A Hybrid Ensemble Filtering Data Assimilation Scheme based on Coupling Physical and Deep Learning Models

Traditional ensemble filter assimilation is limited by the fact that only a single physical model can be used. The quality of the physical model largely determines the quality of assimilation. In the era of big data, deep learning models have shown strong performance in describing the dynamics of natural systems. In the assimilation framework of ensemble adjustment Kalman filter (EAKF), being able to fully utilize the interpretability of the physical model and the nonlinear modeling capability of the deep learning model, an ensemble adjustment Kalman filter coupling physical and deep learning models (PDL-EAKF) is designed. Firstly, the theoretical derivation and specific implementation steps of the PDL-EAKF method are presented. In the PDL-EAKF framework, the fitting coefficient (FC) is designed to couple the physical and deep learning models. Secondly, to identify the optimal FC, we created a neural network that integrates physical information related to FC into the loss function. The optimal FC is determined by minimizing the value of the loss function. The PDL-EAKF is systematically evaluated on the five-variable coupled climate model (5VCCM). The experimental results demonstrate that the assimilation effect of PDL-EAKF is superior to that of a single model under a long assimilation window and sparse observations, while it can also be achieved with a minimal ensemble size.By plotting the RMSE, frequency distribution histograms, and probability density curves of various variables at different time steps, PDL-EAKF provides better state estimation and demonstrates robust performance.