Uncertainty in Digital Elevation Models of Axel Heiberg Island, Arctic Canada

Abstract

We analyze errors in several digital elevation models (DEMs) of part of Axel Heiberg Island, Nunavut, Canada. We define total error as the sum of map-reading error, which measures the fidelity of the DEM to the map, and mapping error, which measures the fidelity of the map to the terrain. Three of the DEMs derive from estimates made by eye on maps prepared for research purposes and having scales of 1:10,000 (“10K”), 1:50,000 (“50K”) and 1:100,000 (“100K”), while two are based on spatial interpolation from published topographic maps of scale 1:250,000 (“250K”) and 1:1 000,000 (“1M”). Map-reading errors are reduced markedly by proofreading, and are unbiased but not normally distributed. They are also moderately correlated, with decorrelation distances of 1 to 3 DEM resolution elements. Replicate readings from maps 10K and 50K have rms differences of about 20 m, a figure which shrinks to 12 m when gross errors are identified and excluded. These differences represent the mapping errors. Total error in the 10K DEM may range from ∼1 m up to, at worst, ∼19 m, while for the 50K DEM the total error may reach 20 m. Excluding gross errors, the worst-case estimates of total error decrease to 11–12 m. Total error is estimated as 90 m for 250K and 158 m for 1M. We show that map-reading error is small in comparison with mapping error. However there are three obstacles to formal description of total DEM error. First, there is no objective basis for partitioning the mapping error between the two maps of a comparison pair. Second, gross errors cannot be accommodated satisfactorily. Third, because the usual statistical assumptions are violated the errors define confidence regions narrower than the usual 68% by some unknown amount. Maps of larger scale have steeper slopes. Differences in the frequency distribution of slopes are such that a simple additive correction would worsen, not improve, the gentle-slope bias of the smaller-scale DEMs. Elevation errors are roughly equal to one half of the contour interval of the parent map. It is not obvious why this should be so, but as a practical rule of thumb it should perform well.