An iterative solution of flux–profile relationships in the surface layer for regional model applications

Abstract

Due to the implicit character of flux–profile relationships in the atmospheric surface layer, in mesoscale modeling it is common practice to calculate fluxes of momentum, heat, and moisture with approximate formulas. The study presented here shows that a Newton–Raphson iterative procedure to calculate surface fluxes using broadly accepted formulations for universal stability functions is always convergent when an interval for the solution is properly specified. Independent of surface type ( z 0 , z H / z 0 ) , iterations converge to a solution for Obukhov stability parameter ζ with an accuracy of 1 × 10 - 3 within three iterations for the unstable stratification, and within four iterations for the stable stratification. Thus, this investigation suggests that a proper iterative procedure to obtain surface fluxes is not only always convergent but is also computationally efficient and remains a practical alternative to approximate explicit methods.