## 2 Datasets and Methods
### Methods  
A linear regression model was used to detect trends in NDVI time series, and an F-test was used to check for statistical significance. Considering the potential TP in the NDVI time series, we also used a piecewise regression model [56] to see if trends in NDVI changed over the study period.  
Figure 1: _Cont._  
_Remote Sens._**2014**, \(6\)  
\[\text{NDVI}_{i}=\begin{cases}b_{0}+b_{1}t_{i}+\varepsilon,t_{i}\leq t_{k}\\ b_{0}+b_{1}t_{i}+b_{2}(t_{i}-t_{k})+\varepsilon,t_{i}>t_{k}\end{cases} \tag{1}\]  
where \(\textit{NDVI}_{i}\) is the NDVI time series, \(t_{i}\) is time, and \(t_{k}\) is the TP; when \(t_{i}\) is before \(t_{k}\), the slope of \(\textit{NDVI}_{i}\) is \(b_{l}\). After \(t_{k}\), the slope of \(\textit{NDVI}_{i}\)is \(b_{1}+b_{2}\). In addition, \(k\) is limited to between 4 and n-3, to avoid using a segment that is too short before or after the TP. The model parameters are estimated using the maximum likelihood method. This model has been widely applied in many previous studies [16, 17, 41, 57, 58, 59, 60]. We fitted the models to the NDVI time-series data using the maximum likelihood (least-squares error) method, and evaluated to see if the TPs were significant using the Akaike Information Criterion (AIC) [61]. The AIC value of a regression model (either normal regression model or piecewise regression model) is defined as  
\[\text{AIC}=\text{nlog}\left(\frac{\text{RSS}}{\text{n}}\right)+2\text{k}+\frac {2\text{k}(\text{k}+1)}{\text{n}-\text{k}-1} \tag{2}\]  
where _RSS_ is the residual sum of squares, \(n\) is the sample size, and \(k\) is the number of parameters in the regression model. If the difference between the AIC values of the two models is greater than 2, the model with the lower AIC value is considered more effective, _i.e._, if AIC value of the piecewise regression model is less than that of the normal regression model by \(-2\), the TP is considered significant [62]. Using this method, we determined whether the NDVI time series should be fitted using the linear regression or piecewise regression model. Furthermore, the trend of the TP will change significantly if the null hypothesis of \(b_{2}=0\) is rejected, as occurs with the difference between the trend before and after the TP.  
In addition, we applied Spearman partial correlation analysis to the monthly and annual NDVI time series data and climate factors (temperature and precipitation) to provide robust insights into their correlations, taking into account the nonlinear relationship and interaction between dynamic vegetation indices and climatic variables (temperature and precipitation). A lag time is defined as the number of months after which the NDVI shows the highest significant positive correlation coefficient with previous temperature or precipitation. The lag time is assumed to be limited to less than 6 months, based on the [PERSON] _et al._[63] finding that the effect of climate factors can persist into the next season.  
One-way analysis of variance was used to test whether there is an overall difference between trends in different vegetation regions. The Games-Howell post hoc [64] analysis was used to check if vegetation regions were significantly different from each other.