Fractal analysis of river flow fluctuations

We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at s_1×∼12 and s_2×∼130 months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second one is approximately equal to the well-known cycle of sun activity. Using Fourier Detrended Fluctuation Analysis, the sinusoidal trend is eliminated. The values of Hurst exponents of the runoff water of rivers without the sinusoidal trend show a long-range correlation behavior. For the Daugava river, the value of Hurst exponent is 0.52±0.01 and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.