Neural networks (NNs) are increasingly used for data-driven subgrid-scale parameterization in weather and climate models. While NNs are powerful tools for learning complex nonlinear relationships from data, there are several challenges in using them for parameterizations. Three of these challenges are 1) data imbalance related to learning rare (often large-amplitude) samples; 2) uncertainty quantification (UQ) of the predictions to provide an accuracy indicator; and 3) generalization to other climates, e.g., those with higher radiative forcing. 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 the test case. WACCM has complex, state-of-the-art parameterizations for orography-, convection- and frontal-driven GWs. Convection- and orography-driven GWs have significant data imbalance due to the absence of convection or orography in many 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 on when a NN gives inaccurate predictions. Finally, we show that the accuracy of these NNs decreases for a warmer climate (4XCO2). However, the generalization accuracy is significantly improved by applying transfer learning, e.g., 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.

We train random and boosted forests, two machine learning architectures based on regression trees, to emulate a physics-based parameterization of atmospheric gravity wave momentum transport. We compare the forests to a neural network benchmark, evaluating both offline errors and online performance when coupled to an atmospheric model under the present day climate and in 800 and 1200 ppm CO2 global warming scenarios. Offline, the boosted forest exhibits similar skill to the neural network, while the random forest scores significantly lower. Both forest models couple stably to the atmospheric model, and control climate integrations with the boosted forest exhibit lower biases than those with the neural network. Integrations with all three data-driven emulators successfully capture the Quasi-Biennial Oscillation (QBO) and sudden stratospheric warmings, key modes of stratospheric variability, with the boosted forest more accurate than the random forest in replicating their statistics across our range of carbon dioxide perturbations. The boosted forest and neural network capture the sign of the QBO period response to increased CO2, though both struggle with the magnitude of this response under the more extreme 1200 ppm scenario. To investigate the connection between performance in the control climate and the ability to generalize, we use techniques from interpretable machine learning to understand how the data-driven methods use physical information. We leverage this understanding to develop a retraining procedure that improves the coupled performance of the boosted forest in the control climate and under the 800 ppm CO2 scenario.

An intermediate complexity moist General Circulation Model is used to investigate the sensitivity of the Quasi-Biennial Oscillation (QBO) to resolution, diffusion, tropical tropospheric waves, and parameterized gravity waves. Finer horizontal resolution is shown to lead to a shorter period, while finer vertical resolution is shown to lead to a slower period and to an accelerated amplitude in the lowermost stratosphere. More scale-selective diffusion leads to a faster and stronger QBO, while enhancing the sources of tropospheric stationary wave activity leads to a weaker QBO. In terms of parameterized gravity waves, broadening the spectral width of the source function leads to a longer period and a stronger amplitude although the amplitude effect saturates when the half-width exceeds $\sim25$m/s. A stronger gravity wave source stress leads to a faster and stronger QBO, and a higher gravity wave launch level leads to a stronger QBO. All of these sensitivities are shown to result from their impact on the resultant wave-driven momentum torque in the tropical stratosphere. Atmospheric models have struggled to accurately represent the QBO, particularly at moderate resolutions ideal for long climate integrations. In particular, capturing the amplitude and penetration of QBO anomalies into the lower stratosphere (which has been shown to be critical for the tropospheric impacts) has proven a challenge. The results provide a recipe to generate and/or improve the simulation of the QBO in an atmospheric model.

An intermediate complexity moist General Circulation Model is used to investigate the factor(s) controlling the magnitude of the surface impact from Southern Hemisphere springtime ozone depletion. In contrast to previous idealized studies, a model with full radiation is used, which allows focus on the full range of feedbacks between incoming ultraviolet radiation and temperature variations. In addition, the model can be run with a varied representation of the surface, from a zonally uniform aquaplanet to a highly realistic configuration. The model captures the positive Southern Annular Mode response to ozone depletion evident in observations and comprehensive models in December through February. It is shown that while synoptic waves dominate the long-term poleward jet shift, the initial response includes changes in planetary waves which simultaneously moderate the polar cap cooling (i.e., a negative feedback), but also constitute nearly half of the initial momentum flux response that shifts the jet polewards. Enhanced ultraviolet absorption at the surface due to the ozone hole drives an additional negative feedback on the poleward jet shift. The net effect is that stationary waves and surface radiative effects weaken the circulation response to ozone depletion, and also delay the response until summer rather than spring when ozone depletion peaks.

Wave-induced adiabatic mixing in the winter midlatitudes is one of the key processes impacting stratospheric transport. Understanding its strength and structure is vital to understanding the distribution of trace gases and their modulation under a changing climate. age-of-air is often used to understand stratospheric transport, and this study proposes refinements to the vertical age gradient theory of Linz et al. (2021). The theory assumes exchange of air between a well-mixed tropics and a well-mixed extratropics, separated by a transport barrier, quantifying the adiabatic mixing flux across the interface using age-based measures. These assumptions are re-evaluated and a refined framework that includes the effects of meridional tracer gradients is established to quantify the mixing flux. This is achieved, in part, by computing a circulation streamfunction in age-potential temperature coordinates to generate a complete distribution of parcel ages being mixed in the midlatitudes. The streamfunction quantifies the “true” age of parcels mixed between the tropics and the extratropics. Applying the revised theory to an idealized and a comprehensive climate model reveals that ignoring the meridional gradients in age leads to an underestimation of the wave-driven mixing flux. Stronger, and qualitatively similar fluxes are obtained in both models, especially in the lower-to-middle stratosphere. While the meridional span of adiabatic mixing in the two models exhibits some differences, they show that the deep tropical pipe, i.e. latitudes equatorward of 15$^{\circ}$ barely mix with older midlatitude air. The novel age-potential temperature circulation can be used to quantify additional aspects of stratospheric transport.