VAE-Var: Variational-Autoencoder-Enhanced Variational Assimilation
This addresses the problem of inaccurate state estimation in numerical weather prediction and similar systems for meteorologists and researchers, though it appears incremental as it builds on existing variational assimilation with a machine learning enhancement.
The paper tackles the limitation of traditional variational assimilation methods that assume Gaussian errors in background states, which reduces accuracy, by introducing VAE-Var, a novel algorithm that uses a variational autoencoder to model non-Gaussian background error distributions. Experimental results on low-dimensional chaotic systems show that VAE-Var consistently outperforms traditional methods in accuracy across various observational settings.
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.