Outlier problem for gradient-based scaling in the stable boundary layer

Traditionally, the non-dimensional gradients of wind speed and potential temperature are plotted versus z/L, where L is the Obukhov length. A troubling feature of this analysis is that the two quantities between which a functional relationship is sought have built-in correlation (or self-correlation) because of their shared variables. The atmospheric boundary-layer community has recognized that artificial self-correlation is one of the major problems in analyzing atmospheric turbulence, especially the presumably universal functions of Monin-Obukhov similarity theory. Self-correlation may lead to spurious dependencies that are not associated with real physics. Another approach for overcoming the self-correlation in flux-gradient relationships for stably stratified conditions replaces z/L with the gradient Richardson number, Ri, (gradient-based scaling). However, in this case, a problem related to the influence of outliers on the bin-averaging comes into play. This problem is associated with the existence of outliers with high values of Ri for conditions that are ‘really' near-neutral. These outliers get mapped into the very stable range in Ri-based plots. The outlier problem is more important for Ri-based scaling than for traditional z/L-scaling. This is because the slope of Ri versus z/L in log-log coordinates for very stable conditions is less than one; therefore the range of Ri is relatively small compared to the range of z/L (the bulk of data is associated with Ri < 1). Furthermore, the number of outliers with high values of Ri in near-neutral conditions is comparable with a number of points that truly have high value of Ri, i.e., 'really' very stable conditions. As a result, these Ri-outliers transposed from the near-neutral range may significantly distort the picture in the very stable regime. This study uses the SHEBA (Surface Heat Budget of the Arctic Ocean) dataset to examine the outlier problem and considers methods to limit the influence of outliers on the bin-averaging.