Variability and Clustering of Midlatitude Summertime Convection: Testing the Craig and Cohen Theory in a Convection-Permitting Ensemble with Stochastic Boundary Layer Perturbations

The statistical theory of convective variability developed by Craig and Cohen in 2006 has provided a promising foundation for the design of stochastic parameterizations. The simplifying assumptions of this theory, however, were made with tropical equilibrium convection in mind. This study investigates the predictions of the statistical theory in real-weather case studies of nonequilibrium summertime convection over land. For this purpose, a convection-permitting ensemble is used in which all members share the same largescale weather conditions but the convection is displaced using stochastic boundary layer perturbations. The results show that the standard deviation of the domain-integrated mass flux is proportional to the square root of its mean over a wide range of scales. This confirms the general applicability and scale adaptivity of the Craig and Cohen theory for complex weather. However, clouds tend to cluster on scales of around 100 km, particularly in the morning and evening. This strongly impacts the theoretical predictions of the variability, which does not include clustering. Furthermore, the mass flux per cloud closely follows an exponential distribution if all clouds are considered together and if overlapping cloud objects are separated. The nonseparated cloud mass flux distribution resembles a power law. These findings support the use of the theory for stochastic parameterizations but also highlight areas for improvement.