Contour models for physical boundaries enclosing star-shaped and approximately star-shaped polygons

Abstract

Boundaries on spatial fields divide regions with particular features from surrounding background areas. Methods to identify boundary lines from interpolated spatial fields are well established. Less attention has been paid to how to model sequences of connected spatial points. Such models are needed for physical boundaries. For example, in the Arctic ocean, large contiguous areas are covered by sea ice, or frozen ocean water. We define the ice edge contour as the ordered sequences of spatial points that connect to form a line around set(s) of contiguous grid boxes with sea ice present. Polar scientists need to describe how this contiguous area behaves in present and historical data and under future climate change scenarios. We introduce the Gaussian Star-shaped Contour Model (GSCM) for modelling boundaries represented as connected sequences of spatial points such as the sea ice edge. GSCMs generate sequences of spatial points via generating sets of distances in various directions from a fixed starting point. The GSCM can be applied to contours that enclose regions that are star-shaped polygons or approximately star-shaped polygons. Metrics are introduced to assess the extent to which a polygon deviates from star-shapedness. Simulation studies illustrate the performance of the GSCM in different situations.