1. An Introduction to Systems
DaisyWorld
An Introduction to Systems

2. Key Questions What are systems? What are feedback loops?
What are equilibrium states?
Does viewing Earth as a system allow for deeper insight into the interrelationships among the physical and biological worlds?
Can Earth’s climate be self-regulating?
Chapter focus – the fundamentals of systems theory needed to study Earth

3. Systems Approach Human physiology
Systems interrelated, function together to maintain the body in a healthy state

4. System Essentials
System – composed of diverse but interrelated components that function as a complex whole
Components can be:
reservoir of matter
reservoir of energy
system attribute
subsystem
Feedback Loops: How nature gets its rhythms

5. State of a System
Set of important attributes that characterize the system at a particular time
Components interact so that a change in state is sensed by the whole system
This linkage allows for the control of important attributes

6. Couplings
Links between systems that allow the flow of information from one component to the next
Electric blanket example

7. Systems Diagrams Keep track of couplings within a system
Positive Coupling – a change ( or ) in one component leads to a change in the same direction in the linked component
- represented by 
Negative Coupling - a change in one component leads to a change in the opposite direction in the linked component
- represented by 

8. Feedback Loops
Positive Feedback Loops – amplify the effects of the disturbance
Negative Feedback Loops – diminish the effects of the disturbance
“Sign” of the Loop –
odd number of negative couplings – negative
even number of negative or all positive couplings- positive
Feedback is a self-perpetuating mechanism of change and response to that change

9. Equilibrium State
Condition will not change unless the system is disturbed
Stable
Created by negative feedback loops
Modest disturbances will be followed by return to equilibrium state
Unstable
Slight disturbance carry the system further and further away from the state

10. Stable State
Small disturbances followed by return to equilibrium state
Large disturbances can lead to a new different equilibrium state
There are limits to the stability of stable equilibrium states

11. Unstable States Will not return to original state on its own
No region of stability
Will not return to original state on its own
Slightest disturbance pushes system to a new stable equilibrium

12. Equilibrium State
For natural systems with a single feedback loop it is usually true that
Stable systems result from negative feedback loops
Unstable systems result from positive feedback loops

13. Perturbations and Forcings
Perturbation – temporary disturbance of a system
Volcanic eruption example – average climatic response to the 5 largest eruptions in the last 100 years

14. Perturbations and Forcings
Forcing – more persistent disturbance of a system
Solar Luminosity example
Increase in temperature countered by decrease in CO2
LLGHG = Long Lived Greenhouse Gases

15. Daisyworld Hypothetical planet with a simpler climate system
Only life forms are daisies
Creation of Lovelock & Watson
DaisyWorld (1): James Lovelock and Gaia
DaisyWorld (2): Gaia and Daisyworld
DaisyWorld (3): Self regulation
DaisyWorld (4): Gaia theory and the real world
Demonstrates that natural systems can be self-regulating on a global scale without the need for intelligent intervention
This World Is Black and White

16. Daisyworld Climate System
A two component system
Area of white daisy coverage
Average surface temperature
Daisy coverage affects temperature
Temperature affects daisy coverage

17. Daisyworld Couplings Albedo – reflectivity of a surface
Expressed as a decimal fraction of the total incoming energy reflected from the surface

18. Surface Temperature vs Daisy Coverage
Negative Coupling
Negative slope
Daisy Coverage - Surface Temp 

19. Coupling: Daisy Coverage – Albedo - Temperature

20. Daisy Coverage in Response to Temperature

21. Equilibrium States Put the two together Intersection shows
Effect of daisies on temperature
AND
Effect of temp on daisies
EQUILIBRIUM STATES
Two Feedback loops
One above optimum
One below

22. Feedback Loops

23. THE DAISY WORLD CLIMATE SYTEM
Response of Daisy world to perturbations depends on the temperature
Below optimum has negative feedback loop and is stable
Above optimum has positive feedback loop and is unstable

24. Response to External Forcing
Increased solar luminosity
Daisies would increase (immediately) and albedo increase and warming would be slowed
Persistent increasing solar luminosity would eventually lead to a new higher equilibrium temperature, but it would happen at a much slower rate (daisies & environment feedback loops)

25. More Accurate Response to External Forcing
Assumption – daisies respond to temperature change only
So – no change to 

26. However, change in surface temperature and daisy coverage expected
Temperature will be higher for any amount of daisy coverage
So – change to 

27. Combine the two Graphs P1' stable P2' unstable
Both temperature and daisy coverage higher at new stable equilibrium
Stability limit for P1' is lower
New equilibrium state less resistant to perturbations

28. Mathematically Speaking . . .
Comparing equilibrium temperature with and without feedback
∆Teq = ∆T0 + ∆Tf
The overall temperature change resulting from increase solar luminosity is the sum of the temperature change with no feedback and the temperature change due to feedback

29. For Any Stable Equilibrium in a System Involving Feedback Loops
The change in state of a system as it moves from one equilibrium to the next is the sum of the state change that would result without feedback and the effect of the feedback itself
To qualify the strength of the feedback effect . . .

30. The Feedback Factor
The ratio of the equilibrium response to forcing (the response with feedback) to the response without feedback
 = temperature change with feedback = ∆Teq
temperature change w/out feedback ∆T0
Negative feedback loop if 0 <  < 1
Positive feedback loop if 1 < 
Feedback factor defined only for stable systems

31. Daisyworld Climate History
History of Daisy Coverage
Temperature History
-Initially temp rises quickly
Once min temp for daisies met, daisies increase
Growth of daisies cools planet
Eventually, when optimal temp is met, daisy coverage at max
Increasing solar luminosity not countered by daisy growth and daisies die, causing increasing temp
Feedback loop positive & unstable
Surface temp rises, daisies extinct

32. The Lessons of Daisyworld
A planetary climate system is not passive in the face of internal or external forces
Negative feedback loops counter external forcings
Non-human systems that self-regulate seem intelligent, yet no foresight or planning is involved
In a natural self-regulating system, there is no preset state that the system is programmed to “seek-out”
Thresholds often exist in systems that when surpassed can lead to rapid changes in system state
Abrupt changes can have no forewarning
Earth is like Daisyworld
Strong negative feedback loops lead to long-term stability
Are we approaching a climate threshold that will result in a much warmer state?