An Integrated Turbulence Scheme for Boundary Layers with Shallow Cumulus Applied to Pollutant Transport

Abstract

Abstract A scheme is described that provides an integrated description of turbulent transport in free convective boundary layers with shallow cumulus. The scheme uses a mass-flux formulation, as is commonly found in cumulus schemes, and a 1.5-order closure, involving turbulent kinetic energy and eddy diffusivity. Both components are active in both the subcloud and cloud layers. The scheme is called “mass flux–diffusion.” In the subcloud layer, the mass-flux component provides nonlocal transport. The scheme combines elements from schemes that are conceptually similar but differ in detail. An entraining plume model is used to find the mass flux. The mass flux is continuous through the cloud base. The lateral fractional entrainment rate is constant with height, while the detrainment-rate profile reduces the mass flux smoothly to zero at the cloud top. The eddy diffusivity comes from a turbulent kinetic energy–length scale formulation. The scheme has been implemented in a simple one-dimensional (single column...