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Abstract

The parameterization of shallow cumuli across a range of model grid resolutions of kilometrescales faces at least three major difficulties: (1) closure assumptions of conventional parameterization schemes are no longer valid, (2) stochastic fluctuations become substantial and increase with grid resolution, and (3) convective circulations that emerge on the model grids are under-resolved and grid-scale dependent. Here we develop a stochastic parameterization of shallow cumulus clouds to address the first two points, and we study how this stochastic parameterization interacts with the under-resolved convective circulations in a convective case over the ocean. We couple a stochastic model based on a canonical ensemble of shallow cumuli to the Eddy-Diffusivity Mass-Flux parameterization in the icosahedral nonhydrostatic (ICON) model. The moist-convective area fraction is perturbed by subsampling the distribution of subgrid convective states. These stochastic perturbations represent scale-dependent fluctuations around the quasiequilibrium state of a shallow cumulus ensemble. The stochastic parameterization reproduces the average and higher order statistics of the shallow cumulus case adequately and converges to the reference statistics with increasing model resolution. The interaction of parameterizations with model dynamics, which is usually not considered when parameterizations are developed, causes a significant influence on convection in the gray zone. The stochastic parameterization interacts strongly with the model dynamics, which changes the regime and energetics of the convective flows compared to the deterministic simulations. As a result of this interaction, the emergence of convective circulations in combination with the stochastic parameterization can even be beneficial on the high-resolution model grids.