Quantifying fractal dynamics of groundwater systems with detrended fluctuation analysis

Li, Zhongwei; Zhang, You‐Kuan

doi:10.1016/j.jhydrol.2006.12.017

Cited by 71 publications

(71 citation statements)

References 21 publications

(35 reference statements)

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“…The values of H obtained using R/S analysis were between about 0.6 to around 0.9, while the MF-DFA analysis 30 resulted in slightly higher values, ranging from 0.65 to around 1.1 (Figure 1); MF-DFA can give estimates slightly higher than 1 (Serinaldi, 2010), suggesting that the process is persistent (Li and Zhang, 2007).…”

Section: Resultsmentioning

confidence: 93%

Technical note: Long-term memory loss of urban streams as a metric for catchment classification

Jovanović

Jovanovic

Mejía

et al. 2017

Preprint

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Abstract. 10Urbanisation has been associated with a reduction in the long-term correlation within a streamflow series, quantified by the Hurst exponent (H). This presents an opportunity to use the H exponent as an index for the classification of catchments on a scale from natural to urbanised conditions. However, before using the H exponent as a general index, the relationship between this exponent and level of urbanisation needs to be further examined and verified on catchments with different levels of imperviousness and from different climatic regions. In this 15 study, the H exponent is estimated for 38 (deseasonalized) mean daily runoff time series, 22 from the USA and 16 from Australia, using the traditional rescaled-range statistic (R/S) and the more advanced multi-fractal detrended fluctuation analysis (MF-DFA). Relationships between H and catchment imperviousness, catchment size, annual rainfall and specific mean discharge were investigated. No clear relationship with catchment area was found, and a weak negative relationship with annual rainfall and specific mean streamflow was found only when 20 the R/S method was used. Conversely, both methods showed decreasing values of H as catchment imperviousness increased. The H exponent decreased from around 1.0 for catchments in natural conditions to around 0.6 for highly urbanised catchments. Three significantly different ranges of H exponents were identified, allowing catchments to be parsed into groups with imperviousness lower than 5% (natural), catchments with imperviousness between 5 and 15 % (peri-urban), and catchments with imperviousness larger than 15% (urban). The H exponent thus 25 represents a useful metric to quantitatively assess the impact of catchment imperviousness on streamflow regime.

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Section: Resultsmentioning

confidence: 93%

Technical note: Long-term memory loss of urban streams as a metric for catchment classification

Jovanović

Jovanovic

Mejía

et al. 2017

Preprint

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“…(Li, Zhang 2007) speculated the effect that river stage fractal properties would have on that 495 of groundwater levels, especially at the larger scales. However, River Thames, which is generally 496 groundwater dominated (with a BFI of 0.64 measured 8 km upstream of the site), is expected to 497 have fractal properties similar to that of groundwater fluctuation.…”

Section: Results and Discussion 430mentioning

confidence: 99%

“…The time periods ( L ) where 148 such changes occur are referred to as crossovers (Kantelhardt, Koscielny-Bunde et al 2001, Hu, 149 Ivanov et al 2001, Li, Zhang 2007. Even though DFA is a reliable method for identifying fractal 150 behaviour, determining the number and locations of crossovers, has been rather subjective.…”

Section: Determining Scaling Exponents and Crossovers For Mono-fractamentioning

confidence: 99%

“…In previous studies researchers removed periodicity in a time series prior to DFA in order to 185 determine 'true scaling exponents' ((Sadegh Movahed, Jafari et al 2006, Li, Zhang 2007, Hu, Ivanov 186 et al 2001, Kavasseri, Nagarajan 2004). In this study, periodicity is considered to be part of the 187 fluctuation structure that is naturally induced by meteorological and hydrological processes, and 188 hence will not be removed and instead will be identified in the fractal behaviour.…”

Section: Determining Scaling Exponents and Crossovers For Mono-fractamentioning

confidence: 99%

“…Hydrological and hydro-meteorological time series such as rainfall, river stage, river flow, 89 temperature and more recently, groundwater levels have been characterised as being fractal 90 (Eichner, Koscielny-Bunde et al 2003, Zhang, Schilling 2004, Zhang, Yang 2010, Fraedrich, Larnder 91 1993, Gelhar 1974, Kavasseri, Nagarajan 2004, Li, Zhang 2007, Little, Bloomfield 2010, Zhu, Young et 92 al. 2012, Liang, Zhang 2013, however, high resolution hydrological datasets are generally not 93 available and this makes the study of the full range of fractal behaviour difficult.…”

Section: Introduction 37mentioning

confidence: 99%

See 2 more Smart Citations

Temporal scaling phenomena in groundwater-floodplain systems using robust detrended fluctuation analysis

Habib

Sorensen

Bloomfield

et al. 2017

Journal of Hydrology

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The spatial scale dependence of water vapor variability inferred from observations from a very tall tower

2014

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Recent studies have established that atmospheric water vapor fields exhibit spatial spectra that take the form of power laws and hence can be compactly characterized by scaling exponents. The power law scaling exponents have been shown to exhibit substantial vertical variability. In this work, Taylor's frozen turbulence hypothesis is used to infer the first‐order spatial structure function and generalized detrended fluctuation function scaling exponents for scales between 1 km and 100 km. Both methods are used to estimate the Hurst exponent (H) using 10 Hz time series of water vapor measured at 396 m altitude from an Ameriflux tower in Wisconsin. Due to the diurnal cycle in the boundary layer height at the 396 m observational level, H may be estimated for both the daytime convective mixed layer and the nocturnal residual layer. Values of H≈13 are obtained for the convective mixed layer, while values of H>12 apply in the nocturnal residual layer. The results are shown to be remarkably consistent with a similar analysis from satellite‐based observations as reported in Pressel and Collins (2012).

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Quantifying fractal dynamics of groundwater systems with detrended fluctuation analysis

Cited by 71 publications

References 21 publications

Technical note: Long-term memory loss of urban streams as a metric for catchment classification

Technical note: Long-term memory loss of urban streams as a metric for catchment classification

Temporal scaling phenomena in groundwater-floodplain systems using robust detrended fluctuation analysis

The spatial scale dependence of water vapor variability inferred from observations from a very tall tower

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