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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. 

Abstract We present estimates of gravity wave momentum fluxes calculated from Project Loon superpressure balloon data collected between 2013 and 2021. In total, we analyzed more than 5,000 days of data from balloon flights in the lower stratosphere, flights often over regions or during times of the year without any previous in‐situ observations of gravity waves. Maps of mean momentum fluxes show significant regional variability; we analyze that variability using the statistics of the momentum flux probability distributions for six regions: the Southern Ocean, the Indian Ocean, and the tropical and extratropical Pacific and Atlantic Oceans. The probability distributions are all approximately log‐normal, and using their geometric means and geometric standard deviations we statistically explain the sign and magnitude of regional mean and 99th percentile zonal momentum fluxes and regional momentum flux intermittencies. We study the dependence of the zonal momentum flux on the background zonal wind and argue that the increase of the momentum flux with the wind speed over the Southern Ocean is likely due to a varying combination of both wave sources and filtering. Finally, we show that as the magnitude of the momentum flux increases, the fractional contributions by high‐frequency waves increases, waves which need to be parameterized in large‐scale models of the atmosphere. In particular, the near‐universality of the log‐normal momentum flux probability distribution, and the relation of its statistical moments to the mean momentum flux and intermittency, offer useful checks when evaluating parameterized or resolved gravity waves in models. 

Abstract Breaking atmospheric gravity waves (GWs) in the tropical stratosphere are essential in driving the roughly 2‐year oscillation of zonal winds in this region known as the Quasi‐Biennial Oscillation (QBO). As Global Climate Models (GCM)s are not typically able to directly resolve the spectrum of waves required to drive the QBO, parameterizations are necessary. Such parameterizations often require knowledge of poorly constrained physical parameters. In the case of the spectral gravity parameterization used in this work, these parameters are the total equatorial GW stress and the half width of phase speed distribution. Radiosonde observations are used to obtain the period and amplitude of the QBO, which are compared against values obtained from a GCM. We utilize two established calibration techniques to obtain estimates of the range of plausible parameter values: History matching & Ensemble Kalman Inversion (EKI). History matching is found to reduce the size of the initial range of plausible parameters by a factor of 98%, requiring only 60 model integrations. EKI cannot natively provide any uncertainty quantification but is able to produce a single best estimate of the calibrated values in 25 integrations. When directly comparing the approaches using the Calibrate, Emulate, Sample method to produce a posterior estimate from EKI, history matching produces more compact posteriors with fewer model integrations at lower ensemble sizes compared to EKI; however, these differences become less apparent at higher ensemble sizes. 

Abstract The study presents (a) a 44‐year wintertime climatology of resolved gravity wave (GW) fluxes and forcing in the extratropical stratosphere using ERA5, and (b) their composite evolution around gradual (final warming) and abrupt (sudden warming) transitions in the wintertime circulation, focusing on lateral fluxes. The transformed Eulerian mean equations are leveraged to provide a glimpse of the importance of GW lateral propagation (i.e., horizontal propagation) toward driving the wintertime stratospheric circulation by analyzing the relative contribution of the vertical versus meridional flux dissipation. The relative contribution from lateral propagation is found to be notable, especially in the Austral winter stratosphere where lateral (vertical) momentum flux convergence provides a peak climatological forcing of up to −0.5 (−3.5) m/s/day around 60°S at 40–45 km altitude. Prominent lateral propagation in the wintertime midlatitudes also contributes to the formation of belts of GW activity in both hemispheres. 

