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The thermal structure of Sau Reservoir (NE: Spain): a simulation approach
Ecological Modelling 125 (2000) 109 – 122 www.elsevier.com/locate/ecolmodel
The thermal structure of Sau Reservoir (NE: Spain): a simulation approach Bo-Ping Han a,b, Joan Armengol a,*, Juan Carlos Garcia a, Marta Comerma a, Montse Roura a,c, Josep Dolz c, Milan Straskraba d a
Department Ecologia, Facultat de Biologia, Uni6ersitat de Barcelona, A6. Diagonal, 645, 08028 Barcelona, Spain b Institute of Hydrobiology, Jinan Uni6ersity, Guangzhou, 510632, People’s Republic of China c Department Enginyeria Hidraulica, Maritima i Ambiental, Escola Tecnica Superior d’Enginyers de Camins, Canals Ports, Uni6ersitat Politecnica de Catalunya, Catalunya, Spain d Biomathematical Laboratory, Academy of Sciences of the Czech Republic and Faculty of Biological Science, Uni6ersity of South Bohemia, Branisˇo6ska´ 31, 370 05 C& eske´ Budeˇjo6ice, Czech Republic Accepted 29 June 1999
Abstract In this study, a 1D model of reservoir hydrodynamics DYRESM has been applied to Sau Reservoir, a river valley reservoir in the North-Eastern Spain. Simulation is undertaken for 3 years (1995 – 1997). Meteorological input data measured at the dam are only available from May of 1997. In this case the simulation results fit measured temperatures very well. In the remaining periods, some meteorological data (radiation, wind and rainfall) were obtained from two nearby stations. Simulated temperature distribution in 1996 is close to the observed one. In 1995, however, the simulated result is far from the observed data. Inflows , outflow and local meteorological events such as storms and gusts of wind seem to be responsible for the differences. By changing some parameters, the effects of flow, light extinction coefficient and outlet elevation on thermal stratification are investigated. Simulations demonstrate that the inflow with high temperature is the main factor controlling the thermal structure in Sau Reservoir and demonstrate that the effect of residence time on thermal stratification is manifested mainly by the changes in the depth of thermocline. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Thermal stratification; Numerical simulation; Sau Reservoir
1. Introduction Most deep temperate and subtropical lakes develop thermal stratification every summer. The * Corresponding author. Fax: +34-3-4111438. E-mail address: [email protected] (J. Armengol)
stratified water column is usually segregated into epi-, meta-and hypolimnion by the density differences produced via warming of surface water. The stratification strongly affects chemical and biological gradients in vertical direction (Reynolds, 1992; Watanabe, 1992). The stratification is mainly affected by external forces such as heat
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input, wind and internal variables such as lake morphometry and light extinction coefficient of water. Reservoirs, man-make lakes, usually are built to store water for later use, water supply, flood control or power generation. Inflow and withdrawal lead to decrease in water retention time of reservoir comparing with a lake of the same morphometry (Ford, 1990). For this reason, reservoirs are usually considered as water bodies intermediate between rivers and lakes, sharing some characteristics with both. A deep and large reservoir may behave more similarly to a lake or to a river in dependence mainly on residence time. The degree of stratification varies also with inflow temperature (Straskraba, 1973; Riera et al., 1992; Straskraba et al., 1993; Armengol et al., 1994; Hocking and Straskraba, 1994). Another characteristic of reservoirs that differs from that of lakes results from the location of outflow. In a natural lake, water usually overflows from water surface. In a reservoir, the outflow is released from one fixed outlet or several selective outlets at different depths. Therefore, inflow with temperature different from that of the surface of the reservoir and outflow at different depths appear to be the main sources of the difference in hydrodynamics between a reservoir and a lake. Usually, inflow temperature is lower than surface temperature of reservoir water. The heavy water first plunges to some depth and then insert into reservoir water at a certain level. As a result, the inflow causes thermocline erosion to a great degree by entraining water in the main reservoir body (the transitional and lacustrine zones). Inflow is one of the main sources of nutrients and other chemical material entering a reservoir, its intrusion can to a great degree influence the vertical gradient of nutrients (Armengol et al., 1986; Vidal and Om Tubau, 1993; Koma´rkova´ and Hejzlar, 1996). Inflow temperature determines mainly at which layers the inflow inserts into the reservoir. Thus, recognition of temperature distribution in the reservoirs is at the base of understanding the performance and functioning of reservoir ecosystems (Owens et al., 1986; Kimmel et al., 1990). As heat input and flow pattern vary daily, measured data are not enough to recognize and understand the effect of each factor mentioned above on the
heat and water exchange processes and the resulting thermal structure in reservoirs. Numerical hydrodynamic models appear to be helpful by expressing physical processes. A number of models contributed to this goal (Stefan et al., 1982; Orlob, 1983; French, 1985; Anonymous, 1986; Price et al., 1986; Martin, 1988; Virtanen et al., 1994; Herman, 1996). Among them, DYRESM (Imberger and Patterson, 1981) is a one dimensional model which has been widely verified. In this study, it is applied to Sau Reservoir, located in the North-Eastern Spain. We first confront the simulation results with the observed data to verify the validity of the numerical model. By changing some parameters such as outlet depth, flow and its pattern, and light extinction coefficient, their possible effects on thermal stratification in Sau Reservoir has been investigated. Basing on these simulations, we attempt to testify and discuss some early conclusions about reservoir hydrodynamics by sensitivity analysis.
2. Materials and methods Sau Reservoir is the first one among a cascade of reservoirs situated in the central part of the river Ter and was first filled in 1963. Fig. 1 and Table 1 outline its mophometry and main hydraulic features. In this reservoir, three selective outlets are available, located between 383.1– 386.1, 397.58–400.58 and 412.06–415.06m a.s.l., respectively. Correspondingly, we refer them as bottom outlet, middle outlet and surface outlet. A detailed description of Sau Reservoir is given by Vidal and Om Tubau (1993). Inflow and outflow input data were measured from 1995 to 1997, daily inflow temperature was obtained by interpolating linearly the data measured once a month. Meteorological data on radiation, wind speed, air temperature and rainfall are available only after May 20, 1997 when a meteorological station was established on Sau Reservoir. From January 1995 to July 20 1995, the meteorological data are from a meteorological station at Caldes de Montbui 50 km away from Sau Reservoir. From July 21 of 1995 to December 31 of 1996, the data are from a meteorological station at Perafita 30 km away
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from the reservoir. The long wave radiation is calculated on the basis of cloudiness. Cloudiness data in simulation were calculated from the mea-
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sured short wave radiation data. Assuming no cloud during the maximal radiation, the cloudiness for each day is obtained as the relative difference between the observed daily radiation and the corresponding short wave maximal radiation obtained as the envelope of the highest values measured.
