Estimation of average DEM accuracy under linear interpolation considering random error at the nodes of TIN model

The concept of a digital elevation model (DEM) can be used for a digital representation of any single-valued surface such as a terrain relief model (digital terrain model, DTM). DEMs are widely used in remote sensing, geographical information systems (GIS), and virtual reality. Estimating the accuracy of a DEM is an essential issue in the acquisition of spatial data, particularly for applications that require a highly accurate DEM, such as engineering applications. The accuracy of a DEM is subject to many factors such as the number of sampling points, the spatial distributions of the sampling points, the methods used for interpolating surface elevations, the propagated error from the source data, and other factors. Of these factors, this study will focus on estimating the mean elevation error in a DEM surface that is caused by errors of component nodes in a triangulated irregular network (TIN). This paper will present a newly derived mathematical formula, with the details of the procedure used to derive this formula, to study the relationship between the errors at the TIN nodes and the propagated mean elevation error of a DEM surface that is linearly constructed from the TIN. We have verified the analytical formula by numerical simulation. The experimental results confirm the theoretical derivation of the formula.