Investigating the Effects of DEM Error in Scaling Analysis

Digital elevation models (DEMs) are prone to error that, as they can never be entirely eliminated, must be managed effectively. Thus, it is important to understand the nature of error and their sources, especially in the context of the intended use of a DEM. This paper investigates the effects that can be expected when common DEM errors propagate through a scaling analysis. The errors investigated include those associated with perturbation of camera exterior orientation parameters, focal length, and DEM image coordinates, which were simulated numerically. The role of detrending was also investigated. Scaling analysis, by way of the fractal dimension, using a new two-dimensional approach was carried out on a variety of surfaces before and after the introduction of error and the application of detrending. The results reveal some serious procedural implications on scaling analysis and cast doubt on the authenticity of some scaling analysis results in the absence of robust quality assessment and of independent supporting evidence. Introduction Like any measurement, digital elevation models (DEMs) are prone to error associated with the methods and conditions of their generation. Although error can never be entirely eliminated, it can be minimized and must be managed effectively. Thus, there is always a need to understand how the presence of error will affect DEM data. However, perhaps more important is how error will affect information derived from DEM data on which conclusions are based (Wise, 1998). This proactive approach to data collection and analysis will enable users of topographic data to make informed decisions about how best to quantify, to prevent, to correct or to accept any errors in a dataset. This has been addressed in conventional data collection and applications (e.g., Gong et al., 2000; Huang, 2000; Wolf and Dewitt, 2000). However, the development of automated digital methods has produced Investigating the Effects of DEM Error in Scaling Analysis Timothy D. James, Patrice E. Carbonneau, and Stuart N. Lane a change in the nature of DEM error and in the way topographic data is applied. The availability of large, high-resolution datasets has made possible the description and quantification of surface characteristics across a large range of scales in a single dataset. Scaling analysis is a method used to describe how the elevation change of a surface varies as a function of scale. It is an important type of analysis, as it can provide additional information about a surface including the nature of the physical processes that have acted over time (Butler et al., 2001). There are many ways this can be accomplished (see Klinkenberg, 1994; Klinkenberg and Goodchild, 1992), but all methods involve comparing the change of some parameter (i.e., elevation) against a change in scale (i.e., distance between points on a grid). In many cases, the scaling characteristics of natural surfaces obey a power law, which can be quantified by estimating the fractal dimension (D) (e.g., Butler et al., 2001; Nikora et al., 1998; Robert, 1991; Robert and Richards, 1988). Russ (1994) explains that a surface with fractal characteristics has irregularities at all scales, and when magnified reveals more detail showing the same characteristics as the whole. D is a parameter used to quantify this phenomenon and is discussed at length in Mandelbrot (1967), Mandelbrot (1982), and Russ (1994). In terms of topography, it is potentially important as a means of estimating river bed roughness (Helmlinger et al., 1993), which is a key parameter as it influences many river processes including average flow, turbulence, flow resistance, and sediment transport (Butler et al., 2001; Griffiths, 1989; Hey, 1988). It can also be important for understanding processes relevant in aquatic habitats (i.e., Nikora et al., 1998) and in DEM quality assessment exercises (i.e., Carbonneau et al., 2003). However, the effects of even common errors on the results of scaling analyses are not well understood. Since the quality of parameters derived from a DEM depends, not only on the magnitude of error but also on its structure (Heuvelink, 1998; Hunter and Goodchild, 1997; Lee et al., 1992), it is important that the effect of error on scaling analysis be investigated further. Aim and Objectives This research aimed to investigate the effects that can be expected when common DEM errors propagate through a scaling analysis. The research objectives were: (a) to use numerical modeling to simulate common photogrammetric PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING J a n ua r y 2007 67 Timothy D. James is at the School of Environment and Society, University of Wales, Swansea, SA3 5LQ, UK and formerly at the School of Geography, University of Leeds, Leeds, LS2 9PS, UK ([email protected]). Patrice E. Carbonneau is at the Department of Geography, Durham University, Durham, DH1 3LE, UK and formerly at the Institut National de la Recherche Scientifique, Centre Eau, Terre et Environement, 490 rue da la Couronne, Québec, Canada ([email protected]). Stuart N. Lane is at the Department of Geography, Durham University, Durham, DH1 3LE, UK and formerly at the School of Geography, University of Leeds, Leeds, LS2 9PS, UK ([email protected]). Photogrammetric Engineering & Remote Sensing Vol. 73, No. 1, January 2007, pp. 067–078. 0099-1112/07/7301–0067/$3.00/0 © 2007 American Society for Photogrammetry and Remote Sensing 07-04-087 12/11/06 3:28 PM Page 67