2.1. The one dimensional model
Fig. 1. Catchment and morphometry of Sau Reservoir. The temperature is measured at sampling point 1. Table 1 Main mophmetry characteristics of Sau Reservoir after Vidal and Om Tubau (1993) Variable
Value
Latitude Catchment area Max. volume Max. area Max. depth Max. length Bottom elevation Basin width at crest Drag coefficient of the stream bed Slope of the stream bed Stream half angle
46°46%N 4°51%E 1.79×109 m2 0.1486×109 m3 5.8×106 m2 75 m 1.8×104 m 362 m a.s.l. 260 m 0.016 3.85×10−3 75°
DYRESM was developed in the Water Research Center of the University of Western Australia. An extensive description of the model has been given in Imberger and Patterson (1981), Hocking et al. (1988), Hocking and Patterson (1991) and Casamitjana and Schladow (1993). In this model, physical processes of heat exchange across water surface, heat distribution by mixing based on a turbulent energy budget formulation which includes the effects of convective overturn, stirring by the wind and shear production at the interface between the epilimnion and hypolimnion, are modeled. Turbulent diffusion is modeled by the solution of the diffusion equation with a variable coefficient determined from energy released by the plunging of streams, wind induced seiching, and stratification. The inflow process is divided into three parts. As the stream enters the reservoir it pushes the stagnant reservoir water ahead of itself until buoyancy forces dominate, then either flows over water surface or plunges beneath the surface. Once submerged, the stream will flow down the river valley and entrain reservoir water. The modeling of withdrawal enables selection among two assumptions: point sink and line sink. Each of the physical processes is modeled separately using parameterization based on theory, experiments and field studies and consequently, the model is generally applicable without calibration.
3. Simulation and results Daily averaged wind speed from 1995 to 1997 is plotted in Fig. 2. The corresponding simulation results for the 3 years and the temperature measured at sampling point 1 near the dam are shown
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Fig. 2. Wind speed used in simulations. Only the data from May 20 1997 were measured at Sau Reservoir near sampling point 1. The data from January 1995 to July 20 1995 are from a meteorological station at Caldes de Montbui 50 km away from Sau Reservoir. The data from July 21 of 1995 to May 19 of 1997 are from a meteorological station at Perafita 30 km away from Sau Reservoir.
in Fig. 3. In comparison with the measured data, the best fit is from 1997. A comparison of temperature profiles between the observations and simulations on several individual Julian days is illustrated in Fig. 4. On each of these days, the simulated metalimnion covers the same depth range as the observed, the simulated temperatures in hypolimnion is almost identical with the observed. On Julian days 195 and 245, simulated surface temperature is about 1°C lower than the
observation, and on Julian day 282, about half a degree lower than the observation. On Julian day 309, the simulated epilimnetic temperature is about one degree lower than the observed. Differences between the simulations and the observations probably result from measurements of the temperature profiles being done from 10:00 am to 3:00 pm and the simulated temperature represents a daily average. The temperature measured in daytime near noon can be expected to become
B.-P. Han et al. / Ecological Modelling 125 (2000) 109–122 Fig. 3. Comparison of temperature isolines between simulations (the right column) and observations (the left column). In 1995, the centerline of the outlet is at 22 m above the bottom. In 1996 and 1997, the centerline of the outlet is at about 37 m above the bottom. The arrows indicate outlet location.
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higher than the daily mean temperature. Particularly in the autumn (Julian day 309), when a relatively strong wind mixes the water column well, the daily mean temperature in epilimnion can be expected to be lower than the simulated temperature. On all the 4 days mentioned above the change in metalimnetic temperature is sharper in the simulation than in the observed profiles. In Fig. 3 this results in individual temperature isolines being more clearly separated from each other in the observed than in the simulated series. In DYRESM, heat distributions in the epilimnion and hypolimnion are simulated by different algorithms. In the epilimnion, the model simulates convective overturn, stirring and shear production. Hypolimnetic temperature distribution is obtained by solving a diffusion equation with an
Fig. 4. Comparison of temperature profiles between the observed and the simulated results on four Julian days: 195, 245, 282, 309 of 1997. Filled circle: the observation, Open circle: the simulation.
eddy diffusivity coefficient. A better fit of numerical models requires to pay attention to energy exchange between epilimnion and hypolimnion that has not theoretically been well solved yet. The 1996 simulation result being generally comparable with the observation implies that the data used from the nearby meteorological station can be a good approximation of the Sau data. Generally speaking, humidity and wind speed as well as its variation with time are dependent of the morphometry and surroundings of the reservoir. The difference between the meteorological data from the nearby station and the actual data can contribute to the differences between the simulation and observation results. However, the simulation of 1995 is far from the observation, 1995 is an extremely dry year. The outflow was released at the bottom outlet, while the outflow was withdrawn from the middle outlet in 1996 and 1997. The observed temperature distribution in 1995 is significantly distinct from that in 1996 and 1997. The water column was much more intensively mixed during the whole year. In the summer, the temperature at the bottom is only one or two degrees lower than at the surface. Generally speaking, stratification of a water column is mainly affected by residence time and modified by the inflow temperature and wind speed. The residence time of water in 1995 is much longer than in 1996 and 1997. The inflow and wind speed seems to be the factors leading to the different temperature distribution. The inflow temperature and the water surface temperature are plotted in Fig. 5. The inflow temperature in 1995 is only a little higher in spring and lower in the summer than in 1996 and 1997, therefore, the inflow temperature can not explain the differences. During the year 1995 the inflow was largely reduced and the reservoir became much shallower (35 m at the deepest point instead of 75 m when the reservoir is fully filled). It is improbable that a 35 m deep water body will be thoroughly mixed by wind during high summer air temperatures. Tentatively, due to the reduction in the reservoir volume, the inflow may introduce a relative high mechanical energy to erode the thermocline and mix it with hypolimnetic water. Another possible explanation could be that there are unusual wind
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deed strong storms during the summer. Unfortunately, data from the meteorological station at the dam of Sau Reservoir were unavailable at that time. To test the effect of wind, we increased the wind speed in the summer: the calculated profiles did not become closer to the observed ones. The temperature distribution depends not only on the daily average wind speed but also on its time and local variation over the reservoir surface. Such exact data are not available. To support the reality of intensive mixing and exclude a possible error in our observed data, the oxygen distribution in 1995 shown in Fig. 6 confirm that the water is indeed well mixed during this year. According to the above comparison between the simulations and the observations, the simulated temperature distribution by DYRESM can be accepted to be a good approximation of actual temperature distribution if the input data are accurately provided.
