TIAGO GARCIA CARNEIRO ANA PAULA AGUIAR GILBERTO CÂMARA ANTÔNIO MIGUEL MONTEIRO TerraME - A tool for spatial dynamic modelling LUCC Workshop Amsterdam, October 2004 C5J9F6

Part 1 – The challenges LUCC Workshop Amsterdam, October 2004 C5J9F6 WHAT ARE THE REQUIREMENTS FOR SPATIAL DYNAMICAL MODELLING?

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

What is Computational Modelling? Design and implementation of computational enviroments for modelling  Requires a formal and stable description  Implementation allow 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)

The challenges: multi-scale models Using nested scales

Old Settlements (more than 20 years) Recent Settlements (less than 4 years) Farms Settlements 10 to 20 anos Behavior can be heterogeneous in space and time Source: Escada, 2003

Change is a multi-scale process (Source: Turner II, 2000)

Matogrosso State Mato Grosso State Land change Amazonia requires representation of: Actors Processes Speed of change Connectivity relations Rondônia State

Agent based models Cellular automata models (Rosenschein and Kaelbling, 1995) (Wooldbridge, 1995) (von Neumann, 1966)(Minsky, 1967) (Aguiar et al, 2004) (Pedrosa et al, 2003) (Straatman et al, 2001) Modelling conceptions

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)

Segregation Segregation is an outcome of individual choices

Schelling’s Model of Segregation < 1/3 Micro-level rules of the game Stay if at least a third of neighbors are “kin” Move to random location otherwise

Schelling’s Model of Segregation Intolerance values > 30%: formation of ghettos

What are complex adaptive systems?

Agent Agent: flexible, interacting and autonomous An agent is any actor within an environment, any entity that can affect itself, the environment and other agents.

Agents: autonomy, flexibility, interaction football players

Agent-Based Modelling Goal Environment Representations Communication Action Perception Communication Gilbert, 2003

Agents are… Identifiable and self-contained Goal-oriented  Does not simply act in response to the environment Situated  Living in an environment with which interacts with other agents Communicative/Socially aware  Communicates with other agents Autonomous  Exercises control over its own actions

Bird Flocking No central authority: Each bird reacts to its neighbor Bottom-up: not possible to model the flock in a global manner. It is necessary to simulate the INTERACTION between the individuals

Bird Flocking: Reynolds (1987) Cohesion: steer to move toward the average position of local flockmates Separation: steer to avoid crowding local flockmates Alignment: steer towards the average heading of local flockmates

Agents changing the landscape

Part 2 – The building blocks LUCC Workshop Amsterdam, October 2004 C5J9F6 WHAT TOOLS DO WE NEED FOR SPATIAL DYNAMICAL MODELLING?

Nested-CA Cell Spaces Components  Cell Spaces  Generalizes Proximity Matrix – GPM  Hybrid Automata model  Nested enviroment

Cell Spaces

The Nested-CA spatial model The space local properties, constraints, and connectivity can be modeled by: - a set of geographic data: each cell has various attributes GIS - a spatial structure: a lattice of cells Each cell has a neighborhood that can be, possibly, different. - Space is nether isomorphic nor structurally homogeneous. (Couclelis 1997) - Actions at a distance are considered. (Takeyana 1997), (O’Sullivan 1999)

An environment is… …representation where analytical entities (rules) change the properties of space in time. Several interacting entities share the same spatiotemporal structure.

Multiple scale model construction Using nested scales

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

The TerraLib Framework for Spatial Dynamic Modelling 40 An Example in Hydrology A water balance Automata DRY soilwater=soilwater+pre-evap WET Surplus=soilwater-infilcp Soilwater=infilcp input soilwater>=infilcp input Surplus>0 TRANSPORTING MOVE(LDD, surplus, infilcp) discharge Control Mode Flow ConditionJump ConditionEventTransition DRYSolwat=solwat+pre-evapSolwat>=infcapWET Surplus=soilwater-infilcapSurplus>0dischargeTRANSP MOVE(LDD,surplus, infilcap)Surplus=0inputDRY input

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?

