Systems Theory
Pedro Ribeiro de Andrade
Münster, 2013
Geoinformatics enables crucial links between nature
and society
Nature: Physical equations
Describe processes
Society: Decisions on how to
Use Earth´s resources
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
P h y s ic a l C lim a te S y s te m
C lim a te
Change
A tm ospheric P hysics/D ynam ics
O cean D yn am ics
T errestrial
E n erg y/M o istu re
H u m an
A ctivities
G lo b al M o istu re
M arin e
B io g eo ch em istry
T errestrial
E co system s
T ro p o s p h e ric C h e m is try
B io g e o c h e m ic a l C y c le s
(fro m E art h Syst em S cie nce : A n O ve rvie w , N A S A , 1 98 8 )
S o il
C O2
La nd
Use
C O2
P olluta nts
Systems Theory
 Provides a unified classification for scientific knowledge.
 Enunciated by biologist Ludwig Von Bertalanffy:
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1920s: earliest developments
1937: Charles Morris Philosophy Seminar, University of Chicago
1950: “An Outline of General Systems Theory”, Journal for the Philosophy
of Science
 Scientists that introduced Systems Theory in their fields:
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Parsons, sociologist (1951)
J.G Miller, psychiatrist & psychologist (1955)
Boulding, economist (1956)
Rapoport, mathematician (1956)
Ashby, bacteriologist (1958)
Short History of System Dynamics
The System Dynamics approach was developed in the
1960s at M.I.T. by Jay Forrester.
A system in Modelica
Conception of Reality
 Any measurable part of reality can be modeled
 Systems are represented as stocks and flows

Stocks represent energy, matter, or information

Flows connect and transport stocks
 Systems are opened or closed
A system
 Can you identify parts? and
 Do the parts affect each other? and
 Do the parts together produce an effect that is different from
the effect of each part on its own? and perhaps
 Does the effect, the behavior over time, persist in a variety of
circumstances?
Source: (Meadows, 2008)
Systems Building Blocks
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Stocks
Flows
Information Links
Decision Points
Converters
Auxiliary Variables
slide
15
Stocks
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“Things” that accumulate in a system
Physical or non-physical things
Value is a quantity or level
Persistent (remain even if all flows stop)
Conservation (stock units enter from environment
and return to environment)
slide
16
Flows
 Movement of “things” in and out of stocks
 Not persistent (can be stopped and started)
 Value is a rate of change (will always have a time
dimension)
 Flow unit = stock unit / time
 The unit of measurement for a flow will always be
the unit of measurement of a stock divided by an
element of time
slide
17
Stock and Flow Diagram
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Stocks in boxes
Flows as straight double arrows
Information Links as thin curved arrows
Decision Points as closed in X
slide
18
System Dynamics Modelling
Control
Material Flaw
to Stock
Control
Material Flaw
from Stock
Stock
Send information
from the Stock
Add New
information
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
The interesting thing to do is to put
couplings together in feedback loops…
Negative Feedback Loops:
Electric Blankets
person A’s
body
temperature
person A’s
blanket
temperature
person B’s
blanket
temperature
person B’s
body
temperature
A Positive Feedback Loop:
Mixed-up Electric Blankets
person A’s
body
temperature
person A’s
blanket
temperature
person B’s
blanket
temperature
person B’s
body
temperature
A Positive Feedback Loop:
Mixed-up Electric Blankets
Any perturbation will cause both people to adjust
their blanket controls, but with undesired
consequences.
Ultimately, one person will freeze (become infinitely
cold) and the other person to swelter (become
infinitely hot).
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
When pushed by a perturbation, a stable
equilibrium state, returns to (or near) the
original state.
Tools for system dynamics
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Dinamo
Vensim
Simile
STELLA
Water in the tub
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Initial stock: water in tub = 40 gallons
water in tub(t) = water in tub(t – dt) – outflow x dt
t = minutes
dt = 1 minute
Runtime = 8 minutes
Outflow = 5 gal/min
Cell
(description extracted from “TerraME types and functions”)
Event
Temporal model
(1) Get first EVENT
1:32:00
cs:load( )
1:32:10
ag1:execute( )
1:38:07
ag2:execute( )
1:42:00
cs:save()
(2) Update current time
(3) Execute the ACTION
...
(4) ACTION
return value
true
false
(5) Schedule EVENT again
Source: (Carneiro et al., 2013)
Observer
Water in the tub
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Initial stock: water in tub = 40 gallons
water in tub(t) = water in tub(t – dt) – outflow x dt
t = minutes
dt = 1 minute
Runtime = 8 minutes
Outflow = 5 gal/min
Water in the tub 2
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Initial stock: water in tub = 40 gallons
water in tub(t) = water in tub(t – dt) – outflow x dt
t = minutes
dt = 1 minute
Runtime = 8 minutes
Outflow = 5 gal/min
Inflow = 40 gal every 10 min
Conclusions
 Two ways to increase stocks
 Stocks act as delays or buffers
 Stocks allow inflows and outflows to be decoupled