A Cumulus Parameterization Including Mass Fluxes, Vertical Momentum Dynamics, and Mesoscale Effects

A formulation for parameterizing cumulus convection, which treats cumulus vertical momentum dynamics and mass fluxes consistently, is presented. This approach predicts the penetrative extent of cumulus updrafts on the basis of their vertical momentum and provides a basis for treating cumulus microphysics using formulations that depend on vertical velocity. Treatments for cumulus microphysics are essential if the water budgets of convective systems are to be evaluated for treating mesoscale stratiform processes associated with convection, which are important for radiative interactions influencing climate. The water budget (both condensed and vapor) of the cumulus updrafts is used to drive a semi-empirical parameterization for the large-scale effects of the mesoscale circulations associated with deep convection. The parameterization for mesoscale effects invokes mesoscale ascent to redistribute vertically water detrained at the tops of the cumulus updrafts. The local cooling associated with this mesoscale ascent is probably larger than radiative heating of the mesoscale anvil clouds, and the mesoscale ascent may be in part a response to such radiative heating. The parameterization was applied to two tropical thermodynamic profiles whose diagnosed forcing by convective systems differed significantly. A spectrum of cumulus updrafts was allowed. The deepest of the updrafts penetrated the upper troposphere, while the shallower updrafts penetrated into the region of the mesoscale anvil. The relative numbers of cumulus updrafts of characteristic vertical velocities comprising the parameterized ensemble corresponded well with available observations. However, the large-scale heating produced by the ensemble without mesoscale circulations was concentrated at lower heights than observed or was characterized by excessive peak magnitudes. Also, an unobserved large-scale source of water vapor was produced in the middle troposphere. When the parameterization for mesoscale effects was added, the large-scale thermal and moisture forcing predicted by the parameterization agreed well with observations for both cases. The significance of mesoscale processes, some of which may depend in part on radiative forcing, suggests that future cumulus parameterization development will need to treat some radiative processes. Further, the long time scale of the mesoscale processes relative to that of the cumulus cells indicates a possible requirement for carrying some characteristics of the convective system in time as cumulus parameterizations are incorporated in large-scale models whose resolutions remain too large to capture explicitly the mesoscale processes.