom tempera- riod ͑September 2–5͒, a predominantly southward ͑seaward͒ wind ture was much warmer than the surface temperature in the later of moderate strength was observed. However, from September part of the study period, especially when substantial surface cool- 5–22, the wind was mixed and of moderate strength, blowing ing started in the middle of October. This is due to warmer Gulf northward during the daytime and southward during the night- of Mexico water having entered the bay with the heavier and time. These findings suggest a predominantly sea and land breeze saltier bottom-layer water. A sudden drop in surface salinity oc- system. This 24 h signal wind constitutes an important force curred between September 25 and 28, which may be associated which, along with the diurnal tides, has a pronounced impact on

262 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 Fig. 3. Forcing functions used to force model along model boundaries: ͑a͒ River ﬂows through four major rivers entering Pensacola Bay system; ͑b͒ water level variations, measured at station BAY1, along open boundary near Bay bridge, dashed line indicates 34 h low pass water level variations; ͑c͒ surface and bottom temperature and salinity variations, measured at station BAY1, along open boundary near Bay bridge; and ͑d͒ wind speed and direction, measured at I-10 bridge, applied at center of model grids

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 263 Table 1. Characteristics of Principal Tidal Constituents in Pensacola Bay salinity. The model appears to capture all of these events very Constituents Period ͑h͒ Amplitude ͑mm͒ well. Another important measure of model performance is con- O1 25.819 134.94 cerned with the top to bottom salinity difference, especially in K1 23.934 87.08 highly stratified systems such as the Pensacola–Escambia Bay Q1 26.868 33.79 system. The data are quite spatially variable, a feature nicely re- M2 12.421 26.59 produced by the model results as shown in Fig. 5. Stations ER3 S2 12.000 13.02 and ER4 in the Escambia River remain stratified for the entire study period. At certain times, the bay stations ͑C1A, C2A, C4A͒ experienced well-mixed conditions, particularly when the winds the stratification regime of the bay. For the rest of the study pe- were strong and predominantly towards the north. Here again this riod, the wind was predominantly of subtidal scale, with 6–7 feature is well reproduced by the model. events observed during this period.

Calibration/Validation with Continuous Recorded Calibration/Validation with Hydrographic Cast Data Data

