Name ___________________________________ Lab section ____________________

1

EAS1600 Lab 02 “DaisyWorld”

Objectives

In this lab we will investigate systems, their couplings and feedbacks using a computer

simulation of an imaginary planet with white and black daisies – the “DaisyWorld” system. After

completion of this exercise you should be able to:

determine the type of couplings between system components;

identify positive and negative feedbacks;

give your own examples of systems with feedbacks;

estimate the value of feedback factors and know the meaning of feedback factors;

explain how and why the DaisyWorld system evolves with time (with an increase in the

sun’s brightness) and

explain how white and black daisy coverage provides feedback responses.

Theoretical background

Coupling and feedbacks. The Earth system (as any other complex system) is composed

of many interacting components and subsystems which, altogether, determine the system’s state.

For example, the heart, arteries, veins, and capillaries are components of a human’s circulatory

system. The interaction or coupling between the components may be either positive or negative.

In a positive coupling, a change in some property of one component leads to a change of a

property of the linked component in the same direction (increase in one results in increase of the

other one; or decrease in one results in decrease of the other). In a negative coupling, a change in

some property of one component leads to a change of a property of the linked component in the

opposite direction (increase in one results in decrease of the other one; or decrease in one results

in increase of the other).

Positive couplings are usually denoted as ( ) while negative couplings are

denoted as ( ). Figures 1 and 2 show examples of positive and negative couplings.

Figure 1. Example of a positive coupling. The rate of most simple chemical reactions increases

with an increase in temperature, and vise versa - the rate decreases with a decrease in temperature.

Figure 2. Example of a negative coupling. The amount of clothing needed to stay comfortable

outdoors decreases with an increase in ambient temperature. A decrease of temperature results in

an increase in the amount of clothing needed to stay warm.

Name ___________________________________ Lab section ____________________

2

Please note that in the real world the sign of the couplings is not always constant. A significant

change in the physical conditions or configuration of the system could cause the sign to change.

In other words, a coupling might exist within a certain range of conditions. For example, if the

chemical reaction in Figure 1 occurs in a water solution, the increase of the temperature above

the boiling temperature will eventually evaporate the water and stop the reaction completely, thus

destroying the existing coupling.

When components are related in such a way that couplings form a loop, a feedback loop

is formed. Positive feedback loops tend to amplify the initial changes acting on a system

(perturbation) while negative feedback loops act to decrease the initial perturbation and thus

stabilize the system. An example of a negative feedback that stabilizes the system is shown in

Figure 3.

You can use a simple rule to determine the sign of the system feedback: multiply all the

couplings within the loop (a positive coupling has value of +1, and a negative coupling has a

value of -1 ). If the result of multiplication is positive, the system has a positive feedback, and if

the result is negative, the system has a negative feedback.

Figure 3. Example of a system with negative feedback. The amount of perspiration increases as

temperature increases (and vise versa), which constitutes a positive coupling. At the same time as

the amount of water that evaporates off the body increases, the cooling effect increases and the

temperature of the body decreases. This is a negative coupling. Multiplication ( +1 -1 = -1)

suggests that the feedback is negative. Indeed, perspiration is an effective way of stabilizing body

temperature.

It is important to remember however that even systems with negative feedbacks can still

be changed by a perturbation; the existence of a negative feedback does not necessarily prevent

the change. The feedback just acts to reduce the magnitude of the change.

The feedback factor F is a measure of the strength of the feedback. It is defined as the

ratio of the change of the system parameter with feedback acting (ΔΤeq) to the change of the

system parameter with no feedback (ΔΤο):

F = ΔΤeq/ΔΤο

where ΔTeq = ΔΤο + ΔΤf ; ΔΤf – change due to feedback

Response of the system, in which the temperature T is the main system parameter, can be

calculated as the difference between final temperature and initial temperature for the specific

time period:

∆T = Tfinal - Tinitial

where Tfinal is a system temperature at the end of the time period, and Tinitial is a system

temperature at the beginning of the time period. The feedback factor also describes the state of

the system at any point (i.e., stability).

Name ___________________________________ Lab section ____________________

3

DaisyWorld simulation. The DaisyWorld concept was introduced by James Lovelock and

Andrew Watson to illustrate the plausibility of their hypothesis that life regulates the planet’s

environment to make it more habitable for all living things. The DaisyWorld climate system

illustrates examples of coupling and feedbacks and will help you better understand these

concepts.

