A note on MOST and HOST for turbulence parameterization

An extended expression of the (u(*), U) relationship (u(*) is the square root of turbulent momentum fluxes and U is the mean wind speed) based on Monin-Obukhov Similarity Theory (MOST) is compared qualitatively with an observed (u(*), U) relationship for its variation between near neutral and stably stratified regimes. MOST, in its standard or classic form, cannot capture the observed characteristics of the increasing u(*) with U from its gradual change in the statically (strongly) stable regime to the sharp change toward the near neutral regime, the so-called HOckey-Stick Transition (HOST). A heuristic formulation based on a drag coefficient is proposed for describing the observed relationship; it is found to be able to capture the tendency of the regime change even though the formulated transition is not as dramatic as the observations imply. For this purpose, almost like in some previous studies, a background flux is assumed. It accounts for cumulative non-traditional effects on turbulence; thus, it renders an extended MOST and HOST, arguably speaking, compatible.