4. Simulation experiments: sensitivity analysis
4.1. Effect of outlet depth on thermal stratification Fig. 5. The inflow, outflow and water surface temperature at the sampling point over 3 years from 1995 to 1997.
speeds during this year. According to one of the present authors (J.C.G.), this year there were in-
Reservoirs are usually designed to control water release with one fixed outlet or several selective outlets. That the outlet depth can exert an obvious effect on hydrodynamics of reservoirs has
Fig. 6. Oxygen distribution measured at sampling point 1 in 1995.
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Fig. 7. The effect of outlet location on the temperature distribution in 1997. (A) Surface outlet at about 51 m above the bottom; (B) Bottom outlet located at about 22 m above the bottom. The arrows indicate outlet location.
been recognized for a long time (Fontane and Labadie, 1981). To investigate the effect of outlet depth, we simulated temperature distribution of 1997 by changing the outlet depth, but leaving other inputs intact. Fig. 7A,B show the temperature distribution corresponding to the surface and bottom outlets, respectively. It is evident that the thermocline is deeper with the bottom outlet. In the surface outlet and middle outlet simulation, however, the thermocline location is very similar. The temperature distribution simulated with the surface outlet is quite similar to another simulation obtained by reducing both inflow and outflow to zero (see Fig. 9B). This means that in 1997, the inflow and outflow exert little influence on the temperature when water is withdrawn from the surface outlet. In the summer of this year, the inflow temperature is about 2°C lower than the surface temperature, thus the inflow will insert in a water layer about 5 m below the water surface. The surface outlet is just located between 414.1 and 412.1 m, almost the same depth where the inflow inserts. As a consequence, the released water comes directly from the inflow, i.e. a shortcut exists between the inflow and the outflow. This usually occurs when inflow temperature is
much lower than surface water in reservoirs and when wind speed is high. When warmer surface water is replaced by colder water from deeper layers, wind speed, particularly a stronger one, is capable to produce deeper mixing of the water column, and the temperature of surface water decreases further down. The situation in Sau is different, as the inflow water is only by up to two degrees lower than the reservoir water, but usually is higher. To investigate how far wind is responsible for mixing under the conditions characterizing Sau Reservoir, we run the model by multiplying wind speed of the year 1997 by a factor of 3.0. Simulated temperature profile is shown in Fig. 8A, where a deepened thermocline in comparison with the original wind speed can be seen. In this case, the inflow with high temperature contributes to warming the water in the epilimnion. With the same modification of wind speed but without inflow and outflow, the simulated temperature distribution is given in Fig. 8B: epilimnion temperatures are evidently lower than those in Fig. 8A. This means that the shortcut between the near-surface inflow and surface outlet is broken by mixing and the inflow obviously warms the water column.
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4.2. Effect of throughflow on thermal stratification In 1995, reduction of the inflow largely increased the theoretical residence time of water in Sau Reservoir. Using an average inflow and outflow during the whole year, the residence times are 118, 43 and 84 days, and for the April to July period of stratification development 124, 53 and 105 days, respectively, in 1995, 1996, 1997. As the speed pattern was different in 1995 from those in 1996 and 1997, a direct comparison between 1995 and the other 2 years is not helpful to understand the effect of flow on thermal structure. To investigate the effect of flow, we reduce both inflow and outflow simultaneously by a factor of 0.5 and 0.0, i.e. the half amounts and no inflow and no outflow at all during the whole year. As a result, residence time increased twice and to infinity, respectively. Simulations with 1997 data, assuming the middle outlet, are shown in Fig. 9A,B. When without inflow and outflow, the thermocline is very shallow and below the thermocline temperature decreases slowly (Fig. 9B). This is due to the relatively weak wind speeds during this summer, the average speed from July to August is 1.18 m s − 1 (see also Fig. 2). According to these two figures as well as to Fig. 3C, it is found that the thermocline is shifted up with reduction in inflow and outflow but bottom temperatures are
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identical and surface temperature just slightly higher in the longer retention time case. Remarkable in Fig. 9B are the practically constant temperatures in the lower strata. What is not seen in the simulation results is that the actual temperature differences between the surface and the bottom during the period of maximum surface temperatures (late July–early August) decrease with the decreasing theoretical retention time: from 18°C in 1995 to 17.3°C in 1996 and 17°C in 1997. The difference of the observed surface temperatures between the 3 years is much higher: 28.7, 24.7 and 23.9°C, respectively, in 1995, 1996 and 1997. Observed bottom temperature at the time of maximum surface temperatures systematically decrease with the prolongation of retention time. The above results are consistent with the empirical and DYRESM-based conclusions by Straskraba (1998) as demonstrated in Fig. 10. The figure demonstrates the position of Sau Reservoir (about 46°N) in this respect, as compared with the observed trends for a reservoir in Texas (about 30°N), for different reservoirs in the Czech Republic and Germany (latitude 50–53°N) and calculated dependencies for R& ´ımov Reservoir, Czech Republic at 50°N and Canning Reservoir in Australia (34°S). Evidently the theoretical residence time is a very important variable of thermal stratification. The relationship seems to be asymptotic, but parameters of this relationship are largely
Fig. 8. The temperature distributions of 1997, outflow from the surface outlet (at 51 m above the bottom) and a wind speed increased by a factor of 3: (A) with inflow and outflow; (B) without inflow and outflow.
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Fig. 9. The effects of inflow and withdrawal rates on temperature distribution in 1997. (A) Half of normal inflow and outflow with the middle outlet; (B) No inflow and no outflow; (C) half of normal inflow and outflow and the bottom outlet. The arrows indicate outlet location.
modified by geographic situation and associated variables. In the same geographical situation river temperature, wind speed and reservoir size as well
as optical qualities of water and other variables cause spreading along the general trend. DYRESM treats inflow as a two dimensional movement consisting of plunging and intrusion, which are both closely related to the river temperature (in addition to flow rates, stratification and other variables). When the river temperature is close to the metalimnetic temperature, river water can directly erode the thermocline. If river temperature is significantly colder or warmer so that the river inserts into the hypolimnion or epilimnion, the effect of inflow on thermal stratification is combined with the effect of outlet elevation. In Sau Reservoir, the inflow temperature is higher or lower than surface temperature in different periods of spring but usually two degrees lower in the summer (see Fig. 5). In normal years such as 1996 and 1997, the inflow temperature is always higher than the outflow temperature before September. This means that inflow is a significant heat source to the epilimnion of the reservoir. To further support this deduction, we run the model with half inflow and half outflow as well as the bottom outlet. The simulation result is shown in Fig. 9C, the thermocline is deepened to 20 m above the water bottom, but shifting up against the simulation with the normal inflow and outflow and with the same outlet shown in Fig. 7A. Therefore, inflow with high temperature indeed exerts significant influence on the thermal stratification. Because of this, an obvious stratification in Sau Reservoir usually appears in the middle of June and lasts to September when the inflow temperature became lower than the outflow temperature. With the decrease in inflow temperature, inflow contributes to cooling the surface water and then begins to erode largely the thermocline. When both inflow and outflow reduce, it can be expected that the thermocline could be shifted up in the summer.
