Stochastic and scale-adaptive shallow cumulus parameterization (EDMF-DualM-S in ICON)

Numerical cloud-resolving studies of cumulus clouds reveal the small-scale variability of convection that is not fully controlled by the large scale environment. From the parameterization point of view, this means that there is a whole distribution of the sub-grid convective states that can correspond to the same large scale forcing. Moreover, the stochastic variability becomes higher with the increasing model resolution. As the cloud sample within a model grid box becomes smaller, the most probable realization of the sub-grid convection deviates further away from the convective ensemble mean. Therefore, as the atmospheric models approach higher and higher resolution, it becomes more important to develop stochastic schemes that sub-sample the convective cloud ensemble and adapt to the model resolution.

We propose an approach to represent the stochastic variability of the unresolved shallow-convective states, and the dependence of the distribution of sub-grid states on the model horizontal resolution. We combine the theory of fluctuations in a convective ensemble based on a statistical mechanics approach and Large-Eddy Simulation (LES) of shallow cumulus clouds of an idealized case over the ocean. Based on the empirical and theoretical findings, a stochastic cloud generator is developed and coupled to the EDMF-DualM cloud scheme in the ICON model as a stochastic process that runs simultaneously with the EDMF scheme. The stochastic scheme adds more complexity to the cloud parameterization in EDMF, but on the other side, the cloud mass flux profiles are locally sampled instead of using the buoyancy sorting closure for the bulk vertical profile. The scheme also relaxes the statistical equilibrium assumption by applying it only at the scale at which it is appropriate and by including the memory component. Preliminary results show that the variability is well reproduced and that the scheme is scale-adaptive. Impact on the mean profiles is small, except for a significant decrease in cloud liquid water due to the different treatment of cloud profiles, which improves the performance of the EDMF-DualM scheme for an idealized shallow cumulus case.