PREDICTION OF THERMAL STRATIFICATION OF THE KOTMALE RESERVOIR USING A HYDRODYNAMIC MODEL

Strong thermal stratification in a reservoir may resul t in oxygen depletion along t h e vertical profile downwards leading to its eutrophication. The paper is an investigation of thermal stratification behaviour of the Kotmale reservoir, which experienced several water quality linked problems in recent times. A one-dimensional reservoir hydrodynamics model is calibrated and validated for the Kotmale reservoir. The calibration and validation a r e strengthened by calculating several goodness-of-fit statistics. The study further shows the possibility to change the strong thermal s t rat i f icat ion of t h e Kotmale reservoir by manipulating the releases from it. The model that ensures a reasonable prediction of thermal stratification enables taking precautionary measures to avoid adverse reservoir water quality conditions.


INTRODUCTION
The desire to manage the quality of water stored in reservoirs led to the development of numerical models for the simulation of internal dynamics of them.Lakes or reservoirs that do not show significant thermal stratification during the yearly cycle could be modeled assuming that complete mixing occurs throughout its volume during the whole year,11J2 However, for reservoirs in which the foregoing condition does not apply, complex models have to be developed to predict thermal gradients, density stratification and the impact that various operating rules may have on these and other physical, chemical and biological quality characteristics of the impoundment water.Much of the development in modeling reservoir dynamics h a s been done by assuming onedimensionality, where vertical motion is inhibited and transverse and longitudinal variations are quickly evened out.Even with this simplification, Reservoirs are built for storing water to increase it is difficult to model the interactions of a number availability by preventing waste during the of complex processes occurring in a reservoir.Over periods of high runoff.As these storage the last several decades diverse models of varying impoundments become many and were called on complexity a n d success have been to serve more and users, the quality of the produced.2,3,4,6,'7,10There has also been to a less water stored in and released from them have come extent some development of two-and threeunder strict scrutiny to determine its suitability dimensional stratification model^.^^^,'^However, for various purposes.Therefore, the ability to the increasing complexity and computational predict the quality of water in reservoirs became requirements have severely limited their important in the management of water resources development.development works.
When a flowing river is dammed and becomes an impoundment, two major changes occur, which have a marked effect in water quality.Firstly, creating an impoundment greatly increases the time required for water to travel the distance from the headwaters to the discharge a t Although three-dimensional models describe the water quality and ecology of reservoirs better, one-dimensional models remain attractive, appropriate and convincing for understanding the physical processes occurring in reservoir^.^,^,'^ the dam.Secondly, thermal or density and Dynamic Reservoir Simulation Model7 therefore, chemical stratification may take place.
(DYRESM) is a one-dimensional numerical model Both increased detention time and thermal that can simulate thermal behavior and water stratification frequently cause adverse water quality distribution in a reservoir and predict the quality conditions in reservoirs.
distribution of temperature (and therefore, density) in reservoirs in response to meteorological forcing, inflow and outflow.The model provides a means ofpredicting seasonal and inter-annual variability of lakes and reservoirs as well as sensitivity testing to long-term changes in environmental factors or watershed properties.
The Kotmale reservoir, the uppermost reservoir in t h e comprehensive Mahaweli Development Scheme faced several water quality related problems in the recent past.The ability to predict its temperature distribution, which is closely related to its water quality, would enable precautionary measures to prevent expected poor quality conditions.This paper presents the calibration and validation of DYRESM for the Kotmale reservoir to predict i t s thermal stratification behavior.Further, the possibility to reduce thermal stratification by manipulating the discharge from the reservoir was also studied.
The paper first presents a brief description of the Kotmale reservoir and its catchment, followed by t h e descriptions of DYRESM and the statistical methods used in the study.Analysis carried out including calibration and verification of the model for the Kotmale reservoir, a statistical analysis, a study on the the reservoir area.Table 1 presents monthly averages of data observed over the period from 1990 to 1999.As it shows, the lowest temperatures occured from January to February and highest temperatures from February to April.Rainfall varied considerably during the year.Seasonal variation in wind speed (measured a t 2m above ground surface) was small.The mean monthly wind speed was highest in June and lowest in the period from October to December.Monthly variation of evaporation follows the mean temperature and total radiation variations.The average annual evaporation around the Kotmale reservoir was 1442 mm.impact of releases on reservoir thermal The climatological data collected a t a recording station located close to the dam was used to describe the climatic conditions around

