A preliminary modeling analysis of water quality in Lake Okeechobee, Florida: Calibration results

~

Pergamon

0043-1354(95)00116-6

Wat. Res. Vol. 29, No. 12, pp. 2755 2766, 1995 Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0043-1354/95 $9.50 + 0.00

A P R E L I M I N A R Y M O D E L I N G A N A L Y S I S OF W A T E R Q U A L I T Y IN LAKE OKEECHOBEE, FLORIDA: C A L I B R A T I O N RESULTS R. T H O M A S J A M E S ~* and V I C T O R J. B I E R M A N Jr 2 IOkeechobee Systems Research Division, South Florida Water Management District, P.O. Box 24680, West Palm Beach, FL 33416-2468 and 2Limno-Tech, Inc., 20780 S. Gatehouse Drive, South Bend, IN 46637, U.S.A. (First received November 1993; accepted in revised .form April 1995)

AbstractTo gain understanding of nutrient and phytoplankton dynamics in Lake Okeechobee, Florida, we developed and applied a deterministic, mass balance, water quality model at the whole-lake spatial scale. The model was calibrated to a comprehensive set of field data for 1985-1986, and then used to simulate the period 1973-1992. The model represented the mean behavior of in-lake total phosphorus, dissolved available phosphorus, total nitrogen and chlorophyll a concentrations reasonably well during the calibration period. The model did not represent dissolved available nitrogen concentrations very well, nor did it capture much of the observed temporal variability during the calibration period. The model results identified important information needs to improve our understanding of the nitrogen cycle including, sediment-water nitrogen fluxes, denitrification and nitrogen fixation. Results from the 1973-1992 simulation indicated that model assumptions and/or calibration parameters were not uniformly applicable over this period. Total phosphorus concentration results from this model were compared with results from two site-specific, empirical loading models for the lake. None of these models represented annual average concentrations uniformly well over the entire 20-year period, and none captured much of the observed inter-annual variability. External total phosphorus loadings and lake hydrology are not sufficient to fully describe total phosphorus dynamics in Lake Okeechobee. Other important factors are diffusive sediment water fluxes, wind-induced sediment resuspension, and the spatial heterogeneity in the lake. Key words--mass balance model, water quality model, empirical loading model, phytoplankton, chlorophyll, phosphorus, nitrogen, sediment flux, tributary loads, phosphorus loads

INTRODUCTION In the Seminole I n d i a n language, " O k e e c h o b e e " m e a n s "Big W a t e r . " This is a n a p p r o p r i a t e n a m e for the largest lake in Florida a n d the s o u t h e r n U n i t e d States (Fig. 1). Lake Okeechobee is 1730 k m 2 in area with an average d e p t h of 2.7 m. It is encircled by a dike 7.6 m in ' fight a b o v e m e a n lake level. T h e lake is a source of water for agricultural, residential, recreational, a n d industrial use. It is also the source of waters flowing s o u t h into the Everglades. The lake has an extensive littoral zone characterized by a diverse vegetative c o m m u n i t y , a n d is i m p o r t a n t habitat for wading birds, alligators, a n d o t h e r wildlife. Since the early 1970s, there has been a growing concern of potential cultural e u t r o p h i c a t i o n o f the lake. In 1973 the S o u t h Florida W a t e r M a n a g e m e n t District ( S F W M D ) established a m o n i t o r i n g network o n Lake Okeechobee to determine the extent a n d impacts of cultural eutrophication. F r o m 1972 to the present, various forms o f Best M a n a g e m e n t Practices (BMPs) have been i m p l e m e n t e d within the Lake Okeechobee basin to reduce p h o s p h o r u s n o n - p o i n t *Author to whom all correspondence should be addressed.

source pollution to lake tributaries. In 1986 the Lake Okeechobee Technical C o m m i t t e e r e c o m m e n d e d p h o s p h o r u s loads be reduced to a n a m o u n t calculated by a modified Vollenweider model p r o p o s e d by Federico et al. (1981). In the same year, a 300 k m z algal b l o o m occurred on the lake, p r o m p t i n g the S F W M D to increase m o n i t o r i n g a n d research programs. In addition, the S F W M D began to focus data collection a n d research efforts toward gaining a predictive u n d e r s t a n d i n g of algal blooms. We present results from a deterministic water quality model of Lake Okeechobee to synthesize d a t a from various studies, to analyze total p h o s p h o r u s loads to the lake, and to direct further study. The primary purpose of this modeling application is to increase o u r u n d e r s t a n d i n g of Lake Okeechobee, not to produce an empirical description of field observations. The model was calibrated to a n extensive set o f field data for 1985-1986 and further tested with a 20-year simulation for the period 1973-1992. The predicted in-lake total p h o s p h o r u s c o n c e n t r a t i o n s were c o m p a r e d to predictions from th~ modified Vollenweider model (Kratzer a n d Brezonik, 1984) a n d the model of J a n u s et al. (1990). The second

2755

2756

R. Thomas James and Victor J. Bierman Jr

paper in this series contains results from a series of diagnostic and sensitivity analyses conducted with this calibrated water quality model (Bierman and James, 1995). EMPIRICAL LOADINGMODELS There is a history of empirical loading model applications to Lake Okeechobee. Federico et al. (1981) and Kratzer and Brezonik (1984) attempted to improve on the original Vollenweider and DillonRigler models using earlier historical data for phosphorus and nitrogen from Lake Okeechobee and other Florida lakes. Janus et al. (1990) applied a recent Organization for Economic Cooperation and Development (OECD) model, models developed by Kratzer and Brezonik (1984), and Salas and Maitino (1988), and a multiple regression model to more current historical data for Lake Okeechobee. The predictive capabilities of these models when applied to the 20 year period of record of Lake Okeechobee were modest at best (r~< 0.30). Limno-Tech (1993) developed new empirical loading models for phosphorus and nitrogen based on

two data sets: a data set for warm water lakes (Baker et al., 1981), and a data set that included tropical and sub-tropical lakes and reservoirs in Texas and Central and South America (Salas and Martino, 1990). These two models accounted for 84% and 57% respectively in the variability of the annual average phosphorus and nitrogen concentrations in these data sets. However when applied solely to Lake Okeechobee for the period 1973 1992 the results were poor (r'~< 0.05, data not shown). A major obstacle to the successful application of empirical loading-plot models to Lake Okeechobee is that extreme spatial-temporal variability in the lake violates fundamental assumptions in these models. Schelske (1989) pointed out that hydro-meteorological conditions and their effect on water levels and sediment resuspension in Lake Okeechobee strongly influence in-lake nutrient concentrations. Canfield and Hoyer (1988) noted a significant positive correlation between total phosphorus concentration and mean depth in the lake and speculate that it is due to flooding of marshlands and former croplands. Maceina and Soballe (1990) emphasized the role of wind-driven sediment resuspension and contend that

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9

Fig. 1. Map of Lake Okeechobee showing major inflows and 8 permanent lake sampling stations.

