Diagnostic equations for the stable boundary layer height : evaluation and dimensional analysis

The performance of diagnostic equations for the stable boundary layer height h is evaluated with four observational datasets that represent a broad range of latitudes, land use, and surface roughness. In addition, large-eddy simulation results are used. Special care is given to data-quality selection. The diagnostic equations evaluated are so-called multilimit equations as derived by Zilitinkevich and coworkers in a number of papers. It appears that these equations show a serious negative bias, especially for h <100 m, and it was found that the parameters involved could not be determined uniquely with calibration. As an alternative, dimensional analysis is used here to derive a formulation for h that is more robust. The formulation depends on the surface friction velocity u*, surface buoyancy flux Bs, Coriolis parameter, and the free-flow stability N. The relevance of the Coriolis parameter for the boundary layer height estimation in practice is also discussed. If the Coriolis parameter is ignored, two major regimes are found: h u*/N for weakly stable conditions and h (|Bs|/N¿3)1/2 for moderate to very stable conditions.