Examination of convective parameterization closures and their scale awareness using cloud-resolving model simulations

Closure is the main component of a mass flux-based convective parameterization scheme and it determines the amount of convection under a given large-scale condition. In this study, we use cloud-resolving model output from simulations of both tropical and midlatitude convection to evaluate commonly used closures for a range of global climate model (GCM) horizontal resolutions, taking convective precipitation and mass flux at 600 hPa as measures for deep convection. To mimic different GCM horizontal resolutions, we use high resolution CRM data to create domain averages representing GCM horizontal resolutions of 128 km, 64 km, 32 km, 16 km, 8 km and 4 km. Lead-lag correlation analysis shows that except moisture convergence and turbulent kinetic energy (TKE), none of the other closure variables evaluated in this study show any relationship with convection for the six subdomain sizes. It is found that the correlation between moisture convergence and convective precipitation is largest when moisture convergence leads convection. This correlation weakens as the subdomain size decreases to 8 km or smaller. Although convective precipitation and mass flux increase with moisture convergence, as the subdomain size increases the rate at which they increase becomes smaller. This suggests that moisture convergence-based closure should scale down the predicted mass flux for given moisture convergence as GCM resolution increases. Lead-lag correlation and composite analysis show that TKE is largely a result of convection and therefore its use in a closure variable is not supported.