The position of the lowest levels in the boundary layer of atmospheric circulation models

Abstract

The error associated with the position of the lowest wind level in atmospheric boundary‐layer modelling is studied in connection with vertical resolutions typical of parametrization schemes for atmospheric circulation models. The test case is the neutrally stratified steady‐state boundary layer. Finite‐difference and finite‐element schemes of two types are used: in one case the lowest wind level is centred with respect to the surface and the lowest internal level where the shear stress is calculated, in the other case the lowest wind level is set very close to the surface (5 m). It is found that schemes of the latter type underestimate the friction force at the lowest level and consequently overestimate the wind and the surface stress. This error is largest at low resolution since it is due to the uncentring of the lowest wind level with respect to the stress levels. The error in schemes of the former type is different, and is associated with the determination of the surface stress from a wind at a height that may exceed the extent of the surface layer. For all neutral cases, this error can be made small by adding a corrective term to the traditional logarithmic formulation. This paper shows that considerably more error is generated by uncentred differencing than by deepening the surface layer.