Introduction to Spatial Dynamical Modelling

Gilberto CâmaraDirector, 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?

Atmospheric Physics/Dynamics

Tropospheric Chemistry

Global Moisture

Ocean Dynamics

MarineBiogeochemistry

Terrestrial Ecosystems

Terrestrial Energy/Moisture

Climate Change

Pollutants

CO2

CO2

Soil

Land Use

Physical Climate System

Biogeochemical Cycles

Human Activities

(from Earth System Science: An Overview, NASA, 1988)

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 everyoneEO data: benefits to everyone

CBERS-2 image of Manaus

Slides from LANDSATAral Sea

Bolivia

1975 1992 2000

1973 1987 2000

source: USGS

Source: Carlos Nobre (INPE)

Can we avoid that this….

Fire...

Source: Carlos Nobre (INPE)

….becomes this?

Taxa de Desmatamento Anual na Amazônia Legal

0

5000

10000

15000

20000

25000

30000

35000

88(a)

89 90 91 92 93(b)

94(b)

95 96 97 98 99 00 01 02 03 04 05 06

Ano

Km

2/an

o

We might know the past….

Yearly deforestation rate in Legal Amazonia

What’s coming next?

Até 10%

10 - 20%

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 %

5 - 10%

10 – 15%

15 – 20%

20 – 24%

24 – 29%

29 – 34%

34 – 39%

39 – 43%

43 – 49%

20 municipalities with greater desforestation in 2005 (área km2)

Total deforestation

2005 = 8.296 km2

2006 = 3.283 km2

Reduction: 60%

-73%65239MTBrasnorte

-52%116242ROMachadinho D'Oeste

-72%68245MTPeixoto de Azevedo

-71%73255MTNova Ubiratã

-74%66257MTVila Rica

-24%214280PAPacajá

-71%81280PASanta Maria das Barreiras

-79%61292MTCotriguaçu

-56%128294MTNova Bandeirantes

-75%75303PAParagominas

-74%81312RONova Mamoré

-84%52332MTAripuanã

-89%42385MTNova Maringá

-50%200403MTJuara

-72%136486PASantana do Araguaia

-58%217517MTColniza

-47%285542PAAltamira

-70%175580PACumaru do Norte

-41%382646ROPorto Velho

-46%7641.406PASão Félix do Xingu

Variação20062005UFNome

Deforestation classes per area

13%22%27%32%31%68%38%More than 300 ha

10%11%11%12%14%6%12%150 a 300 ha

7%7%7%7%8%3%8%100 a 150 ha

16%14%13%12%13%6%12%50 a 100 ha

19%16%13%11%11%5%11%25 a 50 ha

25%20%16%14%12%6%11%10 a 25 ha

10%9%9%8%6%4%5%Less than 10 ha

2006200520042003200220012000

Tendência de Aumento Tendência de ReduçãoAproxim. Estável

Au

men

toR

edu

çãoE

stável

Deforested areas with more than 300ha em 2003

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 2004-05-21, 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 Factorsdriving proximate causes

Causative interlinkages atproximate/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)

  1970 1995/1996 %

Legal Amazonia 5,375,16532,932,15

8 513

Brazil33,038,02

799,485,58

0 203

Source: IBGE - Agrarian Census

photo source: Edson Sano (EMBRAPA)

Unidade 1992 2001 %Amazônia Legal 29915799 51689061 72,78% Brasil 154,229,303 176,388,726 14,36%Fonte: PAM - IBGE

Cattle in Amazonia and Brazil

Cattle in Amazonia and Brazil

Unidade 1992 2001 %

Amazônia Legal 29,915,799 51,689,061 72,78%

Brasil154,229,30

3176,388,72

6 14,36%

photo source: Edson Sano (EMBRAPA)

Trends in deforestation and soya prices

-

5

10

15

20

25

30

35

40

1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

R$

ou

IG

P

0

5.000

10.000

15.000

20.000

25.000

30.000

K2

des

mat

ado

s

Soja (Média anual) deflacionado R$/sc 60 kg - MT Km2 desmatado na Amazônia

Source: Paulo Barreto (IMAZON)

Trends in deforestation and meat prices

-

10

20

30

40

50

60

1994199519961997199819992000200120022003200420052006

R$

ou

IG

P

0

5.000

10.000

15.000

20.000

25.000

30.000

K2

des

mat

ado

s

Preço boi (IGP) São Paulo Km2 desmatado na Amazônia

Source: Paulo Barreto (IMAZON)

Deforestation classes per area

13%22%27%32%31%68%38%More than 300 ha

10%11%11%12%14%6%12%150 a 300 ha

7%7%7%7%8%3%8%100 a 150 ha

16%14%13%12%13%6%12%50 a 100 ha

19%16%13%11%11%5%11%25 a 50 ha

25%20%16%14%12%6%11%10 a 25 ha

10%9%9%8%6%4%5%Less than 10 ha

2006200520042003200220012000

Tendência de Aumento Tendência de ReduçãoAproxim. Estável

Au

men

toR

edu

çãoE

stável

Deforested areas with more than 300ha em 2003

+ 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

E0

E4owns

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 ( 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)

tp - 20 tp - 10

tp

Calibration Calibration tp + 10

ForecastForecast

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

EcologyEconomyPolitics

ScenariosDecisionMaker

Desired System

State

ExternalInfluences

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=a0 + a1x1 + a2x2 + ... +aixi +E

Factors Affecting Deforestation

Category VariablesDemographic Population Density

Proportion of urban populationProportion of migrant population (before 1991, from 1991 to 1996)

Technology Number of tractors per number of farmsPercentage of farms with technical assistance

Agrarian strutucture Percentage of small, medium and large properties in terms of areaPercentage of small, medium and large properties in terms of number

Infra-structure Distance to paved and non-paved roadsDistance to urban centersDistance to ports

Economy Distance to wood extraction polesDistance to mining activities in operation (*)Connection index to national markets

Political Percentage cover of protected areas (National Forests, Reserves, Presence of INCRA settlementsNumber of families settled (*)

Environmental Soils (classes of fertility, texture, slope)Climatic (avarage precipitation, temperature*, relative umidity*)

Statistics: Humans as cloudsMODEL 7: R² = .86

Variables Description stb p-level

PORC3_ARPercentage of large farms, in terms of area 0,27 0,00

LOG_DENS Population density (log 10) 0,38 0,00

PRECIPIT Avarege precipitation -0,32 0,00

LOG_NR1Percentage of small farms, in terms of number (log 10) 0,29 0,00

DIST_EST Distance to roads -0,10 0,00

LOG2_FER Percentage of medium fertility soil (log 10) -0,06 0,01

PORC1_UC Percantage of Indigenous land -0,06 0,01

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 (R2 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 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)

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

t1

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 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

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

Demands Requirements

Underlying Factorsdriving proximate causes

Causative interlinkages atproximate/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

Demands Requirements

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

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

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

Un

cert

ain

ty o

n b

asic

eq

uat

ion

s

Solar System DynamicsMeteorology

ChemicalReactions

HydrologicalModels

ParticlePhysics

Quantum Gravity

Living Systems

GlobalChange

Social and EconomicSystems