  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 weeks, 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 related fluctuation function F_2(s) ~ 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) /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.

Geophysics;Statistical Mechanics;Data Analysis, Statistics and Probability