| Popis: |
During night time, when the air close to the surface cools-down and the atmosphere becomes stable, katabatic down-slope ows may occur in mountainous regions. Contrary, during day time, when the sun heats-up the air close to the surface, and the atmosphere becomes unstable, anabatic upslope ows are prevalent. Up to date, slope winds in the WKB Prandtl model are determined solely by means of specifying the height zj of the maximum turbulent jet above ground. Furthermore, depending on zj parameters K0 and h for a height-dependent eddy thermal diffusivity function KH(z) and a parameter C determining the amplitude for the Prandtl wind speeds must be specified. They are most often estimated from height-dependent wind speeds u, including slope angle α and fixed Prandtl number Pr = KM/KH with KH = KH(z) and KM the eddy viscosity. Having estimated those parameters, friction velocity u*, friction temperature θ* and sensible heat ux QH may be calculated. This article takes the reverse approach: From specified slope angle α, Pr, u*, θ*, QH and specified form of the eddy thermal diffusivity function KH(z) the corresponding WKB Prandtl model is identified. Furthermore, the relationship between u* and θ* calculated via Monin-Obukhov similarity theory for at terrain and those for the WKB Prandtl model are investigated. Using this relationship, we give hints how our new parametrization of the WKB Prandtl model may be used to determine slope ows and free air ows in a micro meteorological model of an alpine valley for pollutant dispersion calculations. We illustrate our derivations by applying our algorithms for the calculation of the WKB Prandtl model to four examples with two taken from Grisogono et al. (2015). |
