Grachev A. A., E. L. Andreas, C. W. Fairall, P. S. Guest and P. O. G. Persson (August 2012): Outlier Problem in Evaluating Similarity Functions in the Stable Atmospheric Boundary Layer. Bound. Lay. Meteorol., 144 (2), 137-155. doi:10.1007/s10546-012-9714-9Full text not available from this repository.
The gradient-based similarity approach removes turbulent fluxes as governing parameters and replaces them with vertical gradients of mean wind speed and potential temperature. As a result, the gradient Richardson number, Ri, appears as a stability parameter instead of the Monin–Obukhov stability parameter z/L (L is the Obukhov length). The gradient-based scaling is more appropriate for moderate and very stable conditions when the gradients are large and their errors are relatively small whereas z/L becomes ambiguous in these conditions because turbulent fluxes are small. However, the gradient-based formulation is faced with a problem related to the influence of Ri outliers: outliers with high values of Ri can exist in conditions that are really near-neutral. These outliers are mapped into the very stable range in plots in which Ri is the independent variable and may lead to spurious dependencies for bin-averaged data (spurious bin-averaging). This effect is quite large for functions that are steep for the gradient-based scaling. The present study uses the Surface Heat Budget of the Arctic Ocean (SHEBA) data to examine the problem and proposes two methods, conditional analysis and independent binning, to limit the influence of outliers on bin-averaging. A disadvantage of the conditional analysis is associated with eliminating outliers based on criteria that could be considered as subjective. The independent bin-averaging method does not have this disadvantage, but the scatter of the bin-averaged points is higher than for the conditional analysis, rendering data analysis and interpretation difficult.
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