4.3. Effect of light extinction coefficient on thermal stratification Light absorption of water is an internal factor to influence the heat distribution. In most of hydrodynamic or water quality models, it is usually assumed that the short wave radiation decays
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exponentially through the water column and long wave radiation is absorbed very quickly into the surface layer which would be around 1 m in depth. By running DYRESM at different level of light extinction coefficient, and confronting the results of observations from different localities Straskraba (1998) found that the light attenuation can exert a profound effect on thermal stratification. In the version of DYRESM we are using here, the light extinction coefficient has to be set as a single constant for a simulation period. In all the simulations shown in Figs. 3 – 9, the mean extinction coefficients are applied. The light extinction coefficient is calculated from the measured Secchi depths that varied with time. For example, in 1996, the value is about 0.5 in the winter and the early spring and the maximal value of 2.0 is found in the summer. In order to detect the effect of light absorption of water on temperature stratification in Sau Reservoir, DYRESM is run at two levels of this parameter: 0.5 and 1.5 for the data of 1996. The temperature distributions are shown in Fig. 11.A and B. No obvious change in thermocline is found, yet the isolines of 24, 22, 20° are deepened when light extinction coefficient
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is reduced to 0.5. The fact that the differences due to light extinction are not high in Sau Reservoir can be explained by the previous statement that the inflow is the main factor to control the temperature distribution in this reservoir so that the effect of light absorption is minimized. At each of the two levels of light extinction coefficient, the model is performed under two different throughflows, i.e., reducing the inflow and outflow to the half amount and to zero, the simulations are shown in Fig. 11C–F, respectively. Only without inflow and outflow, the thermal stratification at the lower light extinction coefficient is markedly different from that at the high light extinction coefficient. In Sau Reservoir, therefore, the thermal structure is mainly controlled by the inflow. A significant light absorption dependence of thermal stratification was reported by Straskraba (1998) for Slapy Reservoir, a middle reservoir among a cascade of reservoirs. The inflow to Slapy Reservoir, released from the upstream reservoir, has a relatively low temperature, inserting into the deep water layers. Thus, the effect of light absorption is easily detected in Slapy Reservoir.
Fig. 10. The effect of theoretical retention time on stratification conditions in different reservoirs. The degree of stratification is expressed by a very simple measure, temperature difference between the surface and the bottom, observed during the time of maximum surface temperatures. Dots: 3 years in Sau Reservoir. (1) Curve derived from observations in Czech Republic and Sachsian (Germany) reservoirs (Straskraba et al., 1993). (2) Curve derived from applying DYRESM to Rimov Reservoir, Czech Republic and modifying only RT. (3) Curve derived from observations in Canyon lake, Texas, by Groeger and Tietjen (in press). (4) Curve derived from applying DYRESM to Canning Reservoir, Australia , supplied by Hocking.
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Fig. 11. The effect of light extinction coefficient (LEC) on temperature distributions in 1996. (A) LEC = 0.5 with normal inflow and outflow; (B) LEC = 1.5, with normal inflow and outflow. (C) LEC = 0.5 with half amount of both inflow and outflow. (D) LEC = 1.5 with half amount of both inflow and outflow; (E) LEC =0.5 without inflow and outflow; (F) LEC = 1.5 without inflow and outflow. In all cases, the water is released from the middle outlet.
5. Conclusions In conclusion, the application of DYRESM to Sau Reservoir shows that the model can accu-
rately describe physical processes in reservoirs if the data are accurately given. In this reservoir, the simulations demonstrate that the thermal structure is mainly controlled by inflow, for the inflow
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with high temperature together with its relative strength (theoretical retention time around 100 days) composes the main heat source. By running the model under different situations, the simulations confirm that the inflows, outflows and their patterns are the main external factors to affect the hydrodynamics of reservoirs. As inflows may have significantly different temperature from the reservoir water and the outflows can be released from the outlet located at different depth, these two factors can strongly modify hydrodynamic processes in a reservoir. As an internal factor, light attenuation of water may bring a significant change to the epilimnetic temperature of a reservoir. At the present stage, however, we have to set a constant light extinct coefficient for the whole simulation period, although light extinction coefficient is continuously changing. We suggest that a variable parameter of light extinction need to replace the constant one.
Acknowledgements The limnological study of Sau is part of a long term project founded by Aigues Ter-Liobregat Water Supply Facility (ATLL) to which we gratefully recognize its collaboration. This study benefits of the projects of the Spanish Interministerial Commission of Science and Technology (CICYT) IN96-141, HID96-1374-CO2-O1 and O2 (Polytechnic University of Catalonia and the University of Barcelona, respectively). MC benefits of UB doctorate grant and JCG of the CPI-20 grant for a collaboration research grant in the UB. The contribution of the Comissio Interministerial de Ciencia i Tecnologia (CIRIT) 1995SGR is greatly appreciated. Support from the Grant Agency of the Academy of Sciences of the Czech Republic No. A6007610 and Grant No. VS96086 by the Ministry of Education, Youth and Sports of the Czech Republic is appreciated. A travel support from Environmental Assessment Centre (EIA) of Finland to BP Han is acknowledged.
