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Estuarine, Coastal and Shelf Science 95 (2011) 377e387

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Estuarine, Coastal and Shelf Science

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Empirical tools for simulating salinity in the estuaries in EvergladesNational Park, Florida

F.E. Marshall a,*, D.T. Smith b, D.M. Nickerson c

aCetacean Logic Foundation, Inc., 2022 Spyglass Lane, New Smyrna Beach, FL 32169, United Statesb Everglades National Park, 950 North Krome Avenue, Homestead, FL 33030, United StatescDepartment of Statistics, University of Central Florida, Orlando, FL 328916-2370, United States

a r t i c l e i n f o

Article history:Received 7 July 2011Accepted 1 October 2011Available online 15 October 2011

Keywords:Floridasalinity modelingregression analysismultivariate analysisestuariesconceptual modeling

* Corresponding author.E-mail addresses: clfinc@earthlink.net (F.E. Marsha

T. Smith), nickersn@mail.ucf.edu (D.M. Nickerson).

0272-7714/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.ecss.2011.10.001

a b s t r a c t

Salinity in a shallow estuary is affected by upland freshwater inputs (surface runoff, stream/canal flows,groundwater), atmospheric processes (precipitation, evaporation), marine connectivity, and windpatterns. In Everglades National Park (ENP) in South Florida, the unique Everglades ecosystem exists asan interconnected system of fresh, brackish, and salt water marshes, mangroves, and open water. For thiseffort a coastal aquifer conceptual model of the Everglades hydrologic system was used with traditionalcorrelation and regression hydrologic techniques to create a series of multiple linear regression (MLR)salinity models from observed hydrologic, marine, and weather data. The 37 ENP MLR salinity modelscover most of the estuarine areas of ENP and produce daily salinity simulations that are capable ofestimating 65e80% of the daily variability in salinity depending upon the model. The Root Mean SquaredError is typically about 2e4 salinity units, and there is little bias in the predictions. However, the absoluteerror of a model prediction in the nearshore embayments and the mangrove zone of Florida Bay may berelatively large for a particular daily simulation during the seasonal transitions. Comparisons show thatthe models group regionally by similar independent variables and salinity regimes. The MLR salinitymodels have approximately the same expected range of simulation accuracy and error as higher spatialresolution salinity models.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Estuarine salinity is hydrology-dependent and the salt concen-tration at any point in an estuary is a function of the variouselements of the water budget e rainfall, evaporation, and fresh-water supply from the watershed e as well as the level of influencefrom the marine end member and wind forcing (Hansen andRattray, 1966; Pritchard, 1968; Kjerfve et al., 1996; Nuttle et al.,1999; Kelble et al., 2006). One of the primary drivers of theecological composition of an estuary is the salinity variability(Montague and Ley, 1999; Thayer et al., 1999; Ogden et al., 2005). Aunique example of a coastal ecosystem with freshwater wetlandsand estuarine areas that support high species diversity anda number of threatened and endangered species is the GreaterEverglades Ecosystem of South Florida within Everglades NationalPark (ENP). The Greater Everglades Ecosystem is an International

ll), dewitt_smith@nps.gov (D.

All rights reserved.

Biosphere Reserve, a World Heritage Site, and a Wetland of Inter-national Importance (Davis and Ogden, 1994).

Outside of ENP, changes were made to the hydrology over thepast 100 years for agricultural and urban expansion. In general, thefreshwater supply to the Everglades has been reduced, therebyaltering the salinity regime(s) of the estuaries within ENP. Thenegative impact of this reduction in freshwater on the uniqueEverglades estuarine ecosystem has been well-documented for thepast quarter-century (Tabb, 1967; Davis et al., 1994, 2005;Fourqurean and Robblee, 1999; Rudnick et al., 1999; Schaffraneket al., 2001; Burd and Jackson, 2002; Ogden et al., 2005; Renkenet al., 2005; Yarbro and Carlson, 2008). The program that hasbeen implemented to restore the Everglades (ComprehensiveEverglades Restoration Plan, or CERP) includes restoration of thehydrology and salinity of the Greater Everglades Ecosystem as a keycomponent (www.evergladesplan.org).

This study of the Everglades coastal system has identified therelationships of the various hydrologic components, wind, andmarine influence to salinity in the estuaries using statisticalmethods.Where there was sufficient correlation between salinity and theinfluential factors, stepwise variable selection was used to develop

Fig. 1. Map of the Everglades National Park study area showing monitoring station locations for salinity, stage, flow, sea surface elevation, and wind data.

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387378

multiple linear regression (MLR) models for simulation of salinity.The objective was to provide meaningful and quantitative informa-tion for hydrologists, ecologists, managers, and others about therelationship between salinity and the physical factors that affect it inestuarine environments, to the benefit of Everglades restoration.

Within ENP there are a number of estuarine environments witha relatively wide range of salinity regimes. They provide a variety ofwell-monitored waters that are useful for a statistical analysis ofthe influence of observable physical factors on the salinity regimes.Data onwater level and flow in the freshwater marshes and salinity

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387 379

in the estuaries of ENP have been collected for a relatively long timeand over a large area. In some areas, hydrology and salinity havebeen measured synoptically since the 1930s, and data have beencollected continuously since the 1980s across the South Floridaregion.

One of the first attempts to use statistical methods to modelsalinity was made by Tabb (1967) in a study of estuarine biota andsalinity in the estuaries of ENP. Based on an analysis of these data,Tabb (1967) concluded that the salinity variability in the estuarineareas can be estimated using groundwater levels in the upstreamwatersheds. He suggested that hypersaline conditions developed inFlorida Bay when groundwater levels fell below a certain range ofvalues. Tabb (1967) indicated that the applicability of the predictionrelationships was limited at times because of observed anomalieswhen the wet season changed to the dry season.

Scully (1986) used monthly stage data in the upstream fresh-water marsh at P33 and Florida Bay salinity data to develop simplelinear regression models for salinity. Cosby (1993) used correlationanalysis and linear regression to examine relationships betweenstage, flow, rainfall, and salinity in Florida Bay. Nuttle (1997)developed improved statistical models after transformingmonthly grab sample salinity data collected in Florida Bay. Buildingon the work of Nuttle (1997), Marshall (2000) used cross-correlation techniques from time series analysis to evaluate theadditional effects of wind, tide, and local meteorological conditions,suggesting that acceptable multiple linear regression models couldbe developed. In addition to statistical models, a number ofnumeric hydrology/salinity models have also been developed forENP estuaries (Wang et al., 1994; Sheng et al., 1995; Cerco et al.,2000; Langevin et al., 2004; Swain et al., 2004; Cosby et al., 2005;Tetra Tech, 2005) with mixed success (Marshall and Nuttle, 2011).In 2002, the Committee on Restoration of the Greater EvergladesEcosystem (CROGEE) recommended the use of statistical models,time series analysis, and the coupling of salinity models with theoutput from watershed hydrology models (CROGEE, 2002) forEverglades restoration activities.