The model was calibrated by using a subgrid scale horizontal Model performance was also assessed using continuously mea- mixing coefficient, Cs =0.1, defined by Smagorinsky’s horizontal sured salinity, temperature and water level data at station I-10 in diffusion parameterization in Eqs. ͑2͒–͑4͒ in the Appendix. A the middle of Escambia Bay. Fig. 6 presents the model results value of z0 =0.003 m to represent the bottom roughness charac- comparison for surface and bottom salinity and temperature as teristics of the bay and a bottom friction coefficient CD =0.0025 well as water level output against data collected at Station I-10. were used for model calibration. The background vertical mixing The observed salinity and temperature data are shown averaged of 1ϫ10−6 m2 /s was used throughout the modeling simulation. over 1 day ͑diurnal scale͒. Also presented in these figures are the To start with the model computations, it is necessary to specify model computed and observed water level at the same location. initial conditions for water level, velocity, salinity, and tempera- To facilitate the analysis, the wind measured at the I-10 bridge ture. Three-dimensional initial conditions for salinity and tem- station is shown in Fig. 6͑d͒. perature were constructed based on the observed data available on It appears from Fig. 6 that the model reproduces the observed September 3, 1997 across the bay. Initial water level was assumed surface salinity quite well. The model does not quite reproduce horizontal and at mean sea level, and the velocity components the bottom salinity as well as it does the surface salinity. How- were set to zero throughout the model domain. ever, the vertical salinity stratification and its temporal variations The model-computed and observed surface and bottom salini- in response to various forcing functions, particularly the wind, are ties at five stations are shown in Fig. 4. The five stations ͑ER3, well reproduced by the model. A strong mixing event following a ER4, C1A, C2A, and C4A͒ represent locations in lower Escambia stratified condition was observed in the data on September 24. River and Escambia Bay. Computed surface and bottom salinity This mixing mechanism was closely tied with wind-generated values compare very well with the observed data. The surface and internal velocity shear ͑described in the following section͒, fol- bottom salinity observed at stations ER3 and ER4 did not change lowing a south wind event that began a day earlier. The destrati- in time and remained very stratified, until October 3, when a fication processes observed during October 4–10, 13, and 24 were predominantly south-east wind began that persisted for the next invariably preceded by considerably large south winds and may 10 days. This northward-directed wind generated up-estuary sur- also be correlated with similar mixing mechanisms. The success face currents, which resulted in compensating bottom currents in of the model in capturing these events is a general indication that the down-estuary direction. The bottom down-estuary currents the overall circulation in the bay is well reproduced by the hydro- brought fresher Escambia River water into Escambia Bay and dynamic model. Pensacola Bay. This unstable stratification leads to periods of in- It is evident that the mixing events are not permanent in na- tense vertical mixing. The bottom salinity declined by approxi- ture, but rather are highly transient. This concept is demonstrated mately 10 psu at ER3 and ER4. It is interesting to note that the by the quick restratification that occurred when the wind abated decline in bottom salinity shown at the upper bay stations ͑C1A, or changed its direction, particularly towards the south. Such C2A͒ is not as pronounced as that shown for the river stations, events can be seen in both the model and observed data ͑Fig. 6͒ ER3 and ER4. This drop in bottom salinity is not apparent in the during the periods of September 26–29, October 14–20, and Oc- lower bay station, C4A. While the bottom salinity continued to tober 26–29. Fig. 6 also presents a comparison of model- decline during this period, the surface salinity remained relatively computed versus observed data ͑Station I-10͒ for surface and bot- constant. However, the bottom salinity quickly recovered when tom temperature. The model-computed surface temperature the wind reversed on October 14 and continued to blow towards shows more variability than the observed temperature. At certain the south until October 20. The southward wind brought fresher, times ͑e.g., September 10͒, the model predicts a diurnal tempera- upper Escambia Bay surface water into the lower bay, promoting ture variation of approximately 5°C, while the observed data a downwelling movement of water near the Gulf Breeze Penin- variation was approximately 2°C. In general, the model captures sula, which, in turn generated compensating bottom currents that the overall features, which exist in the data. For example, two forced bottom saline water in the up-estuary direction. This rever- major cooling events occurred on September 24 and October 15, sal of bottom currents seemed to be accentuated by the Gulf which the model captures quite well. Moreover, the model main- Breeze Peninsula. While the bottom salinity continued to increase tains a reasonable level of vertical temperature stratification simi- in the up-estuary direction, the horizontal and vertical mixing and lar to that observed in the data. It is important to note that during the upwelling of the bottom saline water in the upper bay redis- the 2 month study period, the Escambia and Pensacola Bays ex- tributed the vertical salinity structure, causing elevated surface hibited higher bottom temperatures than surface temperatures.

264 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 Fig. 4. Model computed surface and bottom salinity are compared against observed salinity at locations indicated in each panel ͑see Fig. 1 for their physical locations͒. Wind vectors measured at continuous recorder meteorological station at I-10 bridge station for this study is illustrated at bottom panel to facilitate understanding of system’s responses to winds.

This may be due to warmer Gulf water entering the bay and which leads to a strong vertical mixing and produces nearly well remaining with the heavier bottom salt water moving up the es- mixed water column as illustrated in Fig. 7 ͑top panel͒.Onthe tuary. The model output compares reasonably well with this ob- other hand, the southward-directed wind produces an advecting servation. mechanism that brought fresher river water into the bay and pro- Finally, a comparison of the model-computed and measured duces a stable and strong stratified water column with a very water levels is shown in Fig. 6. It shows that the model slightly weak vertical mixing. In order to view these processes throughout underestimates the water level ranges; however, the model repro- Escambia and Pensacola Bays, a longitudinal section of salinity duces the overall diurnal and subtidal scale water level fluctua- and current velocity distribution are presented in Fig. 8. Fig. 8 tions very well, with negligible phase differences. presents profiles of salinity and currents along a vertical section, passing through the middle of Pensacola Bay and Escambia Bay. This vertical slice is viewed from the east, such that Pensacola Stratification and Destratification Processes Bay ͑south͒ is on the left and Escambia Bay ͑north͒ is on the right-hand side of the figure. The previous section suggests that stratification and destratifica- The upper panel of Fig. 8 represents conditions on October 13 tion events are tied to the advecting and mixing properties of the at 1,200 hrs, when the wind was blowing towards the northwest at wind. The northward-directed wind produces velocity shear, 6ms−1. The northward-directed wind, blowing over a stratified

