| Summary: | Climate change is a growing concern that causes sea level risings, heatwaves, and loss of habitats, and impacts the ecology. The climate change in the Arctic is specifically important as the Arctic helps reflect a significant amount of sunlight. This thesis applies Optimal Transport (OT) and Topological Data Analysis (TDA) to analyse the arctic ice data collected by NASA in 1999-2009. OT and TDA are fields in mathematics that consist of computational methods that study the shape and distribution of data. Our method is based on Wasserstein distance, a geometry-aware distance between distributions. Our method enables visualization tools such as time series plots and low-dimensional embeddings. These visualizations in combination with persistent homology reveal important insights from the data. In particular, we were able to identify missing data in the dataset, and detect and compare the freezing and melting times across years. Our most striking finding is a fundamental asymmetry between the freezing and melting processes. These preliminary findings demonstrate the potential of OT and TDA to reveal structure in climate change data, and more generally to satellite image data.
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