## 2 Materials and Methods
### Methods
#### 2.3.5 EVI Assessment  
Calculation of EVI Indicators for Assessment  
An ecological vulnerability assessment model for the study area was established using temporally aligned datasets for four target years (2005, 2010, 2015, and 2020). For each target year, all input variables were extracted from the corresponding annual datasets to ensure temporal consistency, using genetic projection pursuit and comprehensive evaluation models to assess the ecological vulnerability of the study area. Combined with the environmental characteristics of the study area, five variables were selected to analyze EVI (Figure 4). For the vegetation environment aspect, we use Fractional Vegetation Coverage (FVC) and Habitat Quality Index (HQI) to characterize the vegetation environment. FVC is commonly defined as the percentage of the vertical projection area of vegetation (including leaves, stems, and branches) to the total area of the statistical region. It is an important parameter for describing surface vegetation coverage and can intuitively reflect the vegetation prosperity within a region, serving as an important indicator of vegetation growth status. In remote sensing, vegetation coverage is typically calculated using the pixel binary method. **HQI** displays the ecological environment quality that supports species and persistence. According to the reference of \"Technical Standards for Ecological Environment Assessment\"  
Figure 4: Spatial distribution maps of normalized factors in the study area (2020). and based on standards promulgated by China's Ministry of Environmental Protection (MEP-2015), **HQI** and **NDVI** can be calculated as Equations (1) and (2):  
\[HQI=\left(0.35A_{f}+0.25A_{g}+0.28A_{w}+0.11A_{c}+0.04A_{i}+0.01A_{b}\right)/A \tag{1}\]  
\[FVC=\frac{NDVI-NDVI_{soil}}{NDVI_{seg}-NDVI_{soil}} \tag{2}\]  
where \(A_{f}\) is forest area, \(A_{g}\) is grassland area, \(A_{w}\) is water body area, \(A_{c}\) is cultivated land area, \(A_{i}\) is impervious surface area, \(A_{b}\) is bare land area, and \(A\) is total area. When calculating **FVC**, **NDVI** values with cumulative probabilities of 0.5% and 99.5% are used as \(\textbf{NDVI}_{soil}\) and \(\textbf{NDVI}_{seg}\), respectively, and **NDVI** values outside this range are considered as pure soil and pure vegetation. MODIS data is used to calculate vegetation coverage for each vegetation area. Calculation and Classification of Ecological Vulnerability Index  
The projection pursuit model is used to find the optimal projection direction vector by constructing projection indicators, and then calculate sample projection eigenvalues from the optimal projection direction vector, thereby conducting comprehensive evaluation of ecological vulnerability. Here, a projection pursuit model based on genetic algorithms is used to evaluate EVI, with a detailed introduction to the construction steps of Genetic Projection Pursuit (GPP). The model is as follows: First, samples are normalized because different indicators have different dimensions. To solve the variability of different indicator scales, each indicator set needs to be normalized by applying the equation:  
\[x_{ij}=\left(x_{ij}^{*}-x_{min,j}\right)/\left(x_{max,j}-x_{min,j}\right)\]  
where \(x_{max,j}\) and \(x_{min,j}\) are the maximum and minimum values of the \(j\)-th indicator in the sample set, respectively, and \(x_{ij}\) is the normalized indicator value of the sample set. Subsequently, the projection index function is constructed. Under the execution of projection direction \(a_{T}\) = (a\({}_{1}\), a\({}_{2}\), \(\ldots\), a\({}_{m}\)), the m-dimensional data [x\({}_{ij}\) ] i = 1, 2, \(\ldots\), m] for \(i\) = 1, 2, \(\ldots\), n can be processed into a one-dimensional value \(z_{i}\) through the following formula:  
\[z_{i}=\sum_{j=1}^{m}a_{j}x_{ij},i=1,2,\ldots,n\]  
The distribution characteristics of projection values \(z_{i}\) are required to be as follows: local projection points may be concentrated, while overall projection points may be dispersed.