
September 12, 2017 

An Introduction to Planetary Energy Balance,
Richard McGehee, School of Mathematics 


A planet's global mean temperature can be estimated using elementary physics:
conservation of energy and the theory of black body radiation. Much of the recent interest in
the search for extrasolar planets focuses on the "Goldilocks Zone," the region around a star
where a planet could have liquid water on its surface. 


September 19, 2017 

An Introduction to Budyko's Model,
slides by Richard McGehee, presentation by Alice Nadeau, School of Mathematics 


Budyko's equation models the global mean surface temperature as a function of latitude, taking into account the solar input, the surface albedo, the outgoing radiation, the redistribution of heat across latitudes. Since the surface albedo is a function of latitude, the equation can be used to model glaciations. 


October 3, 2017 

Dynamical systems for planetary and lunar climates,
Alice Nadeau, School of Mathematics 


October 10, 2017 

An Energy Balance Model of Arctic Sea Ice,
Kaitlin Hill, School of Mathematics 


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 icealbedo feedback is parameterized. We analyze an Arctic energy balance model in the limit as a smoothing parameter associated with icealbedo 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 albedosmoothed system.



October 17, 2017 

Permafrost Response to Climate Change via Budyko’s Model,
Richard McGehee, School of Mathematics 


As the Arctic permafrost melts, it releases sequestered carbon into the atmosphere. Budkyo's model can be used to predict the loss of permafrost due to increasing global temperatures.



October 31, 2017 

Huybers' 2007 glacial cycles model,
Somyi Baek, School of Mathematics 


One of the most interesting open questions in Paleoclimate science is the midPleistocene Transition (MPT) problem, which surrounds the unknown cause that drove the change in the dominant period of deglaciation from 41 kyr to 100 kyr. Huybers’ model was first suggested by Peter Huybers in 2007 to explain the glacial variability of the earth’s climate, in hopes of shedding light on what prompted the sudden shift in the periodicity of the midPleistocene. I will be presenting his 2009 paper, which roughly goes through these four chapters: (1) proposal of the depth derived age model, (2) statistical testing to determine which of the three Milankovitch cycles paces the glacial cycles, (3) observation of skipped obliquity cycles and linear trend in power spectrum and mean (which serves as motivation for his model structure), (4) proposal of Huybers' model and discussion of model fit. brium disappears in the nonsmooth limit, a pseudoequilibrium of the sliding flow appears. 


November 7, 2017 

Saddle behavior in a nonsmooth limit of some planar nonsmooth systems,
Kaitlin Hill, School of Mathematics 


Many conceptual climate models are formulated as nonsmooth systems, or with a nonsmooth limit. Inspired by behavior seen in several conceptual climate models that limit to nonsmooth systems, we investigate the persistence of a saddle equilibrium in the nonsmooth (Filippov) limit of three planar systems. Although the saddle equilibrium disappears in the nonsmooth limit, a pseudoequilibrium of the sliding flow appears. 


November 21, 2017 

How can we define and identify stability  or persistence?  in diverse ecological communities?,
Adam Clark, German Centre for Integrative Biodiversity Research, Leipzig 





