1. Pedro Ribeiro de Andrade Gilberto Camara
Systems Theory
Pedro Ribeiro de Andrade
Gilberto Camara

2. How to model Natural-Society systems?
Connect expertise from different fields
Make the different conceptions explicit
If (... ? ) then ...
Desforestation?

3. “A hypothesis or theory [model] is clear, decisive, and positive, but it is believed by no one but the man who created it. Experimental findings [observations], on the other hand, are messy, inexact things, which are believed by everyone except the man who did that work”
Harlow Shapley ( ), American astronomer

4. Models
“[The] advantage of a mathematical statement is that it is so definite that it might be definitely wrong…..Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.”
Lewis Fry Richardson ( ) – first to apply mathematical methods to numerical weather prediction

5. What is a System?
Definition: A system is a group of different components that interact with each other
Example: The climate system includes the atmosphere, oceans, polar caps, clouds, vegetation…and lots of other things

6. How do we study systems? Identify the components
Determine the nature of the
interactions between components

9. Earth as a system

10. Growth and decay
source: Ford,1999

11. Growth and decay
source: Ford,1999

12. Growth limited by resources (food, nutrients)
Limited growth
Growth limited by resources (food, nutrients)
source: Ford,1999

13. Limited growth
source: Ford,1999

14. Systems Theory
source: Meadows,2008

15. Systems Theory: stocks and flows
Stocks: measurable elements
Flows: changes in stocks over time
source: Meadows,2008

16. Systems Theory: stocks and flows
Multiple inflows and outflows
source: Meadows,2008

17. Systems Theory: stocks and flows
Stock of trees and stock of lumber
source: Meadows,2008

18. Systems Theory: feedbacks
Room temperature controlled by feedbacks from furnace and outside air
source: Meadows,2008

19. Shrimp farming

20. Simple model for shrimp farm

21. Results?
Figure 7

22. Positive Coupling An increase in atmospheric CO2 causes
Greenhouse
effect
An increase in atmospheric CO2 causes
a corresponding increase in the greenhouse
effect, and thus in Earth’s surface temperature
Conversely, a decrease in atmospheric CO2
causes a decrease in the greenhouse effect

23. Negative Coupling An increase in Earth’s albedo causes a
(reflectivity)
Earth’s
surface
temperature
An increase in Earth’s albedo causes a
corresponding decrease in the Earth’s surface
temperature by reflecting more sunlight back to
space
Or, a decrease in albedo causes an increase in
surface temperature

24. Conditions under which the system will remain indefinitely
Equilibrium State:
Conditions under which the system will remain indefinitely
--If left unperturbed

25. An Unstable Equilibrium State

26. An Unstable Equilibrium State
Perturbation

27. When pushed by a perturbation, an unstable equilibrium state shifts to a new, stable state.

28. A Stable Equilibrium State

29. A Stable Equilibrium State
Perturbation

30. A Stable Equilibrium State
Perturbation

31. Conclusions Two ways to increase stocks
Stocks act as delays or buffers
Stocks allow inflows and outflows to be decoupled