Testing for the source of multifractality in water level records

Abstract

The multifractality in hydrologic data has been studied in many literatures, but few literatures focus on its source which is helpful for understanding the underlying mechanisms that generate hydrologic data. We propose a hypothesis testing procedure for the source of multifractality in water level records based on the empirical distributions of generalized Hurst exponent estimated from a set of shuffled or surrogate series. The proposed hypothesis testing procedure can show more details about the source of multifractality than previous methods with some statistics, especially about the effects of large and small fluctuations on multifractality. The generalized Hurst exponents are estimated via multifractal detrended fluctuation analysis. The data set contains about two million high-frequency water level records of a northern China river at its 10 observation stations. The testing results show that the multifractality in water levels is mainly caused by nonlinear correlations in small fluctuations and linear correlations in small and large fluctuations, and is also related to the probability distribution of small fluctuations. This conclusion is validated via some constructed semi-surrogate series and values of statistics for source testing.