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As a part of the block of the active layer of many climatic models, the calculation of soil moisture, runoff during snow melting, slope flow, and dynamic processes in reservoirs is carried out. The development of computer technology (in particular the development of supercomputers) and, as a result, an increase in the resolution of models has led to the fact that the most modern modifications of climate models - the so-called Earth system models (ESM) require an increasingly detailed description of all processes entering the climate system. These include processes occurring in the active layer of the land, including hydrological ones. Little attention is paid to the description of the dynamic processes occurring in surface watercourses. So the authors attempted to create a one-dimensional hydrodynamic model for inclusion in the block of the active layer of models of the Earth's system. To do this, we use the mathematical apparatus of the kinematic wave equation with the corresponding assumptions. Its numerical realization is represented by a finite explicit central-difference scheme. The main difference from analogues is the possibility of including the calculation of water temperature, heat exchange with various media, as well as the flow of biogeochemical processes. The work is being done in Lomonosov Moscow State University and supported by grants RFBR №17-05-01165.