Unit 4: Daisyworld

On completing this module, students are expected to be able to:

• Create Watson and Lovelock's Daisyworld model
• Differentiate between positive and negative feedbacks
• Evaluate the impact of changing growth and death rates on system behavior
• Evaluate the impact of changing albedo on system behavior
• Evaluate the impact of changing different heat conduction scenarios on system behavior
• Explain the faint young sun paradox
• Explain the concept of homeostasis
• Demonstrate understanding of the fact that systems may exhibit multiple stable states as well as hysteresis

This exercise addresses several of the guiding principles of the InTeGrate program. In particular, it requires the use of systems thinking, develops students' abilities to use numerical modeling to generate and test geoscientific hypotheses, develops understanding of positive and negative feedbacks, and explores two major ideas in Earth Science/History, the Faint Young Sun paradox and the Gaia Hypothesis.

This unit is intended to be used in a three- to four-hour class period that meets once a week. It can be used as part of this modeling course or it can be adapted as a lab exercise for courses in environmental science. For this course, students should come to class prepared to take a short quiz on the assigned reading. Thereafter they will be led through a series of prompts designed to help them create and experiment with a number of simple models using the iconographic box modeling software STELLA (see https://www.iseesystems.com/store/products/ for different options for purchasing student or computer lab licenses of STELLA or for downloading a trial version). Students should have access to Microsoft Excel or similar spreadsheet software to allow them to graph the growth functions early in the lab.

For those learning to use STELLA, we suggest the online "play-along" tutorials from isee systems. You can find them here: isee Systems Tutorials .

In addition to the Watson and Lovelock paper, students should complete the Unit 4 Student Reading, which contains extra background information as well as some explanation of some of the mathematics involved.

Students should complete the Daisyworld reading quiz (Microsoft Word 2007 (.docx) 62kB Aug11 16) before coming to class. The

can be found here.

In class, students should be provided with a copy of the Daisyworld exercise (Microsoft Word 2007 (.docx) 36kB Nov30 16).

The

contains answers as well as tips and strategies instructors can use to guide students through the exercise and information on typical stumbling blocks.

Instructors can download a version of the STELLA Dasiyworld model by clicking here: Documented Daisyworld Model (Stella Model (v10 .stmx) 29kB Aug11 16). The model was created using STELLA Professional and should open on any subsequent version of STELLA. If you are using an earlier version of STELLA, the complete model graphic and equations can be found in the answer key so that you can reconstruct the model yourself.

We generally post the readings and assignments for students to an LMS site (e.g. Moodle, Blackboard, Canvas). Students can open the assignment in Microsoft Word on the same computer they are using to construct the STELLA model and then answer the questions by typing directly into the document. Students can then either print a paper copy to hand in to the instructor or email their modified file to the instructor. It is very straightforward to copy graphs and model graphics out of STELLA and to paste them into Word. Simply select the items to be copied, hit copy in STELLA, and paste into Word. There is no need to export graphics to jpg.

We teach the course in a three- to four-hour block once a week because we have found that models require a lot of uninterrupted time to construct. If students have a 50- or 75-minute class period several times a week, they spend at least 20 minutes of subsequent class periods trying to figure out where they were in the exercise at the beginning of the week. This is not a good use of time, hence the recommended three- to four-hour class session once per week. However, we also know that sustaining attention for this length of time can be difficult. We therefore recommend allowing students the freedom to take breaks throughout the modeling session to get snacks or coffee.

A typical 4-hour class session might be broken up into the following sections:

• 20-minute discussion of the reading to ensure all the students are familiar with the mathematics behind the model, specifically Fourier's law of heat conduction.
• 1.5 to 2 hours to build the model
• 1.5 hours to conduct experiments

For instructors who have more limited contact hours with their students, we suggest that the model construction parts of this exercise be assigned as a pre-lab to be handed in a day or two before class along with the completed STELLA model itself. This would allow the instructor to determine whether students' models are working correctly and to provide feedback to address errors in construction, omissions in documentation, problems with unit conversions, and inappropriately sized time steps that might lead to spurious model behavior. Class time could then be devoted to running experiments and analyzing the results. If access to STELLA outside of class time is impossible due to computer lab scheduling or to financial constraints that prevent students from purchasing their own STELLA licenses, students could be asked to create a pencil and paper sketch of what their model should look like, annotated with equations and then sent to the instructor in advance of class for feedback. This should facilitate a faster model construction time during the limited class hours.

Answers to exercise questions are located in the answer key for this unit (see Description and Teaching Materials section above). Instructors may download an assessment rubric for the modeling exercise here: Assessment rubric (Microsoft Word 2007 (.docx) 121kB Jan8 15). Rather than assign a point value to every question in the exercise, we employ a holistic approach that determines the extent to which a student has correctly built the model, supplied appropriate documentation of equations and units, thoroughly answered questions throughout the assignment, and provided appropriately labeled graphs and figures in answering questions.

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

The NASA Goddard Space Flight Center has created a short animated film describing Daisyworld that can be found at http://svs.gsfc.nasa.gov/vis/a010000/a010800/a010898/