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

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: mu = 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 mu 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 mu or h/L-s, but also of the external stability parameter mu(N) = N/|f| (where N is the Brunt-Vaisala frequency in the free atmosphere above the PBL), the parameter of baroclinicity mu(Gamma) = Gamma/N (or the free-flow Richardson number Ri = (N/Gamma)(2) = mu(Gamma)(-2), where Gamma 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 mu 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.