Measurements of the von Kármán constant in the atmospheric surface layer—further discussion

We obtained estimates of the von Kármán constant, k, by analyzing wind speed profiles and eddy-correlation measurements of turbulent fluxes from two large data sets—one obtained over Arctic sea ice; the other, over Antarctic sea ice. A perfectly logarithmic wind speed profile is a robust feature of both sets although stratification is not necessarily neutral during these observations nor is the atmospheric surface layer necessarily a layer of constant momentum flux.

We suggest that, theoretically, k should depend on the roughness Reynolds number R_*, as others have reported. And in fact, both data sets show that k depends dramatically on R_*. That correlation seems to be totally fictitious, however. Evaluating both k and R_* requires some of the same measured variables, the friction velocity u_*, for example. Our mathematical analysis based on the assumption that none of these variables are correlated shows that, because k and R_* share variables, the fictitious correlation between the two is essentially the same as what we see in the data.

On the other hand, when we evaluate R_* from a bulk flux algorithm, k shows virtually no correlation with this bulk roughness Reynolds number. Consequently, we have over 600 individual measurements of k that scatter between 0.25 and 0.55—well beyond our experimental precision—and we have no obvious explanation why.