A simplified PDF parameterization of subgrid-scale clouds and turbulence for cloud-resolving models

Over the past decade a new type of global climate model (GCM) has emerged, which is known as a multiscale modeling framework (MMF). Colorado State University's MMF represents a coupling between the Community Atmosphere Model and the System for Atmospheric Modeling (SAM) to serve as the cloud-resolving model (CRM) that replaces traditionally parameterized convection in GCMs. However, due to the high computational expense of the MMF, the grid size of the embedded CRM is typically limited to 4 km for long-term climate simulations. With grid sizes this coarse, shallow convective processes and turbulence cannot be resolved and must still be parameterized within the context of the embedded CRM. This paper describes a computationally efficient closure that aims to better represent turbulence and shallow convective processes in coarse-grid CRMs. The closure is based on the assumed probability density function (PDF) technique to serve as the subgrid-scale (SGS) condensation scheme and turbulence closure that employs a diagnostic method to determine the needed input moments. This paper describes the scheme, as well as the formulation of the eddy length which is empirically determined from large eddy simulation (LES) data. CRM tests utilizing the closure yields good results when compared to LESs for two trade-wind cumulus cases, a transition from stratocumulus to cumulus, and continental cumulus. This new closure improves the representation of clouds through the use of SGS condensation scheme and turbulence due to better representation of the buoyancy flux and dissipation rates. In addition, the scheme reduces the sensitivity of CRM simulations to horizontal grid spacing. The improvement when compared to the standard low-order closure configuration of the SAM is especially striking.