Resistance and heat‐transfer laws for stable and neutral planetary boundary layers: Old theory advanced and re‐evaluated

Abstract

Abstract The planetary boundary layer (PBL) resistance and heat‐transfer laws express the surface fluxes of momentum and heat through the PBL governing parameters. Since the late sixties, the dimensionless coefficients ( A , B and C ) in these laws were considered as single‐valued functions of internal stability parameters: µ= u * /| f | L s in the steady state PBLs, or h / L s in the evolving PBLs ( u * is the friction velocity, f is the Coriolis parameter, L s is the surface Monin–Obukhov length, and h is the PBL depth). Numerous studies revealed very wide spread of data in empirical plots of A , B and C versus µ or h / L s. It is not surprising that the above laws, although included in all modern textbooks on boundary‐layer meteorology, are not practically used. In the present paper the resistance and heat‐transfer laws are revised, accounting for the free‐flow stability, baroclinicity and the rise of a capping inversion. The coefficients A , B and C become functions not only of µ or h / L s, but also of the external stability parameter µ N = N /| f | (where N is the Brunt–Väisälä frequency in the free atmosphere above the PBL), the parameter of baroclinicity µ Γ =Γ/ N (or the free‐flow Richardson number Ri=( N /Γ) 2 =µ Γ −2 , where Γ is the geostrophic wind shear), and the ratio of the actual and equilibrium PBL depths h / h E. Moreover, the coefficient C is redefined to account for the effect of a capping inversion. It follows that A , B and C can be considered as single‐valued functions of µ only in the steady‐state, barotropic, nocturnal (that is short‐lived) PBL. On the other hand, the advanced laws cover a wide range of the PBL regimes. They are validated through large‐eddy simulations of different types of PBLs: truly neutral, conventionally neutral, nocturnal and long‐lived. This new development explains why prior formulations performed so poorly, and promotes advanced resistance and heat‐transfer laws as practical tools for use in environmental modelling applications. Copyright © 2005 Royal Meteorological Society.