## 3 Results
### Analysis of the Impact of Spatial Differentiation on Vegetation GPP
#### 3.4.2 Impact of Multifactor Interactions on Vegetation GPP  
The interactions between the different drivers were probed using an interaction detector, and the results are shown in the Figure 12, where the explanatory power of any two factors interacting with each other is greater than the single-factor results. The results showed that the interactions among the environmental factors significantly enhanced the influence of a single factor on GPP, and the two relationships showed two-factor enhancement and nonlinear enhancement, indicating that the growth and change in vegetation was the result of the joint action of the factors.  
Through multifactor interaction detection using the geographical detector, we found that any two factors demonstrated nonlinear enhancement effects. The q-values for two-factor interactions in the study area were significantly higher than those for single factors. The interaction between any two GPP driving factors exhibited a nonlinear enhancement pattern, suggesting that such two-factor interactions can substantially improve the explanatory power of GPP influencing factors, as presented in Table 4.  
Figure 12: _Cont._  
Figure 12: Interacting factor effects results: (**a**) 2001; (**b**) 2006; (**c**) 2011; (**d**) 2016; (**e**) 2022; (**f**) 2001\(\sim\)2022.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Year**} & **First-Order Dominant** & **Second-Order Dominant** & **Third-Order Dominant** \\  & **Interaction** & **Interaction** & **Interaction** \\ \hline  & LAI \(\cap\) VPD & LAI \(\cap\) Precipitation & LAI \(\cap\) Temperature \\
2001 & X2 \(\cap\) X6 & X2 \(\cap\) X3 & X2 \(\cap\) X5 \\  & 0.9032 & 0.9019 & 0.8993 \\  & LAI \(\cap\) Temperature & LAI \(\cap\) Precipitation & LAI \(\cap\) Radiation \\
2006 & X2 \(\cap\) X5 & X2 \(\cap\) X3 & X2 \(\cap\) X4 \\  & 0.7806 & 0.7782 & 0.7779 \\  & LAI \(\cap\) Precipitation & ET \(\cap\) LAI & LAI \(\cap\) VPD \\
2011 & X2 \(\cap\) X3 & X1 \(\cap\) X2 & X2 \(\cap\) X6 \\  & 0.9071 & 0.9069 & 0.9063 \\  & ET \(\cap\) LAI & ET \(\cap\) Temperature & ET \(\cap\) Precipitation \\
2016 & X1 \(\cap\) X2 & X1 \(\cap\) X5 & X1 \(\cap\) X3 \\  & 0.9801 & 0.9771 & 0.9767 \\  & ET \(\cap\) LAI & LAI \(\cap\) Precipitation & LAI \(\cap\) VPD \\
2022 & X1 \(\cap\) X2 & X2 \(\cap\) X3 & X2 \(\cap\) X6 \\  & 0.9152 & 0.9150 & 0.9125 \\  & LAI \(\cap\) VPD & LAI \(\cap\) Precipitation & LAI \(\cap\) Temperature \\
2001\(\sim\)2022 & X2 \(\cap\) X6 & X2 \(\cap\) X3 & X2 \(\cap\) X5 \\  & 0.9051 & 0.9040 & 0.9025 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Interacting values of vegetation GPP in five representative years.  
This study ranked the dominant interaction factors for five representative years based on the magnitude of their explanatory power (q-values), revealing that the most influential interaction factor consistently involved the combination of the dominant GPP single factor with another relevant influencing factor in each corresponding year.  
Using a geographical detector to analyze the effects of both individual and multifactor interactions on vegetation GPP variations, this study determined that the leaf area index, evapotranspiration, and precipitation factors exhibit dominant influence under single-factor conditions. Notably, the interaction between any two high-impact factors demonstrates a linear enhancement effect on vegetation GPP, revealing a synergistic relationship among multiple influencing factors.