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Spatial Dynamical Modelling with TerraME (lectures 3 – 4)
Gilberto Câmara
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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
Escada et al. (2005)
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Amazonian new frontier hypothesis (Becker)
“The actual frontiers are different from the 60’s and the 70’s
In the past it was induced by Brazilian government to expand regional economy and population, aiming to integrate Amazônia with the whole country.
Today, induced mostly by private economic interests and concentrated on focus areas in different regions.
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Modelling Land Change in Amazonia
Territory(Geography)
Money(Economy)
Culture(Antropology)
Modelling(GIScience)
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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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What Drives Tropical Deforestation?
Underlying Factorsdriving proximate causes
Causative interlinkages atproximate/underlying levels
Internal drivers
*If less than 5%of cases,not depicted here.
source:Geist &Lambin (Université Louvain)
5% 10% 50%
% of the cases
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Land-Use modelling example
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Vale do Anari (Rondonia.mdb database)
Small-scale government planned rural settlement in Vale do Anari (RO), established in 1982 and land parcels sized around 50 ha
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TYPOLOGY OF LAND CHANGE ACTORS IN VALE DO ANARI REGION
Land use patterns
Spatial distribution
Clearing size
Actors Main land use
Description
Linear (LIN)
Roadside Variable Small households
Subsistence agriculture
Settlement parcels less than 50 ha. Deforestation uses linear patterns following government planning.
Irregular (IRR)
Near main settlements and main roads
Small
(< 50 ha)
Small farmers
Cattle ranching and subsistence agriculture
Settlement parcels less than 50 ha. Irregular clearings near roads following settlement parcels.
Regular (REG)
Near main settlements and main roads
Medium and large (> 50 ha)
Midsized and large farms
Cattle ranching
Patterns produced by land concentration.
irregular linear regular
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Vale do Anari – 1985
Geometrical
Irregular
Linear
source: Escada (2006)
Pattern type
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Vale do Anari – 1985 - 1988source: Escada (2006)
Geometrical
Irregular
Linear
Pattern type
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Vale do Anari – 1988 - 1991source: Escada (2006)
Geometrical
Irregular
Linear
Pattern type
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Vale do Anari – 1991 - 1994source: Escada (2006)
Geometrical
Irregular
Linear
Pattern type
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Vale do Anari – 1994 - 1997source: Escada (2006)
Geometrical
Irregular
Linear
Pattern type
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Vale do Anari – 1997 - 2000source: Escada (2006)
Geometrical
Irregular
Linear
Pattern type
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Vale do Anari – 1985 - 2000source: Escada (2006)
Geometrical
Irregular
Linear
Pattern type
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Can you grow it?
Anari -1985 Anari -1995 Anari -2000
1. Simple diffusive model: number of deforested neighbours
2. Diffusive model: : number of deforested neighbours + additional factors
3. Statistical model without neighbours
4. Statistical model with neighbours
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Can you grow it?
