On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

TL;DR

This paper examines the saddle formulation in weakly-constrained 4D-VAR data assimilation, identifies issues with divergence, and proposes convergent variants that maintain parallelization benefits, tested on Burgers and Quasi-Geostrophic models.

Contribution

It introduces convergent variants of the saddle formulation for weakly-constrained 4D-VAR, improving stability while preserving parallel computing advantages.

Findings

Proposed variants often outperform original in practical tests.

Variants maintain parallelization benefits.

Performance varies depending on the number of computing processes.

Abstract

This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm are then proposed whose practical performance is compared to that of other formulations. This comparison is conducted on two data assimilation instances (Burgers equation and the Quasi-Geostrophic model), using two different assumptions on parallel computing environment. Because these variants essentially retain the parallelization advantages of the original proposal, they often --- but not always --- perform best, even for moderate numbers of computing processes.