Modelling the Spatial Distribution of DEM Error

Abstract

Assessment of a DEM's quality is usually undertaken by deriving a measure of DEM accuracy -how close the DEM's elevation values are to the true elevation. Measures such as Root Mean Squared Error and standard deviation of the error are frequently used. These measures summarise elevation errors in a DEM as a single value. A more detailed description of DEM accuracy would allow better understanding of DEM quality and the consequent uncertainty associated with using DEMs in analytical applications. The research presented addresses the limitations of using a single root mean squared error (RMSE) value to represent the uncertainty associated with a DEM by developing a new technique for creating a spatially distributed model of DEM quality -an accuracy surface. The technique is based on the hypothesis that the distribution and scale of elevation error within a DEM are at least partly related to morphometric characteristics of the terrain. The technique involves generating a set of terrain parameters to characterise terrain morphometry and developing regression models 2 to define the relationship between DEM error and morphometric character. The regression models form the basis for creating standard deviation surfaces to represent DEM accuracy.The hypothesis is shown to be true and reliable accuracy surfaces are successfully created.These accuracy surfaces provide more detailed information about DEM accuracy than a single global estimate of RMSE.Keywords: digital elevation models, quality, error, accuracy, uncertainty 3 IntroductionAssessments of the accuracy of DEMs tend to result in a single measure of how closely the DEM's elevation values represent "reality". Measures such as Root Mean Squared Error and standard deviation of the error are frequently used (Carlisle, 2002;Day and Muller, 1988;Eklundh and Mårtensson, 1995; Fisher, 1998;Kumler, 1994;Li, 1991;Sasowsky, 1992). These measures summarise elevation errors in a DEM as a single value. There is increasing demand for more detailed description of spatial data quality (Canters et al., 2002). A more detailed description of DEM accuracy would allow better understanding of DEM quality and the consequent uncertainty associated with using DEMs in analytical applications.Anecdotal and empirical evidence shows that DEM error is spatially variable, spatially correlated and heteroscedastic, being related to the form of the terrain (Ehlschlaeger and Shortridge, 1997; Fisher, 1998;Hunter and Goodchild, 1997;Kyriakidis et al., 1999;Theobald, 1989;Weibel and Brändli, 1995;Wood, 1994;Zhang and Montgomery, 1994). However, very little research has attempted to model this heteroscedasticity. This paper reports on research to test the hypothesis that DEM error is related to terrain character and then to develop a more detailed description of DEM accuracy by representing the spatial variation in error across a DEM as an accuracy surface that is generated from regression modelling of the relationship between DEM error and terrain characteristics. The resulting spatially varia...

Geostatistical modeling of topography using auxiliary maps

“…In this case study, errors were positively correlated with terrain complexity (stdev), hillshading (shade) and with vegetation (NDVI). This confirms the previous results of Fisher (1998), Holmes et al (2000, p. 162) and Carlisle (2005). Finally, we showed that regressionkriging and auxiliary maps can be used to downscale existing coarse DEMs.…”

“…The more robust, more sophisticated solutions are yet to be developed. The spatially correlated error component will also often correlate with the auxiliary information (Carlisle, 2005;Oksanen, 2006b). For example, in traditional cartography, it is known that the error of measuring elevations is primarily determined by the complexity of terrain (the slope factor), land cover (density of objects) and relative visibility (the shadow effect).…”

Geomorphic mapping in endorheic catchments in the Spanish Pyrenees: An integrated GIS analysis of karstic features

“…However, adequate DEMs are not always available. It is also known that digital elevation data and other spatial data sets are subject to inherent errors (Carlisle, 2005). Furthermore, modelling karstic areas using a DEM is more difficult than modelling normal landscapes, due to sinks in the DEM that are usually explained as errors influenced by the rounding of the elevations to the nearest integer value (Tarboton et al, 1991).…”

“…This paper presents the advantages of topographical and geomorphological mapping of karstic landscapes with the assistance of GIS techniques, as well as a methodology for obtaining accurate stream nets. We investigate the hypothesis that the errors in a DEM are at least partly related to the nature of the terrain (Carlisle, 2005) and examine the relationship between the DEM errors and the LS factor values.…”

Assessing uncertainties associated with digital elevation models for object based landslide delination

“…However, according to Wechsler (2007) the RMSE method sometimes does not calculate an accurate assessment of how precisely each grid in a DEM represents topographical features. To solve this issue, number of researchers proposed spatial simulation methods for assessing the uncertainty of elevation estimates in each DEMs grid (Holmes et al, 2000;Carlisle, 2005;Wechsler and Kroll, 2006;Abd Aziz et al, 2012). The spatial simulation process analyses the spatial correlation in data to produce equiprobable estimates (realizations) of each particular grid in the DEMs.…”