On the Importance of Learning Non-Local Dynamics for Stable Data-Driven Climate Modeling: A 1D Gravity Wave-QBO Testbed

Model instability remains a core challenge for data-driven parameterizations, especially those developed with supervised algorithms, and rigorous methods to address it are lacking. Here, by integrating machine learning (ML) theory with climate physics, we demonstrate the importance of learning spatially non-local dynamics using a 1D quasi-biennial oscillation model with parameterized gravity waves (GW) as a testbed. While common offline metrics fail to identify shortcomings in learning non-local dynamics, we show that the receptive field (RF) can identify instability a-priori. We find that neural network-based parameterizations, though predicting GW forcings from wind profiles with 99% accuracy, lead to unstable simulations when RFs are too small to capture non-local dynamics. Additionally, we demonstrate that learning non-local dynamics is crucial for the stability of a data-driven spatiotemporal emulator of the zonal wind field. This work underscores the need to integrate ML theory with physics in designing data-driven algorithms for climate modeling.