## 3 Results
### Characteristics of Spatial and Temporal Changes in WUE in Gansu Province  
From 2000 to 2020, the WUE in Gansu Province generally showed a decreasing trend. During the study period, the minimum value of annual average WUE, 1.29 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\), representing an 11.64% decrease from the multi-year average, appeared in 2011. In contrast, the maximum value, 1.81 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\), representing a 23.97% increase from the multi-year average, was observed in 2000. During these 21 years, the vegetation WUE decreased continuously, from 1.81 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\) in 2000 to 1.51 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\) in 2020, a decrease of 16.57%.  
During the period 2000-2020, the vegetation WUE in Gansu Province fluctuated between 1.29 and 1.81 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\). The areas with significant increases in this parameter were mainly concentrated in Maiji District in Tianshui City, Hui County, Xihe County, Cheng County, Wen County in Longnan, and Zhouqu County in Gannan Tibetan Autonomous  
Figure 3: Spatial distributions of GPP, ET, and WUE (from left to right, respectively) in Gansu Province, 2000–2020.  
Prefecture, and some areas of Minle County and Ganzhou District in Zhangye also showed a significant increase in WUE. The areas with significant decreases in WUE included most of Tianshui City, Kongdong District, Jingchuan County, Lintai County, and Chongxin County in East Gansu; most areas of Qingyang City, such as Zhenyuan County, Xifeng District, Ning County, Zhengning County, Huachi County, and Heshui County; parts of Lanzhou City, Jingyuan County, and Jingtai County in Baiyin City; Liangzhou District; parts of Minqin County in Wuwei City; parts of Jinchang City; and parts of Sunan Yugur Autonomous County in Zhangye City. In general, the vegetation water utilization efficiency in Gansu Province showed a decreasing trend.  
Theil-Sen slope estimation is employed to calculate trend values, which are typically utilized in conjunction with the M-K nonparametric test. In this approach, the Sen trend value is initially calculated, and then the M-K method is employed to determine the trend significance. The vegetation GPP/ET/WUE trends in Gansu Province for the period from 2000 to 2020 are shown in Figure 4. The areas with an overall increasing trend in WUE accounted for 13.79%, with the area with the most significant increase being the largest, at 10.86%. In contrast, the areas with a decreasing trend accounted for 41.23%, with the area with a slightly significant decrease being the largest, at 24.61%. These areas are primarily located in Liangzhou District in Wuwei City, Jinchang City, Ganzhou District, Shandan County, and Sunan Yugur Autonomous County in Zhangye City in the Hexi Corridor; Kongdong District, Huating City, Jingchuan County, Lingtai County, and Chongxin County in Pingliang City; and Xifeng District, Ning County, Zhenyuan County, and Zhending County in Qingyang City in the eastern part of Gansu. The distribution of the spatial trends in vegetation WUE in Gansu Province from 2000 to 2020 may be related to the differences in the response of different vegetation cover types to climate change.