Evaluation and model impacts of alternative boundary-layer height formulations

We study bulk formulations for the boundary-layer height which are currently in use for atmospheric modelling. The formulations are based on various forms of the Richardson number, and these are evaluated with Cabauw field data in stable conditions. Results for both a large-eddy simulation model and an E-epsilon turbulence closure model for neutral boundary layers are also utilised. An updated formulation is introduced, which combines the effects of shear in the outer region of the boundary layer with surface friction. The updated formulation has a better performance for neutral boundary layers with upper level stratification. The findings are illustrated with a single-column model for a case with relatively high winds over the tropical ocean including shallow cumulus convection, and for a case with fair weather over land. We also show that for stable conditions, the updated formulation performs better than estimates on the basis of surface friction alone.