1. Modelling Theory Part I: Basics
Tiago Garcia de Senna Carneiro
Gilberto Câmara
Pedro Ribeiro de Andrade
Münster, 2014

2. What is a model?
A model is a simplified representation of a phenomenon, process, actor, system, or any complex entity.
The truth about reality is intangible.
Everything science knows about reality is a model of reality.

3. Modelling starts with a good question
A good model:
Has a goal
Serves to answer a (scientific) question
There is no GENERAL model
Thinking in a map as a model for a region…
Which information layers (variables) will you draw in your map? ?

4. When models need to be changed?
When they are not enougth to explain the observed phenomenon
When the added variables or rules improve the model’s capacity in reproducing the observed behavior

5. Models versus Scientific Knowledge
The truth is not tangible.
Everything that science knows about reality is a model.

6. Examples of models – atom
Concept
Indivisible entities over which matter is built
Model
Dalton, 1807  solid sphere
Thomson, 1904  plum pudding
Rutherford, 1911  Positive nucleus + negative electrosphere
Bohr, 1913  Nucleus + electrons with different levels of energy
Schrondinger, Pauli  Subatomic particles
Dalton, 1807
Thomson, 1904
Rutherford, 1911
Bohr, 1913

7. Examples of models – Shape of the Earth
Concept
Place where we live. Environment.
Model
Flat  archaic belief
Spherical
Pythagoras (AD 570)  Suggested that Earth could be spherical
Aristotle (AD 330)  First evidence: semi-circular shadow at moon
Eratosthenes (AD 240)  First estimate of Earth’s circumference
Mathematics
Scotsman McLaurin (1742)  Flat
Carl Jacobi (1834)  Elipsoidal
Henri Poincaré (1885)  Periform
Dynamic  Modern geodesy
Dynamic geoid
Flat
Spheric
Ellipsoid
Periform

8. Hubble: Photo of a Supernova Satellite launching rockets
Models work?
GPS constellation
Hubble: Photo of a Supernova
Satellite
Satellite launching rockets
Taiyuan, na China

9. Which is the better model?

10. Earth – Our Environment

11. Limits for Models Uncertainty on basic equations
Social and Economic
Systems
Quantum
Gravity
Particle
Physics
Living
Systems
Global
Change
Hydrological
Models
Chemical
Reactions
Meteorology
Solar System Dynamics
Complexity of the phenomenon
source: John Barrow
(after David Ruelle)

12. What is a Model? Deforestation in Amazonia in 2020?
simplified representation of a process
Model = entities + attributes + relationships + interactions
graphics: INPE, Pesquisa FAPESP

13. What is a model?
Deforestation process model
Farmer
cuts
balance E0 E4
Land
owns
soilType
coverType
Model = entities + atributes + relationships + interactions

14. Source: Miller and Page 2005?
Dynamic Models
Time t
Time t + 1
F(S) S
World
E(S)
E(S)
f(s) s
Model
Source: Miller and Page 2005?

15. Dynamic Models
1997
2007 ? S ? ?
World
Modell
f(s)

16. Why modeling? Understand how the system behaves
Simulate future and alternative scenarios
Make experiments that are not feasible in the real world
Support decision making and public policies using scientific knowledge

17. Global Change Human actions and global change
photo: C. Nobre
Global Change
Where are changes taking place?
How much change is happening?
Who is being impacted by the change?
What is causing change?
photo: A. Reenberg

18. Modelling approaches Theory-driven models Data-driven models Hybrids
There are well accepted theories
Equations are known
Results are general
Data-driven models
Application of inferential methods: statistical regression, neural networks, association rules, etc..
Do not represent causal relationships (cause-consequence)
Based on the assumption that the processes are stationeries.
Hybrids

19. Water in a tube (bottle) model
Question #1: Where the water will stop? At the hole's top? At the hole's bottom? At the middle?

20. Observations can surprise you!
Question #1: Where to water will stop? At the hole's top? At the hole's bottom? At the middle?
Top of the hole
Middle of the hole
Bottom of the hole

21. Water in a tube (bottle) model
Question #2: Could you tell what will be the height of the water column at a given moment?

22. Some data-driven models
Question #2: Could you tell what will be the height of the water column at a given moment?

23. Water in a tube (bottle) model
Question #3: Could you explain the process? I mean cause-effects relationships taking place in the experiment?

24. One theory–driven model
Bernoulli’s principle:  An increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

25. AGAIN: Modelling approaches
Theory-driven models
There are well accepted theories
Equations are known
Results are general
Data-driven models
Application of inferential methods: statistical regression, neural networks, association rules, etc..
Do not represent causal relationships (cause-consequence)
Based on the assumption that the processes are stationeries.
Hybrids