Nonlinear modeling of annual runoff of main rivers in Belarus

The article investigates the problem of mathematical description of long-term fluctuations of river runoff, which is relevant for solving problems of modeling and forecasting in engineering hydrology. The description of the process of runoff fluctuations is based on the stochastic differential equations of Orshtein-Uhlenbeck and Fokker-Planck-Kolmogorov. A technique that makes it possible to apply low-parameter nonlinear dynamic models of river runoff has been developed. Mechanisms of the cyclicity of long-term fluctuations the Pripyat, Neman, West Dvina, Dnieper, and Berezina rivers are described. Comparison of the forecasting results according to the methodology developed by us showed better results than the modeling method using a simple Markov chain. The nonlinear model makes it possible to predict a series that has a correlation function similar to the original series with a shift of 4 or more years, and the Markov model gives good results only for an autocorrelation function with a shift of one year. The simulated series of annual runoff have statistical parameters that differ from the parameters of the original series within +/- 5-10%.