On the Probability Distribution of Sea Level Changes in the Caspian Sea
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Pure and Applied Geophysics
On the Probability Distribution of Sea Level Changes in the Caspian Sea ALEXANDER KISLOV1 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. Keywords: Caspian sea, PDF of a sea level changes, Fokker– Planck equation.
1. Introduction Climate variability exists at all timescales. Atmospheric variability, from seconds to decades, is described, synthesised, and summarised in the special Geophysical Research Letters collection (see Williams et al. 2017). Millennial-scale climate variability, known as the Milankovitch domain, is due to various direct and indirect astronomical influences (Berger and Loutre 1991). However, centennial-scale climate changes, manifested, for example, in the level/area changes of large lakes, ocean level variations, and large mountain glacier and ice sheet dynamics [see the special collection of the Past Global Changes magazine (Crucifix et al. 2017)], are poorly understood. The centennial scale is difficult to study as instrumental observations are often too short, timewise, and it is challenging to reconstruct data
1
Lomonosov Moscow State University, Moscow, Russia. E-mail: [email protected]
with the required temporal resolution. Rhythmic effects of solar forcing and volcanic activity on centennial scales are also little understood. Therefore, the internal dynamics of climate systems should be investigated to understand events on this scale. The dynamics of the Caspian Sea (hereafter referred to as CS) sea level and its area show variations on timescales of years, decades, centuries, millennia, and tens of millennia (Rychagov 1997; Yanina 2014; Krijgsman et al. 2019). The CS (36–47° N, 47–54° E) is the world’s largest lake (Fig. 1). Its mean sea level has varied between - 25 and - 29 m (relative to mean ocean level) over the last * 100 years. Its main water source is the Volga River (80% of inflow), whose catchment area covers a large part of the Eastern European Plain. The water inflow is offset by evaporation over the CS. Its level is also affected by other rivers, precipitation over the sea, and subsurface runoff into the sea; however, their contributions are significantly lower, uncoordinated and irregular. The current CS sea level variability has been investigated extensively, (e.g., Rodionov
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