Error propagation in the computation of volumes in 3D city models with the Monte Carlo method

Abstract. This paper describes the analysis of the propagation of positional uncertainty in 3D city models to the uncertainty in the computation of their volumes. Current work related to error propagation in GIS is limited to 2D data and 2D GIS operations, especially of rasters. In this research we have (1) developed two engines, one that generates random 3D buildings in CityGML in multiple LODs, and one that simulates acquisition errors to the geometry; (2) performed an error propagation analysis on volume computation based on the Monte Carlo method; and (3) worked towards establishing a framework for investigating error propagation in 3D GIS. The results of the experiments show that a comparatively small error in the geometry of a 3D city model may cause significant discrepancies in the computation of its volume. This has consequences for several applications, such as in estimation of energy demand and property taxes. The contribution of this work is twofold: this is the first error propagation analysis in 3D city modelling, and the novel approach and the engines that we have created can be used for analysing most of 3D GIS operations, supporting related research efforts in the future.