Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies

Eva Koscielny-Bunde, Jan W. Kantelhardt, Peter Braun, Armin Bunde, Shlomo Havlin

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262 Scopus citations

Abstract

We study temporal correlations and multifractal properties of long river discharge records from 41 hydrological stations around the globe. To detect long-term correlations and multifractal behaviour in the presence of trends, we apply several recently developed methods [detrended fluctuation analysis (DFA), wavelet analysis, and multifractal DFA] that can systematically detect and overcome non-stationarities in the data at all time scales. We find that above some crossover time that usually is several weeks, the daily runoffs are long-term correlated, being characterized by a correlation function C(s) that decays as C(s)∼s. The exponent γ varies from river to river in a wide range between 0.1 and 0.9. The power-law decay of C(s) corresponds to a power-law increase of the related fluctuation function F2(s)∼sH where H=1-γ/2. We also find that in most records, for large times, weak multifractality occurs. The Renyi exponent τ(q) for q between -10 and +10 can be fitted to the remarkably simple form τ ( q ) = - ln ( aq + bq ) / ln 2, with solely two parameters a and b between 0 and 1 with a+b≥1. This type of multifractality is obtained from a generalization of the multiplicative cascade model.

Original languageEnglish
Pages (from-to)120-137
Number of pages18
JournalJournal of Hydrology
Volume322
Issue number1-4
DOIs
StatePublished - 15 May 2006

Bibliographical note

Funding Information:
We would like to thank Daniel Schertzer, Alberto Montanari, and Diego Rybski for valuable discussions on the manuscript. This work was supported by the BMBF, the DAAD, and the DFG. We also would like to thank the Water Management Authorities of Bavaria and Baden-Württemberg (Germany), and the Global Runoff Data Center (GRDC) in Koblenz (Germany) for providing the observational data.

Funding

We would like to thank Daniel Schertzer, Alberto Montanari, and Diego Rybski for valuable discussions on the manuscript. This work was supported by the BMBF, the DAAD, and the DFG. We also would like to thank the Water Management Authorities of Bavaria and Baden-Württemberg (Germany), and the Global Runoff Data Center (GRDC) in Koblenz (Germany) for providing the observational data.

FundersFunder number
Deutscher Akademischer Austauschdienst
Deutsche Forschungsgemeinschaft
Bundesministerium für Bildung und Forschung

    Keywords

    • Long-term correlations
    • Multifractality
    • Multiplicative cascade model
    • Runoff
    • Scaling

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