# Application of Compound Terrain Factor LSW in Vegetation Cover Evaluation
## 4 Results and Discussion
### Correlation Analysis of Erodibility Factor
#### 4.3.2 Expression and Analysis of the Quantitative Relationship between LSW and K  
To quantitatively describe the relationship between K and LSW, the association between the mean value of LSW and K was calculated based on the data from the six experimental areas, as shown in Figure 7. It is evident from the observation that as the LSW rises, the K value tends to decrease accordingly, which is in agreement with the qualitative analysis of the slope width mechanism and the distribution pattern of CF values corresponding to LSW in Table 1.  
Further, as the LSW value increases from 0 to 0.2, the decrease rate of K becomes slower. This pattern can be illustrated in Figure 6: categories 2 to 5 in Figure 6a are in a phase of growth in LSW values, while the shrinking trend in the K value is gradually moderating.  
When the LSW value is in the range of 0.2\(-\)0.3, the K value tends to be stable. Together with Figure 6a, it can be seen that the elevated LSW values basically represent a change in the slope development. A study has pointed out that when precipitation conditions are stable, the width-to-depth ratio of slope gulles tends to first decrease and then increase with slope development [23]. In terms of geometric characteristics, when the slope length increases, the slope width increases due to lateral erosion [38], whereas increasing rate of slope relative to the slope width shows a dynamic change of first increasing and then decreasing. This can be interpreted as an increase in slope runoff volume with a concomitant decrease in runoff velocity, so that the change in sediment yield is not significant [23; 95], which triggers the stabilization of the K value in the phase. During this stage, vegetation growth may be more related to other factors such as temperature and rainfall in the local site environment.  
If the mean LSW value continues to increase and exceeds 0.30, the K value will revert to a decreasing trend, correlating with runoff degradation as the slope develops to a certain level [96]. Moreover, a study conducted in the mountainous region of Yunnan, China,  
Figure 7: LSW versus K value.  
showed that the K values decreased significantly for slopes greater than 15\({}^{\circ}\)[97]. This finding is partially consistent with the overall trend of the K value. In general, Figure 7 still obeys the pattern of decreasing average erosion rate with slope development, which in turn has a dynamic effect on vegetation growth.  
According to the SPSS software ([[https://www.ibm.com/cn-zh/spss](https://www.ibm.com/cn-zh/spss)]([https://www.ibm.com/cn-zh/spss](https://www.ibm.com/cn-zh/spss))), there is a highly significant negative correlation between LSW and K values (\(p<0.01\)), with a correlation coefficient of \(-0.388\). This quantitative relationship has never been proposed in the past. The negative correlation coefficient asserts that LSW is an important factor influencing the K value, which is a good indication for describing the resistance of soil to water erosion. Regarding the direct impact of the K value on soil erosion, the validity of the LSW factor's feedback on vegetation growth and development was also sideways confirmed.