MOMENTUM FLUX BY THERMALLY-INDUCED INTERNAL GRAVITY-WAVES AND ITS APPROXIMATION FOR LARGE-SCALE MODELS

Gravity wave momentum flux induced by thermal forcing representing lat ent heating due to cumulus convection is investigated analytically fro m a viewpoint of a subgrid-scale drag for the large-scale how and a po ssible way to parameterize the momentum flux in large-scale models is proposed. For the formulations of the momentum flux and its vertical d erivative, 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 f orcing top depends on the basic-state wind according to the wave energ y-momentum flux relationship. Inside the forcing region, there exists a vertical convergence or divergence of the momentum flux that can inf luence the zonal mean flow tendency. The maximum magnitude of the zona l mean flow tendency contributed by the wave momentum flux in the forc ing 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 t he cloud region can be parameterized based on the analytical formulati on, it is not practically applied in large-scale models because subgri d-scale diabatic forcing considered in this study comes from cumulus p arameterization that is activated only in a conditionally unstable atm osphere. Thus, the convection-induced momentum flux is parameterized f rom 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 met hod is to specify a linearly decreasing vertical profile with height a nd the other is to apply the wave saturation theory in terms of the Ri chardson number criterion. The formulations of the minimum Richardson number and saturation momentum flux are surprisingly analogous to thos e in mountain drag parameterization except that the nonlinearity facto r of thermally induced waves is used instead of the Froude number. Gra vity wave drag by convection can have a relatively strong impact on th e large-scale flow in midlatitude summertime when the surface wind and stability are weak and in the tropical area where deep cumulus convec tion persistently exists.