The effect of error in gridded digital elevation models on the estimation of topographic parameters

Abstract

Digital elevation models (DEMs) provide the basic information required to characterise the topographic attributes of terrain. The primary derived topographic parameters associated with DEMs are slope and aspect. Slope and aspect maps are used in a wide variety of applications. Slope and aspect can be used to calculate other significant topographic parameters such as upslope area and topographic index. The topographic index, in turn, can be used by distributed hydrological models to characterise the spatial distribution of terrain moisture. Many algorithms have been developed to calculate slope, aspect and upslope area from DEMs – specifically from gridded DEMs – but little work has gone into determining the uncertainty in these parameters, or the affect of this uncertainty in further applications. The accuracy of these parameters is dependent both on the algorithm and on the errors associated with the DEM itself. Since it is almost impossible to model all the errors associated with a given slope/aspect algorithm and since a DEM is normally only provided with a single rms error, simple error propagation is not adequate to determine the error associated with the derived topographic parameters. A more rigorous method of determining the affect of DEM errors on derived topographic parameters is with statistical analysis using Monte Carlo simulation and error realisations of the DEMs. In this research we demonstrate that the error sensitivity of slope decreases as the number of neighbours used in the algorithm increases, hence steepest neighbour algorithms, which are common in hydrology are more sensitive to DEM error than algorithms that use four or more neighbours. In contrast, the average error sensitivity of aspect to DEM error is not dependent on the algorithm used. However, while the mean variability of this sensitivity was lower for the steepest neighbour algorithms, their errors were spread over a greater variety of slopes while the eight neighbour algorithms had errors confined to flat regions. The error sensitivity of upslope area and topographic index is related to the use of steepest neighbour flow routing algorithm.