## 3 Results
### Sensitivity Analysis of WUE to Drought Index  
Ridge regression was used to explore the sensitivity of WUE to drought index (\(\gamma\)), and a clear seasonal divergence was observed in the spatial patterns of \(\gamma\) during the period of 2001-2019 (Figure 5). Figure 4: Spatial (left) and temporal (right) distribution of seasonal vegetation water-use efficiency (WUE) on the Loess Plateau. Figure 5: _Cont._Generally, negative \(\gamma_{\text{spring}}\) values (81%), meaning spring drought led to increased WUE, were observed in the spring in the study region, with a mean (\(\gamma_{\text{spring}}\)) of \(-0.06\)  
Figure 5: Spatial distribution of the sensitivity coefficient(\(\gamma\)) of water-use efficiency (WUE) to seasonal drought (SPEI) (**a1–a4**) and scatter plot of the change in WUE sensitivity of each season in relation to the magnitude of drought (**b1–b4**). (Figure 5(a1)). The significant test area (8.2%) was mainly dominated by shrublands and grasslands (Figure S1(a)). The relationship between interannual sensitivity of WUE to SPEI and drought index in spring (Figure 5(b1)) showed a consistently increasing \(\gamma_{\text{spring}}\), along with an increasing magnitude of drought in the Loess Plateau. When the drought continued to increase, the magnitude of the increase, \(\gamma_{\text{spring}}\), was smaller, which means that the higher magnitude of drought, the lower the sensitivity of WUE to drought (Figure 5(b1)). In comparison, a pervasively positive sensitivity of WUE to SPEI, which means summer drought led to a decrease in WUE, was found (accounting for 70.8% of the whole region). In summer, \(\gamma_{\text{summer}}\) was significantly positive (11%) in the northwest of the Loess Plateau (including the Gansu and Ningxia Provinces and southwestern Inner Mongolia), which is dominated by shrublands and grasslands (Figure 5(a2), Figure S1b). There were three magnitudes of drought in summer; the higher the magnitude of drought (moderate drought), the larger the response of WUE to SPEI (Figure 5(b2)). Similar to spring, a generally negative sensitivity of WUE to drought (accounting for 80.2% of the whole region), which means fall drought increased WUE, was shown in fall, with eastern Gansu, western Shaanxi, and northern Shanxi being the most significant regions (\(p<0.05\)) (Figure 5(a3), Figure S1c). The relationship between SPEI and \(\gamma_{\text{fall}}\) (Figure 5(b3)) showed that with decreased SPEI, a negative \(\gamma_{\text{fall}}\) gradually changed to a positive \(\gamma_{\text{fall}}\), which indicates that when the SPEI value > 0 and there is no drought, the higher the SPEI, the lower the negative sensitivity of WUE to SPEI, whereas when the SPEI value < 0 during mild drought, fall drought decreased WUE. A generally clear negative sensitivity of WUE to SPEI (accounting for 74.2% of the whole region) was found in winter (Figure 5(a4)). Significantly negative \(\gamma_{\text{winter}}\) (with 7.8% of the areas passing the significance test) was distributed in the southeast of the Loess Plateau (including the south of Shaanxi and Shanxi), where the vegetation type is dominated by forests (Figure 5(a4), Figure S1d). In winter, relatively uniform sensitivity coefficients were shown, and \(\gamma_{\text{winter}}\) did not change with the varying SPEI, which suggests a minimal effect of SPEI on WUE in winter when SPEI > 0 and there is no drought (Figure 5(b4)). To further explore the seasonal difference of \(\gamma\) in climate regions of the Loess Plateau, the seasonal \(\gamma\) in humid, semi-humid, semi-arid, and arid areas was extracted. The results showed a clear seasonal divergence in four climate regions, along with the increased magnitude of drought (Figure 6, Table A2). Figure 6: Water-use efficiency (WUE) sensitivity coefficients in response to seasonal drought in climates regions. Note: SP: spring; SU: summer; FA: fall; WI: winter. Mild drought in spring increased WUE in arid, semi-arid, and semi-humid regions and decreased WUE in humid regions.