Authors:

Ulrich Achatz, Young-Ha Kim, and Georg Sebastian Voelker

Read the full paper here

Abstract:

The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The development of this theory is reviewed here. It applies to all interesting regimes of atmospheric stratification, i.e., also to moderately strong stratification as occurring in the middle atmosphere, and thereby extends classic assumption for the derivation of quasi-geostrophic theory.

At strong wave amplitudes a fully nonlinear theory arises that is complemented by a quasilinear theory for weak GW amplitude. The latter allows the extension to a spectral description that forms the basis of numerical implementations that avoid instabilities due to caustics, e.g., from GW reflection. Conservation properties are discussed, for energy and potential vorticity, as well as conditions under which a GW impact on the larger-scale flow is possible. The numerical implementation of the theory for GW parameterizations in atmospheric models is described, and the consequences of the approach are discussed, as compared to classic GW parameterizations. Although more costly than the latter, it exhibits significantly enhanced realism, while being considerably more efficient than an approach where all relevant GWs are to be resolved. The reported theory and its implementation might be of interest also for the efficient and conceptually insightful description of other wave-mean interactions, including those where the formation of caustics presents a special challenge.

Plain Language Summary:

Gravity waves are atmospheric waves with oscillations in wind, temperature, pressure etc that are emitted by heavy weather like thunderstorms, weather fronts etc, but also by winds blowing over mountains. Their wavelengths are so short (down to a few km) that present-day weather and climate models cannot resolve all of them with their coarse grids. Yet their impact on weather and climate is important. Atmospheric models must describe the dynamics and effects of gravity waves without resolving them explicitly, by modules called parameterizations, in order to get weather forecasts and climate simulations right. By now we understand that the traditional construction of gravity-wave parameterizations is too simple in several regards. This limits especially the reliability of climate-change simulations. The paper outlines the general theory to be used for gravity-wave parameterizations and it describes how it can be used in models.