Articles | Volume 22, issue 2
https://doi.org/10.5194/hess-22-1175-2018
https://doi.org/10.5194/hess-22-1175-2018
Research article
 | 
12 Feb 2018
Research article |  | 12 Feb 2018

Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

Qian Zhang, Ciaran J. Harman, and James W. Kirchner

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Cited articles

Aubert, A. H., Kirchner, J. W., Gascuel-Odoux, C., Faucheux, M., Gruau, G., and Mérot, P.: Fractal water quality fluctuations spanning the periodic table in an intensively farmed watershed, Environ. Sci. Technol., 48, 930–937, https://doi.org/10.1021/es403723r, 2014.
Beran, J.: Long-range dependence, Wiley Interdiscip. Rev. Comput. Stat., 2, 26–35, https://doi.org/10.1002/wics.52, 2010.
Beran, J., Feng, Y., Ghosh, S., and Kulik, R.: Long-Memory Processes: Probabilistic Properties and Statistical Methods, Berlin, Heidelberg, Springer Berlin Heidelberg, 884 pp., 2013.
Boutahar, M., Marimoutou, V., and Nouira, L.: Estimation Methods of the Long Memory Parameter: Monte Carlo Analysis and Application, J. Appl. Stat., 34, 261–301, https://doi.org/10.1080/02664760601004874, 2007.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C.: Time Series Analysis, Fourth Edition. Hoboken, NJ, John Wiley & Sons, Inc., 47–92, 2008.
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Short summary
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. This paper provides a comprehensive overview of the various approaches for quantifying fractal scaling in irregularly sampled data and provides new understanding and quantification of the methods’ performances. More generally, the findings and approaches may be broadly applicable to irregularly sampled data in other scientific disciplines.
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