Anari -1985 Anari -1995 Anari -2000
-- CONSTANTS (MODEL PARAMETERS)
CELL_AREA = 0.25; -- 500 x 500 meters or 0.25 km2
DEMAND= 500; -- 100 km2
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Vale do Anari (1985)
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Vale do Anari (1995)
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Vale do Anari (2000)
Geometrical
Irregular
Linear
Pattern type
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General outline of land change models
Demand forchange
Order cells accordingto potential
Allocate changeon cells
Calculate potential for change
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Spatial Iterator in TerraME
it = SpatialIterator { csQ, function(cell) return cell.champion == “Brazil”; end}
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Ordering cells in TerraME
Demand forchange Order cells according
to potential
Allocate changeon cells
Calculate potential for change
-- Step 2: Order cells according to potentialit = SpatialIterator { csQ, function(cell) return cell.pot > 0; end, function (c1,c2) return c1.pot > c2.pot; end} -- Step 3: allocate changes to most suitable cells count = 0; for i, cell in pairs( it.cells ) do if (count < num_cells_ch) and (count < it.count) then
cell.cover_ = "deforested"; count = count + 1; end
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Exercise 1 – Simple diffusive model
Expansion based on neighbourhood potential
More deforested neigbours, more potential for change
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Exercise 2 – Modified diffusive model
Expansion based on five factors:1.Neighbourhood potential2.Distance to main road (dist_rodovia_BR)3.Distance to primary side roads (dist_ramal_princ)4.Distance to secondary side roads (dist_ramal_sec)5.Distance to urban centers (dist_urban)
main road
primary side road
secondary side road
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Exercise 3 – Neighbourhood + regression
Expansion based on two factors:1.Neighbourhood potential (50%)2.Linear regression (50%)
poti= - 0.0012* dist_rodovia_BR - 0.06* dist_ramal_princ - 0.003* dist_ramal_sec(normalize to [0,1])
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0
2
4
6
8
10
12
14
16
18
20
-0.5 0 0.5 1 1.5forest deforested
Simple Linear Regression
R2= 0.43
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Exercise 4 – Spatial regression
Expansion based on spatial regression (includes neighbourhoods)
poti = 0.173*num_deforested_neigh
-0.1 * math.log10 (cell.dist_rodovia_BR/1000) + 0.053*math.log10 (cell.dist_ramal_princ/1000)-0.157 * math.log10 (cell.dist_ramal_sec/1000)(normalize to [0,1])
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Exercise 4 – Spatial Regression
R2= 0.84
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Aula 9 – Modelo Bayesiano
Tiago CarneiroGilberto Câmara
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Método Bayesiano
Conceitos do método probabilidade a priori probabilidade a posteriori
Probabilidade a priori – o que sei quando tenho informação geral e não conheço os dados
Probabilidade a posteriori – o que sei a mais quando tenho informação adicional
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Teorema de Bayes
Chove 60 dias por ano em Campos do Jordão Será que vai chover amanhã? Probabilidade a priori = 60/360 = 0.15
Será que vai chover amanhã, dado que estamos no verão?
Sabemos que metade dos dias de chuva em Campos ocorrem no verão
Probabilidade a posteriori = (30/60) = 0.5
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Teorema de Bayes
Prob (chuva no verão) = (dias de chuva no verão)/(dias de verão)
)(
)()|(
VP
VCPVCP
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Dinâmica - Arquitetura
http://www.csr.ufmg.br/
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Área de Estudo, E
Evidência: Distancia, D = pres.
Evento: Floresta_Desmate, FD
Evidência: Distancia, ~D = aus.
Teorema de Bayes aplicado ao espaço
Usar evidências adicionais para aumentar a informação disponível
Quanto maior for a intersecção entre a área da evidência e o evento, maior será o peso da evidência
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Teorema de Bayes aplicado a uma evidência
)(
)|(log)|(
)(
)|(log)(log)|log(
)(
)|()()|(
1
11
1
11
1
11
EP
TEPETpot
EP
TEPTPET
EP
TEPTPETP
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Teorema de Bayes aplicado a duas evidências
)(
)|(log
)(
)|(log))|((
2
2
1
121 EP
TEP
EP
TEPEETPpot
)(
)|(
)(
)|()()|(
2
2
1
121 EP
TEP
EP
TEPTPEETP
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Teorema de Bayes aplicado a uma evidência e uma ausência
)(
)|(log
)(
)|(log))|((
2
2
1
121 EP
TEP
EP
TEPEETPpot
)(
)|(
)(
)|()()|(
2
2
1
121 EP
TEP
EP
TEPTPEETP
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Teorema de Bayes aplicado a duas evidências
)(
)|(log
)(
)|(log)|(
)(
)|(log
)(
)|(log)|(
)(
)|(log
)(
)|(log)|(
)(
)|(log
)(
)|(log)|(
2
2
1
121
2
2
1
121
2
2
1
121
2
2
1
121
EP
TEP
EP
TEPEETpot
EP
TEP
EP
TEPEETpot
EP
TEP
EP
TEPEETpot
EP
TEP
EP
TEPEETpot
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Como calcular as probabilidades (caso discreto)?