Lake Okeechobee model calibration

2757

although wind and lake stage are positively related, wind speed is a better predictor of total phosphorus concentration than lake level. Maceina (1993) noted a positive relationship between lake water levels and summer (May-October) chlorophyll a concentrations. Janus et al. (1990) speculated that variations in total phosphorus concentrations in the lake as a function of mean depth and/or surface area could be due to additional internal loadings from the littoral zone. Apart from these site-specific complications, empirical loading models do not contain explicit mechanisms that represent actual environmental processes. Consequently, loading-plot models can only provide very limited understanding of cause-effect mechanisms that lie behind field observations.

coupled water-sediment models to Lake Varese (Italy) and Lake Kinneret (Israel), respectively, and investigated lag times in total phosphorus concentration responses that can occur due to sediment feedback. Van der Molen (1991) developed a simple model for phosphorus retention and net phosphorus release in Lake Veluwe (The Netherlands) that represented changes in sediment release as a function of external phosphorus loadings. Canale and Effler (1989) applied a deterministic phosphorus model to Onondaga Lake (New York) that does not explicitly include water-sediment coupling, but does include an analysis of impacts of natural variations of flow and load on total phosphorus concentrations in the lake using Monte Carlo techniques.

D E T E R M I N I S T I C MASS BALANCE M O D E L S

M O D E L I N G A P P R O A C H FOR LAKE O K E E C H O B E E

Deterministic mass balance models have been used extensively in the Great Lakes to better understand phytoplankton-nutrient dynamics and to compare predicted responses of these systems to various nutrient control strategies (e.g. Bierman and Dolan, 1981, 1986a; DiToro and Matystik, 1980; DiToro and Connolly, 1980; Thomann and Segna, 1980). Results from five different models, ranging in complexity from simple empirical models to sophisticated deterministic models, were used to develop the target phosphorus loadings to the Great Lakes as part of the 1978 Water Quality Agreement between the U.S. and Canada (Bierman, 1980). The deterministic models for Saginaw Bay (Lake Huron) (Bierman and Dolan, 1986b) and Lake Erie (DiToro et al., 1987) were successfully post-audited by comparing a priori predictions to comprehensive sets of field data acquired after implementation of substantial reductions in phosphorus loadings. Several recent deterministic modeling and associated experimental studies emphasized factors controlling phytoplankton-nutrient dynamics in shallow lakes. Janse et al. (1992) applied a coupled watersediment model to Lake Loosdrecht (The Netherlands) for both pre- and post-restoration periods. They concluded that high internal recycling is a major cause for the delayed response in total phosphorus concentration and no significant change in chlorophyll a concentration in the lake. Shanahan et al. (1991) investigated different kinetic formulations and linkages between hydrodynamics and water quality processes in Lake Balaton (Hungary). Their study is supported by extensive field experiments to quantify resuspension and deposition of bottom sediments due to episodic storm events (Luettich et al., 1990). Hellstrom (1991) studied the effect of wind-induced resuspension and associated light attenuation on algal production in Lake Tamnaren (Sweden). Other studies emphasized the impact of sediment storage and wind resuspension on phosphorus concentration and retention in lakes. Rossi and Primazzi (1991) and Herman et al. (1989) applied simple

The conceptual framework of the Lake Okeechobee water quality model includes the state variables phytoplankton carbon, phosphorus (dissolved available and unavailable forms), nitrogen (ammonium, nitrate plus nitrite, and unavailable forms), dissolved oxygen, and carbonaceous biological oxygen demand (Fig. 2). Only the phytoplankton and nutrient state variables are of interest in this application because the shallow water column of Lake Okeechobee typically remains aerobic. User-specified external forcing functions include water flows into and out of the lake, nutrient loads, boundary conditions, sediment fluxes, water temperature, incident solar radiation, and underwater light attenuation. Although this model contains only a moderate degree of chemical-biological complexity, it requires a considerable amount of field data for specification of external forcing functions, as well as for comparison with model output. This conceptual model was implemented for Lake Okeechobee using a modified version of the Water Assessment Simulation Package (WASP4) computer coding framework (Ambrose et al., 1988). Principal modifications to WASP4 for this application included additions of MichaelisMenten half-saturation equations for organic nutrient mineralization (DiToro and Matystik, 1979) and phytoplankton decomposition in the water column (Rodgers and Salisbury, 1981). This is the first application of a deterministic, mass balance, water quality model for ,Lake Okeechobee. We use the top-down approach, beginning with the simplest case, representing the lake as a single homogenous b o x ~ e s p i t e the known spatial heterogeneity of the lake (Phlips et al., 1993~because, (1) it is more efficient to start from the simple case and work to the more complex, building upon this foundation, (2) a preliminary understanding of phytoplankton and nutrient dynamics is easier to obtain without the complications of spatial segmentation, (3) it is easier to modify a single homogenous box model than a spatially segmented model, which allows for component, diagnostic, and sensitivity

2758

R. Thomas James and Victor J. Bierman Jr

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Fig. 2. Schematic representation of principal model state variables and processes.

