Resolution-dependent behavior of subgrid-scale vertical transport in the Zhang-McFarlane convection parameterization

Abstract:

We examine the resolution-dependence of subgrid-scale vertical transport of moist static energy as parameterized by the Zhang-McFarlane convection parameterization (ZM) under a diagnostic framework. Grid-scale input to ZM is supplied by coarsening output from cloud resolving model (CRM) simulations onto sub-domains ranging in size from 8x8 to 256x256 km^2. Then the ZM based parameterization of vertical transport of moist static energy for scales smaller than the sub-domain size (w'h'_ZM) are compared to those directly calculated from the CRM simulations (w'h'_CRM) for different sub-domain sizes. We find that the overall strength of w'h'_CRM decreases by more than half as the sub-domain size decreases from 128 to 8 km across while w'h'_ZM decreases with sub-domain size only for strong convection cases and increases for weaker cases. The resolution dependence of w'h'_ZM is determined by the positive-definite change rate of grid-scale convective available potential energy (CAPE) used in the convective quasi-equilibrium (QE) closure. Further analysis shows the change rate of actual grid-scale CAPE itself (before taking the positive definite value) and w'h'_CRM behave very similarly as the sub-domain size changes because they are both tied to grid-scale advective tendencies. We suggest a simple algorithm to improve the resolution awareness of ZM based on our analysis. The overall strength of w'h'_CRM decreases with increasing resolution while its variability increases dramatically. We find that ZM can capture neither the magnitude nor the pattern of this variability at relatively high resolutions (8 or 16 km grid spacing), suggesting the urgent need for stochastic treatment of convection at high resolutions.