Surface Flux Similarity in the Layer Near the Surface over Mountainous Terrain

The applicability of similarity theory for the scaled standard deviations of temperature and humidity is studied in complex terrain. The degree to which similarity theory applies, even under surface conditions for which it is in principle not designed, can shed some light on the appropriateness and potential problems of boundary layer and surface exchange parameterizations in numerical models of the atmosphere (numerical weather prediction and climate models) and in applied models (hydrology, air pollution, etc.) over complex terrain. The study area is a steep Alpine valley in Austria, with six measurement sites of different slope angle, orientation, and roughness (i.e., the i-Box, Inn Valley). Some of the basic assumptions of Monin-Obukhov Similarity theory (MOST), which was designed for horizontally homogeneous and flat conditions, are violated in this complex terrain, specifically the assumption of approximately constant turbulence fluxes with height. As a result, the analysis was performed based on a local similarity hypothesis.

The scaled standard deviations as a function of local stability were compared with previous studies over various types of terrain (horizontally homogeneous and flat, horizontally inhomogeneous and flat, as well as complex terrain). Since even for horizontally homogeneous and flat terrain, no unique similarity function could be found from the literature, we used similarity formulas derived from the weakly inhomogeneous and flat terrain of the Cabauw experimental site in the Netherlands (KNMI) as a reference for our study. Considering the low measurement height of 3 m, the terrain inhomogeneity is in fact very weak. Exactly the same post-processing method was applied for both datasets (i-Box and Cabauw) before the analysis. Local best-fit curves were then fitted to the data from each site separately.

A characteristic feature of (scaled) temperature standard deviations in complex terrain appears to be that significantly larger values are obtained than over flat ground. None of the investigated reasons could explain this behavior – so that the terrain itself must be the reason for this. The slopes and magnitudes of the best-fit similarity curves exhibit significant differences among the i-Box sites, as well as between the i-Box sites and the reference, for both unstable and stable stratification. Although the derived best-fit similarity equations are highly site dependent, no specific relation between the best-fit coefficients and the terrain characteristics, such as terrain slope angle, could be detected.