Skip to main content
Log in

Estimating the probabilities of Caspian level transition from one state into another based on the solution of Kolmogorov’s inverse equation

  • Hydrophysical Processes
  • Published:
Water Resources Aims and scope Submit manuscript

Abstract

Variations in Caspian Sea level are examined by using its water balance equation. Two important problems of modern hydrology are solved. The first problem consists in determining the transition probabilities from a fixed sea level to its upper (lower) equilibrium level, and the second problem involves the determination of the appropriate transition times. Detail solutions of both problems are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Varushchenko, S.I., Izmenenie Rezhima Kaspiiskogo Morya i Besstochnykh Vodoemov v Paleovremeni (Changes in the Level Regime of the Caspian Sea and Other Water Bodies without Outflow in Paleotime), Moscow: Nauka, 1987.

    Google Scholar 

  2. Gardiner, C.W., Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, Berlin: Wiley, 1971.

    Google Scholar 

  3. Kozhevnikova, I.A. and Naidenov, V.I., A Nonlinear Stochastic Model of Caspian Sea Level Variations, Vodn. Resur., 1998, vol. 25, no. 6, pp. 661–670 [Water Resour. (Engl. Transl.), vol. 25, no. 6, pp. 607–616].

    Google Scholar 

  4. Naidenov, V.I., Nelineinaya dinamika poverkhnostnykh vod sushi (Nonliinear Dynamics of Surface Continental Waters), Moscow: Nauka, 2004.

    Google Scholar 

  5. Naidenov, V.I. and Kozhevnikova, I.A., On Nonlinear Variations in Caspian Sea Level and Global Climate, Dokl. Akad. Nauk, 2001, vol. 378, no. 1, pp. 51–57 [Dokl. (Engl. Transl.), vol. 378, no. 1].

    Google Scholar 

  6. Naidenov, V.I. and Krutova, N.M., Studying Long-term Variations in the Caspian Sea with the Use of the Theory of Stochastic Differential Equations, Vodn. Resur., 2002, vol. 2, no. 3, pp. 299–310 [Water Resour. (Engl. Transl.), vol. 2, no. 3, pp. 270–281].

    Google Scholar 

  7. Pontryagin, L.S., Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow: Nauka, 1970.

    Google Scholar 

  8. Seber, G., Linear Regression Analysis, New York: Wiley, 1977.

    Google Scholar 

  9. Khorstkhemke, V. and Lefevr, R., Indutsirovannye shumom perekhody (Noise-Induced Transitions), Moscow: Mir, 1987.

    Google Scholar 

  10. Abarbanel, H.D.I. and Lall, U., Nonlinear Dynamics of the Great Salt Lake: System Identification and Prediction, Clim. Dyn., 1996, vol. 12, pp. 287–305.

    Article  Google Scholar 

  11. Ito, K., Stochastic Differential Equations on Differentiable Manifold, Nagoya Math., 1950, vol. 1, pp. 35–41.

    Google Scholar 

  12. Lall, Ul., Nonlinear Dynamics of the Great Salt Lake: Nonparametric Short-Term Forecasting, Water Resour. Res., 1996, vol. 32, no. 4, pp. 975–982.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © V.I. Shveikina, I.A. Kozhevnikova, 2008, published in Vodnye Resursy, 2008, Vol. 35, No. 1, pp. 45–52.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shveikina, V.I., Kozhevnikova, I.A. Estimating the probabilities of Caspian level transition from one state into another based on the solution of Kolmogorov’s inverse equation. Water Resour 35, 43–50 (2008). https://doi.org/10.1134/S0097807808010053

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0097807808010053

Keywords

Navigation