Reproduction Using the LAKE Model of the Temperature of the Surface of the Earth’s Largest Lakes: an Automatic Calibration System based on MODIS Data

Due to their computational efficiency, one-dimensional models of land reservoirs are used in a wide range of applications from studies of thermohydrodynamics and lake ecology to weather forecasting and assessment of future climate change. This paper presents a system for optimizing well-known one-dimensional LAKE model in terms of reproducing surface temperature using meteorological variables from the ERA5 (ECMWF Reanalysis v.5) reanalysis and satellite data for the lakes Baikal, Balkhash, Great Bear, Superior, Victoria, Winnipeg, Ladoga, Onega, and Tanganyika. Optimization of the background diffusion coefficient (thermal diffusivity) and the absorption coefficient of photosynthetically active radiation in the water column is carried out by the ROPE (RObust Parameter Estimation) method, implemented in the SPOTPY (Statistical Parameter Optimization Tool for PYthon) library. The LAKE reservoir model satisfactorily reproduces the time course of average monthly surface temperature, with standard deviation in the range of 1–2°C after parameter calibration. The coefficients of absorption and background diffusion regulate the vertical distribution of heat in a reservoir; this leads to the effect of “equifinality,” i.e., nonuniqueness of the optimal combination of these parameters. Calibration of the selected parameters makes it possible to effectively reduce the annual amplitude of surface temperature; at the same time, the problem of the model underestimating the surface temperature in summer, caused by the delayed melting of the ice cover in the model, is not solved by varying these parameters. The model systematically overestimates the surface temperature of the tropical lakes Victoria and Tanganyika by 2–3°C. The prospects for the development of this work lie in the elaboration of new physically correct parameterizations of the vertical transfer of momentum and scalar quantities in the meta- and hypolimnion of water bodies. In addition, in the LAKE model it is advisable to revise the model of radiation transfer in snow and ice cover and include the parameters of this model in the calibration system.