Effect of Sampling Spacing on the Accuracy of Volume of a Medium-Size Gully

Abstract

Accurate morphological parameters are key to understand the process and mechanism of gully erosion, but little information exists regarding the accuracy of gully volume influenced by sampling spacing. In order to assess the influence of sampling spacing on volume of medium gully under the condition of different shapes of gully cross-sections, as well as to provide information for proposed surveys, a MultiStation was utilized to obtain the point cloud of a U-and V-shaped gully. The coordinates were subsequently rarefied to a certain sampling spacing, and the gully volumes of three modes (Mode 1 only including rarefied terrain points; Mode 2 including detailed terrain and rarefied terrain points; Mode 3 including the rarefied detailed terrain points and terrain points with a given sampling spacing) were calculated in ArcGIS. The results showed that the error of gully volume increased non-monotonously with sampling spacing increased, and that the detail points had greater influence on the gully volume of a U-shaped than a V-shaped gully. As to Mode 1 and 2, the relative error (RE) of U-shaped gully volume increased faster with sampling spacing increasing, and presented high positive correlation. However, in the case of a V-shaped gully, a middle positive correlation for Mode 1 can be observed, and the RE was below 3% for Mode 2. For Mode 3, an increase in the sampling spacing of the terrain led to the larger RE, average RE, and variance of absolute error. If extremely high accuracy (2.5% of RE) is required, sampling spacing is less than 0.5 m; if high accuracy (5% of RE) is set, the sampling spacing of terrain points is below 0.8 m for a U-shaped gully, while the corresponding sampling spacing of terrain points and detail points are 2.0 m and 1.85 m, 3.0 m and 1.80 m, and 4.0 m and 0.75 m for a V-shaped gully. The shape of the gully's cross-section, as well as the exact location of the shoulder line will affect the accuracy of the gully's volume. This study will increase the efficiency of detail survey in the field for medium gully.