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Stochastic subgrid models have been proposed to capture the missing variability and correct systematic medium-term errors in general circulation models. In particular, the poor representation of subgrid-scale deep convection is a persistent problem that stochastic parametrizations are attempting to correct. In this paper, we construct such a subgrid model using data derived from large-eddy simulations (LESs) of deep convection. We use a data-driven stochastic parametrization methodology to construct a stochastic model describing a finite number of cloud states. Our model emulates, in a computationally inexpensive manner, the deep convection-resolving LES. Transitions between the cloud states are modelled with Markov chains. By conditioning the Markov chains on large-scale variables, we obtain a conditional Markov chain, which reproduces the time evolution of the cloud fractions. Furthermore, we show that the variability and spatial distribution of cloud types produced by the Markov chains become more faithful to the LES data when local spatial coupling is introduced in the subgrid Markov chains. Such spatially coupled Markov chains are equivalent to stochastic cellular automata.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

A data-driven multi-cloud model for stochastic parametrization of deep convection