DaisyWorld is an imaginary planet where groups of white and black daisies grow in gray

soil and receive energy from the Sun. Like the Earth’s Sun, DaisyWorld’s Sun is slowly

increasing in brightness over time. Changes in the population of white and black daisies act to

either resist or amplify initial warming caused by the increasing brightness of the Sun (solar

luminosity).

Figure 4. A view of the DaisyWorld from space.

The steady increase in solar luminosity over time is called an external forcing, because it is a

continuous, external disturbance.

According to the model, the optimum surface temperature for daisy growth is 22.5oC.

New daisies do not grow when the temperature falls below 5oC and goes above 40

oC.

Name ___________________________________ Lab section ____________________

4

In the model, the daisies experience a constant death rate. (This means that the life

expectancy of the daisies does not vary with temperature. The growth of the daisies, however,

varies with the temperature, as noted above).

The reflectivity (albedo) of all objects, including daisies, takes on values between 0 and

1. A perfectly reflecting object has an albedo of 1, while a perfectly absorbing object has an

albedo of 0. The white daisies reflect light from the sun and their albedo is close to 1, while black

daisies absorb light very efficiently with albedo close to 0. If the population of white daisies

increases (decreases) as the time progresses, they reflect more light and this tends to resist

(amplify) any external forcing that causes an initial increase in temperature. This constitutes a

negative (positive) feedback loop. Another way to determine whether a negative or positive

feedback loop is created is to estimate a feedback factor.

If you want to learn more about the DaisyWorld concept, look at the original paper by

Watson and Lovelock that first presented the DaisyWorld model, or at a recent publication that

summarises the current knowledge:

Watson, A.J.; J.E. Lovelock (1983). "Biological homeostasis of the global environment: the

parable of Daisyworld". Tellus B 35 (4): 286-9. International Meteorological Institute.

Wood, A. J., G. J. Ackland, J. G. Dyke, H. T. P. Williams, and T. M. Lenton (2008), Daisyworld:

A review, Rev. Geophys., 46, RG1001, doi:10.1029/2006RG000217.

Online exercises/activities

Take a look at the following flash animation that demonstrates the principles of DaisyWorld:

http://library.thinkquest.org/C003763/flash/gaia1.htm

To practice at home or to return back to DaisyWorld after the lab is over, you can run a slightly

different online version of the DaisyWorld simulation at:

http://gingerbooth.com/courseware/daisy.html (requires Java )

Figure 5. Graph (a) and system diagrams

(b) of the effect of DaisyWorld

temperature changes on daisy growth rate.

Name ___________________________________ Lab section ____________________

5

Lab assignment.

1. Problems for individual work

Problem 1. (4 Pts.) Think of

1) an example of a positive coupling between two components of a system and

2) example of a negative coupling.

While answering this and the next questions, please do not use examples from the textbook. Think

up examples that apply from your own life experiences.

For each example,

1) illustrate the graphical relationship between the components and

2) draw the corresponding system diagram using the diagrams given below (next page).

Label each axis and each system component.

Figure 6. The diagram for your example of positive coupling.

Figure 7. The diagram for your example of negative coupling.

Name ___________________________________ Lab section ____________________

6

Problem 2. (8 Pts.) Now think of two-component systems that illustrate negative and positive

feedbacks. For each case, fill-in the system component boxes below and indicate whether the

feedback leads to an unstable or a stable system.

Stability: _______________

Figure 8. The diagram for your example of positive feedback scenario with 2 positive couplings.

Stability: _______________

Figure 9. The diagram for your example of negative feedback scenario with 1 negative and 1

positive coupling.

Answer the following questions using your Clicker :

Question 1. (2 Pts.) Which of the above feedback loops (positive or negative feedback loops) is

resistant to the initial perturbation? Answer by typing in your Clicker “P” for positive or “N” for

negative.

Question 2. (2 Pts.) Does the negative feedback acts to stabilize or destabilize the system?

Answer by typing “D” for destabilize or “S” for stabilize.

Question 3. (2 Pts.) What kind of feedback loop acts to magnify the initial perturbation? Answer

by typing “P” for positive or “N” for negative

Question 4. (2 Pts.) Is the system with 2 positive and 2 negative couplings stable or unstable?

Answer by typing “S” for stable or “U” for unstable.

7

2. Model and procedures in the lab

Start the “DaisyWorld” Excel spreadsheet on your lab computer. Read through the

introduction and theory before starting (tabs t1 through t5). This will familiarize you with some

of the basics used in the program. Then go to the “Variable parameters” box in the

DAISYWORLD2 spreadsheet (tab) that allows you to vary initial conditions - initial white and

black daisy coverage. Change the initial conditions (initial area of daisies) to see how daisy

coverage affects the planet. The model will plot graphs of temperature, daisy coverage, and

albedo as a function of increasing luminosity (time). Perform the following simulation

experiments:

(1) First, set the initial area of both white and black daisies to 0. This is your reference

simulation – with no daisies. Look at the plots and note how the temperature changes as

time progresses and the Sun’s luminosity increases.

