A theory for the estimation of surface fluxes in simple katabatic flows

The classical Prandtl model describes the basic dynamics of katabatic flows , but it fails in determining the gradients near the surface because the ed dy diffusivity, K, is independent of height, z. An improvement is proposed to the Prandtl model by using the WKB method to solve the dynamic equation for any prescribed, reasonably smooth, K(z) profile. The surface fluxes are obtained by extrapolation from the katabatic jet dow n to the surface, thus the fluxes depend primarily on the jet which is well captured by the WKB method. The profiles of wind. temperature, momentum an d heat fluxes, as well as the surface fluxes calculated using the model, ar e tested against observations from a meteorological field campaign on the P asterze glacier, Austria, in 1994, and their numerical simulations. General ly there is a good agreement between observations and theory.