The influence of elevation uncertainty on derivation of topographic indices

Abstract Digital elevation models at a variety of resolutions are increasingly being used in geomorphology, for example in comparing the hypsometric properties of multiple catchments. A considerable body of research has investigated the sensitivity of topographic indices to resolution and algorithms, but little work has been done to address the impact of DEM uncertainty and elevation value error on derived products. By using higher resolution data from the Shuttle Radar Topography Mission — of supposed higher accuracy — for comparison with the widely used GLOBE 1 km data set, error surfaces for three mountainous regions were calculated. Correlation analysis showed that error surfaces are related to a range of topographic variables for all three regions, namely roughness, minimum and mean extremity and aspect. This correlation of error with local topography was used to develop a model of uncertainty including a stochastic component, permitting Monte Carlo Simulations. These suggest that global statistics for a range of topographic indices are robust to the introduction of uncertainty. However, the derivation of watersheds and related statistics per watershed (e.g. hypsometry) is shown to vary significantly as a result of the introduced uncertainty.

[1]  David G. Vaughan,et al.  BEDMAP: a new ice thickness and subglacial topographic model of Antarctica , 2001 .

[2]  G. Suna,et al.  Validation of surface height from shuttle radar topography mission using shuttle laser altimeter , 2003 .

[3]  S. S. R. Jamiesona,et al.  Tectonic forcing of longitudinal valleys in the Himalaya : morphological analysis of the Ladakh Batholith , North India , 2003 .

[4]  David R. Montgomery,et al.  Modeling large-scale fluvial erosion in geographic information systems , 2003 .

[5]  K. Jones.  A comparison of algorithms used to compute hill slope as a property of the DEM , 1998 .

[6]  J. Hothmer.  Book reviewInternational archives of photogrammetry and remote sensing: ISPRS, Editor S. Murai: volume 27 part A, Tokyo-Japan-Japan 1989 , 1989 .

[7]  Peter F. Fisher,et al.  Causes and consequences of error in digital elevation models , 2006 .

[8]  N. Drake,et al.  Comparison of slope estimates from low resolution DEMs: scaling issues and a fractal method for their solution , 1999 .

[9]  Nicole M. Gasparini,et al.  An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks , 2001 .

[10]  T. Sarjakoski,et al.  Error propagation analysis of DEM‐based drainage basin delineation , 2005 .

[11]  D. Harding,et al.  ICESat validation of SRTM C‐band digital elevation models , 2004 .

[12]  I. Evans.  Statistical Characterization of Altitude Matrices by Computer. Report 6. An Integrated System of Terrain Analysis and Slope Mapping. , 1979 .

[13]  Mark Mulligan,et al.  Practical use of SRTM data in the tropics : Comparisons with digital elevation models generated cartographic data , 2004 .

[14]  D. Staley,et al.  Surficial patterns of debris flow deposition on alluvial fans in Death Valley, CA using airborne laser swath mapping data , 2006 .

[15]  Thorsten Behrens,et al.  Digital soil mapping using artificial neural networks , 2005 .

[16]  T. Hoey,et al.  Surface process models and the links between tectonics and topography , 2006 .

[17]  J. Casalí,et al.  Digital Terrain Modelling of Drainage Channel Erosion , 1999 .

[18]  F. Lucazeau,et al.  Effect of drainage area on hypsometry from an analysis of small-scale drainage basins in the Siwalik Hills (Central Nepal) , 1999 .

[19]  Michael Eineder,et al.  SRTM X-SAR calibration results , 2001, IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No.01CH37217).

[20]  Joseph. Wood,et al.  The geomorphological characterisation of Digital Elevation Models , 1996 .

[21]  John P. Wilson,et al.  Terrain analysis : principles and applications , 2000 .

[22]  Ashton Shortridge.  Shuttle Radar Topography Mission Elevation Data Error and Its Relationship to Land Cover , 2006 .

[23]  S. Marshall.  Modelled nucleation centres of the Pleistocene ice sheets from an ice sheet model with subgrid topographic and glaciologic parameterizations , 2002 .

[24]  Tapani Sarjakoski,et al.  Error propagation of DEM-based surface derivatives , 2005, Comput. Geosci..

[25]  David J. Maguire,et al.  Geographical information systems : principles and applications , 1991 .

[26]  Jonathan L. Bamber,et al.  An improved elevation dataset for climate and ice-sheet modelling: validation with satellite imagery , 1997 .

