Space-Time Contour Models
Boundaries on spatial fields divide regions with particular features from surrounding background areas. These boundaries are frequently described with contour lines. To measure and record these boundaries, contours are often represented as ordered sequences of spatial points that connect to form a line. While methods to identify boundary lines from interpolated spatial fields are well-established, less focus has been placed on modeling data composed of multiple observed sequences of spatial points. I introduce the Gaussian Star-shaped Contour Model (GSCM) to model data of the latter form. GSCMs can be employed for inference and prediction of contours that enclose regions that are star-shaped polygons or approximately star-shaped polygons. GSCM performance is shown under various scenarios using simulation studies.
My development of GSCMs is partially motivated by the increasing need for accurate forecasts of the Arctic sea ice edge contour. In the rapidly changing Arctic, forecasts of the location of the sea ice edge contour, or the boundary around the ice-covered region, are needed for maritime planning. I introduce Mixture Contour Forecasting (MCF), a method that forecasts the location of the sea ice edge weeks to months in advance. MCF combines statistical modeling of sea ice edge contours with outputs of physical sea ice models, known as dynamic ensembles. Performance is evaluated for 2008-2016 using the European Centre for Medium-Range Weather Forecasts ensemble. MCF produces better calibrated forecasts than dynamic ensemble forecasts and other statistical reference forecasts.
I also briefly review Contour-Shifting, a statistical post-processing technique I developed to correct systematic errors in forecasts of the ice edge contour produced by dynamic ensembles.