Parameterization of a surface drag coefficient in conventionally neutral planetary boundary layer

Modern large-scale models (LSMs) rely on surface drag coefficients to parameterize turbulent exchange between surface and the first computational level in the atmosphere. A classical parameterization in an Ekman boundary layer is rather simple. It is based on a robust concept of a layer of constant fluxes. In such a layer (log-layer), the mean velocity profile is logarithmic. It results in an universal dependence of the surface drag coefficient on a single internal non-dimensional parameter, namely the ratio of a height within this layer to a surface roughness length scale. A realistic near-neutral planetary boundary layer (PBL) is usually much more shallow than the idealized Ekman layer. The reason is that the PBL is developing against a stably stratified free atmosphere. The ambient atmospheric stratification reduces the PBL depth and simultaneously the depth of the log-layer. Therefore, the first computational level in the LSMs may be placed above the log-layer. In such a case, the classical parameterization is unjustified and inaccurate. The paper proposes several ways to improve the classical parameterization of the surface drag coefficient for momentum. The discussion is focused on a conventionally neutral PBL, i.e. on the neutrally stratified PBL under the stably stratified free atmosphere. The analysis is based on large eddy simulation (LES) data. This data reveals that discrepancy between drag coefficients predicted by the classical parameterization and the actual drag coefficients can be very large in the shallow PBL. The improved parameterizations provide a more accurate prediction. The inaccuracy is reduced to one-tenth of the actual values of the coefficients.