Topographic characterization for DEM error modelling
Creators: name: Xiao, Yanni
Publisher: name: University of British Columbia
Year: 2009

description: Digital Elevation Models have been in use for more than three decades and have become a major component of geographic information processing. The intensive use of DEMs has given rise to many accuracy investigations. The accuracy estimate is usually given in a form of a global measure such as root-mean-square error (RMSE), mostly from a producer's point of view. Seldom are the errors described in terms of their spatial distribution or how the resolution of the DEM interacts with the variability of terrain. There is a wide range of topographic variation present in different terrain surfaces. Thus, in defining the accuracy of a DEM, one needs ultimately to know the global and local characteristics of the terrain and how the resolution interacts with them. In this thesis, DEMs of various resolutions (i.e., 10 arc-minutes, 5 arc-minutes, 2 km, 1 km, and 50 m) in the study area (Prince George, British Columbia) were compared to each other and their mismatches were examined. Based on the preliminary test results, some observations were made regarding the relations among the spatial distribution of DEM errors, DEM resolution and the roughness of terrain. A hypothesis was proposed that knowledge of the landscape characteristics might provide some insights into the nature of the inherent error (or uncertainty) in a DEM. To test this statistically, the global characteristics of the study area surfaces were first examined by measures such as grain and those derived from spectral analysis, nested analysis of variance and fractal analysis of DEMs. Some important scale breaks were identified for each surface and this information on the surface global characteristics was then used to guide the selection of the moving window sizes for the extraction of the local roughness measures. The spatial variation and complexity of various study area surfaces was characterized by means of seven local geomorphometric parameters. The local measures were extracted from DEMs with different resolutions and using different moving window sizes. Then the multivariate cluster analysis was used for automated terrain classification in which relatively homogeneous terrain types at different scale levels were identified. Several different variable groups were used in the cluster analysis and the different classification results were compared to each other and interpreted in relation to each roughness measure. Finally, the correlations between the DEM errors and each of the local roughness measures were examined and the variation of DEM errors within various terrain clusters resulting from multivariate classifications were statistically evaluated. The effectiveness of using different moving window sizes for the extraction of the local measures and the appropriateness of different variable groups for terrain classification were also evaluated. The major conclusion of this study is that knowledge of topographic characteristics does provide some insights into the nature of the inherent error (or uncertainty) in a DEM and can be useful for DEM error modelling. The measures of topographic complexity are related to the observed patterns of discrepancy between DEMs of differing resolution, but there are variations from case to case. Several patterns can be identified in terms of relation between DEM errors and the roughness of terrain. First of all, the DEM errors (or elevation differences) do show certain consistent correlations with each of the various local roughness variables. With most variables, the general pattern is that the higher the roughness measure, the more points with higher absolute elevation differences (i.e., horn-shaped scatter of points indicating heteroscedasticity). Further statistical test results indicate that various DEM errors in the study area do show significant variation between different clusters resulting from terrain classifications based on different variable groups and window sizes. Cluster analysis was considered successful in grouping the areas according to their overall roughness and useful in DEM error modelling. In general, the rougher the cluster, the larger the DEM error (measured with either the standard deviation of the elevation differences or the mean of the absolute elevation differences in each cluster). However, there is still some of the total variation of various DEM errors that could not be accounted for by the cluster structure derived from multivariate classification. This could be attributed to the random errors inherent in any of the DEMs and the errors introduced in the interpolation process. Another conclusion is that the multivariate approach to the classification of topographic surfaces for DEM error modelling is not necessarily more successful than using only a single roughness measure in characterizing the overall roughness of terrain. When comparing the DEM error modelling results for surfaces with different global characteristics, the size of the moving window used in geomorphometric parameter abstraction also has certain impact on the modelling results. It shows that some understanding of the global characteristics of the surface is useful in the selection of appropriate/optimal window sizes for the extraction of local measures for DEM error modelling. Finally, directions for further research are suggested.