Quantifying horizontal and vertical tracer mass fluxes in an idealized valley during daytime

Abstract. The transport and mixing of pollution during the daytime evolution of a valley boundary layer is studied in an idealized way. The goal is to quantify horizontal and vertical tracer mass fluxes between four different valley volumes: the convective boundary layer, the slope wind layer, the stable core, and the atmosphere above the valley. For this purpose, large eddy simulations (LES) are conducted with the Weather Research and Forecasting (WRF) model for a quasi-two-dimensional valley. The valley geometry consists of two slopes with constant slope angle and is homogeneous in the along-valley direction. The surface sensible heat flux is horizontally homogeneous and prescribed by a sine function. The initial sounding is characterized by an atmosphere at rest and a constant Brunt–Väisälä frequency. Various experiments are conducted for different combinations of surface heating amplitudes and initial stability conditions. A passive tracer is released with an arbitrary but constant rate at the valley floor and resulting tracer mass fluxes are evaluated between the aforementioned volumes.

As a result of the surface heating, a convective boundary layer is established in the lower part of the valley with a stable layer on top – the so-called stable core. The height of the slope wind layer, as well as the wind speed within, decreases with height due to the vertically increasing stability. Hence, the mass flux within the slope wind layer decreases with height as well. Due to mass continuity, this along-slope mass flux convergence leads to a partial redirection of the flow from the slope wind layer towards the valley centre and the formation of a horizontal intrusion above the convective boundary layer. This intrusion is associated with a transport of tracer mass from the slope wind layer towards the valley centre. A strong static stability and/or weak forcing lead to large tracer mass fluxes associated with this phenomenon. The total export of tracer mass out of the valley atmosphere increases with decreasing stability and increasing forcing. The effects of initial stability and forcing can be combined to a single parameter, the breakup parameter B. An analytical function is presented that describes the exponential decrease of the percentage of exported tracer mass with increasing B. This study is limited by the idealization of the terrain shape, stratification, and forcing, but quantifies transport processes for a large range of forcing amplitudes and atmospheric stability.