A Simple, Efficient Solution of Flux–Profile Relationships in the Atmospheric Surface Layer

This note describes a simple scheme for analytical estimation of the surface-layer similarity functions from state variables. What distinguishes this note from the many previous papers on this topic is that this method is specifically targeted for numerical models in which simplicity and economic execution are critical. In addition, it has been in use in a mesoscale meteorological model for several years. For stable conditions, a very simple scheme is presented that compares well to the iterative solution. The stable scheme includes a very stable regime in which the slope of the stability functions is reduced to permit significant fluxes to occur, which is particularly important for numerical models in which decoupling from the surface can be an important problem. For unstable conditions, simple schemes generalized for varying ratios of aerodynamic roughness to thermal roughness (z0/z0h) are less satisfactory. Therefore, a simple scheme has been empirically derived for a fixed z0/z0h ratio, which represents quasi-laminar sublayer resistance.