Efficient high-dimensional variational data assimilation with machine-learned reduced-order models

TL;DR

This paper introduces a novel approach to data assimilation in geophysical sciences by replacing traditional models with machine-learned reduced-order emulators, significantly accelerating computations while maintaining accuracy.

Contribution

The paper presents a data-driven, differentiable emulator for variational data assimilation, enabling rapid gradient computations and faster forecasts compared to traditional methods.

Findings

Emulator-assisted DA is four orders of magnitude faster than traditional DA.

The approach maintains accuracy comparable to conventional DA methods.

Computations can be performed on a standard workstation instead of high-performance computers.

Abstract

Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior, and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by four orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA).