A major source of uncertainty in hydraulic downslope flow models is the parameterization of turbulent exchange processes between the slope-wind layer and the ambient atmosphere. Usually this exchange is parameterized in terms of an entrainment parameter that depends on the bulk Richardson number, based on relationships found in laboratory experiments. Mixing at the top of the slope-wind layer is regarded as a one-way process, with the downslope mass-flux steadily increasing along the slope through incorporation of entrained fluid. A different aspect of slope flows is captured by so-called equilibrium (or 'Prandtl') models that resolve the vertical structure of the flow but neglect along-slope nonlinear advective terms. This is justified in cases of steep, homogeneous slopes in strongly stratified environments. Under such conditions the buoyancy force is locally balanced by turbulent stress divergence, and surface cooling is locally balanced by advective warming in the presence of a background stratification. What happens when the upper parts of a steep slope are weakly stratified, while the lower parts are embedded in a stably stratified cold air pool? This situation occurs frequently in valleys and basins. It is shown that the standard hydraulic approach is unable to handle an abrupt along-slope change to more stable conditions because entrainment is always positive. The strong deceleration of the modelled flow as it enters the stable layer, combined with a steadily increasing mass-flux leads to a strong increase in layer depth and does not permit adaptation to shallow equilibrium flow.

Recent laboratory experiments suggest that in order to understand the behaviour of downslope flows in stratified environments the process of detrainment must be taken into account. Based on results from these experiments, a new parameterization of net entrainment (=entrainment-detrainment) is being tested within the framework of the classical hydraulic model. With the new parameterization the model is able to adapt to an abrupt increase in stability along the slope by net detrainment of fluid. This way the hydraulic approach can be reconciled with equilibrium models. Tethersonde measurements taken during the VTMX October 2000 IOP's in Salt Lake City allow to test the new parameterization in the limit of very gentle slopes. Using the classical entrainment parameterization, the model predicts a significant increase of layer depth from the uppermost tethersonde (TS3) to the lowermost one (TS1), the two being about 2 km apart. It also predicts a decrease in wind-speed, and a decrease in inversion strength down the slope. Observations, however, show that the depth of the slopewind layer increases only slightly, and flow speed and inversion strength tend to increase rather than decrease in downslope direction. Generally the observed flow appears to be very close to local equilibrium. With the new entrainment parameterization, the model produces more realistic results. Layer depth increases only by a small amount from TS3 to TS1, and the modelled flow is close to equilibrium, as observed. However, flow speed and inversion strength still show a slight decrease along the slope, in contrast to observations.