Baek, Somyi2020-11-172020-11-172020-07https://hdl.handle.net/11299/217142University of Minnesota Ph.D. dissertation. July 2020. Major: Mathematics. Advisor: Richard McGehee. 1 computer file (PDF); vii, 71 pages.Arctic ice extent serves as one of the best proxy indicators of climate change. The annual Arctic ice extent average has declined at an alarming and continual rate for the last 50 years. The Arctic ice is without a doubt becoming vulnerable and fragile in both thickness and resilience, and scientists around the world worry about witnessing an ice-free summer in the imminent future. Most climate scientists predict that the first ice-free Arctic summer will happen before or around 2050, including the researchers of the Intergovernmental Panel on Climate Change (IPCC). The majority of these forecasts are made with ocean-atmosphere general circulation models (GCMs), highly complex in their input and output, which often renders traditional mathematical analysis difficult. This thesis aims to develop a mathematically tractable and analyzable model of the Arctic sea ice extent using the structure of Budyko-type energy balance models (EBM) and a previous master's student Wen Xing's model, with the goal of making a deterministic prediction for the first ice-free Arctic summer. The new model, which will be called the Daily Budyko model, extends the original annual average Budyko-type EBM to the daily scale and recalibrates model parameters for the domain of the northern polar region. In addition, new model equations are constructed using the main idea of proportional growth in Xing's model. The Daily Budyko model predicts September of 2051 for the first ice-free Arctic summer, which is in line with the IPCC's forecast of around 2050.enArctic IceClimate ChangeDynamical SystemsEnergy Balance ModelThesis or Dissertation