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dc.contributor.author
Zhang, Qian
dc.contributor.author
Harman, Ciaran J.
dc.contributor.author
Kirchner, James W.
dc.date.accessioned
2019-01-31T17:03:32Z
dc.date.available
2019-01-31T17:03:32Z
dc.date.issued
2018
dc.identifier.issn
1027-5606
dc.identifier.issn
1607-7938
dc.identifier.other
10.5194/hess-22-1175-2018
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/322180
dc.identifier.doi
10.3929/ethz-b-000242983
dc.description.abstract
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 (β) 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 (β  =  0) to Brown noise (β  =  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 β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. 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 β 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 β 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.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Copernicus Publications
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/3.0/
dc.title
Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 3.0 Unported
dc.date.published
2018-02-12
ethz.journal.title
Hydrology and Earth System Sciences
ethz.journal.volume
22
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
Hydrol. earth syst. sci.
ethz.pages.start
1175
en_US
ethz.pages.end
1192
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Göttingen
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02350 - Dep. Umweltsystemwissenschaften / Dep. of Environmental Systems Science::02722 - Institut für Terrestrische Oekosysteme / Institute of Terrestrial Ecosystems::03798 - Kirchner, James W. / Kirchner, James W.
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02350 - Dep. Umweltsystemwissenschaften / Dep. of Environmental Systems Science::02722 - Institut für Terrestrische Oekosysteme / Institute of Terrestrial Ecosystems::03798 - Kirchner, James W. / Kirchner, James W.
ethz.date.deposited
2018-02-22T04:26:58Z
ethz.source
SCOPUS
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2019-01-31T17:03:44Z
ethz.rosetta.lastUpdated
2019-01-31T17:03:44Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/242983
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/321948
ethz.COinS
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