Stability of the surface generated from distributed points of uncertain location

Abstract

Conversion of a point distribution into a surface is one of the spatial operations used in GIS. This supports the visual analysis of point patterns, which is usually followed by more sophisticated statistical and mathematical analysis. If the location of points is uncertain, however, the surface obtained becomes unstable and consequently the results of analysis may be unreliable. Though unavoidable in spatial data, locational uncertainty has been rather neglected in the context of spatial analysis. To fill this gap, this paper proposes a method for representing and analysing the stability of the surface generated from an uncertain point distribution. The surface stability is represented by a scalar function called the slope stability function. Its definition, calculation procedure, visualization method, and summary indices are proposed. The method is evaluated through an empirical study, and some findings are shown which help us understand the effect of the smoothing parameter, locational uncertainty, and spatial pattern of points on the stability of a surface.