Discrete displacement analysis for geographic linear features and the application to glacier termini

The extent of glacier terminus displacement is instrumental in investigations of natural or artificial geographic changes. Its importance to earth science and engineering is reflected in the considerable efforts that have been devoted to the development of several boundary displacement analysis methods. Among the methods, the buffering-based approach compares favorably with other approaches in objectivity and robustness. However, it does not consider the relative positions of boundaries, because its buffering operation cannot determine features' relative directions. This limitation incurs inaccurate calculation results – underestimation of mean shifts and overestimation of shape variations, especially when the two compared boundaries intersect. Discrete displacement analysis (DDA), an alternative method that considers given geographic objects as a set of a finite number of points, is proposed here. In a series of tests carried out, including Jakobshavn glacier's calving front, DDA was found to correctly calculate mean shift and shape variation even in cases where the conventional buffering-based method failed. Moreover, this approach is independent of the dimension of space in which it is implemented, and thus is expected to be utilized for analysis of 3D geographic object displacement.