A method of DEM construction and related error analysis

The concept and the computation of terrain representation error (ETR) are investigated and total DEM error is presented as an accuracy index for DEM evaluation at a global level. A promising method of surface modelling based on the theorem of surfaces (SMTS) has been developed. A numerical test and a real-world example are employed to comparatively analyze the simulation accuracy of SMTS and the classical interpolation methods, including IDW, SPLINE and KRIGING performed in ARCGIS 9.1 in terms of sampling and interpolation errors and of total DEM error. The numerical test shows that SMTS is much more accurate than the classical interpolation methods and ETR has a worse influence on the accuracy of SMTS than those of the classical interpolation methods. In a real-world example, DEMs are constructed with SMTS as well as the three classical interpolation methods. The results indicate that, although SMTS is more accurate than the classical interpolation methods, a real-world test indicates that there is a large accuracy loss. Total DEM error composed of, not only sampling and interpolation errors, but also ETRs can be considered as a good accuracy measure for DEM evaluation at a global level. SMTS is an alternative method for DEM construction.

[1]  Manuel A. Aguilar,et al.  Accuracy assessment of digital elevation models using a non‐parametric approach , 2007, Int. J. Geogr. Inf. Sci..

[2]  Saffet Erdogan,et al.  A comparision of interpolation methods for producing digital elevation models at the field scale , 2009 .

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

[4]  Ludwig Ries.  Areas of influence for IDW-interpolation with isotropic environmental data , 1993 .

[5]  David Theobald.  Accuracy and bias issues in surface representation , 1989 .

[6]  Jay Gao,et al.  Resolution and Accuracy of Terrain Representation by Grid DEMs at a Micro-Scale , 1997, Int. J. Geogr. Inf. Sci..

[7]  Andrew K. Skidmore,et al.  A comparison of techniques for calculating gradient and aspect from a gridded digital elevation model , 1989, Int. J. Geogr. Inf. Sci..

[8]  David W. Henderson,et al.  Differential Geometry: A Geometric Introduction , 1997 .

[9]  Timothy A. Davis,et al.  Direct methods for sparse linear systems , 2006, Fundamentals of algorithms.

[10]  P. Kyriakidis,et al.  Error in a USGS 30-meter digital elevation model and its impact on terrain modeling , 2000 .

[11]  Radoslav Bonk,et al.  Scale-Dependent Effect of Input Data Design on DEM Accuracy , 2007 .

[12]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[13]  Bruce H. Carlisle,et al.  Modelling the Spatial Distribution of DEM Error , 2005, Trans. GIS.

[14]  A. Gray,et al.  Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Studies in Advanced Mathematics) , 2006 .

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

[16]  Tianxiang Yue,et al.  The YUE-HASM method , 2008 .

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

[18]  Sten Blomgren.  A digital elevation model for estimating flooding scenarios at the Falsterbo Peninsula , 1999, Environ. Model. Softw..

[19]  J. Chorowicz,et al.  Description of terrain as a fractal surface, and application to digital elevation model quality assessment , 1991 .

[20]  Xuejun Liu,et al.  Analysis of errors of derived slope and aspect related to DEM data properties , 2004, Comput. Geosci..

[21]  Z. HUANG,et al.  Representing and reducing error in natural‐resource classification using model combination , 2005, Int. J. Geogr. Inf. Sci..

[22]  Tianxiang Yue,et al.  A new method of surface modeling and its application to DEM construction , 2007 .

[23]  Jay Gao,et al.  Impact of Sampling Intervals on the Reliability of Topographic Variables Mapped from Grid DEMs at a Micro-Scale , 1998, Int. J. Geogr. Inf. Sci..

[24]  P. Pizor.  Principles of Geographical Information Systems for Land Resources Assessment. , 1987 .

[25]  G. H. Schut,et al.  Review of Interpolation Methods for Digital Terrain Models , 1976 .

[26]  P. Bolstad,et al.  An evaluation of DEM accuracy: elevation, slope, and aspect , 1994 .

[27]  W. Rees,et al.  The accuracy of Digital Elevation Models interpolated to higher resolutions , 2000 .

[28]  Y. D. Huang.  Evaluation of Information Loss in Digital Elevation Models With Digital Photogrammetric Systems , 2000 .

[29]  PETER F. FISHER,et al.  Algorithm and Implementation Uncertainty in Viewshed Analysis , 1993, Int. J. Geogr. Inf. Sci..

[30]  A. Gray.  Modern Differential Geometry of Curves and Surfaces , 1993 .

[31]  Robert J. Peckham,et al.  Digital Terrain Modelling: Development and Applications in a Policy Support Environment (Lecture Notes in Geoinformation and Cartography) , 2007 .

[32]  Michael F. Goodchild,et al.  The accuracy of spatial databases , 1991 .

[33]  Bor-Wen Tsai,et al.  The Effect of DEM Resolution on Slope and Aspect Mapping , 1991 .

[34]  Y.-J. Song,et al.  Spatial Models and Geographic Information Systems , 2008 .

[35]  Gabriele Bitelli,et al.  Comparison of Techniques for Generating Digital Terrain Models from Contour Lines , 1997, Int. J. Geogr. Inf. Sci..

[36]  G. Metternicht,et al.  Testing the performance of spatial interpolation techniques for mapping soil properties , 2006 .

[37]  S. Wechsler,et al.  Quantifying DEM Uncertainty and its Effect on Topographic Parameters , 2006 .

[38]  Lawrence W. Martz,et al.  Topographic parameterization in continental hydrology: a study in scale , 2003 .

[39]  Carlos López-Vázquez,et al.  Locating Some Types of Random Errors in Digital Terrain Models , 1997, Int. J. Geogr. Inf. Sci..

[40]  Vladimir D. Liseikin,et al.  A Computational Differential Geometry Approach to Grid Generation (Scientific Computation) , 2003 .

[41]  Stephen J. Walsh,et al.  Recognition and assessment of error in geographic information systems , 1987 .

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

[43]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .