An updated parameterization of convective gravity waves induced by diabatic and nonlinear forcings

Momentum flux spectrum of convectively forced internal gravity waves that are induced by diabatic and nonlinear forcings is analytically formulated for use in large-scale numerical models. The nonlinear forcing is obtained from the wind and temperature perturbations induced by a specified diabatic forcing in a weakly nonlinear framework. It is found that the nonlinear forcing has a negative phase relation with the diabatic forcing, and consequently, magnitude of waves induced by both forcings is less than that induced by diabatic forcing alone. The momentum flux spectrum is determined by four terms: momentum fluxes by diabatic forcing, nonlinear forcing, and cross correlation terms between the two forcings. The momentum flux spectrum is validated by explicitly calculated convective gravity waves using a mesoscale numerical model. It is found that including nonlinear forcing gives spectral peaks of the momentum flux at higher phase-speeds, and thus can provide stronger impact in the middle atmosphere circulation. The convective gravity wave drag in the middle atmosphere is estimated by adapting two saturation methods, Lindzen and Warner & McIntyre schemes, using a global reanalysis data set, and comparison to the spectral convective gravity wave drag parameterization proposed by Song and Chun (2005) with diabatic forcing alone is carried out.