A practical approach to scale-adaptive deep convection in a GCM by controlling the cumulus base mass flux

As the horizontal resolution of general circulation model (GCM) is increased, the sub-grid scale vertical transport has to be decreased appropriately. In the present study, a resolution-dependent (so-called scale-adaptive or scale-aware) deep convection was formulated by controlling the cumulus base mass flux. Using a three-dimensional cloud resolving model simulation, we estimated the appropriate ratios of the sub-grid scale vertical transport to the total vertical transport of moist static energy for different horizontal resolutions, whose values are about 0.8 for 100？km resolution and about 0.6 for 50？km resolution. Those values were used as a guideline to decrease to the ratio of convective precipitation to the total precipitation in a high-resolution GCM. The cumulus base mass flux is reduced by multiplying a reduction coefficient, which is 0.2 for the 100？km resolution and 0.09 for the 50？km resolution in the present GCM. The GCM with the scale-adaptive deep convection produces the climatological mean precipitation similar to that of the original GCM, whereas it simulates the heavy precipitation frequency and the Madden and Julian Oscillation much better than those of the original GCM