Effects of Topographic Variability and Lidar Sampling Density on Several DEM Interpolation Methods

This study aims to quantify the effects of topographic variability (measured by coefficient variation of elevation, CV) and lidar (Light Detection and Ranging) sampling density on the DEM (Digital Elevation Model) accuracy derived from several interpolation methods at different spatial resolutions. Interpolation methods include natural neighbor (NN), inverse distance weighted (IDW), triangulated irregular network (TIN), spline, ordinary kriging (OK), and universal kriging (UK). This study is unique in that a comprehensive evaluation of the combined effects of three influencing factors (CV, sampling density, and spatial resolution) on lidar-derived DEM accuracy is carried out using different interpolation methods. Results indicate that simple interpolation methods, such as IDW, NN, and TIN, are more efficient at generating DEMs from lidar data, but kriging-based methods, such as OK and UK, are more reliable if accuracy is the most important consideration. Moreover, spatial resolution also plays an important role when generating DEMs from lidar data. Our results could be used to guide the choice of appropriate lidar interpolation methods for DEM generation given the resolution, sampling density, and topographic variability. Introduction As defined by the U.S. Geological Survey, a grid Digital Elevation Model (DEM) is the digital cartographic representation of the elevation of the land at regularly spaced intervals in the x and y directions, using z-values referenced to a common vertical datum (Aguilar et al., 2005). DEMs are essential to various applications, such as terrain modeling, soil-landscape modeling, and hydrological modeling (Anderson et al., 2006; Walker and Willgoose, 1999). Consequently, the quality of the DEM and its derived terrain attributes becomes important in a range of spatial modeling techniques (Thompson et al., 2001). Recently, lidar (Light Detection and Ranging) has emerged as an important technology for the acquisition of high quality DEMs due to its ability to generate 3D terrain point data with high density and accuracy (Lohr, 1998; Wehr and Lohr, 1999; Lefsky et al., 2002). Lidar is an optical remote sensing technology that measures properties of scattered light to find the range and/or other information of a distant object. The range to an object is calculated by measuring the time delay between transmission of a laser PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING J u n e 2010 1 Sierra Nevada Research Institute, School of Engineering, University of California at Merced, Merced, CA 95344 ([email protected]). Photogrammetric Engineering & Remote Sensing Vol. 76, No. 6, June 2010, pp. 000–000. 0099-1112/10/7606–0000/$3.00/0 © 2010 American Society for Photogrammetry and Remote Sensing Effects of Topographic Variability and Lidar Sampling Density on Several DEM Interpolation Methods Qinghua Guo, Wenkai Li, Hong Yu, and Otto Alvarez pulse and detection of the reflected signal (Wehr and Lohr, 1999). With high-density lidar data, very detailed highresolution DEMs can be generated with great accuracy using appropriate interpolation methods (Liu et al., 2007a). Compared to the traditional DEM derived from photogrammetric techniques, such as the U.S. Geological Survey 30 m DEM data, the lidar-derived DEM is more reliable and accurate with a higher resolution. The principles of lidar and its application to produce high-quality DEMs have been well documented (Lohr, 1998; Wehr and Lohr, 1999; Lloyd and Atkinson, 2002; Liu et al., 2007b). The use of airborne lidar sensors for topographic mapping is rapidly becoming a standard practice in a range of applications, such as storm water assessment, flood control, visualization, etc. (Hodgson and Bresnahan, 2004). As the DEM plays an important role in spatial modeling, it is necessary to consider the accuracy of the DEM and its derived terrain attributes (Thompson et al., 2001). Several studies have indicated that morphology-derived variables, such as average terrain slope, are positively correlated with the increase in the global error of the modeled surface (Toutin, 2002). Despite the ability of lidar to gather point samples at very small separation distances, these points are obtained irregularly, and thus interpolation is necessary to generate continuous surfaces. As a result, the interpolation from points to a grid introduces uncertainties into the DEM (Lloyd and Atkinson, 2002; Smith et al., 2004). Previous studies have demonstrated that the accuracy of derived DEMs is significantly influenced by various factors, such as topographic variability, sampling density, interpolation methods, spatial resolution, etc. (Quattrochi and Goodchild, 1997; Caruso and Quarta, 1998; Gong et al., 2000; Thompson et al., 2001; Kienzle, 2004; Smith et al., 2004; Aguilar et al., 2005; Anderson et al., 2006; Liu et al., 2007a). For example, MacEachren and Davidson (1987) studied the relationship between observation point density and the accuracy of the derived DEM, and they demonstrated that as the density of observation points increases, the accuracy of the resulting DEM increases. Anderson et al. (2006) investigated the effects of data density reduction on DEMs of various horizontal resolutions, and their research showed that lidar datasets could withstand substantial data reductions without decreasing the DEM quality, but the level of reduction that