Momentum Flux by Thermally Induced Internal Gravity Waves and Its Approximation for Large-Scale Models

Gravity wave momentum flux induced by thermal forcing representing latent heating due to cumulus convection is investigated analytically from a viewpoint of a subgrid-scale drag for the large-scale flow, and a possible way to parameterize the momentum flux in large-scale models is proposed. For the formulations of the momentum flux and its vertical derivative, two-dimensional, steady-state, linear perturbations induced by thermal forcing in a uniform basic-state wind are considered. The calculated momentum flux is zero below the forcing bottom, varies with height in the forcing region, and remains constant above the forcing top with the forcing top value. The sign of the momentum flux at the forcing top depends on the basic-state wind according to the wave energy–momentum flux relationship. Inside the forcing region, there exists a vertical convergence or divergence of the momentum flux that can influence the zonal mean flow tendency. The maximum magnitude of the zonal mean flow tendency contributed by the wave momentum flux in the forcing region is as large as 24 m s−1 d−1. A parameterization scheme of subgrid-scale convection-induced gravity wave momentum flux for use in large-scale models is proposed. Even though the momentum flux in the cloud region can be parameterized based on the analytical formulation, it is not practically applied in large-scale models because subgrid-scale diabatic forcing considered in this study comes from cumulus parameterization that is activated only in a conditionally unstable atmosphere. Thus, the convection-induced momentum flux is parameterized from the cloud-top height. The momentum flux at the cloud-top height is parameterized based on the analytical formulation, while above it two methods can be used following mountain drag parameterization. One method is to specify a linearly decreasing vertical profile with height and the other is to apply the wave saturation theory in terms of the Richardson number criterion. The formulations of the minimum Richardson number and saturation momentum flux are surprisingly analogous to those in mountain drag parameterization except that the nonlinearity factor of thermally induced waves is used instead of the Froude number. Gravity wave drag by convection can have a relatively strong impact on the large-scale flow in midlatitude summertime when the surface wind and stability are weak and in the tropical area where deep cumulus convection persistently exists.