VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation

TL;DR

VAE-Var introduces a variational autoencoder-based approach to improve data assimilation by modeling non-Gaussian background error distributions, outperforming traditional Gaussian assumptions in chaotic systems.

Contribution

The paper presents a novel variational assimilation algorithm that incorporates VAE to handle non-Gaussian errors, enhancing accuracy over traditional methods.

Findings

VAE-Var outperforms traditional methods in accuracy.

VAE-Var effectively models non-Gaussian error distributions.

Experimental results confirm improved performance in chaotic systems.

Abstract

Data assimilation refers to a set of algorithms designed to compute the optimal estimate of a system's state by refining the prior prediction (known as background states) using observed data. Variational assimilation methods rely on the maximum likelihood approach to formulate a variational cost, with the optimal state estimate derived by minimizing this cost. Although traditional variational methods have achieved great success and have been widely used in many numerical weather prediction centers, they generally assume Gaussian errors in the background states, which limits the accuracy of these algorithms due to the inherent inaccuracies of this assumption. In this paper, we introduce VAE-Var, a novel variational algorithm that leverages a variational autoencoder (VAE) to model a non-Gaussian estimate of the background error distribution. We theoretically derive the variational cost under the VAE estimation and present the general formulation of VAE-Var; we implement VAE-Var on low-dimensional chaotic systems and demonstrate through experimental results that VAE-Var consistently outperforms traditional variational assimilation methods in terms of accuracy across various observational settings.