Introduction to Spatial Dynamical Modelling Gilberto Câmara Director, National Institute for Space Research

Course objectives Teach the fundamentals of spatial dynamical models Emphasis on Land Change modelling Computational tools for spatial models - TerraME

Course outline Monday  Motivation, introduction to complexity and cellular automata, examples from real-life problems Tuesday  Introduction to TerraME, software tutorial Wednesday  Land change modelling in TerraME  Lab exercise – course exam

“Give us some new problems” What about saving the planet?

Earth as a system

The fundamental question of our time fonte: IGBP How is the Earth’s environment changing, and what are the consequences for human civilization?

Global Change Where are changes taking place? How much change is happening? Who is being impacted by the change?

Global Land Project What are the drivers and dynamics of variability and change in terrestrial human- environment systems? How is the provision of environmental goods and services affected by changes in terrestrial human- environment systems? What are the characteristics and dynamics of vulnerability in terrestrial human- environment systems?

Impacts of global land change More vulnerable communities are those most at risk

Earth observation satellites provide key information about global land change

EO data: benefits to everyone CBERS-2 image of Manaus

Slides from LANDSAT Aral Sea Bolivia source: USGS

Source: Carlos Nobre (INPE) Can we avoid that this….

Fire... Source: Carlos Nobre (INPE) ….becomes this?

We might know the past…. Yearly deforestation rate in Legal Amazonia

What’s coming next?

Até 10% % 20 – 30% 30 – 40% 40 – 50% 50 – 60% 60 – 70% 70 – 80% 80 – 90% 90 – 100% Total Deforestation up to 1997

Increment – 1997 to 2000

Até 3 % 3 - 6% 6 – 10% 10 – 13% 13 – 16% 16 – 20% 20 – 23% 23 – 26% 26 – 29% 29 – 33% Increment – 2000 to 2003

Increment – 2003 to 2006 Até 3 % 3 - 6% 6 – 8% 8 – 11% 11 – 14% 14 – 17% 17 – 20% 20 – 22% 22 – 25% 25 – 28%

Incremento – 2000 a 2006 Até 5 % % 10 – 15% 15 – 20% 20 – 24% 24 – 29% 29 – 34% 34 – 39% 39 – 43% 43 – 49%

20 municipalities with greater desforestation in 2005 (área km 2 ) Total deforestation 2005 = km = km 2 Reduction: 60%

Deforestation classes per area 13%22%27%32%31%68%38%More than 300 ha 10%11% 12%14%6%12%150 a 300 ha 7% 8%3%8%100 a 150 ha 16%14%13%12%13%6%12%50 a 100 ha 19%16%13%11% 5%11%25 a 50 ha 25%20%16%14%12%6%11%10 a 25 ha 10%9% 8%6%4%5%Less than 10 ha Tendência de Aumento Tendência de Redução Aproxim. Estável Aumento Redução Estável

Deforested areas with more than 300ha em 2003

+ protected areas

Altamira (Pará) – LANDSAT Image – 22 August 2003

Altamira (Pará) – MODIS Image – 07 May 2004

Imagem Modis de , com excesso de nuvens Altamira (Pará) – MODIS Image – 21 May 2004

Altamira (Pará) – MODIS Image – 07 June 2004

6.000 hectares deforested in one month! Altamira (Pará) – MODIS Image – 22 June 2004

Altamira (Pará) – LANDSAT Image – 07 July 2004

Underlying Factors driving proximate causes Causative interlinkages at proximate/underlying levels Internal drivers *If less than 5%of cases, not depicted here. source:Geist &Lambin  5% 10% 50% % of the cases What Drives Tropical Deforestation?

Modelling Land Change in Amazonia How much deforestation is caused by:  Soybeans?  Cattle ranching?  Small-scale setllers?  Wood loggers?  Land speculators?  A mixture of the above?

Large-Scale Agriculture Agricultural Areas (ha) /1996% Legal Amazonia5,375,16532,932, Brazil33,038,02799,485, Source: IBGE - Agrarian Census photo source: Edson Sano (EMBRAPA)

Cattle in Amazonia and Brazil Unidade % Amazônia Legal29,915,79951,689,06172,78% Brasil154,229,303176,388,72614,36% photo source: Edson Sano (EMBRAPA)

Trends in deforestation and soya prices Source: Paulo Barreto (IMAZON)

Trends in deforestation and meat prices Source: Paulo Barreto (IMAZON)

Deforestation classes per area 13%22%27%32%31%68%38%More than 300 ha 10%11% 12%14%6%12%150 a 300 ha 7% 8%3%8%100 a 150 ha 16%14%13%12%13%6%12%50 a 100 ha 19%16%13%11% 5%11%25 a 50 ha 25%20%16%14%12%6%11%10 a 25 ha 10%9% 8%6%4%5%Less than 10 ha Tendência de Aumento Tendência de Redução Aproxim. Estável Aumento Redução Estável

Deforested areas with more than 300ha em protected areas

New Frontiers Deforestation Forest Non-forest Clouds/no data INPE 2003/2004: Dynamic areas (current and future) Intense Pressure Future expansion

Challenge: How do people use space? Loggers Competition for Space Soybeans Small-scale Farming Ranchers Source: Dan Nepstad (Woods Hole)

Rondônia (Vale do Anari) People changing the landscape Field knowledge is fundamental!

