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The grid raster of DEM, Ks, K, and Ks·K with the resolution of 100 m were used to calculate TI and TI′. The spatial distributions of TI and TI′ in YLX, WJB, and HQ are plotted in Figure 3 and their statistical results are listed in Table 2. As shown in Figure 3, the spatial distribution of TI1, TI2, and TI3 for each watershed are significantly different from that of TI after incorporating Ks, K, and Ks·K, respectively. Since almost all of the Ks values are greater than 1, all of the K values are less than 1 (shown in Table 1), and both Ks and K are incorporated into the denominator of the index α/tanβ, so the values of TI1 and TI2 are less and greater than TI, respectively. Depending on the product of Ks and K, TI3 is generally lower than TI, as the Ks values are commonly much larger than K. The changes of TI1 and TI3 are more obvious than the changes of TI2 because the Ks and Ks·K values are larger than K to cause more evident changes. The spatial heterogeneities of TI1 and TI3 are much stronger than TI and TI2.
Table 2

Statistics of TI and TI′ for study watersheds

WatershedsTI or TIMaxMinMeanStd. dev.
YLX TI 15.981 3.622 7.747 1.527 
TI1 13.595 0.048 4.748 1.564 
TI2 16.343 3.285 8.229 1.465 
TI3 13.990 0.974 5.723 1.567 
WJB TI 14.639 3.705 8.294 1.230 
TI1 13.050 0.210 6.039 1.530 
TI2 16.171 3.791 9.585 1.259 
TI3 14.585 1.454 7.330 1.547 
HQ TI 14.665 3.694 7.850 1.365 
TI1 14.642 1.572 6.382 1.570 
TI2 15.886 4.914 9.158 1.368 
TI3 15.976 2.686 7.686 1.608 
WatershedsTI or TIMaxMinMeanStd. dev.
YLX TI 15.981 3.622 7.747 1.527 
TI1 13.595 0.048 4.748 1.564 
TI2 16.343 3.285 8.229 1.465 
TI3 13.990 0.974 5.723 1.567 
WJB TI 14.639 3.705 8.294 1.230 
TI1 13.050 0.210 6.039 1.530 
TI2 16.171 3.791 9.585 1.259 
TI3 14.585 1.454 7.330 1.547 
HQ TI 14.665 3.694 7.850 1.365 
TI1 14.642 1.572 6.382 1.570 
TI2 15.886 4.914 9.158 1.368 
TI3 15.976 2.686 7.686 1.608 
Figure 3

Spatial distributions of TI and TI′ in study watersheds.

Figure 3

Spatial distributions of TI and TI′ in study watersheds.

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