Multi-scale response of runoff to climate fluctuation in the headwater region of the Kaidu River in Xinjiang of China

Based on the climatological-hydrological daily data recorded in the headwater region of the Kaidu River during 1972–2011, the multi-scale characteristics of runoff variability and four climatic factor fluctuations (i.e. temperature, precipitation, relative humidity and evaporation) are analyzed using detrended fluctuation analysis. Furthermore, multi-scale response of runoff to climate fluctuation is investigated using detrended cross-correlation analysis. Main findings are as follows: (1) The temporal scaling behaviors of runoff and four climate factor series all exhibit two different power laws. In shorter temporal scaling, all the series indicate the similar persistence corresponding to the annual cycle. However, in longer temporal scaling, their different trends reflect the different inherent dynamic nature of various hydro-climatic change. (2) In the double logarithm curve logF²(s) ∼ logs, the long-range correlation of runoff and temperature, long-range correlation of runoff and precipitation and long-range correlation of runoff and relative humidity (hereafter referred to as Lrc-R-T, Lrc-R-P and Lrc-R-H, respectively) show two scaling regimes with two different scale indexes and a critical time scale of about 1 year; the long-range correlation of runoff and evaporation (hereafter referred to as Lrc-R-E) presents three scaling regime with three different scale indexes and with two critical time scales of about 1 and 10 years. These results reflect the multi-scale response characteristics of the runoff to climate change on different time scales.