## 5 Discussion  
Although the improved probability model can be used to discriminate between river blockages, it cannot reflect the degree of influence of each factor on river blockages. Thus, correlation analysis was carried out to identify their influence degree based on 60 landslide cases. The correlation coefficients were calculated as  
\[R(X,B)=\frac{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{X}\right)\left(B_{i}- \overline{B}\right)}{\sqrt{\frac{\sum\limits_{i=1}^{n}\left(X_{i}-\overline{X }\right)^{2}\cdot\sum\limits_{i=1}^{n}\left(B_{i}-\overline{B}\right)^{2}}}}, \tag{5}\]  
where \(B\) indicates the logistic variable of river blockage and \(X\) indicates the influence factor. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{2}{c}{**Real Landslide Cases**} & \multicolumn{3}{c}{**Prediction Results**} \\ \hline
**Blockage State** & **Total Number** & **Number of** & **Number of** & **Accuracy** \\
**of Landslide Case** & **of Cases** & **Partial Blockage** & **Complete Blockage** & **Accuracy** \\ \hline Partial blockage & 16 & 9 & 7 & 56.3\% \\ Complete blockage & 44 & 3 & 41 & 93.2\% \\ Overall accuracy & & & & 83.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction accuracies of the improved probability model based on real landslide cases. Figure 19: Discriminant results of the real landslide cases. The correlation coefficients between the nine factors in the above analysis and river blockages were calculated, and the results are presented in Figure 20. Most of the factors present a positive correlation with river blockage, except valley width. These factors were sorted in descending order according to their degree of influence on river blockages. The top four factors are the thickness of the landslide \(T\), the maximum width of the landslide \(W_{\text{max}}\), the height difference between the maximum and minimum values of the landslide variable \(H\), and the volume of the landslide \(V\). These factors are the geometric sizes of the landslide and can be classified as a category related to landslide volume. Thus, the geometric sizes of landslides have the greatest influence on river blockage. Among the geometric sizes, landslide thickness has the highest correlation with river blockage, which is approximately 0.25, which means that a landslide with a higher volume per unit width is more likely to trigger a complete river blockage. The second category in the order is the steepness of topography, which includes the steepness of landslide slope \(\alpha\) and steepness of riverbed \(\theta\). Their correlations with river blockages are almost the same. River blockages are more likely to form in valleys with steeper topography. The third category in the order is valley width \(W_{\text{V}}\), which has a negative correlation with river blockage. The possibility of river blockage decreases as the valley width increases. The fourth category in the order is the length of the landslide, which includes the total length of the landslide \(L_{\text{T}}\) and the length of the landslide body \(L_{\text{L}}\). They were also the geometric sizes of landslides, but they may have less influence on the landslide volume, so they have the lowest correlation with river blockage. Overall, according to the degree of influence, the order of these factors reflects some key geometric attributes, including landslide size, steepness of the topography, width of the valley, and length of the landslide. The resulting influence degrees of various factors are consistent with some indexes that were used to estimate the degree of river blockage, such as the Morphological Obstruction Index (MOI) proposed by [PERSON] et al. [37] and the Blockage Index (BI) proposed by [PERSON] et al. [22]. The MOI takes the landslide volume and the valley width as two important factors that affect the formation of river blockages, while the BI takes the landslide volume and the wet cross-sectional area as two important factors.