Landslide susceptibility mapping using the fuzzy gamma operation in a GIS, Kakan catchment area, Iran
Theory and Methodology
Quantitative prediction models for landslide hazard are based on a spatial database consisting of several layers of digital maps representing the casual factors of the occurrence of landslides. Three mathematical frameworks used for the models are (1) probability theory; (2) fuzzy set theory; (3) Dempster-Shafer evidential theory. Corresponding to the three theories, the conditional probability function, the fuzzy membership function, or the belief function are used to represent a quantitative measure of future landslide hazard. These functions representing the landslide hazard were termed favourability functions. The favourability functions can be estimated in many different ways depending upon the availability of the input data and upon the assumptions made in the processes of modelling and estimation. All models are based on two basic assumptions: (1) that future landslides will occur under circumstances similar to the ones of past landslides in either the study area or in areas in which the experts have obtained their knowledge on the relationship between the causal factors and the occurrences of the landslides; and (2) that the spatial data representing the causal factors contained in the GIS database can be used to formulate the future landslide.
When producing landslide susceptibility maps, some researchers have employed quantitative methods (Carrara et al 1991; Anbalagan 1992; Juang et al 1992; Maharaj 1993; Gokceoglu and Aksoy 1996; van Westen et al 1997; Atkinson and Massari 1998; Pachauri et al 1998; Guzzetti et al 1999; Gritzner et al 2001; Ercanoglu and Gokceoglu 2002). All the available methods for regional landslide assessment have some uncertainties arising from lack of knowledge and variability. This is because regional landslide assessments require some generalizations and simplifications, although these assessments are complex. For this reason, a perfect assessment method for landslide susceptibility does not exist. The fuzzy logic introduced by Zadeh (1965) is one of the tools to solve these complex problems. The idea of fuzzy logic is to consider the spatial objects on a map as members of a set. In classical set theory, an object is a member of a set if it has a membership value of 1, or not a member if it has a membership value of 0. In fuzzy set theory, membership can take on any value between 0 and 1 reflecting the degree of certainty of membership. Fuzzy set theory employs the idea of a membership function that expresses the degree of membership with respect to some attribute of interest. With maps, generally the attribute of interest is measured over discrete intervals, and the membership function can be expressed as a table relating map classes to membership values.
The idea of using fuzzy logic in landslide susceptibility mapping is to consider the spatial objects on a map as members of a set. For example, the spatial objects could be areas on an evidence map and the set defined as “ areas susceptible to landslide”. Fuzzy membership values must lie in the range (0,1), but there are no practical constraints on the choice of fuzzy membership values. Values are simply chosen to reflect the degree of membership of a set, based on subjective judgment. Anabalgan (1992) introduced a landslide hazard evaluation factor (LHEF) rating scheme for some of the landslide causal factors. The LHEF rating scheme is a numerical system which is based on major inherent causative factors of slope instability such as geology, slope morphometry, relative relief, land use, land cover and groundwater conditions. Numerical ratings suggested by LHEF scheme were modified as fuzzy membership functions for each map class. Those evidence maps not listed in Anabalgan (1992) were classified and rated according to the experiences gained from the study of factors and their impact on landslides with conditions anticipated in the area of study.