A mathematical model of the dynamics of biogeochemical processes in a freshwater lake including oxygen circulation with the development of the thermal bar

In this paper, а nonhydrostatic mathematical model is described for reproducing hydrophysical and biogeochemical processes including the dynamics of dissolved oxygen in a freshwater lake during the thermal bar. The biogeochemical part of the model includes the following variables: oxygen, nitrate, ammonium, phosphate, chlorophyll a, phytoplankton, zooplankton, and small and large detritus. The oxygen supply from the atmosphere to the lake is parameterized taking into account the solubility of oxygen in water and the variability of wind speed on the lake surface. The biochemical dynamics of oxygen are described by processes of photosynthesis, respiration, nitrification, and remineralization. The solution of reaction–convection–diffusion equations of the model is based on the finite volume method with the use of second-order implicit difference schemes in space and time. The results of simulation showed that the highest level of dissolved oxygen was observed in the thermoactive area on the surface of the lake. The concentration of dissolved oxygen was high throughout the entire depth (due to intense mixing of waters with different temperatures) in the vicinity of the thermal bar, isolines of oxygen were qualitatively similar to isotherms in the estuary region. The content of ammonium supplied with the tributary waters was maximum at the confluence of the river, and in the thermoactive area in front of the thermal bar it decreased due to the growth of phytoplankton biomass. Qualitatively, the distribution patterns of nitrates and phosphates in the thermoinert area were identical.