The dynamical-stochastical mesoscale model of heat and water exchange between the land surface and the atmosphere has been developed to solve the problem of regionalization of hydrological processes (i.e. translating processes across spatial scales). This model describes the dynamics of soil water storage and other components of the soil water balance during the whole year on a regional scale for heterogeneous areas of the steppe and forest steppe zones. It takes into account both physical determinism of hydrological processes and spatial variability of such factors as precipitation, leaf area index, soil water storage, field capacity of soil, snowpack, and soil water conductivity at saturation.
In such approach, the considered heterogeneous area is presented as statistical ensemble of patches for which the above mentioned factors are treated to be random variables with known statistical parameters. In this case the problem consists in analytical or numerical solution of equations describing the dynamics of statistical moments of output variables or their distribution functions. This approach (usually named statistical) has the following advantages compared with other known techniques of regionalization: (1) limited body of data required; (2) lower demand for computer resources; (3) correct operating with nonlinearity and correlation between variables.
The presented model allows us to calculate the temporal variation of statistical characteristics of soil water balance components and soil freezing depth, including their probability functions. The statistical characteristics of the above mentioned factors for heterogeneous regions of the steppe and forest steppe zones of the European part of the Former Soviet Union (FSU) have been studied and systematised. The comparison of simulated and observed data on spatial distribution of water storage in 1-m soil layer and soil freezing depth for the Kiev and Kursk regions has been performed.
Using the developed model, the effect of taking into account the spatial variability of precipitation and land surface parameters when estimating the area averaged values of water balance components and their standard deviations was studied for the above mentioned regions of the forest-steppe zone of the FSU. Herewith, the following results were obtained. (1) Taking into account the spatial variability of the above mentioned factors results in decrease of the area averaged values of evapotranspiration approximately by 6-7% compared with the calculations without accounting for spatial variability. (2) The main contribution to the spatial variability of soil water storage and evapotranspiration (up to 70-75 %) is made by the spatial variability of precipitation. (3) Taking into account the spatial variability of the main land surface parameters changes the results of estimation of the water balance components for the winter- spring period insignificantly.
Analysis of the obtained results shows that the suggested mesoscale model is quite suitable for solving the problems related to the calculation of statistical parameters of spatial distribution of the water balance components for heterogeneous land surfaces of the steppe and forest-steppe zones. The scheme allows one to estimate both the area averaged values and the spatial variability (even a function of distribution) with satisfactory accuracy.