1. The Standard Case
We'll begin our exploration of Daisyworld by looking at the standard case, with the model set up as originally described. This model is rather difficult to predict, so you should carefully study the model before forming a prediction of what will happen when you run it.
Remember that initially, there are no daisies on the planet (just a few seeds) and the sun's luminosity is very low. What will happen at first? Will the both types of daisies start to grow right away? Or just one type? What do we need to know in order to figure out whether or not the daisies will grow? We need to know the local temperature for each daisy. But to get the local temperature, we first need to know the average planetary temperature. We can in fact figure out the starting temperature for Daisyworld using the following equation:
T planet = (Solar Energy * (1-A planet )/s) 0.25 - 273
At the start of the experiment, the solar energy is found by multiplying the luminoisty (0.6) times the solar flux constant (917 W/m2); the planetary albedo is 0.5 (no daisies); and s is 5.669E-8 W/°K4, so the planetary temperature is about -9°C in the beginning. This means that the local temperature for the black daisies (if there were any) would be -4°C and for the white daisies, it would be -14°C -- both of these temperatures are too cold for the daisies to grow, so initially, the daisies will be incapable of altering the albedo and thus the planetary temperature. This gives us a starting point for developing a prediction about what will happen, but there are many more questions to think about before running this model.
But what will happen as the planet begins to warm, driven by the increasing energy output of the sun? Which type of daisy will begin to grow first? What will happen to the planetary temperature when the first daisies begin to grow? How will that change in the planetary temperature change the growth of the daisies. Will both types of daisies grow during the same time period? If so, what will be their combined effect on the planetary temperature?
Run the model for 200 time units, with a DT of 0.25. It will be instructive to plot the three area reservoirs on one graph, and the average planetary temperature and the temperature of the "dead" planet on another graph. Various other graphs will be necessary to fully understand what is going on to drive the observed behavior.
2. Changing Albedos
Initially, the black albedo is set at 0.25, while the white albedo is 0.75. In this experiment, modify these albedos, first to more extreme values (.05 and .95) and then to more moderate values (.4 and .6). Be sure to make some careful predictions before running these models.
One of the critical parts of this model is the growth factor for daisy growth. In this experiment, we will alter the growth factor and see how the model responds.
a) First, alter the optimum temperature for the daisies' growth, which is initially set at 22.5°, to 15°. To do this, alter the equations for the growth factors, replacing 22.5 with 15. As always, make predictions before running the model.
b) Next, restore the optimum temperature to 22.5 and then reduce the range of temperatures that the daisies can tolerate. Initially, the daisies can grow in temperatures ranging from 5 to 40. Now restrict the range so that the daisies grow only between 18 and 27; this can be done by replacing the 0.003265 with 0.05 in the equations for the growth factors. As always, make predictions before running the model.
4. Plagues
This experiment explores the resilience of Daisyworld by programming a set of plagues into the model. These plagues decimate the populations periodically for brief periods. An interesting question here is whether or not the daisies will be able to recover fast enough to return the planetary temperature to the "comfort zone". To implement this change, double-click on the death rate converter and replace 0.3 with "time" (without the quotation marks), then click on the Become Graph button in the lower left of the window. Next set the number of data points to 101; this should give you one input value every 2 time units, thus allowing us to make fairly brief plagues (still, these are 20 Myr long!). Then, select the entire output column by clicking directly on the word "Output" at the top of the column and enter 0.3, then click on one of the other boxes in the graph window to register this change -- this should set the background death rate to 0.3. Next, scroll along the horizontal axis and make a spike with a value of 1.0 at time units 50, 100, and 150; click on the OK button and the plagues should be inserted into the model. Run the model as before, after making a prediction about what will happen. Are all of the plagues equal in magnitude (in terms of area lost as a result of the deaths)? Does each plague result in the same kind and magnitude of temperature change? Does the system recover from each plague? What determines whether or not the planet recovers from a plague?
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