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Environmental Effects. American Geophysical Union, Washington, DC, Geophys. Monogr. 17, 517 – 535 Straskraba, M., Tundisi, J.G., Duncan, A., 1993. State-of-theart of resevoir limnology and water quality management. In: Straskraba, M., Tundisi, J.G., Duncan, A. (Eds.), Comparitive Resevoir Limnology and Water Quality Management. Kluwer Academic Publishers, pp. 213 – 288. Straskraba, M., 1998. Coupling of hydrobiology and hydrodynamics: lakes and reservoirs. In: Imberger, J. (Ed.), Physical Processes in Lakes and Reservoirs, Coastal and Estuarine Studies, American Geophysical Union, pp. 601 – 622. Vidal, C., Om Tubau, J., 1993. The eutrophication processes in Sau In Sau Reservoir (NE Spain): a long term study. Verh. Internat. Verein. Limnol. 25, 1247 – 1256. Virtanen, M., Koponen, J., Holstein, S., Nenonen, O., Kinnunen, K., 1994. Principles for calculation of transport and water quality in strongly regulated reservoirs. Ecol. Model. 74, 103 – 123. Watanabe, Y., 1992. Effects of thermal stratification on trophic linkages among plankton communities in eutrophic lakes. Arch Hydrobiol. Beih Ergebn. Limnol. 35, 1 – 12.
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The thermal structure of Sau Reservoir (NE: Spain): a simulation approach Bo-Ping Han a,b, Joan Armengol a,*, Juan Carlos Garcia a, Marta Comerma a, Montse Roura a,c, Josep Dolz c, Milan Straskraba d a
Department Ecologia, Facultat de Biologia, Uni6ersitat de Barcelona, A6. Diagonal, 645, 08028 Barcelona, Spain b Institute of Hydrobiology, Jinan Uni6ersity, Guangzhou, 510632, People’s Republic of China c Department Enginyeria Hidraulica, Maritima i Ambiental, Escola Tecnica Superior d’Enginyers de Camins, Canals Ports, Uni6ersitat Politecnica de Catalunya, Catalunya, Spain d Biomathematical Laboratory, Academy of Sciences of the Czech Republic and Faculty of Biological Science, Uni6ersity of South Bohemia, Branisˇo6ska´ 31, 370 05 C& eske´ Budeˇjo6ice, Czech Republic Accepted 29 June 1999
Abstract In this study, a 1D model of reservoir hydrodynamics DYRESM has been applied to Sau Reservoir, a river valley reservoir in the North-Eastern Spain. Simulation is undertaken for 3 years (1995 – 1997). Meteorological input data measured at the dam are only available from May of 1997. In this case the simulation results fit measured temperatures very well. In the remaining periods, some meteorological data (radiation, wind and rainfall) were obtained from two nearby stations. Simulated temperature distribution in 1996 is close to the observed one. In 1995, however, the simulated result is far from the observed data. Inflows , outflow and local meteorological events such as storms and gusts of wind seem to be responsible for the differences. By changing some parameters, the effects of flow, light extinction coefficient and outlet elevation on thermal stratification are investigated. Simulations demonstrate that the inflow with high temperature is the main factor controlling the thermal structure in Sau Reservoir and demonstrate that the effect of residence time on thermal stratification is manifested mainly by the changes in the depth of thermocline. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Thermal stratification; Numerical simulation; Sau Reservoir
1. Introduction Most deep temperate and subtropical lakes develop thermal stratification every summer. The * Corresponding author. Fax: +34-3-4111438. E-mail address: [email protected] (J. Armengol)
stratified water column is usually segregated into epi-, meta-and hypolimnion by the density differences produced via warming of surface water. The stratification strongly affects chemical and biological gradients in vertical direction (Reynolds, 1992; Watanabe, 1992). The stratification is mainly affected by external forces such as heat
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input, wind and internal variables such as lake morphometry and light extinction coefficient of water. Reservoirs, man-make lakes, usually are built to store water for later use, water supply, flood control or power generation. Inflow and withdrawal lead to decrease in water retention time of reservoir comparing with a lake of the same morphometry (Ford, 1990). For this reason, reservoirs are usually considered as water bodies intermediate between rivers and lakes, sharing some characteristics with both. A deep and large reservoir may behave more similarly to a lake or to a river in dependence mainly on residence time. The degree of stratification varies also with inflow temperature (Straskraba, 1973; Riera et al., 1992; Straskraba et al., 1993; Armengol et al., 1994; Hocking and Straskraba, 1994). Another characteristic of reservoirs that differs from that of lakes results from the location of outflow. In a natural lake, water usually overflows from water surface. In a reservoir, the outflow is released from one fixed outlet or several selective outlets at different depths. Therefore, inflow with temperature different from that of the surface of the reservoir and outflow at different depths appear to be the main sources of the difference in hydrodynamics between a reservoir and a lake. Usually, inflow temperature is lower than surface temperature of reservoir water. The heavy water first plunges to some depth and then insert into reservoir water at a certain level. As a result, the inflow causes thermocline erosion to a great degree by entraining water in the main reservoir body (the transitional and lacustrine zones). Inflow is one of the main sources of nutrients and other chemical material entering a reservoir, its intrusion can to a great degree influence the vertical gradient of nutrients (Armengol et al., 1986; Vidal and Om Tubau, 1993; Koma´rkova´ and Hejzlar, 1996). Inflow temperature determines mainly at which layers the inflow inserts into the reservoir. Thus, recognition of temperature distribution in the reservoirs is at the base of understanding the performance and functioning of reservoir ecosystems (Owens et al., 1986; Kimmel et al., 1990). As heat input and flow pattern vary daily, measured data are not enough to recognize and understand the effect of each factor mentioned above on the
heat and water exchange processes and the resulting thermal structure in reservoirs. Numerical hydrodynamic models appear to be helpful by expressing physical processes. A number of models contributed to this goal (Stefan et al., 1982; Orlob, 1983; French, 1985; Anonymous, 1986; Price et al., 1986; Martin, 1988; Virtanen et al., 1994; Herman, 1996). Among them, DYRESM (Imberger and Patterson, 1981) is a one dimensional model which has been widely verified. In this study, it is applied to Sau Reservoir, located in the North-Eastern Spain. We first confront the simulation results with the observed data to verify the validity of the numerical model. By changing some parameters such as outlet depth, flow and its pattern, and light extinction coefficient, their possible effects on thermal stratification in Sau Reservoir has been investigated. Basing on these simulations, we attempt to testify and discuss some early conclusions about reservoir hydrodynamics by sensitivity analysis.