Statistical methods such as correlation and regression are usefulempirical tools for characterizing the relationships betweenhydrologic parameters of freshwater systems (Riggs, 1968; Pionkeand Nicks, 1970; Jackson, 1975; Jensen, 1976; Hubert et al., 1992).A full analysis includes the selection of important factors, a way ofcharacterizing the factors (i.e. data), development of a regressionmodel including the error and goodness-of-fit statistics, andinterpretation of the model output (Riggs, 1968). A regressionequation provides a way of quantifying relationships, even whenmore than two quantities are being used to characterize the asso-ciation (Kachigan, 1991; Helsell and Hirsch, 1991). The developedstructure of a regression model contains the important factors thatmay be reasonably expected to affect the dependent variable. Likea correlation coefficient, a regression equation or model does notimply cause and effect between dependent and independent vari-ables because some unmeasured factor may be influencing both.Even so, when there is a physical tie between the dependent andindependent variables, the results can be considered to havemeaning (Riggs, 1968). In this manner, river flow can be quantifiedstatistically using regression methods and stage (water level) data.

In the field of hydro-geology and water supply engineering, theGhybeneHerzberg principle is often used to describe the locationof the fresh/salt water interface in the coastal aquifer as a functionof the height of freshwater in thewatershed relative to the height ofthe sea surface above a common datum, and the relative densitiesof the water masses (Anderson et al., 2000). Following a review ofthe relevant literature, we hypothesized that a coastal aquiferconceptual model with a dynamic balance between fresh and saltwater modified by the effects of wind could be used to study the

variability in salinity in Florida Bay and the estuaries discharginginto the Gulf of Mexico within ENP. To test the hypothesis, linearregression models of hydrology, salinity, sea level, and wind factorswere developed using accepted multiple regression methods(stepwise regression, SAS� PROC REG routines) to select theindependent variables and estimate the coefficients of the models,as described below.

2. Description of study area and data

The study area encompasses the Greater Everglades Ecosystemwithin ENP and the immediately adjacent protected areas (Fig. 1).This includes the freshwater marshes and swamps in the Ever-glades and Big Cypress National Preserve; the estuarine areas ofFlorida Bay, Whitewater Bay, and the southern coast of the Gulf ofMexico (Gulf); and the semi-enclosed sounds and bays betweenFlorida Bay and Biscayne Bay referred to locally as South BiscayneBay. Fresh surface water flowing into ENP across Tamiami Trail intoShark River Slough is augmented by rainfall and lost to evaporationand groundwater as it moves south and southwest, primarilytoward the Gulf of Mexico andWhitewater Bay. A secondary flow ofwater discharges into Florida Bay via Taylor Slough and the SouthDade Conveyance System, a man-made drainage canal. Freshwatercan recharge the surficial aquifer through the highly transmissiveupper substrate, and surficial aquifer groundwater may re-emergeas surface water to augment overland flows in lower-elevationTaylor Slough. East of the Taylor Slough drainage basin in the ENP“panhandle” freshwater flows as overland flow, groundwater, andcreek/stream flow to discharge into northeast Florida Bay and southBiscayne Bay. A number of studies indicate that freshwater beingdelivered to the estuarine receiving waters in ENP has beensignificantly reduced for flood protection and water supply to serveareas outside of the park (Davis and Ogden, 1994; Fourqurean andRobblee, 1999; Renken et al., 2005).

The climate of South Florida exhibits distinct wet and dryseasonal patterns but is spatially highly variable (Nuttle et al.,1999). The pattern during the wet season (May or June throughOctober or November) is driven by tropical wind and sea breezeinteractions on a daily scale causing frequent convective storms,less frequent tropical storms, and high spatial variability. Rainfalldata between gauges that are only tens of miles apart often showwidely varying rainfall volumes for a single event during the wetseason. During the dry season rain is usually delivered by frontalsystems with reduced frequency compared to the wet season.Evaporation is also seasonal, but with a different temporalpattern than rainfall. Evaporation peaks at the end of the dryseason when rainfall is low. This difference in timing hasa significant effect on the stage in the freshwater marshes andsalinity in the estuaries.

Wind has a seasonal pattern similar to rainfall. During the wetseason the wind direction is predominately from the south andsoutheast, and during the dry season wind blowing from the northis more common. However, wind direction and speed can changerapidly when a weather system is moving through South Florida(Smith, 1997a,b). Because wind can vary hourly and daily as well asseasonally, wind is considered an element of short-term weatherand not long-term climate for this analysis. Nonetheless, wind is animportant factor in salinity modeling in this study.

The elevation of the sea surface (sea level) and the hydraulicallyconnected elevation of the water surface in ENP estuaries havesimilar seasonal patterns of maximum and minimum elevationsthat are different than hydrologic and wind maxima and minima(Smith and Pitts, 1995). When a hurricane or other significantweather event occurs, wind and storm surge effects can alter thesea surface elevation dramatically over short periods.

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387380

The salinity data used for this statistical modeling effort wereobtained from the ENP Marine Monitoring Network (MMN) data-base. These salinity data are available from South Florida NaturalResources Center (SFNRC) by request (EVER_data_request@nps.gov). Details about these data can be found in EvergladesNational Park (1997a,b), and Smith (1997a,b), Smith (1998, 1999,2001). The ENP MMN stations used for this study are shown inFig. 1. There are 36 salinity stations and the list of stations andlocations are presented in Table 1, along with the start date for datacollection and the period-of-record mean daily value throughOctober 31, 2002. As the Practical Salinity Scale is being used,salinity has no units.

The stage data used for model development were also collectedby ENP and are available from SFNRC by request (site addressabove). Several of the ENP continuous water level (stage) moni-toring stations in the Everglades began recording data in the 1950sbut most stage records date from the late 1980s to the 1990s. Thestations are used as independent variable candidates for modeldevelopment purposes and their locations are presented in Table 2and Fig. 1. The units of stage are ft relative to the NGVD29 datum.Because the raw data and the data used in application of thedescribed models are typically in English units, the primary unitspresented herein are English units.

Daily average sea surface elevation data at the Key West NOAAtide station were obtained from the NOAA Tides Online website(http://tidesonline.nos.noaa.gov/). The Key West tide station loca-tion, start date for data collection, and the period-of-record meandaily value through October 31, 2002 are presented in Table 2.