Generalized Proximity Matrices Forest Deforested No data Non-forest- Water Roads 100 km Transamazônica Br São Felix do Xingu Source: Prodes/INPE Source: Aguiar et al., 2003

Generalized Proximity Matrices Consolidated areaEmergent area

(a)land_cover equals deforested in 1985

Part I – TerraME main characteristics

Software Architecture TerraLib TerraME Framework C++ Signal Processing librarys C++ Mathematical librarys C++ Statistical librarys TerraME Virtual Machine TerraME Compiler TerraME Language RondôniaModelSão Felix Model Amazon ModelHydro Model

Loading Data -- Loads the TerraLib cellular space csCabecaDeBoi = CellularSpace { dbType = "ADO", host = "amazonas", database = "c:\\cabecaDeBoi.mdb", user = "", password = "", layer = "cellsSerraDoLobo90x90", theme = "cells", select = { "altimetria", "qtdeAgua", "capInf" } } csCabecaDeBoi:load(); csCabecaDeBoi:loadNeighbourhood(“Moore_SerraDoLobo1985"); GIS

MODELLING LAND CHANGE IN RONDONIA Part III: Modeling Examples

Deforestation Forest Non-forest Deforestation Map – 2000 (INPE/PRODES Project) Introduction: Rondônia modeling exercise study area Federal Government induced colonization area (since the 70s): Small, medium and large farms. Mosaic of land use patterns. Definition of land units and typology of actors based on multi-temporal images (85- 00) and colonization projects information (Escada, 2003). Intersects 10 municipalities (~100x200 km).

Actors and patterns 9 o S 10 o S 9 o 30’ S 10 o 30’ S 9 o S 9 o 30’ S 10 o S 10 o 30’ S 0 50 Km 62 o 30’ W62 o W 62 o 30’ W62 o W Model hypothesis: Occupation processes are different for Small and Medium/Large farms. Rate of change is not distributed uniformly in space and time: rate in each land unit is influenced by settlement age and parcel size; for small farms, rate of change in the first years is also influenced by installation credit received. Location of change: For small farms, deforestation has a concentrated pattern that spreads along roads. For large farmers, the pattern is not so clear. Large farms Medium farms Urban areas Small farms Reserves

Model overview Global study area rate in time Deforestation Rate Distribution from 1985 to Land Units Level: Large/Medium Rate Distribution sub-model Small Farms Distribution sub-model Allocation of changes - Cellular space level: Large/Medium allocation sub-model Small allocation sub-model m (large and medium) 500 m (small) Large farms Medium farms Urban areas Small farms Reserves Land unit 1 rate t Land unit 2 rate t

Model implementation in TerraME Land Unit n Land Unit 2 Land Unit 1... Rondônia G Global rate R small R large R small (two types of agentes R small and R large ) A small A large A small... (two types of agentes A small and A large ) Each Land Unit is an environment, nested in the Rondônia environment. Environment Agent Legend

Deforestation Rate Distribution Module Newly implanted Deforesting Slowing down latency > 6 years Deforestation > 80% Small Units Agent Factors affecting rate: Global rate Relation properties density - speedy of change Year of creation Credit in the first years (small) Iddle Year of creation Deforestation = 100% Large and Medium Units Agent Deforesting Slowing down Iddle Year of creation Deforestation = 100% Deforestation > 80%

Allocation Module: different factors and rules Factors affecting location of changes: Small Farmers (500 m resolution): Connection to opened areas through roads network Proximity to urban areas Medium/Large Farmers (2500 m resolution): Connection to opened areas through roads network Connection to opened areas in the same line of ownerships

Allocation Module: different resolution, variables and neighborhoods 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

Simulation Results 1985 to 1997