Analysis and simulation of surface-layer winds using multiplicative cascade models with self-similar probability densities

Statistical analysis techniques based on multiplicative cascades are investigated for use with surface-layer wind data sets collected in the atmospheric boundary layer over flat farm land. The data were found to exhibit multiscaling statistics, allowing the surface-layer winds to be simulated with the use of multiplicative random cascades. The study found evidence that, for the surface-layer at least, these cascade models (and hence the methods of multifractal analysis) should be applied in separate ways to the microscale inertial range, and the mesoscale. This is at odds with the view found in the existing literature, which proposes a 'universal multifractal' model to replace the widely held view that there exists separate microscale, mesoscale and synoptic scales for which the processes governing each are different. At least two separate ranges of scaling are suggested for surface-layer wind data, corresponding to the microscale inertial range and the mesoscale. For the case of the mesoscale range, a self-similar distribution of weighting factors was found for the wind speed data themselves, rather than for an intermediate (dissipation) field, as is required for the microscale data.