Evaluating fractal behavior in groundwater level fluctuations time series

Rakhshandehroo, Gholamreza; Amiri, Seyed Mehrab

doi:10.1016/j.jhydrol.2012.07.030

Cited by 29 publications

(28 citation statements)

References 21 publications

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“…Unlike the general finding of fBm-type behavior in groundwater level fluctuations (Li and Zhang, 2007;Little and Bloomfield, 2010;Rakhshandehroo and Amiri, 2012;Yu et al, 2016), Joelson et al (2016) found persistent scaling behavior in the analysis of hourly groundwater level fluctuation time series for a 14-month duration and fit the fluctuation data with the Lévy stable distribution to account for the observed non-Gaussian heavy-tailed behavior.…”

mentioning

confidence: 60%

“…They analyzed 4 years of continuous hourly data from seven wells and found that groundwater level fluctuations are likely to follow fractional Brownian motion (fBm) and that temporal scaling crossovers exist in the fluctuations. These findings were later confirmed by Little and Bloomfield (2010), Rakhshandehroo and Amiri (2012), and Yu et al (2016) with the application of DFA to hourly or 15 min interval data for up to 5 years from 7 wells, daily data for 6 years from 2 wells, and daily data from 22 wells that have more than 2500 records, respectively. Rakhshandehroo and Amiri (2012) further utilized MF-DFA to evaluate the multifractality of groundwater level fluctuations and concluded that the extent of multifractality in groundwater level fluctuations is stronger than that in river runoff.…”

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confidence: 69%

“…This also suggests that different exponents should be used to illustrate the fractal scaling behavior (self-affinity) of different time intervals of the data. Moreover, h(q) continuously decreases as q increases in both figures, implying that relatively small fluctuations occur more frequently in the time series than large ones (Grech and Czarnecki, 2009;Rakhshandehroo and Amiri, 2012).…”

Section: Multifractal Analysismentioning

confidence: 97%

“…Groundwater in both confined and unconfined aquifers is usually a complex and dynamic system that highly interacts with surface water and even climate systems in most hydroclimatic settlings due to its discharge to rivers and streams and its recharge affected by various related physical processes, such as precipitation, evapotranspiration, and infiltration (Green et al, 2011;Joelson et al, 2016;Li and Zhang, 2007;Rakhshandehroo and Amiri, 2012;Taylor et al, 2013). These processes, which take place over various spatiotemporal scales, add further complexity to groundwater systems.…”

Section: Introductionmentioning

confidence: 99%

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Fractal scaling analysis of groundwater dynamics in confined aquifers

Ercan

Kavvas

2017

Earth Syst. Dynam.

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Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

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confidence: 60%

mentioning

confidence: 69%

Section: Multifractal Analysismentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Fractal scaling analysis of groundwater dynamics in confined aquifers

Ercan

Kavvas

2017

Earth Syst. Dynam.

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“…In statistical hydrology, Khaliq et al (2009) reported that unambiguous identification of ARFIMA models requires long data sets. As another example, Rakhshandehroo and Amiri (2012) demonstrated that a minimum number of data are required to provide stable estimates of fractal dimension for groundwater level time series. However, it is unclear how thoroughly this question is addressed in many practical water resources or climatology applications, and in particular, rarely does the question of record length specifically arise in empirical identification of power-law scaling from the observational spectra of hydroclimatic data sets.…”

Section: Introductionmentioning

confidence: 99%

A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series

Fleming¹

2013

Hydrological Sciences Journal

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Power-law spectral scaling violates assumptions of standard analyses such as statistical change detection. However, hydroclimatic data sets may be too short to differentiate the spectra of 1/f α vs low-order linear memory processes, an ambiguity exacerbated by the ubiquity of both process types. We explore this non-uniqueness problem by applying a heuristic tool to four examples from each of four hydroclimatic data types: circulation indices, station climate, river and aquifer conditions, and glacier mass balance. This selection spans much of the globe and includes some of the longest instrumental data sets available. The most common outcome is that power-law scaling is apparent, but the record is insufficiently long to discriminate between underlying mechanisms. The use of palaeoclimatic data to extend the instrumental record was investigated, but produced mixed results. Conversely, a balance-of-evidence approach, additionally incorporating physical process considerations, may help us recognize variate classes for which 1/f α scaling can be concluded. Practical recommendations are offered.Key words spectrum; persistence; streamflow; groundwater; glacier; palaeoclimate Un problème de non-unicité dans l'identification de la scalance spectrale des lois de puissance pour des séries chronologiques hydroclimatiques Résumé La scalance spectrale d'une loi de puissance ne satisfait pas les hypothèses des analyses classiques telles que la détection des changements statistiques. Les ensembles de données hydroclimatiques peuvent cependant être trop courts pour différencier les processus de spectres en 1/fα des processus linéaires à mémoire courte, ambiguïté exacerbée par l'omniprésence de ces deux types de processus. Nous avons exploré ce problème de non-unicité en appliquant un outil heuristique à quatre exemples de chacun de quatre types de données hydroclimatiques suivants: indices de circulation, climat d'une station, caractéristiques d'une rivière et d'un aquifère et bilan de masse d'un glacier. Cette sélection est répartie sur une grande partie du globe et comprend certaines des plus longues séries disponibles de données instrumentales. Le premier résultat est que la scalance selon une loi de puissance est évidente, mais que les séries ne sont pas suffisamment longues pour distinguer entre les mécanismes sous-jacents. L'utilisation des données paléoclimatiques pour étendre la durée des séries instrumentales a été étudiée, mais n'a fourni que des résultats mitigés. Inversement, une approche par bilan des informations, intégrant en outre des considérations de processus physiques, peut nous aider à reconnaître les classes de variables pour lesquelles on peut conclure à une scalance en 1/fα. Des recommandations pratiques sont proposées.

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The effects of extremes and temporal scale on multifractal properties of river flow time series

Hekmatzadeh

Haghighi

Guyomi

et al. 2019

River Research & Apps

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For accurate forecasting of extreme events in rivers, streamflow time series with sub-daily temporal resolution (1-6 hour) are preferable, but discharge time series for long rivers are usually available at daily or monthly resolution. In this study, the scaling properties of hourly and daily streamflow time series were measured. As an innovation, the effects of extreme values on the multifractal behavior of these series were evaluated. Interestingly, both hourly and daily discharge records led to nearly identical scaling trends and identical crossover times. Daily and hourly discharge time series appeared to be non-stationary when the timescale ranged from 75 to 366 days. Otherwise, the signals may be considered stationary time series. In addition, the results indicated that the extreme values strongly contribute to the multifractality of the series. The width of singularity spectra decreased considerably when the extreme events were removed from both hourly and daily discharge records.

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Evaluating fractal behavior in groundwater level fluctuations time series

Cited by 29 publications

References 21 publications

Fractal scaling analysis of groundwater dynamics in confined aquifers

Fractal scaling analysis of groundwater dynamics in confined aquifers

A non-uniqueness problem in the identification of power-law spectral scaling for hydroclimatic time series

The effects of extremes and temporal scale on multifractal properties of river flow time series

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