Quantifying the Influence of Random Errors in Turbulence Measurements on Scalar Similarity in the Atmospheric Surface Layer

The influence of random errors in turbulence measurements on scalar similarity for temperature, water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\) is investigated using two eddy-covariance datasets collected over a lake and a cattle feedlot. Three measures of scalar similarity, namely, the similarity constant in the flux–variance relationship, the correlation coefficient between two scalars and the relative transport efficiency, are examined. The uncertainty in the similarity constant \(C_{s}\) in the flux–variance relationship resulting from random errors in turbulence measurements is quantified based on error propagation analyses and a Monte-Carlo sampling method, which yields a distribution instead of a single value for \(C_{s}\). For different scalars, the distributions of \(C_{s}\) are found to significantly overlap, implying that scalars are transported similarly under strongly unstable conditions. The random errors in the correlation coefficients between scalars and the relative transport efficiencies are also quantified through error propagation analyses, and they increase as the atmosphere departs from neutral conditions. Furthermore, the correlation coefficients between three scalars (water vapour, \(\hbox {CO}_{2}\), and \(\hbox {NH}_{3}\)) are statistically different from unity while the relative transport efficiencies are not, which highlights the difference between these two measures of scalar similarity. The results suggest that uncertainties in these measures of scalar similarity need to be quantified when using them to diagnose the existence of dissimilarity among different scalars.