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With climate change, the area covered by sea ice, or frozen ocean water, has rapidly reduced in the Arctic. Reduced sea ice cover has increased commercial shipping and tourism, while also increasing coastal inundation from surface waves and inhibiting mobility of Indigenous communities who travel and hunt on the sea ice. The opening of the Arctic and increased variability of the sea ice has increased demand for forecasts of where sea ice will be located weeks to months in advance. Predicting the location of the sea ice edge contour, or the boundary around the ice-covered region, is the primary need of forecast users. Typical sea ice forecasts are made using dynamic models, or physics-based prediction systems that approximate the evolution of sea ice and its surrounding environment. While these state-of-the-art models have predictive skill, they are hindered by biases and poorly reproduce observed variability. In this talk, I will present two statistical methods that combine to produce sea ice forecasts without these limitations. I first introduce Contour-Shifting, a technique that anticipates and corrects biases in dynamic model predictions of ice edge contours. I then introduce Mixture Contour Forecasting, a method for generating distributions of sea ice edge contours that accurately represent the frequency that different ice edges occur. Both these methods directly represent the ice edge contour as a connected sequence of points that are modeled jointly. The good performance of these methods highlights the potential for low-dimensional contour models as an alternative to traditional field-based spatial models for identifying and predicting boundaries around contiguous areas. This research also illustrates how combining the strengths of physics-based modeling and statistical methods can enhance predictions of climate change and aid in adaptation to its effects.