Modeling long term lake variations by physically based stochastic dynamic models

Several physically based stochastic dynamic models (SDM) are described including year-to-year variations of water volume in terminal and non-terminal lakes, streamflow of lake-fed rivers, and salinity of an inland sea (the Sea of Azov). All of these models are based upon the SDM of water volume of terminal lakes developed by Kritzky and Menkel in 1946 in co-operation with Kolomogorov. Explicit formulae are derived for second order statistical moments of the output processes, including variance, correlation function, spectra, etc., under the assumption that the forcing functions from stationary random sequences. The least-squares prediction problem is solved for both stationary and non-stationary cases. Some of the processes are shown to possess high statistical predictability. Actual predictions are compared with independent observations. Problems for further study are stated.