# Application of Compound Terrain Factor LSW in Vegetation Cover Evaluation
## 4 Results and Discussion
### Correlation Analysis of Erodibility Factor
#### 4.3.1 Qualitative Relationship Reasoning between LSW and K  
According to Figure 6a, the average value of LSW increases gradually during the transition from plains to mountains. This situation may be related to the positive increase in slope length due to the development of the slope body [23]. There is an exponential growth relationship between slope length and slope width [38], so the corresponding LSW value will increase if the slope change is stable. Figure 6c also shows that vegetation coverage remained largely positively expanding during this phase, which is consistent with the results in Table 1. The decrease in mean LSW values during the transition from category 5 to 6 may be due to the disruption of slope ductility by excessive undulation [87], which in turn decreases the level of mean LSW values. Based on Figure 6a,b, the LSW maintains a positive expansion trend over the course of category 1 to 5, while the K mean value changes in the opposite direction. In addition, the status of mean LSW and mean K value change during category 5 to 6 also conforms to the inverse trend. Overall, mean LSW values are roughly negatively correlated with K values, which is highly consistent with the idea that topography has a direct negative effect on K values [88]. Combined with the data in Table 1, it can be seen that as the value of LSW increases, the larger the CF value corresponding to the grade, the larger the vegetation growth potential is. K value serves as a measure of how soil properties affect soil erosion [89], with larger K values being detrimental to vegetation development. The negative correlation between LSW and K values is consistent with the results of the theoretical analysis. Based on Figure 6c, it can be seen that the vegetation coverage and LSW showed a trend of increasing in the same direction as the transition from plains to mountains. This is in agreement with the rule known in Table 1 that LSW has a positive indicative effect on vegetation growth potential. Upon analysis, the most significant increase in LSW values between the plains to hills transition (i.e., category 1 to 3) is attributed to the significant difference in slope morphology between the plains and hills, as well as the later stage of gully development on the slopes. It was calculated that the decrease of K value in this stage reached a peak value of 0.00256 (t\(\cdot\)hm\({}^{2}\cdot\)h)/(hm\({}^{2}\cdot\)M)\(\cdot\)mm) (the value decreased from 0.01028 to 0.00772), and the drop amounted to 24.8%. In terms of soil type, the K level was basically converted from loessial soil to purple soil [90], and this change triggered an increase in soil fertility and soil erodibility with a non-negligible effect on the growth of vegetation [91]. Based on the positive role of gullies in modifying the site environment in Section 2, the differences in LSW levels across terrain categories validate the indicative role of this factor for vegetation growth potential. In addition, the most significant amount of vegetation cover increase at this transition stage can be seen in conjunction with Figure 6c, justifying the mechanism analyses. According to Figure 6b, the mean value of K shows a gradual decrease from the plain to the small rolling mountains (i.e., category 1 to 4), and if the K value and the LSW value show opposite trends, the K value should continue to decrease during the transition from small rolling to medium rolling mountains (i.e., categories 4 to 5). However, the mean value of K in the corresponding part of Figure 6b shows a small rebound, which is contrary to the mean value of LSW in the corresponding area maintaining an increasing trend.