  Parametrizations for internal gravity waves in atmospheric models are
traditionally subject to a number of simplifications. Most notably, they rely
on both neglecting wave propagation and advection in the horizontal direction
(single-column assumption) and an instantaneous balance in the vertical
direction (steady-state assumption). While these simplifications are well
justified to cover some essential dynamic effects and keep the computational
effort small it has been shown that both mechanisms are potentially
significant. In particular, the recently introduced Multiscale Gravity Wave
Model (MS-GWaM) successfully applied ray tracing methods in a novel type of
transient but columnar internal gravity wave parameterization (MS-GWaM-1D). We
extend this concept to a three-dimensional version of the parameterization
(MS-GWaM-3D) to simulate subgrid-scale non-orographic internal gravity waves.
The resulting global wave model -- implemented into the weather-forecast and
climate code ICON -- contains three-dimensional transient propagation with
accurate flux calculations, a latitude-dependent background source, and
convectively generated waves. MS-GWaM-3D helps reproducing expected temperature
and wind patterns in the mesopause region in the climatological zonal mean
state and thus proves a viable IGW parameterization. Analyzing the global wave
action budget, we find that horizontal wave propagation is as important as
vertical wave propagation. The corresponding wave refraction includes
previously missing but well-known effects such as wave refraction into the
polar jet streams. On a global scale, three-dimensional wave refraction leads
to a horizontal flow-dependent redistribution of waves such that the structures
of the zonal mean wave drag and consequently the zonal mean winds are modified.
