CGRG Bibliography of Canadian Geomorphology
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Author : Cogley, J.G.; and Jung-Rothenhäusler, F.
Date : 2002.
Title : Digital elevation models of Axel Heiberg Island Glaciers.
Publication : Technical Note. Department of Geography, Trent University, Peterborough.
Issue : 2002-1.
Page(s) : 49 p.
Abstract
We describe two digital elevation models (DEMs) of the extensively glacierized Expedition Fiord area of central Axel Heiberg Island, Nunavut, Canada. Both derive from estimates made by eye on large-scale maps. The White Glacier (WG) DEM, with 50m resolution, is based on a 1:10 000 scale map and aerial photographs dating from 1960. The Thompson Glacier (TG) DEM, with 100m resolution, is based mainly on a 1:50 000 scale map and on 1959 aerial photographs. Part of it derives from a 1:100 000 scale map, from which many of the elevations were estimated by a spatial interpolation algorithm. The Expedition Fiord area is well mapped by comparison with the rest of the Canadian High Arctic, for most of which the largest scale of map coverage is 1:250 000. We compare the Expedition Fiord DEMs with each other and with the CDED DEM, based on the 1:250 000 scale map of the area, and with the GLOBE DEM, based on a 1:1 000 000 scale map. The resolution of CDED is 92m 34m (meridional zonal). The resolution of GLOBE is 930m 170 m. We present a procedure for converting the local coordinates of the Expedition Fiord maps to transverse Mercator coordinates. This procedure gives good accuracy, although the derivation of the local coordinate system remains somewhat mysterious. Replicate readings by multiple map readers allow us to estimate the map-reading error for the large-scale DEMs. The errors are reduced markedly by proofreading. The di erences between replicate readings are unbiased. For theWG DEM, the random map-reading error is of the order of 1 m. Analysis of the frequency distributions and the spatial autocorrelation of di erences shows that they are not normally distributed. They are also moderately correlated, with deorrelation distances of 1-3 DEM resolution elements. That is, map-reading errors tend to occur in clusters. For the TG DEM the map-reading error is of the order of 4-8 m. The greater error is due partly to less thorough proofreading, but mainly to the greater contour interval, 25m as opposed to 10m on the WG map. Replicate readings from the two maps have root-mean-square differences of about 20 m, a gure which shrinks to 12m when gross errors are identifed and excluded. Partitioning this mapping error between the two maps requires an assumption about which, if either, of them is the truth. Depending on this assumption, the total error in the WG DEM (the map-reading error and some share of the mapping error, added in quadrature) may range from its map-reading error, about 1 m, up to about 19 m, while for the TG DEM the total error may reach 20 m. Excluding gross errors, the maximum estimates of total error decrease to 11m for the WG DEM and 12m for the TG DEM. Thus we have identi ed two obstacles to formal description of the DEM errors. First, there is no objective basis for partitioning the mapping error between the two maps. Second, the gross errors cannot be accommodated satisfactorily. A third obstacle is that the errors are only nominally \one-sigma" errors. Because the usual statistical assumptions are violated, the errors define confidence regions narrower than the usual 68% by some unknown amount. The spatial interpolation algorithm used for the 1:100 000-scale portion of the TG DEM performs well. Comparisons with visual estimates suggest a map-reading error of 13m and a total error of 13-24 m. Comparisons between TG and the smaller-scale CDED and GLOBE DEMs show that the latter are significantly more uncertain. Total error is estimated as 90m for CDED and 158m for GLOBE. Each of the DEMs contains artefacts related to the contour interval of its parent map. These artefacts, while they look disconcerting, appear to make only a modest contribution to map-reading error. The available evidence suggests that, in comparison with mapping error, map-reading error is small but not necessarily negligible. That is, the DEMs are good to very good representations of the information in the maps. The maps, however, are less good representations of the terrain than the DEMs are of the maps. Errors in slopes calculated from the DEM increase as map scale decreases. For example, if the WG DEM represents truth, the uncertainty in slope estimates is about 2 for TG, 5 for CDED, and 9 for GLOBE. There is some evidence that map-reading errors make a proportionally greater contribution to total error for slopes. A more clear-cut nding is that maps of larger scale have steeper slopes. Smaller scale implies more generalization of the terrain. It is not clear, however, how this bias might be corrected in the smaller-scale DEMs. Di erences in the frequency distribution of slopes are such that a simple additive correction would reduce, not increase, the resemblance of the smaller-scale DEMs to the larger-scale DEMs. It has not been possible through this analysis to specify elevation errors rigorously, but the errors are well correlated with the contour interval of the parent map, appearing to be roughly equal to one half of the contour interval. There is no obvious reason why this should be so, but as a rule of thumb for practical contexts it should work well.
Bibliography of Canadian Geomorphology