Objective Aiming at the limitations of traditional cross-section methods in the special survey of check dam siltation on the Loess Plateau, such as sparse spatial sampling, rough interpolation, and channel morphology interference, this study systematically evaluates the applicability of three spatial interpolation methods—Kriging, inverse distance weighting (IDW), and spline function method—and proposes a high-precision algorithm for calculating siltation volume.

Methods Taking typical gullies in the hilly-gully region of the Loess Plateau as the research objects, based on high-resolution DEM data, the theoretical channel baseline was generated. The elevation points outside the siltation area and node data of the thalweg were merged, and three interpolation methods were used to reconstruct the channel DEM, respectively. The closed volume between the specified siltation elevation and the DEM was calculated to represent the silted storage capacity. Nine check dams in Yulin and Yan'an cities of Shaanxi province were selected to compare the simulation results of this method with those of the traditional cross-section methods at different elevations.

Results The Kriging method showed the best performance in gully microtopography restoration and storage capacity calculation, with a DEM reconstruction root mean square error (1.54 m) significantly lower than that of IDW (5.67 m) and the spline function method (2.32 m). In the calculation of siltation volume, the absolute deviation rate of the Kriging method was 5.78%, which was significantly better than that of the spline function method (16.03%), IDW (46.40%), and the optimized cross-section method with 2.5 m spacing (13.27%). The absolute deviation rate of the Kriging method was 1.06%–8.33% in the low elevation range (≤ 10 m), and increased nonlinearly to 15.80%–19.63% when the elevation exceeded 20 m, showing significant elevation dependence.

Conclusions The Kriging method can effectively improve the calculation accuracy of siltation volume by quantifying the spatial heterogeneity of topography through a variogram, but its deviation rate increases nonlinearly with the increase of elevation. In the future, the error should be optimized using methods such as segmented slope correction and data fusion.