Sampling stations and major
The Kotmale reservoir faced several water quality related problems in the recent past.During a severe drought in 1991, the reservoir water-level dropped and a thick bloom of Microcystis aeruginosa was observed in the upstream region.This shifted towards the dam due to wind action covering the whole surface of t h e reservoir.16Based on a water quality assessment carried out using water quality data in the Kotmale reservoir from March 1987 to February 1988, Piyasirils concluded that the Kotmale reservoir thermally stratifies and is subjected to oxygen depletion along the vertical profile indicating sensitivity to eutrophication.

Hydrodynamic Model: DYRESM
The assumption of one-dimensionality i n DYRESM is based on the density stratification usually found in lakes and reservoirs, which inhibits vertical motions while lateral a n d longitudinal variation in density are quickly Thermal Stratification of the Kotmale Reservoir relaxed by horizontal convection, occurring on time scales shorter than vertical advection.The model has been developed with emphasis on parameterization of the physical processes rather t h a n numerical solution of the appropriate differential equations.
DYRESM uses a Lagrangian Layer Scheme in which the reservoir is represented by a series of horizontal layers of uniform property but of variable thickness.As inflows and outflows enter or leave the reservoir, the affected layers expand or contract and those above move up or down to accommodate the volume change.The vertical movement of layers is accompanied by a thickness change as the layer surface areas change with vertical position in accordance with the reservoir bathymetry.Mixing is modeled by amalgamation of adjacent layers, and the layer thicknesses are dynamically set internally by the model to ensure that for each process, an adequate resolution is obtained.
Even with t h e assumption of onedimensionality, the vertical density structure is the result of a complex interaction of a number of processes active in lakes and reservoirs.These individual processes are parameterized in DYRESM.The development of DYRESM is described in detail in the l i t e r a t ~r e , " ~~~~" ~~ including descriptions of the process parameterizations.The processes included in the model are surface heat, mass and momentum exchanges, surface mixed layer deepening model, inflow, outflow, mixing in t h e hypolimnion and bubble plume destratification.
DYRESM has been validated on several lakes and reservoirs; Lake Burragorang (large and deep) during a drought and Prospect reservoir (small and shallow) both located near Sydney, Australia, over a period of 8 years, are two applications18 of it.Its major development and validation was in Wellington reservoir, a n irrigation supply reservoir situated in the southwest of Western Australia.A quantitative measure of the performance of the model is given in Patterson et aZ.l4 The data required for the DYRESM model are daily values of air temperature, relative humidity, wind velocity, solar radiation, rainfall, evaporation, inflow quantity, and outflow quantity.The RMSE is defined as the square root of the mean of the squared difference between observed and simulated values.
As such, t h e RMSE is similar to a standard deviation of the error,lS roughly twothirds of the errors are expected to fall within +I.RMSE values have the units of the quantity of interest, and lower values indicate a better fit.For the statistic to be relevant, however, one must know the range of the fitted data to determine whether an RMSE indicates an excellent or poor fit.
The MRAE is the mean of the absolute value of relative errors.Lam et al.9The daily values of air temperature, relative humidity, wind velocity, rainfall, evaporation, reservoir inflow quantity, inflow quality and outflow quantity, which are required for the model were collected from the Headworks Administration, Operation and Maintenance unit of the Mahaweli Authority of Sri Lanka.Actual duration of sunshine hours, which were used to estimate solar radiation, were collected from Natural Resource Management Centre a t Peradeniya.

