Background Gully erosion is an important environmental hazard in the basin of Northwest Hebei mountains, which produces a tremendous amount of sediment-inducing siltation of downstream reservoirs and causes some flooding and pollution. Therefore, the prevention and control of gully erosion have become the top priority of soil and water conservation in recent years. Moreover, the erosion prone gully area and control gully erosion can be determined by modeling and mapping the gully erosion over a large scale, and the estimation model of the gully volume is the basic issue in the research of gully erosion. However, little research on modeling gully volume in this area has been published. The objective of this study is to develop a model to assess the gully volume using the morphological parameters of gullies.

Methods In order to measure the morphological parameters of 17 gullies located at Yangyuan county, Hebei province, a 3-D laser scanner (Rigel) was used to obtain the point cloud data, and then the digital elevation model (DEM) with the pixel size of 0.15 m×0.15 m was created based on Delaunay triangulate irregular network (TIN) using ArcGIS 10.3. The morphological parameters were extracted from DEM and finally the gully length (L, m), area (A, m²), top width (T_W, m), bottom width (B_W, m), depth (D, m), cross-sectional area (C_SA, m²) and volume (V, m³) were calculated.

Results 1) The development of gullies were imbalance in this study area. The lengths, areas and volumes of gullies varied greatly, however the parameter values of the same parameter at each section just had little difference. 2) The Pearson correlation analysis showed that there was significant positive relationship between V and L, A and D, and the Pearson's correlation coefficient were 0.949, 0.870 and 0.814, respectively, indicating that L, A and D can be used to estimate the gully erosion amount at the large spatial scale. 3) There was power function relationship between V and L and A, and the determination coefficients of the regression equation were 0.770 6 and 0.915 9, respectively. Furthermore, the RMSE and MAE between the measured and predicted gully volumes suggested that the V=0.046 53A^1.499+24.08D^1.916-44.26(R²=0.974 8) was more preferred for predicting the volume of a gully, compared with the V-L and V-A relation.

Conclusions Above results V(A, D) relationship can be used to assess the gully volume in the basin of Northwest Hebei mountains. The results of this study may provide a method and basis for assessing the gully volume over a large scale, and will be greatly helpful to assess the soil and water conservation.