Skip to main content

An Evaluation of Spatial Interpolation Accuracy of Elevation Data

  • Chapter
Progress in Spatial Data Handling

Abstract

This paper makes a general evaluation of the spatial interpolation accuracy of elevation data. Six common interpolators were examined, including Kriging, inverse distance to a power, minimum curvature, modified Shepard’s method, radial basis functions, and triangulation with linear interpolation. The main properties and mathematical procedures of the interpolation algorithms were reviewed. In order to obtain full evaluation of the interpolations, both statistical (including root-mean-square-error, standard deviation, and mean) and spatial accuracy measures (including accuracy surface, and spatial autocorrelation) were employed. It is found that the accuracy of spatial interpolation of elevations was primarily subject to input data point density and distribution, grid size (resolution), terrain complexity, and interpolation algorithm used. The variations in interpolation parameters may significantly improve or worsen the accuracy. Further researches are needed to examine the impacts of terrain complexity in details and various data sampling strategies. The combined use of variogram models, accuracy surfaces, and spatial autocorrelation represents a promising direction in mapping spatial data accuracy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ackermann F (1994) Digital Elevation Models: Techniques and Applications, Quality Standards, Development. In: Proc of the Symp on Mapping and Geographic Information Systems, ISPRS, vol 30, no 4. University of Georgia, Athens, GA, pp 421–432

    Google Scholar 

  • Ackermann F (1996) Techniques and strategies for DEM generation. In: Greve C (ed) Digital Photogrammetry: An Addendum to the Manual of Photogrammetry. American Society of Photogrammetry and Remote Sensing, Falls Church, VA, pp 135–141

    Google Scholar 

  • Burrough PH (1986) Methods of spatial interpolation. In: Principles of Geographic Information Systems for Land Resources Assessment. Clarendon Press, Oxford, England, pp 147–166

    Google Scholar 

  • Carr JR (1995) Numerical Analysis for the Geological Sciences. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  • Davis JC (1986) Statistics and Data Analysis in Geology, 2nd ed. John Wiley and Sons, New York

    Google Scholar 

  • Ehlschlaeger CR, Goodchild MF (1994) Uncertainty in spatial data: defining, visualizing, and managing data error. In: GIS/LIS 1994 Proc, pp 246–253

    Google Scholar 

  • Flowerdew R, Green M (1994) Areal interpolation and types of data. In: Fotheringham S, Rogerson P (eds) Spatial Analysis and GIS. Taylor & Francis, Bristol, pp 121–146

    Google Scholar 

  • Gao J (1997) Resolution and accuracy of terrain representation by grid DEMs at a micro-scale. Int J of Geographic Information Science 11(2):199–212

    Article  Google Scholar 

  • Golden Software Inc. (1999) Surfer User’s Guide. Golden, Colorado

    Google Scholar 

  • Golden Software Inc. (2001) Didger User’s Guide. Golden, Colorado

    Google Scholar 

  • Goodchild MF (1993) Data models and data quality: problems and prospects. In: Goodchild MF, Parks BO, Steyaert LT (eds) Environmental Modeling with GIS. Oxford University Press, New York, pp 94–103

    Google Scholar 

  • Goodchild MF, Gopal S (eds) (1989) Accuracy of Spatial Databases. Taylor and Francis, New York

    Google Scholar 

  • Guth P (1992) Spatial analysis of DEM error. In: Proc ASPRS/ACSM Annual Meeting, pp 187–196

    Google Scholar 

  • Hunter GJ, Caetano M, Goodchild MF (1995) A methodology for reporting uncertainty in spatial database products. J of the Urban and Regional Information Systems Association 7:11–21

    Google Scholar 

  • Isaaks EH, Srivastava RM (1989) An Introduction to Applied Geostatistics. Oxford University Press, New York

    Google Scholar 

  • Lam NS (1983) Spatial interpolation methods: a review. The American Cartographer 10(2):129–149

    Article  Google Scholar 

  • Li Z (1993) Theoretical models of the accuracy of digital terrain models: An evaluation and some observations. Photogrammetric Record 14(82):651–659

    Google Scholar 

  • Li Z (1998) A comparative study of the accuracy of digital terrain models (DTMs) based on various data models. ISPRS J of Photogrammetry and Remote Sensing 49(1):2–11

    Article  Google Scholar 

  • Monckton C (1994) An investigation into the spatial structure of error in digital elevation data. In: Innovations in GIS 1. Taylor and Francis, London, pp 201–211

    Google Scholar 

  • NCGIA (1989) The research plan for the National Center for Geographic Information and Analysis. Int J of Geographical Information Systems 3(2):117–136

    Google Scholar 

  • R-WEL Inc. (1996) CAPTURE Digitizing Program, Version 3.1. Athens, Georgia. http://www.rwel.com

    Google Scholar 

  • Shearer JW (1990) The accuracy of digital terrain models. In: Petrie G, Kennie TJM (eds) Terrain Modeling in Surveying and Engineering. Whittles Publishing Services, Caithness, pp 315–336

    Google Scholar 

  • Shepard D (1968) A two dimensional interpolation function for irregularly spaced data. In: Proc 23rd National Conf ACM. Brandon/Systems Press, Princeton, pp 517–523

    Chapter  Google Scholar 

  • Smith WHF, Wessel P (1990) Gridding with continues curvature splines in tension. Geophysics 55(3):293–305

    Article  Google Scholar 

  • Wang L (1990) Comparative Studies of Spatial Interpolation Accuracy. Master Thesis, The University of Georgia, Athens, Georgia

    Google Scholar 

  • Weibel R, Heller M (1991) Digital terrain modeling. In: Maguire DJ, Goodchild MF, Rhind DW (eds) Geographical Information Systems: Principles and Applications. Longman, London, pp 269–297

    Google Scholar 

  • Weng Q (2002) Quantifying uncertainty of digital elevation models derived from topographic maps. In: Richardson D, van Oosterom P (eds) Advances in Spatial Data Handling. Springer-Verlag, New York, pp 403–418

    Google Scholar 

  • Wood J (1996) The Geomorphological Charaterisation of Digital Elevation Models. PhD Thesis, Department of Geography, University of Leicester, Leicester, UK

    Google Scholar 

  • Wood J, Fisher P (1993) Assessing interpolation accuracy in elevation models. IEEE Computer Graphics and Applications 13(2):48–56

    Article  Google Scholar 

  • Wren AE (1975) Contouring and the contour map: a new perspective. Geographical Prospecting 23:1–17

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Weng, Q. (2006). An Evaluation of Spatial Interpolation Accuracy of Elevation Data. In: Riedl, A., Kainz, W., Elmes, G.A. (eds) Progress in Spatial Data Handling. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-35589-8_50

Download citation

Publish with us

Policies and ethics