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 265 Fig. 5. Model computed salinity profiles compared against observed salinity at locations indicated in each panel ͑see Fig. 1 for their physical locations͒ at different periods indicated in top of panel water column, produced surface currents in the up-estuary direc- mately 5 m s−1. During this period the north wind advected tion causing a downwelling of water in the upper bay region. The fresher surface water in the down-estuary direction, while the downwelling of water movement occurs when the surface cur- bottom water moved up the estuary causing stratification in the rents encounters the head end boundary. This process in turn water column ͓see also Fig. 7͑b͔͒. This response was substantially drives bottom currents in the down-estuary direction. This depth- reinforced by the Gulf Breeze Peninsula separating the bay from dependent mechanism is very effective in generating vertical the Gulf of Mexico. In contrast to the event described in Fig. 8͑a͒, shear ͓see also Fig. 7͑a͔͒. A vertical instability occurs due to the the estuarine proper appears expanded and the salinity distribu- generation of current shear across the pycnocline, causing suffi- tion lengthened. cient mixing to destratify the water column. It is also apparent Figs. 9 and 10 present the surface and bottom salinity distri- from Fig. 8͑a͒ that, with a constant source of freshwater from the butions and current vectors for the above two periods, respec- Escambia River, the length of the estuary proper is shortened, i.e. tively. The surface and bottom salinity distributions on October the longitudinal salinity distribution has been compressed. 13 at 1200 hrs, when the wind was blowing in a northwest direc- On the other hand, a relatively rapid restratification can occur tion ͑Fig. 9͒, suggest that the water column was nearly or com- when the wind abates or changes its direction, particularly to- pletely mixed throughout the bay system. The surface currents wards the south, as is the case during October 16, 1997 illustrated were mainly driven by the wind, with little or no time lag; the in Fig. 8͑b͒. Because of the increasing longitudinal pressure gra- bottom currents were in the opposite direction, responding to the dients, gravitational circulation tends to occur and reestablishes downwelling movement of water in the upper Escambia Bay re- the stratification regime. For example, on October 16, 1997 at gion. In contrast, conditions on October 16 at 1000 hrs ͑Fig. 10͒ 1000 hrs, the wind was blowing towards the south at approxi- represent a strongly stratified system, especially in upper Escam-

266 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 Fig. 6. Model calibration results for surface and bottom salinity and temperature, and water level at station I-10. Panels ͑a͒ and ͑b͒ represent model comparison against observed salinity and temperature. Observed data are shown averaged over 1 day ͑diurnal scale͒, with average represented by triangles and range represented by vertical bars. Filled upward triangles represent surface data and filled downward triangles represent bottom data. Surface model output is shown with solid line, and bottom model output with dashed line. Panel ͑b͒ illustrates model computed and observed water level at same location; solid line represents model water level output; and dashed line represents observed data. Bottom panel in these figures shows wind stick diagram ͑as previously described͒ for data collected on top of I-10 bridge. bia Bay and Blackwater Bay, with relatively weak stratification in a relatively complete observational data set. The estuarine system, the rest of the bay system. It is interesting to note that the fresh- Pensacola–Escambia Bay, is rather geomorphologically complex water plume emanating from the Escambia River, Blackwater and strongly responds to winds and freshwater inflows. A River, and Yellow River remains in the western part of both Es- 2 month period from September through October, 1997 was used cambia Bay and Blackwater Bay, a result of the Coriolis force. in the analyses. This period reflects summer, low-flow conditions that are typical for the Pensacola–Escambia Bay system. The model was able to represent the overall circulation and mixing Conclusions characteristics of the Pensacola Bay system because of the reasonable agreement between observed and calculated temporal, The processes responsible for stratification and destratification in spatial, and vertical distributions of salinity, temperature, and an estuarine system have been elucidated through the use of a water elevations. Modeling simulations and data analyses suggest high-resolution three-dimensional ͑3D͒ hydrodynamic model and that mixing mechanisms are closely tied with the wind-generated

