## 3 Results
### The Spatiotemporal Characteristics of the Impact of Environmental Factors on GPP
#### 3.3.2 The Spatial Characteristics of the Impact of Environmental Factors on GPP  
Based on the comprehensively evaluated environmental factor satellite data, we conduct a correlation analysis with the GPP satellite data inverted by the MLR model to reveal the spatial relationship between environmental factors and GPP. GPP in arid regions still exhibits a strong positive correlation with PAR, VPD, SWC, Tair, and Tsoil at the spatial scale, with distinct regional characteristics (Figure 9). Among these values, the correlation coefficient between GPP and PAR is lowest in the Gurbantunggut Desert and southern TM, and highest in Central Tianshan. The correlation coefficient between GPP and PAR ranges from 0.56 to 0.94 within the study area, indicating that the overall influence on GPP is significant. The spatiotemporal correlation of VPD is significantly consistent with that of PAR. The correlation is lowest in the Gurbantunggut Desert and highest in Central Tianshan. The correlation coefficient between GPP and VPD ranges from 0.50 to 0.85 within the study area, indicating that the overall influence on GPP is relatively weak. The overall spatial correlation characteristics of Tair and Tsoil are similar to those of PAR and VPD. However, the spatiotemporal correlation between GPP and Tair and Tsoil is more significant than that with VPD. The spatiotemporal correlation coefficient between GPP and Tair ranges from 0.50 to 0.89, while that between GPP and Tsoil ranges from 0.50 to 0.86 within the study area, indicating a secondary overall influence on GPP. Figure 9: The spatial correlation changes between five environmental factors (PAR, VPD, SWC, Tair, and Tsoil) and GPP, where \(p\)-value is the significance test for the correlation coefficient. The spatial distribution characteristics of SWC show some differences compared to those of PAR, VPD, Tair, and Tsoil. Areas with low correlation coefficients are distributed in areas with sparse vegetation and high evapotranspiration, such as the Gurbantunggut Desert. In contrast, the maximum attribute values are displayed in the TM and their northern and southern slopes, and the Altai Mountains. However, due to the comprehensive influence of artificial irrigation, the correlation between GPP and SWC in some farmland areas on the north and south slopes of the TM is higher than that with PAR, VPD, Tair, and Tsoil. The correlation coefficient between GPP and SWC ranges from 0.10 to 0.98 within the study area, and the overall influence on GPP is the weakest. The Expression Pattern of the Relationship Between Environmental Factors and the Comprehensive Impact on GPP  
The spatiotemporal correlation between GPP (inverted by the MLR model based on parameter optimization) and various environmental factors indicates that there are varying degrees of correlation between the two at different time and spatial scales. However, we have not clearly defined the linear or non-linear expression patterns of the comprehensive impact of environmental factors on GPP. Therefore, we believe it is necessary to further explore the expression patterns of the comprehensive impact of various environmental factors on GPP. In arid regions, at the annual scale, there are certain differences in the expression of the comprehensive impact of various environmental factors on GPP in different ecosystems (Figure 10). In farmland areas, the comprehensive impact of the five environmental factors on GPP can be expressed based on a linear pattern. Among these factors, PAR shows the best expression effect, while SWC shows a weaker expression effect. In grassland areas, the comprehensive impact of VPD on GPP can follow a linear pattern, but the comprehensive impact of PAR, Tair, Tsoil, and SWC is based on a non-linear pattern. PAR and VPD have the strongest expression effects, while the expression effect of SWC is weaker.