The Fallacy of Drifting Snow

A common parametrization over snow-covered surfaces that are undergoing saltation is that the aerodynamic roughness length for wind speed (z(0)) scales as alpha u(*)(2)/g, where u(*) is the friction velocity, g is the acceleration of gravity, and a is an empirical constant. Data analyses seem to support this scaling: many published plots of z(0) measured over snow demonstrate proportionality to u(*)(2). In fact, I show similar plots here that are based on two large eddy-covariance datasets: one collected over snow-covered Arctic sea ice; another collected over snow-covered Antarctic sea ice. But in these and in most such plots from the literature, the independent variable, u(*), was used to compute z(0) in the first place; the plots thus suffer from fictitious correlation that causes z(0) to unavoidably increase with u(*) without any intervening physics. For these two datasets, when I plot z(0) against u(*) derived from a bulk flux algorithm- and thus minimize the fictitious correlation-z(0) is independent of u(*) in the drifting snow region, u(*) >= 0.30 ms(-1). I conclude that the relation z(0) = alpha u(*)(2)/g when snow is drifting is a fallacy fostered by analyses that suffer from fictitious correlation.