Multifractality of river runoff and precipitation: Comparison of fluctuation analysis and wavelet methods

We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima technique and obtain agreement within the error margins. In contrast to previous studies, we find non-universal behaviour: On long time scales, above a crossover time scale of several months, the runoff records are described by fluctuation exponents varying from river to river in a wide range. Similar variations are observed for the precipitation records which exhibit weaker, but still significant multifractality. For all runoff records the type of multifractality is consistent with a modified version of the binomial multifractal model, while several precipitation records seem to require different models. The analysis of river flows has a long history. Already more than half a century ago the engineer H. E. Hurst found that runoff records from various rivers exhibit ’long-range statistical dependencies’ [1]. Later, such long-term correlated fluctuation behaviour has also been reported for many other geophysical records including precipitation data [2,3], see also [4]. These original approaches exclusively focused on the absolute values or the variances of the full distribution of the fluctuations, which can be regarded as the first moment F1(s) [1–3] and the second moment F2(s) [5], respectively. In the last Preprint submitted to Elsevier Science April 5, 2003 1873 1874 1875 time [years] 0 500