Empirical optimization of DEM interpolation: a comparative study of four algorithms for minimum vertical error in topographic modeling

Abstract Digital Elevation Models (DEMs) are fundamental to engineering projects, influencing the accuracy of hydrologic modeling, earthwork calculations, and infrastructure design. The resolution and quality of a DEM are primarily determined by the density of survey points and the interpolation algorithm used. This study presents a comparative evaluation of four common interpolation techniques—Natural Neighbor (NN), Kriging, Inverse Distance Weighting (IDW), and Spline—to generate a high-accuracy local DEM for a bare land area, typical of civil engineering project sites, on the Najran University campus, Saudi Arabia. A total of 7,026 high-precision GPS points were collected and divided into training (80%) and validation (20%) datasets. The vertical accuracy was assessed using Root Mean Square Error (RMSE) and the coefficient of determination (R 2 ). The results demonstrated that the Natural Neighbor interpolation method achieved superior performance with the lowest RMSE of 0.124 m and the highest R 2 of 0.969. Critically, the study evaluated the impact of data density by thinning the training dataset by 0% to 75%. It was found that a 75% reduction in data points—which equates to a significant saving in surveying time and cost—increased the RMSE by only ~ 2 cm when using the NN algorithm. This finding indicates that the Natural Neighbor method is not only the most accurate but also the most robust and cost-effective solution for generating reliable DEMs. The outcomes of this research provide a practical framework for engineers to optimize surveying efforts and produce high-fidelity terrain models essential for precise earthwork volume calculation, drainage design, and flood risk assessment in local-scale projects.