An improvement of the two-stream model for vertical mixing of passive tracer in the convective boundary layer

The two-stream model (TSM; Chatfield and Brost, J. Geophys. Res. 92 (1987) 13263-13276) was developed to account for advection-like vertical mixing features of a passive tracer in the convective boundary layer (CBL). In the TSM, the tracer is advected by two-streams (that is, mean updraft and downdraft), of which the vertical profiles are prescribed as functions of the CBL similarity scales, that is, the CBL height and velocity scales. Compared to the results from large-eddy simulation (LES) and laboratory model, the TSM shows similar plume propagation behavior, but the plume propagation speed appears to be too slow. This drawback of the TSM is found to be mainly due to too weak updraft and downdraft. To improve the TSM, therefore, we modify the prescribed vertical profiles of the mean updraft and downdraft using the LES data. Compared to the original up and down draft velocity profiles, the modified profiles have significantly larger magnitudes in the lower CBL while having similar magnitudes in the upper CBL. The realism of the modified TSM simulation of vertical mixing in the CBL is tested for near surface and elevated tracer sources against the LES results of which validity has been well verified with laboratory experiments and observation. For comparison purpose, we introduce other non-local closure models such as the Blackadar model, the asymmetric convective model, and the transilient turbulence parameterization as well as a local K-theory-based scheme. The modified TSM not only predicts much more improved tracer propagation than the original TSM but also yields the most superior results among the models introduced in this study, showing a remarkably realistic description of the temporal behavior for the concentration distributions and the ground and source level concentrations.