Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere

TL;DR

This paper introduces a data-driven stochastic parametrization method for coarsened 2D Euler equations on the sphere, improving simulation accuracy by incorporating high-fidelity data into the coarse model.

Contribution

It presents a novel resolution-independent approach that uses high-fidelity data to enhance coarse fluid simulations without relying on specific discretization assumptions.

Findings

Accurately reproduces kinetic energy spectra from high-fidelity data.

Maintains stable and accurate large-scale dynamics over long simulations.

Effective at significantly coarser resolutions.

Abstract

A resolution-independent data-driven stochastic parametrization method for subgrid-scale processes in coarsened fluid descriptions is proposed. The method enables the inclusion of high-fidelity data into the coarsened flow model, thereby enabling accurate simulations also with the coarser representation. The small-scale parametrization is introduced at the level of the Fourier coefficients of the coarsened numerical solution. It is designed to reproduce the kinetic energy spectra observed in high-fidelity data of the same system. The approach is based on a control feedback term reminiscent of continuous data assimilation. The method relies solely on the availability of high-fidelity data from a statistically steady state. No assumptions are made regarding the adopted discretization method or the selected coarser resolution. The performance of the method is assessed for the two-dimensional Euler equations on the sphere. Applying the method at two significantly coarser resolutions yields good results for the mean and variance of the Fourier coefficients. Stable and accurate large-scale dynamics can be simulated over long integration times.