UNIT 40 - SPATIAL INTERPOLATION I

UNIT 40 - SPATIAL INTERPOLATION I

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

  • A. INTRODUCTION
  • B. CLASSIFICATION OF INTERPOLATION PROCEDURES
  • C. POINT BASED INTERPOLATION - EXACT METHODS
  • D. POINT BASED INTERPOLATION - APPROXIMATE METHODS
  • REFERENCES
  • DISCUSSION AND EXAM QUESTIONS
  • NOTES

    UNIT 40 - SPATIAL INTERPOLATION I

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

    A. INTRODUCTION

    B. CLASSIFICATION OF INTERPOLATION PROCEDURES

    1. Point Interpolation/Areal Interpolation

    2. Global/Local Interpolators

    3. Exact/Approximate Interpolators

    4. Stochastic/Deterministic Interpolators

    5. Gradual/Abrupt Interpolators

    C. POINT BASED INTERPOLATION - EXACT METHODS

    1. Proximal

    2. B-splines

    3. Kriging

    Variograms

    Deriving the variogram

    Computing the estimates

    4. Manual Interpolation or "eyeballing"

    D. POINT BASED INTERPOLATION - APPROXIMATE METHODS

    1. Trend Surface Analysis

    2. Fourier Series

    3. Moving average/distance weighted average

    REFERENCES

    Burrough, P.A., 1986. Principles of Geographical Information Systems for land Resources Assessment, Clarendon, Oxford. See Chapter 8.

    Davis, J.C., 1986. Statistics and Data Analysis in Geology, 2nd edition, Wiley, New York. (Also see the first, 1973, edition for program listings.)

    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Procedures in the Display and Analysis of Spatial Data: A Comparative Analysis of Conceptual and Computer Contouring, unpublished Ph.D. Thesis, Department of Geography, University of Calgary, Calgary, Alberta.

    Hearn, D., and Baker, M.P., 1986. Computer Graphics, Prentice-Hall Inc, Englewood Cliffs, N.J.

    Jones, T.A., Hamilton, D.E. and Johnson, C.R., 1986. Contouring Geologic Surfaces with the Computer, Van Nostrand Reinhold, New York

    Lam, N., 1983. "Spatial Interpolation Methods: A Review," The American Cartographer 10(2):129-149.

    Mather, P.M., 1976. Computational Methods of Multivariate Analysis in Physical Geography, Wigley, New York.

    Sampson, R.J., 1978. Surface II, revised edition, Kansas Geological Survey, Lawrence, Kansas.

    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.

    An important class of interpolation methods is missing here - so called radial basis functions, such as multiquadrics, thin plate spline, thin plate spline with tension, regularized spline with tension and a large number of other flavours of this approach (also sometimes refered to as variational approach). These methods are available in almost every GIS, from ArcINFO, GRASS, SURFER to specialized visualization packages. The description can be found at Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley, M.F. Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Information Systems: Principles, Techniques, Management and Applications, GeoInformation International, Wiley, 481-492.

    DISCUSSION AND EXAM QUESTIONS

    1. Are there other techniques for surface generation? How many of the above procedures are commonly used? How would they be ranked in terms of popularity? Give examples from the literature of where they have been used.

    2. How does hand contouring rate as an alternative? What did you think of it and have you changed your mind? What are the key features and processes involved in hand contouring?

    3. Explain the advantages and disadvantages of manual interpolation as used in hand contouring over computer based interpolation as used in a computer contouring package.

    4. Describe the different ways in which spatial interpolation algorithms can be classified.


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