## 3 Results  
### Distribution of Spatial and Temporal Variations in GPP, ET, and WUE  
From 2000 to 2020, the GPP of Gansu Province showed an overall increasing trend, with a change rate of 9.63 gC\(\cdot\)m\({}^{-2}\) (Figure 2a) and an average value of 510.22 gC\(\cdot\)m\({}^{-2}\), and its spatial distribution was generally characterized by high values in the east and low values in the west. The mean value of GPP in eastern Gansu was 578.23 gC\(\cdot\)m\({}^{-2}\), and that in western Gansu, also known as the Hexi Corridor area, was 300.40 gC\(\cdot\)m\({}^{-2}\). The eastern Longnan Mountains area is characterized by large mountain ranges, high mountains and deep valleys, abundant forest vegetation, and rich precipitation; thus, it presented the highest value of GPP. The western Hexi Corridor area is rich in cultivated vegetation and crops and is an important crop-production area; it presented the second-highest GPP. The area north of the Hexi Corridor, close to the Tengger Desert and the Badain Jaran Desert, has strong winds and sand, exposed mountains and rocks, and continuous deserts; it presented the lowest GPP value (Figure 3a).  
Figure 2: Trends in annual average changes in GPP, ET, and WUE in Gansu Province from 2000 to 2020. Figures (**a,b**) show the trends in GPP and ET, and WUE, respectively.  
The overall ET in Gansu Province from 2000 to 2020 also showed an increasing trend, with a rate of change of 7.43 mm (Figure 2a) and a mean value of 343.68 mm, and the spatial distribution also showed the characteristics of high values in the east and low values in the west. The mean value of ET in eastern Gansu was 372.67 mm, and that in the Hexi Corridor area was 254.08 mm. In eastern Gansu, there are the Longnan Mountainus area and Gannan grassland, and the Taohe, Huanghe, Weihe, and Bailongjiang Rivers flowing through them provide sufficient moisture; thus, it presented the highest ET value. Oasis farmland exists in the Hexi Corridor area, which also had high ET values due to irrigation and water supply, while the periphery of the oasis presents relatively low moisture values. The area north of the Hexi Corridor, on the other hand, has a dry climate and high evaporation intensity, but it was identified as a low-ET area due to insufficient water supply (Figure 3b).  
The spatial distribution characteristics of vegetation WUE in Gansu Province from 2000 to 2020 were similar to the patterns of vegetation GPP and ET, showing the characteristics of high values in the east and low values in the west. During the study period, the mean value of vegetation WUE in Gansu Province was 1.46 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\), and the overall WUE showed a decreasing trend, with a rate of change of \(-0.007\) gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\) (Figure 2b). The average value of WUE in the eastern part of Gansu was 1.54 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\), and that in the western part of the Hexi Corridor was 1.23 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\). The Longnan area in eastern Gansu is situated within a region with high vegetation GPP and ET, as well as vegetation WUE, with an overall range between 0.31 and 4.19 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\). In the oasis region of the Hexi Corridor, due to the high evapotranspiration, the vegetation WUE was found to be in a middle range of about 0.12-3.59 gC\(\cdot\)mm\({}^{-1}\cdot\)m\({}^{-2}\), even at the same GPP level (Figure 3c). Most areas in the Hexi Corridor region, aside from oases, are part of the Gobi Desert, including the Tengger and Badain Jaran Deserts, which are interspersed among the oases, covering a vast expanse of the Hexi Corridor and creating a typical arid landscape. Since the MODIS GPP/ET product incorporates land-use-type parameters in its calculations, GPP and ET values are null in sparsely vegetated desert areas and residential zones, leading to corresponding null values for WUE in these regions.