An Updated Parameterization of Convectively Forced Gravity Wave Drag for Use in Large-Scale Models

Abstract

An updated parameterization of gravity wave drag forced by subgrid-scale cumulus convection (GWDC) in large-scale models is proposed. For an analytical formulation of the cloud-top wave stress, two-dimensional, steady-state, linear perturbations induced by diabatic heating are found in a two-layer structure with a piecewise constant shear with a critical level in the lower layer, a uniform flow in the upper layer, and piecewise constant buoyancy frequencies in each layer. The dynamical frame considered is relative to the diabatic forcing and the gravity waves obtained are stationary relative to the diabatic forcing, not necessarily stationary relative to the ground. The cloud-top wave momentum flux is proportional to the square of the magnitude of the convective heating, inversely proportional to the basic-state wind speed, and related to the buoyancy frequencies in each layer. The effect of wind shear in the convective region on the cloud-top momentum flux is negligible, while a difference in the stability between the two layers affects the momentum flux significantly. The cloud-top momentum flux increases as the stability in the convective region decreases and the stability above it increases. A global distribution of the 200-mb wave stress calculated using climatological data reveals that the wave stress in the present study is larger than that in a uniform wind and stability case. This is mainly due to the stability difference between the convective region and the region above it. A methodology of parameterizing GWDC in large-scale models using the wave saturation hypothesis is presented.