Modelling the seasonal evolution of temperature in lake Bourget (France)
In 1981, important works including the diversion of the main sewers entering Lake Bourget (one of the largest French alpine lakes) were undertaken in order to restore acceptable water quality standards. A detailed water quality survey will be performed in 1988-89 to complete the data base which already covers ten years. It should help in quantifying the evolution of the lake since the 1981 restoration works. The following activities will be undertaken as part of the survey : measurements within the water column, a study of the bottom sediments, the setting-up of sediment traps and the coupling of Landsat satellite images with measurements performed at some stations at the lake surface. A thermal and biogeochemical (phosphorus, oxygen, nitrogen) model will be used to summarise the information available and to forecast the evolution of water quality and the effect of other restoration measures. This paper reports on the first part of the study : the thermal modelling of Lake Bourget. A one-dimensional, vertical model based on the advection-diffusion equation is used. This equation is solved using a finite difference, semi-implicit method. The resolution grid has 145 layers (1 meter high) and the time step is 3 hours. The heat fluxes at the air-water interface are computed with the three-hourly meteorological data collected at the Chambéry airport station, at the south end of the lake. The formulas are empirical and well established in the literature. The expression for the eddy diffusion coefficients is based on a model of the lake of Geneva (Tassin, 1986). Different equations are used for the epilimnion, metalimnion and hypolimnion. In the epilimnion, the eddy diffusion coefficient expresses, by the Richardson gradients number, the interaction between the shear stress of the wind and the water column stability. It depends on the value of the eddy diffusion in neutral conditions and on a stability function which includes the Richardson number. The vertical profile of the horizontal number. The vertical profile of the horizontal currents is computed following Ekman (1905) and Simons (1981) and is approximated by a gradient which decays exponentially. In the metalimnion and the hypolimnion, the water layer stability is characterised by the Brünt-Väisälä frequency. In the hypolimnion, the eddy diffusion coefficient includes a corrective term, which is a function of depth; this term serves to reduce the dispersion near the bottom of the lake. The thermal model also includes the mixing of the first layers by waves, the vertical advective transport induced by rivers inflows into the lake and by surface water withdrawal, as well as the thermal convection induced by local instabilities of the water column. The eight parameters occurring in the heat flux equations and the eddy diffusion coefficients were estimated using data from 1981. The model has been validated over an 8 years period 1976-1983). Results of the model agree with the observed seasonal and long-term evolutions of temperature in Lake Bourget. The main characteristics of the annual cycle are reproduced : set-up of the thermocline in spring, depth of the epilimnion, thermocline and metalimnion, value of the temperature gradient in the metalimnion, deepening of the thermocline in fall and winter overturn. Significant differences between observed and simulated temperatures occur in the metalimnion and they may be partially explained by internal waves which are dominant features at this level during summer stratification. This kind of mechanism cannot be accounted for in a one-dimensional vertical model. Profiles and values of eddy diffusion coefficients calculated for Lake Bourget show a good agreement with those obtained in other large takes from measurements of temperature or natural isotopes concentrations. In general, the thermal model gives a good account of heat transport mechanisms in Lake Bourget. Accordingly, it provides acceptable dispersion coefficients which can be used to model the distribution of dissolved species in the lake.