Table 1Summary of information for the dependent variable (salinity) database, including the locain model development and verification for estuaries within ENP. All data were collected

Station name Map label Location Start

Blackwater Sound BS Florida Bay Nearshore 9/11Bob Allen Key BA Central Florida Bay 4/27Broad River BR Gulf Coast 1/18Broad River Lower BD Gulf Coast 4/12Buoy Key BK Central Florida Bay 4/27Butternut Key BN Central Florida Bay 4/27Cane Patch CN Gulf Coast 1/19Cannon Bay CA Big Cypress Estuary 1/12Clearwater Pass CW Whitewater Bay 5/10Duck Key DK Central Florida Bay 4/26Garfield Bight GB Florida Bay Nearshore 7/3/1Gunboat Island GI Gulf Coast 3/22Harney River HR Gulf Coast 3/13Highway Creek HC Florida Bay Mangroves 4/27Joe Bay JB Florida Bay Nearshore 7/14Johnson Key JK Western Florida Bay 1/1/1Lane River LN Gulf Coast 4/18Little Blackwater Sound LB Florida Bay Nearshore 9/11Little Madeira Bay LM Florida Bay Nearshore 4/28Little Rabbit Key LR Western Florida Bay 4/27Long Sound LS Florida Bay Nearshore 3/28Lostmans River LO Big Cypress Estuary 8/25Manatee Bay MB South Biscayne Bay 6/13Middle Key MD South Biscayne Bay 10/1Murray Key MK Western Florida Bay 4/27North River NR Gulf Coast 2/3/1Peterson Key PK Western Florida Bay 4/27Shark River SR Gulf Coast 5/2/1Tarpon Bay East TE Gulf Coast 4/3/1Taylor River TR Florida Bay Mangroves 5/12Terrapin Bay TB Florida Bay Nearshore 9/12Trout Cove TC Florida Bay Nearshore 4/28Watson Place WP Big Cypress Estuary 1/1/2Whipray Basin WB Central Florida Bay 4/28Whitewater Bay WE Whitewater Bay 8/27Willy Willy WW Big Cypress Estuary 6/27

a Start through October 31, 2002.

Smith and Pitts (1995) discuss the influence of the variability in theelevation of the oceanwaters around Florida Bay on the variation ofwater levels in Florida Bay. For this study, the Key West sea surfaceelevation data were compared to the period-of-record stage data atMMN estuarine stations using correlation and regression analyses.It was found that estuarine stage data were significantly correlatedto Key West sea surface elevation at the 95% level of significance.Therefore, the variation of the Key West sea surface elevation isconsidered to be representative of the variability of the waterelevation in the ENP estuaries.

A number of the stations in this study were located north ofCape Sable along the Gulf of Mexico coast, so the data from theNaples and Fort Myers tide stations were evaluated for use. Tidedata at both of these Gulf coast stations have been collectedcontinuously since 1996. Prior to 1996, only predicted daily averagetide levels are available. A comparison of predicted and actual tideelevations for the post-1996 period indicated that, at times, therewere relatively large differences. Because of the correlationbetween KeyWest sea surface elevation and stage at MMN stationsalong the Gulf coast and in Whitewater Bay, the sea surfaceelevation measured at Key West was used as a potential indepen-dent variable for all salinity models. The units of Key West waterlevel are feet (ft) relative to the NGVD29 datum, and the variablename used for modeling is KWWATLEV.

Long-term wind data are available at several locations in theregion. National Weather Service (NWS) wind data were obtainedfrom the Southeast Regional Climate Center for Key West andMiami stations because of the length of the continuous records. The

tion of the salinity monitoring stations and the period-of-record for salinity data usedby ENP.

data N Meana North latitude West longitude

/1991 2596 24.7 25:10:43.43 80:26:17.20/1988 1802 33.2 25:01:34.43 80:40:54.26/1999 1512 2.2 25:28:41.59 80:59:23.03/1996 1245 11.6 25:29:10.50 81:06:39.67/1988 1802 33.6 25:07:16.43 80:50:01.25/1988 4343 30.9 25:05:18.92 80:31:07.79/1990 1605 0.8 25:25:18.66 80:56:32.17/2000 733 18.8 25:42:06.30 81:11:09.28/1996 2054 16.9 25:17:47.65 81:00:46.44/1988 4247 28.7 25:10:54.30 80:29:22.78991 2303 28.7 25:10:19.42 80:47:47.26/1996 2061 10.9 25:22:41.84 81:01:45.62/1996 1622 8.4 25:25:27.52 81:03:35.28/1988 4270 11.5 25:15:22.03 80:26:39.48/1988 4878 15.2 25:13:28.28 80:32:27.51988 4079 35.5 25:03:08.03 80:54:15.05/1996 1658 6.5 25:17:04.45 80:53:37.72/1991 3517 20.1 25:12:49.43 80:25:59.23/1988 4743 23.6 25:10:32.45 80:37:55.24/1988 1829 35.2 24:58:53.08 80:49:31.91/1988 4886 17.8 25:14:06.40 80:27:26.21/1997 1378 15.8 25:33:21.46 81:10:06.06/1991 1713 23.4 25:14:25.40 80:25:23.231/1991 1894 25.8 25:17:13.42 80:23:41.24/1988 1579 33.4 25:06:21.96 80:56:31.31990 2746 6.0 25:20:24.47 80:54:40.32/1988 2466 34.5 24:55:06.46 80:44:45.24996 1960 24.9 25:21:13.21 81:05:58.16996 1635 2.1 25:24:36.18 80:57:50.90/1988 4644 9.6 25:13:29.42 80:39:10.26/1991 3833 23.6 25:09:25.45 80:43:29.24/1988 4871 18.7 25:12:40.97 80:31:59.16000 717 20.3 25:42:34.13 81:14:52.55/1988 4287 36.1 25:04:42.46 80:43:38.24/1995 2016 11.5 25:13:53.51 80:56:18.74/1997 1589 5.1 25:35:13.09 81:02:37.86

Table 2Summary of information for the independent variable database used in model development and verification for ENP estuarine salinity regression models. Units are: stage e ftNGVD29, wind e vector quantity, Key West sea surface elevation e ft NGVD29, flow e ft3 s�1.

