A parametrization of convective momentum transport

While most GCMs ignore the effect of convection on the momentum budget, a few of them do include a convective momentum transport (CMT) parametrization in the form of cumulus friction, thus ignoring the important effects of upscale buildup of momentum from the unresolved mesoscales to large scales. However, there is observational evidence of upscale as well as downscale CMT, due organized mesoscale systems. Here we present a simple parametrization scheme for CMT incorporating the upscale fluxes of momentum due unresolved organized mesoscale convection conditioned on the large-scale vertical shear which is believed to favor mesoscale convective systems (MCS) and strati form anvils in the wake of deep convection that induce a vertical tilt in the MCS's, a necessary condition for upscale CMT flux. We follow an idea first put forward by Majda and Stechmann of switching back and forth between upscale (active) and dowscale (frictional) CMT regimes via a stochastic jump process condition on the underlying large scale shear. But here we propose a much simpler deterministic approach based on an exponential partition between the two regimes which can be regarded as the mean field limit of the former. The new parametrization is tested in the context of a toy GCM (2 and half vertical layers along the equatorial ring, ignoring effects of rotation and meridional dependence) using the simple multicloud parametrization of Khouider and Majda. The results show that CMT strengthens the emergence and persistence of slow moving planetary-scale (MJO-like) wave envelopes of the higher frequency synoptic scale gravity waves.