## 5 Discussion  
### Vegetation Indices Response to Water Stress  
The spatial analysis of the correlation between vegetation indices and SPEI3 reveals notable differences in the responses of SIF, NDVI, and kNDVI to moisture stress. These differences are particularly pronounced in the Tibetan Plateau and Guangdong Province. In the Tibetan Plateau, SIF demonstrated a positive correlation with SPEI3. In contrast, the relationships between NDVI-SPEI3 and kNDVI-SPEI3 were less significant, exhibiting no correlation or even negative correlation in certain areas. SPEI3, which accounts for factors such as precipitation and potential evaporation [32], is a critical indicator in assessing the water balance on the surface. The precipitation changes over time are especially crucial in determining the carbon balance of the Tibetan Plateau [33,34]. Our findings suggest that NDVI may not adequately capture the impact of moisture variations on vegetation in this region. This disparity likely arises from the differing sensitivities and mechanisms through which NDVI, kNDVI, and SIF reflect the physiological state of vegetation [35], NDVI primarily indicates vegetation cover and biomass, while SIF is more directly related to the photosynthetic activity of plants [36,37]. Historical data from 2001 to 2020 show an increase in grassland areas and an upward trend in NDVI in the Tibetan Plateau, which may have partially obscured the response of NDVI to moisture changes [38]. In Guangdong province, earlier studies have identified temperature as a primary factor affecting vegetation growth [39,40]. The saturation effect in NDVI may have contributed to the high positive correlation observed between NDVI and SPEI3. Conversely, kNDVI, with its desaturation property, exhibited a lower correlation with SPEI3, suggesting a more minor different response to moisture conditions. The spatial heterogeneity of vegetation density and growth stages is also an important factor in evaluating the performance of NDVI and  
Figure 8: Relationships between tower flux site GPP and kNDVI (temporal), kNDVI (spatial). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sites**} & \multicolumn{3}{c}{**R\({}^{2}\) Values between kNDVI (Temporal) and GPP at Different Time Lags (Months)**} \\ \cline{2-6}  & **0** & **1** & **2** & **3** & **4** \\ \hline QYZ & 0.83 & 0.82 & 0.47 & 0.04 & 0.06 \\ DHS & 0.58 & 0.33 & 0.18 & 0 & 0.35 \\ XSBN & 0.38 & 0.63 & 0.6 & 0.2 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: R\({}^{2}\) values resultant from correlations between monthly GPP and monthly kNDVI (temporal) at different time lags. kNDVI. In regions with high spatial variability, kNDVI may be better than NDVI because it can better handle this spatial complexity. The SHAP interpretations for SIF, NDVI and kNDVI all underscore the importance of VPD as a key influencing factor for subtropical terrestrial vegetation growth over southern China. A notable region of high correlation between these three vegetation indices and SPEI3 is the southwestern Yunnan-Guizhou Plateau. This area, characterized by its energy-limited and alpine nature, is highly sensitive to temperature variations, impacting vegetation growth and surface water storage [41]. The diverse landforms of this region, including plateaus, basins, and hills, coupled with unique climatic characteristics and topography, facilitate rapid vegetative responses to changes in moisture conditions. VPD, a primary factor influencing vegetation growth in the Yunnan-Guizhou Plateau, indicates drier air conditions at higher levels, which can enhance water loss through transpiration and stress vegetation [42; 43]. Furthermore, SHAP values for SIF reveal that maximum temperature (Tmmx) is a significant influencing factor for vegetation in Guangdong province. In contrast, SHAP interpretations for NDVI indicate that VPD predominantly affects NDVI variations in this region.