analysis, (4) the historical d a t a set used to calib r a t e a n d validate this m o d e l t e n d s to r e p r e s e n t the c e n t r a l m u d - z o n e area o f the lake, w h i c h is r a t h e r h o m o g e n o u s , (5) i n f o r m a t i o n o n w a t e r circulation in the lake for this t w e n t y - y e a r p e r i o d o f r e c o r d d o e s n o t exist, a n d (6) we can c o m p a r e this w a t e r quality m o d e l to past empirical m o d e l s that also a s s u m e d the lake was an h o m o g e n o u s single-box. D e s p i t e the c o n c e r n s o f using a spatially simplified m o d e l , this effort r e p r e s e n t s a m a j o r a d v a n c e in t e r m s o f m o d e l i n g s o p h i s t i c a t i o n for L a k e O k e e c h o b e e b e c a u s e there is explicit r e p r e s e n t a t i o n o f p h y t o p l a n k t o n a n d n u t r i e n t kinetic processes, m a s s b a l a n c e o f water, n i t r o g e n , a n d p h o s p h o r u s , a n d t e m p o r a l variability. O t h e r simplifying a s s u m p t i o n s were m a d e . M a s s b a l a n c e s for m o d e l state variables are calculated only in the w a t e r c o l u m n . S e d i m e n t i n t e r a c t i o n s are repr e s e n t e d in the m o d e l by user-specification o f net settling velocities for the p h y t o p l a n k t o n a n d unavailable n u t r i e n t state variables, a n d by s e d i m e n t - w a t e r diffusive fluxes o f dissolved available nutrients. METHODS Calibration to 1985-1986field data

Water flows for 1985 and 1986 were obtained for 29 inflows and 7 outflows from Lake Okeechobee. This information is stored in the South Florida Water Management

District's Data Base, DBHYDRO. Additional data obtained from this data base were photo-active radiation, rainfall, stage height, water temperature, and evaporation. Information on nutrients at these inflows/outflows, and rainfall chemistry is also stored on data bases at the District. Tributary loads of total phosphorus, dissolved available phosphorus, total nitrogen, nitrate-nitrogen, and ammonium-nitrogen were estimated on a monthly basis with a load calculation program, developed at the SFWMD, that used the methods of Scheider et al. (1979). Rainfall on the lake was estimated as 0.8 of the geometric mean of rainfall measurements from stations surrounding the lake (Riebsame et al., 1974). Rainfall loads were estimated by multiplying the geometric mean of monthly rainfall chemistry by rainfall and the area of the lake within the dike. The years 1985 and 1986 were chosen because they represented average years for rainfall in this region. In 1985 there was 102 cm of rainfall and 1986 there was 112 cm of rainfall. These are close to the 20-year average of 104 cm of rainfall. The boundary condition of phosphorus flux from the sediments (0.665mgm ' d -~) was taken directly from measurements obtained by Reddy (1993). This flux measurement was an average of fluxes from the different sediment types, weighted by area of each sediment type, and adjusted to standard temperature (20°C). This flux was measured as dissolved phosphate-phosphorus and was specified to the model as the dissolved available form. Because of the large sediment area:water volume ratio in the lake, this flux from the sediment represents one-half of the total phosphorus load to the lake water column (Fig. 3). Tributary inflow and rainfall account for approx. 44 and 6% respectively of the total phosphorus loading for these 2 years. The water quality model represents sediment phosphorus loading as

Lake Okeechobee model calibration Sediment 438 50%

Rainfall 53 6%

Tributary 389 44 % Fig. 3. A v e r a g e a n n u a l (1985 1986) loadings rates (metric tons y r - ~) a n d percent c o n t r i b u t i o n o f p h o s p h o r u s to L a k e O k e e c h o b e e f r o m sediments, tributaries a n d rainfall.

diffusive flux o f dissolved a v a i l a b l e p h o s p h o r u s a n d does n o t include r e s u s p e n s i o n o f p a r t i c u l a t e p h o s p h o r u s . W e inferred a m m o n i u m n i t r o g e n flux from the sediments (8.6 m g N m -2 d -~) by scaling m e a s u r e d s e d i m e n t phos-

2759

p h o r u s flux in p r o p o r t i o n to the observed total p h o s p h o r u s : total n i t r o g e n ratio in the sediments. This a m m o n i u m nitrogen flux value is consistent with earlier results from a F i c k i a n diffusion m o d e l (Brezonik e t a l . , 1979). L a k e v o l u m e s derived from the m o d e l s i m u l a t i o n were c o m p a r e d w i t h a c t u a l s t a g e / s t o r a g e relationships o f the lake. M i n o r a d j u s t m e n t s in e v a p o r a t i o n (~<0.02 c m d - l ) were m a d e to m o r e a c c u r a t e l y fit v o l u m e estimate from this m o d e l with the v o l u m e estimate from the s t a g e / s t o r a g e relationship. Seepage is m i n o r c o m p a r e d to all other inflows and outflows as d o c u m e n t e d by tight yearly w a t e r b u d g e t s for L a k e O k e e c h o b e e (James e t a l . , 1995) a n d was ignored. After specification of the a b o v e external forcing functions, values for m o d e l coefficients and process rates were d e t e r m i n e d t h r o u g h c a l i b r a t i o n to a v a i l a b l e field d a t a from 1985 to 1986 (Table 1). The c a l i b r a t i o n a p p r o a c h used here was to fix the values o f as m a n y m o d e l coefficients as possible, based on direct m e a s u r e m e n t s . Subsequently, values for the r e m a i n i n g coefficients were adjusted within r a n g e s from the reported literature to p r o d u c e the best fit between m o d e l o u t p u t a n d field observations. M o d e l coefficients were n o t allowed to a s s u m e a r b i t r a r y values in o r d e r to o b t a i n the best possible curve fit in a strictly m a t h e m a t i c a l sense. The principal literature sources a n d d a t a c o m p e n d i a used to guide the c a l i b r a t i o n effort were A m b r o s e e t al. (1988), Bowie e t a l . (1985), J o r g e n s e n e t al. (1991), a n d Tt~6mann a n d Mueller (1987). Twenty-year

simulation

To d e t e r m i n e if the m o d e l a s s u m p t i o n s a n d c a l i b r a t i o n p a r a m e t e r s a p p l y b e y o n d the c a l i b r a t i o n period, a 20-year

Table 1. Parameters for the water quality model of Lake Okeechobee. All values were taken from the literature source and may have been modified through the calibration procedure Parameter

