## 3 Results  
### Spatial Correlation Distributions of NDVI and GPP  
Using the GPP and NDVI products, we analyzed the distribution of the coupling between NDVI and GPP across the aridity gradients. Our findings demonstrated a distinct contrast in NDVI and GPP values between the northern and southern regions of China. Spatially, there were significant variations across China, with R\({}^{2}\) values from 0 to 0.86, and only 4.73% of the area having an R\({}^{2}\) value larger than 0.50. These higher values were mainly distributed in parts of northern China, while lower R\({}^{2}\) values were observed in southern  
Figure 2: Schematic representation of the analysis of NDVI and GPP relationships along the aridity gradients during the growing season in China from 1982 to 2018.  
China (Figure 3a). This difference is mainly induced by the varying land cover types. The southeast of China is a humid area with abundant precipitation and is mainly characterized by forests (ENF, EBF, DNF, DBF, and MF) and savannas [29]. In contrast, northern China is predominantly covered by grasslands. Overall, the relationship between NDVI-GPP decreased as AI increased (more humid). In the most regions of China, the mean R\({}^{2}\) of the inter-annual growing season NDVI-GPP relationship was quite low (Figure 3a), indicating a weak dependency of GPP on NDVI.  
Meanwhile, we analyzed the density of the R\({}^{2}\) values of NDVI-GPP for all pixels. Obviously, the largest number of pixels had the lowest R\({}^{2}\) values (ca. 0.02), and the overall average temporal R\({}^{2}\) for all the ecosystems was 0.15 (Figure 3b). The frequency of R\({}^{2}\) values declined exponentially as R\({}^{2}\) increased. Moreover, 37.56% of the pixels had R\({}^{2}\) values below average. In comparison, fewer pixels had higher R\({}^{2}\) values. This phenomenon suggested that some external factors or disturbances may have weakened the relationship between the two variables.  
NDVI-GPP coupling was quantified in different aridity gradients (Figure 4a) and PFTs (Figure 4b) for each month. The results showed a divergent trend in R\({}^{2}\) values of NDVI-GPP relationships among different aridity gradients and PFTs. In different aridity gradients, the value of R\({}^{2}\) was significantly higher in arid regions (AI \(<\) 0.65) (Figure 4a). The mean value in the arid region was 0.21. In contrast, the largest R\({}^{2}\) value of 0.24 was found in semi-arid areas (0.20 \(<\) AI \(<\) 0.50). In hyper-arid and arid regions (AI \(<\) 0.20), the R\({}^{2}\) values of NDVI-GPP were 0.19 and 0.21, respectively. As the AI continued to increase, a reverse trend was detected in humid (0.65 \(<\) AI \(<\) 1) and hyper-humid (AI \(>\) 1) regions, where the R\({}^{2}\) values were 0.11. This phenomenon indicated that the dependency of NDVI and GPP increased with the aridity gradients (becoming wetter), suggesting a weak dependency of GPP on NDVI in more humid conditions.  
We also detected divergence among different PFTs. For the grasslands (GAR), the largest NDVI-GPP coupling value was observed, with an R\({}^{2}\) of 0.20, while the lowest value of 0.04 was found in ENF (Figure 4b). In forest ecosystems (ENF, EBF, DNF, DBF, and MF), the mean R\({}^{2}\) values were 0.08, with the largest value occurring in DBF at 0.11. The values in WSA, SAV, CRO, and CNVM were lower than those in GRA, with R\({}^{2}\) values of 0.11, 0.14, 0.14, and 0.11, respectively. By comparing the R\({}^{2}\) values among different PFTs, we found that in dry ecosystems, such as grasslands, the strength of the coupling is greater than in relatively wet ecosystems, such as forests.  
Figure 3: Distribution of (**a**) inter-annual growing season Pearson correlation coefficients between GPP and NDVI during the period of 1982–2018, and (**b**) their density distribution of R\({}^{2}\) calculated for all pixels in China ecosystems. The vertical dashed line represents the mean value.