Significance of trends in long-term correlated records.
Significance of trends in long-term correlated records.
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DOI：
10.1103/physreve.91.032806
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发表时间：
2014-11
期刊：
影响因子：
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通讯作者：
Araik Tamazian;J. Ludescher;A. Bunde
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文献类型：
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作者：
Araik Tamazian;J. Ludescher;A. Bunde
我们研究了长度为L的长期相关记录的相对趋势x的分布P(x；α，L)，其特征是赫斯特指数α在0.51.5之间。相对趋势x是通过线性回归测量的记录中趋势Δ的强度与回归线周围的标准偏差σ之间的比率。我们认为L在400到2200之间，这是重建的全球气候月记录和年度记录的典型长度尺度。引用Lennartz和Bunde的工作[S.Lennartz和A.Bunde，Phys.E 84,021129(2011年)]我们明确地证明了x服从学生t分布P∝[1+(x/a)2/L]-(L+1)/2，其中标度参数a同时取决于L和α，而有效长度L只取决于记录长度L。从P我们可以推导出趋势显著S(x；α，L)=∫(-x)XP(x‘；α，L)dx’和95%显著区间的边界线的解析表达式。我们表明，结果几乎与记录中数据的分布无关，对于高斯数据和高度倾斜的非高斯数据都是成立的。作为应用，我们使用我们的方法来估计南极中西部变暖的重要性。
We study the distribution P(x;α,L) of the relative trend x in long-term correlated records of length L that are characterized by a Hurst exponent α between 0.5 and 1.5. The relative trend x is the ratio between the strength of the trend Δ in the record measured by linear regression and the standard deviation σ around the regression line. We consider L between 400 and 2200, which is the typical length scale of monthly local and annual reconstructed global climate records. Extending previous work by Lennartz and Bunde [S. Lennartz and A. Bunde, Phys. Rev. E 84, 021129 (2011)] we show explicitly that x follows the Student's t distribution P∝[1+(x/a)2/l]-(l+1)/2, where the scaling parameter a depends on both L and α, while the effective length l depends, for α below 1.15, only on the record length L. From P we can derive an analytical expression for the trend significance S(x;α,L)=∫(-x)xP(x';α,L)dx' and the border lines of the 95% significance interval. We show that the results are nearly independent of the distribution of the data in the record, holding for Gaussian data as well as for highly skewed non-Gaussian data. For an application, we use our methodology to estimate the significance of central west Antarctic warming.