Multifractal analysis of 1-min summer rainfall time series from a monsoonal watershed in eastern China

Abstract

Multifractal analysis can provide parameters associated with different scales of rainfall, which may be useful for setting up parsimonious downscaling models of rainfall, or for revealing climate-specific properties. Time series of rain rate with 1-min resolution collected from ten stations over a monsoon watershed in eastern China were used to study the multifractal properties. The power spectra estimated by fast Fourier transform (FFT) and discrete Haar wavelet transform (DWT) showed three scaling regimes: the sub-hourly scaling regime with β ≈ 1.2, the scaling regime from 1 h to 1 day with β close to 0.6, and the low-frequency spectra plateau with β ≈ 0.1. From the hyperbolic tails of exceeding probability distributions, the estimated values of parameter qc are in 2–2.5, which were consistent with the critical order of K(q) curves. The statistical moments display two main scaling regimes: the high-frequency regime from 3 min to 5 days and the scaling regime beyond 5 days. The scales of 5–10 days seem a transitional regime. The reason that the regimes, revealed by the power spectra, disagree with the statistical moments may be that both FFT and DWT power spectra have limited abilities of analyzing low-frequency scaling but are sensitive to the properties in high-frequency scales. The H values estimated for the regime of sub-hourly scales are larger than 0.4, and the values for the regime 1 h–1 day are close to 0.1. For the low-frequency scales beyond 1 day, negative H is obtained by DWT power spectra. The parameters of universal multifractal models were also estimated. The values of α for the scaling range of 1 min–5 days are 0.486 ± 0.047, and for the low-frequency scaling range, its values are 0.808 ± 0.323. For the high- and low-frequency scaling ranges, the values of C1 are 0.5 and 0.169, respectively, which is different from the values for daily rainfall series collected at the same rain gages.