Finite-Difference Errors in Estimation of Gradients in the Atmospheric Surface Layer

Abstract

Errors associated with the linear and the logarithmic finite-difference approximations of gradients in the surface layer are computed using the well-known Monin-Obukhov flux-profile relations. It is shown that while the logarithmic approximation is much superior to the linear one in near-neutral and unstable conditions, the latter is equally good or better for stable conditions. The computed ratios of the estimated to the ?exact? gradients are given as functions of stability and the ratio between the two heights used for finite-difference approximation. The results can be used for correcting the estimated gradients using either linear or logarithmic approximation over wide ranges of stability and height ratio.