A multi-stream model for vertical mixing of a passive tracer in the convective boundary layer

While many Eulerian air quality models use so-called K-theory concepts to represent the subgrid-scale vertical mixing in the atmospheric boundary layer, it is well known that the K-theory-based schemes where the vertical mixing processes are confined to adjacent layers represent turbulent mixing processes inadequately, especially in the convective boundary layer (CBL). The CBL is composed of narrow updrafts and broad downdrafts, which can extend most of the depth of the CBL and consequently transport air mass vertically across large distances. The poor representation of the vertical mixing in the K-theory-based schemes is mainly caused by this advective-like vertical mixing process. In this study, we propose a simple transport-diffusion model (TDM) to describe the vertical mixing of a passive tracer in the CBL.

In TDM, the tracer is allowed to be advected by mean updrafts and downdrafts, and at the same time, it is diffused by subgrid-scale turbulence. The mean updrafts and downdrafts are prescribed from large-eddy simulation (LES) results and mixed-layer similarity theory. The subgrid eddy viscosity is parameterized in terms of grid size and energy dissipation rate that can be obtained from mixed-layer similarity relation. The applicability of the TDM is tested against LES results for both surface and elevated tracer sources.