Station/variable Variable type Data source Location Data start N Meana North latitude West longitude

CP Stage ENP Taylor Slough 10/1/1978 8266 1.20 25:13:39 80:42:15E146 Stage ENP Taylor Slough 3/24/1994 3003 1.24 25:15:13 80:40:01EVER1 Stage ENP C-111 Basin 4/23/1985 5797 1.46 25:19:42 80:25:47EVER4 Stage ENP C-111 Basin 9/20/1985 5197 2.00 25:20:32 80:32:42EVER6 Stage ENP C-111 Basin 12/24/1991 3699 2.02 25:17:49 80:30:42EVER7 Stage ENP C-111 Basin 12/24/1991 3589 2.22 25:18:31 80:32:33G3273 Stage ENP East of S.R. Slough 3/14/1984 6749 5.98 25:37:36 80:34:33NP206 Stage ENP East of S.R. Slough 10/1/1974 9500 5.17 25:32:38 80:40:20NP46 Stage ENP East of S.R. Slough 1/15/1966 8581 1.44 25:19:05 80:47:46NP62 Stage ENP East of S.R. Slough 1/4/1964 10774 2.39 25:26:17 80:46:59P33 Stage ENP Shark River Slough 2/15/1953 17892 5.95 25:36:49 80:42:09P35 Stage ENP Shark River Slough 2/15/1963 17899 1.60 25:27:34 80:51:53PA8 Stage SFWMD Big Cypress Preserve 12/18/1990 4294 2.31 25:53:25 81:16:13PA11 Stage SFWMD Big Cypress Preserve 12/28/1990 4260 4.71 25:47:22 81:05:59UWNDKW EeW Wind NWS Key West 1/1/1965 13819 1.29b 24:33:12 81:47:18VWNDKW NeS Wind NWS Key West 1/1/1965 13819 4.06b 24:33:12 81:47:18UWNDMIA EeW Wind NWS Miami 1/1/1965 13819 �0.37b 25:45:20 80:22:33VWNDMIA NeS Wind NWS Miami 1/1/1965 13819 3.11b 25:45:20 80:22:33KWWATLEV Sea Elevation NOS Key West 1/1/1965 13819 0.04b 24:33:12 31:47:18S18C Flow SFWMD C-111 Basin 1/1/1970 12357 181.70 25:19:50 80:31:30S197 Flow SFWMD C-111 Basin 1/1/1969 11992 34.01 25:17:13 80:26:29

a Start through October 31, 2002.b January 1, 1994eOctober 31, 2002.

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387 381

Key West and Miami NWS station information is presented inTable 2. South Florida is characterized by a regional wind pattern ofprevailing winds from the southeast in the summer, and from thenortheast and east in the fall, winter, and spring (Wang et al., 1994;Lee and Smith, 2002), and wind forcing is similar across Florida Bay(Smith, 1997a,b). The observed Key West and Miami wind data alsoshow this seasonal pattern and are considered to be the bestavailable, long-term wind data. Hourly wind speed and directiondata were processed into vector quantities and daily averages werecomputed. The independent variables UWNDMIA and VWNDMIAwere constructed as the U and V vectors of wind measured at theMiami wind station; UWNDKW and VWNDKW are the U and Vvectors of wind measured at Key West. These components werecomputed as follows:

U ¼ ðResultant wind speedÞ*CosineðResultant directionÞ

V ¼ ðResultant wind speedÞ*SineðResultant directionÞFor the calculation of wind vectors the units of wind speed are ft s�1

and the units of direction are bearing degrees.

3. Methods

To begin the analysis, the raw data were plotted to observe anycommonpatterns and anomalies in the daily values overmulti-yearperiods. Fig. 2 presents an example of the plots used in the initialanalysis. The seasonal patterns in the data and the inverse rela-tionship between stage in the upstream freshwater marshes and

Fig. 2. A comparison of the variability in observed data for P33 stage a

salinity in the downstream estuarine embayments are clear. Theeffect of very dry conditions and low P33 stage values can be seen in2001, when the salinity at TB exceeded 50 salinity units at themaximum. This can be compared to the normal dry season condi-tions in 1996, 1997, 1999, and 2000 when the maximum annualsalinity value was at least 10 salinity units lower. When a relation-ship between variability of a candidate independent variable andsalinity was observed the candidate was included in the correlationanalysis.

Correlation analysis was used to determine the level of asso-ciation between the dependent variable and the independentvariables as a “first-cut” for the identification of candidate inde-pendent variables for regression modeling. Lagged variables wereincluded and missing values were filled using time series (ARIMA)models. Cross-correlation plots produced by the SAS� PROCARIMA routine for time series analysis assisted the correlationanalysis for unlagged and lagged values, normally accomplished byanalyzing numerous correlation matrices. Lags up to 50 days wereevaluated.

Independent variables that displayed r values greater than thecritical r value at the 0.05 significance level (two-tailed p) in thecorrelation analyses were included as candidate variables forregression modeling (Kachigan, 1991). The number of candidateindependent variables submitted to the stepwise regression processat theonsetofmodeldevelopmentwasusuallyon theorderof 20e30when lagged variables were included. The SAS� PROC REG routineemployeda stepwise regressionprocedure to identify thestatisticallysignificant parameters for a multiple linear regression equation andcomputed parameter estimates at each ENP MMN station.

nd Terrapin Bay (TB) salinity for the example period 1994e2002.

Table 3Multiple linear regression models for nearshore embayments, mangrove zone, central, and western regions of Florida Bay; and south Biscayne Bay.

Region Model

Nearshore embayments andmangrove zone of Florida Bay

JB¼ 37.05� 3.06CP� 3.47EVER6(lag6)� 10.50E146(lag6)� 019uwndkw� 0.09uwndkw(lag2)� 0.10vwndkw� 0.16 vwndmia(lag1)TC¼ 70.97� 5.40P33(p33lag1)� 15.26E146(lag3)� 0.22vwndmia� 0.32uwndmiaþ 2.10kwwatlevLM¼ 66.37� 3.56CP(lag2)� 6.25P33(lag2)� 0.82(P33�NP206)� 0.21 uwndkwþ 0.15uwndmia� 0.14vwndmia(lag1)þ 0.76kwwatlev(lag2)TB¼ 106.87� 6.31CP(lag1)� 11.12P33(lag2)� 0.45uwndkw� 0.23uwndkw(lag1)� 0.20uwndkw(lag2)� 0.14vwndkw(lag2)þ 0.46uwndmiaþ 1.87kwwatlev(lag2)LS¼ 42.24� 9.49CP(lag4)� 5.15EVER7(lag2)� 1.73EVER6(lag2)� 0.04vwndmia(lag1)TR¼ 83.17� 15.09CP(lag4)� 7.83(P33� P35)(lag1)� 4.34(P33� P35)(lag4)HC¼ 49.89� 5.34CP� 16.28EVER6(lag4)� 6.29(EVER7� EVER4)(lag2)þ 0.20uwndmia(lag3)þ 0.73kwwatlevLB¼ 42.54� 7.65CP(lag6)� 6.29EVER7(lag5)þ 0.12vwndkwGB¼ 56.09� 9.23CP(lag1)� 4.63NP62(lag1)� 0.46uwndkw(lag1)� 0.48uwndkw(lag4)þ 0.35uwndmia(lag1)þ 0.64uwndmia(lag4)BS¼ 21.97� 1.11(P33� P35)þ 0.22LSþ 0.34LS(lag3)

