## 2 Materials and Methods
### Methods  
Trajectory analysis that provides the spatiotemporal pattern of LUCC caused by natural and anthropogenic factors [45; 46; 47] can be utilised to recognise vegetation succession related to ERPs effectively [13]. Afforestation and grass planting have been adopted as major restoration activities to counter rocky desertification in Southwest China. Afforestation is generally defined as the replanting of trees in an area that was previously forested [48]. However, trees were also planted in previously unforested lands in the study area to improve ecological resistance in the karst region. To recognise the effects of natural and anthropogenic factors on vegetation cover in restoration areas, we used LUCC trajectory (LUCCT) to distinguish LUCCs driven by afforestation and grass planting (Table 1). Each cell in the interannual LUCCT to the overlaid annual land use and land cover data is analysed to recognise the spatiotemporal distribution of a restoration activity (Figure 3).  
The actual GPP change in this study is divided into ERP-driven (e.g., afforestation and grass planting) and non-ERP-driven (e.g., self-growth and climate factors) GPP changes. An ERP-driven GPP change is defined as the difference between the GPPs of the previous year and the year of ERP implementation. A contribution index (CI) (Equation (1)), defined as the ratio of ERP-driven and actual GPP trends, was established to assess the contribution of ERP to GPP dynamics. The ERP-driven GPP trend represents the multiyear mean GPP change caused by afforestation or grass planting (Equation (2)). The actual GPP trend calculated using a linear regression model represents interannual GPP variations in afforestation and grass planting areas or the entire study area (Equation (3)). CI, ERP-driven GPP trend and actual GPP trend can be expressed as follows:  
\[CI=\frac{|slope\_GPP_{ERP-driven}|}{|slope\_GPP_{actual}-slope\_GPP_{ERP -driven}|+|slope\_GPP_{ERP-driven}|}\times 100\% \tag{1}\]  
\[slope\_GPP_{ERP-driven}=\frac{1}{n}\sum_{i=1}^{n}interGPP_{i} \tag{2}\]  
\begin{table}
\begin{tabular}{c c} \hline
**Restoration Activity** & **LUCCT** \\ \hline \hline \multirow{6}{*}{Afforestation} & Sparse vegetation \(\rightarrow\) forest \\  & Agricultural land \(\rightarrow\) forest \\  & Grassland \(\rightarrow\) forest \\  & Shrubland \(\rightarrow\) forest \\  & Bare area \(\rightarrow\) forest \\ \hline \multirow{6}{*}{Grass planting} & Sparse vegetation \(\rightarrow\) grassland \\  & Agricultural land \(\rightarrow\) forest \\ \cline{1-1}  & Settlement \(\rightarrow\) forest \\ \cline{1-1}  & Bare area \(\rightarrow\) forest \\ \hline \hline \end{tabular}
\end{table}
Table 1: Definition of LUCCT for afforestation and grass planting in Southwest China.  
\[slope\_GPP_{actual}=\frac{\sum_{i=1}^{n}GPP_{i}t_{i}-\frac{1}{n}\sum_{i=1}^{n}GPP_{i }\sum_{i=1}^{n}t_{i}}{\sum_{i=1}^{n}t_{i}^{2}-\frac{1}{n}{\left(\sum_{i=1}^{n}t_ {i}\right)}^{2}} \tag{3}\]  
where \(CI\) represents the percentage of GPP variations caused by afforestation and grass planting, \(slope\_GPP_{ERP\_driven}\) represents the multiyear mean GPP variations caused by afforestation and grass planting, \(interGPP_{i}\) represents the interannual GPP variations between years \(i-1\) and \(i\), \(slope\_GPP_{actual}\) represents the actual annual GPP trend from year \(i\) to year \(n\) in afforestation and grass planting areas, \(GPP_{i}\) represents GPP in year \(i\) and \(t_{i}\) represents year \(i\).  
Partial correlation based on Pearson's correlation was used to explore the effects of temperature or precipitation on GPP changes in each cell and avoid the interaction effects of the two variables. All analyses were conducted using MATLAB (The MathWorks Inc., Natick, MA, USA).