Harmonic analysis of valley distribution in typical areas of Loess Plateau

In order to study the topographic periodicity of the Loess Plateau, and to explore the distribution law of tributary valleys, so as to explore a new method for assessment of the Loess Plateau soil erosion, the paper briefly describes basic principles of harmonic analysis and periodgram analysis. Taking Xifeng in Gansu、Jixian in Shanxi、Ansai in Shaanxi、Guyuan in Ningxia as study areas, the valley distribution in the Loess Plateau was studied based on harmonic analysis and periodgram analysis. The results indicated that in the Loess Plateau regions of different types, the period of main channel differed significantly. Generally speaking, the period of the gully region of loess plateau was greater than the transitional region, and the period of the transitional region was greater than the hill and gully area of Loess Plateau; The period of branch gully in the Loess Plateau mainly ranged from 400 to 800 m, which accounted for 97.5% of the overall periods. Based on t-test of the period of branch gully in four different research areas, the results showed that the mean periods of Xifeng、Jixian and Ansai had no significant difference (P>0.05), while in the two side test，all the probability of mean period of branch gully in Guyuan、Xifeng、Jixian and Ansai was less than 0.01 (P<0.01), so it can be considered that the difference was extremely significant. On analyzing the average terrain slope greater than 5° in the regions of different types, it was found that Xifeng in Gansu is steeper than Jixian in Shanxi, and Jixian in Shanxi is steeper than Ansai in Shaanxi, which is steeper than Guyuan in Ningxia. It was also found that the average period of branch gully decreased continuously with the increasing of the average slope. Therefore, it can be concluded that the average terrain slope can directly affect the formation of branch gully in the Loess Plateau.