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Components of multifractality in the central England temperature anomaly series
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Figures

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FIG. 1.

Excerpt of Great Britain's map with climate reference stations locations according to the legend shown in the figure. Reproduced with permission from the Met Office. Copyright 2009 Crown.

Image of FIG. 2.

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FIG. 2.

Daily temperature anomaly averaged over a 11-year sliding window (step size of one year) for the CET time series.

Image of FIG. 3.

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FIG. 3.

The symbols were obtained from a series of 10 elements following a ( = 3)-Student distribution (or a ( = 3/2)-Gaussian with ) which was shuffled in order to remove any possible dependence between the variables due to the pseudo-random generator and the symbols represent the Gaussian of the surrogate time series that is obtained by the phase randomization procedure.

Image of FIG. 4.

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FIG. 4.

Multifractal spectrum vs for the original CET anomaly and for the surrogates generated by shuffling, phase randomizing, shuffling plus phase randomizing and phase preservation.

Image of FIG. 5.

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FIG. 5.

Power spectrum vs for the CET anomaly obtained using the Burg algorithm. The dashed lines represent the error margins (5% of the power spectrum value).

Image of FIG. 6.

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FIG. 6.

Multifractal spectrum vs for the original CET anomaly and for the surrogate in which the power spectrum is kept. In spite of being shifted one another, it is visible that the width of both spectra is very similar. Moreover, the multifractal width lies within .

Image of FIG. 7.

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FIG. 7.

Multifractal width of the Central England temperature anomaly between 1777 and 2002, coarse and effective. The is obtained after removing finite size effects and systematic algorithmic error, by subtracting from the original , the value of as described in Eq. (16) . Each curve follows the legend in the figure.

Image of FIG. 8.

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FIG. 8.

Non-Gaussian and linear dependence (correlations) contributions to the effective multifractal width of the Central England temperature anomaly between 1777 and 2002. Each curve follows the legend in the figure. The non-Gaussian character is related to the width of the multifractal spectrum of the shuffled time series, while the linear dependence is related to the width of the multifractal spectrum of the randomized time series. Allthe calculations have been performed using the effective given by Eq. (16) .

Image of FIG. 9.

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FIG. 9.

Nonlinear dependence contribution to the effective multifractal width of the Central England temperature anomaly between 1777 and 2002. This contribution is measured by the width of the curve of the surrogate time series with the same Fourier spectrum of the original one, but without linear dependence. All the calculations have been performed using the effective given by Eq. (16) .

Image of FIG. 10.

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FIG. 10.

Amplitude of Fourier transform ( ) of the maximum and the minimum values of , against frequency. The circles identify the local maxima described in the text.

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/content/aip/journal/chaos/23/2/10.1063/1.4811546
2013-06-24
2014-04-23

Abstract

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The data are analyzed in two ways: as a single set and by using a sliding window of 11 years. In both cases, we quantify the width of the multifractal spectrum as well as its components, which are defined by the deviations from the Gaussian distribution and the dependence between measurements. The results of the first approach show that the key contribution to the multifractal structure comes from the dynamical dependencies, mainly weak ones, followed by a residual contribution of the deviations from the Gaussian. The sliding window approach indicates that the peaks in the evolution of the non-Gaussian contribution occur almost at the same dates associated with climate changes that were determined in previous works using component analysis methods. Moreover, the strong non-Gaussian contribution from the 1960 s onwards is in agreement with global results recently presented.

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Scitation: Components of multifractality in the central England temperature anomaly series
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/2/10.1063/1.4811546
10.1063/1.4811546
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