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DOI | 10.5194/hess-22-1175-2018 |
Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling | |
Zhang, Qian1; Harman, Ciaran J.2; Kirchner, JamesW.3,4,5 | |
发表日期 | 2018-02-12 |
ISSN | 1027-5606 |
卷号 | 22期号:2 |
英文摘要 | River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling in the form of spectral slope (beta) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (beta = 0) to Brown noise (beta = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on beta estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate beta under a wide range of prescribed beta values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently under-estimates beta. A previously published modified form, using only the lowest 5% of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of prescribed beta values and gap distributions. The aliasing method, however, does not itself account for sampling irregularity, and this introduces some bias in the result. Nonetheless, the wavelet method is recommended for estimating beta in irregular time series until improved methods are developed. Finally, all methods' performances depend strongly on the sampling irregularity, highlighting that the accuracy and precision of each method are data specific. Accurately quantifying the strength of fractal scaling in irregular water-quality time series remains an unresolved challenge for the hydrologic community and for other disciplines that must grapple with irregular sampling. |
语种 | 英语 |
WOS记录号 | WOS:000424971300001 |
来源期刊 | HYDROLOGY AND EARTH SYSTEM SCIENCES
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来源机构 | 美国环保署 |
文献类型 | 期刊论文 |
条目标识符 | http://gcip.llas.ac.cn/handle/2XKMVOVA/61295 |
作者单位 | 1.Univ Maryland, Ctr Environm Sci, US EPA, Chesapeake Bay Program Off, 410 Severn Ave,Suite 112, Annapolis, MD 21403 USA; 2.Johns Hopkins Univ, Dept Environm Hlth & Engn, 3400 North Charles St, Baltimore, MD 21218 USA; 3.ETH, Dept Environm Syst Sci, Univ Str 16, CH-8092 Zurich, Switzerland; 4.Swiss Fed Res Inst WSL, Zurcherstr 111, CH-8903 Birmensdorf, Switzerland; 5.Univ Calif Berkeley, Dept Earth & Planetary Sci, Berkeley, CA 94720 USA |
推荐引用方式 GB/T 7714 | Zhang, Qian,Harman, Ciaran J.,Kirchner, JamesW.. Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling[J]. 美国环保署,2018,22(2). |
APA | Zhang, Qian,Harman, Ciaran J.,&Kirchner, JamesW..(2018).Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling.HYDROLOGY AND EARTH SYSTEM SCIENCES,22(2). |
MLA | Zhang, Qian,et al."Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling".HYDROLOGY AND EARTH SYSTEM SCIENCES 22.2(2018). |
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