551.048 Modelling influence of outflow into the Kara-Bogaz-Gol Bay on probability density of the Caspian Sea level fluctuations

Frolov A. V. (Water Problems Institute of the Russian Academy of Sciences)

THE CASPIAN SEA LEVEL, PROBABILITY DENSITY DISTRIBUTION, FOKKER — PLANCK — KOLMOGOROV EQUATION, NONLINEAR HYDROLOGICAL SYSTEM, BIMODALITY.


doi: 10.18698/2309-3684-2016-3-7992


The paper considers long-term fluctuations of the Caspian Sea level as a nonlinear system output with positive and negative feedbacks. The Caspian Sea model with due consideration of an outflow into the Kara-Bogaz-Gol Bay is designed. Density distribution of the sea level is obtained as a solution to the corresponding Fokker — Planck — Kolmogorov equation. The bimodal probability density of the sea level distribution, which meets the endorheic Caspian Sea (if you cut off the Kara-Bogaz-Gol Bay), is shown to turn into the single-mode probability density in case of simultaneous influence of evaporation and seawater outflow into the Kara-Bogaz-Gol Bay on the sea level.


[1] Kritsky S.N., Menkel M.F. Nekotorye polozheniya statisticheskoi teorii kolebanii urovnei estestvennykh vodoemov i ikh primenenie k issledovaniyu rezhima Kaspiiskogo morya [Some statistical theory problems of natural reservoir level fluctuations and their application in the research into the Caspian Sea regime]. Trudy Pervogo soveschaniya po regulirovaniyu stoka [Proceedings of the First meeting on flow regulation]. Moscow, Leningrad, USSR AS Publisher, 1946, pp. 76–93.
[2] Golitsyn G.S., Ratkovich D.Ya., Fortus M.I., Frolov A.V. Vodnye resursy — Water resources, 1998, vol. 25, no. 2, pp. 133–139.
[3] Muzylev S.V., Privalsky V.E., Ratkovich D.Ya. Stoкhasticheskie modeli v inzhenernoi gidrologii [Stochastic models in engineering hydrology]. Moscow, Nauka Publ., 1982, 184 p.
[4] Frolov A.V. Modelirovanie mnogoletnikh kolebanii urovnya Kaspiiskogo morya: teoriya i prilozheniya [Modeling long-term fluctuations of the Caspian Sea level: theory and applications]. Moscow, GEOS Publ., 2003, 171 p.
[5] Semenov V.A., Nikitina N.G., Mokhov I.I. Research Activities in Atmospheric and Oceanic Modelling, 2013, no. 43, pp. 16–17.
[6] Parkhomenko V.P. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modelling and Computational Methods, 2015, no. 1, pp. 94–108.
[7] Arpe K., Bengtsson L., Golitsyn G.S., Mokhov I.I., Semenov V.A., Sporyshev P.V. Geophysical Research Letters, 2000, vol. 27, no. 17, pp. 2693–2696.
[8] Arpe K., Leroy S.A.G., Wetterhall F., Khan V., Hagemann S., Lahijani H. Theoretical and Applied Climatology, 2014, no. 117, pp. 41–60. DOI 10.1007/s00704-013-0937-6
[9] Kritsky S.N., Korenistov D.V., Ratkovich D.Ya. Kolebaniya urovnya Kaspiiskogo morya [The Caspian Sea level fluctuations]. Moscow, Nauka Publ., 1975, 158 p.
[10] Giralt S., Juliа R., Leroy S., Gasse F. Earth and Planetary Science Letters, 2003, vol. 212, no. 1–2, pp. 225–239.
[11] Muzylev S.V. Vodnye resursy — Water resources, 1980, no. 5, pp. 21–40.
[12] Panin G.N. Isparenie i teploobmen Kaspijskogo morya [Evaporation and heat exchange of the Caspian Sea]. Moscow, Nauka Publ., 1987, 89 p.
[13] Khublaryan M.G., Naidenov V.I. O teplovom mehanizme kolebaniy urovnya vodoemov [About the thermal mechanism of the reservoir level fluctuations]. Doklady Akademii Nauk SSSR [Reports of the USSR Academy of Sciences]. 1991, vol. 319, no. 6, pp. 1438–1444.
[14] Golitsyn G.S. Statistika i dinamika prirodnyh processov i yavlenii: metody, instrumentarii, rezultaty [Statistics and dynamics of natural processes and phenomena: methods, tools, results]. Moscow, KRASAND Publ., 2013, 398 p.
[15] Demchenko P.F., Kislov A.V. Stokhasticheskaya dinamika prirodnykh obyektov. Brounovskoe dvizhenie i geofizicheskie primery [Stochastic dynamics of natural objects. Brownian motion and geophysical examples]. Moscow, GEOS Publ., 2010, 189 p.
[16] Dolgonosov B.M. Nelinejnaya dinamika ekologicheskikh i gidrologicheskikh protsessov [Nonlinear dynamics of ecological and hydrological processes]. Moscow, LIBROKOM Publ., 2009, 440 p.
[17] Aleksandrov A.A., Dimitrienko Yu.I. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modelling and Computational Methods, 2014, no. 1, pp. 3–4.
[18] Malinetskiy G.G., Faller D.S. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modelling and Computational Methods, 2014, no. 3 (3), pp. 111–125.
[19] Laio F., Porporato A., Ridolfi L., Tamea S. Nonlinear Processes in Geophysics, 2004, vol. 11, pp. 463–470. DOI 10.5194/npg-11-463-2004.
[20] Salas J.D., Kim H.S., Eykholt R., Burlando P., Green T.R. Nonlinear Processes in Geophysics, 2005, vol. 12, pp. 557–567.
[21] Tikhonov V.I., Mironov M.A. Markovskie protsessy. [Markov processes], Moscow, Sovetskoe radio Publ., 1977, 488 p.
[22] Horsthemke V., Lefevr R. Indutsirovannye shumom perekhody [Noise-induced transitions]. Moscow, Mir Publ., 1987, 400 p.
[23] Frolov A.V. The Caspian Sea as Stochastic Reservoir. Hydrological Models for Environmental Management, Dordrecht, Boston, London, Kluwer Acad. Publishers, 2002, pp. 91–108.


Frolov A. Modelling influence of outflow into the Kara-Bogaz-Gol Bay on probability density of the Caspian Sea level fluctuations. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 79-92



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