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Figure 4(a) reveals that the main periodicities in the annual runoff of the three headstreams were 6, 17, and 22 years and that the main periods were significant at a confidence level of 95% for a 2–6-year period, but not significant for periods longer than 6 years. According to Figure 4(b), an alternative high-frequency oscillation was apparent in the annual runoff for the 6-year period. The abrupt change points of the 17-year period were in 1969, 1983, 1995, and 2008, and the phases had four abrupt changes (positive–negative–positive–negative). In addition, the annual runoff of the Tarim River abruptly changed in 1987 in terms of the 22-year period. According to the wavelet coefficients of runoffs in the three significant periods, the fitting equations were acquired to predict the future runoff change (Figure 4(c) and Table 3). Figure 4(c) shows that there were significant shorter periods in 1957–1967, 1970–1981, and 1988–1997 for 2–6-year periods at a confidence level of 95%.

Table 3

Fitting equation of period of runoff in the headstreams of the Tarim River

Period of runoff (year)Fitting equationR2FP
Y= 0.693 sin(1.771x 6.28) + 0.0033 0.47 14.03 <0.0001 
17 Y= 1.0186 sin(0.2014x 6.28) + 0.0086 0.72 40.69 <0.0001 
22 Y= 1.3981 sin(0.0987x+ 5.0544) + 0.0146 0.999 180262.00 <0.0001 
Period of runoff (year)Fitting equationR2FP
Y= 0.693 sin(1.771x 6.28) + 0.0033 0.47 14.03 <0.0001 
17 Y= 1.0186 sin(0.2014x 6.28) + 0.0086 0.72 40.69 <0.0001 
22 Y= 1.3981 sin(0.0987x+ 5.0544) + 0.0146 0.999 180262.00 <0.0001 

Y’ is period of drought flood index, ‘x’ is year series.

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