## 2 Research Methodology
### Determination of Factor Weights  
Analytic hierarchy process (AHP) is one of the most common methods used to determine the weight of each factor in the study of ecological sensitivity. It is a process of modeling and quantifying the decision-making thinking process of decision-makers on complex systems. Using this method, a complex problem can be decomposed into several levels and many factors, and a simple importance comparison among the factors can obtain the weight of the importance degree of different schemes/indicators, providing a basis for decision-making choices [39]. This method mainly includes the following steps:  
1. Define the objectives of the analysis, identify the various factors related to the objectives of the analysis and the correlation between the various factors, then establish a hierarchical structure model. 2. Construct a judgment matrix and invite relevant experts to score each of the two factors according to their relative importance. 3. Calculate the weights and maximum eigenvalue of each indicator using the sum-product method. 4. Conduct a consistency test. If the consistency ratio CR < 0.10, it means that the judgment matrix passes the consistency test and the weights determined above are valid. In this study, a hierarchy of indicators was constructed, and expert opinions were introduced into the hierarchical analysis method to compare the importance of eleven indicators from three aspects: natural environment, human disturbance, and soil erosion. With the help of YAAHP software [40], the calculation is realized and the consistency test is carried out. Finally, the weight results of each factor are obtained (Table 3). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type of Sensitivity**} & \multirow{2}{*}{**Sensitive Indicators**} & \multicolumn{5}{c}{**Sensitivity Classification**} \\ \cline{3-6}  & & & **Slightly** & **Modelately** & **Highly** & **Extremely** \\  & & & **Sensitivity** & **Sensitive** & **Sensitive** & **Sensitive** \\ \hline \multirow{4}{*}{Natural environment} & Mean annual temperature (\({}^{\circ}\)C) & \textless{}1.68 & 1.68–2.79 & 2.79–3.84 & 3.84–4.94 & \textgreater{}4.94 \\  & Annual precipitation (mm) & \textless{}621 & 621–652 & 652–688 & 688–721 & \textgreater{}721 \\  & Elevation (m) & \textless{}200 & 200–500 & 500–800 & 800–1200 & \textgreater{}1200 \\  & Distance to water (m) & \textgreater{}2000 & 1000–2000 & 500–1000 & 200–500 & \textless{}200 \\  & Type of land use & Construction land, bare land & Cultivated land & Woodland & Grassland & Water, wetlands \\ \multirow{2}{*}{Human disturbance} & Distance to & \textgreater{}2000 & 1000–2000 & 500–1000 & 200–500 & \textless{}200 \\  & construction land (m) & \textgreater{}1000 & 500–1000 & 250–500 & 100–250 & \textless{}100 \\  & Distance to road (m) & \textgreater{}1000 & 500–1000 & 20–500 & 100–300 & \textgreater{}300 \\  & Topographic relief & \textless{}20 & 20–50 & 50–100 & 100–300 & \textgreater{}300 \\  & Rainfall erosivity (MJ\text\text\text\text\text\text\text\text\text\text\texttext\text {-}mm/(hm^{2}\text\text\text\text{-}h\text\text\texttexttext {-}a)\)) & \textless{}500 & 500–1000 & 1000–1500 & 1500–2000 & \textgreater{}2000 \\  & & & & & Clay loam, & \\  & Soil texture & Sand & Clay (heavy), & Loam, sandy & silt loam, & \\  & & & & & clay & sandy clay & \\  & Vegetation coverage & \textgreater{}0.8 & 0.6–0.8 & 0.4–0.6 & 0.2–0.4 & \textless{}0.2 \\  & Assignment & 1 & 3 & 5 & 7 & 9 \\ \hline \hline \end{tabular}  
* According to the expert advice, we used the natural breakpoint method to classify the annual average temperature and annual average precipitation. Referring to the factor classification method in the previous research literature, and making appropriate revisions according to the data characteristics of this study area, we completed the classification of the other 9 factors [2; 7; 13; 24; 38].  
\end{table} 
Table 2: Evaluation indicators and classification of ecological sensitivity.