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 runoff's are long-term correlated, being characterized by a correlation function C(s) that decays as C(s) similar to s(-gamma). The exponent gamma 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) similar to s(H) where H = 1 - gamma/2. We also find that in most records, for large times, weak multifractality occurs. The Renyi exponent tau(q) for q between -10 and +10 can be fitted to the remarkably simple form tau(q) = -ln(a(q) + b(q))/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. (c) 2005 Elsevier B.V. All rights reserved.