Central and western Florida Bay WB¼ 21.15þ 0.24LM(lag3)þ 0.18TBþ 0.15TB(lag3)� 0.04vwndkw(lag2)� 0.54kwwatlev(lag2)DK¼ 10.21þ 0.33LM(lag1)þ 0.41LM(lag3)þ 0.10uwndkw(lag1)þ 0.13vwndkw(lag2)þ 0.53kwwatlevBN¼ 15.40þ 0.14LM(lag1)þ 0.44LM(lag3)þ 0.03TB(lag3)� 0.08uwndkw� 0.10uwndkw(lag2)þ 0.37kwwatlevBA¼ 19.37þ 0.31LMþ 0.25LM(lag3)þ 0.08TB(lag3)� 0.04uwndkw� 0.07uwndkw(lag2)� 0.06vwndkw(lag2)BK¼ 24.83þ 0.24TBþ 0.15TB(lag4)� 1.14CP(lag4)MK¼ 50.44þ 0.14TB(lag4)� 3.16P33JK¼ 53.14� 3.54P33þ 0.10LM(lag4)þ 0.08TB(lag4)þ 0.05vwndmiaþ 0.55kwwatlevLR¼ 51.32þ 0.20LM(lag4)� 3.19P33(lag1)þ 0.60kwwatlevPK¼ 39.77þ 0.25LM(lag1)� 1.58P33(lag4)� 0.05uwndkw(lag1)� 0.06vwndkwþ 0.09vwndmia

South Biscayne Bay MD¼ 23.34þ 0.16LB(lag3)þ 0.27LS� 1.21CP� 2.19EVER1� 0.11uwndkw(lag2)þ 0.10uwndmia(lag2)MB¼ 23.23þ 0.39LB� 2.87EVER1(lag2)� 1.65CP(lag1)� 0.22uwndkw� 0.17uwndkw(lag2)� 0.09vwndkw(lag1)þ 0.10uwndmiaþ 0.18uwndmia(lag2)MB¼ 13.24þ 0.40LBþ 0.16LB(lag3)� 0.13uwndkw� 0.15vwndkw� 0.06vwndkw(lag1)þ 0.13vwndmia� 0.002s197(lag1)� 0.002s197(lag2)� 0.001s18C

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387382

A pattern of independent variables selection was noted in thedifferent estuarine areas of ENP so a consistent form of regressionmodel was implemented for the different regions. In northeastFlorida Bay, Gulf coast, and Big Cypress estuaries the common formused was:

salinity ¼ ðstage variablesÞ þ ðsea surface elevationÞþ ðwind variablesÞ

In central and western Florida Bay and in south Biscayne Bay theregression models were improved substantially with the inclusionof salinity in the nearshore embayments or in adjacent estuarineareas, so the models at locations in those areas have the commonform:

Table 4Multiple linear regression models for the Gulf coast estuaries, Whitewater Bay, and the

Region Model

Gulf Coast estuaries andWhitewater Bay

CW¼ 83.0� 1.95P35(lag4)� 3.50NP62(lagþ 0.19uwndmia(lag1)þ 0.7kwwatlev(lag4)WE¼ 80.1� 2.42(P33� P35)(lag2)� 8.73PNR¼ 58.7� 1.70G3273(lag4)� 2.60NP206(GI¼ 70.9� 2.67G3273(lag1)� 4.65P35(lag3� 0.20uwndmiaþ 0.11uwndmia(lag3)þ 2.5SR¼ 67.4� 2.90P35� 1.80P35(lag3)� 5.0PLN¼ 56.43� 1.47P35(lag2)� 2.82P33� 4.7CN¼ 7.86� 1.21NP206(lag4)þ 0.24vwndmTE¼ 22.18� 1.03P33(lag4)� 2.24NP206(laHR¼ 51.1� 2.84P35(lag4)� 6.12NP206(lagBR¼ 20.83� 3.12NP206(lag4)� 0.06vwndkBD¼ 73.21� 4.82P35(lag3)� 4.04P33� 4.1þ (0.11vwndmia(lag3)þ 4.42kwwatlev(lag

Big Cypress estuaries WW¼ 19.10� 2.23PA8(lag2)� 2.23460PA1LO¼ 43.19� 6.09PA8(lag2)� 3.11PA11(lagCA¼ 38.13� 5.58PA8(lag2)� 1.89PA11(lagWP¼ 41.54� 9.6PA8(lag1)� 0.10uwndkw

salinity ¼ðsalinity variablesÞ þ ðstage variablesÞ

þ ðsea surface elevationÞ þ ðwind variablesÞ

The following guidelines were used to select the candidateindependent variables for modeling and for controlling the modeldevelopment process:

1. For the proof-of-concept models (JB, LM, TB, WB, NR) theindependent freshwater stage variables selected by the SASprocedure (PROC REG) were accepted for the final model alongwith Key West sea surface elevation and wind vectors;

2. After that, in the nearshore embayments andmangrove zone ofnortheast Florida Bay, the Gulf coast estuaries, and the Big

coastal waters of Big Cypress National Preserve.

2)� 7.75P33� 0.08uwndkw� 0.23uwndkw(lag1)� 0.29vwndkw(lag1)

33(lag5)� 0.06uwndkw(lag2)� 0.52kwwatlev(lag1)lag3)� 2.80NP62(lag2)� 2.80P33(lag1)þ 0.47kwwatlev(lag2))� 4.87NP62� 4.04(P33� P37)� 0.20vwndkw� 0.11vwndkw(lag1)9kwwatlev(lag3)33� 0.13vwndkw0.07vwndkw(lag2)� 0.14uwndmia(lag1)þ 0.96kwwatlev(lag2)1NP206(lag4)� 0.076uwndkw(lag1)� 0.14vwndkw(lag1)� 0.05vwndmia(lag3)iag4)2)� 0.23vwndkw� 0.12vwndkw(lag1)� 0.17uwndmiaþ 2.46kwwatlev(lag1)w(lag1)5NP206(lag2)� 0.31vwndkw� 0.23uwndmiaþ 0.28uwndmia(lag2)2)

1(lag2)2)� 0.14vwndkwþ 3.25kwwatlev(lag1)2)� 0.24vwndmia (Provisional model, limited data)

Fig. 3. Comparison of salinity simulated by the Long Sound (LS) MLR model (sim) with observed data (obs) for the combined calibration and verification period (verification periodis beginning of record through September 30, 1995), adjusted R2¼ 0.80. This model is representative of the nearshore embayments and mangrove zone of Florida Bay.

