TIAGO GARCIA CARNEIROANA PAULA AGUIARGILBERTO CÂMARAANTÔNIO MIGUEL MONTEIRO

TerraME - A tool for spatial dynamic

modelling

LUCC WorkshopAmsterdam, October 2004

C5J9F6

Part 1 – The challenges

LUCC WorkshopAmsterdam, 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 ( It+n )

. . FF

f (It) f (It+1) f (It+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

ActionPerception

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)

www.red3d.com/cwr/boids/

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 WorkshopAmsterdam, October 2004

C5J9F6

WHAT TOOLS DO WE NEED FOR SPATIAL DYNAMICAL MODELLING?

Nested-CACell 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 cellsEach 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

VariablesControl graphFlow and Jump conditionsEvents

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

DRYsoilwater=soilwater+pre-evap

WETSurplus=soilwater-infilcp

Soilwater=infilcp

input soilwater>=infilcp

input

Surplus>0

TRANSPORTINGMOVE(LDD, surplus,

infilcp)

discharge

Control Mode

Flow Condition Jump Condition Event Transition

DRY Solwat=solwat+pre-evap

Solwat>=infcap

WET

WET Surplus=soilwater-infilcap

Surplus>0 discharge

TRANSP

TRANSP MOVE(LDD,surplus, infilcap)

Surplus=0 input DRY

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 163

São Felix do Xingu Source:Prodes/INPE

Source: Aguiar et al., 2003

Generalized Proximity Matrices

Consolidated area Emergent area

(a) land_cover equals deforested in 1985 (a) land_cover equals deforested in 1985

attr_id object_id initial_time final_time land_cover dist_primary_road dist_secondary_roadC34L181985-01-0100:00:001985-12-3123:59:59C34L18 01/01/1985 31/12/1985 forest 7068.90 669.22C34L181988-01-0100:00:001988-12-3123:59:59C34L18 01/01/1988 31/12/1988 forest 7068.90 669.22C34L181991-01-0100:00:001991-12-3123:59:59C34L18 01/01/1991 31/12/1991 forest 7068.90 669.22C34L181994-01-0100:00:001994-12-3123:59:59C34L18 01/01/1994 31/12/1994 deforested 7068.90 669.22C34L181997-01-0100:00:001997-12-3123:59:59C34L18 01/01/1997 31/12/1997 deforested 7068.90 669.22C34L182000-01-0100:00:002000-12-3123:59:59C34L18 01/01/2000 31/12/2000 deforested 7068.90 669.22C34L191985-01-0100:00:001985-12-3123:59:59C34L19 01/01/1985 31/12/1985 forest 7087.29 269.24C34L191988-01-0100:00:001988-12-3123:59:59C34L19 01/01/1988 31/12/1988 deforested 7087.29 269.24C34L191991-01-0100:00:001991-12-3123:59:59C34L19 01/01/1991 31/12/1991 deforested 7087.29 269.24C34L191994-01-0100:00:001994-12-3123:59:59C34L19 01/01/1994 31/12/1994 deforested 7087.29 269.24C34L191997-01-0100:00:001997-12-3123:59:59C34L19 01/01/1997 31/12/1997 deforested 7087.29 269.24C34L192000-01-0100:00:002000-12-3123:59:59C34L19 01/01/2000 31/12/2000 deforested 7087.29 269.24

Part I – TerraME main characteristics

Software Architecture

TerraLib

TerraLib TerraME Framework

C++ Signal Processing

librarys

C++ Mathematical

librarys

C++ Statisticallibrarys

TerraME Virtual Machine

TerraME Compiler

TerraME Language

RondôniaModel São Felix Model Amazon Model Hydro Model

http://www.terralib.org/

Loading Data-- Loads the TerraLib cellular spacecsCabecaDeBoi = 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

km

Projetos de Colonização

10

8

15

1614

13

Projetos antigosNovos projetosProjetos planejados

km

Projetos de Colonização

10

8

15

1614

13

Projetos antigosNovos projetosProjetos planejados

Projetos antigosNovos projetosProjetos planejados

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 patterns9o S

10o S

9o 30’ S

10o 30’ S

9o S

9o 30’ S

10o S

10o 30’ S

0 50Km

62o 30’ W 62o W

62o 30’ W 62o 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 2000 - 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

2.500 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 Unitn

Land Unit2

Land Unit1

...Rondônia

G

Global rate

...

+

+

+

Rsmall

Rlarge

Rsmall

(two types of agentes Rsmall and R large)

+

+

+

Asmall

Alarge

Asmall

...

(two types of agentes Asmall 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 AgentDeforesting

Slowing downIddle

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

1985

1997 1997Large 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 Results1985 to 1997