A Spectral Parameterization of Drag, Eddy Diffusion, and Wave Heating for a Three-Dimensional Flow Induced by Breaking Gravity Waves

There are three distinct processes by which upward-propagating gravity waves influence the large-scale dynamics and energetics of the middle atmosphere: (i) nonlocalized transport of momentum through wave propagation in three dimensions that remotely redistributes atmospheric momentum in both zonal and meridional directions from wave generation to wave dissipation regions; (ii) localized diffusive transport of momentum, heat, and tracers due to mixing induced by wave breaking; and (iii) localized transport of heat by perturbing wave structures due to dissipation that redistributes the thermal energy within a finite domain. These effects become most significant for breaking waves when momentum drag, eddy diffusion, and wave heating- the "breaking trinity"-are all imposed on the background state. This paper develops a 3D parameterization scheme that self-consistently includes the breaking trinity in large-scale numerical models. The 3D parameterization scheme is developed based on the general relationship between the wave action flux and the subgrid-scale momentum and heat fluxes developed by Zhu in 1987 and a mapping approximation between the wave source spectrum and momentum deposition distribution developed by Alexander and Dunkerton in 1999. For a set of given input wind and temperature profiles at each model grid, the parameterization scheme outputs the vertical profiles of the subgrid-scale force terms together with the eddy diffusion coefficients in the momentum and energy equations for a 3D background flow.