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

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 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)/ln2τ(q)=−ln(aq+bq)/ln2, 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.