Modelling fluctuations of Caspian Sea levels using a mixed probability distribution

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Abstract

By applying a nonlinear regression root analysis, this paper evaluates the significance of an emerging third stable steady state for the Caspian Sea level. A theoretical probability density function (PDF) is built and fitted to empirical data by mixing three different normal distributions. From this mixed probability distribution, a drift coefficient is obtained for the corresponding diffusive process. A stochastic model is then proposed, which uses the derived drift coefficient. This model demonstrates better performance than that exhibited by polynomial approximations and open possibilities for hydrological risk assessment of systems with several stable steady states.

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