Momentum flux spectrum of convective gravity waves. Part I: An update of a parameterization using mesoscale simulations

The convective source and momentum flux spectra of a parameterization of convective gravity wave drag (GWDC) are validated in a three-dimensional spectral space using mesoscale numerical simulations for various ideal and real convective storms. From this, two important free parameters included in the GWDC parameterization-the moving speed of the convective source and the wave propagation direction-are determined. In the numerical simulations, the convective source spectrum shows nearly isotropic features in terms of magnitude, and its primary peak in any azimuthal direction occurs at a phase speed that equals the moving speed of the convective source in the same direction. It is found that the moving speed of the convective source is closely correlated with the basic-state wind averaged below 700 hPa (ū₇₀₀ and v̄₇₀₀). When the analytic convective source spectrum of the parameterization is calculated using the moving speed of the convective source as determined by ū₇₀₀ and v̄₇₀₀, its shape in all storm cases agrees with that from the simulation. The momentum flux spectrum at launch level (cloud top) is also calculated using the basic-state conditions and the moving speed of the convective source as determined by ū₇₀₀ and v̄₇₀₀. A comparison between the parameterization and simulation results shows that the parameterization reproduces the momentum flux spectrum from the simulation reasonably well. In the parameterization, two wave propagation directions of 45°(northeast and southwest) and 135° (northwest and southeast) best represent the momentum flux spectra from the simulations integrated over all directions when the minimum number of wave propagation directions is required for computational efficiency.