A Framework for Four-Dimensional Variational Data Assimilation Based on Machine Learning

Abstract

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 [d=Dong.R]network networks (BNN). The framework replaces the traditional physical model with the BNN model for prediction. Moreover, it directly makes use of [d=Dong.R]the ML model obtained from the simulation data the simulation data obtained from the learning model to implement the primary process of 4D-Var, including the realization of [d=Dong.R]the short-term forecast process the model short-term forecast 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.

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

“…Furthermore, Dong et al. (2022) also proved that the auto‐differentiableauto function of the DL framework could provide a simple adjoint model for the 4DVar method. Additionally, in Kotamarthi (2022), the differentiable reduced‐order surrogate model is merged into an optimization strategy where observations of the genuine state are used to enhance the forecast of the surrogate.…”

“…A variety of ML‐based surrogate models have been proposed to replace tangent linear and adjoint models of 4DVar methods (Dong et al., 2022; Kotamarthi, 2022; Nonnenmacher & Greenberg, 2021). These studies generally learn the numerical model by relying on an NN.…”

“…We evaluate our approach using the Lorenz96 physical model (Lorenz, 1996), a system of nonlinear differential equations that models atmospheric chaos and serves as a standard benchmark for DA and ML tasks in Earth science (Brajard et al., 2020; Dong et al., 2022; Hassanzadeh et al., 2019; Huang et al., 2021; Nonnenmacher & Greenberg, 2021). Lorenz96 is a good test case for our purposes, as it can be accurately differentiated automatically by any deep learning (DL) framework.…”

A hybrid data assimilation system based on machine learning

“…3 as a function and build a suitable NN model for simulating the forecast model. Due to the existence of bilinear calculations in the forecast model, the simulation effect of the traditional CNN models deteriorate (Fablet et al, 2018;Dong et al, 2022). Therefore, a forecast model based on a bilinear neural network (FM-BNN) is established in this paper, and its structure is shown in Figure 1, where i represents the ith moment, j represents the jth grid point, x represents the state values, and dx dt represents the derivative.…”

Reconstruction of the Sound Speed Profile in Typical Sea Areas Based on the Single Empirical Orthogonal Function Regression Method

“…Oceanic numerical simulation refers to the process of discretizing and solving seven ocean dynamic equations with the help of boundary conditions and part of ocean observation data to obtain the three-dimensional distribution of hydrological elements. The method can cover the global oceans with a spatial resolution reaching up to 3 km × 3 km [13], and the reliability of the simulated data can be significantly improved by the numerical assimilation technology [14][15][16][17]. Up to now, the simulation data from numerical models have been widely used in the analysis of various physical phenomena in oceanography.…”