Methods for approximating the coefficients of a stochastic differential equation and their application to the analysis of intra-annual variability of heat fluxes in the North Atlantic
Abstract:
To analyze heat fluxes, observational data for 1979-2018 were used in the North Atlantic. The spatiotemporal variability of the total heat flux was modeled by a stochastic diffusion process. The coefficients of the stochastic differential equation representing the stochastic process were statistically estimated using nonparametric statistics methods. Previously, the existence and uniqueness of a solution in the strong sense of the stochastic differential equation generated by the constructed diffusion process was proven using the Kolmogorov's criterion. In this work, the coefficients of the equation were approximated in time by trigonometric polynomials, the amplitudes and phases of which depended on the flow values. Using a given series of 40 years in length from 1979 to 2018, spatial maps and time curves were constructed, the results are shown for 1999 as examples, and also studied average monthly heat flow data from 1979 to 2022. Numerical calculations realized on the Lomonosov-2 supercomputer of the Lomonosov Moscow State University.
Keywords:
time series analysis, climatic seasonal cycle, maximum and minimum heat fluxes and temperature values within a climatic year, approximation of the coefficients of a stochastic differential equation
