Eigenvector decomposition for joint analysis of spatial characteristics in the North Atlantic from 1979 to 2024

The extension of the use of Itô stochastic differential equations (SDEs) for joint analysis of spatio-temporal characteristics in the North Atlantic region, such as sea surface temperature (SST), the sum of sensible and latent heat fluxes, and surface atmospheric pressure for the period between 1979 and 2024 is introduced. Previously, this model was used only for the fluxes. The joint point estimates for the random coefficients of SDEs as multidimensional matrices (the drift vector and the diffusion matrix) are obtained for the entire considered period. The numerical estimations of these values were carried out using high-performance computing equipment with software implementation in Python language using the reanalysis data from the ERA5 database. Developed methods and tools are used for the statistical analysis of the temporal evolution of the coefficients of the Itô equation, analysis of joint and marginal diffusion matrices, their finite-dimensional Karhunen–Loéve’s decomposition into eigenvalues and eigenvectors, determination of their interrelations, temporal trends, as well as dynamic visualization on geographical maps of the region under study. The spatial structure of the eigenvectors of the diffusion matrix, their time evolution and the relationship to jet streams and large-scale heat waves that determine latitudinal heat transfer in the North Atlantic are shown. It is also demonstrated that there is a positive trend in the interannual variability in drift and diffusion coefficients. This indicates a quantitative and qualitative increase in the air–sea interaction and the relationship between heat fluxes and ocean surface temperature. It also makes it possible to quantify the energy exchange between the ocean and atmosphere on an interannual scale. The way of using quantities from a stochastic model to improve the neural network forecasts is also discussed.