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 267 Fig. 7. Mechanisms of stratification and destratification events are tied to advecting and mixing properties of wind. Top panels demonstrate that south wind ͑blowing northwest͒ produces velocity shear which, in turn, generates strong vertical mixing that produces well-mixed water column. Bottom panels illustrate north wind ͑blowing south͒ that produces advecting mechanism and produces stable and strong stratified water column with very weak vertical mixing.

ץ ץ .internal velocity shear, especially during up-estuary wind events ͑U,V͒ + ͓U ͑u,v͒ + f͑− v,u͔͒ x iץ tץ A vertical instability occurs due to the generation of shear across the pycnocline, causing vertical mixing to destratify the water i ץ ץ Pץ Pץ column. However, down-estuary wind event causes strong strati- 1 =− ͫ , ͬ + ͫK ͑u, ͒ͬ + ͑F ,F ͒͑2͒ v U V ץ M ץ ץ ץ ␳ fication. This stratification is resulted from the two layer estuarine o x y z z flow generation by the down-estuary wind which advects upper layer fresh water in to the down estuary and a compensating Tץ ץ ץ Tץ bottom flow in the up-estuary regions. The compensating bottom + ͑U T͒ = ͫK ͬ + F ͑3͒ T ץ H ץ i ץ ץ flow is accentuated by the Gulf Breeze Peninsula separating the t xi z z estuary from the Gulf of Mexico. Sץ ץ ץ Sץ + ͑U S͒ = ͫK ͬ + F ͑4͒ S ץ H ץ i ץ ץ t xi z z ͑ ͒ Acknowledgments The horizontal diffusion terms, FU ,FV , FT, and FS, in Eqs. ͑2͒–͑4͒ are calculated using a Smagorinsky ͑1963͒ horizontal dif- The writers thank Mr. Allan Niedoroda of URS Greiner Wood- fusion formulation ͑Blumberg and Mellor 1980͒. Under the shal- ward Clyde for his support in data analysis and interpretation. Mr. low water assumption, the vertical momentum equation is re- John G. Sondey contributed in graphical productions. duced to a hydrostatic pressure equation. Vertical accelerations due to buoyancy effects and sudden variations in bottom topography are not taken into account. The hydrostatic approximation Appendix: Hydrodynamic Modeling Framework yields ␩ ␳Ј ␳ The model solves a coupled system of differential, prognostic P − o = g͑␩ − z͒ + ͵ g dzЈ ͑5͒ equations describing the conservation of mass, momentum, tem- ␳ ␳ o z o perature, salinity, turbulence energy, and turbulence macroscale. ͑ ͒ ␩͑ ͒ The governing equations for velocity Ui = u,v,w , temperature where P=pressure; z=water depth; x,y,t =free surface eleva- ͑ ͒ ͑ ͒ ͑ ͒ ␳ ␳ ␳͑ ͒ T , salinity S , and xi = x,y,z are as follows: tion; o =reference density; and = T,S =density, which is a function of T and S, as defined by Fofonoff ͑1962͒. ͑ ͒ ͑ ͒ The vertical mixing coefficients, KM and KH, in Eqs. 2 – 4 1 ץ Ui are obtained by appealing to a 2 order turbulence closure =0 ͑1͒ 2 ץ xi scheme and are given by

268 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 Fig. 8. Upper panel ͑a͒ represents conditions on October 13 at 1,200 hrs, when south-east wind was blowing at approximately 6 m s−1. South-east wind, over stratified water column, produced surface currents in up-estuary direction prompting downwelling of water movement in upper bay region. Lower panel ͑b͒ demonstrates quick occurrence of restratification when wind abates or changes its direction on October 16, 1997. The north wind advected fresher surface water in down-estuary direction, while bottom water moved up estuary causing stratification in water column.

