LoRA-EnVar: Parameter-Efficient Hybrid Ensemble Variational Assimilation for Weather Forecasting

Abstract

Accurate estimation of background error (i.e., forecast error) distribution is critical for effective data assimilation (DA) in numerical weather prediction (NWP). In state-of-the-art operational DA systems, it is common to account for the temporal evolution of background errors by employing hybrid methods, which blend a static climatological covariance with a flow-dependent ensemble-derived component. While effective to some extent, these methods typically assume Gaussian-distributed errors and rely heavily on hand-crafted covariance structures and domain expertise, limiting their ability to capture the complex, non-Gaussian nature of atmospheric dynamics. In this work, we propose LoRA-EnVar, a novel hybrid ensemble variational DA algorithm that integrates low-rank adaptation (LoRA) into a deep generative modeling framework. We first learn a climatological background error distribution using a variational autoencoder (VAE) trained on historical data. To incorporate flow-dependent uncertainty, we introduce LoRA modules that efficiently adapt the learned distribution in response to flow-dependent ensemble perturbations. Our approach supports online finetuning, enabling dynamic updates of the background error distribution without catastrophic forgetting. We validate LoRA-EnVar in high-resolution assimilation settings using the FengWu forecast model and simulated observations from ERA5 reanalysis. Experimental results show that LoRA-EnVar significantly improves assimilation accuracy over models assuming static background error distribution and achieves comparable or better performance than full finetuning while reducing the number of trainable parameters by three orders of magnitude. This demonstrates the potential of parameter-efficient adaptation for scalable, non-Gaussian DA in operational meteorology