A simple 2D SOC model for one of the main sources of geomagnetic disturbances: Flares

Meirelles, M. C.; Dias, Vitor H. A.; Oliva, David; Papa, Andrés R. R.

doi:10.1016/j.physleta.2009.12.038

Cited by 4 publications

(1 citation statement)

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“…Long-range persistent behaviour occurs also in a few (but not in all) models of selforganized criticality (Bak et al 1987;Turcotte 1999;Hergarten 2002;Kwapień and Dro_ zd_ z 2012); as an example the Bak-Sneppen model (Bak and Sneppen 1993;Daerden and Vanderzande 1996) is a simple model of co-evolution between interacting species and has been used to describe evolutionary biological processes. The Bak-Sneppen model has also been extended to solar and geophysical phenomena such as X-ray bursts at the Sun's surface (Bershadskii and Sreenivasan 2003), solar flares (Meirelles et al 2010), and for Earth's magnetic field reversals (Papa et al 2012). Nagler and Claussen (2005) found that cellular automata models (i.e.…”

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Quantification of Long-Range Persistence in Geophysical Time Series: Conventional and Benchmark-Based Improvement Techniques

2013

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Time series in the Earth Sciences are often characterized as self-affine long-range persistent, where the power spectral density, S, exhibits a power-law dependence on frequency, f, S(f) ~ f^(−β) , with β the persistence strength. For modelling purposes, it is important to determine the strength of self-affine long-range persistence β as precisely as possible and to quantify the uncertainty of this estimate. After an extensive review and discussion of asymptotic and the more specific case of self-affine long-range persistence, we compare four common analysis techniques for quantifying self-affine long-range persistence: (a) rescaled range (R/S) analysis, (b) semivariogram analysis, (c) detrended fluctuation analysis, and (d) power spectral analysis. To evaluate these methods, we construct ensembles of synthetic self-affine noises and motions with different (1) time series lengths N = 64, 128, 256, …, 131,072, (2) modelled persistence strengths β_model = −1.0, −0.8, −0.6, …, 4.0, and (3) one-point probability distributions (Gaussian, log-normal: coefficient of variation c_v = 0.0 to 2.0, Levy: tail parameter a = 1.0 to 2.0) and evaluate the four techniques by statistically comparing their performance. Over 17,000 sets of parameters are produced, each characterizing a given process; for each process type, 100 realizations are created. The four techniques give the following results in terms of systematic error (bias = average performance test results for β over 100 realizations minus modelled β) and random error (standard deviation of measured β over 100 realizations): (1) Hurst rescaled range (R/S) analysis is not recommended to use due to large systematic errors. (2) Semivariogram analysis shows no systematic errors but large random errors for self-affine noises with 1.2 ≤ β ≤ 2.8. (3) Detrended fluctuation analysis is well suited for time series with thin-tailed probability distributions and for persistence strengths of β ≥ 0.0. (4) Spectral techniques perform the best of all four techniques: for self-affine noises with positive persistence (β ≥ 0.0) and symmetric one-point distributions, they have no systematic errors and, compared to the other three techniques, small random errors; for anti-persistent self-affine noises (β < 0.0) and asymmetric one-point probability distributions, spectral techniques have small systematic and random errors. For quantifying the strength of long-range persistence of a time series, benchmark-based improvements to the estimator predicated on the performance for self-affine noises with the same time series length and one-point probability distribution are proposed. This scheme adjusts for the systematic errors of the considered technique and results in realistic 95 % confidence intervals for the estimated strength of persistence. We finish this paper by quantifying long-range persistence (and corresponding uncertainties) of three geophysical time series—palaeotemperature, river discharge, and Auroral electrojet index—with the three representing three different types of probability d...

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