Unit

Value

K1C KIT GPtoBIO

d ~ unitless unitless

IS1 KMNGI KMPGI CCHL NCRB PCRB KIRC K I RT KID KMCDI KtG

lyd ~ mg N I ~ mg P 1 ~ mg C mg ~ Chlorophyll mg N mg ~C mg P mg ~C d ~ unitless d ~ mg C I ~ d ~

K1GT

unitless

1.07

FON FOP K1320C K 1320T KNIT KI40C K 140T KNO3 KI013C

unitless unitless d ~ unitless mg O 21 ~ d ~ unitless mg O., 1 ~ d ~

0.5 0.5 0.4 1.07 2 0.1 1.045 0.1 0.075

K 1013T K58C

unitless d ~

1.07 0.15

K58T

unitless

1.07

KMPHYT NSET KESG FNH4 FPO4

mg C cm d m ~ mg m mgm

0.5 0.05 2.5 8.645 0.665

1 ~ ~ 2d ~ 2d ~

2.0 1.07 0.8

Description Maximum algal growth rate at 20"C Algal growth rate temperature factor Gross production efficiency

100 0.015 0.003 50.0

Saturation light intensity Nitrogen half-saturation Phosphorus half-saturation Carbon:chlorophyll a mass ratio

0.125 0.018 0.15 1.07 0.5 100.0 1.0

Nitrogen :carbon mass ratio Phosphorus:carbon mass ratio Maximum algal respiration rate at 20°C Respiration temperature factor Maximum algal death rate Algal death half-saturation Maximum zooplankton grazing rate at 20"C Grazing rate temperature factor Recycle fraction to organic N Recycle fraction to organic P Maximum nitrification rate at 20"C Nitrification temperature factor Nitrification half saturation Maximum denitrification rate at 20°C Denitrification temperature factor Denitrification half-saturation factor Maximum organic N mineralization at 20°C N mineralization temperature factor Maximum organic P mineralization at 20"C P mineralization temperature coeffcient Mineralization half-saturation Net settling rate Extinction coeffcient Ammonium flux from sediment Dissolved ortho-phosphorus flux from sediments

Source Jones and Federico (1984) Ambrose et al. (1988) Vadstein et al. (1989) and Zlottnik and Dubinsky (1989) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Ambrose el al. (1988) Ambrose et al. (1988) Bowie et aL (1985) Ambrose et aL (1988) Bowie et al. (1985) Rodgers and Salisbury (1981) Thomann and Mueller (1987) Assume a doubling from 20 to 30'C Ambrose et al. (1988) Ambrose et al. (1988) Bowie et al. (1985) Bowie et al. (1985) Ambrose et aL (1988) Bowie et aL (1985) Bowie et al. (1985) Ambrose et aL (1988) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Ambrose et al. (1988) Bowie et al. (1985) Calibration Reddy (1993) Reddy (1993)

2760

R. Thomas James and Victor J. Bierman Jr

Table 2. Student's t-test and regression analysis c o m p a r i n g actual and model data. The r 2 values determine the a m o u n t of variance explained by the data, the t-tests determine if the means are significantly different assuming unequal variances

Comparison

N

Calibration 1985 1986 Chlorophyll a Total phosphorus Dissolved available phosphorus Total nitrogen Nitrate + nitrite Ammonium

21 23 23 24 24 24

22.3 0.072 0.018 1.550 0.088 0.016

22.7 0.073 0.020 1.498 0.835 0.044

0.123 0.033 0.000 0.002 0.004 0.010

0.119 0.408 0.925 0.857 0.785 0.658

-0.236 -0.308 - 1.028 1.009 -21.724 9.180

0.815 0.760 0.314 0.323 <0.001 <0.001

168 233 232

23.6 0.080 1.735

21.9 0.069 1.514

0.024 0.007 0.004

0.044 0.203 0.299

2.190 5.126 6.168

0.029 0.001 < 0.001

20 20 20

0.079 0.079 0.079

0.088 0.063 0.068

0.274 0.012 0.010

0.018 0.647 0.672

1.773 3.052 2.251

0.085 0.004 0.034

Twenty-),ear simulation Chlorophyll a Total phosphorus Total nitrogen Annual total pho,ff~horus mean Janus et al. (1990) Kratzer and Brezonik (1984) WASP

simulation was conducted for the period 1973 1992. External forcing functions for this simulation were specified using actual average monthly values for inflow, outflow, photoactive radiation, rainfall, stage height, water temperature, and external nutrient Ioadings. Boundary conditions for sediment nutrient fluxes, net settling rates, and all model coefficients and process rates were constant values defined in the 1985 1986 calibration. Empirical loading models

The water quality model was compared to two empirical loading models that have been previously used on Lake Okeechobee, the model of Janus et al. (1990) and the modified Vollenweider model of Kratzer and Brezonik (1984). These empirical loading models provide estimates of annual total phosphorus concentration in the lake. The equation for Janus et al. (1990) is p)

0 4~7 =2.28"Pj(~ t)'Z "z~4

and for Kratzer and Brezonik (1984) is

Model data mean

Value

P

Student's t Value (unequal variances)

Field data mean

r~

P

regression analysis (SAS Institute, 1990) of monthly averaged model output (independent variable) to monthly averaged field data (dependant variable). Similarly, the 20-year simulation of model output was compared graphically with monthly averaged field data, with a Student's t-test between the 20-year means of model output and field data, and with regressions between monthly means of model output and field data. Finally, empirical models and the water quality model were compared to measurements from field data using the Student's t for the 20-year means of phosphorus, and regressions between the yearly phosphorus means from field data and the predicted yearly values for each model. The best model would be one with a significant and high r ~' value and a non-significant difference in the Student's t-test between the means of the model and the field data. RESULTS

Calibration to 1 9 8 5 - 1 9 8 6 f i e l d data

P; = 0.682' [Lp/q~" ( 1/( 1 + x/%))]°934 P~ is the predicted average annual total phosphorus concentration in the lake, PII,. ~) is the annual flow-weighted input concentration of total phosphorus in the previous year, Z is the average annual depth of the lake (m), Lp is the areal loading rate to the lake (g m-2), qs is the areal water loading rate (m y e a r ~ ) , and z~ is the turnover time in the lake (years). These models were compared to the annual average of field measurements of total phosphorus concentrations in the lake for the 20-year period. Calibration and validation criteria

