Coupling a minimal stochastic lattice gas model of a cloud system to an atmospheric general circulation model

We propose a strategy to couple a stochastic lattice gas model of a cloud system to a rather general class of convective parametrization schemes. As proposed in similar models recently presented in the literature, a cloud system in a grid box of a general circulation model (GCM) is modelled as a subgrid lattice of N elements that can be in one of S states, each corresponding to a different convective regime. The time evolution of each element of the lattice is represented as a Markov process characterized by transition rates dependent on large-scale fields and/or local interactions. In order to make application to GCMs computationally feasible, we propose a reduction method leading to a system of S - 1 stochastic differential equations with multiplicative noise. The accuracy of the reduction method is tested in a minimal version of the model. The coupling to a convective scheme is performed in such a way that, in the limit of space- and time-scale separation, the modified stochastic parametrization converges to the original deterministic version of the host scheme. Experiments with a real GCM are then performed, coupling the minimal version of the stochastic model to the Betts-Miller scheme in an aquaplanet version of the Planet Simulator. In this configuration, the stochastic extension of the parametrization keeps the climatology of its deterministic limit but strongly impacts the statistics of the extremes of daily convective precipitation.