Multifractal process of runoff fluctuation of the Kaidu River in Xinjiang,China

Based on the hydrological data in the headwater region of the Kaidu River during 1972-2011, the multifractal process of runoff fluctuation was analyzed. Results indicated that, in the past 40 years, the overall runoff of the Kaidu River in Xinjiang has shown significant multifractal behavior. Its singular curve lnχ_q(ε)-ln(ε) verified a favorable scale invariance over the entire time scale. τ(q)-q proved that evolution of the runoff time series presented multifractal characteristics. Moreover, the multifractal spectrum f(α)-α curve was hooklike leftward which indicated that, compared to relatively large runoff events. And Δf<0 indicated that these relatively small events took the leading role; B<0 explained the Kaidu River's daily-runoff ascending tendency presented during 1972-2011. Besides that, the multifractal behavior of the Kaidu River's runoff variability over four decades was also analyzed. Generally speaking, by decades, their four corresponding spectrum variations were not noticeable. These Δα values showed larger runoff events occupied the leading position with some local values falling. During the 1970s to the 1990s, Δf<0 illustrated the probability of the daily runoff at the lowest point is always larger than that of the highest during three continuous decades. At the beginning of the 21st century, for Δf>0 the trend presented was contrary from the 1970s to the 1990s. B values suggested an overall trend of increases during 1972-2011. Until the 21st century, the runoff with a slightly descending tendency on the whole explained these relatively large runoff events taking the leading role for the Kaidu River; but sometimes, some small events also played the dominant role.