Water quality model outputs of chlorophyll a, total nitrogen, nitrate+nitrite nitrogen, ammonium-nitrogen, total phosphorus, and dissolved available phosphorus concentrations were compared with field measurements. Dissolved available phosphorus calculated by the water quality model is that phosphorus readily available for algal uptake. These results were compared to soluble reactive phosphorus measurements of in-lake waters. The soluble reactive phosphorus was considered equivalent to dissolved available phosphorus and was labelled as such throughout this paper. The model was compared to the field data for the 1985 1986 calibration period in three ways, (1) graphing model output over time to box plots of monthly averaged field data from the eight station network, (2) a Student's t-test (SAS Institute, 1990) between the 2-year mean of model output and the 2-year mean of field data, and (3)

T h e c o r r e s p o n d e n c e s b e t w e e n the w a t e r quality m o d e l o u t p u t a n d o b s e r v e d d a t a were p o o r (r 2 < 0.15, T a b l e 2). H o w e v e r , the 2-year m e a n o f the m o d e l o u t p u t was n o t significantly different f r o m the 2-year m e a n o f field d a t a for in-lake total p h o s p h o r u s , dissolved available p h o s p h o r u s , a n d c h l o r o phyll a c o n c e n t r a t i o n s . This is d e m o n s t r a t e d in the graphical c o m p a r i s o n o f the m o d e l o u t p u t a n d field d a t a [Fig. 4 ( A - C ) ] . T h e box plots o f m o n t h l y field d a t a r e p r e s e n t the m e d i a n value as the h o r i z o n t a l line w i t h i n the box a n d the 25-75 percentiles as the u p p e r a n d lower b o u n d . C a l i b r a t i o n results for total n i t r o g e n were also p o o r ( r 2 < 0 . 0 5 ) , but the 2-year m e a n s o f m o d e l o u t p u t a n d field d a t a were n o t significantly different f r o m one a n o t h e r [Table 2, Fig. 5(A)]. T h e t w o - y e a r m e a n s o f a m m o n i u m - n i t r o g e n a n d nitrate + nitriten i t r o g e n calculated by the m o d e l were three and ten times higher, respectively, t h a n field d a t a m e a n s [Fig. 5(B) a n d (C), Table 2]. Essentially the m o d e l was in the c o r r e c t r a n g e o f field d a t a for all p a r a m e t e r s b u t nitrate a n d a m m o n i u m , h o w e v e r it did n o t explain m u c h o f the variability in the field data.

Lake Okeechobee model calibration A

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As an independent check on the model calibration,

2761

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in situ phytoplankton growth rates calculated by the

model were compared with the limited available data on primary productivity. Using the light and dark bottle method, primary productivity measured at a depth of 0.2 m at two stations is reported to range between 0.6 and 3.0 mg C 1-~ d -~ (Jones and Federico, 1984). The corresponding values from the calibrated model ranged between 2.0 and 4.0 mg C 1-1d ].

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Model results for chlorophyll a, total phosphorus, and total nitrogen for the 20-year simulation ranged within the distributions of the actual field data [Fig. 6(a-c)], but overall the 20-year model means of chlorophyll a and total phosphorus were lower than the 20-year means of the field data (Table 2). The model simulation values of chlorophyll a and total phosphorus were high compared to monthly field data means prior to 1981, in the middle range of the data from 1981 to 1987, and low from 1988 to t992. Total nitrogen was under-calculated by the model as well. However from 1989 to 1993 total nitrogen values generated by the model simulation exceed most of the monthly field data means. Because external forcing functions of temperature and light are incorporated into the phytoplankton production equation, temporal dynamics of the simuA 7~

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Because the empirical loading models presented here only predict annual average phosphorus concentrations in the lake, the only way to compare them to each other and to the water quality model is with respect to total phosphorus predictions. The empirical loading model of Janus et al. (1990) explained the greatest amount of variance in annual averaged total phosphorus, but the 20-year total phosphorus mean for this model was higher than the actual in-lake mean (P < 0.1) (Fig. 7, Table 2). This model overpredicted the annual average total phosphorus concentration of Lake Okeechobee before 1984, but predicted rather well after that. The modified Vollenweider model (Kratzer and Brezonik, 1984) was much less successful, under-predicting every year after 1981. The water quality model, unlike the empirical models, predicts phosphorus concentrations on a daily basis, not an annual average, as demonstrated in Fig. 7. This model produced total phosphorus values that were higher than the annual averages prior to 1980, within the range of the averages

2762

R. Thomas James and Victor J. Bierman Jr

between 1980 and 1986, and lower than the average after 1986. Overall the predicted 20-year mean total phosphorus from this model was significantly less than the twenty-year field data mean (Table 2). DISCUSSION

Calibration to 1 9 8 5 - 1 9 8 6 f i e l d data

Phosphorus loads to Lake Okeechobee occur from three major sources: tributaries, rainfall, and internal fluxes from the sediments. Because the lake is very large and shallow, the sediment area :water volume ratio is very large. The flux values calculated from Reddy (1993) indicate that the sediments are a net source of dissolved available phosphorus to the water column. Settling rates of non-available nutrients and phytoplankton were adjusted as a calibration parameter to maintain the mass-balance in the lake and to more accurately represent the observed water column nutrient concentrations. A settling rate of 0.05 m d ~gave the best results. This is a typical value found in the literature from shallow lakes (Bowie et al., 1985). Using this rate, the water quality model calculated that the amount of phosphorus settling out of the water column was greater than the net flux of phosphorus into the water column from the sediments. Thus, the model indicates that the sediments are a net sink of phosphorus. This is an independent validation of the work of Janus et al. (1990) and James et al. (1995) who demonstrated that the sedi-

