The latest Assessment Report of the Intergovernmental Panel on Climate Change (http://www.ipcc.ch/report/ar5/) states the current warming of our climate system is unequivocal. This warming is driven by positive radiative forcing, which has led to an uptake of energy by the climate system. Moreover, atmospheric greenhouse gas concentrations have increased to levels unprecedented in the last 800,000 years. In addition, the ongoing loss of Arctic Sea ice, Northern Hemisphere spring snow cover, and ice mass in the Greenland ice sheet is contributing to a positive feedback loop that leads to warmer temperatures. In this presentation we demonstrate how insights into each of these fundamentally important factors in climate change can be conveyed to students through Energy Balance Models (EBM).
We begin with an EBM for global average surface temperature, highlighting the role played by parameters representing atmospheric greenhouse gas concentrations and ice cover in determining the radiative energy balance. We then present an EBM for the average surface temperature as a function of latitude, thereby incorporating the transportation of heat by the atmosphere and oceans across latitudes. Finally, we couple the surface temperature with an ice sheet whose southern edge is allowed to move with changes in the local surface temperature. Depending upon greenhouse gas concentrations, the model yields stable equilibrium behavior running the gamut from a completely glaciated "Snowball Earth" to an ice-free "hothouse Earth," each of which has occurred in the Earth’s past (though with the hothouse world perhaps of greater current interest). Important concepts such as climate tipping points and hysteresis occur naturally in this model.
After teaching mathematics in the Peace Corps, followed by three years as a public high school mathematics teacher, Jim Walsh began his graduate studies at Boston University. Specializing in dynamical systems, Jim received the PhD degree in 1991. Jim has been a member of the Mathematics Department at Oberlin College since 1991, where he teaches a variety of courses and engages in research in applied dynamical systems. Jim has written articles concerning mathematical models in celestial mechanics, queueing theory, economics, wastewater treatment systems and, most recently, conceptual climate systems. A member of the Mathematics and Climate Research Network, Jim was part of a group of mathematicians that designed and offered short courses on conceptual climate modeling for the Mathematical Association of America, at both the national and sectional levels. Jim was also invited to present a minitutorial on conceptual climate models at the inaugural 2016 SIAM Mathematics of Planet Earth Conference. In addition to incorporating climate modeling into his differential equations course at Oberlin, Jim has offered a junior-level course on mathematics and climate modeling. Jim’s research program in climate modeling was recognized by Oberlin through his receipt of a 2016-17 Research Status Award. During the 2016-17 academic year Jim continued his ongoing research into the study of interesting mathematical questions arising in the analysis of the dynamics of conceptual climate models.