Multifractal characterization of aircraft-based measurements of turbulence and passive scalar fields within the surface boundary layer

This thesis represents the first large-scale, systematic study to use the double trace moment (DTM) technique in order to characterize the universal multifractal nature of aircraft-based measurements of wind velocity and several passive scalar concentrations under a variety of ambient conditions. Power-law scaling behaviour was demonstrated for the examined fields, from the smallest accessible measurement scales up to at least 250 km, right through the "mesoscale gap" postulated by the standard model of atmospheric dynamics. DTM results indicate remarkable stability in the estimates of the multifractality index, $ alpha$, and the codimension of mean singularity, $C sb1$, for wind velocity measured under different conditions of surface type, time of year, and measurement height within the surface boundary layer. Estimates for $ rm CO sb2, H sb2O, and O sb3$ were largely dominated by the wind velocity statistics as expected, but slightly sensitive to measurement height and moderately sensitive to significant changes in the underlying surface. Results showed that all of the fields examined may be classified as "unconditionally hard" multifractals, which is consistent with previously-published results for ground-based wind velocity measurements. It was demonstrated using probability distribution and multifractal analyses that ensemble statistical moments above approximately second-order can be expected to diverge for all examined fields due to the extremely singular nature of the fields at sub-resolution scales, and that the currently-employed quasi-local aircraft based sampling strategy is capable of reliably characterizing the statistical behaviour of the examined fields up to this physically-imposed limit. (Abstract shortened by UMI.