On the Probability Distribution of Sea Level Changes in the Caspian Sea

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.