Characterizing gully cross section and modelling gully volume in hilly loess region of western Shanxi Province

Abstract: Morphological characteristics of gully cross section are important in reflecting environmental factors of the development of the gully and understanding the mechanism of the gully erosion. Gully volume is a key parameter representing gully erosion amount, and the estimation model of the gully volume is the basic issue in the research of gully erosion. However, it has been rarely published as to characterizing gully cross section and modeling gully volume for the hilly loess region of western Shanxi Province, which has restricted the survey and evaluation of the regional soil erosion. The aim of this paper was to explore the features of the gully cross section, and to build a model to assess the gully volume with gully parameters that may be determined by high resolution satellite images. In this research, a 3-D (three-dimensional) laser scanner (TOPCON IS-IMAGING STATION) was used to measure the parameters of 31 dissected valleys, and an interval between 2 measurement points was set as 0.15 m. Then the DEM (digital elevation model) with the pixel size of 0.15 m × 0.15 m was created based on Delaunay triangulate irregular network (TIN) using ArcGIS 10.1. The morphological parameters were extracted from DEM and finally the volume, gully length, gully area, top width, bottom width, depth and cross-sectional area were calculated. The results showed that the maximum, minimum and average values of the gully top width were 19.8, 4.8, and 9.0 m, respectively; those of gully bottom width were 15.0, 0.4, and 3.8 m, respectively; those of gully depth were 10.9, 2.5, and 6.2 m, respectively; and those of cross-sectional area were 9.7, 139.2, and 41.8 m2, respectively. The values of top width, bottom width, depth and cross-sectional area at the gully mouth were higher than that at the gully head and middle, and, sequentially, there was no significant difference except the depth among gully head, gully middle and gully mouth with one-way analysis of variance (ANOVA). The ratio of gully top width to depth ranged between 0.37 and 5.0, with an average of 1.55, which was greater than 1, indicating the gully-wall collapsing was faster than the deep-cutting erosion. Among gully head, gully middle and gully mouth, the minimum value of the ratio of gully top width to depth was in the gully head. The regression analysis showed that there was a very prominent relationship of power function between gully volume and gully length, gully area, and the determination coefficients of the regression equation were 0.68 and 0.85, respectively, indicating the gully length and the gully area can be used to estimate the gully erosion rate at the large spatial scales because they can be easily determined from very high-resolution satellite images. The relative error and Nash-Sutcliffe efficiency between the measured and predicted gully volumes suggested that the gully volume-area relationship had a better predictive ability for the gully volume, and therefore the corresponding equation can be used to assess the gully volume in the hilly loess region of the western Shanxi Province. The results in this paper have a number of potential applications in modeling and mapping the gully erosion over a large scale, and will be critically helpful in the assessment of the soil and water conservation.