The temperature profile and heat transfer law in a neutrally and stably stratified planetary boundary layer

A logarithmic + polynomial approximation is proposed for the vertical temperature profile in a neutrally or stably stratified planetary boundary layer (PBL) in conditions of quasi-stationarity. Using this approximation with the asymptotic logarithmic + linear law of the Monin-Obukhov similarity theory for the near-surface layer and with the Zilitinkevich formula for the PBL thickness allows one to derive an analytical expression for the function C in the heat transfer law, which permits simple parameterization of the thermal interaction between the atmosphere and the underlying medium in terms of external parameters, such as the geostrophic wind velocity and the temperature difference across the PBL.