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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 Based on 20-day control forecasts by the 9-km Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasts (ECMWF) for selected periods of summer and winter events, this study investigates global distributions of gravity wave momentum fluxes resolved by the highest-resolution-ever global operational numerical weather prediction model. Two supplementary datasets, including 18-km ECMWF IFS experiments and the 30-km ERA5, are included for comparison. In the stratosphere, there is a clear dominance of westward momentum fluxes over the winter extratropics with strong baroclinic instability, while eastward momentum fluxes are found in the summer tropics. However, meridional momentum fluxes, locally as important as the above zonal counterpart, show different behaviors of global distribution characteristics, with northward and southward momentum fluxes alternating with each other especially at lower altitudes. Both events illustrate conclusive evidence that stronger stratospheric fluxes are found in the ECMWF forecast with finer resolution, and that ERA5 datasets have the weakest signals in general, regardless of whether regridding is applied. In the troposphere, probability distributions of vertical motion perturbations are highly asymmetric with more strong positive signals especially over latitudes covering heavy rainfall, likely caused by convective forcing. With the aid of precipitation accumulation, a simple filtering method is proposed in an attempt to eliminate those tropospheric asymmetries by convective forcing, before calculating tropospheric wave-induced fluxes. Furthermore, this research demonstrates promising findings that the proposed filtering method could help in reducing the potential uncertainties with respect to estimating tropospheric wave-induced fluxes. Finally, absolute momentum flux distributions with proposed approaches are presented, for further assessment in the future. 

Abstract Over the course of his career, Fuqing Zhang drew vital new insights into the dynamics of meteorologically significant mesoscale gravity waves (MGWs), including their generation by unbalanced jet streaks, their interaction with fronts and organized precipitation, and their importance in midlatitude weather and predictability. Zhang was the first to deeply examine “spontaneous balance adjustment”—the process by which MGWs are continuously emitted as baroclinic growth drives the upper-level flow out of balance. Through his pioneering numerical model investigation of the large-amplitude MGW event of 4 January 1994, he additionally demonstrated the critical role of MGW–moist convection interaction in wave amplification. Zhang’s curiosity-turned-passion in atmospheric science covered a vast range of topics and led to the birth of new branches of research in mesoscale meteorology and numerical weather prediction. Yet, it was his earliest studies into midlatitude MGWs and their significant impacts on hazardous weather that first inspired him. Such MGWs serve as the focus of this review, wherein we seek to pay tribute to his groundbreaking contributions, review our current understanding, and highlight critical open science issues. Chief among such issues is the nature of MGW amplification through feedback with moist convection, which continues to elude a complete understanding. The pressing nature of this subject is underscored by the continued failure of operational numerical forecast models to adequately predict most large-amplitude MGW events. Further research into such issues therefore presents a valuable opportunity to improve the understanding and forecasting of this high-impact weather phenomenon, and in turn, to preserve the spirit of Zhang’s dedication to this subject. 

Here we present a new theoretical framework that connects the error growth behavior in numerical weather prediction (NWP) with the atmospheric kinetic energy spectrum. Building on previous studies, our newly proposed framework applies to the canonical observed atmospheric spectrum that has a -3 slope at synoptic scales and a -5/3 slope at smaller scales. Based on this realistic hybrid energy spectrum, our new experiment using hybrid numerical models provides reasonable estimations for the finite predictable ranges at different scales. We further derive an analytical equation that helps understand the error growth behavior. Despite its simplicity, this new analytical error growth equation is capable of capturing the results of previous comprehensive theoretical and observational studies of atmospheric predictability. The success of this new theoretical framework highlights the combined effects of quasi-two-dimensional dynamics at synoptic-scales (-3 slope) and three-dimensional turbulence-like small-scale chaotic flows (-5/3 slope) in dictating the error growth. It is proposed that this new framework could serve as a guide for understanding and estimating the predictability limit in the real world.