Stable boundary layer height on a gentle slope

Height of the stable boundary layer (SBL) presents an important diagnostic used to describe the relevant processes governing the evolution and characteristics of SBL, and the extent to which the surface is communicating with the free atmosphere.  Here we investigate the SBL height over a gentle (1°) mesoscale slope on which relatively deep mid-latitude katabatic flows (with jet maxima between 20 and 50 m) develop during clear nights. We show that detecting the SBL top depends on the method used (Richardson number, flux- and anisotropy-profiles). The detected SBL depth, mostly deviates from the jet maximum height or the top of the near-surface inversion. The flat terrain formulations for the SBL height correlate well with the detected top of the SBL if instead of background stratification, near-surface stratification is used in their formulations, however, they mostly largely overestimate the SBL height. The difference to flat-terrain SBL is also shown through the dependence of size of the dominant eddy with height. In katabatic flows the eddy size is semi-constant with height throughout the SBL, whereas in flat terrain eddy size varies significantly with height.