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ments were a net sink of phosphorus based on yearly budgets. The other major calibration parameter was light extinction. A value of 2.5 m ~ provided the best fit of model chlorophyll a, total phosphorus, and dissolved available phosphorus to actual in-lake values. This number is within the range of light extinction calculated from 1.6/Secchi Depth (7.8q?.8 m ~, Ed Phlips, University of Florida, Pers. Comm.) and 1.9/Secchi Depth (9.3-1.3 m ~, Effler, 1985). Because of the simplifying assumptions of the model: the lake is homogenous and values for net settling, sediment flux, and light extinction are constant; we did not expect the model to accurately track the variation in the actual data. However, the results are within the range of field data. One explanation for the agreement between model and field data is that the field sampling program is driven by a time schedule, but major wind and storm events are avoided for reasons of safety. Because samples are taken during more quiescent periods, the conditions in the lake are more constant and can be represented in the model by average constant values. To better understand the dynamic changes that occur on the lake, more intensive sampling needs to be taken using autosamplers on permanent platforms in the lake. This sampling program is currently under way in co-operation between the U S G S and S F W M D . Uncertainties in total nitrogen budget

Total nitrogen in this two year calibration was well within the variance of the actual in-lake values. Despite this, their was poor agreement for ammonium- and nitrate + nitrite nitrogen, indicating that the model misrepresented nitrogen processes in the lake. The probable reasons were that the present version of the model did not include potential losses due to sediment denitrification or potential gains due to nitrogen fixation. Sediment nitrogen flux was specified to the model; however, this value was intended to represent only a m m o n i u m nitrogen flux and was not corrected to account for potential losses due to denitrification. At the present time, the nitrogen cycle in this model of Lake Okeechobee is not well represented. The best available information indicates that sediment a m m o n i u m - n i t r o g e n flux, sediment denitrification, and planktonic nitrogen fixation may all be of comparable magnitudes. The value for ammonium nitrogen flux from the sediments (8.6 mg N m ' d ~) was inferred by scaling measured sediment phosphorus flux in proportion to the observed total phosphorus: total nitrogen ratio in the sediments. This was consistent with earlier results from a Fickian diffusion model (Brezonik et al., 1979). Messer and Brezonik (1983) report that sediment denitrification rates in Lake Okeechobee range between 0.70 and 8.40 mg N m 2d-~. Planktonic nitrogen fixation is estimated to range between 2.0 and 10.0mg N m 2 d l, based on acetylene reduction measurements

Lake Okeechobee model calibration

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YEAR Fig. 7. Annual average total phosphorus concentrations in Lake Okeechobee, predicted annual average concentrations from the models of Janus et al. (1990), Kratzer and Brezonik (1984), and the daily predicted values from the current water quality model. conducted by Phlips and Ihnat (1995) and Brezonik et aL (1979). If these three nitrogen processes are indeed of comparable magnitudes, then exclusion of denitrification and nitrogen fixation would result in self-canceling errors in the total nitrogen mass balance. This hypothesis is consistent with the calibration results for total nitrogen [Fig. 5(A) and 6(C)]. The exclusion of denitrification would result in over-computation of nitrate + nitrite nitrogen concentrations. This is also consistent with the calibration results [Fig. 5(C)]. The over-computation of ammonium nitrogen concentration [Fig. 5(B)] could be due to underestimation of water column nitrification or overestimation of nitrogen remineralization. The present calibration results for nitrogen are an example of the utility of a mass balance approach in synthesizing information at the whole-lake scale and identifying important information gaps. These results indicate a need for more information on the sediment ammonium flux, nitrogen fixation, and denitrification in Lake Okeechobee. Twenty-year simulation

The 20-year simulation results showed that the model under-calculated chlorophyll a and total phosphorus (Table 2). This tells us that the model assumptions and/or calibration parameters that we applied were not equally valid over the whole twenty-year period. We assumed a constant settling and a constant flux from the sediments. The net sedimentation, however, has changed over the twenty-year period

(Janus et al., 1990; James et al., 1995). We did not include explicit representation of wind-induced resuspension of sediment although its impact has been documented (Maceina and Soballe, 1990). This suspended material directly influences light extinction (Limno-Tech, 1993), which influences algal production. This material also is related to total phosphorus concentrations in Lake Okeechobee (Maceina and Soballe, 1990). To improve model predictions of total phosphorus and chlorophyll a, wind-induced resuspension of sediments should be included in future water quality modeling efforts in Lake Okeechobee. The model did not represent the temporal variability of the field data very well. Monthly average values for nutrient loads, flows, temperature, and photoactive radiation used in the model did not adequately reflect the temporal variability that existed within each month. The lake is not homogenous; it consists of a number of ecological zones (Phlips et al., 1993). Seasonal dynamics were observed in the model outputs because of the influence of forcing functions of temperature and solar radiation which change over time. In addition, the nutrient seasonal dynamics are influenced by changes in the monthly loads and flows that are a result of changes from the wet to dry season that are common in South Florida. Empirical and water quality model comparisons

The typical empirical loading models take the average yearly conditions of water depth, inflows, outflows, and loads to estimate annual average in-lake

2764

R. Thomas James and Victor J. Bierman Jr

phosphorus concentrations. The modified Vollenweider model of Kratzer and Brezonik (1984) is of this type. Although this model predicted well in the 1970s, it consistently under-predicted the total phosphorus concentration in the lake after 1981 (Fig. 7). This model assumes that phosphorus loads into and out of the lake are at a steady state, the lake is a single homogenous box, and internal nutrient cycling is small, All three of these assumptions are invalid for Lake Okeechobee and may have an impact on the poor predictive ability of the modified Vollenweider model. The failure of this empirical model also is consistent with the findings of van der Molen and Boers (1994). They suggested that empirical models fail when external loading is reduced, because the internal sediment loading becomes more significant. Since external loads to the lake have declined (James et al., 1995), the under-prediction by the modified Vollenweider model was expected. The model of Janus et al. (1990) removes the steady state assumption by the use of the previous year's average phosphorus input concentration to predict the current year in-lake total phosphorus concentration. This time lag produces a pseudo non-steady state model, and for the more recent years it predicts in-lake phosphorus concentrations well (r 2= 0.274). This good agreement is possible because the model was calibrated to the data set from 1973 to 1987. Although this model explained the most variability in the data, it overestimated the 20-year mean of total phosphorus concentrations from the field data. Janus et al. (1990) note a step increase of in-lake total phosphorus concentration around 1979. Because the water quality model was calibrated to the years 1985 and 1986, it was not surprising that this model computed total phosphorus on the high end of the spectrum prior to 1980. To a large extent this was a result of the assumption that sediment flux rates were constant throughout the 20-year period. After 1987, the water quality model computed total phosphorus on the low end of the actual data. The flux rates of phosphorus from the sediments be increasing and/or settling rates may be decreasing in the lake. The only way to compare these empirical models to the water quality model was through total phosphorus calculations (Fig. 7). Comparison of annual steady state predictions from the empirical models to the dynamic prediction of the water quality model can be done by averaging the phosphorus prediction of the water quality model. Although Janus et al. (1990) predicted the year-to-year variability of total phosphorus in the lake well, the seasonal dynamics cannot be observed, nor were predictions made as to chlorophyll a biomass. Both of these variables are predicted daily by the water quality model [Fig. 6(a, b)]. For the 20-year period the average of annual mean field data was significantly greater than the water quality model data. Furthermore, the water quality model did not explain a significant amount of

