Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise

TL;DR

This paper develops a particle filter-based data assimilation method for high-dimensional geophysical fluid models, utilizing model reduction and stochastic parametrizations to improve efficiency and accuracy in a quasi-geostrophic setting.

Contribution

The authors introduce a novel ensemble data assimilation algorithm combining model reduction, tempering, jittering, and nudging for high-dimensional stochastic fluid models.

Findings

Reduced computational complexity to O(10^4) degrees of freedom.

Analyzed the impact of observational data dimension on assimilation accuracy.

Proved consistency of the stochastic time-stepping scheme.

Abstract

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model reduction, tempering, jittering, and nudging. The methodology is tested on a two-layer quasi-geostrophic model for a $\beta$-plane channel flow with $O(10^6)$ degrees of freedom out of which only a minute fraction are noisily observed. The model is reduced by following the stochastic variational approach for geophysical fluid dynamics introduced in Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parametrisations for unresolved scales. The reduction is substantial: the computations are done only for $O(10^4)$ degrees of freedom. We introduce a stochastic time-stepping scheme for the two-layer model and prove its consistency in time. Then, we analyze the effect of the different procedures (tempering combined with jittering and nudging) on the performance of the data assimilation procedure using the reduced model, as well as how the dimension of the observational data (the number of "weather stations") and the data assimilation step affect the accuracy and uncertainty of the results.