## Dan Stinebring, PhD

**Professor and Chair of the Physics and Astronomy Department**

** Oberlin College**

“Introduction to Climate Modeling” is a seminar-style course that I teach to Oberlin College students who are serious about science but do not consider themselves particularly math or computer oriented. Students don”t need to have any prior experience with the course”s two foci: climate science and computational modeling. In spring 2013 I taught the course to nine students, most of whom were Geology or Environmental Studies majors. I found it an interesting demographic that 7 of the 9 students were women. Nova is the modeling platform for the course, and it was a spectacular success in giving students quick entry into a rich and visually oriented modeling environment.

The course is built around a series of heuristic (i.e. teaching-oriented) models, most of which were drawn from Walter Robinson”s book “Modeling Dynamic Climate Systems.” For example, in the first week of the class we studied the Leaky Bucket model. In Nova the bucket is a stock, and there is a constant flow of water into the bucket. The interesting feature of the model, however, is that the outflow rate depends on the height of water in the bucket, as it would in an actual bucket because of increased water pressure as the level rises. By the end of our first class meeting I had been able to show ”” in a credible and convincing way ”“how this model is constructed in Nova. For their first assignment students were able to manipulate this Nova model and explore it fully in a series of guided exercises, which even included the introduction of stochastic input flow. Very exciting stuff for students who had no programming experience but had always wanted to be able to model real-world situations!

Honestly, I never had to worry about comfort level with Nova. I spent very little time on explicit Nova instruction in the classroom. As part of weekly assignments I referred them to the excellent online tutorials and then built exercises around those tutorials with a climate modeling theme. In class I would show them more complex models drawn from Robinson”s book and then ask them to modify and explore the models further on their own. These capable and motivated students had no trouble using Nova because we stayed with a basic stock-flow paradigm and because they found the visual interface intuitive, robust, and full-featured. (With more time and more personal expertise I would expand our use of Nova to spatial and agent-based models.)

It was easy for me to use the stock-flow models in Robinson”s book in my class. Robinson built them in STELLA because his book was part of a series in modeling using the stock-flow paradigm, the only modeling paradigm available in STELLA. Conversion to Nova was a simple two-step process. I loaded the model in STELLA and exported the underlying equations to a text file. I then used a STELLA to Nova converter that the Nova Team provided to produce a working Nova model that was fully equivalent and contained all of the complicated equations, constants, and parameter settings that are typical of the interesting models that Robinson presents in his book. (Some visual tweaking of the models was then needed, but the functionality was present from the beginning.) This allowed me to build the course around heuristic models that were integrated with the climate science that students were learning on a weekly basis from their textbook reading and class discussion. These models included Earth”s energy balance without an atmosphere (Naked Earth), a model for how the greenhouse effect works (One-layer Atmosphere), and a model for how an ice sheet grows and shrinks. The latter also included the ability to introduce quasi-periodic Milankovitch forcing due to slight Earth orbital and tilt variations, which leads to the approximately 100,000 year periodicity in the onset of ice ages.

The course also included two half-semester group modeling projects where teams of three students would build a model, present it to the class, and then write a report about its fundamentals and its behavior. The three projects that the groups undertook in the second half of the semester give a good sense of the level of sophistication that the students were able to achieve with Nova and their own growing sense of how to extract essentials from a complicated situation. One group modeled the growth of algal blooms on Lake Erie resulting in hypoxic dead zones in the lake, a serious current problem for our region. They started with a simple two stock model based on the standard predator-prey equations. However, they realized that this didn”t properly capture the situation and ultimately expanded this to a four stock system ”” algae, detritus, nutrients, and oxygen ”“that they found described in an applied mathematics journal article. By this time in the semester they were able to go from the four coupled differential equations presented in the article to a working Nova model within a few hours with no help from me and with little formal background in differential equations (all of the students were familiar with calculus concepts, but none of them considered themselves particularly mathematically adept). The behavior of their model made it clear that, when nutrient levels are high (e.g. because of fertilizer runoff), it was all too easy to create self-sustaining algal blooms that eliminated oxygen in large portions of the lake!

The other two groups started with models presented in the Robinson book ”” a model of thermohaline circulation in an ocean basin and an energy balance model for different latitude zones ”” and explored them and started to extend beyond them. Because Nova has a much richer set of tools than STELLA for modularization and spatially extending models, students were able to at least get started on extending the models in this manner.

In summary, because of its intuitive interface and high quality construction, Nova was an excellent platform for Introduction to Climate Modeling. Its ability to easily import STELLA models was a huge plus since I was then able to employ the well-constructed and thoroughly discussed heuristic models in Robinson”s book as a mainstay of the class. I used them throughout the semester, and students worked exercises on them and then, in some cases, used them as the basis for their group modeling efforts.

In my 23 years of teaching at Oberlin this was one of the most intellectually stimulating and pedagogically satisfying courses that I have taught. From discussions with them during the semester and from my own sense of what excitement looks like in the classroom, it was clear that this hands-on, Nova-based pedagogical approach worked for them, too!

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