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387 383

Cypress estuaries candidate independent stage variables werelimited to stations as directly upstream as possible;

3. For the stations in the central and western parts of Florida Bayand south Biscayne Bay, salinity at LM and TB or other adjacentstation was included as a candidate independent variable;

4. The significance level for retaining an independent variable ina regressionmodel was set at a¼ 0.001 to limit the overall TypeI error;

5. Any independent variable that created a model with MallowsC(p) less than the number of variables in the model plus 1 waseliminated from the model; and

6. Independent variables were eliminated when the modelrepresentation was contrary to known physical relationships(such as an increasing stage in the Everglades indicating anincrease in salinity), which can occur when there are cross-correlation effects and strong collinearity between some ofthe independent variables.

Several stage gradient variables (stage upstream minus stagedownstream) were included as candidate independent variables.However, gradient variables were not consistently selected by thestepwise procedure and are only found in a limited number ofmodels.

The guidelines above were utilized to produce the model withthe highest adjusted R2 value when compared to the observed data(calibration period). The final model goodness-of-fit and perfor-mance was then verified using a portion of the observed salinitydata that were not used for model development. Plots of the outputfrom the final model were compared to observed data for the fullmodel dataset (calibrationþ verification) and were analyzed forunexpected deviations. Residual plots were examined and errorstatistics were interpreted. If necessary the model developmentstep was re-visited.

4. Results

At the onset of the analysis the elements of hydrology consid-ered for the model development of salinity models included stagein the freshwater marshes of the Everglades, wind, sea surfaceelevation, flow into Shark River Slough and Taylor Slough, rainfall,and evaporation. After reviewing data plots, correlation analysiswas conducted separately for all 36 MMN stations. Patterns wereseen in the correlation analyses. Pearson’s product moment

Fig. 4. Comparison of salinity simulated by the Whipray Basin (WB) MLR model (sim) withperiod is beginning of record through March 24, 1995), adjusted R2¼ 0.80. This model is re

correlation coefficient values (r) were, in general, higher forfreshwater stage and salinity compared to sea surface elevation,wind parameters, freshwater flows, rainfall and evaporation.Correlation values (jrj> 0.7) were consistently high betweensalinity data and stage data for CP and P33. Consistently lowcorrelation values were seen for flows, rainfall and evaporation. Innortheastern Florida Bay, data from stage stations at locationsdirectly upstream of a salinity station were usually correlated withsalinity, along with CP and P33. In the central Florida Bay area,salinity data were correlated at higher levels with salinity at the LMand TB nearshore stations than freshwater stage, though there wasalso correlation between stage and salinity at the central FloridaBay stations. At thewestern Florida Bay salinity stations, correlationcoefficients were similar for P33 freshwater stage and for salinity atLittle LM and TB. For the Whitewater Bay and Gulf coast salinitystations correlations with freshwater stage at various upstreamstations in Shark River Slough (which include P33) were at rela-tively high levels. Across Florida Bay, salinity was not alwayscorrelated to sea surface elevation at Key West, though salinity atmost stations was frequently correlated with wind parameters.

Flow, rainfall, and evaporation were not highly significant insalinity models when stage in the freshwater marshes of theEverglades, wind, sea surface elevation were already selected asmodel parameters by the stepwise regression process (Marshallet al., 2004). The only exception to this was in Manatee Bay. Flowfrom the S197 canal was a significant independent variable becauseManatee Bay is a small embayment and the S197 flow can be large.Marshall and Smith (2008) showed that the inclusion of evapora-tion did not improve MLR salinity models when stage, sea surfaceelevation and wind were already a part of the model. When thelevel of significance for retaining an independent variable ina model was raised to a¼ 0.001, the stepwise regression processselected only stage in the upstream marshes, wind, and sea surfaceelevation at KeyWest as the most significant independent variablesand retained them in the models.

The models that were developed according to the methodologypresented above are presented in Tables 3 and 4. The models aregrouped by similarity of form into models for the nearshoreembayments and mangrove zone of Florida Bay, central andwestern Florida Bay, and south Biscayne Bay (Table 3); and modelsfor Gulf coast estuaries/Whitewater Bay and Big Cypress estuaries(Table 4). The independent variables appearing in these modelsreflect the correlation with the dependent variable and the level of

observed data (obs) for the combined calibration and verification period (verificationpresentative of central Florida Bay.

Fig. 5. Comparison of salinity simulated by the Murray Key (MK) MLR model (sim) with observed data (obs) for the combined calibration and verification period (verification periodis January 1, 2001 through the end of the record), adjusted R2¼ 0.80. This model is representative of western Florida Bay.

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387384

variance explained relative to the other independent variables alsoin the models. The selected independent variables also reflect theguidelines used to select the variables that were ultimatelyincluded in the final models. The values of the coefficients may alsoreflect collinearity effects between independent variables.

Calibrationeverification plots are presented in Figs. 3e7 for fiverepresentative models (one for each region). These plots illustratetypical model fidelity over several ranges of salinity and differingsalinity variability patterns that displays the flexibility of theregression modeling method. The error statistics computed for thefinal MLR salinity models are presented in Tables 5 and 6. The R2

values for the models range from a low of 0.4 to a high of 0.85, andNasheSutcliffe Efficiency absolute values range from 0.42 to 0.96. Ingeneral the error statistics indicate that the daily resolution MLRsalinity models are capable of explaining about 65e80% of thevariation in daily salinity. However, individual residuals cansometimes be large (maximum absolute error) particularly in thenearshore embayments of Florida Bay. When daily predictions areaveraged to weekly or monthly values, large residuals areuncommon. The model output for the nearshore embaymentmodels (JB, LM, TB, and GB) has larger errors compared to othermodels based on the error and goodness-of-fit statistics, implyinggreater uncertainty in simulations. In general the error statistics forthe Gulf coast estuaries indicate the least error in prediction.

