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Multivariate Regression Analysis for Landslide Hazard Zonation

  • Chang-Jo F. Chung
  • Andrea G. Fabbri
  • Cees J. Van Westen
Part of the Advances in Natural and Technological Hazards Research book series (NTHR, volume 5)

Abstract

Based on several layers of spatial map patterns, multivariate regression methods have been developed for the construction of landslide hazard maps. The method proposed in this paper assumes that future landslides can be predicted by the statistical relationships established between the past landslides and the spatial data set of map patterns. The application of multivariate regression techniques for delineating landslide hazard areas runs into two critical problems using GIS (geographic information systems): (i) the need to handle thematic data; and (ii) the sample unit for the observations. To overcome the first problem related to the thematic data, favourability function approaches or dummy variable techniques can be used.

This paper deals with the second problem related to the sample units. In this situation, the unique condition subareas are defined where each subarea contains a unique combination of the map patterns. Weighted least squares techniques are proposed for the zonation of landslide hazard using those unique condition subareas. The traditional pixel-based multivariate regression model becomes a special case of the proposed weighted regression model based on the unique condition subareas. This model can be directly applied to vector-based GIS data without the need of rasterization.

A case study from a region in central Colombia is used to illustrate the methodologies discussed in this paper. To evaluate the results adequately, it was pretended that the time of the study was the year 1960 and that all the spatial data available in 1960 were compiled including the distribution of the past landslides occurred prior to that year. The statistical analyses performed are based on these pre-1960 data about rapid debris avalanches. The prediction was then compared with the distribution of the landslides which occurred during the period 1960–1980.

Keywords

Debris Flow Sample Unit Multivariate Regression Analysis Landslide Hazard Pyroclastic Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Aronoff S., 1989. Geographic Information Systems: A management perspective. WDL Pub., Ottawa. 294 pp.Google Scholar
  2. Carrara A., 1983. Multivariate Models for landslide hazard evaluation. Mathematical Geology, v. 15:3, 403–427.CrossRefGoogle Scholar
  3. Carrara A., 1988. Landslide hazard mapping by statistical methods. A “black box” approach. The Proceedings of the Workshop on Natural disasters in European Meditteranean Countries, Italy, 205-224.Google Scholar
  4. Carrara A., Cardinali M., Detti R., Guzzetti F., Pasqui V., and Reichenbach P., 1991. GIS techniques and statistical models in evaluating landslide hazard. Earth Surface Processes and Landforms, v. 16:5, 427–445.CrossRefGoogle Scholar
  5. Carrara A., Cardinali M., and Guzzetti F., 1992. Uncertainty in assessing landslide hazard and risk. ITC Journal, v. 2, 172–183.Google Scholar
  6. Christensen R., 1990. Log-Linear Models. Springer-Verlag, New York, 408 pp.Google Scholar
  7. Chung C.F., 1978. Computer program for the logistic model to estimate the probability of occurrence of discrete events. Geological Survey of Canada Paper 78-11, 23 pp.Google Scholar
  8. Chung C.F., 1983, SIMSAG: Integrated computer system for use in Evaluation of mineral and energy resources. Math. Geology, v. 15:1, 47–58.CrossRefGoogle Scholar
  9. Chung C.F., and Agterberg F.P., 1980. Regression models for estimating mineral resources from geological map data. Math. Geology, v. 12:5, 473–488.CrossRefGoogle Scholar
  10. Chung C.F., and Fabbri A.G., 1993. The representation of geoscience information for data integration. Nonrenewable Resources, v. 2:2, 122–139.CrossRefGoogle Scholar
  11. Chung C.F., and Leclerc Y., (in preparation). Quantitative data integration techniques for landslide hazard mapping.Google Scholar
  12. Draper N.R., and Smith H., 1981. Applied Regression Analysis. 2nd ed., Wiley, New York, 709 pp.Google Scholar
  13. Fournier D’Albe E.M., 1976. Natural disasters. Bulletin Int. Assoc. Engin. Geol., v. 14, 187.Google Scholar
  14. Hansen A., 1984. Landslide hazard. In: Brunsden D., and Prior D.B., (Editors), Slope Instability, Wiley, New York, 523–602.Google Scholar
  15. Rao C.R., 1973. Linear Statistical Inference and its Applications. 2nd ed., Wiley, New York, 366–374.CrossRefGoogle Scholar
  16. Roussas G., 1973. A First Course in Mathematical Statistics. Addison-Wesley, Reading, Mass. 506 pp.Google Scholar
  17. Schuster R.L., 1994. Socioeconomic significance of landslides. In: Turner A.K., and Schuster R.L., (Editors), Landslides, investigation and mitigation, Transport Research Board Manual. (in press).Google Scholar
  18. Searle S.R., 1971. Linear Models. Wiley, New York, 532 pp.Google Scholar
  19. van Westen C.J., 1993. Application of Geographic Information Systems to Landslide Hazard Zonation. Ph.D. Thesis, Technical University of Delft, International Institute for Aerospace Surveys and Earth Sciences, Enschede, The Netherlands, ITC Pubblication 15, v. 1, 245 pp.Google Scholar
  20. van Westen C.J., van Düren H.M.G., Kruse I., and Terlien M.T.J., 1993. GISSIZ: Training Package for Geographic Information Systems in Slope Instability Zonation. ITC Publication 15, ITC, Enschede, The Netherlands. Volume 1 — Theory, 245 pp., v. 2 — Exercises, 359 pp. with 10 diskettes.Google Scholar
  21. Wang S.-Q., and Unwin D.J., 1992. Modeling landslide distribution on loess soils in China: an investigation. International Journal of Geographic Information Systems, v. 6:5, 391–405.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Chang-Jo F. Chung
    • 1
  • Andrea G. Fabbri
    • 2
  • Cees J. Van Westen
    • 2
  1. 1.Geological Survey of CanadaOttawaCanada
  2. 2.International Institute for Aerospace Survey and Earth SciencesEnschedeNetherlands

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