2. Materials and methods Sau Reservoir is the first one among a cascade of reservoirs situated in the central part of the river Ter and was first filled in 1963. Fig. 1 and Table 1 outline its mophometry and main hydraulic features. In this reservoir, three selective outlets are available, located between 383.1– 386.1, 397.58–400.58 and 412.06–415.06m a.s.l., respectively. Correspondingly, we refer them as bottom outlet, middle outlet and surface outlet. A detailed description of Sau Reservoir is given by Vidal and Om Tubau (1993). Inflow and outflow input data were measured from 1995 to 1997, daily inflow temperature was obtained by interpolating linearly the data measured once a month. Meteorological data on radiation, wind speed, air temperature and rainfall are available only after May 20, 1997 when a meteorological station was established on Sau Reservoir. From January 1995 to July 20 1995, the meteorological data are from a meteorological station at Caldes de Montbui 50 km away from Sau Reservoir. From July 21 of 1995 to December 31 of 1996, the data are from a meteorological station at Perafita 30 km away
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from the reservoir. The long wave radiation is calculated on the basis of cloudiness. Cloudiness data in simulation were calculated from the mea-
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sured short wave radiation data. Assuming no cloud during the maximal radiation, the cloudiness for each day is obtained as the relative difference between the observed daily radiation and the corresponding short wave maximal radiation obtained as the envelope of the highest values measured.
2.1. The one dimensional model
Fig. 1. Catchment and morphometry of Sau Reservoir. The temperature is measured at sampling point 1. Table 1 Main mophmetry characteristics of Sau Reservoir after Vidal and Om Tubau (1993) Variable
Value
Latitude Catchment area Max. volume Max. area Max. depth Max. length Bottom elevation Basin width at crest Drag coefficient of the stream bed Slope of the stream bed Stream half angle
46°46%N 4°51%E 1.79×109 m2 0.1486×109 m3 5.8×106 m2 75 m 1.8×104 m 362 m a.s.l. 260 m 0.016 3.85×10−3 75°
DYRESM was developed in the Water Research Center of the University of Western Australia. An extensive description of the model has been given in Imberger and Patterson (1981), Hocking et al. (1988), Hocking and Patterson (1991) and Casamitjana and Schladow (1993). In this model, physical processes of heat exchange across water surface, heat distribution by mixing based on a turbulent energy budget formulation which includes the effects of convective overturn, stirring by the wind and shear production at the interface between the epilimnion and hypolimnion, are modeled. Turbulent diffusion is modeled by the solution of the diffusion equation with a variable coefficient determined from energy released by the plunging of streams, wind induced seiching, and stratification. The inflow process is divided into three parts. As the stream enters the reservoir it pushes the stagnant reservoir water ahead of itself until buoyancy forces dominate, then either flows over water surface or plunges beneath the surface. Once submerged, the stream will flow down the river valley and entrain reservoir water. The modeling of withdrawal enables selection among two assumptions: point sink and line sink. Each of the physical processes is modeled separately using parameterization based on theory, experiments and field studies and consequently, the model is generally applicable without calibration.
3. Simulation and results Daily averaged wind speed from 1995 to 1997 is plotted in Fig. 2. The corresponding simulation results for the 3 years and the temperature measured at sampling point 1 near the dam are shown
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Fig. 2. Wind speed used in simulations. Only the data from May 20 1997 were measured at Sau Reservoir near sampling point 1. The data from January 1995 to July 20 1995 are from a meteorological station at Caldes de Montbui 50 km away from Sau Reservoir. The data from July 21 of 1995 to May 19 of 1997 are from a meteorological station at Perafita 30 km away from Sau Reservoir.
in Fig. 3. In comparison with the measured data, the best fit is from 1997. A comparison of temperature profiles between the observations and simulations on several individual Julian days is illustrated in Fig. 4. On each of these days, the simulated metalimnion covers the same depth range as the observed, the simulated temperatures in hypolimnion is almost identical with the observed. On Julian days 195 and 245, simulated surface temperature is about 1°C lower than the
observation, and on Julian day 282, about half a degree lower than the observation. On Julian day 309, the simulated epilimnetic temperature is about one degree lower than the observed. Differences between the simulations and the observations probably result from measurements of the temperature profiles being done from 10:00 am to 3:00 pm and the simulated temperature represents a daily average. The temperature measured in daytime near noon can be expected to become
B.-P. Han et al. / Ecological Modelling 125 (2000) 109–122 Fig. 3. Comparison of temperature isolines between simulations (the right column) and observations (the left column). In 1995, the centerline of the outlet is at 22 m above the bottom. In 1996 and 1997, the centerline of the outlet is at about 37 m above the bottom. The arrows indicate outlet location.
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higher than the daily mean temperature. Particularly in the autumn (Julian day 309), when a relatively strong wind mixes the water column well, the daily mean temperature in epilimnion can be expected to be lower than the simulated temperature. On all the 4 days mentioned above the change in metalimnetic temperature is sharper in the simulation than in the observed profiles. In Fig. 3 this results in individual temperature isolines being more clearly separated from each other in the observed than in the simulated series. In DYRESM, heat distributions in the epilimnion and hypolimnion are simulated by different algorithms. In the epilimnion, the model simulates convective overturn, stirring and shear production. Hypolimnetic temperature distribution is obtained by solving a diffusion equation with an
Fig. 4. Comparison of temperature profiles between the observed and the simulated results on four Julian days: 195, 245, 282, 309 of 1997. Filled circle: the observation, Open circle: the simulation.
eddy diffusivity coefficient. A better fit of numerical models requires to pay attention to energy exchange between epilimnion and hypolimnion that has not theoretically been well solved yet. The 1996 simulation result being generally comparable with the observation implies that the data used from the nearby meteorological station can be a good approximation of the Sau data. Generally speaking, humidity and wind speed as well as its variation with time are dependent of the morphometry and surroundings of the reservoir. The difference between the meteorological data from the nearby station and the actual data can contribute to the differences between the simulation and observation results. However, the simulation of 1995 is far from the observation, 1995 is an extremely dry year. The outflow was released at the bottom outlet, while the outflow was withdrawn from the middle outlet in 1996 and 1997. The observed temperature distribution in 1995 is significantly distinct from that in 1996 and 1997. The water column was much more intensively mixed during the whole year. In the summer, the temperature at the bottom is only one or two degrees lower than at the surface. Generally speaking, stratification of a water column is mainly affected by residence time and modified by the inflow temperature and wind speed. The residence time of water in 1995 is much longer than in 1996 and 1997. The inflow and wind speed seems to be the factors leading to the different temperature distribution. The inflow temperature and the water surface temperature are plotted in Fig. 5. The inflow temperature in 1995 is only a little higher in spring and lower in the summer than in 1996 and 1997, therefore, the inflow temperature can not explain the differences. During the year 1995 the inflow was largely reduced and the reservoir became much shallower (35 m at the deepest point instead of 75 m when the reservoir is fully filled). It is improbable that a 35 m deep water body will be thoroughly mixed by wind during high summer air temperatures. Tentatively, due to the reduction in the reservoir volume, the inflow may introduce a relative high mechanical energy to erode the thermocline and mix it with hypolimnetic water. Another possible explanation could be that there are unusual wind
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deed strong storms during the summer. Unfortunately, data from the meteorological station at the dam of Sau Reservoir were unavailable at that time. To test the effect of wind, we increased the wind speed in the summer: the calculated profiles did not become closer to the observed ones. The temperature distribution depends not only on the daily average wind speed but also on its time and local variation over the reservoir surface. Such exact data are not available. To support the reality of intensive mixing and exclude a possible error in our observed data, the oxygen distribution in 1995 shown in Fig. 6 confirm that the water is indeed well mixed during this year. According to the above comparison between the simulations and the observations, the simulated temperature distribution by DYRESM can be accepted to be a good approximation of actual temperature distribution if the input data are accurately provided.
