Daisy World Lab
Exercise 11.11 Verify high end of the span of control.
Use the Bweb model (http://www.wsu.edu/%7Eforda/models.html ) to test a
heat shock scenario. Be sure to select variety #5; then experiment with heat
shocks that raise the solar luminosity to 1.1, 1.2, 1.3, 1.4, and 1.5. The
temperatures at the end of the simulation (for a 1.25 heat shock) should match
Figure 11.6 below and the areas of Black and white daisies should match Figure
11.8. (you should set the initial values for the area of white and black daisies to
250 and the empty area to 500)
Make a comparative graph of area of white daisies for each solar heat shock
experiment.
Insert graph here
Make a comparative graph of area of black daisies for each solar heat shock
experiment.
Insert graph here
Make a comparative graph of area of planet’s average temperature for each solar
heat shock experiment.
Insert graph here
Which color of daisy dominates in a warmer world? Explain why this makes
sense.
Insert answer here
Insert graph here
For what solar luminosity does the planet “die”?
Insert answer here
Insert graph here
Figure 11.6 Above
Figure 11.8 Above. Equilibrium Areas for 12 tests with different solar
luminosities.
Exercise 11.12 Verify low end of the span of control.
Use the Bweb model to test a cold shock scenario. Be sure to select variety #5;
then experiment with cold shocks that lower the solar luminosity to 0.9, 0.8, 0.7,
and 0.6. The areas should match Figure 11.8.
Make a comparative graph of area of white daisies for each solar cold shock
experiment
Insert graph here
Make a comparative graph of area of black daisies for each solar cold shock
experiment
Insert graph here
Make a comparative graph of area of planet’s average temperature for cold solar
heat shock experiment.
Insert graph here
Which color of daisy dominates in a colder world? Explain why this makes sense.
Insert answer here
For what solar luminosity does the planet “die”?
Insert answer here
11.13 Adding black ponds to Daisy World
Expand the BWeb model to include the effects of ponds. For every 1000 acres of landscape,
there is a pond that typically holds 1,000 acre-feet of water and covers a surface area of 200
acres. (Lower the initial values of the empty area by 200 acres to make room for the pond.) The
volume of water in the pond would be a new stock in the model. It would be fed by run-off that
is constant at 400 acre-feet/yr. The volume is reduced by evaporation, which is the surface
area multiplied by the evaporation rate. Set the surface are to a nonlinear function of the
volume of water. Create a nonlinear graphical function and make sure that you have 200 acres
when the pond holds 1,000 acre-ft ).
It is stated to make the area a non-linear
function of volume. Using the general
shape of monolake is a good start for this.
The graph below shows the lake area as a
function of volume for Monlake (Chapter
5). Your numbers will be different but the
general shape should be roughly the same.
Of course when the volume is 0.0 the area
=0.0, and when the volume is 1000.0 Acreft the area =200.0 acres
The shape of Mono Lake from Chapter 5
data.
Adding a pond.
Other considerations: As the pond grows, the black daisy area decreases and as
the pond shrinks the black daisy increases. (We have assumed that the ponds are
near the black daisies). We need a biflow connected to the empty area that
models this. The Stella DERIVN(PondArea,1) function gives the net inflow into
the area and could easily be used to control the bi-flow connected to the black
daisy. That is, add a converter DA that has PondArea connected to it and set it
equal to DERIVN(PondArea,1). Now connect DA to the biflow affecting the black
daisy (see figures above).
The planetary albedo must be altered also. Set the albedo of the black pond
surface to be 0.25, and include the pond surface area in the calculation of the
planet’s average albedo. Simulate the new model with the solar luminosity at 1.0.
Can the ponds maintain their normal size (200 acres) under these conditions?
After these modifications run the model to find the new equilibrium areas (see
graph on next page). Click and hold the mouse on the graph near the right edge
to read the new values. Replace the former initial areas of white, black, and
empty with these new equilibrium values. If your model is working, the total area
should remain at 1000. If not try to change the DT in run specs to a smaller value.
Run the model again. You should get a graph like the one below.
This is an important step because we want to make sure the model starts in
equilibrium before we make a new perturbation study or significantly alter the
model again.
What are your equilibrium areas?
Awhite=__________ ABlack=__________ AEmpty=__________ APond=___________
Next Step.
The normal evaporation rate is 2 ft/yr, so we expect evaporation to be 400 acreft/yr, which keeps the pond in dynamic equilibrium. But the actual evaporation
rate depends on the temperature near the ponds. The ponds are located next to
the black daisies, so the temperature near the black daisies influences the
evaporation rate. Assume that a 5 oC increase in black daisy temperature causes
the evaporation rate to double. The figure below shows 2 possible methods that
will do this. Both equations agree fairly well for temperature not too far above
27.5 but are quite different for temperatures below 27.5. We use the number
27.5 because that is the final equilibrium temperature near the black daisies in
the base run, this black daisy temperature may be different for you. If it is the
you black daisy equilibrium temperature should be used.
Set the albedo of the black pond surface to be 0.25, and include the pond surface
area in the calculation of the planet’s average albedo. Simulate the new model
with the solar luminosity at 1.0.
Can the ponds maintain their normal size (200 acres) under these conditions?
Make a graph including Area of white daisies, area of black daisies, empty area,
area of ponds, and total area. You can make a converter and use the summer
feature for the total area. If your model is working, the total area should remain
at 1000.
Show the results of a solar heat shock (S=1.25 at 2010) to your above graph. How
is the new daisy world altered by this heat shock.
Insert graph here
Answer here
Show the results of a solar cold shock (s=0.75 at 2010) to your above graph. How
is the new daisy world altered by this heat shock.
Insert graph here
Answer here
As a final experiment get rid of all connectors going into Solar luminosity
Set up a Sensi-Spec run with the solar luminosity varying from 0.6 to 1.5 (10 steps).
This should give 06., 0.7, 0.8,….. For these runs make a comparative graph showing planet Average
temperature.
For this run you should get a graph looking something like the one on the next page
Replace the graph above with your graph.
Now change the pond albedo to 0.05, clear your graph, and rerun the sensitivity run. Include you new
graph below.
What changes do you see when the pond albedo drops from 0.25 to 0.05.
Include 2nd graph here.
Now change the pond albedo to 0.8, clear your graph, and rerun the sensitivity run. Include you new
graph below.
What changes do you see when the pond albedo jumps up from 0.25 to 0.80.
Include 3rd graph here.