Data for the model
The DYRESM model for the Kotmale reservoir was calibrated using the data collected during 1995.Except short wave radiation and daily inflow temperatures, all the other data required for the model were available for that year.However, records of daily sunshine duration were available for the area.Using that, the short wave radiation were estimated based on the Angstrom f ~r m u l a ' ~~~ which relates solar radiation to extraterrestrial radiation and relative sunshine duration.Maximum possible duration of sunshine hours and extraterrestrial radiation for different latitudes listed in FA0 publication No.56 were adopted in the study.lThe constants in the Angstrom formula were obtained from the modified Fre're curves for Sri Lanka by Samuel.20 Daily inflow temperatures were estimated as the average of the air temperatures during the 4 days preceding the date of the inflow entering the reservoir, as suggested by the model developers.
Initial reservoir water level, temperature and salinity are required to start a simulation.Initial water level was set to the observed water level of the reservoir on the first day of the simulation period.Observed water temperature and salinity profiles a t St.1 on that day were available for the initial condition of the reservoir.

Model parameters
The model parameters are given in Table 3.However, many of them cannot be measured directly and were obtained by a trial and error procedure of comparing the temperature obtained from the model DYRESM simulations with observations.Most of the hydrodynamic and thermal processes in a reservoir are simulated in the DYRESM model.The mean albedo of water, emissivity of water surface and light extinction coefficient were found to be very sensitive parameters, while the other parameters were relatively insensitive.

Reservoir mass balance
The model gives the reservoir water level during the simulation period.Comparison with the observed reservoir water levels during the simulation period from lgth January to 3lSt December, 1995 shows good agreement as evident from Figure 2. RMSE between measured and simulated water levels was 0.133 m.The difference between the measured and simulated water levels ranged from -0.56 m to 0.53 m with a mean difference of 0.076 m.

Temperature variation
Near-surface and near-bottom (50 m below water surface) water temperatures obtained from the model DYRESM at the calibration were compared with the observed values in Figure 3. Simulated near-surface and near-bottom water temperatures were generally within 1°C of the corresponding observed values indicating a good fit.Differences between simulated and observed values ranged from -1.3"C to 1.2"C and the average difference was 0.5"C.

during calibration
The DYRESM simulated w a t e r temperatures (84 observations) for January through December 1995 were compared with corresponding observed values for St.1 during the calibration stage to decide the model parameter values.Figure 4 presents the comparison, which indicates a very good fit.Measured water temperatures ranged from 22.2"C to 28.1°C.Differences between measured and simulated temperatures ranged from -1.2"C to 1.5"C with a RMSE of 0.47"C.The MARE between measured and simulated water temperatures was 2.18% of the observed values.Eighty eight percent of the simulated temperatures were within 1°C of the measured temperature.
The monthly goodness of-fit statistics between observed and simulated temperatures for the calibration period are given in Table 4.These two fit-statistics have been used to investigate the suitability of models in simulating real situations in many areas.Rounds and Woodlg examined the fitness of a water quality model developed for a river based on them.In summary; 0.008 5 RMSE k 0 C ) 2 0.864, 0.226 5 MRAE (%) 5 3.304 The monthly goodness of-fit statistics between observed and simulated temperatures for the calibration period are given in Table 4.These two fit-statistics have been used to investigate the suitability of models in simulating real situations in many areas.Rounds and WoodlS examined the fitness of a water quality model developed for a river based on them.

Sensitivity analysis
Sensitivity analysis is the determination of the effects of small changes in calibrated model parameters on model results.Many simulations were conducted as a component of the model calibration.Results from these simulations form the basis for the sensitivity analysis.
Of the hydraulic and thermal parameters in Table 3, simulated temperatures were most sensitive to changes in the emissivity of water surface (EWS), mean albedo of water (MAW) and light extinction coefficient (LEC).Figure 5 presents the results of this analysis based on temperature profiles on the days 2 1 March, 3 June, 25 September and 28 December in the year 1995.The epilimnetic temperature is very sensitive to EWS and MAW and less sensitive to LEC, while the hypolimnetic

Model verification
To verify the accuracy of the parameters of the model calibrated using the data in the year 1995, the reservoir was simulated for the year 1996 and the results were compared with the observed temperatures.For the verification period, fit statistics are as follows.The monthly goodness of-fit statistics between observed and simulated temperatures are given in Table 5.