(2) Then, change the initial white daisy coverage to 10% and keep the initial black daisy

coverage at 0%. The plots generated for these initial conditions show temperature and the

daisy coverage feedback response for a steady increase in sun luminosity from 0.7 to 2.2

in terms of its current luminosity (assumed to be equal to 1). Print out both plots on the

same sheet of paper and turn them in with other pages for this lab. Use these plots to

answer questions 9-25.

(3) Now, change both initial white and black daisy coverage to 10%. Note any difference in

plots (compare with your printed plots). Answer the questions below.

Questions 5 and 6 refer to the modeling experiment (1)

with 0 initial white and 0 initial black daisy coverage.

Question 5. (2 Pts.) What type of coupling exists between solar luminosity and planet

temperature for the case with zero initial daisy coverage? Answer by typing “P” for positive or

“N” for negative, using your Clicker.

Question 6. (2 Pts.) Does a feedback loop exist in this scenario where there is no initial daisy

coverage? Answer by typing “Y” for yes or “N” for no using your clicker.

Questions 7 - 10 refer to the modeling experiment (2)

with 10% initial white daisy coverage and 0% initial black daisy coverage.

Question 7. (2 Pts.) Examine two curves present on the “Luminosity versus Temperature” plot.

What effect does the white daisy feedback have on surface temperature: stabilizing or

destabilizing? Answer “D” for destabilizing or “S” for stabilizing using your clicker.

Question 8. (3 Pts.) Why is white daisy coverage increases very slowly at the beginning of the

plot? Choose from the following and enter the letter that corresponds to your answer into Clicker.

A. There were very few daisies to start with.

B. The temperature was too hot.

C. The temperature was too cold.

D. The daisies reflected all light.

E. The positive feedback was killing the daisies.

8

Question 9. (3 Pts.) Give a reason why the daisies recover from this initial drop in coverage?

Choose from the following and enter the letter that corresponds to your answer into Clicker.

A. The albedo of the planet was increasing.

B. The albedo of the planet was decreasing.

C. The temperature was getting colder.

D. The temperature was getting warmer.

E. The death rate of daisies decreased.

Question 10. (3 Pts.) What is the main consequence of the negative feedback on the lifespan of

the daisies as species? Choose from the following and enter the letter that corresponds to your

answer into Clicker.

A. The life span of the daisies has decreased as a result of the positive feedback.

B. There is no consequence of the feedback on the lifespan of the daisies as species.

C. The amount of time daisies can live on the planet increased as a result of the feedback.

D. The feedback mechanism changed the planet’s temperature, but not the lifespan of the

daisies.

Investigation of the Stability of the DaisyWorld system. (15 Pts.)

On both plots that you have printed for the experiment (2), label the following regions of solar

luminosity:

Area of interest Solar luminosity

(relative to the current value of 1)

Region I 0.975 – 1.0

Region II 1.1 – 1.3

Region III 1.5 – 1.8

On the following system diagrams (Figures 10-12), the DaisyWorld components are

listed in boxes. The coupling of the three components represent a feedback loop. Your goal is to

determine the type of feedback loop (positive or negative) and the state of the system (stable or

unstable) present in each region. Complete the following steps for each region:

1) From the graph of luminosity dependence on temperature (or from tabulated

luminosity/temperature data), determine the range of temperature changes within the region.

Put the temperature range values on the diagram, in the designated place.

2) By examining Figure 5, and looking at the graphs of the tempeature changes within the region,

draw in the appropriate coupling arrow between the temperature and daisy area: Do the same

for the coupling between the daisy area and albedo and the coupling between albedo and

temperature. As the result, you must have the coupling type determined between all components

of the system.

3) Determine the type of feedback that exists in your DaisyWorld system at this time interval (in

this region).

4) Determine the stability state of your DaisyWorld system at this time interval (in this region).

Name __________________________________ Lab section ____________

9

Figure 10. Region 1.

Figure 11. Region 2

Figure 12. Region 3

10

Questions (continued)

Question 11. (3 Pts.) Think of a reason that would explain the presence of the type of feedback

that you have determined for Region III. From the following list, choose one reason that is

closest to your explanation and enter the corresponding letter into Clicker.

