Daisy World Model:
Amount of bare ground available for
daisy growth.
D = area covered by daisies
x = area of bare ground
x = (1 - D)
Average planetary albedo Ap
Ag = albedo of bare ground
Ad = albedo of daisies
Ap = x*Ag + D*Ad
Ag = 0.25
Ad = 0.75
Average planetary temperature
Te = avg. planetary temperature
S = solar luminosity
sig = Stefan-Boltzmann constant
Te = ((S/sig *(1 - Ap))^0.25 - 273
Growth rate of daisies
G = growth rate of daisies
Topt = optimal growth temperature
dT = temperature interval where growth
is possible
G = 1 - (1/dT)^2 * (Te - Topt)^2
Change in area covered by daisies
per timestep
y = death rate of daisies
dD/dt = D*(x*G - y)
New area covered by daisies
ND = dD/dt + D
The model reads the initial parameters
specified and calculates the amount of
bare ground, planetary albedo, daisy
growth rate, and new area covered by
daisies.
S = 1370
sig = 5.67E-8
Topt = 22.5 C
dT = 17.5 C
y = 0.2
It then uses these parameters as
input for the next modelling step
and iterates the model through 70
steps, the first 60 of which are
displayed in the graph.
Simulating Daisyworld in Excel
The spreadsheet consists of three pages: the first page is where you will do all the calculations.
The green box contains the parameters of the model. You will change the following parameters:
Initial Daisy Coverage (cell B5), Solar Luminosity (cell B8). The other cells in the green box define
the parameters of Daisyworld, such as the albedo of the bare ground and the daisies, the biological
properties of the daisies, their death rate etc. The model is slightly different from the one shown in
class. It calculates a propagation rate and has a fixed death rate to calculate daisy abundance after
every step.
The brown box shows the final output of the model after you have entered your starting parameters.
It tells you the final surface temperature and daisy coverage. It also tells you whether the model
reached a stable state or not.
The graph on the right side of the spreadsheet shows you how the surface temperature changes as
the model progresses.
The large table at the bottom of the sheet shows the actual calculations. the model takes the initial
parameters, shown in the first line in red and calculates the resulting values for daisy coverage and
surface temperature, which will serve as the input for the next calculation. The model repeats these
calculations 75 times and shows the final values in the brown box discussed above.
Report report the answers of your model runs on page two.
The third page contains some of the details and numerical values used in the model calculations.
Exercises
1. No Daisies - lifeless case
Set the initial number of daisies in cell B5 to zero. This will ensure that no daisies grow on the planet.
Now calculate the planet's surface temperature for the luminosities given in column A of the answer
page. Graph the resulting surface temperature as a function of luminosity using the x-y scatter plot
option.
2. Constant initial daisy abundance
Set the initial number of daisies to 0.2 (20% of the planet are covered by daisies). Repeat exercise 1
by changing the solar luminosity and enter the resulting surface temperatures into column C of the
answer page. Add your results to the graph of surface temperature vs. solar luminosity.
3. Variable initial daisy abundance
Repeat exercise 2, but now start each new model using the final daisy abundance of the previous run
as the starting value for the next run. Add your results to the graph.
4. Maximum solar luminosity
What is the maximum solar luminosity that allows for the growth of daisies? What is the abundance of
daisies in this case? Why is it not 100%?
5. Think!
Explain the differences in your results between exercise 2 and 3. What do these results tell you about
the effects of the rate of change? Why might this be important (remember the global temperature
reconstructions shown in class). What might rapid environmental change mean for the survival of
certain species? You should write about half a page and be prepared to talk about your answers in
class!