Model = entities + relations + attributes + rules What is a Model? Model = a simplified description of a complex entity or process E0E0 E4E4 owns deforest space land use soil type Deforestation Farmer income

Modelling Complex Problems Application of interdisciplinary knowledge to produce a model. If (... ? ) then... Desforestation?

What is Computational Modelling? Design and implementation of computational environments for modelling  Requires a formal and stable description  Implementation allows experimentation Rôle of computer representation  Bring together expertise in different field  Make the different conceptions explicit  Make sure these conceptions are represented in the information system

f ( I t+n ). FF f (I t )f (I t+1 )f (I t+2 ) Dynamic Spatial Models “A dynamical spatial model is a computational representation of a real-world process where a location on the earth’s surface changes in response to variations on external and internal dynamics on the landscape” (Peter Burrough)

t p - 20 t p - 10 tptp Calibration t p + 10 Forecast Dynamic Spatial Models Source: Cláudia Almeida

GIScience and change We need a vision for extending GIScience to have a research agenda for modeling change

The Renaissance Vision “No human inquiry can be called true science unless it proceeds through mathematical demonstrations” (Leonardo da Vinci) “Mathematical principles are the alphabet in which God wrote the world” (Galileo)

The Renaissance vision for space Rules and laws that enable: Understanding how humans use space; Predicting changes resulting from human actions; Modeling the interaction between humans and the environment.

Modelling Land Change in Amazonia Territory (Geography) Money (Economy) Culture (Antropology) Modelling (GIScience)

Modelling and Public Policy System Ecology Economy Politics Scenarios Decision Maker Desired System State External Influences Policy Options

Modelling Human Actions: Two Approaches Models based on global factors  Explanation based on causal models  “For everything, there is a cause”  Human_actions = f (factors,....) Emergent models  Local actions lead to global patterns  Simple interactions between individuals lead to complex behaviour  “More is different”  “The organism is intelligent, its parts are simple- minded”

Emergence: Clocks, Clouds or Ants? Clocks  Paradigms: Netwon’s laws (mechanistic, cause-effect phenomena describe the world) Clouds  Stochastic models  Theory of chaotic systems Ants  The colony behaves intelligently  Intelligence is an emergent property

Statistics: Humans as clouds Establishes statistical relationship with variables that are related to the phenomena under study Basic hypothesis: stationary processes Exemples: CLUE Model (University of Wageningen) y=a 0 + a 1 x 1 + a 2 x a i x i +E

Factors Affecting Deforestation

Statistics: Humans as clouds Statistical analysis of deforestation

Modelling Tropical Deforestation Fine: 25 km x 25 km grid Coarse: 100 km x 100 km grid Análise de tendências Modelos econômicos

Modelling Deforestation in Amazonia High coefficients of multiple determination were obtained on all models built (R 2 from 0.80 to 0.86). The main factors identified were:  Population density;  Connection to national markets;  Climatic conditions;  Indicators related to land distribution between large and small farmers. The main current agricultural frontier areas, in Pará and Amazonas States, where intense deforestation processes are taking place now were correctly identified as hot-spots of change.

The trouble with statistics Extrapolation of current measured trends How do we know if tommorow will be like today? How do we incorporate feedbacks?

Complex Adaptive Systems: Humans as Ants Cellular Automata:  Matrix,  Neighbourhood,  Set of discrete states,  Set of transition rules,  Discrete time. “CAs contain enough complexity to simulate surprising and novel change as reflected in emergent phenomena” (Mike Batty) Simple agents following simple rules can generate amazingly complex structures.

Complex adaptative systems How come that a city with many inhabitants functions and exhibits patterns of regularity? How come that an ecosystem with all its diverse species functions and exhibits patterns of regularity? How can we explain how similar exploration patterns appear on the Amazon rain forest?

What are complex adaptive systems? Systems composed of many interacting parts that evolve and adapt over time. Organized behavior emerges from the simultaneous interactions of parts without any global plan.

Emergence or Self-Organisation We recognise this phenomenon over a vast range of physical scales and degrees of complexity Source: John Finnigan (CSIRO)

From galaxies….

…to cyclones ~ 100 km Source: John Finnigan (CSIRO)

Ribosome E Coli Root Tip Amoeba Gene expression and cell interaction Source: John Finnigan (CSIRO)

The processing of information by the brain Source: John Finnigan (CSIRO)

Animal societies and the emergence of culture Source: John Finnigan (CSIRO)

Results of human society such as economies Source: John Finnigan (CSIRO)

One Definition of a CAS A complex, nonlinear, interactive system which has the ability to adapt to a changing environment. Potential for self-organization, existing in a nonequilibrium environment. Examples include living organisms, the nervous system, the immune system, the economy, corporations, societies, and so on.

