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

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.

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? ?

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

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

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

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

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

Which is the better model?

Earth – Our Environment

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)

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

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

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?

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

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

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

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

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?

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

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

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

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

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.

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