# Application of Compound Terrain Factor LSW in Vegetation Cover Evaluation
## 4 Results and Discussion
### Vegetation Susceptibility Evaluation and Test  
After obtaining the distribution of CF values for each class of potential impact factors in the study area, the idea that LSW is closely related to vegetation cover was proposed from a qualitative perspective, while further demonstration is needed for the quantitative description of LSW that can be used for vegetation cover. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Impact Factor** & **Grade** & **Total Graded Area/km\({}^{2}\)** & **Vegetation Coverage\%** & **CF** \\ \hline \multirow{8}{*}{LSW} & I & 2279.97 & 17.27 & \(-\)0.92 \\  & II & 5044.07 & 66.45 & \(-\)0.30 \\  & III & 8210.95 & 79.39 & 0.25 \\  & IV & 6942.36 & 83.66 & 0.44 \\  & V & 3700.43 & 89.95 & 0.68 \\ \hline \multirow{8}{*}{LS} & I & 25,807.17 & 73.97 & \(-\)0.007 \\  & II & 356.12 & 84.75 & 0.48 \\  & III & 12.00 & 70.02 & \(-\)0.18 \\  & IV & 2.11 & 56.22 & \(-\)0.55 \\  & V & 0.40 & 57.64 & \(-\)0.52 \\ \hline \multirow{8}{*}{TWI} & I & 10,255.48 & 86.07 & 0.56 \\  & II & 9427.70 & 77.17 & 0.15 \\  & III & 4647.56 & 53.83 & \(-\)0.59 \\  & IV & 1405.18 & 43.05 & \(-\)0.73 \\  & V & 441.8 & 43.33 & \(-\)0.73 \\ \hline \multirow{8}{*}{Aspect} & I(plane) & 57.55 & 0.80 & \(-\)0.99 \\  & II(N) & 3124.87 & 73.74 & \(-\)0.01 \\ \cline{1-1}  & III(NE) & 3261.75 & 73.48 & \(-\)0.03 \\ \cline{1-1}  & IV(E) & 3966.14 & 71.82 & \(-\)0.10 \\ \cline{1-1}  & V(SE) & 3552.50 & 72.04 & \(-\)0.10 \\ \cline{1-1}  & VI(S) & 3262.89 & 73.04 & \(-\)0.05 \\ \cline{1-1}  & VII(SW) & 3044.32 & 75.92 & 0.09 \\ \cline{1-1}  & VIII(W) & 2964.20 & 76.35 & 0.11 \\ \cline{1-1}  & IX(NW) & 2943.54 & 79.31 & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: CF values calculated for each class of LSW and control group factors. The ROC curve is widely used in the evaluation of medical diagnostic test performance and landslide prediction [79; 80]. In the case of single factor evaluation, the susceptibility and specificity at different thresholds can be calculated by constructing a logistic regression model [81]. Afterwards, the ROC curve was plotted with sensitivity as the ordinate and specificity as the abscissa [82]. Among them, susceptibility is the true positive rate (TPR) and specificity is the false positive rate (FPR) (Table 2, reproduced with permission from [82], Elsevier, 2023). The formulas are as follows:  
\[\text{TPR}=\frac{\text{TP}}{\text{TP}+\text{FN}} \tag{4}\]  
\[\text{FPR}=\frac{\text{FP}}{\text{FP}+\text{TN}} \tag{5}\]  
The area under curve (AUC) can be used as a gauge of the model prediction accuracy. Intuitively, the ROC curve divides the closed graph of Figure 5 into two parts, and the size of the area below the curve is the AUC. The closer the AUC value is to 1 (or expressed as a percentage, i.e., 100%), the stronger the judgment of the model is [83]. Based on the above analysis, this paper intends to use the ROC curve to prove the correctness and reliability of the evaluation method. After acquiring the raster of vegetation susceptibility evaluation results under the impact factors, the cumulative percentage of susceptible area and the cumulative percentage of actual vegetation occurrence curves were established (seen in Figure 5). It is evident from comparing the AUC values in the four cases that the prediction of vegetation cover based on the LSW factor is the most accurate, with an AUC value of 72.9%; the evaluation of both LS and slope aspect factors is the second most effective with a stable AUC value of about 50%, while the prediction of TWI is the worst with an AUC value of less than 30%. As illustrated by the control group experiments, the LSW factor has a unique advantage in conducting vegetation cover susceptibility evaluation.