A Four-Dimensional Variational Constrained Neural Network-Based Data Assimilation Method

Advances in data assimilation (DA) methods and the increasing amount of observations have continuously improved the accuracy of initial fields in numerical weather prediction during the last decades. Meanwhile, in order to effectively utilize the rapidly increasing data, Earth scientists must further improve DA methods. Recent studies have introduced machine learning (ML) methods to assist the DA process. In this paper, we explore the potential of a four-dimensional variational (4DVar) constrained neural network (NN) method for accurate DA. Our NN is trained to approximate the solution of the variational problem, thereby avoiding the need for expensive online optimization when generating the initial fields. In the context that the full-field system truths are unavailable, our approach embeds the system's kinetic features described by a series of analysis fields into the NN through a 4DVar-form loss function. Numerical experiments on the Lorenz96 physical model demonstrate that our method can generate better initial fields than most traditional DA methods at a low computational cost, and is robust when assimilating observations with higher error outside of the distributions where it is trained. Furthermore, our NN-based DA model is effective against Lorenz96 physical models with larger variable numbers. Our approach exemplifies how ML methods can be leveraged to improve both the efficiency and accuracy of DA techniques. The use of machine learning (ML) to approximate mappings from data has made a significant impact on numerical weather prediction. In the data assimilation (DA) process, several recent studies have applied ML to accelerate or improve the accuracy of DA output. In this paper, we investigate the potential of employing physical constraints based on four-dimensional variational (4DVar) DA to further enhance the accuracy of an end-to-end ML-based DA model. Our objective is to determine whether the 4DVar-constrained ML model can perform the DA task more efficiently and produce comparable accuracy to the traditional DA methods. We trained our NN-based model without true values as labels and tested it on the Lorenz96 physical model. Several experiments have been applied to verify that the 4DVar-constrained ML model can be used as a potential substitute for the DA process. A physics-informed neural network trained without ground truths can provide accurate initial fields for numerical predictions The system's kinetic features are embedded into the model through our four-dimensional variational form loss function We show on Lorenz96 that the proposed method can be used directly for accurate data assimilation as a low computational cost