## 3 Data and Methods
### Methods  
#### 3.3.1 Calculation of the Ecosystem Quality Index (EQI)  
The ecosystem quality index reflects the general situation of vegetation and ecosystem in a region, referring to the ecosystem quality assessment standards issued by the Ministry of Ecology and the Environment of China [49]. This study constructed the ecosystem quality index based on the relative density of the remote sensing ecological parameters, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Primary Index** & **Secondary Index** & **Specific Index** & **Content** \\ \hline \multirow{6}{*}{Physical elements} & Terrain & Relief amplitude (\(X1\)) & Extracted from the filled DEM by the block statistics tool of ArcGIS 10.3 \\  & Land use & Land-use diversity (\(X2\)) & Using the Shannon–Wiener index to measure the richness, complexity, and order of land use in all counties in Henan Province \\ \cline{2-4}  & \multirow{2}{*}{Climate} & Average annual rainfall (\(X3\)) & Average annual rainfall of all county units in Henan Province \\ \cline{3-4}  & & Average annual temperature (\(X4\)) & Average annual temperature of all county units in Henan Province \\ \hline \multirow{3}{*}{Socioeconomic elements} & Population and economy & Population density (\(X5\)) & The total resident population of the county divided by the area of the county \\ \cline{2-4}  & & GDP per square kilometer (\(X6\)) & County GDP divided by county area \\ \hline \multirow{3}{*}{Policy adjustments} & Ecological engineering & \multirow{3}{*}{Forestry engineering (\(X7\))} & Statistics of density engineering policies in all counties in Henan Province, including conversion of farmland into forests, natural forest protection, and shelter forest projects \\ \cline{1-1} \cline{2-4}  & & & \\ \cline{1-1} \cline{2-4}  & & & \\ \end{tabular}
\end{table} 
Table 1: Driving factor index system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Basic Index** & **Tolerance** & **Variance Inflation Factor** \\ \hline \(X1\) & 0.266 & 3.76 \\ \(X2\) & 0.236 & 2.229 \\ \(X3\) & 0.205 & 4.86 \\ \(X4\) & 0.160 & 6.237 \\ \(X5\) & 0.206 & 4.851 \\ \(X6\) & 0.314 & 3.180 \\ \(X7\) & 0.459 & 2.179 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multivariate collinearity test results. namely, the vegetation coverage index (FVC), leaf area index (LAI), and gross primary productivity (GPP), to calculate the ecosystem quality index (EQI) of Henan Province. According to the National Ecological Function Zoning legislation issued by the Ministry of Ecology and the Environment of China, the vegetation coverage, leaf area index, and relative density of gross primary productivity in Henan Province were calculated for four types of vegetation: forests, shrubland, grassland, and farmland. The value range of each index was converted into the range of 0-1 through normalization; see Equation (1):  
\[\text{RVI}_{i,j,k}=\frac{F_{i,j,k}}{F_{\text{max}i,j,k}} \tag{1}\]  
where \(\text{RVI}_{i,j,k}\) is the relative density of the \(k\)th vegetation parameter in the \(j\)th area in the \(i\)th year; \(F_{i,j,k}\) is the ecological parameter value of the \(k\)th vegetation parameter in the \(j\)th area in the \(i\)th year; \(F_{\text{max}i,j,k}\) is the maximum value of the ecological parameters of the \(k\)th vegetation parameter in the \(j\)th area in the \(i\)th year. The method of calculating the ecosystem quality index (\(EQI\)) is shown in Equation (2):  
\[EQI_{i,j}=\frac{LAI_{i,j}+FVC_{i,j}+GPP_{i,j}}{3}\times 100 \tag{2}\]  
where \(EQI_{i,j}\) is the environmental quality of the ecosystem in the \(j\)th zone of the \(i\)th year; \(LAI_{ij}\) is the relative density of the ecological leaf area index in the \(j\)th zone in the \(i\)th year; \(GPP_{i,j}\) is the relative density of the total gross primary productivity of the ecosystem in the \(i\)th year and the \(j\)th zone.