High-precision algorithm for sediment capacities of check dams on the Loess Plateau for special sedimentation survey

Objective Traditional cross-section methods used for silt dam sedimentation surveys on the Loess Plat-eau face limitations like sparse spatial sampling and inaccurate interpolation of complex gully morphol-ogy, hindering precise sediment capacity calculation. This study evaluated systematically spatial inter-polation methods, addressing itself to these challenges and developing a high-precision algorithm for calculating sediment capacity. Methods This study focuses on typical gullies in the hilly and gully re-gion of the Loess Plateau. Based on high-resolution DEM data, a theoretical channel baseline was gener-ated along the gully alignment. Elevation points outside the deposition area and thalweg node data were merged, and three interpolation methods were applied to reconstruct the channel DEM. The closed volume between a specified deposition elevation and the DEM was calculated to characterize the deposited storage capacity. Furthermore, nine check dams in Yulin city and Yan'an city, Shaanxi province, were selected as validation cases. The simulated deposited storage capacities at different elevations derived from this method were compared with those obtained using the traditional cross-section method. Results 1) DEM reconstruction accuracy varied significantly among methods. Kriging demonstrated superior performance with a Root Mean Square Error (RMSE) of 1.54 m, substantially lower than the errors associated with Spline functions (2.32 m) and IDW (5.67 m). Kriging’s capability to capture micro-topographic features in the gully bottom was notably superior. 2) In sediment capacity calculation, Kriging again proved most accurate, yielding an absolute deviation rate of 5.78% from the benchmark value. This was significantly better than the deviation rates of Spline functions (16.03%), IDW (46.40%), and the optimized traditional cross-section method with a 2.5m interval (13.27%). 3) 3) Verification was conducted through the selec-tion of nine check dams in Yulin city and Yan'an city, Shaanxi province (with sediment retention dam heights of 45%, 70%, and 100% for each dam). The results show that the absolute deviation rate of the Kriging method ranges from 1.06% to 4.68% in the low elevation segment (≤10 m), and nonlinearly in-creases to 17.35%–19.63% when the elevation exceeds 20 m, indicating significant elevation depend-ence.Conclusions Kriging effectively improves the calculation accuracy of sediment volume by utiliz-ing variograms to quantify the spatial heterogeneity of topography; however, its deviation rate increases nonlinearly with elevation. Further optimization of this error is required through methods such as seg-mented slope correction and data fusion.