将 Hessian 近似与反向传播应用于可自动微分数值模型和机器学习模型的 4D-Var
4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models
AI总结：
针对 4D-Var 需维护切线性与伴随模型的问题，本文提出结合反向传播和 Hessian 近似的 Gauss-Newton 近似方法，并在 Lorenz-96 与准地转模型上验证其有效性。
摘要：
通过四维变分（4D-Var）数据同化，用观测约束数值天气预报（NWP）模型在实践中往往难以实现，原因是需要开发并维护基于软件的切线性模型和伴随模型。最常见的 4D-Var 算法之一采用增量更新过程，该过程已被证明是 Gauss-Newton 方法的一种近似。本文表明，当使用支持自动微分的预报模型时，可以通过将误差反向传播与 Hessian 近似相结合，应用一种高效且在某些情况下更准确的 Gauss-Newton 方法替代近似。该方法既可用于在支持自动微分的软件框架内实现的传统数值模型，也可用于基于机器学习（ML）的代理模型。我们在多种 Lorenz-96 和准地转模型上测试了这种新方法。结果表明，在利用专为支持自动微分而设计的天气模型的下一代业务预报系统中，建模、数据同化与新技术有望实现更深度的融合。
英文摘要：
Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear model and adjoint model. One of the most common 4D-Var algorithms uses an incremental update procedure, which has been shown to be an approximation of the Gauss-Newton method. Here we demonstrate that when using a forecast model that supports automatic differentiation, an efficient and in some cases more accurate alternative approximation of the Gauss-Newton method can be applied by combining backpropagation of errors with Hessian approximation. This approach can be used with either a conventional numerical model implemented within a software framework that supports automatic differentiation, or a machine learning (ML) based surrogate model. We test the new approach on a variety of Lorenz-96 and quasi-geostrophic models. The results indicate potential for a deeper integration of modeling, data assimilation, and new technologies in a next-generation of operational forecast systems that leverage weather models designed to support automatic differentiation.
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