## 3 Results
### Sensitivity Analysis of WUE to Drought Index
There was no moderate or severe drought in spring. The sensitivity of WUE to no drought and mild drought was quite different in the four climate regions. The sensitivity coefficients of WUE to no drought in arid, semi-arid, and humid areas were \(-0.129\), \(-0.051\), and \(-0.008\), respectively, whereas the coefficient was positive (\(\gamma=0.015\)) in the semi-humid area. The sensitivity coefficients of WUE to mild drought in arid, semi-arid, and semi-humid areas were \(-0.011\), \(-0.039\), and \(-0.023\), respectively, whereas the coefficient was positive (\(\gamma=0.017\)) in the humid area. In the summer, the magnitude of drought significantly influences the sensitivity of WUE to SPEI. Mild drought in the summer reduced WUE in four climate regions, whereas moderate drought decreased WUE in arid and semi-arid areas and increased WUE in semi-humid areas, and severe drought decreased WUE in arid and semi-arid areas. The sensitivity coefficient of WUE to mild drought was positive in arid, semi-arid, semi-humid, and humid areas, and the sensitivity coefficients were \(0.102\), \(0.007\), \(0.005\), and \(0.018\), respectively, with the highest sensitivity coefficient occurring in arid areas. The sensitivity coefficients of WUE to moderate drought in arid and semi-arid areas were \(0.096\) and \(0.039\), respectively, whereas the coefficient was negative in semi-humid areas (\(\gamma=-0.005\)). The sensitivity of WUE to severe drought was positive in both arid and semi-arid areas. In the fall, mild drought reduced WUE in arid and semi-arid areas and increased WUE in semi-humid areas; there were no moderate or severe droughts in the fall. The sensitivity coefficients of WUE to no drought or mild drought were low in different climate regions. The sensitivity of WUE to no drought was negative in arid, semi-humid, and humid areas, with values of \(-0.003\), \(-0.017\), and \(-0.017\), respectively. The sensitivity coefficient of WUE to mild drought in arid and semi-arid areas was \(0.005\) and \(0.002\), respectively, whereas that in semi-humid areas was negative (\(\gamma=-0.004\)). In the winter, in most regions with SPEI \(>0\) and no drought, the sensitivity coefficient of WUE to SPEI was negative. When SPEI \(<0\) and mild drought occurred, the sensitivity of WUE to SPEI was negative in arid and semi-arid areas, with the sensitivity coefficient being highest in arid areas (\(\gamma=-0.172\)), whereas the sensitivity coefficient was positive in semi-humid and humid areas, with coefficients of \(0.029\) and \(0.035\), respectively. The sensitivity coefficients of WUE to moderate drought in semi-arid, semi-humid, and humid areas were \(-0.032\), \(-0.009\), and \(-0.013\), respectively. The sensitivity coefficients of WUE to severe drought in semi-arid and sub-humid regions were negative. On the whole, mild drought in winter increased WUE in arid and semi-arid regions but decreased WUE in semi-humid and humid regions. Moderate and severe drought increased water-use efficiency in semi-arid and semi-humid regions. On the whole, in arid and semi-arid areas, mild drought in the spring and winter increased WUE, whereas mild, moderate, and severe droughts in the summer decreased WUE. In semi-humid areas, mild droughts in the spring and fall, moderate droughts in the summer, and moderate and severe droughts in the winter increased WUE, although mild drought in the summer and winter decreased WUE. Mild drought in the spring, summer, and winter all decreased WUE in humid areas, whereas the sensitivity coefficient of WUE to SPEI in the arid region of the Loess Plateau was generally higher than that in the semi-arid, semi-humid, and humid regions. That means that vegetation is more sensitive to water change in arid regions than in other climate regions in the study region.