Geophysical flows under location uncertainty, Part II: Quasi-geostrophy and efficient ensemble spreading

TL;DR

This paper develops stochastic geophysical models incorporating location uncertainty, demonstrating through simulations that ensemble approaches improve small-scale structure recovery and model error prediction, aiding data assimilation.

Contribution

It introduces stochastic formulations for QG and SQG models derived from a Boussinesq framework, enhancing uncertainty quantification in geophysical flows.

Findings

Single realizations recover small-scale structures.

Ensemble methods outperform perturbed deterministic models.

High uncertainty quantification improves data assimilation.

Abstract

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion terms and a multiplicative noise contribution. In this paper, simplified geophysical dynamics are derived from a Boussinesq model under location uncertainty. Invoking usual scaling approximations and a moderate influence of the subgrid terms, stochastic formulations are obtained for the stratified Quasi-Geostrophy (QG) and the Surface Quasi-Geostrophy (SQG) models. Based on numerical simulations, benefits of the proposed stochastic formalism are demonstrated. A single realization of models under location uncertainty can restore small-scale structures. An ensemble of realizations further helps to assess model error prediction and outperforms perturbed deterministic models by one order of magnitude. Such a high uncertainty quantification skill is of primary interests for assimilation ensemble methods. MATLAB code examples are available online.