A. The system has negative feedback because the area covered by white daisies is decreasing.

B. The system has negative feedback because the temperature is still lower than it would be with

the absence of daisies, i.e. white daisies lower the temperature of the planet.

C. In this region the temperature has exceeded the optimum temperature for daisy growth,

therefore as the temperature increases, the white daisy coverage decreases. This leads to even

higher temperatures through rapidly decreasing albedo.

D. In this region the system has positive feedback and therefore is unstable. Positive feedback

appears because as the temperature of the sun increases, the temperature of the planet also

increases.

E. Increasing solar luminosity leads to increasing planet temperature. The feedback is not

compensating for this disturbance; therefore it is not a negative feedback.

Question 12. (3 Pts.) What does a feedback factor of F=1 mean? Use the definition of feedback

factor to figure this out. Choose from the following and enter the letter that corresponds to your

answer into Clicker.

A. The feedback mechanism has no effect.

B. There is a positive feedback in the system, and the system is unstable.

C. There is a negative feedback in the system, and the system is stable.

D. The system has compensated the initial disturbance.

E. The negative feedback has compensated for a part of the initial disturbance.

Question 13. (2 Pts.) What does a feedback factor F > 1 mean? Choose from the following and

enter the letter that corresponds to your answer into Clicker.

A. There is a negative feedback, and the response of the system is less than the initial

disturbance.

B. The system has compensated the initial disturbance.

C. There is no feedback.

D. There is a positive feedback in the system, and initial disturbance is amplified.

E. The negative feedback has compensated for a part of the initial disturbance.

11

Question 14. (2 Pts.) What does a feedback factor of F=0 mean? Choose from the following and

enter the letter that corresponds to your answer into Clicker.

A. There is a negative feedback, and the response of the system is less than the initial

disturbance.

B. The system has negative feedback which completely compensated the initial disturbance.

C. There is a positive feedback in the system, and initial disturbance is amplified.

D. There is no feedback.

E. The negative feedback has compensated for a part of the initial disturbance.

Question 15. (2 Pts.) What does a feedback factor of 0 < F < 1 mean? Choose from the

following and enter the letter that corresponds to your answer into Clicker.

A. There is a positive feedback, and the response of the system is more than the initial

disturbance.

B. The negative feedback has compensated a part of the initial disturbance.

C. There is a positive feedback in the system, and initial disturbance is amplified.

D. The system has negative feedback which completely compensated the initial disturbance.

E. There is no feedback.

Question 16. (3 Pts.) Calculate the feedback factor for Region I determined above. Remember

that response of the system is determined as final temperature minus initial temperature for the

region of interest. Enter the answer to Clicker.

Question 17. (3 Pts.) Calculate the feedback factor for region II determined above. Enter the

answer to Clicker.

Question 18. (3 Pts.) Calculate the feedback factor for region III determined above. Enter the

answer to Clicker.

On the daisy coverage/albedo vs. luminosity plot find a point at which daisy coverage is the

highest. Label this point as ‘’.

Question 19. (2 Pts.) Why do the daisies begin to die after (to the right of) this point? Choose

from the following and enter the letter that corresponds to your answer into Clicker.

A. The temperature was too cold.

B. The optimum temperature for daisies has been exceeded.

C. There were too many daisies.

D. The feedback is negative, and it’s killing the daisies.

E. The feedback is positive, and it’s killing the daisies.

12

Question 20. (2 Pts.) What is the feedback factor after (to the right of) the ‘’ point? Choose

from the following and enter the letter that corresponds to your answer into Clicker.

A. F = 0

B. F = 1

C. 0 < F < 1

D. F > 1

Question 21. (2 Pts.) What is the feedback factor before (to the left of) the ‘’ point? Choose

from the following and enter the letter that corresponds to your answer into Clicker.

A. F = 0

B. F = 1

C. 0 < F < 1

D. F > 1

Question 22. (2 Pts.) What is the feedback factor at ‘’ point? Choose from the following and

enter the letter that corresponds to your answer into Clicker.

A. F = 0

B. F = 1

C. 0 < F < 1

D. F > 1

Name ________________________________________ Lab section _____________

13

Conclusions on the lab

1. What is unique about point ‘*’ in terms of the conditions of the system? [3 pts]

2. How did the addition of black daisies in the experiment (3) change the temperature of the

planet at the beginning of the planet’s life? Was there any effect later, when the luminosity of

the Sun increased? Why ? (4 pts.)

3. Please write several sentences in the space below, summarizing what you have learned in this

lab. (4 pts.)