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Figure 3 presents a wavelet analysis of the drought–flood index for the headstream mountain areas of the Tarim River. In Figure 3(a), the drought–flood index represents the interdecadal change with a period of 22 years, which is also verified in Figure 3(b). In the 22-year period, the index abruptly changed from drought to flood in 1988 (Figure 3(b)). Additionally, the curve for the 22-year period was not closed in the positive-phase isogram for 2007, indicating that the drought–flood index would continue to denote a flood period in the coming years. The interannual change in the index was the most significant in the period range of 3–8 years, with the peak values of wavelet variance corresponding to 4-year and 8-year periods at a confidence level of 0.05 in the chi-square test. Positive and negative phases represent periodic alternative variations with high frequency. Therefore, based on the wavelet coefficients of drought and flood indexes in the three primary periods (i.e., 4-year, 8-year, and 22-year) of the recent 50-year study period, the prediction equations were attained by non-linear fitting to analyze the change characteristics in the future. Table 2 shows the wavelet coefficients of drought and flood indexes fitted significantly at a test level of 0.01, and it indicated that the prediction results of the fitting equations were reliable. Future values of drought and flood indexes in the significant periods can thus be calculated for the Tarim River. In addition, there was significant interannual change during the period 1970–2001 in the period of 3–8 years (Figure 3(c)).
Table 2

Fitting equation of the period of the drought–flood index

Period of drought flood index (year)Fitting equationR2FP
Y= 0.5283sin(2.2642x 6.28) −0.0145 0.35 8.26 0.0002 
Y= 0.9876sin(1.2752x+ 6.28) −0.0227 0.59 22.26 <0.0001 
22 Y= 1.6871sin(0.1003x+ 1.708) + 0.004 0.999 187697.44 <0.0001 
Period of drought flood index (year)Fitting equationR2FP
Y= 0.5283sin(2.2642x 6.28) −0.0145 0.35 8.26 0.0002 
Y= 0.9876sin(1.2752x+ 6.28) −0.0227 0.59 22.26 <0.0001 
22 Y= 1.6871sin(0.1003x+ 1.708) + 0.004 0.999 187697.44 <0.0001 

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

Figure 3

Wavelet variances (a), wavelet coefficients (b), and significant time sections (c) of drought–flood indexes in the headstream mountain areas of the Tarim River. In (b), the positive wavelet coefficient indicates the positive phase (flood period), the negative wavelet coefficient indicates the negative phase (drought period), and zero value represents the abrupt change year of drought and flood.

Figure 3

Wavelet variances (a), wavelet coefficients (b), and significant time sections (c) of drought–flood indexes in the headstream mountain areas of the Tarim River. In (b), the positive wavelet coefficient indicates the positive phase (flood period), the negative wavelet coefficient indicates the negative phase (drought period), and zero value represents the abrupt change year of drought and flood.

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