Long-range dependence in North Atlantic sea level

Barbosa, Susana; Fernandes, Joana; Silva, Maria Eduarda

doi:10.1016/j.physa.2006.03.046

Cited by 29 publications

(22 citation statements)

References 19 publications

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“…Recently, due to the developments in the area of complex systems as well as data measurements and data analysis, one can find many opportunities for examination and interpretation of climate change which exhibit irregular systems [1][2][3][4][5][6][7][8]. It is well shown that the climate system is enforced by the well-defined seasonal periodicity, however the existence of unpredictable perturbation and chaotic functioning lead to extreme climate events.…”

Section: Introductionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

132

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We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, (12 − 24) ≤ s ≤ 130 months, is λ = 1.17 ± 0.04 which is almost similar for all underlying rivers at 1σconfidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ ∈ (0.76, 0.85) and γ× ∈ (0.30, 0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), λ ≈ (hsun + hriver)/2 is confirmed.

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Section: Introductionmentioning

confidence: 99%

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Hajian

Movahed

2010

Physica A: Statistical Mechanics and its Applications

132

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“…Sea level time series has the property of long-range dependence (LRD), as can be seen from Ercan et al [90], Barbosa et al [91], Beretta et al [92], and Li et al [93] …”

Section: Discussionmentioning

confidence: 99%

Power-Type Functions of Prediction Error of Sea Level Time Series

Leng

2015

Entropy

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“…Since the pioneering work of Hurst (1951) on the longmemory behavior (or persistent fractal) of the storage capacity of reservoirs in the Nile River, the Hurst exponent has been regarded as the best-known estimator indicating the magnitude of long-range dependence in time series and has been widely used to study fractal scaling behavior in geophysical sciences, specifically for river flows and turbulence (Nordin et al, 1972;Szolgayova et al, 2014;Vogel et al, 1998), porosity and hydraulic conductivity in subsurface hydrology (Molz and Boman, 1993), climate variability (Bloomfield, 1992;Franzke et al, 2015;Koutsoyiannis, 2003), and sea level fluctuations (Barbosa et al, 2006;Ercan et al, 2013). The Hurst exponent H may be defined as follows:…”

Section: Methodsmentioning

confidence: 99%

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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Long-range dependence in North Atlantic sea level

Cited by 29 publications

References 19 publications

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

Power-Type Functions of Prediction Error of Sea Level Time Series

Fractal scaling analysis of groundwater dynamics in confined aquifers

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