A Dual Mass Flux Framework for Boundary Layer Convection. Part II: Clouds

This paper presents the extension of the eddy diffusivity mass flux (EDMF) framework for turbulent transport into the statistical modeling of boundary layer clouds. The advection-diffusion decomposition that defines EDMF is projected onto the turbulent distribution as used in the statistical cloud model. Each EDMF component is thus assigned its own independent probability density function (PDF), resulting in an updraft PDF and a diffusive PDF. This double PDF system is configured and integrated in conserved variable space, with the position and orientation of each PDF determined by its unique nature. The parameterization of the associated updraft/diffusion decomposition of variance introduces close ties to the transport scheme; whereas the grid box mean variance is reconstructed using a prognostic variance budget, the variance of the updraft component is parameterized as a function of the spread among various resolved model updrafts. Individual model components and the scheme as a whole are evaluated in detail against large-eddy simulations of a number of prototype subtropical trade wind cases. The results show that various structures in cloud fraction, condensate, and variance are reproduced. The diffusive PDF acts to represent stratiform clouds; the advective PDF represents cumuliform clouds in conditionally unstable layers. This allows representation of complex scenarios in which both cloud forms occur, such as the transitional trade wind regime featuring cumulus rising into stratocumulus.