Comments on deriving the equilibrium height of the stable boundary layer

Recently, the equilibrium height of the stable boundary layer received much attention in a series of papers by Zilitinkevich and co-workers. In these studies the stable boundary-layer height is derived in terms of inverse interpolation of different boundary-layer height scales, each representing a prototype boundary layer. As an alternative we propose an inverse interpolation of the eddy diffusivities for each prototype before applying the definition of the Ekman layer depth. The new equation for the stable boundary-layer height improves performance in a comparison against four observational dataset