2ᐉ͒ ͑ץ 2ᐉ͒ ͑ץ 2ᐉ͒ ͑ץ 2ᐉ͒ ͑ץ 2ᐉ͒ ͑ץ q ץ K = Kˆ + ␷ , K = Kˆ + ␷ ͑6͒ q uq vq wq M M M H H H + + + = ͫK ͬ zץ z qץ zץ yץ xץ tץ ␳ q3ץ v 2 gץ u 2ץ ᐉͭ ͫͩ ͪ ͩ ͪ ͬ ͮ + E K + + K − + Fᐉ ␻ ץ ␳ H ץ ץ Kˆ = qᐉS , Kˆ = qᐉS ͑7͒ 1 M M M H H z z o z B1˜ where q2 /2=turbulent kinetic energy; ᐉ=turbulence length scale; ͑9͒ SM and SH =stability functions defined by solutions to algebraic ͑ ͒ equations given by Mellor and Yamada 1982 as modified by where K =0.2qᐉ, the eddy diffusion coefficient for turbulent ki- ͑ ͒ ␷ ␷ 2 q Galperin et al. 1988 ; and M and H =constants. The variables q netic energy; Fq and Fᐉ represent horizontal diffusion of the tur- and l are determined from the following equations: bulent kinetic energy and turbulence length scale and are param- eterized in a manner analogous to either Eq. ͑6͒ or ͑7͒; ␻˜ =wall proximity function defined as ␻˜ =1+E ͑ᐉ/␬L͒2; ͑L͒−1 =͑␩−z͒−1 wq2͒ 2͑ץ vq2͒͑ץ uq2͒͑ץ q2ץ + + + +͑H+z͒−1; ␬=von Karman constant; H=water depth; ␩=free sur- zץ yץ xץ tץ face elevation; and E1, E2, and B1 empirical constants set in the .␳ q3 closure modelץ vͪ2ͬ 2gץ ͩ uͪ2ץ ͩͫ ͬ q2ץ ͫ ץ = Kq +2KM + + KH −2 The basic Eqs. ͑1͒–͑9͒ are transformed into a terrain following z B ᐉץ z ␳ץ zץ zץ zץ o 1 the ␴-coordinate system in the vertical scale and an orthogonal ͑ ͒ + Fq 8 curvilinear coordinate system in the horizontal scale. The result-

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 269 Fig. 9. Model computed surface and bottom current vectors and salinity distributions on October 13 at 1,200 hrs. Wind was blowing in north-west direction. Water column is nearly or completely mixed in upper Escambia Bay system. Surface currents were mainly driven by wind, with little or no time lag; Bottom currents were in opposite direction, responding to downwelling movement of water in upper Escambia Bay region.

ing equations are vertically integrated to extract barotropic vari- q2ᐉ =0 ͑10d͒ ables; and a mode splitting technique is introduced such that the fast-moving, external barotropic modes and relatively much- ␩ץ ␩ץ ␩ץ slower internal baroclinic modes are calculated by prognostic equations with different time steps. Detailed solution techniques W = U + V + ͑10e͒ tץ yץ xץ .are described in Blumberg and Mellor ͑1987͒ ␩͑ ͒ The boundary conditions at the free surface z= x,y are ͑␶ ␶ ͒ where ox , oy =surface wind stress vector with the friction ve- ␶ V locity u␶s, the magnitude of the vector. The surface wind stressץ Uץ ␳ ͩ ͪ ͑␶ ␶ ͒͑͒ oKM , = ox, oy 10a is computed based in Large and Pond ͑1981͒ as follows: zץ zץ

S ␶ = C ␳ W͉W͉͑11͒ץ Tץ ␳ K ͩ , ͪ = ͑H˙ ,S˙͒͑10b͒ o Ds a ץ ץ o H z z ␳ ͑ 3͒ where a =density of air 1.25 kg/m ; W=wind vector measured at 10 m above the ground; and C =surface drag coefﬁcient with 2 2/3 2 ͑ ͒ Ds q = B1 u␶s 10c a value given by

270 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 Fig. 10. Model computed surface and bottom current vectors and salinity distributions on October 16 at 1,000 hrs. This illustrates strongly stratiﬁed system, especially in upper Escambia Bay and Blackwater Bay, with relatively weak stratiﬁcation in rest of bay system. Wind was blowing from north. Freshwater plume emanating from Escambia River, Blackwater River, and Yellow River stays in western part of both Escambia Bay and Blackwater Bay.

