Learning to filter: snow data assimilation using a Long Short-Term Memory network

Abstract. Trustworthy estimates of snow water equivalent and snow depth are essential for water resource management in snow-dominated regions. While ensemble-based data assimilation techniques, such as the Ensemble Kalman Filter (EnKF), are commonly used in this context to combine model predictions with observations therefore to improve model performance, these ensemble methods are computationally demanding and thus face significant challenges when integrated into time-sensitive operational workflows. To address this challenge, we present a novel approach for data assimilation in snow hydrology by utilizing Long Short-Term Memory (LSTM) networks. By leveraging data from 7 diverse study sites across the world to train the algorithm on the output of an EnKF, the proposed framework aims to further unlock the use of data assimilation in snow hydrology by balancing computational efficiency and complexity. We found that a LSTM-based data assimilation framework achieves comparable performance to state estimation based on an EnKF in improving open-loop estimates with only a small performance drop in terms of RMSE for snow water equivalent (+6 mm on average) and snow depth (+6 cm), respectively. All but 2 out of 14 site-specific-LSTM configurations improved on the Open Loop estimates. The inclusion of a memory component further enhanced LSTM stability and performance, particularly in situations of data sparsity. When trained on long datasets (25 years), this LSTM data assimilation approach also showed promising spatial transferability, with less than a 20 % reduction in accuracy for snow water equivalent and snow depth estimation. Once trained, the framework is computationally efficient, achieving a 70 % reduction in computational time compared to a parallelized EnKF. Training this new data assimilation approach on data from multiple sites showed that its performance is robust across various climate regimes, during dry and average water-year types, with only a limited drop in performance compared to the EnKF (+6 mm RMSE for SWE and +18 cm RMSE for snow depth). This work paves the way for the use of deep learning for data assimilation in snow hydrology and provides novel insights into efficient, scalable, and less computationally demanding modeling framework for operational applications.