The fallacy of drifting snow

            A common premise used for estimating the turbulent fluxes over snow-covered surfaces is a Charnock-like relation in which the aerodynamic roughness for the wind speed profile (z₀) scales as the square of the friction velocity (u_*) when snow is drifting and blowing.  Two large datasets obtained over snow-covered winter sea ice—one from the Arctic, one from the Antarctic—corroborate this premise when I plot z₀ against the measured u_*.  But this result seems to be fictitious correlation because u_* is the independent variable in such plots but is also required for computing the dependent variable, z₀.  In other words, z₀ and the measured u_* have built-in correlation because of shared errors.  On the other hand, when I plot z₀ against the u_* value that comes from a bulk turbulent flux algorithm (denoted u_*,B) and, thus, does not have built-in correlation with z₀, z₀ is independent of u_*,B for u_*,B in the drifting snow regime, u_*,B > 0.3 m/s.  The premise that z₀ increases with u_* when snow begins to drift is, therefore, a fallacy that ensues from flawed analyses.