DaisyWorld

Apparatus

The 2 dimensional DaisyWorld simulation is available online at

Discussion

DaisyWorld is a simulation based upon the work of James Lovelock, originally conceived by Lovelock and Watson. The intent of the simulation is to show that by examining external factors, describing how the overall system reacts to them, and then going to the next step in the progression we can determine how a system tries to alter itself to maintain optimal/desired conditions. In scientific terms, the simulation utilizes feedback loops to discover how a system maintains a reasonable state of homeostasis.

This particular simulation can also be related to the topic of global warming, and vividly brings to life the impact a small temperature change can have on an ecosystem. This fact shows how an excess amount of energy, leading to a small temperature rise, could greatly affect our planet, and how Physics can be used to analyze this problem. Of the two simulations offered on the website, the simulation that is of most immediate use in this context is the two-dimensional version.

The two-dimensional key points are that you have a flat portion of a planet, without an atmosphere, that is either covered by barren earth, white daisies, or black daisies. The daisies find a temperature of 22.5° C the ideal growing temperature. The temperature of the planet is calculated using the Stefan-Boltzmann Law coupled with the reflectances, or albedos, of each daisy species and the bare earth. When run, the simulation allows the solar luminosity to vary from 0.6 to2.0 times the base value luminosity (set at the present day to be 1.0) over a period from 4 billion years before the present day to 10 billion years afterward. As the simulation runs, the graphs show the percentage covered by white daisies, black daisies, and barren ground and how they are responding to the change in solar luminosity, trying to maintain their ideal temperature (Figure 1).

Figure 1

To maintain the system at optimal temperature levels, the daisies can only change their relative amount of coverage area, up to a maximum value. When the simulation is run, two plots are shown. The first is a percentage of area covered versus the solar luminosity, which shows the amount of coverage by barren earth, white daisies, black daisies, and the combined number of daisies. The second graph shows the barren ground temperature and the temperature where the daisies are. It should be noted that while the daisies have an optimal temperature for growth, they are also given a range in which they can exist. The daisies appear once the minimal number is reached, and they completely die off if the maximal value is exceeded.

This system is similar to the one layer model of the Earth; i.e., no atmosphere. We will use this simulation to explore how varying certain parameters can lead to good, bad, or catastrophic changes in the system, always with an eye toward how this applies to, and uses, principles of Physics. When using the simulation, to discover how minor changes can affect the outcome, we only vary one parameter at a time. This gives us a certain amount of control, and the ability to state specifically which value/parameter caused the change. After having varied these parameters in a logical sequence, you can vary the parameters in logical groupings to explore the results of a cumulative effect.

The simulation lists the parameters to be changed in a menu at the top of its display (Figure 2). Scenarios allows you to change from the Black and White scenario to others that may be of interest (Figure 3). Run allows you to start the simulation after changing parameters. Stop will halt a running simulation. Daisies allows you to change the albedos of the barren earth, white and black daisies in the simulation (Figure 4). Colors allows you to change the colors of the Daisies that you will see on the screen. Parameters gives you the opportunity to change the settings for much of the ‘nuts and bolts’ of the simulation (Figure 5).

Figure 2

Figure 3

Figure 4

Figure 5

Procedure and Questions

  1. Run the intial simulation.
  2. Note the albedo for each of the three items in the simulation. If you were to try and compare them to the albedos of real entities, to what would they correspond? Are they realistic, given those comparisons?
  3. Note the values in the parameter menu. Explain what each of these is, why each of these values might have been chosen, and how each affects the simulation.
  4. Looking at the graphs from the first simulation run, complete the following table:

At what luminosity are the number of black and white daisies equal?
At what temperature does this occur?
At what luminosity does the first daisy appear, and what color is it?
At what luminosity does total death occur?
What was the percentage of black daisies just before total death?
What was the percentage of white daisies just before total death?
Characterize the temperature variation between the appearance of daisies and total death.
  1. Explain, qualitatively, how the temperature fluctuation might correspond to the daisy fluctuation.
  2. Can you characterize the curve for the temperature of barren earth, knowing that it is based upon the Stefan-Boltzmann law?
  3. Can you characterize when the living world temperature crosses from above to below the barren earth temperature? Can you use your hypothesis as a predictive tool? Try your predictions on a different scenario to see.
  1. Under the Parameters menu there is a “step by” option. Change this to 0.1 and then to 0.001, running the simulation for each of these values.
  2. Do you get the same results for each of these, and/or as the original? If not, why not?
  3. Of the three values, 0.1, 0.01, and 0.001, which do you believe is the ‘best’ to use, and why? Whichever value you choose, be sure to use this for the remainder of the lab exercises.
  4. The death rate parameter is set to 0.3. Compare this to the total amount of living space occupied by the daisies at any given time. How do these values relate to one another, and why?
  5. Vary the death rate to 2 values above and 2 values below 0.3. Note the values and complete a table similar to that in step 2 for each value used.
  6. With the results you’ve obtained, qualitatively explain how varying the death rate affects the ability of the system to maintain its ideal temperature.
  7. Given your results, is there an ‘ideal’ death rate that will allow the system to maintain the desired temperature range? If so, what might it be and why? If not, why not?
  8. When done with the above scenarios, return the death rate to the initial value.
  9. Here are some albedo values for planet Earth, that I obtained from the website:

Ground cover / Albedo
deep water / .05 - .20
Desert / .20 - .35
short greenery / .10 - .20
dry vegetation / .20 - .30
summer conifers / .10 - .15
deciduous forest / .15 - .25
Snowy forest / .20 - .35
dry snow / .60 - .90
  1. Do a search and find the albedo for asphalt from a reputable source. Document the source and record the value they give. Change the black daisies albedo to this value and run the simulation. Record your results in a table like that in step 2.
  2. Return the black albedo to the intial value and make the white value something in the dry snow range and run the simulation. Record your results in a table like that in step 2. How does your response differ from when you changed the black daisies albedo? Why the difference?
  3. Now change the black daisy albedo to asphalt and the white daisy albedo to something in dry snow and run the simulation. Qualitatively explain how and why the changing of two parameters affected the scenario in comparison to changing just one.
  1. Raise the ideal temperature parameter to 30° C. How does this affect the simulation? Compare and contrast this with the results you got in step 2.
  2. Return the ideal temperature to the 22.5° C, and lower the minimum acceptable temperature to 10° C. How does this affect the simulation? Compare and contrast this with the results you got in step 2.
  3. You may notice that the simulation, when the minimum temperature is reached, begins with all black daisies and then white ones slowly appear. However, by the end, only white daisies are present. Why is this? Can you construct a scenario that allows some black daisies to survive until the maximum luminosity is reached? Is this scenario ‘realistic?’
  4. Explain how this simulation helps us understand the energy balance for a one layer model, and make rudimentary predictions about our planet’s response to change.