Modeling of atmospheric wind speed sequence using a lognormal continuous stochastic equation

Calif, Rudy; Schmitt, François G

doi:10.1016/j.jweia.2012.06.002

Cited by 65 publications

(37 citation statements)

References 31 publications

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“…The spectral analysis showed that the Fourier spectra E v (f ) follows a power law: E(f ) ∼ f −β for the small-scale and the mesoscale range. Thus, for the small timescales (0.05 T 1 s) corresponding to the inertial range, the Fourier spectrum was close to the Kolmogorov spectrum, with β = 1.68, in agreement with previous studies (Schmitt et al, 1993;Katul et al, 1995;Schmitt, 2007;Böttcher et al, 2007;Morales et al, 2011;Calif and Schmitt, 2012). The structure function analysis highlighted the concavity and the nonlinearity of the exponent function ζ vH (q).…”

Section: The Atmospheric Wind Speedsupporting

confidence: 90%

“…This power law has been verified many times for wind atmospheric data (Schmitt et al, 1993(Schmitt et al, , 1994Katul et al, 1995;Schmitt, 2007;Morales et al, 2011;Calif and Schmitt, 2012). In the energycontaining range where the scales extend from a few minutes to a few days, the properties of turbulent wind speed depend on their strong anisotropy and their dependence on the flow domain boundary characteristics (Katul and Chu, 1998;Katul et al, 2012).…”

Section: Description Of the Datamentioning

confidence: 61%

“…Several approaches can be used to consider the scaling intermittency of small-scale turbulence, the most classical one being structure functions analysis. In recent years several studies have been dedicated to the analysis of scaling laws and turbulent intermittency at small scales in the laboratory (Anselmet et al, 1984;She and Levêque, 1994) and in the atmospheric boundary layer (Schmitt et al, 1993(Schmitt et al, , 1994Katul et al, 1995;Schmitt, 2007;Böttcher et al, 2007;Morales et al, 2011;Calif and Schmitt, 2012). These studies have shown that atmospheric turbulent speed at small scales has multifractal scaling fluctuations and exhibits long-range power correlations.…”

Section: Introductionmentioning

confidence: 99%

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Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm

Calif¹,

Schmitt²

2014

Nonlin. Processes Geophys.

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Abstract. We consider here wind speed time series and the aggregate output wind power from a wind farm. We study their scaling statistics in the framework of fully developed turbulence and Kolmogorov's theory. We estimate their Fourier power spectra and consider their scaling properties in the physical space. We show that the atmospheric wind speed and the aggregate power output from a wind farm are intermittent and multifractal over a wide range of scales. The coupling between simultaneous data of the wind speed and aggregate power output is investigated through a joint multifractal description using the generalized correlation functions (GCFs). This multiscaling test is compatible with a linear relation between the wind speed and the aggregate power output fluctuations for timescales T 10 3 s 15 min.

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Section: The Atmospheric Wind Speedsupporting

confidence: 90%

Section: Description Of the Datamentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

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Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm

Calif¹,

Schmitt²

2014

Nonlin. Processes Geophys.

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“…The details concerning the scale range of τ and q are given in the following references [24,[32][33][34]. As shown in [24,[32][33][34], the straight lines of structure functions indicate that the scaling of the relationship is well respected. Consequently, the scaling exponents ζðqÞ are extracted from the slopes of the straight lines using a linear regression.…”

Section: Multifractal Analysis Of Sustainable Energy Datamentioning

confidence: 92%

−5/3 Kolmogorov Turbulent Behaviour and Intermittent Sustainable Energies

Calif

Schmitt²,

Medina³

2016

Sustainable Energy - Technological Issues, Applications and Case Studies

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The massive integration of sustainable energies into electrical grids (non-interconnected or connected) is a major problem due to their stochastic character revealed by strong fluctuations at all scales. In this paper, the scaling behaviour or power law correlations and the nature of scaling behaviour of sustainable resource data such as flow velocity, atmospheric wind speed, solar global solar radiation and sustainable energy such as, wind power output, are highlighted. For the first time, Fourier power spectral densities are estimated for each dataset. We show that the power spectrum densities obtained are close to the 5/3 Kolmogorov spectrum. Furthermore, the multifractal and intermittent properties of sustainable resource and energy data have been revealed by the concavity of the scaling exponent function. The proposed analysis frame allows a full description of fluctuations of processes considered. A good knowledge of the dynamic of fluctuations is crucial to management of the integration of sustainable energies into a grid.

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“…Specifically, these distributions have shown to exhibit strong non-Gaussian behavior at small increments, then become more Gaussian as separation increases [15,56,[61][62][63][64][65]. A few years ago, Barndorff-Nielsen et al [56] demonstrated that the normal inverse Gaussian (NIG) distribution has the inherent ability to capture such scale-dependent traits in a parsimonious manner.…”

Section: Quantifying Uncertainty In Structure Function Estimatesmentioning

confidence: 99%

Estimating higher-order structure functions from geophysical turbulence time series: Confronting the curse of the limited sample size

DeMarco

Basu

2017

Phys. Rev. E

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Utilizing synthetically generated random variates and laboratory measurements, we document the inherent limitations of the conventional structure function approach in limited sample size settings. We demonstrate that an alternative approach, based on the principle of maximum likelihood, can provide nearly unbiased structure function estimates with far less uncertainty under such unfavorable conditions. The superiority of this approach over the conventional approach does not diminish even in the case of strongly correlated samples. Two entirely different types of probability distributions, which have been reported in the turbulence literature, are found to be compatible with the proposed approach.

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Modeling of atmospheric wind speed sequence using a lognormal continuous stochastic equation

Cited by 65 publications

References 31 publications

Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm

Multiscaling and joint multiscaling description of the atmospheric wind speed and the aggregate power output from a wind farm

−5/3 Kolmogorov Turbulent Behaviour and Intermittent Sustainable Energies

Estimating higher-order structure functions from geophysical turbulence time series: Confronting the curse of the limited sample size

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