Mathematics of Planet Earth

On the closing afternoon of the Joint Meetings of the AMS and the MAA in San Diego, the attendees were treated to a fascinating talk by Kenneth Golden (from the University of Utah), who gave this year’s Gerald and Judith Porter Public Lecture, entitled “Mathematics and the melting polar ice caps”.

Ken was introduced by MAA president Paul Zorn, who explained that the Porter Public Lectures really were intended for the public, not just mathematicians, and he told us a little about Ken’s long fascination with and fundamental work on the polar ice, not based only on theoretical mathematics but important experiments that have taken him on expeditions to the Earth’s polar regions 15 times now, often accompanied by students, both graduate and undergraduate, who gain practical, life-changing experience as well as mathematical knowledge.

Paul mentioned that Ken had been the subject of an article yesterday in the San Diego Union Tribune, where the reported had compared Ken to “Indiana Jones”, and obligingly, that film’s theme music heralded Ken’s appearance on the podium, which drew a chuckle from the audience.

Ken started by stating that, yes, our climate is changing, and that, probably, the most dramatic changes are taking place at the poles. He reminded the audience of the evidence based on the satellite data from 1979 to 2000 showing how the Arctic sea ice summer minimum had fallen dramatically below the average sea ice minimum during that period, but he pointed out something evident from the data that most of us didn’t know: The observed decreases in the minimum Arctic sea ice were very much greater than what all of the accepted models predicted, which showed that something was missing in the current models.

Ken pointed out that it wasn’t just polar bears and walruses that care about sea ice, but oil companies and, eventually all of us. After all, the cryosphere (the part of the Earth’s surface that is covered with ice) makes up 7-10% of the surface of the Earth, and anything that affects it is very likely to affect the rest of the planet in a series of ripple effects that could induce dramatic changes in the climate of the whole Earth. For example, having much of the sea ice melt increases the danger that the land ice sheets over Greenland and Antarctica will also experience significant melting, which would raise sea levels around the world. As Ken said, sea ice is not just an indicator, it’s a major player in governing the world’s climate.

Ken then introduced his major mathematical themes visually by exhibiting photographs of sea ice at a wide range of scales, from sub-millimeter to more than 100 kilometers, pointing out that sea ice, far from being a homogeneous medium, has complicated structures at all scales, and understanding how these interact and induce macroscopic properties that can be incorporated into global-scale climate models is a fundamental challenge that has been the focus of his work and that of his students.

His point was that, while, at first glance, sea ice looks like a barren, frozen, impermeable cap, it’s really a complex, porous composite material, whose structure is strongly affected by the amount of brine (i.e., salt) in the ice, which causes the formation of micro-brine channels that support percolation effects and generate an astonishing array of phenomena, interacting strongly not only with physical processes but biological processes as well. For example, salt water transport brings nutrients into the ice to feed the algae, which feed the krill, which feed the whales, and so on.

The main part of the talk that followed explored how mathematical concepts such as percolation theory, composite materials, fractals, statistical physics, and multi-scale homogenization (a set of techniques for approximating complicated local composite structures by more homogeneous models that can help incorporate some of properties generated by the local structures into models at higher scales) have entered into his work and allowed him to make discoveries that have greatly expanded our ability to model what is happening to the sea ice in the polar regions.

As exciting as it was to see how formerly exotic and abstract concepts such as fractal dimensions enter into these practical models, an equally exciting part of the story was Ken’s experimental work, which had taken him on polar expeditions a total of 15 times so far, had given him a chance to do very fundamental experiments, and had also allowed him to engage undergraduates and graduate students in fundamental research. He told some great stories about his students in Utah who had become intrigued with his work and wound up doing creative, original work AND had had the chance to go on polar expeditions as well.

Another of his main themes was that the power of mathematics was in its cross-pollination of different areas, that concepts developed in one area turn out to have applications in many other areas, and he convincingly demonstrated this by giving many examples that had come up in his research.

Ken finished by premiering a truly entertaining and informative video of his most recent polar expedition, his 15th, to study sea ice around Antarctica, at the end of which he was roundly applauded.

The audience left with a deep appreciation, not only of the importance of understanding the challenges that climate change poses for us, nor even just that mathematics has a crucial role to play, but for the power of enthusiasm and dedication to teaching and research to make a difference in people’s lives.

Robert L. Bryant, Director
Mathematical Sciences Research Institute
17 Gauss Way
Berkeley, CA 94720-5070
MSRI
bryant@msri.org