Handling editor: Evelyn Sander

Climate Math in San Diego

Mary Lou Zeeman, Chair, SIAG/DS

Earth and its atmosphere. The atmosphere is just visible as the thin blue shell around the earth. From http://pds.jpl.nasa.gov/planets/welcome/earth.htm

It is a pleasure for me to serve as the new chair of SIAG/DS. Our activity group, journal and web portal are healthy, we have an active, forward looking group of officers, and our program directors already have the plans for Snowbird 2009 well under way.

My own research has been primarily on searching for relationships between the geometry, algebra, and dynamics in models of competing species and on rhythms in our neuroendocrine axes, particularly in the menstrual cycle. The research and teaching collaborations I have established with biologists, environmental scientists and computer scientists have been extremely enriching for me, and have shown me the power and breadth of dynamical systems as an intellectual framework for addressing problems in the applied and social sciences. This experience, and the data, are what drive my conviction that we offer a wealth of largely untapped resources for addressing problems related to the state of our planet.

The climate science community is already very mathematical, and open to joint conferences and collaboration with mathematicians. At the Climate Math sessions of the Joint Math Meetings (JMM) in San Diego in January, we had a four day program of lectures and discussions featuring climate scientists, mathematicians, economists and California Congressman Jerry McNerney. See the recent articles describing the sessions by Pat Kenschaft [1,2], and the lecture notes from the talks posted at [3,4, and 5]. In particular, we had a productive audience discussion focused on how we can empower our community to help tackle the mathematical challenges in climate research, so I would like to share some of those ideas here.

Mathematical Opportunities

A group of us at Cornell teach a class called the State of the Planet [6], where our theme is "Whatever your talent, whatever your passion, you can use them to help the planet."

It's a powerful philosophy - giving each of us the liberty to figure out how to focus the type of math we enjoy on problems that we care about. Climate change research is full of mathematical challenges, ranging from process modeling with continuous and stochastic dynamical systems, to inverse problems, data assimilation, efficient numerical methods, quantifying uncertainty in models of inherently chaotic systems, integrating climate and economics models to address “what if” questions, and more. For more detail, see the white paper by Dana McKenzie [7] resulting from the first MSRI Climate Change workshop in April 2007, [8], the “Short Introduction” to the consequences of chaos for weather and climate prediction by Leonard Smith [9], and the 2007 Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) [10] for an up-to-date objective summary of the Climate Change literature and associated data. Global sustainability and resource management questions from fisheries and forests to energy and carbon emissions raise new classes of problems at the interface of mathematics, economics and computer science, in which a dynamical system modeling the resource is perturbed at discrete points in time by optimization based policy or management decisions. How do we classify the behavior of such systems?
		1000 year observed changes in atmospheric greenhouse gas concentrations from ice core and modern data. Measurements are shown from ice cores (symbols with different colors for different studies) and atmospheric samples (red lines). From IPCC, AR4, WG1, SPM, 2007.

The classic tragedy of the commons problem can be viewed as a game theoretic but also multi-scale problem, as it lies in the tension between the short- and long-term effects of our behavior. Spread of disease and ecosystem preservation both take on new dynamic spatial components as species move poleward in response to warming habitats. The concept of tipping point that has emerged in the popular press in the context of polar ice melting, ocean circulation, fisheries and more is completely natural to us as a bifurcation, and begs our attention. Another way to learn more about questions that could use your skills is to explore an interface journal such as Natural Resource Modeling [11]. The 1997 AAAS Presidential Address by Jane Lubchenco [12] is also both informative and inspiring.

Bridging Communitees

To collaborate with colleagues in another discipline, we need to learn enough of each other's language to be able to understand the subtleties our colleagues are explaining to us. In the interface between dynamical systems and biology, it becomes most exciting when the mathematician knows enough about how the data is collected to be able to suggest precise experiments to distinguish between models, or when the biologist can point to a surprising jump in the data, and suggest we analyze the bifurcation. As a community, we don't yet know the language of climate change research. Given the importance of the problems, the mathematical richness they contain, our potential to help, and the motivating power of the subject, let's work with SIAM and SIAG/DS to create an active learning community and accelerate the process.
		150 year observed changes in global mean temperature, sea level and snow cover. All differences are relative to corresponding averages for the period 1961-1990. Smoothed curves represent decadal averaged values while circles show yearly values. From IPCC, AR4, WG1, SPM, 2007.

Conferences.

