Atmospheric gravity waves (GWs), or buoyancy waves, transport momentum and energy through Earth’s atmosphere. GWs are important at nearly all levels of the atmosphere, though,  the momentum they transport is particularly important in general circulation of the middle and upper atmosphere. Primary sources of atmospheric GWs are flow over mountains, moist convection, and imbalances in jet/frontal systems. Secondary GWs can also be generated as a result of dissipation of a primary GWs. Gravity waves typically have horizontal wavelengths of 10’s to 100’s of kilometers, though, they can have scales of 1’s to 1000’s of kilometers as well. Current effective resolutions of climate models, and even numerical weather prediction models, do not resolve significant portions of the momentum- and energy-flux-carrying GW spectrum, and so parameterizations are necessary to represent under- and unresolved GWs in most current models.  Here, an overview of GWs generated by orography, convection, jet/front systems, primary wave breaking, and secondary wave generation is provided. The basic theory of GW generation, propagation, and dissipation relevant to parameterization is presented. Conventionally used GW parameterizations are then reviewed. Lastly, we describe uncertainties and parameter tuning in current parameterizations and discuss known processes that are currently missing.

Convection-generated gravity waves (CGWs) transport momentum and energy, and this momentum is a dominant driver of global features of Earth’s atmosphere’s general circulation (e.g. the quasi-biennial oscillation, the pole-to-pole mesospheric circulation). As CGWs are not generally resolved by global weather and climate models, their effects on the circulation need to be parameterized. However, quality observations of GWs are spatiotemporally sparse, limiting understanding and preventing constraints on parameterizations. Convection-permitting or -resolving simulations do generate CGWs, but validation is not possible as these simulations cannot reproduce the forcing convection at correct times, locations, and intensities. Here, realistic convective diabatic heating, learned from full-physics convection-permitting Weather Research and Forecasting (WRF) simulations, is predicted from weather radar observations using neural networks and a previously developed look-up table. These heating rates are then used to force an idealized GW-resolving dynamical model. Simulated CGWs forced in this way did closely resemble those observed by the Atmospheric InfraRed Sounder in the upper stratosphere. CGW drag in these validated simulations extends 100s of kilometers away from the convective sources, highlighting errors in current gravity wave drag parameterizations due to the use of the ubiquitous single-column approximation. Such validatable simulations have significant potential to be used to further basic understanding of CGWs, improve their parameterizations physically, and provide more restrictive constraints on tuning \textit{with confidence}.

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 (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 ($\Delta x =3~km$) simulations using weather research and forecasting model (WRF). 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.

Nudging is a ubiquitous capability of numerical weather and climate models that is widely used in a variety of applications (e.g. crude data assimilation, “intelligent’ interpolation between analysis times, constraining flow in tracer advection/diffusion simulations). Here, the focus is on the momentum nudging tendencies themselves, rather than the atmospheric state that results from application of the method. The initial intent was to interpret these tendencies as a quantitative estimation of model error (net parameterization error in particular). However, it was found that nudging tendencies depend strongly on the nudging time scale chosen, which is the primary result presented here. Reducing the nudging time scale reduces the difference between the model state and the target state, but much less so than the reduction in the nudging time scale, resulting in increased nudging tendencies. The dynamical core, in particular, appears to increasingly oppose nudging tendencies as the nudging time scale is reduced. These results suggest nudging tendencies cannot be quantitatively interpreted as model error. Still, nudging tendencies do contain some information on model errors and/or missing physical processes and still might be useful in model development and tuning, even if only qualitatively.