Convective forcing fluctuations in a cloud-resolving model: Relevance to the stochastic parameterization problem

Idealized cloud-resolving model (CRM) simulations spanning a large part of the tropical atmosphere are used to evaluate the extent to which deterministic convective parameterizations fail to capture the statistical fluctuations in deep-convective forcing, and to provide probability distribution functions that may be used in stochastic parameterization schemes for global weather and climate models. A coarse-graining methodology is employed to deduce an effective convective warming rate appropriate to the grid scale of a forecast model, and a convective parameterization scheme is used to bin these computed tendencies into different ranges of convective forcing strength. The dependence of the probability distribution functions for the coarse-grained temperature tendency on parameterized tendency is then examined. An aquaplanet simulation using a climate model, configured with similar horizontal resolution to that of the coarse-grained CRM fields, was used to compare temperature tendency variation (less the effect of advection and radiation) with that deduced as an effective forcing function from the CRM. The coarse-grained temperature tendency of the CRM is found to have a substantially broader probability distribution function than the equivalent quantity in the climate model. The CRM-based probability distribution functions of precipitation rate and convective warming are related to the statistical mechanics theory of Craig and Cohen and the "stochastic physics" scheme of Buizza et al. It is found that the standard deviation of the coarse-grained effective convective warming is an approximately linear function of its mean, thereby providing some support for the Buizza et al. scheme, used operationally by ECMWF.