PROBABILITY REGULARITIES OF CATASTROPHIC FLOODS

V. I. Naidenov, V. I. Shveikina, and M. A. Vikhrova

Probability regularities of catastrophic floods are considered. It is shown that the water balance equation for a river basin, with nonlinear dependence of runoff on water content, can be transformed into a stochastic differential equation with multiplicative white noise. A stationary solution of the Fokker—Planck—Kolmogorov equations for the probability density distribution of runoff is found to contain a Pareto component, which explains the appearance of power laws of probability distribution of catastrophic floods. Much attention is given to new mathematical methods for processing observed data on maximum water discharges and levels. It is shown that the power law of probability distribution is an intermediate asymptote and invalid for high moisture content in river basins.

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