the variation in the annual mean of total phosphorus (Table 2). Based on the relationship of the predicted values of total phosphorus by each of these models to the actual total phosphorus concentrations in the lake, the results are modest at best (r 2 < 0.30). It is obvious that total phosphorus loads and lake hydrology are not sufficient to completely describe the total phosphorus concentrations in Lake Okeechobee. An important component missing in these three models is the internal phosphorus loading from the sediments due to wind-induced sediment resuspension. To get more precise estimates of total phosphorus we need wind resuspension modeled explicitly. We also need a finer temporal and spatial scale to produce more precise predictions. CONCLUSIONS

The most significant use of this water quality model is an increase in understanding. We have demonstrated an increase in understanding of Lake Okeechobee in this paper through the synthesis of a tremendous amount of data from a variety of sources and through a focus on the potential important mechanisms that exist in this lake that could explain the model limitations. These include net sedimentation, wind resuspension of sediment, light extinction and its relationship to resuspended sediments, and the nitrogen cycle including nitrogen fixation and denitrification processes, This model has highlighted a number of concerns of the lakes that could not possibly be extrapolated from simple empirical loading plot models. Although this water quality model had many simplifying assumptions which inadequately describe Lake Okeechobee, it represents the lake in a more realistic way than empirical models, because it includes nutrient and phytoplankton dynamics. As opposed to the empirical models, the water quality model can and will be enhanced and improved because deterministic, time-variable, spatially segmented models can be revised and adapted to represent a lake more realistically. As our understanding of Lake Okeechobee has increased, the issues and questions have become more complex and sophisticated. These questions can not be answered by empirical based models. Such questions include when, where, and why do algal blooms occur? What impacts does water quality have in the various ecological zones of the lake'? What is the role of sediment-water exchanges in influencing the response of the lake to reductions in external loads? What are the relative importance of nitrogen and phosphorus in this lake? What is the role of nitrogenfixing blue green algae on the nitrogen cycle in this lake? Will changing the stage regulation schedule impact the water quality of the lake? These questions can be addressed by improvements and enhancements of the water quality model that we have

Lake Okeechobee model calibration developed. Some initial examples o f the use o f this model to explore the dynamic interactions a m o n g nutrients, p h y t o p l a n k t o n , sediment fluxes, and light extinction are presented by Bierman and James (1995). REFERENCES

Ambrose Jr R. B., Wool T. A., Connolly J. P. and Schanz R. W. (1988) WASP4, A Hydrodynamic and Water Quality Model Model Theory, User's Manual, and Programmer's Guide. U.S. Environmental Protection Agency, Environmental Research Laboratory, Athens, Georgia. EPA/600/3-87/039. Baker L. A., Brezonik P. L and Kratzer C. R. (1981) Nutrient Loading-Trophic State Relationships in Florida Lakes. Florida Water Resources Research Center, University of Florida, Gainesville, Publication No. 56. Bierman Jr V. J. (1980) A comparison of models developed for phosphorus management in the Great Lakes. In Phosphorus Management Strategies for Lakes (Edited by Loehr R. C., Martin C. S. and Rast W.), pp.235-255. Ann Arbor Science, Mich. Bierman Jr V. J. and Dolan D. M. (1981) Modeling of phytoplankton-nutrient dynamics in Saginaw Bay, Lake Huron. J. Great Lakes Res. 7, 409-439. Bierman Jr V. J. and Dolan D. M. (1986a) Modeling of phytoplankton in Saginaw Bay: I. Calibration phase. J. environ. Engng 112, 400-414. Bierman Jr V. J. and Dolan D. M. (1986b) Modeling of phytoplankton in Saginaw Bay: If. Post-audit phase. J. environ. Engng 112, 415-429. Bierman Jr V. J. and James R. T. (1995) A preliminary modeling analysis of water quality in Lake Okeechobee, Florida: Diagnostic and Sensitivity Analysis. Wat. Res. 29, 2767 2775. Bowie G. L., Mills W. B., Porcella D. B., Campbell C. L., Pagenkopf J. R., Rupp G. L., Johnson K. M., Chan P. W. H. and Gherini S. A. (1985) Rates, Constants, and Kinetics Formulations in Surface Water Quality Modeling (2nd edn). U.S. Environmental Protection Agency, Environmental Research Laboratory, Athens, Georgia. EPA/600/3-85/040. Brezonik P. L., Blancher III E. C., Myers V. B., Hilty C. L., Leslie M. K., Kratzer C. R., Marbury G. D., Snyder B. R., Crisman T. L. and Messer J. J. (1979) Factors Aff~,cting Prima O, Production in Lake Okeechobee, Florida. Report prepared by Department of Environmental Engineering Sciences, University of Florida, Gainesville, for Florida Sugar Cane League, Clewiston, Florida. Report No. 07-79-01. Canale R. P. and Effler S. W. (1989) Stochastic phosphorus model for Onondaga Lake. War. Res. 23, 1009-1016. Canfield D. E. and Hoyer M. V. (1988) The eutrophication of Lake Okeechobee. Lake Reservoir Mgmt 4, 91 99. DiToro D. M. and Matystik Jr W. F. (1979) Phosphorus recycle and chlorophyll in the Great Lakes. J. Great Lakes Res. 5, 233 245. DiToro D. M. and Matystik Jr W. F. (1980) Mathematical Models of Water Quality in Large Lakes, Part I: Lake Huron and Saginaw Bay. U.S. Environmental Protection Agency, Environmental Research Laboratory, Duluth, Minnesota. EPA-600/3-80-056. DiToro D. M. and Connolly J. P. (1980) Mathematical Models of Water Quality in Large Lakes, Part H: Lake Erie. U.S. Environmental Protection Agency, Environmental Research Laboratory, Duluth, Minnesota. EPA600/3-80-065. DiToro D. M., Thomas N. A., Herdendorf C. E., Winfield R. P. and Connolly J. P. (1987) A post-audit of a Lake Erie eutrophication model. J. Great Lakes Res. 13, 801 825.

