Cumulus Parameterization for Gray Zone: A Conceptual Model

Based on a cloud resolving model (CRM) simulation, cumulus parameterization (CP) problem for gray zone is revisited.In the CRM simulation of deep cumulus convections in the tropical Pacific, we can see many intermittent kilo-meter scale ascending updraft bubbles (thermals).If we gather these updraft bubbles in a 20 km grid area into one place, they can be represented by a single hypothetical large plume: equivalent plume (EP).The total updraft in the grid is equivalent to the updraft of EP.It is shown that the mean temperature of EP is almost the same as the environment temperature.As the EP is saturated, the mean specific humidity of EP is the same as the saturation specific humidity at the environment temperature.The EP shows that "moist buoyancy" is essential for cumulus convections.With the mean temperature and mean specific humidity of EP, we can calculate the moist static energy and the entrainment rate for EP.Using this entrainment rate and the updraft mass flux at cloud base which is proportional to fractional convective cloud area, we can calculate the updraft mass flux necessary for a CP scheme for gray zone.