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?

If (... ? ) then ...

Desforestation?

Connect expertise from different fieldsMake the different conceptions explicit

“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

“[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

Models

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

Atmospheric Physics/Dynamics

Tropospheric Chemistry

Global Moisture

Ocean Dynamics

MarineBiogeochemistry

Terrestrial Ecosystems

Terrestrial Energy/Moisture

Climate Change

Pollutants

CO2

CO2

Soil

Land Use

Physical Climate System

Biogeochemical Cycles

Human Activities

(from Earth System Science: An Overview, NASA, 1988)

Earth as a system

Systems Theory

Provides a unified classification for scientific knowledge. Enunciated by biologist Ludwig Von Bertalanffy:

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: 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)

slide 15

Systems Building Blocks

Stocks Flows Information Links Decision Points Converters Auxiliary Variables

slide 16

Stocks

“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 17

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 18

Stock and Flow Diagram

Stocks in boxes Flows as straight double arrows Information Links as thin curved arrows Decision Points as closed in X

Control Material Flaw

to Stock

Add New information

Send informationfrom the Stock

Control Material Flaw

from Stock

Stock

System Dynamics Modelling

Shrimp farming

Simple model for shrimp farm

Results?

Figure 7

Positive Coupling

AtmosphericCO2

Greenhouseeffect

• 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’ssurface

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 putcouplings together in feedback loops…

person A’sbodytemperature

person A’sblankettemperature

Negative Feedback Loops:Electric Blankets

person B’sblankettemperature

person B’sbodytemperature

person A’sbodytemperature

person A’sblankettemperature

A Positive Feedback Loop:Mixed-up Electric Blankets

person B’sblankettemperature

person B’sbodytemperature

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

Dinamo Vensim Simile STELLA

Water in the tub

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

Not yet

(description extracted from “TerraME types and functions”)

Event

Not yet

Not yet

Temporal model

Source: (Carneiro et al., 2013)

1:32:10 ag1:execute( )

1:38:07 ag2:execute( )

1:42:00 cs:save()

. . .

(4) ACTIONreturn value

true

(1) Get first EVENT

1:32:00 cs:load( ) (2) Update current time

(3) Execute the ACTION

false

(5) Schedule EVENT again

Observer

Not yet

Water in the tub

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

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