## 3 Results
### Interactive Detection and Analysis of Driving Factors  
To further investigate the effects of various factors on GPP, ET, and WUE, we employed a geographic detector to delve into the interactive effects among various factors(Figure 5). The analysis revealed that numerous factors (Tem \(\cap\) Pre, Tem \(\cap\) Rad, Tem \(\cap\) SM, Tem \(\cap\) VPD, Tem \(\cap\) LAI, Pre \(\cap\) Rad, Pre \(\cap\) SM, Pre \(\cap\) VPD, Pre \(\cap\) LAI, Rad \(\cap\) SM, Rad \(\cap\) VPD, Rad \(\cap\) LAI, SM \(\cap\) VPD, SM \(\cap\) LAI, and VPD \(\cap\) LAI) exhibited a bifactorial enhancement type of  
Figure 4: Partial correlation between different driving and GPP, ET, and WUE (**(a–f)** shows the partial correlation between GPP, with TEM, PRE, RAD, SM, VPD and LAI; **(g–l)** shows the partial correlation between ET with above variables; **(m–r)** shows the partial correlation between WUE with above variables, while GPP: gross primary productivity, ET: evapotranspiration, WUE: water-use efficiency, TEM: temperature, PRE: precipitation, RAD: solar radiation, VPD: vapor pressure deficit, SM: soil moisture).  
interaction with GPP, ET, and WUE across the entire mainland China scale. Notably, the LAI interaction with other factors was particularly significant, especially the interaction between Tem \(\cap\) LAI, which reached 0.82, 0.83, and 0.66, respectively. Among other factors, Pre \(\cap\) Rad, Tem \(\cap\) Rad, and Pre \(\cap\) Rad strongly interacted with GPP, ET, and WUE, whereas Tem \(\cap\) VPD had a nonlinear enhancement effect on WUE.  
In different climate types, the interactions between the LAI and other factors were more significant than other factors, especially in the mid-temperate semiarid region (II). Here, the interactions between the LAI and GPP and ET reached approximately 0.8, while the influence on WUE was strongest in the mid-temperate and semihumid region (III). Importantly, the interaction effects of factors varied significantly across different climate zones, ranging from dry to wet regions. In the mid-temperate arid region (I), the interactions between factors were characterized predominantly by nonlinear enhancements. However, an exception was found for the interaction of various factors combined with solar radiation (Tem \(\cap\) Rad, Pre \(\cap\) Rad, Rad \(\cap\) SM, Rad \(\cap\) VPD, and Rad \(\cap\) LAI), resulting in nonlinear increases in GPP and WUE. For ET, the interactions primarily showed nonlinear enhancements, with exceptions of Pre \(\cap\) SM, Pre \(\cap\) LAI, and SM \(\cap\) LAI, which were characterized by a bifactorial enhancement. In the md-temperate arid region (I), the interactive effects of TEM and PRE indeed had a nonlinear enhancing effect on GPP and WUE. For ET, Tem \(\cap\) Pre, Tem \(\cap\) Rad, Tem \(\cap\) SM, and Tem \(\cap\) VPD also showed nonlinear enhancements. In the mid-temperate and semihumid region (III), the interactions among TEM, RAD, and other factors, exhibited nonlinear enhancements in GPP, ET, and WUE. In the plateau temperate semiarid region (IV), all interactions between factors exhibited a bifactorial enhancement type. In the warm temperate semihumid region (V), the interactive effects of various factors were significantly weaker, except for interactions with LAI, which had an impact of less than 0.3 on GPP, ET, and WUE.  
Figure 5: The interactive effects detection results and explanatory power of different driving factors on GPP, ET, and WUE in China from 2001 to 2020 (GPP: gross primary productivity, ET: evapotranspiration, WUE: water-use efficiency, TEM: temperature, PRE: precipitation, RAD: solar radiation, VPD: vapor pressure deficit, SM: soil moisture).