Despite recent advances in supercomputing, current general circulation models (GCMs) represent poorly the variability associated with convection and cloud processes in the tropics. The reason for this failure is believed to be due to the inadequate treatment of organized convection by the underlying cumulus parameterizations. Most of these parameterizations are based on the quasi-equilibrium theory which assumes that convection has an instantaneous or rapid response to large scale instability and thus fail to capture the intermittent and sluggish nature of deep convection that are believed to be key for its tremendous capability to organize itself into mesoscale to planetary scale convective systems including synoptic scale convectively coupled waves and the Madden-Julian oscillation (MJO). In this talk I will discuss a new stochastic lattice-gas model with three order parameters to represent the sugrid-scale variability due to the random interactions between the convective activity and the environment as well as the mutual interactions between the three main cloud types, congestus, deep, and stratiform that, according to recent satellite and in situ observations, are the dominant cloud features in organized tropical convective systems (TCS) of all scales.
In particular, I will present a new coarse graining technique for multi-particle lattice-gas models that permits to derive a multi-dimensional birth death process for the particles area coverage (cloud area fraction) that approximate the lattice model so the stochastic dynamics can be integrated with very little computational cost. Some tropical climate simulations will be presented for the case when the stochastic model is coupled to a simplified/toy climate model to demonstrate the multiple advantages of using such a stochastic parameterization for organized tropical convection.
Such particle interacting systems are widely used in science and engineering (Material Science, Pedestrian traffic, Forest fires, etc.) but because of the sheer computational burden many scientists and engineers rely on the corresponding deterministic mean field limit approximation thus eliminating all the benefits of the stochastic dynamics. The coarse-graining strategy presented here can be easily adopted to such applications.