On the importance of learning non-local dynamics for stable data-driven climate modeling: A 1D gravity wave-QBO testbed

TL;DR

This paper demonstrates that learning non-local dynamics with sufficiently large receptive fields in neural networks is essential for stable and accurate data-driven climate modeling, using a 1D gravity wave-QBO testbed.

Contribution

It introduces the concept of receptive field as a theoretical tool to identify and ensure stability in NN-based climate parameterizations, emphasizing the importance of non-local dynamics.

Findings

Large receptive fields in NNs lead to stable simulations.

Common offline metrics fail to detect instability risks.

Learning non-local dynamics improves model stability and accuracy.

Abstract

Machine learning (ML) techniques, especially neural networks (NNs), have shown promise in learning subgrid-scale parameterizations for climate models. However, a major problem with data-driven parameterizations, particularly those learned with supervised algorithms, is model instability. Current remedies are often ad-hoc and lack a theoretical foundation. Here, we combine ML theory and climate physics to address a source of instability in NN-based parameterization. We demonstrate the importance of learning spatially $\textit{non-local}$ dynamics using a 1D model of the quasi-biennial oscillation (QBO) with gravity wave (GW) parameterization as a testbed. While common offline metrics fail to identify shortcomings in learning non-local dynamics, we show that the concept of receptive field (RF) can identify instability a-priori. We find that NN-based parameterizations that seem to accurately predict GW forcings from wind profiles ($\mathbf{R^2 \approx 0.99}$) cause unstable simulations when RF is too small to capture the non-local dynamics, while NNs of the same size but large-enough RF are stable. We examine three broad classes of architectures, namely convolutional NNs, Fourier neural operators, and fully-connected NNs; the latter two have inherently large RFs. We also demonstrate that learning non-local dynamics is crucial for the stability and accuracy of a data-driven spatiotemporal emulator of the zonal wind field. Given the ubiquity of non-local dynamics in the climate system, we expect the use of effective RF, which can be computed for any NN architecture, to be important for many applications. This work highlights the necessity of integrating ML theory with physics to design and analyze data-driven algorithms for weather and climate modeling.