Using second order closure to obtain mesoscale and turbulent heat fluxes

Regional air quality simulation requires robust, forecast simulations of the atmospheric planetary boundary layer (PBL), as well as vertical transports from PBL to the free atmosphere. Both depend quite strongly on the underlying landscape and its heterogeneities. The landscape affects the processing of solar radiation at the land surface: drier or more sparsely vegetated land surfaces produce more sensible heat flux than wetter or more heavily vegetated land surfaces. Partly through its effects on the energy balance, the land surface also affects the boundary conditions for the prognostic equations for momentum, heat and moisture via the surface shear stress, heat and moisture fluxes. Most importantly, landscape heterogeneities can lead to the formation of landscape generated mesoscale circulations (LGMCs), leading to a redistribution of energy from small to large eddies, from turbulent to mesoscale, further impacting the solution to the prognostic equations.

A new approach to boundary layer parameterizations is needed. Research has shown qualitative agreement between the vertical profile of the mesoscale kinetic energy and the mesoscale heat fluxes (MKE). However, MKE is anisotropic while the turbulent kinetic energy (TKE) is isotropic. Thus, while it is reasonable to assume that the TKE can be used to obtain the vertical profile of the K coefficients, no simple relationship exists between the K coefficients and the MKE. Thus, we chose a second order closure model over a first order or one and one-half order TKE scheme because TKE schemes more realistically simulate turbulence than first order schemes, yet TKE schemes cannot be used to obtain realistic flux profiles over heterogeneous domains.

In this presentation, we suggest to use a simplified second order scheme to obtain the subgrid-scale fluxes in regional-scale atmospheric models. The simplifying assumption is that we calculate only the profiles of the vertical fluxes, and ignore horizontal advection of fluxes between grid-elements, the Coriolis force and molecular diffusion. We show how the remaining closure terms vary with the heterogeneity of the landscape and background atmospheric conditions. We use the vertically integrated MKE to obtain these closure terms.

.