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Lab 3 - Daisyworld: Graphs and Applications
In Graph #1a, as Solar Luminosity increases, the world gets warmer until black daisies can begin to grow. As luminosity increases, the black-daisy population decreases and white-daisy population increases. Notice that the Total number of daisies remains fairly constant, except at the warmest temperatures the population increases slightly above the previous total. With increasing luminosity, the temperature becomes too warm for the survival of any daisies. Note that the temperature directly affects population growth or decline in a predictable manner. Also notice that the total for the three lines adds up to 100%. Remembering the optimal temperature for daisies (from the Background section), what would be the expected temperature where the black and white lines cross? Is this verified by inspecting Graph #1b?
Graphs #1 a & b- Basic DaisyWorld Run

Graph #1b shows the effect of increasing solar luminosity on the temperature. Notice that without the daisies, the land temperature would increase in direct proportion to increasing luminosity. With daisies, the temperature stays steady in the range that daisies can survive. This shows dramatically the feedback mechanisms at work: black daisies can heat their environment, white daisies can cool it, and their populations will tend towards equilibrium. Does the graph support the "theoretical" temperature range for daisy survival as mentioned in the Background section? At what temperature do the lines cross? What does this signify?
In Graphs #2a & b, the Deathrate (as manipulated in Parameters) has been changed from 0.3 to 0.6. Notice in Graph #2a how the shape of the lines is basically the same as in Graph 1a, but the Total number of daisies is less, as is the point at which they can no longer sustain themselves. One possible conclusion is that with a higher deathrate, there are not enough white daisies to reflect the heat and so the earth warms much faster. Do all three lines add up to 100%?
Graphs #2 a & b- DaisyWorld with Death Rate 0.6 instead of 0.3

Graph #2b is almost identical to Graph #1b, except that the daisies can sustain equilibrium only until Luminosity 1.3. Again, what is the optimal temperature for survival, as shown by this graph?
Any Daisyworld model readily lends itself to inquiry learning. Students can be given the general situation ("Imagine a world where...") and asked to predict or hypothesize what they think would happen under certain conditions. They could even be asked to draw predictive graphs. Model runs could then be made and results compared with hypotheses. Time can be spent fully analyzing the graphs and asking students to draw out the kinds of information that have been discussed above. Students could then determine what variable(s) they would manipulate, and the effects they predict changes would have on Daisyworld.
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Woodrow Wilson National Fellowship Foundation
CN 5281, Princeton NJ 08543-5281 - Tel:(609)452-7007 - Fax:(609)452-0066 Technical contact: lpt@woodrow.org |