If you are coming to a conference (e.g. Snowbird, the SIAM annual conference, or the JMM) look for the minisymposia and workshops on Environmental and Climate Math. It's an easy way to get a glimpse at the field, and the people in it. Also keep your eyes on the math institutes and the funding agencies, as they embrace this area. For example, there is a Climate Change Summer School at MSRI [13] this summer, and more planned for the future. If you already know a Climate Math question that interests you, please run a minisymposium at any conference you think would have a promising audience. Your minisymposium might have the traditional goal of highlighting what has been achieved, or the less traditional but equally important goal of highlighting the open problems. It helps to choose an interdisciplinary team of organizers, to mix mathematician and experimentalist speakers, and to think creatively about how to stimulate cross-disciplinary discussion among the audience. Note that to bring a speaker to a conference outside their own discipline, you may need to help cover their expenses. The NSF Division of Mathematical Sciences (DMS) welcomes proposals for conferences, either through its disciplinary programs [14] or through its Special Meetings program [15]. Proposals need to be submitted through the Office of Sponsored Research (or its equivalent) at your university; instructions can be found in the 2008 NSF Grant Proposal Guide [16]. In general, it is a good idea to contact the program officer to discuss what are "allowable" expenses; helpful guidelines for conference proposals submitted to DMS are available upon request from Dr. Hans G. Kaper [17]

Anthropogenic climate change drivers, impacts and responses. From IPCC AR4, SYR, 2007.

Publications

Can you write a survey article that would explain an open problem in climate or sustainability research to the dynamical systems or broader math community? If you can't do it alone, could you do it in collaboration with a colleague who knows the question but not our language? Please do! Articles of this nature would really help, whether they be at the level of SIADS, SIAM News, DSWeb Magazine or another appropriate target audience.

Climate Math Website

We are hoping to develop web materials, over the next year or two, designed to introduce mathematicians to climate and sustainability research. Suggestions for the site from the JMM discussion included: 1) a summary of open problems; 2) descriptions of climate models of simple and intermediate complexity, together with matlab code for experimentation with the models; 3) links to survey articles; 4) annotated reading lists focused on particular physical processes or problems; 5) an introduction to the archive of IPCC model output and 6) educational materials for bringing into the classroom at a variety of levels. If you have ideas or materials the site, or would like to help with site development, please let me know [18].

Education

If you have taught a course that included a component on mathematics and sustainability, please share your experience with DSWeb Magazine readers. What worked, and what didn't? For example, if you organized a reading course on climate modeling, what did you read? What resources gave you most insight? If you brought a sustainability theme to your calculus or modeling class, what data are you using? Do you have problem sets on the web that others could use? Can you recommend a textbook for a new course, or papers or book chapters that fit neatly into existing courses in the math curriculum? The October 2008 issue of DSWeb Magazine will include a follow up to this article incorporating your contributions. Send ideas, comments, links and suggestions to DSWeb Magazine Section Chief Editor, Evelyn Sander, at [email protected] by September 15, 2008.

We welcome other suggestions, and look forward to hearing from you!

Mary Lou Zeeman currently splits her time between Bowdoin College, where she is the R. Wells Johnson Professor of Mathematics, and Cornell University, where she is a Visiting Professor of Neurobiology and Behavior.

References

[1]		Pat Kenschaft, "Mathematicians recruited for Climate Change Research," MAA Focus 28 (March 2008) pp14.
[2]		Pat Kenschaft, "Climate Change: a Research Opportunity for Mathematics?" Notices of the AMS, to appear.
[3]		Lecture Notes of AMS-SIAM Special Session on Environmental Mathematics at the 2008 Joint Math Meetings in San Diego..
[4]		Inez Fung, Lecture Notes of the SIAM Invited Lecture at the Joint Math Meetings in San Diego.
[5]		Lecture Notes of the SIAM minisymposia on Climate Math at the Joint math Meetings in San Diego.
[6]		Krystal L. Rypien et al., "Students unite to create State of the Planet course," Nature 445 (June 2007) pp775.
[7]		D. McKenzie, Mathematics of Climate Change, Mathematical Sciences Research Institute, Berkeley, CA, 2007. Link to the PDF of the white paper.
[8]		MSRI Symposium on Climate Change: From Global Models to Local Action, April 2007
[9]		Leonard Smith, CHAOS: A Very Short Introduction, Oxford University Press, 2007.
[10]		"IPCC Fourth Assessment Report," Intergovernmental Panel of Climate Change, Geneva, Switzerland, 2007. Website linking to the report.
[11]		Natural Resource Modeling, Blackwell Publishing.
[12]		Jane Lubchenco, "Entering the Century of the Environment: A New Social Contract for Science," Science, 279 (Jan 1998).
[13]		Climate Change Summer School, Mathematical Sciences Research Institute, Berkeley, CA, July 14-August 1, 2008. Workshop website.
[14]		National Science Foundation, Division of Mathematical Sciences, Disciplinary Programs.
[15]		National Science Foundation, Division of Mathematical Sciences, Special Meetings Program.
[16]		National Science Foundation, Division of Mathematical Sciences, Grant Proposal Guide.
[17]		Hans Kaper, National Science Foundation, Email: [email protected] .
[18]		Mary Lou Zeeman, Bowdoin College, Email: [email protected] .