Multifractal analysis and modeling of wind speeds. Application to wind resource forecasting

The main purpose of this work is the study of atmospheric surface layer wind speeds within the framework of multifractal processes. We show that random cascade models, originally introduced to account for the spatio-temporal intermittency of the velocity and dissipation fields in fully developed turbulence, turn out to be also pertinent to describe the wind fluctuations at mesoscale range. Theoretically, we present a new multifractal formalism we have introduced, the 'mixed asymptotic scaling', that generalizes standard multi-scaling analysis and allows us to estimate the so-called 'negative dimensions' introduced by Mandelbrot twenty years ago. When applied to turbulence data, this approach allows one to distinguish various popular cascade models of dissipation intermittency. By studying both temporal and spatial wind speed increments from various time series gathered at different locations in Corsica and Netherlands, we provide evidences for the intermittent nature of the mesoscale wind fluctuations. By means of magnitude covariance analysis, which is shown to be a more efficient tool to study intermittency than classical scaling analysis, our findings suggest the existence of some 'universal' cascade mechanism associated with the energy transfer between synoptic motions and turbulent micro-scales in the atmospheric boundary layer. Inspired by these observations, we build a time series model of temporal wind dynamics associated with a continuous random cascade. This picture fits remarkably empirical wind speed distributions and allows one to address the problem of wind forecasting at short term horizons (1-12 hours ahead) that leads to a systematic improvement of predictions as compared to reference models. (author)