Impact of releases on thermal stratification
The Kotmale reservoir is observed to be stratified throughout the year.Stratification can cause   Thermal Stratification of the Kotmale Reservoir temperature, hypolimnetic temperature and mixed-layer depths were all in agreement with the observations.The quantitative and qualitative criteria of model prediction showed that the model could simulate the annual dynamics reasonably well.The Kotmale reservoir was observed to be thermally stratified throughout the year.
The model enables the prediction of thermal stratification in the reservoir body using data t h a t can be collected easily, such a s climatological data and reservoir inflow quantity and quality.This could avoid continuous expensive reservoir water quality monitoring programmes.
Since thermal stratification in a reservoir determines the water quality in a reservoir body, the model enables predicting adverse effects with respect to water quality in the reservoir.In such situations, reservoir managers will be able to take precautionary measures by controlling stratification in the reservoir by manipulating withdrawals.The study, based on two different withdrawal p a t t e r n s , h a s shown t h a t stratification in the Kotmale reservoir could be altered by manipulating the withdrawal.Thus, the impact of many alternative operational patterns on thermal stratification in the reservoir could be studied with the help of the model in advance to avoid adverse water quality conditions in the reservoir as well as in water supplied from the reservoir.

Figure 2
Figure 2: Observed and simulated water levels of the Kotmale reservoir during calibration

Figure 4 :
Figure 4: Observed and simulated vertical profiles of water temperature of the Kotmale reservoir at St.1 from January 19 to December 28,1995 Figure 5: Sensitivity analysis of DYRESM parameters, mean albedo of water, emissivity of a water surface and light extinction coefficient based on the temperature profiles of 21/3/1995,3/6/1995, 25/9/1995 and 28/12/1995

Figure 6 Figure 7
Figure 6 presents the comparison of simulated and observed water temperatures at the near-surface and near-bottom (50 m below water surface) of the Kotmale reservoir.Simulated near-surface and near-bottom water temperatures were generally within 1°C of the corresponding observed values.Differences between simulated and measured values ranged from -1.3"C to 1.2"C and the average difference was 0.5"C.

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possibility to reduce stratification by the manipulation of withdrawal from the Kotmale reservoir was of interest.Withdrawals from the reservoir were changed during the first three months of the year 1996 to study the change ma in the stratification that would occur in the reservoir.Initially, the withdrawals during the

Figure 7 :
Figure 7: Comparison of isotherms in the

Table 2 : General and morphometric characteristics and Physico-chemical data of the Kotmale reservoir
expressed this statistic as the following, Variables are as defined before.Where, xs,, and xO,, are the simulated and observed it" values and, n is the s a m ~l e size.In There are limitations for using the above this analysis, we use the root mean square error equation, specifically, there is poor behaviour of as the measure of error between computed and MRAE at low values of xo.i and the variability of observed temperatures.However, an advantage of the MRAE is that this statistic is a readily understood comparison and can provide a gross measure of model adequacy and can be useful in comparing models.The study area of the reservoir and its tributaries are depicted in Figure1.Water samples have been collected once a month from three stations St.1, St.2, and St.3, vertically from top to bottom a t 10 m intervals.St.1 located closer to the dam is the deepest region in the reservoir.St.3 is close to the major inflowing rivers (Kotmale Oya, Pundalu Oya, Puna Oya), while St.2 is in the middle of the reservoir.Physical, chemical and biological water quality parameters measured in these water samples are temperature, dissolved oxygen concentration, electrical conductivity, pH, chloride, total alkalinity, suspended solids, nitrogen, ammonia, nitrate, nitrite, biological oxygen demand, fluoride, heavy metals, chlorophyll and phytoplankton.This study uses the data collected at the station St.1.These water quality data have been collected through a limnology project at Mahaweli reservoirs by the Department of Zoology, University of Sri Jayawardenapura, Nugegoda.17 the data is not adequately recognized.The MRAE is also constrained if xo is much greater than xs,< Data Collection:

Table 4 : Goodness-of-fit statistics between observed and simulated temperatures during the calibration period
These figures reveal the fact that the Kotmale reservoir was thermally stratified throughout the year 1996.During the dry months, February to May, it is very strongly stratified.