| Summary: | Thesis (Ph.D.)--University of Washington, 2020 This dissertation develops statistical methods for modeling contours. Particular emphasis is placed on forecasting the sea ice edge contour, or the boundary around ocean areas that are ice-covered. Current sea ice forecasts are largely based on dynamic ensembles. These physics-based prediction systems numerically solve differential equations to approximate possible evolutions of sea ice and its surrounding environment. While these dynamic ensemble forecasts provide information about future sea ice, they have systematic differences from observations and incorrect variability. I develop two methods to improve forecasts of the sea ice edge contour in the Arctic. I first introduce Contour-Shifting, a statistical method to anticipate and correct systematic errors in forecasts of the sea ice edge contour produced by dynamic ensembles. I then propose Mixture Contour Forecasting, a method to generate sea ice edge contours that have variability similar to observations. These generated contours can be used to predict the probability of sea ice presence weeks-to-months in advance. Both Contour-Shifting and Mixture Contour Forecasting represent the sea ice edge contour directly as a connected sequence of points. I extend this approach of modeling the points on contours directly with the development of the Gaussian Star-Shaped Contour Model. This model can be employed for inference and prediction of contours that enclose star-shaped polygons or approximately star-shaped polygons. Approaches for fitting this model and assessment metrics for contours are also introduced.
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