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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The materials are free and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
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Unit 4: Daisyworld

Louisa Bradtmiller (Macalester College)

Based on materials from Kirsten Menking (Vassar College)

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These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.

Overview

In this unit, students develop a computational model that replicates the Daisyworld model from the published literature. This is simple climate system model that focuses on the effect of albedo on temperature.

Science and Engineering Practices

Using Mathematics and Computational Thinking: Use simple limit cases to test mathematical expressions, computer programs, algorithms, or simulations of a process or system to see if a model “makes sense” by comparing the outcomes with what is known about the real world. HS-P5.4:

Using Mathematics and Computational Thinking: Create and/or revise a computational model or simulation of a phenomenon, designed device, process, or system. HS-P5.1:

Obtaining, Evaluating, and Communicating Information: Critically read scientific literature adapted for classroom use to determine the central ideas or conclusions and/or to obtain scientific and/or technical information to summarize complex evidence, concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. HS-P8.1:

Developing and Using Models: Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system HS-P2.3:

Developing and Using Models: Develop a complex model that allows for manipulation and testing of a proposed process or system. HS-P2.5:

Constructing Explanations and Designing Solutions: Make a quantitative and/or qualitative claim regarding the relationship between dependent and independent variables. HS-P6.1:

Cross Cutting Concepts

Systems and System Models: When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. HS-C4.2:

Systems and System Models: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. HS-C4.3:

Stability and Change: Feedback (negative or positive) can stabilize or destabilize a system. HS-C7.3:

Energy and Matter: Changes of energy and matter in a system can be described in terms of energy and matter flows into, out of, and within that system. HS-C5.2:

Disciplinary Core Ideas

Weather and Climate: The foundation for Earth’s global climate systems is the electromagnetic radiation from the sun, as well as its reflection, absorption, storage, and redistribution among the atmosphere, ocean, and land systems, and this energy’s re-radiation into space. HS-ESS2.D1:

Electromagnetic Radiation: When light or longer wavelength electromagnetic radiation is absorbed in matter, it is generally converted into thermal energy (heat). Shorter wavelength electromagnetic radiation (ultraviolet, X-rays, gamma rays) can ionize atoms and cause damage to living cells HS-PS4.B2:

Performance Expectations

Earth's Systems: Use a model to describe how variations in the flow of energy into and out of Earth’s systems result in changes in climate. HS-ESS2-4:

This material was developed and reviewed through the InTeGrate curricular materials development process. This rigorous, structured process includes:

  • team-based development to ensure materials are appropriate across multiple educational settings.
  • multiple iterative reviews and feedback cycles through the course of material development with input to the authoring team from both project editors and an external assessment team.
  • real in-class testing of materials in at least 3 institutions with external review of student assessment data.
  • multiple reviews to ensure the materials meet the InTeGrate materials rubric which codifies best practices in curricular development, student assessment and pedagogic techniques.
  • review by external experts for accuracy of the science content.


This page first made public: Sep 15, 2017

Summary

Students explore Daisyworld, a model of a self-regulating system incorporating positive and negative feedbacks. Daisyworld is a planet on which black and white daisies are the only things growing. The model explores the effect of a steadily increasing solar luminosity on the daisy populations 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 radiation-absorbing black daisies grow, and cooling it later as reflective 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. Daisyworld was conceived of by Andrew Watson and James Lovelock to illustrate how life might have been partly responsible for regulating Earth's temperature as the sun's luminosity increased over time. This exercise guides students through some of the mathematics behind the modeling and uses the modeling program STELLA to visualize results.

Learning Goals

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.

Context for Use

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.

Description and Teaching Materials

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

Daisyworld reading quiz Answer Key


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

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

Daisyworld answer key


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

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.

Teaching Notes and Tips

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.

Assessment

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.

References and Resources

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/

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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The collection is freely available and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
Explore the Collection »