## 4 Result
### Response of Different Vegetation Indices to Extreme Drought  
From the time series anomaly of SPEI during 2001-2020 in southern China, we can observe a significant drought event between 2009 and 2010 (Figure 6a). The SPEI anomaly values during this period were below \(-1\), indicating an extreme drought condition in this region. This led to the selection of GPP data from 2009-2010 to examine the response of SIF, NDVI, and kNDVI to this drought event, and to evaluate their efficacy in drought monitoring, between September and October 2009, the Precipitation Anomaly (Prec\({}_{\text{SA}}\)) fell below \(-0.5\), while the Soil Moisture Anomaly (SM\({}_{\text{SA}}\)) and Vapor Pressure Deficit Anomaly (VPD\({}_{\text{SA}}\)) reached below \(-1.0\) and above \(1.0\), respectively (Figure 6b). These values indicated a severe soil moisture deficiency and high vapor pressure deficit. Following the drought onset, a decline in the three vegetation indices was observed (Figure 6c), with SIF Anomaly (SIF\({}_{\text{SA}}\)) beginning to decrease slightly earlier (January 2010) compared to NDVI Anomaly (NDVI\({}_{\text{SA}}\)) and kNDVI Anomaly (kNDVI\({}_{\text{SA}}\)), which started in February 2010. All indices reached their lowest anomaly values in April 2010, with SIF\({}_{\text{SA}}\) showing the most significant decline, indicating its higher sensitivity to the extreme drought, followed by kNDVI\({}_{\text{SA}}\), and then NDVI\({}_{\text{SA}}\) showing the least decline. To further investigate these three vegetation indices in monitoring vegetation growth response to drought, GPP estimates from three flux tower sites (QYZ, DHS, XSBN) were selected as a benchmark for comparison. The results show that the monthly SIF-GPP relationship at QYZ and XSBN sites was the strongest among all vegetation indices, with R\({}^{2}\) values of 0.98 and 0.75, respectively (Figure 7). The NDVI-GPP and kNDVI-GPP relationships at all three sites displayed certain similarities. Notably, at the DHS site, the SIF-GPP relationship (R\({}^{2}\) = 0.18) was weaker than the NDVI-GPP and kNDVI-GPP relationships. Conversely, at the XSBN site, the kNDVI-GPP relationship was very weak (R\({}^{2}\) = 0.03).  
Figure 5: Spatial distribution of the SHAP value of environmental factors to NDVI (**a–f**), KNDVI (**g–l**), and SIF (**m–r**) from 2001 to 2020.  
Figure 6: Extreme drought in Southern China during 2001–2020 (**a**), changes of different water resources during extreme drought (**b**), and comparison of responses of vegetation index to extreme drought (**c**).  
Figure 7: Relationships between tower flux site GPP and satellite derived NDVI, kNDVI, and SF.  
A range of time lags, from direct (0 months) to delayed (up to 4 months) time point, were explored to assess the response of the vegetation index to GPP (Table 2). We calculated the Pearson correlation coefficient between VIs and GPP for each specified lag time by temporarily moving the VIs sequence by the considered lag time. Through this analysis process, we determine the time lag for producing the highest statistically significant correlation coefficients. This lag is considered as the optimal lag, and it contains the time interval when VIs responds most significantly to GPP. Generally, the time-lag relationship of SIF with GPP was shorter than that of NDVI and kNDVI with GPP. At the QYZ site, with a one-month time lag, the relationships of NDVI and kNDVI with GPP reached their maximum values (R\({}^{2}\) of 0.8 and 0.81, respectively), whereas the SIF-GPP relationship exhibited no time lag. At the DHS site, no time lag was observed in the relationships between all three vegetation indices and GPP. However, at the XSBN site, the relationships between the vegetation indices and GPP showed different time-lag patterns, with the NDVI-GPP relationship peaking at a two-month lag, the kNDVI-GPP relationship at a three-month lag, and the SIF-GPP relationship at a one-month lag.