Digital Eleveation Model (DEM) error

Digital Elevation Models (DEMs) are becoming extremely important sources of information about the surface of the Earth, particularly as DEM data becomes available at very fine resolution (eg via LiDAR) and at global coverage (eg SRTM data).

As with any GIS processing it is important to develop an understanding of the source and nature of errors in the data and how those errors propagate through to results. DEMs are unusual because as well as the normal measurement error in the original data values, additional errors are introduced because the original data usually need to be interpolated to provide a model of elevation across the whole surface, and not just at the original data points.

My work to date has demonstrated that

Relatively small errors in elevation values in a DEM can produce large errors in the results derived using the DEM

Interpolation errors often have strong and characteristic spatial patterns, which in turn produce strong patterns of error in outputs (see below for an example of this)

Both these findings suggest that the standard measure of DEM error, the root mean square of elevation, may be deficient as an estimate of DEM quality because it considers only errors in elevation and because it is aspatial. Finding alternative measures of error remains a challenge for the future

The figures below show the degree of difference which different interpolation methods can produce. The upper two images show DEMs produced from the same original contours, using two different interpolation algorithms. On the left is the result of using a standard interpolation method, Inverse Distance Weighting. Because this simply averages heights around the point being interpolated, the height estimates near to the contours tend to be very similar to the contour height, leading to flat 'terraces' along the contour lines, with abrupt changes of height midway between contours. These interpolation artefacts are reflected in the TOPMODEL topographic index shown in the lower row, where water is predicted to accumulate along the edges of the terraces. The images on the left come from using the ANUDEM algorithm of Hutchinson ( ), which is implemented in ArcGIS. This is purpose written for generating DEMs from contours, and works by fitting a thin-plate spline to the data. Notice the generally smoother appearance of the hillslopes, although there is a slight 'bumpiness' in some areas where the algorithm fits the surface too closely to the data points. Note also that the sharp break of slope where the hillslopes meet the flat floor of the main river valley is not well modelled, with the result that the valley floor is modelled as being more undulating than it is.

Hillshade
TOPMODEL Topographic Index
	Inverse Distance Weighting	ArcGIS Topo to Raster