Graduate Student Seminar

Title: Nonsmooth dynamical systems and Arctic sea ice
Speaker: Kaitlin Hill
Speaker Info: PhD student in Applied Mathematics at Northwestern
Brief Description:
Special Note:

As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance models have been shown to be sensitive to how ice-albedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing parameter associated with ice-albedo feedback tends to zero, which introduces a discontinuity boundary to the dynamical systems model. Our analysis provides a case study where we use the system in this limit to guide the investigation of bifurcation behavior of the original albedo-smoothed system. In this case study, 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 re-introduced. This analysis provides an alternative perspective on how parameters of the model affect bifurcation behavior. We expect our approach, which exploits the width of repelling sliding intervals for understanding the hysteresis loops, would carry over to other positive feedback systems with a similar natural piecewise-smooth limit, and when the feedback strength is likewise modulated with seasons or other periodic forcing.
Date: Friday, February 26, 2016
Time: 4:00pm
Where: Lunt 105
Contact Person: Corinna Wendisch
Contact email: wendisch@math.northwestern.edu
Contact Phone: 847-644-5889
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