Prognostic modeling of total specific humidity variance induced by shallow convective clouds in a GCM

Abstract. Shallow convective cloud cover prediction is a critical element of climate modeling. In most global climate models (GCMs), the cloud scheme relies on a statistical description of the atmospheric water content. While the mean value of specific humidity is a standard output of the climate model, the upper moments, in particular the variance and skewness, must be prescribed by a dedicated model. Observations and large eddy simulations (LES) have shown that the asymmetry of water distribution is linked to the presence of organized convective cells. To capture this asymetry, the boundary layer convective cells are represented in this work by an eddy diffusivity mass flux model, coupled to a bi-Gaussian statistical cloud scheme. Previously, the variance of each component has been prescribed diagnostically from the difference in specific humidity between updrafts and environment. This cloud scheme has demonstrated its capacity to represent dry shallow convective boundary layers, however, it reveals significant inaccuracies in deep convection situations and in the prediction of skewness. We propose here to develop a unified prognostic model for the total specific humidity variance. We show in particular that the transport of specific humidity and its square in the mass-flux scheme permits to implement the generic prognostic equations of the variance into a GCM. Furthermore, model adjustment is carried out using recently added automatic tuning methods. Based on this adjustment, we show that the prognostic model is consistent with previous work on shallow convective cases while providing significant improvements in the description of variance and third-order moment profiles.