UNIT 41 - SPATIAL INTERPOLATION II

UNIT 41 - SPATIAL INTERPOLATION II

Compiled with assistance from Nigel M. Waters, University of Calgary

  • A. INTRODUCTION
  • B. AREAL INTERPOLATION - NON-VOLUME PRESERVING
  • C. AREAL INTERPOLATION - VOLUME-PRESERVING
  • D. SPECIAL CASES OF SPATIAL INTERPOLATION
  • E. A GIS PERSPECTIVE ON INTERPOLATION
  • REFERENCES
  • DISCUSSION AND EXAM QUESTIONS
  • NOTES

    UNIT 41 - SPATIAL INTERPOLATION II

    Compiled with assistance from Nigel M. Waters, University of Calgary

    A. INTRODUCTION

    B. AREAL INTERPOLATION - NON-VOLUME PRESERVING

    Procedure

    C. AREAL INTERPOLATION - VOLUME-PRESERVING

    1. Overlay

    2. Pycnophylactic

    Boundary conditions

    D. SPECIAL CASES OF SPATIAL INTERPOLATION

    1. Mapping populated areas

    2. Estimating trade areas

    E. A GIS PERSPECTIVE ON INTERPOLATION

    Expert systems for spatial interpolation algorithms

    Conclusion

    REFERENCES

    Bracken, I. and D. Martin, 1989. "The generation of spatial population distributions from census centroid data," Environment and Planning A 21:537-44.

    Dutton-Marion, K.E., 1988. Principles of Interpolation Procedures in the Display and Analysis of Spatial Data: A Comparative Analysis of Conceptual and Computer Contouring, unpublished Ph.D. Thesis, Department of Geography, University of Calgary, Calgary, Alberta.

    Goodchild, M.F., and Lam, N., 1980. "Areal Interpolation: A Variant of the Traditional Spatial Problem," Geo- Processing 1: 297-312.

    Huff, D.L. and R.R. Batsell, 1977. "Delimiting the areal extent of a market area," Journal of Marketing Research 14:581-5.

    MacDougall, E.B., 1976. Computer Programming for Spatial Problems, Arnold, London.

    Maslyn, R.M., 1987. "Gridding Advisor: An Expert System for Selecting Gridding Algorithms," Geobyte 2(4):42-43.

    Silverman, B.W., 1986. Density Estimation for Statistics and Data Analysis, Chapman and Hall, London.

    Tobler, W.R., 1979. "Smooth pycnophylactic interpolation for geographical regions," Journal of the American Statistical Association 74:519-30.

    Waters, N.M., 1988. "Expert Systems and Systems of Experts," Chapter 12 in W.J. Coffey, ed., Geographical Systems and Systems of Geography: Essays in Honour of William Warntz, Department of Geography, University of Western Ontario, London, Ontario.

    DISCUSSION AND EXAM QUESTIONS

    1. What are the main considerations to be aware of in computer contouring? What are the key aspects for the design of an expert system to aid in choosing a computer contouring algorithm within a GIS? How long do you think it will be before such expert systems become widely available?

    2. Describe how Tobler's pycnophylactic method differs from volume-preserving overlay. What model of the underlying spatial distribution is assumed by each? Give examples of phenomena and application which fit each method's assumptions.

    3. Describe the application of areal interpolation in political districting.

    4. One test of a spatial interpolation method is that its results would be judged as equal or better to hand contouring by a specialist, e.g. a field geologist, with detailed knowledge of the phenomenon being mapped. How well do the methods discussed in these two units do against this criterion?


    Back to Geography 370 Home Page

    Back to Geography 470 Home Page

    Back to GIS & Cartography Course Information Home Page



    Please send comments regarding content to: Brian Klinkenberg
    Please send comments regarding web-site problems to: The Techmaster
    Last Updated: August 30, 1997.