Gravity wave refraction by three-dimensionally varying winds and the global transport of angular momentum

Operational gravity wave parameterization schemes in GCMs are columnar; that is, they are based on a ray-tracing model for gravity wave propagation that neglects horizontal propagation as well as refraction by horizontally inhomogeneous basic flows. Despite the enormous conceptual and numerical simplifications that these approximations provide, it has never been clearly established whether horizontal propagation and refraction are indeed negligible for atmospheric climate dynamics. In this study, a three-dimensional ray-tracing scheme for internal gravity waves that allows wave refraction and horizontal propagation in spherical geometry is formulated. Various issues to do with three-dimensional wave dynamics and wave-mean interactions are discussed, and then the scheme is applied to offline computations using GCM data and launch spectra provided by an operational columnar gravity wave parameterization scheme for topographic waves. This allows for side-by-side testing and evaluation of momentum fluxes in the new scheme against those of the parameterization scheme. In particular, the wave-induced vertical flux of angular momentum is computed and compared with the predictions of the columnar parameterization scheme. Consistent with a scaling argument, significant changes in the angular momentum flux due to three-dimensional refraction and horizontal propagation are confined to waves near the inertial frequency.