Errors induced by cloud amount in cumulus parameterization

Errors induced by cloud amount in cumulus parameterization were estimated from data obtained from high-resolution cloud-resolving simulations. A selected case was summertime cumulus ensemble in the tropics of western North Pacific. First of all, an area, equivalent to a relatively coarse grid (e.g., 20 km x 20 km), was set. On the basis of a criterion, the area was divided into three sub-areas: Convective updraft area, convective downdraft area, and environmental area. Cloud amount was defined as the sum of the convective updraft area and convective downdraft area divided by the whole area. Area-averaged quantities, such as mass flux and moist static energy, were calculated in terms of the sub-areas. On the basis of these quantities, tendency of moist static energy induced by cumulus convection and its error were calculated. The relationship between the error and the cloud amount was evaluated. It was found that the error increases with increasing the cloud amount as a whole. It was also found that the error increases as the area equivalent to the coarse grid decreases. The error cannot be negligible when the area is smaller than a grid of 20 km x 20 km. This is because the cloud amount generally increases with decreasing the area. Our results suggest that the effect of cloud amount needs to be considered in cumulus parameterization when horizontal grid spacing becomes smaller than the critical value.