Dealing with double vagueness in DEM morphometric analysis

A method is presented to explicitly incorporate spatial and scale vagueness – double vagueness – into geomorphometric analyses. Known limitations of usual practices include using a single fixed set of crisp thresholds for morphometric classification and the imposition of a single arbitrary number of scales of analysis to the entire digital elevation model (DEM). Among the advantages of the proposed method are: fuzzification of morphometric classification rules, scale-dependent adaptive fuzzy set parametrization and an objective definition of maximum scale of analysis on a cell-by-cell basis. The method was applied to several DEMs ranging from the ocean floor to surface landscapes of both Earth and Mars. The result was evaluated with respect to modal morphometric features and to characteristic scales, suggesting a more robust method for deriving both morphometric classifications and terrain attributes. We argue that the method would be preferable to any single-scale crisp approach, at least in the context of preliminary hands-off morphometric analyses of DEMs.