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.

中文翻译：

---

基于四维变分约束神经网络的数据同化方法

过去几十年来，资料同化（DA）方法的进步和观测数量的增加不断提高了数值天气预报中初始场的准确性。同时，为了有效利用迅速增加的数据，地球科学家必须进一步改进DA方法。最近的研究引入了机器学习（ML）方法来辅助 DA 过程。在本文中，我们探索了四维变分 (4DVar) 约束神经网络 (NN) 方法在精确 DA 方面的潜力。我们的神经网络经过训练可以近似求解变分问题，从而避免在生成初始字段时进行昂贵的在线优化。在全场系统真理不可用的情况下，我们的方法通过 4DVar 形式的损失函数将一系列分析场描述的系统动力学特征嵌入到神经网络中。Lorenz96 物理模型上的数值实验表明，我们的方法可以以较低的计算成本生成比大多数传统 DA 方法更好的初始场，并且在同化训练分布之外具有较高误差的观测值时具有鲁棒性。此外，我们基于神经网络的 DA 模型对于具有较大变量数的 Lorenz96 物理模型非常有效。我们的方法举例说明了如何利用 ML 方法来提高 DA 技术的效率和准确性。