Teaching the Math of Climate Science

When you’re just getting started on simulating the weather, it’s good to start with an aqua-planet. That’s a planet like our Earth, but with no land!

Click on this picture to see an aqua-planet created by H. Miura:

Of course, it’s important to include land, because it has huge effects. Click on this to see what I mean:

This simulation is supposed to illustrate a Madden–Julian oscillation: the largest form of variability in the tropical atmosphere on time scales of 30-90 days! It’s a pulse that moves east across the Indian Ocean and Pacific ocean at 4-8 meters/second. It manifests itself as patches of anomalously high rainfall… but also patches of anomalously low rainfall. Strong Madden-Julian Oscillations are often, but not always, seen 6-12 months before an El Niño starts.

Wouldn’t it be cool if math majors could learn to do simulations like these? If not of the full-fledged Earth, at least of an aqua-planet?

Soon they will.

Climate science at Cal State Northridge

At the huge fall meeting of the American Geophysical Union, I met Helen Steele Cox from the geography department at Cal State Northridge. She was standing in front of a poster describing their new Climate Science Program. They got a ‘NICE’ grant from NASA to develop new courses—where ‘NICE’ means NASA Innovations in Climate Education. This grant also helps them run a seminar every other week where they invite climate scientists and the like from JPL and other nearby places to talk about their work.

What really excited me about this program is that it includes courses designed to teach math majors—and others—the skills needed to go into climate science. Since I’m supposed to be developing the syllabus for an undergraduate ‘Mathematics of the Environment’ course, I’m eager to hear about such things.

She told me to talk to David Klein in the math department there. He used to work on general relativity, but now—like me—he’s gotten interested in climate issues. I emailed him, and he told me what’s going on.

They’ve taught this course twice:

Phys 595 CL. Mathematics and Physics of Climate Change. Atmospheric dynamics and thermodynamics, radiation and radiative transfer, green-house effect, mathematics of remote sounding, introduction to atmospheric and climate modeling. Syllabus here.

They’ve just finished teaching this one:

Math 396 CL. Introduction to Mathematical Climate Science. This course in applied mathematics will introduce students to applications of vector calculus and differential equations to the study of global climate. Fundamental equations governing atmospheric dynamics will be derived and solved for a variety of situations. Topics include: thermodynamics of the atmosphere, potential temperature, parcel concepts, hydrostatic balance, dynamics of air motion and wind flows, energy balance, an introduction to radiative transfer, and elementary mathematical climate models. Syllabus here.

In some ways, the most intriguing is the one they haven’t taught yet:

Math 483 CL. Mathematical Modeling. Possible topics include fundamental principles of atmospheric radiation and convection, two dimensional models, varying parameters within models, numerical simulation of atmospheric fluid flow from both a theoretical and applied setting.

There’s no syllabus it yet, but they want to focus the course on four projects:

1. Modeling a Lorenz dynamical system, using the trajectories as analogies to weather and the attractor as an analogy to climate.


2. Modeling a land-sea breeze.

3. Creating a 2d model of an aqua-planet: that is, one with no land.

4. Doing some projects with EdGCM, a proprietary ‘educational general climate model’.

It would be great to take student-made software and add it to the Azimuth Code Project. If they were well-documented, future generations of students could go ahead and improve on them. And an open-source GCM would be a wonderful thing.

As more and more schools teach climate science—not just to Earth scientists, but also to math and computer science students—this sort of ‘open-source climate modeling software’ should become more and more common.

Some questions:

Do you know other schools that are teaching climate modeling in the math department?

Do you know of efforts to formalize the sharing of open-source climate software for educational purposes?

2 Responses to Teaching the Math of Climate Science

  1. Eric says:

    Many GCMs are essentially open-source these days. CESM and all of its predecessors have been publicly available and community-built. You can now download the source code for the GISS model (the one upon which EdGCM is based) and the GFDL model. Of course they are not simple to compile and run. There is nobody who will get paid to turn these models into “apps” that would be simple to install and run. What would be nice is a web interface to set the parameters and run one of these models. Conceivably, this could be done in such a way that it could either control a local installation of the model or a remote installation hosted somewhere else. This is somewhat akin to what EdGCM is, but the number of parameters that you can change with EdGCM is very limited.

    Herein lies the challenge: The real power of GCMs is to test the sensitivity of the model solution to different boundary conditions or internal physical parameters. There are so many interesting possibilities, that it is difficult to conceive of an interface that students could become familiar enough to use in a short period of time that would also allow them to unlock all of this potential.

    • Nathan Urban says:

      It’s not really feasible to build a web interface to run a modern AOGCM with perturbed parameters. Or rather, you could build the interface, but you wouldn’t get results within any reasonable time frame. CESM takes over 2 real-time days to simulate 100 years of climate … using 2000 cores on a Cray XT5 supercomputer. And if you perturb parameters, you may have to spin the model up for more than 100 years just to get to a self-consistent and physically reasonable quasi-steady state (especially if you perturb something outside of the atmosphere, which has faster response times). If you stick to small perturbations of atmospheric parameters, maybe you could cut this time by 10, but you’re still talking about hours of computing time on thousands of cores. You could also lower the resolution (e.g. closer to EdGCM), but I still don’t see this being feasible.

      Even with a model as simple as EdGCM, I don’t think this is very feasible … you’re certainly not going to get results very quickly, although I haven’t kept up with its performance on multicore systems. (Last time I used it, it wasn’t multicore-aware.) Anyway, I think it’s a benefit, not a limitation, that EdGCM has fewer perturbable parameters than a modern AOGCM. Users aren’t going to know what to do with hundreds of esoteric parameters.

      Perhaps more feasible would be a web interface to browse the output of the existing Climateprediction.net perturbed physics ensembles. These were generated by distributing parts of AOGCM simulations to users’ PCs and waiting the necessary weeks or months for outputs to be produced.

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