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

Abstract

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 F 1 (s) [1][2][3] and the second moment F 2 (s) [5], respectively. In the last

Comparison of detrending methods for fluctuation analysis

“…However, for the reliable characterization of time series, it is also essential to distinguish trends from intrinsic fluctuations, that might be long-term correlated. Monotonous, periodic or step-like trends are caused by external effects, e. g., by the greenhouse warming [22], seasonal variations for temperature records [23] and river runoffs [2,24,25,26], different levels of daily activity in long-term physiological data [27], or unstable light sources in photon correlation spectroscopy [28]. To characterize a complex system based on time series, trends and fluctuations are usually studied separately (see, e.g., [29] for a recent discussion).…”

“…For studies comparing DFA and BMA, see [46,47]; note that [47] also discusses CMA. For studies comparing methods for detrending multifractal analysis (multifractal DFA (MF-DFA) and wavelet transform modulus maxima (WTMM) method), see [5,24,48].…”

Multifractal detrended fluctuation analysis of human EEG: preliminary investigation and comparison with the wavelet transform modulus maxima technique

“…MF-DFA may be More Consistent than WTMM with Shorter EEG Tracings MF-DFA is an established technique for assessing multifractality, which has been used successfully in several different types of analysis, from simulations [33], to geophysics and ion channels [38], to hydrology [47], to cardiology [43]. It has been described as being comparable in terms of results, but needing less computational power than WTMM [24,33].…”

Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets

“…Note that the steps are very similar to those in MF-DFA [2], except that in order to detrend, we use wavelets and MF-DFA uses local polynomial fits.…”

“…Several techniques have been developed to carry out this separation. Among these are, de-trended fluctuation analysis and its variants [1,2] and the wavelet transform [3,4] based multiresolution analysis [5,6]. These methods and earlier methods [7,8] have found wide application in analysis of correlations and characterization of scaling behavior of time-series data in, physiology, finance, and natural sciences [9,10,11,12,13,14,15,16,17,18,19].…”