DRL-EnVar: an adaptive hybrid ensemble–variational data assimilation method based on deep reinforcement learning

Abstract

Accurate estimation of the background error covariance matrix denoted as B remains a critical challenge in numerical weather prediction (NWP), directly influencing data assimilation (DA) performance and forecast accuracy. Although hybrid ensemble–variational (EnVar) methods combine static and flow-dependent matrices to improve assimilation, their effectiveness is constrained by empirically fixed weights. To address this limitation, we propose DRL-EnVar, an adaptive hybrid EnVar DA method enhanced with deep reinforcement learning. DRL-EnVar integrates deep learning (DL) components, including a novel cyclic convolution module to extract abstract features from data, and employs reinforcement learning (RL) to dynamically optimize hybrid weighting strategies. The system adaptively combines multiple ensemble-based flow-dependent matrices with one or more static matrices to construct a time-varying hybrid matrix B that better reflects real-time background errors. Experimental results demonstrate that DRL-EnVar performs better than the traditional ensemble Kalman filter (EnKF) and hybrid covariance DA (HCDA) methods, especially under sparse observations or transitional changes in state variables. It achieves competitive or superior assimilation accuracy with lower computational cost, and can be flexibly integrated into both three-dimensional variational assimilation (3DVar) and four-dimensional variational assimilation (4DVar) frameworks. Overall, DRL-EnVar offers a novel and efficient approach to adaptive DA, particularly valuable for improving forecast skill during transitional weather regimes.

1. Introduction

Data assimilation (DA) is vital in numerical weather prediction (NWP), climate monitoring, and environmental prediction (Sanz-Alonso et al., 2023). It improves the initial state by combining observations with background information from numerical models, improving the accuracy and reliability of predictions. The background error covariance matrix denoted as B plays a central role in DA, quantifying the uncertainty in the background state, balancing observations and model priors, and directly influencing the performance of DA (Kalman, 1960). In scenarios with sparse observations and transitional weather regimes, accurately estimating B to ensure timely responses and precise evolution of background error information remains a key challenge in high-frequency DA research (James et al., 2022).

Among classical DA methods, three-dimensional variational assimilation (3DVar) is widely used in high-frequency assimilation due to its timeliness (Yokota et al., 2024). In 3DVar, B is typically estimated using the national meteorological center (NMC) method (Parrish and Derber, 1992). However, the NMC-derived B is static, climatological, and isotropic (hereafter denoted as Bs) and fails to capture the flow-dependent characteristics of the atmosphere (Bannister, 2008a, 2008b). To address this drawback, many operational DA systems have adopted the hybrid ensemble–variational (EnVar) assimilation method (Leng et al., 2013), which uses ensemble forecast statistics to derive a flow-dependent error covariance (denoted as Be). A weighted average of Be and Bs produces the hybrid background error covariance Bh, which is incorporated into the 3DVar cost function to improve adaptability to flow variability (Bannister, 2017).

The core of the EnVar method is to combine the strengths of Bs and Be and aims to improve assimilation accuracy while maintaining computational efficiency. However, it faces three main challenges: first, the quality of the flow-dependent B depends on the accuracy of the ensemble forecasts; second, the computational cost is limited by the cost of collecting ensemble samples; third, assimilation performance is sensitive to the choice of hybrid weights.