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Introduction to Spatial Dynamical Modelling
Gilberto CâmaraDirector, National Institute for Space Research
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Course objectives
Teach the fundamentals of spatial dynamical models
Emphasis on Land Change modelling
Computational tools for spatial models - TerraME
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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
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“Give us some new problems”
What about saving the planet?
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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
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The fundamental question of our time
fonte: IGBP
How is the Earth’s environment changing, and what are the consequences for human civilization?
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Global Change
Where are changes taking place? How much change is happening? Who is being impacted by the change?
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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?
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Impacts of global land change
More vulnerable communities are those most at risk
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Earth observation satellites provide key information about
global land change
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EO data: benefits to everyoneEO data: benefits to everyone
CBERS-2 image of Manaus
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Slides from LANDSATAral Sea
Bolivia
1975 1992 2000
1973 1987 2000
source: USGS
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Source: Carlos Nobre (INPE)
Can we avoid that this….
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Fire...
Source: Carlos Nobre (INPE)
….becomes this?
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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
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What’s coming next?
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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
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Increment – 1997 to 2000
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Até 3 %
3 - 6%
6 – 10%
10 – 13%
13 – 16%
16 – 20%
20 – 23%
23 – 26%
26 – 29%
29 – 33%
Increment – 2000 to 2003
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Increment – 2003 to 2006
Até 3 %
3 - 6%
6 – 8%
8 – 11%
11 – 14%
14 – 17%
17 – 20%
20 – 22%
22 – 25%
25 – 28%
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Incremento – 2000 a 2006
Até 5 %
5 - 10%
10 – 15%
15 – 20%
20 – 24%
24 – 29%
29 – 34%
34 – 39%
39 – 43%
43 – 49%
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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
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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
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Deforested areas with more than 300ha em 2003
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Deforested areas with more than 300ha em 2003
+ protected areas
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Altamira (Pará) – LANDSAT Image – 22 August 2003
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Altamira (Pará) – MODIS Image – 07 May 2004
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Imagem Modis de 2004-05-21, com excesso de nuvens
Altamira (Pará) – MODIS Image – 21 May 2004
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Altamira (Pará) – MODIS Image – 07 June 2004
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6.000 hectares deforested in one month!
Altamira (Pará) – MODIS Image – 22 June 2004
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Altamira (Pará) – LANDSAT Image – 07 July 2004
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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?
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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?
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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)
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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)
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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$/sc 60 kg - MT Km2 desmatado na Amazônia
Source: Paulo Barreto (IMAZON)
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Trends in deforestation and meat prices
-
10
20
30
40
50
60
1994199519961997199819992000200120022003200420052006
R$
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)
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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
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Deforested areas with more than 300ha em 2003
+ protected areas
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New Frontiers
Deforestation
Forest
Non-forest
Clouds/no data
INPE 2003/2004:
Dynamic areas (current and future)
Intense Pressure
Future expansion
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Challenge: How do people use space?
Loggers
Competition for Space
Soybeans
Small-scale Farming Ranchers
Source: Dan Nepstad (Woods Hole)
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Rondônia (Vale do Anari)
People changing the landscape
Field knowledge is fundamental!
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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
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Modelling Complex Problems Application of interdisciplinary knowledge to
produce a model.
If (... ? ) then ...
Desforestation?
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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
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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)
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tp - 20 tp - 10
tp
Calibration Calibration tp + 10
ForecastForecast
Dynamic Spatial Models
Source: Cláudia Almeida
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GIScience and change
We need a vision for extending GIScience to have a research agenda for modeling change
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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)
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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.
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Modelling Land Change in Amazonia
Territory(Geography)
Money(Economy)
Culture(Antropology)
Modelling(GIScience)
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Modelling and Public Policy
System
EcologyEconomyPolitics
ScenariosDecisionMaker
Desired System
State
ExternalInfluences
Policy Options
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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”
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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
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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
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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*)
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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
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Modelling Tropical Deforestation
Fine: 25 km x 25 km grid
Coarse: 100 km x 100 km grid
•Análise de tendências•Modelos econômicos
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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.
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The trouble with statistics
Extrapolation of current measured trends
How do we know if tommorow will be like today?
How do we incorporate feedbacks?
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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?
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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.
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Emergence or Self-Organisation
We recognise this phenomenon over a vast range of physical scales and degrees of complexity
Source: John Finnigan (CSIRO)
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Source: John Finnigan (CSIRO)
From galaxies….
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…to cyclones ~ 100 km
Source: John Finnigan (CSIRO)
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Ribosome
E Coli
Root Tip
Amoeba
Gene expression and cell interaction
Source: John Finnigan (CSIRO)
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The processing of information by the brain
Source: John Finnigan (CSIRO)
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Animal societies and the emergence of culture
Source: John Finnigan (CSIRO)
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Results of human society such as economies
Source: John Finnigan (CSIRO)
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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.
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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.
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Properties of Complex Adaptive Systems
Many interacting parts Emergent phenomena Adaptation Specialization & modularity Dynamic change Competition and cooperation Decentralization Non-linearities
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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.
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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)
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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.
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Cellular Automata
RulesNeighbourhood
States
Space and Time
t
t1
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Why do we care about CA?
Can be used to model simple individual behaviors
Complex group behaviors can emerge from these simple individual behaviors
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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.
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Game of Life
Static Life
Oscillating Life
Migrating Life
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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.
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Von Neumann Neighborhood
Moore Neighborhood
Most important neighborhoods
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Computational Modelling with Cell Spaces
Cell Spaces
Components Cell Spaces Generalizes Proximity Matriz – GPM Hybrid Automata model Nested enviroment
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Cell Spaces
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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
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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
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Hybrid Automata
Variables Control graph Flow and Jump conditions Events
Control Mode A
Flow Condition
Control Mode B
Flow Condition
Event
Jump condition
Event
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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
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Space is Anisotropic
Spaces of fixed location and spaces of fluxes in Amazonia
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Motivation
Which objects are NEAR each other?
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Motivation
Which objects are NEAR each other?
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Using Generalized Proximity Matrices
Consolidated area Emergent area
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(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
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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
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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
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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?
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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
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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
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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
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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
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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