Quantifying gravity wave forcing using scale invariance

Despite the increasing resolution, forcing on the mean circulation by resolved waves in general circulation models is not yet converging. Parameterization of the forcing remains a major source of model uncertainty. This study examines the scale invariance of zonal spectra of momentum flux and wave forcing, and shows that it can be used to quantify the forcing by unresolved waves with knowledge of the resolved ones in global models. The result reveals the leading order importance of the small-scale wave forcing, which is in general agreement with that required for obtaining the zonal mean wind climatology. It is also found that wave and mean flow interaction is important in maintaining the robust spectral structure. This method may provide a strategy to design physically consistent and scale-aware parameterization schemes for scale invariant quantities, when a model has sufficient resolution to partially resolve their spectra.