Bifurcation Analysis of a Piecewise-Smooth Arctic Energy Balance Model

Kaitlin Hill

doi:https://doi.org/10.21985/N2CX7W

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Bifurcation Analysis of a Piecewise-Smooth Arctic Energy Balance Model

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This dissertation investigates a single-column model for Arctic energy balance in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero. This limit is a common modeling approximation used in conceptual climate models, and we explore the implications of taking this limit on bifurcations associated with the model. The model takes the form of a periodically-forced ordinary differential equation and incorporates key system feedbacks like the sea ice-albedo feedback and nonlinear sea ice thermodynamic effects. Taking the limit as the smoothing parameter associated with ice-albedo feedback goes to zero creates sliding regions along a discontinuity boundary in phase space, so that the system becomes Filippov. Our analysis in the Filippov limit distinguishes between the three possible types of periodic solutions: solutions where the Arctic has sea ice year-round, solutions with no Arctic sea ice year-round, and solutions where the Arctic only has sea ice during part of the year. For each type of periodic solution, we calculate its Poincare map, its stability, and necessary condition(s) for it to exist. We analyze the bifurcations in this system using a case study model. In this case study, we use the Filippov limit of the system to guide an investigation of bifurcation behavior of the original albedo-smoothed system. We demonstrate that certain qualitative bifurcation behaviors of the albedo-smoothed system can have counterparts in the limit with no albedo-smoothing. We use this perspective to systematically explore the parameter space of the model. For example, we uncover parameter sets for which the largest transition, with increasing greenhouse gases, is from a perennially ice-covered Arctic to a seasonally ice-free state, an unusual bifurcation scenario that persists even when albedo-smoothing is reintroduced. This analysis provides an alternative perspective on how parameters of the model affect bifurcation behavior.

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