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 nonstationarities in the data at all time scales. We find that above some crossover time that usually is several months, the daily runoffs are long-term correlated, being characterized by a correlation function C(s) that decays as C(s) ~ 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 corresponding fluctuation function F2(s) ~ s^H where H=1-gamma/2. Below the crossover time, the daily runoffs show a very different behaviour: They are nonstationary and characterized by H values being close to 1.5, similar to Brownian noise. We also study the multifractal properties of the records. We find that in all records, above several months, weak multifractality occurs. For all cases, 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)/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 binomial multifractal model