4. Simulation experiments: sensitivity analysis
4.1. Effect of outlet depth on thermal stratification Fig. 5. The inflow, outflow and water surface temperature at the sampling point over 3 years from 1995 to 1997.
speeds during this year. According to one of the present authors (J.C.G.), this year there were in-
Reservoirs are usually designed to control water release with one fixed outlet or several selective outlets. That the outlet depth can exert an obvious effect on hydrodynamics of reservoirs has
Fig. 6. Oxygen distribution measured at sampling point 1 in 1995.
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Fig. 7. The effect of outlet location on the temperature distribution in 1997. (A) Surface outlet at about 51 m above the bottom; (B) Bottom outlet located at about 22 m above the bottom. The arrows indicate outlet location.
been recognized for a long time (Fontane and Labadie, 1981). To investigate the effect of outlet depth, we simulated temperature distribution of 1997 by changing the outlet depth, but leaving other inputs intact. Fig. 7A,B show the temperature distribution corresponding to the surface and bottom outlets, respectively. It is evident that the thermocline is deeper with the bottom outlet. In the surface outlet and middle outlet simulation, however, the thermocline location is very similar. The temperature distribution simulated with the surface outlet is quite similar to another simulation obtained by reducing both inflow and outflow to zero (see Fig. 9B). This means that in 1997, the inflow and outflow exert little influence on the temperature when water is withdrawn from the surface outlet. In the summer of this year, the inflow temperature is about 2°C lower than the surface temperature, thus the inflow will insert in a water layer about 5 m below the water surface. The surface outlet is just located between 414.1 and 412.1 m, almost the same depth where the inflow inserts. As a consequence, the released water comes directly from the inflow, i.e. a shortcut exists between the inflow and the outflow. This usually occurs when inflow temperature is
much lower than surface water in reservoirs and when wind speed is high. When warmer surface water is replaced by colder water from deeper layers, wind speed, particularly a stronger one, is capable to produce deeper mixing of the water column, and the temperature of surface water decreases further down. The situation in Sau is different, as the inflow water is only by up to two degrees lower than the reservoir water, but usually is higher. To investigate how far wind is responsible for mixing under the conditions characterizing Sau Reservoir, we run the model by multiplying wind speed of the year 1997 by a factor of 3.0. Simulated temperature profile is shown in Fig. 8A, where a deepened thermocline in comparison with the original wind speed can be seen. In this case, the inflow with high temperature contributes to warming the water in the epilimnion. With the same modification of wind speed but without inflow and outflow, the simulated temperature distribution is given in Fig. 8B: epilimnion temperatures are evidently lower than those in Fig. 8A. This means that the shortcut between the near-surface inflow and surface outlet is broken by mixing and the inflow obviously warms the water column.
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4.2. Effect of throughflow on thermal stratification In 1995, reduction of the inflow largely increased the theoretical residence time of water in Sau Reservoir. Using an average inflow and outflow during the whole year, the residence times are 118, 43 and 84 days, and for the April to July period of stratification development 124, 53 and 105 days, respectively, in 1995, 1996, 1997. As the speed pattern was different in 1995 from those in 1996 and 1997, a direct comparison between 1995 and the other 2 years is not helpful to understand the effect of flow on thermal structure. To investigate the effect of flow, we reduce both inflow and outflow simultaneously by a factor of 0.5 and 0.0, i.e. the half amounts and no inflow and no outflow at all during the whole year. As a result, residence time increased twice and to infinity, respectively. Simulations with 1997 data, assuming the middle outlet, are shown in Fig. 9A,B. When without inflow and outflow, the thermocline is very shallow and below the thermocline temperature decreases slowly (Fig. 9B). This is due to the relatively weak wind speeds during this summer, the average speed from July to August is 1.18 m s − 1 (see also Fig. 2). According to these two figures as well as to Fig. 3C, it is found that the thermocline is shifted up with reduction in inflow and outflow but bottom temperatures are
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identical and surface temperature just slightly higher in the longer retention time case. Remarkable in Fig. 9B are the practically constant temperatures in the lower strata. What is not seen in the simulation results is that the actual temperature differences between the surface and the bottom during the period of maximum surface temperatures (late July–early August) decrease with the decreasing theoretical retention time: from 18°C in 1995 to 17.3°C in 1996 and 17°C in 1997. The difference of the observed surface temperatures between the 3 years is much higher: 28.7, 24.7 and 23.9°C, respectively, in 1995, 1996 and 1997. Observed bottom temperature at the time of maximum surface temperatures systematically decrease with the prolongation of retention time. The above results are consistent with the empirical and DYRESM-based conclusions by Straskraba (1998) as demonstrated in Fig. 10. The figure demonstrates the position of Sau Reservoir (about 46°N) in this respect, as compared with the observed trends for a reservoir in Texas (about 30°N), for different reservoirs in the Czech Republic and Germany (latitude 50–53°N) and calculated dependencies for R& ´ımov Reservoir, Czech Republic at 50°N and Canning Reservoir in Australia (34°S). Evidently the theoretical residence time is a very important variable of thermal stratification. The relationship seems to be asymptotic, but parameters of this relationship are largely
Fig. 8. The temperature distributions of 1997, outflow from the surface outlet (at 51 m above the bottom) and a wind speed increased by a factor of 3: (A) with inflow and outflow; (B) without inflow and outflow.
