This exercise is used in an elective senior seminar course on numerical modeling in the Earth and Environmental Sciences. I also occasionally use it in my elective senior seminar on Paleoclimatology.

Students have already acquired basic STELLA modeling skills in exercises earlier in the course. They have been introduced to the concepts of reservoirs and fluxes, boundary conditions, initial conditions, system behavior (e.g. linear, exponential, oscillatory), and how to determine an appropriate time step for simulation.

This is the first in a series of two lab exercises on the climate system. The second is a model of Watson and Lovelock's Daisyworld, which builds on the simple black body plus albedo model in this exercise to incorporate a biosphere made of black and white daisies whose growth depends on temperature and whose albedo affects temperature.

The purpose of this exercise is to demonstrate a method for numerically modeling complex systems by starting simple and adding complexity in a step-wise fashion. Toward the end of my numerical modeling course, students have the opportunity to develop their own project on a topic of interest to them. They often select highly complex systems, and toss in everything but the kitchen sink when they first begin working. They get lost in trying to make the fine points of their models work and often end up neglecting to see if the main architecture is working correctly. When this happens, I ask them to reflect on the Earth energy balance model lab in which we built complexity very gradually and then ask them to try to pick out the most fundamental processes that they're trying to model in their chosen system, make sure those are working correctly, and then add on from there.

Students read two book chapters that discuss the fundamental physics of energy absorption and emission by Earth's surface and its atmosphere and then develop numerical models in STELLA to calculate planetary temperature based on these processes. With each step in complexity, they compare their results to Earth's actual temperature to evaluate how well the model system represents the actual system.

Each week, students present the papers we have read that form the basis of that week's modeling project and thus have an opportunity to work on their oral presentation skills. Students also work on their writing throughout the course as they answer questions in the labs.

In this lab students learn how to create hierarchies of models of increasing complexity to understand some physical process - in this case, the absorption of solar energy by the Earth and its radiation of that energy back to space. Whenever one sets out to understand a complex phenomenon, it is best to start with the simplest possible model that explains most of the behavior of that phenomenon and to build upward in complexity gradually. In this exercise students learn how to do this by modeling the energy balance at Earth's surface. The exercise begins by assuming that the Earth is a perfect black body lacking an atmosphere, then moves on to incorporate the fact that Earth reflects much of the solar radiation incident upon it, and later incorporates the fact that Earth has an atmosphere. Each time something is added to the model students evaluate the output and compare it to actual Earth surface conditions to see how well each refinement captures the reality of the physics of heat absorption, exchange, and emission.

Students write up the answers to a number of questions posed in the exercise and also paste in graphs of their model outputs. I then grade these responses.

Few, A.A., 1996, System Behavior and System Modeling, Sausalito, CA: University Science Books, p. 27-37. I don't have students read this because it gives away too much of the model and I want them to think through the steps themselves. A large part of the models constructed here comes from Few's way of thinking about the problem, however, so you should get this reference for yourself.

Graedel, T.E., and Crutzen, P.J., 1993, Atmospheric Change: An Earth System Perspective, New York: W.H. Freeman and Company, 446 p.

Harte, J., 1988, Consider a Spherical Cow, Sausalito, CA: University Science Books, p. 69-72, p. 160-167.