Tower and aircraft data from a number of field studies are analyzed to: (1) estimate the roughness lengths for local and area-averaged momentum fluxes over various surface types; (2) examine the applicability of the ψ-stability formulations of Paulson and Dyer for momentum fluxes; (3) investigate the possibility that tower flux measurements over tall vegetation are often inadvertently made in the roughness sublayer where Monin–Obukhov (M–O) similarity theory is not valid.
With tower and aircraft data, it is shown that the term ψ(zom/L) evaluated at the roughness height becomes significant with relatively large roughness length and small measurement height. The usual omission of this term in M–O theory is not justified for flux calculations over rough surfaces such as forests.
In stable conditions (z/L<0.5), the Dyer ψ-stability formulation predicts the tower-based momentum fluxes reasonably well over both forest and short vegetation sites. In weakly unstable conditions (−1<z/L), the values of ψ(z/L)−ψ(zom/L) are substantially smaller than the values predicted by the Paulson ψ-stability formulation for many of the tower flux measurements over rough forest canopies, but not over short vegetation sites. To the contrary, the aircraft-based flux measurements over the same forest canopies in weakly unstable conditions yield values of ψ(z/L)−ψ(zom/L) close to the Paulson ψ-stability formulation. Some tower flux measurements over forests were likely in the roughness sublayer during the daytime while the aircraft flux measurements were in the overlying surface layer.
In highly unstable conditions (−2<z/L<−1), the computed values of ψ(z/L)−ψ(zom/L) are observed to be systematically smaller than the Paulson ψ-prediction for most tower sites including those where the computed and predicted values of ψ(z/L)−ψ(zom/L) agree in weakly unstable conditions. These results may indicate the deepening of the roughness sublayer with increasing instability.
Over heterogeneous surfaces, the ψ-stability function for the area-averaged fluxes is found to be larger than the Paulson prediction. The generality of this result is unknown.