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 2Statistics of TI and TI′ for study watersheds
Watersheds
. | TI or TI′
. | Max
. | Min
. | Mean
. | Std. 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 |
Watersheds
. | TI or TI′
. | Max
. | Min
. | Mean
. | Std. 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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