[27]  Carolyn T. Hunsaker,et al.  Spatial uncertainty in ecology : implications for remote sensing and GIS applications , 2002 .

[28]  Garry R. Willgoose,et al.  On the effect of digital elevation model accuracy on hydrology and geomorphology , 1999 .

[29]  Michael F. Goodchild,et al.  Geostatistics for conflation and accuracy assessment of digital elevation models , 1999, Int. J. Geogr. Inf. Sci..

[30]  Michael F. Hutchinson,et al.  Digital elevation models and representation of terrain shape , 2000 .

[31]  Peter F. Fisher,et al.  Improved Modeling of Elevation Error with Geostatistics , 1998, GeoInformatica.

[32]  Michael E. Hodgson,et al.  Comparison of Angles from Surface Slope/Aspect Algorithms , 1998 .

[33]  K. Holmesa,et al.  Error in a USGS 30-meter digital elevation model and its impact on terrain modeling , 2000 .

[34]  Stephen Wise,et al.  Assessing the quality for hydrological applications of digital elevation models derived from contours , 2000 .

[35]  B. Schneider.  On the Uncertainty of Local Shape of Lines and Surfaces , 2001 .

[36]  D. Montgomery.  Slope Distributions, Threshold Hillslopes, and Steady-state Topography , 2001 .

[37]  N. Chrisman,et al.  Proceedings of the 8th International Symposium on Spatial Data Handling , 1999 .

[38]  D. Pollard.  A coupled climate-ice sheet model applied to the Quaternary Ice Ages , 1983 .

[39]  Bernhard Schneider,et al.  Evaluating Methods for Interpolating Continuous Surfaces from Irregular Data: a Case Study , 2004, SDH.

[40]  Jo Wood,et al.  Where is Helvellyn? Fuzziness of multi‐scale landscape morphometry , 2004 .

[41]  Hongxing Liu,et al.  Development of an Antarctic digital elevation model by integrating cartographic and remotely sensed data: A geographic information system based approach , 1999 .

[42]  John Frederick Nye,et al.  The distribution of stress and velocity in glaciers and ice-sheets , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[43]  Norbert Silvera,et al.  Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density , 2006 .

[44]  Gerard B. M. Heuvelink,et al.  Error Propagation in Environmental Modelling with GIS , 1998 .

[45]  Ashton Shortridge,et al.  Characterizing Uncertainty in Digital Elevation Models , 2001 .

[46]  APPLICATION OF THE SHUTTLE LASER ALTIMETER IN AN ACCURACY ASSESSMENT OF GTOPO 30 , A GLOBAL 1-KILOMETER DIGITAL ELEVATION MODEL , 2004 .

[47]  P. Dunbar,et al.  DEVELOPMENT & ASSESSMENT OF THE GLOBAL LAND ONE-KM BASE ELEVATION DIGITAL ELEVATION MODEL (GLOBE) , 1998 .

[48]  Stuart N. Lane,et al.  Landform monitoring, modelling, and analysis , 1998 .

[49]  Tapani Sarjakoski,et al.  Uncovering the statistical and spatial characteristics of fine toposcale DEM error , 2006, Int. J. Geogr. Inf. Sci..

[50]  Menno-Jan Kraak,et al.  Principles of geographic information systems : an introductory textbook , 2000 .

[51]  A. N. Strahler.  Hypsometric (area-altitude) analysis of erosional topography. , 1952 .

[52]  S. Wechsler.  Uncertainties associated with digital elevation models for hydrologic applications: a review , 2006 .

[53]  Christian Heipke,et al.  Analysis of SRTM DTM - Methodology and practical results * , 2002 .

[54]  Michael F. Goodchild,et al.  Modeling the Uncertainty of Slope and Aspect Estimates Derived from Spatial Databases , 2010 .

[55]  Peter L. Guth,et al.  Geomorphometry from SRTM: Comparison to NED , 2006 .

[56]  Theodore A. Endreny,et al.  Representing elevation uncertainty in runoff modelling and flowpath mapping , 2001 .

[57]  Ashley William Gunter,et al.  Getting it for free: Using Google earth™ and IL WIS to map squatter settlements in Johannesburg , 2009, 2009 IEEE International Geoscience and Remote Sensing Symposium.

[58]  Susan Eitelman,et al.  Matlab Version 6.5 Release 13. The MathWorks, Inc., 3 Apple Hill Dr., Natick, MA 01760-2098; 508/647-7000, Fax 508/647-7001, www.mathworks.com , 2003 .