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Fig. 9. The effects of inflow and withdrawal rates on temperature distribution in 1997. (A) Half of normal inflow and outflow with the middle outlet; (B) No inflow and no outflow; (C) half of normal inflow and outflow and the bottom outlet. The arrows indicate outlet location.
modified by geographic situation and associated variables. In the same geographical situation river temperature, wind speed and reservoir size as well
as optical qualities of water and other variables cause spreading along the general trend. DYRESM treats inflow as a two dimensional movement consisting of plunging and intrusion, which are both closely related to the river temperature (in addition to flow rates, stratification and other variables). When the river temperature is close to the metalimnetic temperature, river water can directly erode the thermocline. If river temperature is significantly colder or warmer so that the river inserts into the hypolimnion or epilimnion, the effect of inflow on thermal stratification is combined with the effect of outlet elevation. In Sau Reservoir, the inflow temperature is higher or lower than surface temperature in different periods of spring but usually two degrees lower in the summer (see Fig. 5). In normal years such as 1996 and 1997, the inflow temperature is always higher than the outflow temperature before September. This means that inflow is a significant heat source to the epilimnion of the reservoir. To further support this deduction, we run the model with half inflow and half outflow as well as the bottom outlet. The simulation result is shown in Fig. 9C, the thermocline is deepened to 20 m above the water bottom, but shifting up against the simulation with the normal inflow and outflow and with the same outlet shown in Fig. 7A. Therefore, inflow with high temperature indeed exerts significant influence on the thermal stratification. Because of this, an obvious stratification in Sau Reservoir usually appears in the middle of June and lasts to September when the inflow temperature became lower than the outflow temperature. With the decrease in inflow temperature, inflow contributes to cooling the surface water and then begins to erode largely the thermocline. When both inflow and outflow reduce, it can be expected that the thermocline could be shifted up in the summer.
4.3. Effect of light extinction coefficient on thermal stratification Light absorption of water is an internal factor to influence the heat distribution. In most of hydrodynamic or water quality models, it is usually assumed that the short wave radiation decays
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exponentially through the water column and long wave radiation is absorbed very quickly into the surface layer which would be around 1 m in depth. By running DYRESM at different level of light extinction coefficient, and confronting the results of observations from different localities Straskraba (1998) found that the light attenuation can exert a profound effect on thermal stratification. In the version of DYRESM we are using here, the light extinction coefficient has to be set as a single constant for a simulation period. In all the simulations shown in Figs. 3 – 9, the mean extinction coefficients are applied. The light extinction coefficient is calculated from the measured Secchi depths that varied with time. For example, in 1996, the value is about 0.5 in the winter and the early spring and the maximal value of 2.0 is found in the summer. In order to detect the effect of light absorption of water on temperature stratification in Sau Reservoir, DYRESM is run at two levels of this parameter: 0.5 and 1.5 for the data of 1996. The temperature distributions are shown in Fig. 11.A and B. No obvious change in thermocline is found, yet the isolines of 24, 22, 20° are deepened when light extinction coefficient
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is reduced to 0.5. The fact that the differences due to light extinction are not high in Sau Reservoir can be explained by the previous statement that the inflow is the main factor to control the temperature distribution in this reservoir so that the effect of light absorption is minimized. At each of the two levels of light extinction coefficient, the model is performed under two different throughflows, i.e., reducing the inflow and outflow to the half amount and to zero, the simulations are shown in Fig. 11C–F, respectively. Only without inflow and outflow, the thermal stratification at the lower light extinction coefficient is markedly different from that at the high light extinction coefficient. In Sau Reservoir, therefore, the thermal structure is mainly controlled by the inflow. A significant light absorption dependence of thermal stratification was reported by Straskraba (1998) for Slapy Reservoir, a middle reservoir among a cascade of reservoirs. The inflow to Slapy Reservoir, released from the upstream reservoir, has a relatively low temperature, inserting into the deep water layers. Thus, the effect of light absorption is easily detected in Slapy Reservoir.
Fig. 10. The effect of theoretical retention time on stratification conditions in different reservoirs. The degree of stratification is expressed by a very simple measure, temperature difference between the surface and the bottom, observed during the time of maximum surface temperatures. Dots: 3 years in Sau Reservoir. (1) Curve derived from observations in Czech Republic and Sachsian (Germany) reservoirs (Straskraba et al., 1993). (2) Curve derived from applying DYRESM to Rimov Reservoir, Czech Republic and modifying only RT. (3) Curve derived from observations in Canyon lake, Texas, by Groeger and Tietjen (in press). (4) Curve derived from applying DYRESM to Canning Reservoir, Australia , supplied by Hocking.
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Fig. 11. The effect of light extinction coefficient (LEC) on temperature distributions in 1996. (A) LEC = 0.5 with normal inflow and outflow; (B) LEC = 1.5, with normal inflow and outflow. (C) LEC = 0.5 with half amount of both inflow and outflow. (D) LEC = 1.5 with half amount of both inflow and outflow; (E) LEC =0.5 without inflow and outflow; (F) LEC = 1.5 without inflow and outflow. In all cases, the water is released from the middle outlet.
5. Conclusions In conclusion, the application of DYRESM to Sau Reservoir shows that the model can accu-
rately describe physical processes in reservoirs if the data are accurately given. In this reservoir, the simulations demonstrate that the thermal structure is mainly controlled by inflow, for the inflow
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with high temperature together with its relative strength (theoretical retention time around 100 days) composes the main heat source. By running the model under different situations, the simulations confirm that the inflows, outflows and their patterns are the main external factors to affect the hydrodynamics of reservoirs. As inflows may have significantly different temperature from the reservoir water and the outflows can be released from the outlet located at different depth, these two factors can strongly modify hydrodynamic processes in a reservoir. As an internal factor, light attenuation of water may bring a significant change to the epilimnetic temperature of a reservoir. At the present stage, however, we have to set a constant light extinct coefficient for the whole simulation period, although light extinction coefficient is continuously changing. We suggest that a variable parameter of light extinction need to replace the constant one.
Acknowledgements The limnological study of Sau is part of a long term project founded by Aigues Ter-Liobregat Water Supply Facility (ATLL) to which we gratefully recognize its collaboration. This study benefits of the projects of the Spanish Interministerial Commission of Science and Technology (CICYT) IN96-141, HID96-1374-CO2-O1 and O2 (Polytechnic University of Catalonia and the University of Barcelona, respectively). MC benefits of UB doctorate grant and JCG of the CPI-20 grant for a collaboration research grant in the UB. The contribution of the Comissio Interministerial de Ciencia i Tecnologia (CIRIT) 1995SGR is greatly appreciated. Support from the Grant Agency of the Academy of Sciences of the Czech Republic No. A6007610 and Grant No. VS96086 by the Ministry of Education, Youth and Sports of the Czech Republic is appreciated. A travel support from Environmental Assessment Centre (EIA) of Finland to BP Han is acknowledged.
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