Mathematical Geology

, Volume 25, Issue 6, pp 657–669 | Cite as

Interpolation by regularized spline with tension: II. Application to terrain modeling and surface geometry analysis

  • Helena Mitášová
  • Jaroslav Hofierka
Articles

Abstract

A general approach to the computation of basic topographic parameters independent of the spatial distribution of given elevation data is developed. The approach is based on an interpolation function with regular first and second order derivatives and on application of basic principles of differential geometry. General equations for computation of profile, plan, and tangential curvatures are derived. A new algorithm for construction of slope curves is developed using a combined grid and vector approach. Resulting slope curves better fulfill the condition of orthogonality to contours than standard grid algorithms. Presented methods are applied to topographic analysis of a watershed in central Illinois.

Key words

topographic analysis curvatures flow lines 

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References

  1. ARC/INFO Surface Modeling and Display, 1989, TIN Users Guide: ESRI, Environmental Systems Research Institute, Redlands, California, p. 1–19.Google Scholar
  2. Auerbach, S., and Schaeben, H., 1990, Surface Representation Reproducing Given Digitized Contour Lines: Math. Geol., v. 22, p. 723–742.Google Scholar
  3. Dikau, R, 1990, The Application of a Digital Relief Model to Landform Analysis in Geomorphology:in J. Raper, (Ed.), Three Dimensional Applications in Geographic Information Systems: Taylor & Francis, London, 1989, p. 51–77.Google Scholar
  4. ERDAS Field Guide, Version 7.4, 1990: ERDAS Inc., Atlanta, GA, p. 200–201.Google Scholar
  5. Evans I. S., 1972, General Geomorphometry, Derivatives of Altitude and Descriptive Statistics:in R. J. Chorley, (Eds.), Spatial Analysis in Geomorphology: Methuen, London, p. 17–90.Google Scholar
  6. Flacke, W., Auerswald, K., and Neufang, L., 1990, Combining a Modified USLE with a Digital Terrain Model for Computing High Resolution Maps of Soil Loss Resulting from Rain Wash: Catena, v. 17, p. 383–397.Google Scholar
  7. Franklin, S. E., 1987, Geomorphometric Processing of Digital Elevation Models: Comp. Geosci. v. 13, p. 603–609.Google Scholar
  8. GRASS4.1 Reference Manual, 1993: U.S. Army Corps of Engineers, Construction Engineering Research Laboratories, Champaign, Illinois, p. 422–425.Google Scholar
  9. Heerdegen, R. G., and Beran, M. A., 1982, Quantifying Source Areas Through Land Surface Curvature and Shape: J. Hydrol. v. 57, p. 359–373.Google Scholar
  10. Hutchinson, M. F., 1988, Calculation of Hydrologically Sound Digital Elevation Models: Third International Symposium on Spatial Data Handling, Sydney, International Geographical Union, Columbus, p. 117–133.Google Scholar
  11. Krcho, J., 1973, Morphometric Analysis of Relief on the Basis of Geometric Aspect of Field Theory: Acta UC, Georgr. Physica 1, Bratislava, SPN.Google Scholar
  12. Krcho, J., 1991, Georelief as a Subsystem of Landscape and the Influence of Morphometric Parameters of Georelief on Spatial Differentiation of Landscape-Ecological Processes: Ecology/CSFR/, v. 10, p. 115–157.Google Scholar
  13. Mark, D. M., 1975, Computer Analysis of Topography: A Comparison of Terrain Storage Methods: Geografiska Annaler, v. 57A, p. 179–188.Google Scholar
  14. Markus, B., 1986, Terrain Analysis in Consideration of Surface Curvature Conditions: Periodica Polytechnica 30, Budapest, p. 71–81.Google Scholar
  15. Mitásová, H., 1985, Cartographic Aspects of Computer Surface Modeling: PhD thesis, Slovak Technical University, Bratislava (in Slovak).Google Scholar
  16. Mitásová, H., and Mitás, L., 1993, Interpolation by Regularized Spline with Tension: I. Theory and Implementation: Math. Geol., v. 25, p. 641–655.Google Scholar
  17. Moore, I. D., 1988, A Contour-Based Terrain Analysis Program for the Environmental Sciences (TAPES): Trans. Am. Geophys. Union, v. 69, p. 345.Google Scholar
  18. Moore, I. D., Grayson, R. B., and Ladson, A. R., 1991, Digital Terrain Modelling: A Review of Hydrological, Geomorphological and Biological Applications: Hydrol. Proc., v. 5, p. 3–30.Google Scholar
  19. Panuska, J. C., Moore, I. D., and Krammer, L. A., 1991, Terrain Analysis: Integration into the Agricultural Nonpoint Source (AGNPS) Pollution Model: J. Soil Water Conservation, v. 46, p. 59–63.Google Scholar
  20. Papo, H. B., and Gelbman, E., 1984, Digital Terrain Models for Slopes and Curvatures: Photogrammetric Eng. Remote Sensing, v. 50, p. 695–701.Google Scholar
  21. Rektorys, K., 1969, Survey of Applicable Mathematics: MIT Press, Cambridge, MA; Iliffe Books Ltd., London, p. 365.Google Scholar
  22. Zevenbergen, L. W., and Thorne, C. R., 1987, Quantitative Analysis of Land Surface Topography: Earth Surf. Proc. Landforms, v. 12, p. 47–56.Google Scholar

Copyright information

© International Association for Mathematical Geology 1993

Authors and Affiliations

  • Helena Mitášová
    • 1
    • 2
  • Jaroslav Hofierka
    • 2
  1. 1.Illinois Natural History SurveyChampaign
  2. 2.Department of Physical Geography and CartographyComenius UniversityBratislavaCzechoslovakia

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