I use this exercise in a senior seminar course on numerical modeling in the Earth and Environmental Sciences.

Students have already acquired skills in basic STELLA programing, understand the concepts of reservoirs and flows, initial conditions, boundary conditions, and various types of system behavior (linear, exponential, oscillatory). They have also previously completed an exercise on Earth's energy balance and temperature.

This exercise takes place in the middle of the course as a lab assignment and follows an exercise in which students create models to calculate Earth's temperature based on its radiative balance with incoming solar energy. (See the energy balance model exercise.)

The Daisyworld model introduces students to a simple planetary system that is capable of self-regulation through the presence of negative feedbacks. The model also requires that students use if-then-else logical statements and that they think carefully about model initial conditions.

Students create their own model of Daisyworld in the box modeing software STELLA and then use it to perform a number of experiments, all of which they must critically evaluate.

Each week students present the papers that form the basis for the week's modeling project, giving them an opportunity to work on their oral presentation skills. They also acquire skills in reading articles in the primary Earth and Environmental Science literature, and have the opportunity to work on their writing through their answers to assignment questions.

The Daisyworld model created by Andrew Watson and James Lovelock (1983, Tellus, v. 35B, p. 284-289) is a wonderful example of a self-regulating system incorporating positive and negative feedbacks. The model consists of a planet on which black and white daisies are growing. The growth of these daisies is governed by a parabolic shaped growth function regulated by planetary temperature and is set to zero for temperatures less than 5 ºC or greater than 40 ºC and optimized at 22.5 ºC. The model explores the effect of a steadily increasing solar luminosity on the growth of daisies and the resulting planetary temperature. The growth function for the daisies allows them to modulate the planet's temperature for many years, warming it early on as black daisies grow, and cooling it later as white daisies grow. Eventually, the solar luminosity increases beyond the daisies' capability to modulate the temperature and they die out, leading to a rapid rise in the planetary temperature. Students read Watson and Lovelock's original paper, and then use STELLA to create their own Daisyworld model with which they can experiment. Experiments include changing the albedos of the daisies, changing their death rates, and changing the rate at which energy is conducted from one part of the planet to another. In all cases, students keep track of daisy populations and of planetary temperature over time.

Students answer questions throughout the creation of the Daisyworld model and during the experimentation phase. They also paste in graphs in support of their answers. I then grade the assignment to assess their understanding.

Watson, A.J., and Lovelock, J.E., 1983, Biological homeostasis of the global environment: the parable of Daisyworld, Tellus, v. 35B, p. 284-289.