On the Importance of Momentum Conservation in the Parameterization of Gravity Wave Drag in Atmospheric Models

A realistic simulation of the climate of the middle atmosphere requires the transfer of (angular) momentum by unresolved gravity waves. The associated torque is known as "gravity wave drag" (GWD) and is proportional to the Eliassen-Palm flux divergence. The downward control relation implies that the downwelling (and consequent adiabatic warming) at any given altitude induced by GWD is related to the vertical momentum flux through that level. A key assumption of this relation is that all the vertical momentum flux is absorbed by the large-scale flow, i.e. that momentum is conserved. It follows that (apart from back reflection or meridional propagation) changes to the mean flow cannot induce changes at lower altitudes via GWD feedbacks. This is an important constraint for questions of downward influence such as stratospheric influences on tropospheric climate, or mesospheric influences on the stratosphere. Necessarily a GWD parameterization must conserve momentum to obey such a constraint. However, most current GWD parameterizations in middle atmosphere climate models are not constrained by momentum conservation, either in principle or in the way in which they are implemented.

Here we assess the importance of momentum conservation in the parameterization of GWD in response to radiative perturbations through idealized calculations with a zonal-mean model. Particular attention is paid to the possibility of spurious downward influence (as a consequence of violating momentum conservation) which could be falsely interpreted as stratospheric effects on climate. Several GWD parameterizations are compared and contrasted with Rayleigh drag. The impacts of allowing momentum flux to escape through the model lid and allowing the GWD to interact with a model sponge layer are also investigated. Momentum conservation is found to provide a key constraint on the GWD induced circulation and consequent adiabatic warming and cooling. It is shown that GWD feedbacks from radiative perturbations are not so sensitive to the choice of parameterization as long as the implementation is momentum conserving. However, if momentum conservation is violated there is strong sensitivity to the choice of GWD parameterization and the possibility of spurious downward influence.