Properties of Complex Adaptive Systems In a CAS, agents interact according to certain rules of interaction. The agents are diverse in both form and capability and they adapt by changing their rules and, hence, behavior, as they gain experience. Complex, adaptive systems evolve historically, meaning their past or history, i.e., their experience, is added onto them and determines their future trajectory.

Properties of Complex Adaptive Systems Many interacting parts Emergent phenomena Adaptation Specialization & modularity Dynamic change Competition and cooperation Decentralization Non-linearities

What is a cellular automaton? a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells.

Cellular Automata: Humans as Ants Cellular Automata:  Matrix,  Neighbourhood,  Set of discrete states,  Set of transition rules,  Discrete time. “CAs contain enough complexity to simulate surprising and novel change as reflected in emergent phenomena” (Mike Batty)

2-Dimensional Automata 2-dimensional cellular automaton consists of an infinite (or finite) grid of cells, each in one of a finite number of states. Time is discrete and the state of a cell at time t is a function of the states of its neighbors at time t-1.

Cellular Automata RulesNeighbourhood States Space and Time t t1t1

Why do we care about CA? Can be used to model simple individual behaviors Complex group behaviors can emerge from these simple individual behaviors

Conway’s Game of Life At each step in time, the following effects occur: Any live cell with fewer than two neighbors dies, as if by loneliness. Any live cell with more than three neighbors dies, as if by overcrowding. Any live cell with two or three neighbors lives, unchanged, to the next generation. Any dead cell with exactly three neighbors comes to life.

Game of Life Static Life Oscillating Life Migrating Life

Conway’s Game of Life The universe of the Game of Life is an infinite two- dimensional grid of cells, each of which is either alive or dead. Cells interact with their eight neighbors.

Von Neumann Neighborhood Moore Neighborhood Most important neighborhoods

Computational Modelling with Cell Spaces Cell Spaces Components  Cell Spaces  Generalizes Proximity Matriz – GPM  Hybrid Automata model  Nested enviroment

Cell Spaces

Which Cellular Automata? For realistic geographical models  the basic CA principles too constrained to be useful Extending the basic CA paradigm  From binary (active/inactive) values to a set of inhomogeneous local states  From discrete to continuous values (30% cultivated land, 40% grassland and 30% forest)  Transition rules: diverse combinations  Neighborhood definitions from a stationary 8-cell to generalized neighbourhood  From system closure to external events to external output during transitions

Hybrid Automata Formalism developed by Tom Henzinger (UC Berkeley)  Applied to embedded systems, robotics, process control, and biological systems Hybrid automaton  Combines discrete transition graphs with continous dynamical systems  Infinite-state transition system

Hybrid Automata Variables Control graph Flow and Jump conditions Events Control Mode A Flow Condition Control Mode B Flow Condition Event Jump condition Event

Neighborhood Definition Traditional CA  Isotropic space  Local neighborhood definition (e.g. Moore) Real-world  Anisotropic space  Action-at-a-distance TerraME  Generalized calculation of proximity matrix

Space is Anisotropic Spaces of fixed location and spaces of fluxes in Amazonia

Motivation Which objects are NEAR each other?

Motivation Which objects are NEAR each other?

Using Generalized Proximity Matrices Consolidated areaEmergent area

(a)land_cover equals deforested in 1985

Cell-space x Cellular Automata CA  Homogeneous, isotropic space  Local action  One attribute per cell (discrete values)  Finite space state Cell-space  Non-homogeneous space  Action-at-a-distance  Many attributes per cell  Infinite space state

Spatial dynamic modeling Locations change due to external forces Realistic representation of landscape Elements of dynamic models Geographical space is inhomogeneous Different types of models  discretization of space in cells  generalization of CA  discrete and continous processes  Flexible neighborhood definitions  Extensibility to include user- defined models DemandsRequirements

Underlying Factors driving proximate causes Causative interlinkages at proximate/underlying levels Internal drivers *If less than 5%of cases, not depicted here. source:Geist &Lambin  5% 10% 50% % of the cases What Drives Tropical Deforestation?

Spatial dynamic modeling Locations change due to external forces Realistic representation of landscape Elements of dynamic models Geographical space is inhomogeneous Different types of models  discretization of space in cells  generalization of CA  discrete and continous processes  Flexible neighborhood definitions  Extensibility to include user- defined models DemandsRequirements

Agents and CA: Humans as ants Old Settlements (more than 20 years) Recent Settlements (less than 4 years) Farms Settlements 10 to 20 anos Source: Escada, 2003 Identify different actors and try to model their actions

Agent model using Cellular Automata Large farm environments: 2500 m resolution Continuous variable: % deforested Two alternative neighborhood relations: connection through roads farm limits proximity Small farms environments: 500 m resolution Categorical variable: deforested or forest One neighborhood relation: connection through roads

The trouble with agents Many agent models focus on proximate causes  directly linked to land use changes  (in the case of deforestation, soil type, distance to roads, for instance) What about the underlying driving forces?  Remote in space and time  Operate at higher hierarchical levels  Macro-economic changes and policy changes

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