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Effler S. W. (1985) Attenuation versus transparency. J. eviron. Engng 11, 448~459. Federico A. C., Dickson K. G., Kratzer C. R. and Davis F. E. (1981) Lake Okeechobee Water Quality Studies and Eutrophication Assessment. South Florida Water Management District, West Palm Beach, Florida, Tech. Publ. 81-2. Hellstrom T. (1991) The effect of resuspension on algal production in a shallow lake. Hydrobiologia 213, 183-190. Herman G., Nishri A. and Berman T. (1989) A long-term prediction model for total phosphorus concentration in Lake Kinneret. Wat. Res. 23, 61~56. James R. T., Jones B. L. and Smith V. H. (1995) Historical trends in the Lake Okeechobee ecosystem II. nutrient budgets. Arch. Hydrobiol. Monogr. Beitrdge Suppl. 10"7, 25-47. Janse J. H., Aldenberg T. and Kramer P. R. G. (1992) A mathematical model of the phosphorus cycle in Lake Loosdrecht and simulation of additional measures. Hydrobiologia 233, 119 136. Janus L. L., Soballe D. M. and Jones B. L. (1990) Nutrient budget analyses and phosphorus loading goal for Lake Okeechobee, Florida. Verh. lnternat. Verein. Limnol. 24, 538 546. Jones B. L. and Federico A. C. (1984) Phytoplankton, Chlorophyll a, and Primary Production in Lake Okeechobee. South Florida Water Management District, West Palm Beach, Florida, Tech. Publ. 84-4. Jorgensen S. E., Nielsen S. N. and Jorgensen L. A. (1991) Handbook of Ecological Parameters and Ecotoxicology. Elsevier, Amsterdam. Kratzer C. R. and Brezonik P. L. (1984) Application in nutrient loading models to the analysis of trophic conditions in Lake Okeechobee, Florida. Environ. Mgmt 8, 109 120. Limno-Tech, Inc. (1993) Preliminary Assessment of Nitrogen Impacts on the Lake Okeechobee Ecosystem. Report prepared for South Florida Water Management District, West Palm Beach, Florida, Contract No. C91-2552. Luettich Jr R. A, Harleman D. R. F. and Somlyody L. (1990) Dynamic behavior of suspended sediment concentrations in a shallow lake perturbed by episodic wind events. Limnol. Oceanogr. 35, 1050-1067. Maceina M. J. (1993) Summer fluctuations in planktonic chlorophyll a concentrations in Lake Okeechobee, Florida: the influence of Lake Levels. Lake Reservoir Mgmt 8, 1-11. Maceina M. J. and Soballe D. M. (1990) Wind-related limnological variation in Lake Okeechobee, Florida. Lake Reservoir Mgmt 6, 93-100. Messer J. and Brezonik P. L. (1983) Comparison of denitrification rate estimation techniques in a large, shallow lake. Wat. Res. 17, 631-640. van der Molen D. T. (1991) A simple, dynamic model for the simulation of the release of phosphorus from sediments in shallow, eutrophic systems. Wat. Res. 25, 737 744. van der Molen D. T. and Boers, P. C. M. (1994) Influence of internal loading on phosphorus concentrations in shallow lakes before and after reduction of the external loading. Hydrobiologia 275]276, 379 389. Phlips E. J., Aldridge F. J., Hansen P., Zimba P. V., Ihnat J., Conroy M. and Ritter P. (1993) Spatial and temporal variability of trophic state parameters in a shallow subtropical lake (Lake Okeechobee, Florida, USA). Arch. Hydrobiol. 128, 437-458. Phlips E. J. and Ihnat J. (1995) Planktonic nitrogen fixation in a shallow subtropical lake (Lake Okeechobee, Florida, USA). Arch. Hydrobiol. Beih. Ergebn. Limnol. 45, 191-201. Reddy K. R. (1993): Lake Okeechobee Phosphorus Dynamics Study. 111. Biogeochemical Processes in the Sediments. Report prepared by University of Florida, Gainesville, for

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R. T h o m a s James and Victor J. Bierman Jr

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Restoration Proc. National Conf, Minneapolis', Minnesota, 1978, pp. 77 83. U.S. Environmental Protection Agency, Office of Water Planning and Standards, Washington, D.C. Shanahan P., Luettich Jr R. A. and Harleman D. R. F. (1991) Water quality modeling: Application to lakes and reservoirs: Case study of Lake Balaton, Hungary. In Water Quality Modeling, Volume IV, Decision Support Techniques for Lakes and Reservoirs (Edited by Henderson-Sellers B.), pp. 69-114. C R C Press, Boca Raton, FI. T h o m a n n R. V. and Segna J. S. (1980) Dynamic phytoplankton-phosphorus model of Lake Ontario: ten-year verification and simulations. In Phosphorus Management Strategies ./'or Lakes (Edited by Loehr R. C., Martin C. S. and Rast W.), pp. 153 190. A n n Arbor Science, Mich. T h o m a n n R. V. and Mueller J. A. (1987) Principles of Su~/'ace Water Quality Modeling and Control. Harper & Row, New York. Vadstein O., Harkjerr B. O., Jensen A. Olsen Y. and Reinertsen H. (1989) Cycling of organic carbon in the photic zone of a eutrophic lake with special reference to the heterotrophic bacteria. Limnol. Oceanogr. 34, 840 855. Zlottnik I. and Dubinsky Z. (1989) The effect of light and temperature on D O C excretion by phytoplankton. Limnol. Oceanogr. 34, 831 839.