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Projecting climate change is a generalization problem: We extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller than model grid size, which have been the main source of model projection uncertainty. Recent machine learning (ML) algorithms hold promise to improve such process representations but tend to extrapolate poorly to climate regimes that they were not trained on. To get the best of the physical and statistical worlds, we propose a framework, termed “climate-invariant” ML, incorporating knowledge of climate processes into ML algorithms, and show that it can maintain high offline accuracy across a wide range of climate conditions and configurations in three distinct atmospheric models. Our results suggest that explicitly incorporating physical knowledge into data-driven models of Earth system processes can improve their consistency, data efficiency, and generalizability across climate regimes.

Attempts to use machine learning to develop atmospheric parameterizations have mainly focused on subgrid effects on temperature and moisture, but subgrid momentum transport is also important in simulations of the atmospheric circulation. Here, we use neural networks to develop a subgrid momentum transport parameterization that learns from coarse‐grained output of a high‐resolution atmospheric simulation in an idealized aquaplanet domain. We show that substantial subgrid momentum transport occurs due to convection. The neural‐network parameterization has skill in predicting momentum fluxes associated with convection, although its skill for subgrid momentum fluxes is lower compared to subgrid energy and moisture fluxes. The parameterization conserves momentum, and when implemented in the same atmospheric model at coarse resolution it leads to stable simulations and tends to reduce wind biases, although it over‐corrects for one configuration tested. Overall, our results show that it is challenging to predict subgrid momentum fluxes and that machine‐learning momentum parameterization gives promising results.

Subgrid processes in global climate models are represented by parameterizations which are a major source of uncertainties in simulations of climate. In recent years, it has been suggested that machine‐learning (ML) parameterizations based on high‐resolution model output data could be superior to traditional parameterizations. Currently, both traditional and ML parameterizations of subgrid processes in the atmosphere are based on a single‐column approach, which only use information from single atmospheric columns. However, single‐column parameterizations might not be ideal since certain atmospheric phenomena, such as organized convective systems, can cross multiple grid boxes and involve slantwise circulations that are not purely vertical. Here we train neural networks (NNs) using non‐local inputs spanning over 3 × 3 columns of inputs. We find that including the non‐local inputs improves the offline prediction of a range of subgrid processes. The improvement is especially notable for subgrid momentum transport and for atmospheric conditions associated with mid‐latitude fronts and convective instability. Using an interpretability method, we find that the NN improvements partly rely on using the horizontal wind divergence, and we further show that including the divergence or vertical velocity as a separate input substantially improves offline performance. However, non‐local winds continue to be useful inputs for parameterizating subgrid momentum transport even when the vertical velocity is included as an input. Overall, our results imply that the use of non‐local variables and the vertical velocity as inputs could improve the performance of ML parameterizations, and the use of these inputs should be tested in online simulations in future work.

A promising approach to improve climate‐model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data‐driven. However, neural networks (NNs) often lead to instabilities and climate drift when coupled to an atmospheric model. Here, we learn an NN parameterization from a high‐resolution atmospheric simulation in an idealized domain by accurately calculating subgrid terms through coarse graining. The NN parameterization has a structure that ensures physical constraints are respected, such as by predicting subgrid fluxes instead of tendencies. The NN parameterization leads to stable simulations that replicate the climate of the high‐resolution simulation with similar accuracy to a successful random‐forest parameterization while needing far less memory. We find that the simulations are stable for different horizontal resolutions and a variety of NN architectures, and that an NN with substantially reduced numerical precision could decrease computational costs without affecting the quality of simulations.