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 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 5000 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 only their geometric means and geometric standard deviations we 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.

The study presents (a) a 44-year wintertime climatology of resolved gravity wave (GW) fluxes and associated zonal 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. The connection between transformed Eulerian mean (TEM) equations and the linear GW pseudomomentum is leveraged to provide a glimpse of the importance of GW lateral propagation toward driving the wintertime stratospheric circulation by analyzing the relative contribution of the vertical vs. meridional flux convergence. 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 60oS at 40-45 km altitude. Prominent lateral propagation in the wintertime midlatitudes also contributes to the formation of a belt of GW activity in both hemispheres.

Breaking atmospheric gravity waves in the tropical stratosphere are essential in driving the roughly two 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 gravity wave 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.

Subgrid-scale processes, such as atmospheric gravity waves, play a pivotal role in shaping the Earth’s climate but cannot be explicitly resolved in climate models due to limitations on resolution. Instead, subgrid-scale parameterizations are used to capture their effects. Recently, machine learning has emerged as a promising approach to learn parameterizations. In this study, we explore uncertainties associated with a machine learning parameterization for atmospheric gravity waves. Focusing on the uncertainties in the training process (parametric uncertainty), we use an ensemble of neural networks to emulate an existing gravity wave parameterization. We estimate both offline uncertainties in raw neural network output and online uncertainties in climate model output, after the neural networks are coupled. We find that online parametric uncertainty contributes a significant source of uncertainty in climate model output that must be considered when introducing neural network parameterizations. This uncertainty quantification provides valuable insights into the reliability and robustness of machine learning-based gravity wave parameterizations, thus advancing our understanding of their potential applications in climate modeling.

The drag due to breaking atmospheric gravity waves plays a leading order role in driving the middle atmosphere circulation, but as their horizontal wavelength ranges from tens to thousands of kilometers, part of their spectrum must be parameterized in climate models. Gravity wave parameterizations prescribe a source spectrum of waves in the lower atmosphere and allow these to propagate upwards until they either dissipate or break, where they deposit drag on the large-scale flow. These parameterizations are a source of uncertainty in climate modeling which is generally not quantified. Here, we explore the uncertainty associated with a non-orographic gravity wave parameterization in a global climate model of intermediate complexity, using the Calibrate, Emulate and Sample (CES) method. We first calibrate the uncertain parameters that define the gravity wave source spectrum in the tropics, to obtain climate model settings that are consistent with properties of the primary mode of tropical stratospheric variability, the Quasi-Biennial Oscillation (QBO). Then we use a Gaussian process emulator to sample the calibrated distribution of parameters and quantify the uncertainty of these parameter choices. We find that the resulting parametric uncertainties on the QBO period and amplitude are of a similar magnitude to the internal variability under a 2xCO2 forcing.