Residual plot characteristics were used to evaluate how wella model conforms to the assumptions of constant variance andnormally distributed errors with amean of zero. Most residual plotsindicate that there were no consistent deviations that indicatea problem with the normal distribution assumptions. Predictedvalue/residual value plots for models with observed and predictedsalinity values that were in the range of 0e10 salinity units showthe effects of a small range of observed salinity values. The normalprobability residual plots for these models are also affected to someextent by this issue which increases the uncertainty in predictionsat these stations.

5. Discussion

The estuarine areas of ENP represent a wide range of salinityconditions because of geomorphology and variations in freshwatersupply, both natural and anthropogenic. The extent of that

Fig. 6. Comparison of salinity simulated by the Clearwater Pass (CW) MLR model (sim) withperiod is beginning of record through March 22, 1997), adjusted R2¼ 0.85. This model is re

variability can be seen when observed salinity data are character-ized using the Venice classification scheme (Por, 1972). In thenearshore embayments and mangrove zone areas of Florida Baysalinity can vary widely on a daily to weekly scale with salinityranging from oligohaline to polyhaline conditions, i.e. euryhaline.By comparison, in the open water areas of central Florida Bay,salinity does not drop below the polyhaline range except during anextreme event. Restricted circulation, evaporation, and reducedfreshwater input may allow euhaline or hypersaline conditions todevelop in the central part of the Bay during some dry seasons,particularly back-to-back dry years. In western Florida Bay wherethe dominant factor is the proximity to marine conditions, theregime is euhaline. Even so, the influence of freshwater can dropsalinity into the polyhaline regime for part of a wet season at thewestern Florida Bay stations that are closest to the mainland.

In Whitewater Bay, Gulf coast estuaries, and Big Cypress estu-aries, the salinity regimes range from oligohaline to polyhaline, andhypersaline conditions are rare. The south Biscayne Bay areas aremostly isolated from themarine connections by physical barriers tocirculation and mixing but remain polyhaline. Manatee Bay issubject to intermittent large discharges for water management thatcan reduce the salinity rapidly into the mesohaline range. Hyper-saline conditions are rare, which may be attributed to importantdry season freshwater contributions from overland flow andgroundwater.

The correlation analysis and subsequent regression modeling ofdaily salinity in the estuaries of ENP using hydrologic, marine, andwind factors indicated that the strongest correlative relationshipsexisted between salinity and Everglades freshwater stage, followedby sea level and wind parameters. While freshwater flows in theEverglades, rainfall, and evaporation were also correlated withsalinity, the level of associationwas considerably weaker. It appearsstage data may integrate the temporal and spatial variability of theother hydrologic factors such as rainfall and flow as well as thedynamic storage in the surface water and groundwater compo-nents of the Everglades water budget.

When the partial correlation coefficients for the final modelswere reviewed it was noted that stage was always a primary sourceof variability in the nearshore embayments, mangrove zone, Gulfcoast estuaries, and Big Cypress estuaries. Models for upstreamstations in the Gulf coast and Big Cypress estuaries did not include

observed data (obs) for the combined calibration and verification period (verificationpresentative of the Gulf coast estuaries and Whitewater Bay.

Fig. 7. Comparison of salinity simulated by the Manatee Bay (MB) MLR model (sim) with observed salinity, flow, wind data (obs) for the combined calibration and verification period(verification period is beginning of record through March 24, 1995), adjusted R2¼ 0.77. This model is representative of south Biscayne Bay.

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387 385

wind parameters, and few included sea surface elevation. At thecentral and western Florida Bay stations salinity in the nearshoreembayments (LM and/or TB) provided the most information aboutsalinity variability.

Even though there are collinearity issues within the stage data,the three categories of independent variables used for modeldevelopment (stage, sea surface elevation, wind) are substantiallyindependent of each other. The negative effects of cross-correlationbetween stage variables were minimized to some extent in modeldevelopment by using a high significance level (0.001) for retentionof an independent variable in the final model.

An unexpected outcome of model development at many of thestations was the consistent appearance of CP and P33 freshwaterstages in many of the salinity models. Often CP stage (unlagged orlagged) explained the largest portion of salinity variability or was atleast a primary contributor to explaining salinity variability asexpressed by the partial correlation coefficients. It appears that theCP stage data collected near the mangrove transition zone provideimportant information about the variability of the entire Ever-glades/estuarine hydrology/salinity system, and CP data can readilysimulate stage variability at many freshwater marsh stations in ENPthrough regression modeling.

In verification scenarios, the MLR salinity models were capableof simulating the daily variability in salinity within about 2e4salinity units on average. There is the potential for greater error ofa daily model prediction in the nearshore embayments and themangrove zone of Florida Bay, particularly when the change fromthe dry to the wet season is abrupt (and vice versa). A compilationof the error statistics for other salinity models being used in South

Table 5Comparison of model error statistics for MLR salinity models for nearshore embayments,

Region Station RMSE Meanerror

Nearshore embayments and mangrovezone of Florida Bay

JB 5.1 �0.14TC 5.4 �0.23LM 6.4 �0.66TB 5.7 �0.99LS 3.9 0.31TR 4.6 �0.49HC 4.3 �0.95BS 3.2 0.01GB 6.1 �0.36LB 3.7 �0.14

Central and western Florida Bay WB 2.7 0.11DK 3.1 �0.18BN 3.3 0.10BA 2.7 0.30BK 2.7 0MK 2.9 0.02JK 2.7 0.05LR 2.4 0.09PK 2.0 �0.01

South Biscayne Bay MD 2.6 �0.22MB (stage) 3.1 0.01MB (flow) 2.6 0.25

Florida, including hydrodynamic models, shows that the MLRsalinity models have approximately the same expected range ofsimulation accuracy and error as higher resolution numeric salinitymodels. The R2 and NasheSutcliffe Efficiency values for the MLRsalinity models are comparable and sometimes greater than thesesame goodness-of-fit statistics for higher resolution numericmodels (Marshall and Nuttle, 2011).

Because of their simplicity and cost-effective use, the MLRsalinity models presented herein have been implemented bya number of agencies associated with Everglades restoration. Theavailable MLR salinity models were used by ENP for the InterimOperations Plan (IOP) evaluations for a Congressional report (SouthFlorida Natural Resources Center, 2005). Daily time series simula-tions by these MLR salinity models (1965e2000) are used by theRECOVER Southern Coastal Systems Sub-team for evaluations ofCERP alternative scenarios for Everglades restoration and perfor-mance measures development (Marshall, 2005). The relativesimplicity of themodels has allowed them to be coded into routinesused by the RECOVER Interagency Modeling Center for use withfuture CERP alternative evaluations. They have been adapted for usewith USGS paleoecological characterizations to estimate the salinityregime in Florida Bay thatmay have existed prior to the alteration ofEverglades freshwaterflowsaround1900 (Marshall et al., 2009). Themodels have been used for historical salinity reconstructions, forestablishment of Minimum Flows and Levels for Florida Bay (Cosbyet al., 2005; Marshall, 2011), and for input data to shrimp and sea-grass ecological models. The salinity model output is most usefulwhen the daily values are interpreted using distributional statisticsor monthly, seasonal, and annual average values.

mangrove zone, central, and western regions of Florida Bay; and south Biscayne Bay.

