Systems Theory
Pedro Ribeiro de Andrade
Gilberto Camara
How to model Natural-Society systems?
Connect expertise from different fields
Make the different conceptions explicit
If (... ? ) then ...
Desforestation?
“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 (1885-1972), American astronomer
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 (1881-1953) – first to apply mathematical
methods to numerical weather prediction
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
How do we study systems?
• Identify the components
• Determine the nature of the
interactions between components
Earth as a system
Physical Climate System
Climate
Change
Atmospheric Physics/Dynamics
Ocean Dynamics
Terrestrial
Energy/Moisture
Human
Activities
Global Moisture
Marine
Biogeochemistry
Terrestrial
Ecosystems
Tropospheric Chemistry
Biogeochemical Cycles
(from Earth System Science: An Overview, NASA, 1988)
Soil
CO2
Land
Use
CO2
Pollutants
Growth and decay
source: Ford,1999
Growth and decay
source: Ford,1999
Limited growth
Growth limited by resources (food, nutrients)
source: Ford,1999
Limited growth
source: Ford,1999
Systems Theory
source: Meadows,2008
Systems Theory: stocks and flows
Stocks: measurable elements
Flows: changes in stocks over time
source: Meadows,2008
Systems Theory: stocks and flows
Multiple inflows and outflows
source: Meadows,2008
Systems Theory: stocks and flows
Stock of trees and stock of lumber
source: Meadows,2008
Systems Theory: feedbacks
Room temperature controlled by
feedbacks from furnace and outside air
source: Meadows,2008
Shrimp farming
Simple model for shrimp farm
Results?
Figure 7
Positive Coupling
Atmospheric
CO2
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
Negative Coupling
Earth’s albedo
(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
Equilibrium State:
Conditions under which the
system will remain indefinitely
--If left unperturbed
An Unstable Equilibrium State
An Unstable Equilibrium State
Perturbation
When pushed by a perturbation, an unstable
equilibrium state shifts to a new, stable state.
A Stable Equilibrium State
A Stable Equilibrium State
Perturbation
A Stable Equilibrium State
Perturbation
Conclusions
 Two ways to increase stocks
 Stocks act as delays or buffers
 Stocks allow inflows and outflows to be decoupled