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 eddy-diffusivity/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. Significance Statement Computer models of the atmosphere used to predict future climate are unable to directly represent air motion at small spatial scales because it would take too long to run the model over the entire planet. Instead, models typically use coarse model grid spacing and a simplified statistical representation of the physical processes that cause small-scale motions. This paper improves a particular simplified representation by adding a mechanism to represent statistically rare events of strong small-scale air motion that coherently transport air from near the surface to higher in the atmosphere. This increased transport also improves the representation of clouds, a particularly difficult phenomenon to simulate in models.