Abstract
The Caspian Sea (CS) undergoes significant multiscale variations in sea level. Based on empirical evidence (red noise-like behavior) and general ideas about temporal dynamical laws related to massive inertial objects, the observed changes of CS sea level represent a form of non-linear “self-induced” behavior. From this perspective, the mathematical model for this behavior is represented by the Fokker–Planck equation, the solution for which allows calculation of a probability distribution function (PDF) for CS sea level variations. For verification, the PDF is compared with an empirical histogram calculated using palaeohydrological data covering the last millennium. Despite the scatter, there are similarities between the two functions. In particular, both functions have a non-Gaussian asymmetric structure.
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References
Arpe, K., Leroy, S., Lahijani, H., & Khan, V. (2012). Impact of the European Russia drought in 2010 on the Caspian Sea level. Hydrology and Earth Systems Sciences, 16, 19–27. https://doi.org/10.5194/hess-16-19-2012
Berger, A., & Loutre, M. F. (1991). Insolation values for the climate of the last 10 million years. Quaternary Science Review, 10, 297–317. https://doi.org/10.1016/0277-3791(91)90033-Q
Bolgov, M. V., Korobkina, E. A., Trubetskova, M. D., & Filippova, I. A. (2018). River runoff and probabilistic forecast of the Caspian Sea Level. Russian Meteorology and Hydrology, 43, 639–645. https://doi.org/10.3103/S1068373918100023
Chepalyga, A. (2007). The late glacial great flood in the Ponto-Caspian basin. In V. Yanko-Hombach, A. S. Gilbert, N. Panin, & P. M. Dolukhanov (Eds.), The Black Sea flood question: Changes in coastline, climate, and human settlement (pp. 119–148). The Netherlands: Springer
Crucifix, M., de Vernal, A., & Franzke, C. (2017). Centennial climate change: the unknown variability zone. PAGES Magazine, 25(3), 133–134. https://doi.org/10.22498/pages.25.3.133
Franzke, C. L. E., Graves, T., Watkins, N. W., Gramacy, R. B., & Hughes, C. (2012). Robustness of estimators of long-range dependence and self-similarity under non-Gaussianity. Philosophical Transactions of the Royal Society A, 370, 1250–1267. https://doi.org/10.1098/rsta.2011.0349
Frolov, A. V. (1985). Dynamic and stochastic methods of long-term variations in the level of running-water lakes. Moscow: Nauka. ((in Russian)).
Kislov, A. V. (2016). The interpretation of secular Caspian Sea level records during the Holocene. Quaternary International, 409, 39–43. https://doi.org/10.1016/j.quaint.2015.07.026
Kislov, A. V. (2018). Secular Variability of the Caspian Sea level. Russian Meteorology and Hydrology, 43, 679–685. https://doi.org/10.3103/S1068373918100072
Kislov, A., & Toropov, P. (2006). Modeling of variations in river runoff on the East European Plain under different climates of the past. Water Resources, 33, 471–482. https://doi.org/10.1134/S0097807806050010
Kislov, A., & Toropov, P. (2011). Modeling extreme Black Sea and Caspian Sea levels of the past 21,000 years with general circulation models. In I.V. Buynevich, V. Yanko-Hombach, A.S. Gilbert, & R.E. Martin, (Eds)., Geology and Geoarchaeology of the Black Sea region: Beyond the flood hypothesis: Geological Society of America Special Paper 473 (pp. 27–32). https://doi.org/10.1130/2011.2473(02)
Kislov, A., Panin, A. V., & Toropov, P. (2014). Current status and palaeostages of the Caspian Sea as a potential evaluation tool for climate model simulations. Quaternary International, 345, 48–55. https://doi.org/10.1016/j.quaint.2014.05.014
Krijgsman, W., Tesakov, A., Yanina, T., et al. (2019). Quaternary time scales for the Pontocaspian domain: Interbasinal connectivity and faunal evolution. Earth-Science Reviews, 188, 1–40. https://doi.org/10.1016/j.earscirev.2018.10.013
Rodionov, S. N. (1994). Global and regional climate interaction: the Caspian Sea experience (p. 241). Dordrecht: Kluwer Academic Publications
Rychagov, G. I. (1997). Holocene oscillations of the Caspian Sea, and forecasts based on palaeogeographical reconstructions. Quaternary International, 41(42), 167–172. https://doi.org/10.1016/S1040-6182(96)00049-3
Sardeshmukh, P. D., & Sura, P. (2009). Reconciling non-Gaussian climate statistics with linear dynamics. Journal of Climate, 22, 1193–1207. https://doi.org/10.1175/2008JCLI2358.1
Williams, P. D., Alexander, M. J., Barnes, et al. (2017). A census of atmospheric variability from seconds to decades. Geophysical Research Letters, 44, 11201–11211. https://doi.org/10.1002/2017GL075483
Yanina, T. A. (2014). The Ponto-Caspian Region: environmental consequences of climate change during the Late Pleistocene. Quaternary International, 345, 88–99. https://doi.org/10.1016/j.quaint.2014.01.045
Yanko-Hombach, V., & Kislov, A. (2017). Late Pleistocene and Holocene sea-level dynamics in the Caspian and Black Seas: Data synthesis and Paradoxical interpretations. Quaternary International, 465, 63–71. https://doi.org/10.1016/j.quaint.2017.11.030
Acknowledgements
This is a theoretical paper and has no data to archive. This work has received funding from the Russian Science foundation (Grant 19-17-00215) and Lomonosov Moscow State University (Grant AAAA-A16-116032810086-4). Thank you to Chris Brierley (University College London) and two anonymous reviewers for their helpful comments and suggestions.
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Kislov, A. On the Probability Distribution of Sea Level Changes in the Caspian Sea. Pure Appl. Geophys. 177, 5943–5949 (2020). https://doi.org/10.1007/s00024-020-02598-7
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DOI: https://doi.org/10.1007/s00024-020-02598-7