4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models
This work addresses a practical bottleneck in weather forecasting for meteorologists by enabling easier integration of data assimilation with automatically differentiable models, though it appears incremental as it builds on existing 4D-Var and Gauss-Newton methods.
The authors tackled the difficulty of implementing 4D-Var data assimilation in numerical weather prediction by proposing an alternative Gauss-Newton approximation using automatic differentiation, backpropagation, and Hessian approximation, which they tested on Lorenz-96 and quasi-geostrophic models to show potential for more efficient and accurate operational forecast systems.
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.