Meanabsolute error

Max absoluteerror

NasheSutcliffeefficiency

Adjusted R2

3.7 20.6 0.76 0.754.3 20.9 0.72 0.695.1 22.6 �0.96 0.655.4 5.4 0.67 0.752.7 18.9 0.81 0.803.6 22.9 0.78 0.783.7 17.7 0.76 0.812.4 11.9 0.66 0.634.7 21.1 0.89 0.682.9 15.7 0.76 0.75

2.2 10.1 0.77 0.802.3 14.4 0.71 0.712.7 11.3 0.66 0.652.1 9.2 0.81 0.792.1 7.8 0.79 0.792.3 12.0 0.51 0.622.2 9.7 0.55 0.551.9 8.6 0.45 0.591.6 5.8 0.57 0.55

2.2 11.3 0.71 0.742.0 12.9 0.76 0.692.1 10.7 0.7 0.77

Table 6Comparison of model error statistics for MLR salinity models for Gulf coast estuaries, Whitewater Bay, and the coastal waters of Big Cypress National Preserve.

Region Station RMSE Meanerror

Mean absoluteerror

Max absoluteerror

NasheSutcliffeefficiency

Adjusted R2

Shark River estuariesand Whitewater Bay

CW 3.4 �0.12 2.7 10.8 0.85 0.85WE 3.1 0.46 2.9 10.6 0.88 0.74NR 3.8 0.56 3.2 17.9 0.92 0.77GI 3.4 1.03 3.0 13.3 0.89 0.85SR 2.5 �0.11 2.0 9.1 0.89 0.82LN 2.9 �0.14 2.1 12.5 0.79 0.79CN 1.1 �0.02 0.5 9.0 0.42 0.4TE 1.6 �0.05 1 9.0 0.58 0.62HR 3.8 �0.02 2.9 14.1 0.72 0.77BR 2.3 �0.04 1.3 13.9 0.54 0.6BD 3.9 �0.05 3.0 16.6 0.75 0.73

Big Cypress estuaries LO 4.6 �0.03 3.7 12.8 0.76 0.79CA 6.1 0.01 4.8 22.9 0.9 0.68WP 4.9 �0.01 3.7 20.6 0.86 0.95WW 2.6 �0.31 1.6 10.9 0.72 0.71

F.E. Marshall et al. / Estuarine, Coastal and Shelf Science 95 (2011) 377e387386

In the central and western regions of Florida Bay, better MLRsalinity models were developed using the salinity from the near-shore embayments of LM and TB. Though not obvious at the time,the utility and benefit of this construct became apparent when theMLR salinity models were coupled with salinity output producedby the dynamic mass balance model FATHOM (Cosby et al., 2005)and the hydrodynamic model FTLOADDS TIME (Langevin et al.,2004; Swain et al., 2004).

Because a correlative relationship in data does not prove causeand effect, this study took a different approach inwhich correlationanalysis was only one of the statistical tools employed. The devel-opment of a conceptual model of the coastal aquifer and salinitytransition zone from physical principles was the basis for identi-fying the general factors influencing salinity. Then correlationanalysis was used to provide information on candidate indepen-dent variables that may characterize those factors. Finally, stepwiseregression was used to measure and quantify the level of associa-tion between the independent variables and salinity. According toRiggs (1968) the information from a combination of correlationanalysis and regression models, when properly interpreted,provides strong evidence of the influence of the independentvariables in the regression model on the dependent variable e inthis case, salinity.

Aswith allmodels there are limitations onuse. Theobserveddatathat were used to develop the MLR salinity models are pointmeasurements, but they are usually considered to be characteristicof a somewhat wider spatial extent in the vicinity of monitoringequipment. Grid-based models are generally assumed to provideadditional spatial information on salinity compared to the MLRsalinitymodels. Though the spatial resolution of the point estimatesprovided by the MLR model output may be lower than provided bythe higher spatial resolution numerical models, the existing higherresolution models were developed from the same data or data ofsimilar spatial coverage as were used for the MLR salinity models.

6. Conclusions

This study has shown that MLR salinity models are useful fora wide variety of estuarine conditions, and they seem particularlywell-suited for bar-built or lagoonal estuaries. The conceptualmodel of the coastal aquifer developed for this study should beapplicable to any bar-built estuary with moderate to high trans-missivity in the substrate of the adjacent land form. Sufficient dailyor higher resolution data for observations of stage, flow, andsalinity are available in South Florida, though similar temporalresolution of these data in other coastal areas of the world may not

be as readily available. The regression model methodology alsoworks well with data at lower temporal resolution so long as thereare a sufficient number of observations. The limited availability oflocal or regional sea surface elevation and wind data may limit theindependent variables used for analysis and modeling to the use ofhydrologic data only in other coastal areas of the world.

The MLR salinity models have known levels of uncertainty, andfidelity of the simulations is as good as the currently availablenumerical models. One of the advantages of the regression modelapproach is that detailed bathymetry of the estuary is not neededforMLR salinitymodels as is needed for box and grid-basedmodels.Another benefit of MLR salinity models is that they can be devel-oped by any basic statistical modeling software package, meaningthe models herein can be reproduced by anyone with the data.Once developed the MLR salinity models can be run in predictionmode and output obtained in seconds.

This empirical study has shown that salinity in the estuarineareas of ENP can be represented by simple-to-understand MLRmodels developed from existing data that describe the local andregional hydrology, sea level, and wind conditions. The findings ofthis combination of conceptual modeling, correlation analysis, andregression modeling suggest that overall freshwater supply is theprimary factor in determining the salinity in the ENP estuaries,though the uncontrollable variability of the elevation of the marineend member and wind forcing are also influential. Simulations bythese models show that restoration of the altered hydrology in theEverglades can be combined with the natural variability of themarine and weather influences to provide favorable conditions forthe recovery of the flora and fauna of these important Evergladesecosystems.

Acknowledgments

We greatly appreciate the support of the Everglades NationalPark Critical Ecosystem Studies Initiative and the ComprehensiveEverglades Restoration Plan Restoration Coordination and Verifi-cation (RECOVER) program.

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