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Convective gravity waves are important for the forcing of the quasi biennial oscillation (QBO). There is a wave component that is stationary with respect to the convective cells that is triggered by convection acting like a barrier to the background flow (moving mountain mechanism). Waves from this mechanism have only been observed in a few case studies and are not parameterized in climate models. However, the representation of the whole spectrum of gravity waves is crucial for the simulation of the QBO, especially in the lowermost stratosphere (below 50 hPa) where the QBO amplitudes are under‐estimated in current global circulation models. In this study, we present analysis of convective gravity wave observations from superpressure balloons in boreal winter 2019 and 2021, retrieving phase speeds, momentum fluxes, and drag. We also identify waves generated by the moving mountain mechanism using the theory of the Beres scheme as a basis. These waves do not have a specific period, but are of smaller horizontal scale, on average around 300 km, which is similar to the scale of convective systems. Our results show that gravity waves contribute up to 2/3 to the QBO forcing below 50 hPa and waves from the moving mountain mechanism are responsible for up to 10% of this forcing. 

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 Gravity waves dispersing upward through the tropical stratosphere during opposing phases of the QBO are investigated using ERA5 data for 1979–2019. Log–log plots of two-sided zonal wavenumber–frequency spectra of vertical velocity, and cospectra representing the vertical flux of zonal momentum in the tropical lower stratosphere, exhibit distinctive gravity wave signatures across space and time scales ranging over two orders of magnitude. Spectra of the vertical flux of momentum are indicative of a strong dissipation of westward-propagating gravity waves during the easterly phase and vice versa. This selective “wind filtering” of the waves as they disperse upward imprints the vertical structure of the zonal flow on the resolved wave spectra, characteristic of (re)analysis and/or free-running models. The three-dimensional structures of the gravity waves are documented in composites of the vertical velocity field relative to grid-resolved tropospheric downwelling events at individual reference grid points along the equator. In the absence of a background zonal flow, the waves radiate outward and upward from their respective reference grid points in concentric rings. When a zonal flow is present, the rings are displaced downstream relative to the source and they are amplified upstream of the source and attenuated downstream of it, such that instead of rings, they assume the form of arcs. The log–log spectral representation of wind filtering of equatorial waves by the zonal flow in this paper can be used to diagnose the performance of high-resolution models designed to simulate the circulation of the tropical stratosphere. 

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 There are different strategies for training neural networks (NNs) as subgrid‐scale parameterizations. Here, we use a 1D model of the quasi‐biennial oscillation (QBO) and gravity wave (GW) parameterizations as testbeds. A 12‐layer convolutional NN that predicts GW forcings for given wind profiles, when trained offline in abig‐dataregime (100‐year), produces realistic QBOs once coupled to the 1D model. In contrast, offline training of this NN in asmall‐dataregime (18‐month) yields unrealistic QBOs. However, online re‐training of just two layers of this NN using ensemble Kalman inversion and only time‐averaged QBO statistics leads to parameterizations that yield realistic QBOs. Fourier analysis of these three NNs' kernels suggests why/how re‐training works and reveals that these NNs primarily learn low‐pass, high‐pass, and a combination of band‐pass filters, potentially related to the local and non‐local dynamics in GW propagation and dissipation. These findings/strategies generally apply to data‐driven parameterizations of other climate processes. 

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 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 Tropical waves play an important role in driving the quasi‐biennial oscillation of zonal winds in the tropical stratosphere. In our study we analyze these waves based on temperature observations from the 2021–2022 Strateole‐2 campaign when the Reel‐down Atmospheric Temperature Sensor (RATS) was successfully deployed for the first time. RATS provides long‐duration, continuous and simultaneous high‐resolution temperature observations at two altitudes (balloon float level and 200 m below) allowing for an analysis of vertical wavelengths. This separation distance was chosen to focus on waves near the resolution limit of reanalyses. Here, we found tropical waves with periods between about 6 hr and 2 days, with vertical wavelengths between 1.5 and 5 km, respectively. Comparing our results to Fifth generation European Centre for Medium‐Range Weather Forecasts (ERA5) reanalyses we found good agreement for waves with a period longer than 1 day. However, the ERA5 amplitudes of higher‐frequency waves are under‐estimated, and the temporal evolution of most wave packets differs from the observations. 

Abstract Atmospheric gravity waves (GWs) span a broad range of length scales. As a result, the un‐resolved and under‐resolved GWs have to be represented using a sub‐grid scale (SGS) parameterization in general circulation models (GCMs). In recent years, machine learning (ML) techniques have emerged as novel methods for SGS modeling of climate processes. In the widely used approach of supervised (offline) learning, the true representation of the SGS terms have to be properly extracted from high‐fidelity data (e.g., GW‐resolving simulations). However, this is a non‐trivial task, and the quality of the ML‐based parameterization significantly hinges on the quality of these SGS terms. Here, we compare three methods to extract 3D GW fluxes and the resulting drag (Gravity Wave Drag [GWD]) from high‐resolution simulations: Helmholtz decomposition, and spatial filtering to compute the Reynolds stress and the full SGS stress. In addition to previous studies that focused only on vertical fluxes by GWs, we also quantify the SGS GWD due to lateral momentum fluxes. We build and utilize a library of tropical high‐resolution (Δx = 3 km) simulations using weather research and forecasting model. Results show that the SGS lateral momentum fluxes could have a significant contribution to the total GWD. Moreover, when estimating GWD due to lateral effects, interactions between the SGS and the resolved large‐scale flow need to be considered. The sensitivity of the results to different filter type and length scale (dependent on GCM resolution) is also explored to inform the scale‐awareness in the development of data‐driven parameterizations. 

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.