Background The morphological characteristics of eroded gully are key parameters for understanding the occurrence and development of gully erosion, which is of great significance for a deeper understanding of the formation process and governance work of eroded gully. The mathematical mechanism and applicable conditions of different spatial interpolation methods lead to the difference in the accuracy of DEM （digital elevation model) production, which affect the extraction of the terrain characteristic parameters (TCP) of sub-watersheds and the morphology parameters (MP) of eroded gully, and thus affect the accurate monitoring and prediction of the eroded gully. In view of this, this study aims to compare the differences TCP of sub-watersheds, the MP of eroded gully and the critical topographic parameters (CTP) of gully erosion model extracted from in different interpolation methods and different resolution DEMs.

Methods The eroded gullies and sub-watersheds in the Xilingol League area of Inner Mongolia autonomous region were chosen as the study area. Riegl VZ-1000 stationary laser scanner was placed at the foot of the slope in the study area to collect point cloud data of the sub-watersheds topography. GEO-SLAM ZEB-REVO handheld laser scanner was used to collect the detailed point cloud data of the eroded gullies morphology. Inverse distance weighting, Kriging, natural neighborhood and spline interpolation methods were used to generate DEMs for the fused multi-source point cloud data with the DEM spatial resolutions of 5, 2, 1, 0.5 and 0.1 m respectively. Then the accuracy of different DEMs were evaluated, the TCP of sub-watersheds, the MP of eroded gullies and the CTP of gully erosion model extracted from different resolution DEMs were compared.

Results 1) By comparing parameters such as absolute value of average elevation difference ( \delta _1 ), average deviation of elevation ( \delta _2 ) and maximum deviation of single point elevation ( \delta _3 ), the accuracy of DEM generated by spline and Kriging interpolation methods significantly improves with the increase of DEM resolution, but overall, for low-gentle hilly areas, with the increase of DEM spatial resolution, the spline interpolation method can obtain higher accuracy DEM. 2) The extracted sub-watersheds slope becomes progressively smaller as the DEM resolution decreases, the extracted sub-watersheds slope is the largest with 8.53° at DEM resolution of 0.1 m, the extracted sub-watersheds slope is the smallest with 8.34° at DEM resolution of 5 m. When the DEM resolution is 0.5 and 1 m, the extracted areas of each slope gradient are relatively close, as the DEM resolution decreases, the area of low slope gradient areas continue to increase, such as 0–3° and 5°–8°. 3) By comparing the MP of eroded gullies extracted from different resolution DEMs and the point clouds of field survey according to the evaluation indicators of root mean square error (RMSE), mean error (ME), mean absolute error (MAE) and standard deviation (SD), when the DEM resolution increases to 0.5 m and 1 m, the values of the evaluation indicators are smaller and closer to the measured data. 4) The DEM resolution has a significant impact on the extraction of local slope and upstream catchment area, resulting in significant differences of CTP in gully erosion model. The CTP are close when DEM resolution is 1 and 0.5 m, which indicates that the simulation results of gully erosion model on the distribution condition of eroded gullies are relatively consistent.

Conclusions The combination of cloud data from stationary and handheld 3D laser scanners can make up for the shortcomings of data collected by a single device, and effectively express the TCP of sub-watersheds and the MP of eroded gully. For low-gentle hilly areas, with the increase of DEM spatial resolution, spline interpolation method can obtain higher accuracy DEM data. For the study of erosion in sub-watersheds scale, when the spatial resolution of DEM reaches 0.5 m, the TCP of sub-watersheds and the MP of eroded gully tend to stabilize and are closer to the results of field survey. According to the CTP of gully erosion model, the results of evaluating the impact of terrain factors on eroded gully using 0.5 and 1 m DEM are similar. The increase of DEM resolution will enhance the impact of terrain factors on eroded gully.