Deep learning-enhanced ensemble-based data assimilation for high-dimensional nonlinear dynamical systems

TL;DR

This paper introduces a hybrid ensemble Kalman filter that leverages deep learning to efficiently generate large ensembles, improving data assimilation accuracy in high-dimensional nonlinear systems like weather models.

Contribution

The paper presents a novel hybrid ensemble Kalman filter that integrates deep learning-based surrogates to generate large ensembles, reducing sampling errors without ad-hoc localization.

Findings

Improved initial condition estimation in high-dimensional systems.

Reduced sampling error with deep learning-generated ensembles.

Framework applicable to various ensemble-based data assimilation methods.

Abstract

Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available from the system. Ensemble Kalman filter (EnKF) is a DA algorithm that is widely used in applications involving high-dimensional nonlinear dynamical systems. However, EnKF requires evolving large ensembles of forecasts using the dynamical model of the system. This often becomes computationally intractable, especially when the number of states of the system is very large, e.g., for weather prediction. With small ensembles, the estimated background error covariance matrix in the EnKF algorithm suffers from sampling error, leading to an erroneous estimate of the analysis state (initial condition for the next forecast cycle). In this work, we propose hybrid ensemble Kalman filter (H-EnKF), which is applied to a two-layer quasi-geostrophic flow system as a test case. This framework utilizes a pre-trained deep learning-based data-driven surrogate that inexpensively generates and evolves a large data-driven ensemble of the states of the system to accurately compute the background error covariance matrix with less sampling error. The H-EnKF framework estimates a better initial condition without the need for any ad-hoc localization strategies. H-EnKF can be extended to any ensemble-based DA algorithm, e.g., particle filters, which are currently difficult to use for high dimensional systems.