Augmenting the Double-Gaussian Representation of Atmospheric Turbulence and Convection via a Coupled Stochastic Multi-Plume Mass-Flux Scheme

Modern general circulation models continue to require parameterizations of subgrid transport due to planetary boundary layer (PBL) turbulence and convection. Some schemes that unify these processes rely on assumed joint probability distributions of vertical velocity and moist conserved thermodynamic variables to predict the subgrid-scale contribution to the mean state of the atmosphere. The multivariate double-Gaussian mixture has been proposed as an appropriate model for PBL turbulence and shallow convection, but it is unable to reproduce important features of shallow cumulus convection. In this study, a novel unified PBL turbulence-convection-cloud macrophysics scheme is presented based on the eddydiffusivity/mass-flux framework. The new scheme augments the double-Gaussian representation of subgrid variability with multiple stochastic mass-flux plumes at minimal added computational cost. Improved results for steady-state maritime and transient continental shallow convection from a single-column model implementation of the new scheme are shown with respect to reference large-eddy simulations. Improvements are seen in the cloud layer due to mass-flux plumes occupying the extreme moist, low liquid-water potential temperature tail of the joint temperature-moisture distribution.