A performance comparison between nonlinear similarity functions in bulk parameterization for very stable conditions

Three sets of nonlinear similarity functions for strong stability are selected to compare their performance in bulk parameterization. To uncover their advantages and disadvantages, theoretical and measurement analyses are made with four profile metrics and the Deacon number technique. Main disadvantages include the negligence of the different transfer efficiency between momentum and heat, the flux cutoff due to the upper limit in gradient Richardson number (Ri) and the ignorance of limited stability range where the dimensionless gradient functions ( and ) approach constants. Accordingly, three suggestions are made for future improvement. First, the functions for wind velocity and potential temperature should have the same function form, but with different coefficients. Second, and should approach constants only within a certain stability range. Third, the limit value in Ri should be avoided to widen their applicability in flux modeling. Furthermore, quantitative comparisons in transfer coefficients for moment and sensible heat (C _D and C _H) are made among the similarity functions in the bulk Richardson number (Ri _B) range 0 < Ri _B < 1. Generally, significant discrepancy is found, which may approach a factor of two and three at large Ri _B in C _D and C _H, respectively. Finally, a new recommendation is made to one of the three sets, mainly because of its ability to predict C _D and C _H that decrease rather slowly in very stable conditions.