Vץ Uץ C Ds ␳ K ͩ , ͪ = ͑␶ ,␶ ͒͑13a͒ bx by ץ ץ o M 1.2 ϫ 10−3 for ͉W͉ Ͻ 11 m/s z z = 0.49 + 0.065 ͉W͉ ϫ 10−3 for ͉W͉ Ͼ 11 m/s but Ͻ 25 m/s Ά · 2 2/3 2 ͑ ͒ q = B u␶ 13b 0.49 + 0.065 ϫ 25 ϫ 10−3 for ͉W͉ Ͼ 25 m/s 1 b ͑12͒ q2ᐉ =0 ͑13c͒ 2/3 ͑ ͒ The quantity B1 =empirical constant 6.51 arising from the tur- Hץ Hץ bulence closure relations. The net ocean heat flux is H˙ and here W =−U − V ͑13d͒ ץ b ץ b b ˙ ϵ ͑ ͓͒ ˙ ˙ ͔ ␳ ͑ ˙ ˙ ͒ x y S S 0 E− P / o, where E− P =net evaporation–precipitation ͑ ͒ ͑ ͒ fresh water surface mass flux rate and S 0 =surface salinity. On where H x,y =bottom topography and u␶b =friction velocity as- ͑␶ ␶ ͒ the sidewalls and bottom of the basin, the normal gradients of T sociated with the bottom frictional stress bx , by . The bottom and S are zero so that there are no advective and diffusive heat stress is determined by matching velocities with the logarithmic and salt fluxes across these boundaries. At the lower boundary law of the wall. Specifically,

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / APRIL 2005 / 271 ␶ ␳ ͉ ͉ ͑ ͒ Fofonoff, N. P. ͑1962͒. “Physical properties of sea water.” The sea: Ideas = oCDb V V 14 →b →b →b and observations on progress in the study of the seas, M. N. Hill, ed., with value of the drag coefficient C given by Vol. 1, Wiley Interscience, New York, 3–30. Db Galperin, B., Kantha, L. H., Hassid, S., and Rosati, A. ͑1988͒. “A quasi- 1 −2 equilibrium turbulent energy model for geophysical flows.” J. Atmos. C = ͫ ln͑H + z ͒/z ͬ ͑15a͒ Db ␬ b o Sci., 45, 55–62. Geyer, W. R., and Signell, R. P. ͑1992͒. “A reassessment of the role of where zb and V =distance of the center of the grid point nearest tidal dispersion in estuaries and bays.” Environ. Prog., 15, 97–108. →b Goodrich, D. M. ͑1985͒. “On stratification and wind-induced mixing in the bottom and corresponding velocity; and ␬=von Karman con- the Chesapeake Bay.” PhD thesis, Marine Sciences Research Center, stant. The final result of Eqs. ͑14͒ and ͑15a͒ in conjunction with State Univ. of New York, Stony Brook, N.Y. the turbulent closure derived KM is that the calculations will yield Goodrich, D. M., Boicourt, W. C., Hamilton, P., and Prichard, D. W. ͑ ͒ ͑ ␶ ␬ ͒ ͑ ͒͑͒ 1987 . “Wind-induced destratification in Chesapeake Bay.” J. Phys. V = / u␶b ln z/zo 15b → →b Oceanogr., 17, 2232–2240. Grano, V., and Pritchard, D. ͑1982͒. “A study of the spatial variations in in the lower boundary region if enough resolution is provided. In the nontidal currents of the Upper Chesapeake Bay.” Final Rep. to those instances where the bottom boundary layer is not well re- Maryland Power Plant Stiting Program, Chesapeake Bay Institute, solved, it is more appropriate to specify CDb =0.0025. The actual The John Hopkins Univ., Baltimore. ͑ ͒ algorithm is to set CDb to the larger of the two values given by Eq. Large, W., and Pond, S. 1981 . “Open ocean momentum flux measure- ͑ ͒ ments in moderate to strong winds.” J. 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