Discrepancy and Applicability of Various Similarity Functions in Flux Calculations Under Stable Conditions

Based on data obtained during the Huaihe River Basin Experiment (HUBEX) in 1999, this study intends to detect the quantitative discrepancies in the momentum (τ0), sensible heat (H0) and latent heat (E0) fluxes among six sets of similarity functions with the aerodynamic method. It also aims to clarify the applicability of the functions under stable conditions. The relative discrepancy was studied with the normalized transfer coefficients for τ0, H0 and E0, namely CD, CH and CQ, respectively. Except for one set of functions that adopted a rather small von Karman's constant (0.365), the relative discrepancy in τ0 among the other functions was less than 10%, while that in H0 E0 sometimes reached 25% when the bulk Richardson number (RiB) was less than 0.07. The absolute discrepancy in the fluxes was studied with statistical computations. Among the six sets of functions, the discrepancy in τ0, H0 and E0 sometimes reached 0.03 kg m-1 s-2, 4 W m-2 and 10 W m-2, respectively, and the discrepancy in the energy balance ratio sometimes exceeded 0.1. Furthermore, when RiB exceeded the critical value Ric) for a specific set of functions, no fluxes could be derived with the functions. It is therefore suggested that RiB be compared with Ric before computing the fluxes if RiB is less than Ric. Finally, two sets of nonlinear similarity functions are recommended, due to their unlimited applicability in terms of Ri B.