Resolution‐dependent behavior of subgrid‐scale vertical transport in the Z hang‐ M c F arlane convection parameterization

To better understand the behavior of quasi‐equilibrium‐based convection parameterizations at higher resolution, we use a diagnostic framework to examine the resolution‐dependence of subgrid‐scale vertical transport of moist static energy as parameterized by the Zhang‐McFarlane convection parameterization (ZM). Grid‐scale input to ZM is supplied by coarsening output from cloud‐resolving model (CRM) simulations onto subdomains ranging in size from 8 × 8 to 256 × 256 km 2 . Then the ZM‐based parameterization of vertical transport of moist static energy for scales smaller than the subdomain size (w ′ h ′ ¯Z M) are compared to those directly calculated from the CRM simulations (w ′ h ′ ¯C R M) for different subdomain sizes. The ensemble meanw ′ h ′ ¯C R Mdecreases by more than half as the subdomain size decreases from 128 to 8 km across whilew ′ h ′ ¯Z Mdecreases with subdomain size only for strong convection cases and increases for weaker cases. The resolution dependence ofw ′ h ′ ¯Z Mis determined by the positive‐definite grid‐scale tendency of convective available potential energy (CAPE) in the convective quasi‐equilibrium (QE) closure. Further analysis shows the actual grid‐scale tendency of CAPE (before taking the positive definite value) andw ′ h ′ ¯C R Mbehave very similarly as the subdomain size changes because they are both tied to grid‐scale advective tendencies. We can improve the resolution dependence ofw ′ h ′ ¯Z Msignificantly by averaging the grid‐scale tendency of CAPE over an appropriately large area surrounding each subdomain before taking its positive definite value. Even though the ensemble meanw ′ h ′ ¯C R Mdecreases with increasing resolution, its variability increases dramatically.w ′ h ′ ¯Z Mcannot capture such increase in the variability, suggesting the need for stochastic treatment of convection at relatively high spatial resolution (8 or 16 km).