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

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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 −γ. 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 F 2( s)∼ s H 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 ( a q + b q ) / 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.