A New Scheme for Effective Roughness Length and Effective Zero-Plane Displacement in Land Surface Models

Based on the similarity theory of the atmospheric surface layer and the flux conservation and mass conservation laws, a new scheme for determining the effective roughness length (ERL) and the effective zero-plane displacement (EZPD) for a heterogeneous terrain is proposed. The test for a two-category system case shows that the ERL (EZPD) is larger (smaller) than the area-weighted logarithmic (linear) averaged one, whereas differences between the new ERL/EZPD and their average values are increased with roughness ratio and rough-portion zero-plane displacement (RZPD) in the grid square. Though the ERL and EZPD show some dependence on atmospheric stability, they can be treated as constants in the land surface models unless the seasonal variation must be taken into account. This is due to the fact that the error percentage of the effective drag coefficients, which are dependent on the ERL and EZPD, is less than 2% under all stability conditions. Moreover, the dynamical effects of the underlying surface can be represented jointly by the ERL and the EZPD, either for a heterogeneous terrain or for a homogeneous terrain with high obstacles. The enhancement effect of the roughness ratio on ERL and EZPD is magnified by the RZPD. However, the ratio of rough area over smooth area, where the maximum ratio of ERL over the area-weighted mean as well as the maximum difference between EZPD and area-weighted mean occurs, is dependent on the roughness ratio but independent of the RZPD. The ERLs computed by this new model are also compared with other schemes and large-eddy simulation, where the effect of RZPD is not considered.