The initial field has a crucial influence on numerical weather prediction (NWP). Data assimilation (DA) is a reliable method to obtain the initial field of the forecast model. At the same time, data are the carriers of information. Observational data are a concrete representation of information. DA is also the process of sorting observation data, during which entropy gradually decreases. Four-dimensional variational assimilation (4D-Var) is the most popular approach. However, due to the complexity of the physical model, the tangent linear and adjoint models, and other processes, the realization of a 4D-Var system is complicated, and the computational efficiency is expensive. Machine learning (ML) is a method of gaining simulation results by training a large amount of data. It achieves remarkable success in various applications, and operational NWP and DA are no exception. In this work, we synthesize insights and techniques from previous studies to design a pure data-driven 4D-Var implementation framework named ML-4DVAR based on the bilinear neural network (BNN). The framework replaces the traditional physical model with the BNN model for prediction. Moreover, it directly makes use of the ML model obtained from the simulation data to implement the primary process of 4D-Var, including the realization of the short-term forecast process and the tangent linear and adjoint models. We test a strong-constraint 4D-Var system with the Lorenz-96 model, and we compared the traditional 4D-Var system with ML-4DVAR. The experimental results demonstrate that the ML-4DVAR framework can achieve better assimilation results and significantly improve computational efficiency.
Keywords: four-dimensional variational assimilation; machine learning; numerical weather prediction; tangent linear and adjoint models.