A Multifractal Description of Wind Speed Records

TL;DR

The study investigates long-range correlations in hourly wind speeds by applying Multifractal Detrended Fluctuation Analysis (MFDFA) to four North Dakota sites. It quantifies multifractal scaling via h(q) and the f(α) spectrum and tests the robustness of results with surrogate shuffles. The results reveal consistent multifractal behavior and long-range correlations across sites, with surrogate data destroying these features. The binomial multiplicative cascade provides an analytic fit to the observed spectra, and the similarities in spectra widths across sites suggest broader geographic relevance for wind variability.

Abstract

In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of $1/f^α$ processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis {\em MFDFA}. It is seen that the records at all four locations exhibit similar scaling behavior which is also reflected in the multifractal spectrum determined under the assumption of a binomial multiplicative cascade model.

Figures (6)

• Figure 1: Temporal trace and Power spectrum of a representative record
• Figure 2: A map of the wind monitoring sites
• Figure 3: Fluctuation functions at all sites using MFDFA. Symbols used to indicate the various moments are $q = -6$ (-), $q=-4$(inverted triangle), $q =-2$ (x), $q = 2$ (.), $q = 4$ (o), $q = 6$ (+). The curves are vertically shifted for clarity.
• Figure 4: Generalized scaling exponents for wind speed records at the four sites. Circles indicate the actual values of the scaling indices for $q = -6,-4,-2,2,4 \;$and$\;6$. The solid line represents the fit from the multiplicative cascade model (Eqn.(\ref{['mfcascade']})) obtained from a nonlinear least squares procedure. The values of $a$ and $b$ are indicated for each site.
• Figure 5: Fluctuation functions at all sites using MFDFA for random shuffle surrogates of the original data. Symbols used to indicate the various moments are $q = -6$ (-), $q=-4$(inverted triangle), $q =-2$ (x), $q = 2$ (.), $q = 4$ (o), $q = 6$ (+). The curves are vertically shifted for clarity. Note that the curves are parallel to each other with a slope of $\sim 0.5$.