The effects of terrain factors on the drainage area threshold: comparison of principal component analysis and correlation analysis.

How and to which extent terrain factors affecting the drainage area threshold (DAT) are disputable. This paper uses principal component analysis (PCA) and correlation analysis to study the influence degree of terrain factors on DAT. Firstly, 22 watersheds, locating in the severe soil erosion region (SSER) of Loess Plateau of China, are picked out as the example areas. The purpose of the mean change point method (MCP) to detect the relationship between DAT and gully density (GD) is to get a reasonable DAT. Secondly, nine terrain factors are calculated, and their statistical values are compared and put in the matrix to clear the different effects on DAT. Finally, the effects of statistical eigenvalues of terrain factors on DAT are compared with PCA and the correlation analysis. According to the PCA, the nine terrain factors are summarized into three principal components, which are slope, height variation, and relief factor. By calculating the score weighted by each factor coefficient matrix and eigenvalue, the result states that slope (S), terrain curvatures (K), and surface roughness (SR) are the factors that have great influence on DAT. Meanwhile, the results of correlation analysis indicate that S, SR, and K have exerted a great influence on the DAT, and the significance level was above 0.05. Both the results of PCA and correlation analysis make clear that the slope is the most direct and influential factor affecting DAT, while other factors are more or less related to slope directly and indirectly. The result implies that the vertical variation of terrain has a strong correlation with the slope, and also has a great influence on DAT. This research not only would be of great significance to recognize the mechanism of gully development, but also able to provide a scientific reference for soil and water conservation in the Loess Plateau.