Quantifying the mixed uncertainty for calculating slope from a gridded digital elevation model

Abstract

Digital terrain analysis (DTA) using digital elevation models is influenced by two main uncertainties: propagated elevation uncertainty (PEU) from data and truncation error (TE) from the modeling process. Traditional studies often treat these uncertainties separately, neglecting their coupled nature, which limits the ability to accurately capture overall uncertainty and assess the relative contributions of different factors. This study examines slope calculation using evidence theory, addressing representation with focal elements, propagation through belief and likelihood functions, evaluation metrics based on bias and variability, and sensitivity analysis through changes in the probability envelope area. Experiments with Gaussian synthetic surfaces and high-density LiDAR data reveal that PEU dominates overall uncertainty, with data accuracy affecting slope reliability. TE limits users’ expectations regarding uncertainty, with cognitive limitations influencing belief in slope products. This work offers key insights into uncertainty in slope calculation and other DTA models.