Deep Learning-Enhanced Background Error Covariance Estimation for Massive-Ensemble Kalman Filter in Sea Surface Temperature Forecasting

Abstract. In recent years, deep learning-based ocean forecasting has become a prominent research focus. However, recent studies often rely on operational ocean forecast systems to provide initial conditions. Operational ocean forecast systems typically use Ensemble Data Assimilation (EDA) to generate these initial conditions. Nonetheless, the high computational cost of numerical models limits the ensemble sizes in EDA, resulting in rank deficiencies in the background error covariance matrix and introducing spurious correlations. To address these challenges and advance the operationalization of deep learning-based ocean forecasting, we propose Deepcov-EnKF, a deep learning-enhanced background error covariance method for massive Ensemble Kalman Filter (EnKF) applications in Sea Surface Temperature (SST) forecasting. The proposed method incorporates a deep learning-based SST forecasting model to generate approximately 5,000 ensemble members. It then directly maps this high-dimensional perturbation set into a background error covariance matrix using a deep neural network. This approach reduces the computational cost of covariance estimation by more than 200-fold compared to conventional techniques. Experimental results demonstrate that the forecasting model can initialize reliable 60-day SST predictions with a Root Mean Square Error (RMSE) of approximately 0.6 °C. Furthermore, assimilation diagnostics reveal that Deepcov-EnKF effectively resolves the spurious correlations in the covariance matrix. The method also exhibits robust stability and outperforms advanced numerical assimilation methods during a 360-day cycling forecasting experiment. This study confirms that Deepcov-EnKF overcomes key limitations of traditional EDA frameworks, significantly enhances the accuracy of SST assimilation, and lays the foundation for high-precision marine forecasting systems.