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Abstract Physics‐based atmosphere‐land models with prescribed sea surface temperature have notable successes but also biases in their ability to represent atmospheric variability compared to observations. Recently, AI emulators and hybrid models have emerged with the potential to overcome these biases, but still require systematic evaluation against metrics grounded in fundamental atmospheric dynamics. We evaluate the representation of four atmospheric variability benchmarking metrics in a fully data‐driven AI emulator (ACE2‐ERA5) and hybrid model (NeuralGCM). The hybrid model and emulator can capture the spectra of large‐scale tropical waves and extratropical eddy‐mean flow interactions, including critical levels. However, both struggle to capture the timescales associated with quasi‐biennial oscillation (QBO, ∼28 months) and Southern annular mode propagation (∼150 days). These dynamical metrics serve as an initial benchmarking tool to inform AI model development and understand their limitations, which may be essential for out‐of‐distribution applications (e.g., extrapolating to unseen climates). 

Abstract We document the propagation of annular modes—zonally symmetric patterns of variability—in Mars's atmosphere using a reanalysis dataset. Mars's Northern Annular Mode (MNAM) sees anomalies of zonal‐mean zonal wind emerge near the subtropics and migrate poleward with a period of 150 days, similarly to Earth's Southern Annular Mode. The mechanism of propagation involves the interaction of the two leading empirical orthogonal functions that define the MNAM. Moreover, the propagation encourages alternating bands of surface wind stress to migrate polewards with a 150‐day period. In addition, a 150‐day periodicity in anomalous column dust optical depth most likely emerges in response to extrema of the MNAM. The combination of the impact of the MNAM's internally forced periodicity on the surface wind stress and the seasonal cycle may contribute to the inter‐annual variability of global dust events, as suggested by a Monte Carlo estimate that correctly approximates the observed incidence of global dust events. 

Abstract 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 spatiallynon‐localdynamics 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 spatiotemporalemulatorof the zonal wind field. This work underscores the need to integrate ML theory with physics in designing data‐driven algorithms for climate modeling. 

Abstract We discuss the emerging advances and opportunities at the intersection of machine learning (ML) and climate physics, highlighting the use of ML techniques, including supervised, unsupervised, and equation discovery, to accelerate climate knowledge discoveries and simulations. We delineate two distinct yet complementary aspects: (a) ML for climate physics and (b) ML for climate simulations. Although physics-free ML-based models, such as ML-based weather forecasting, have demonstrated success when data are abundant and stationary, the physics knowledge and interpretability of ML models become crucial in the small-data/nonstationary regime to ensure generalizability. Given the absence of observations, the long-term future climate falls into the small-data regime. Therefore, ML for climate physics holds a critical role in addressing the challenges of ML for climate simulations. We emphasize the need for collaboration among climate physics, ML theory, and numerical analysis to achieve reliable ML-based models for climate applications.