Grid-size dependence of cumulus parameterization
The horizontal grid size in NWP models will continue to decrease. For example, it is now 40 km in the ECMWF model, and even less in many regional models. There are many reasons to decrease the horizontal grid size in LSMs. In general, as the grid size decreases, small-scale processes become better resolved so that the need to parameterize subgrid-scale processes also decreases. Stratiform cloud formation is one example. As the grid size decreases, the cloud fraction (i.e., cloud amount at a given level) tends towards a bimodal, 0 or 1, distribution, as shown in Table 1, which reduces the need to parameterize cloud fraction and cloud overlap. In particular, as the grid size decreases, the processes that determine the location, timing, and intensity of convective rainfall should become better resolved, which should improve forecasts of convective precipitation. Triggering of convection will be better represented, due to increased resolution of mesoscale boundary-layer circulations, such as sea breezes, orographic circulations, and convective outflows. As the horizontal grid size decreases, many of the processes that determine the structure of mesoscale convective systems (MCSs) will also be better resolved. These processes include the interaction of vertical shear of the lower tropospheric horizontal wind with cold pools produced by evaporation of convective precipitation. This process is important for the formation and longevity of some types of squall lines (Rotunno et al. 1988). However, until horizontal grid sizes decrease to 4 km or less, cumulus convection will still need to be parameterized (Weisman et al. 1997). As horizontal grid sizes decrease, parameterized convection becomes more localized. That is, a smaller fraction of the grid columns are convective columns (i.e., columns that contain areas of cumulus convection) and these columns include larger fractional areas of cumulus convection. What are the implications for cumulus parameterization as horizontal grid size decreases and convection becomes more localized? Can we quantify the implications? Do some aspects of the cumulus parameterization for large-scale models described in section 2 become inappropriate as horizontal grid size decreases? If so, which ones? The basic idea of a LSM cumulus parameterization is that a grid column contains an ensemble of cumulus clouds and that the fractional area covered by the active cumulus updrafts is small. In this case, the primary large-scale effects of the cumulus ensemble, heating and drying due to cumulus-induced subsidence and moistening due to cumulus detrainment, are assumed to be distributed over the area of the grid column. In reality, the subsidence would spread over a Rossby radius of deformation. However, the