Abstract Neural networks (NNs) are increasingly used for data‐driven subgrid‐scale parameterizations in weather and climate models. While NNs are powerful tools for learning complex non‐linear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are (a) data imbalance related to learning rare, often large‐amplitude, samples; (b) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and (c) generalization to other climates, for example, those with different radiative forcings. Here, we examine the performance of methods for addressing these challenges using NN‐based emulators of the Whole Atmosphere Community Climate Model (WACCM) physics‐based gravity wave (GW) parameterizations as a test case. WACCM has complex, state‐of‐the‐art parameterizations for orography‐, convection‐, and front‐driven GWs. Convection‐ and orography‐driven GWs have significant data imbalance due to the absence of convection or orography in most grid points. We address data imbalance using resampling and/or weighted loss functions, enabling the successful emulation of parameterizations for all three sources. We demonstrate that three UQ methods (Bayesian NNs, variational auto‐encoders, and dropouts) provide ensemble spreads that correspond to accuracy during testing, offering criteria for identifying when an NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4 × CO₂). However, their performance is significantly improved by applying transfer learning, for example, re‐training only one layer using ∼1% new data from the warmer climate. The findings of this study offer insights for developing reliable and generalizable data‐driven parameterizations for various processes, including (but not limited to) GWs. 

Abstract. The effects of wave–wave interactions on sudden stratospheric warming formation are investigated using an idealized atmospheric general circulation model, in which tropospheric heating perturbations of zonal wave numbers 1 and 2 are used to produce planetary-scale wave activity. Zonal wave–wave interactions are removed at different vertical extents of the atmosphere in order to examine the sensitivity of stratospheric circulation to local changes in wave–wave interactions. We show that the effects of wave–wave interactions on sudden warming formation, including sudden warming frequencies, are strongly dependent on the wave number of the tropospheric forcing and the vertical levels where wave–wave interactions are removed. Significant changes in sudden warming frequencies are evident when wave–wave interactions are removed even when the lower-stratospheric wave forcing does not change, highlighting the fact that the upper stratosphere is not a passive recipient of wave forcing from below. We find that while wave–wave interactions are required in the troposphere and lower stratosphere to produce displacements when wave number 2 heating is used, both splits and displacements can be produced without wave–wave interactions in the troposphere and lower stratosphere when the model is forced by wave number 1 heating. We suggest that the relative strengths of wave number 1 and 2 vertical wave flux entering the stratosphere largely determine the split and displacement ratios when wave number 2 forcing is used but not wave number 1. 

Abstract The climate model hierarchy encompasses models of varying complexity along different axes, ranging from idealized models that elegantly describe isolated mechanisms to fully coupled Earth system models that aspire to provide useable climate projections. Based on the second Model Hierarchies Workshop, which took place in 2022, we present perspectives on how this field has evolved since the first Model Hierarchies Workshop in 2016. In this period, we have witnessed a dramatic increase in the use of (a) machine learning in climate modeling and (b) climate models to estimate risks and influence decision making under climate change. Here, we discuss the implications of these growing areas of research and how we expect them to become integrated into the model hierarchies framework. 

Abstract Atmospheric predictability from subseasonal to seasonal time scales and climate variability are both influenced critically by gravity waves (GW). The quality of regional and global numerical models relies on thorough understanding of GW dynamics and its interplay with chemistry, precipitation, clouds, and climate across many scales. For the foreseeable future, GWs and many other relevant processes will remain partly unresolved, and models will continue to rely on parameterizations. Recent model intercomparisons and studies show that present-day GW parameterizations do not accurately represent GW processes. These shortcomings introduce uncertainties, among others, in predicting the effects of climate change on important modes of variability. However, the last decade has produced new data and advances in theoretical and numerical developments that promise to improve the situation. This review gives a survey of these developments, discusses the present status of GW parameterizations, and formulates recommendations on how to proceed from there. 

Abstract We present single‐column gravity wave parameterizations (GWPs) that use machine learning to emulate non‐orographic gravity wave (GW) drag and demonstrate their ability to generalize out‐of‐sample. A set of artificial neural networks (ANNs) are trained to emulate the momentum forcing from a conventional GWP in an idealized climate model, given only one view of the annual cycle and one phase of the Quasi‐Biennial Oscillation (QBO). We investigate the sensitivity of offline and online performance to the choice of input variables and complexity of the ANN. When coupled with the model, moderately complex ANNs accurately generate full cycles of the QBO. When the model is forced with enhanced CO₂, its climate response with the ANN matches that generated with the physics‐based GWP. That ANNs can accurately emulate an existing scheme and generalize to new regimes given limited data suggests the potential for developing GWPs from observational estimates of GW momentum transport.