## 2 Materials and Methods
### Vegetation Sensitivity in Response to Climate Change  
Vegetation sensitivity here is defined as the mean state of vegetation per unit increase in climate drivers. To this end, coefficients derived from a multiple linear regression (MLR) model were used to quantify the vegetation sensitivity in response to temperature, solar radiation, and water availability. To disentangle the collinearity impact between the climate driving factors, principal component regression (PCR) [41] was used along with the MLR model, and only principal components with a significant coefficient (\(p<0.1\)) in the PCR were kept in the subsequent analyses. The three climate-driving data were normalized via their Z-scores after they were seasonally detrended by subtracting corresponding climatology, which would increase the robustness of the MLR model used and make the resulting regression coefficients comparable to each other. The key formulation to estimate vegetation sensitivity in response to the three climate factors in each pixel is expressed as follows:  
\[VP=\alpha\times Temp+\beta\times Solar+\gamma\times Water+\varepsilon \tag{1}\]  
where \(VP\) denotes one of the vegetation proxies, including EVI, NDVI, LAI, and SIF; \(\alpha\), \(\beta\), and \(\gamma\) are regression coefficients that are used as proxies for the vegetation sensitivity in response to temperature (_Temp_), solar radiation (_Solar_), and water availability (_Water_), respectively; and \(\varepsilon\) denotes residuals.  
We advanced the use of the above time-invariant vegetation sensitivity by using a moving-window-based method in a robust way. The interannual vegetation sensitivity was obtained by applying MLR with PCR to anomaly Z-scores of vegetation and climatic datasets for a 5-year moving window advancing by yearly steps over the experimental periods. The investigation period in our work was restricted to the growing season of the QTP, and therefore the available samples included in the 5-year moving time window were generally limited, which may have led to unreliable estimates of regression coefficients. To address this issue, the Moving Block Bootstrap (MBB) approach [46] was considered here to draw blocks of data quadruplets, i.e., a vegetation datum and three climatic data, included in corresponding 5-year windows stochastically. The MBB method can preserve the temporal auto-correlation in time series data by keeping time series for the same year unchanged during the sample-construction process. To guarantee reliable regression coefficients, the resampling procedure was repeated 500 times for each window, and we took an average of the resulting coefficients to obtain a robust estimate of the regression coefficients. In addition, MLR only works when the number of available monthly samples included in a moving window is greater than 10.  
The 5-year time window was used here to identify the temporal variability of vegetation sensitivity with relatively sufficient statistical power (the number of available samples  
Figure 1: Spatial distribution of the reclassified MODIS land-cover types of the Qinghai–Tibet Plateau. “BSV” denotes “barren or sparsely vegetated area”.  
was typically \(>10\)), while keeping the kernel size of the window short enough to capture the interannual variability of the vegetation sensitivity. The timeframe of our analysis was from 1 January 2000 to 31 December 2021 for the experiments using LAI, EVI, and NDVI data and began at 1 January 2000 and ended at 31 July 2020 for the SIF data.