## 3 Results  
### Impact of ECIs on EIs at the Annual Scale  
The analysis revealed both the weight and the correlations of various climate indices with the EIs. The weight and correlation of these indices with the GPP (Figure 2a) and NDVI (Figure 2b) were analyzed using a combination of random forest regression and a correlation analysis. Among the indices, SU (+) emerged as the most important for the GPP, with a weight of 0.275, followed by the RDI (+) and DTR (\(-\)), with weights of 0.153 and 0.107, respectively ('+' or '\(-\)' represents a positive or negative correlation between the climate index and EIs). These indices not only had a higher weight in terms of their influence on the GPP, but also showed a extremely significant correlation (\(p<0.001\)). While most ECIs were significantly correlated with the GPP, standardized indices and CECIs did not exhibit significant correlations, with the exception of the CDC (+, \(p<0.01\)). Other indices, such as the WDI, CDD, and WSDI, were found to be neither important nor relevant to the GPP. A similar pattern was observed for the NDVI, with SU (+, \(p<0.001\)) and DTR (\(-\), \(p<0.001\)) showing greater importance, with weights of 0.238 and 0.130, respectively. All indices except for the STI and CSDI were extremely significantly correlated with the NDVI (\(p<0.001\)). The correlations between the ETI (+), SDII (+), CWD (+), RDI (+), HPI (+), CSDI (+), GSL (+), FD (-), SU (+), ID (-), and TR (+) and the GPP were stable at a yearly scale, with all being highly significant (\(p<0.001\)) across each time window. The CDC and WDI remained insignificant across all windows (Figure 2c). For the NDVI, some indices showed different behavior over long time-series. For instance, the CDW (+), CDC (+), CDI (-), and CSDI (+) demonstrated temporal stability, maintaining significant correlations for approximately 25 consecutive years (Figure 2d); however, while the STI and WSDI were significantly and positively correlated with the NDVI, they lacked temporal stability. The  
Figure 2: Weights and temporal stability of the ECIs in relation to EIs in SWC (annual scale). (**a**,**b**) display the weights and correlations of the ECIs with the GPP and NDVI, respectively. (**c**,**d**) present similar information but focus on the temporal stability of the ECIs over a 38-year period, using 15-year intervals as the moving window. ETI (+), DTR (\(-\)), SDII (+), HPI (+), GSL (+), FD (\(-\)), SU (+), ID (\(-\)) and TR (+) were consistently significant (\(p<0.001\)) throughout the 1982-2019 period (Figure 2d). In SWC, the impact of ECIs on the EIs varied significantly across regions. In the HDMs (Figure 3a), the RDI had the greatest influence on the GPP (weight = 0.327, \(p<0.001\)), followed by FD (0.194, \(-\), \(p<0.001\)) and the ETI (0.121, +, \(p<0.001\)). In contrast, vegetation in the SCB exhibited a weak response to various climate indices (Figure 3b). The results for the YGP (Figure 3c) and GXB (Figure 3d) were similar, with SU, DTR, the RDI, and TR showing significant positive correlations with the GPP (\(p<0.001\)). However, the YGP had a higher number of indices that were significantly correlated with the GPP compared to the GXB. For the NDVI, the weight of the various indices and their correlations varied significantly across regions. In the HDMs, the DTR (weight = 0.186) and RDI (0.186) were the most important for the NDVI, although the RDI was not significantly correlated with the NDVI in this region. However, the SPI, CWD and CDC showed extremely significant and positive correlations with the NDVI (\(p<0.001\)), which contrasted with their relationships with the GPP. Additionally, in the HDMs, 16 indices were significantly correlated (\(p<0.05\)) with the NDVI (Figure 3e), compared to only 11 indices for the GPP (Figure 3a). This discrepancy was even more pronounced in the SCB, where the NDVI was strongly influenced by various indices, with over 75% of the indices showing extremely significant correlations (\(p<0.001\)) (Figure 3f).