Multifractal analysis of wind velocity data

• Wind velocity variation can be represented by a multifractal spectrum.
• The wind multifractal spectrum is of Weierstrass type.
• The spectrum obtained was interpreted in meteorological terms.

We analyze the wind velocity, v(t), at a location in the Patagonia, Argentina, as a function of time, measured every 10 min, uninterruptedly, over a one-year period, by taking the graph (t, v(t)) as a signal, and applying the tools of multifractal analysis. The multifractal spectrum (α, f(α)) of this signal, obtained by the definition of α and f(α), is strangely smooth, for it fulfills all properties of the twice-differentiable thermodynamical formalism, the theoretical algorithm devised to mimic the spectrum-by-definition (with which it may not coincide, since the latter may not even be continuous). We give arguments to conclude that the wind-spectrum is of Weierstrass type. We take a finite sample of Weierstrass functions, Wλ,s(t), at regular intervals Δt, the size of each sample comparable to that of the wind signal. We take these samples as signals, and construct their multifractal spectra by definition, for different parametric values of λ and s. We compare the different Weierstrass spectra with the wind spectrum, and obtain information on the Weierstrass parametric values that agree with the wind spectrum. We interpret the key points of the wind spectrum in meteorological terms. Any change, from one year to the next, in the position of such key points, or in the shape of the spectral curve—once interpreted in the corresponding meteorological terms—could be some local indicator of climate change.