)(
)(
)(
)|(
/)()(
/)()|(
1
1
1
1
11
11
EN
TEN
EP
TEP
NENEP
NTENTEP
T
T
Influencia adicional de uma evidência = ocorrências conjuntas / total de ocorrências
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Como calcular as probabilidades (caso discreto)?
)(
)(
)(
)|(
/)()(
/)()|(
1
1
1
1
11
11
EN
TEN
EP
TEP
NENEP
NTENTEP
T
T
Influencia de ausência de evidência = eventos sem evidência / total de ausências
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Como calcular as probabilidades (caso contínuo)?
Caso mais simples – potencial baseado em distâncias
Considerar que P(E1) – probabilidade da evidência não condicionada é
uma distribuição normal P(E1| T) – probabilidade da evidência condicionada à
transição é uma distribuição fuzzy
)(
)|(log)|(
1
11
EP
TEPETpot
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Distribuição Fuzzy para o caso de distâncias
0
0,2
0,4
0,6
0,8
1
1,2
20 50 70 90 120
160
Distancia
Valor mínimo
Valor máximo
U(x) = 1 se x ,
U(x) = 1/[1+ (x )2], se x > .
= 1/(z0.5 )2
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Exercício Simples – Modelo Bayesiano
Vale do Anari 1995 projetado para 2000 Baseado nas transições 1985-1995 Três parâmetros
Distância à estrada principal Distância às estradas secundárias Distância às estradas vicinais
Usa as probabilidades bayesianas contínuas (não é pesos de evidência)
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Dados – Vale do Anari (1985)
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Vale do Anari (1995)
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Vale do Anari em 2000 (dado real)
Geométrico
Irregular
Linear
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Vale do Anari (1995 projetado para 2000) - Bayes
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Exercício 4 - Anari 1995 projetado para 2000 (estatístico)
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Comparação Bayes - estatístico
Uso de probabilidade bayesiana é promissor Resultados preliminares são encorajadores Sugestão do Tiago: patcher e expander
Patcher: Antes da mudança verificar se na vizinhança existe alguma células desflorestada. Caso exista, esta célula deve ser desconsiderada.
Expander: Exatamente o contrário. Devo selecionar somente as células cujas vizinhanças possuem células desflorestada.
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Aula 9 – Modelo Bayesiano
Tiago CarneiroGilberto Câmara
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Modelos Estocásticos – DINAMICA
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Modelos Estocásticos – DINAMICA
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Modelos Estocásticos – DINAMICA
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Modelos Estocásticos – DINAMICA
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Modelos Estocásticos – DINAMICA
Módulo externo: VENSIM (Soares Filho et al., 2002)
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Modelos Estocásticos – DINAMICA
Dinamica (Soares Fº e CSR,1998): Modelo de Mudanças da Paisagem
regeneração
desmatamento
mata
PAISAGEM OBSERVADA - 1994
SIMULAÇÃO 2
TERRA NOVA
(MT)
SIMULAÇÕES
1986 - 1994
SIMULAÇÃO 1
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Modelos Estocásticos – DINAMICA
Dinamica (Soares Fº e CSR,1998): Cenários da Amazônia
Cenário: “Governance” Cenário: “Business as Usual”
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Modelos Estocásticos – DINAMICA
Fonte: RIKS, 2000Conjunto de evidências. Ex: densidade de estabelecimentos comerciais
Dados de uso do solo urbano para calibração
Simulações
S1
S2
S3
Método Peso de Evidências
Almeida, 2001
Simulação de Uso do Solo Urbano: Bauru, SP
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Modelos Estocásticos – DINAMICA
Godoy, 2004
Simulação de Uso do Solo Intra-Urbano: Savassi – Belo Horizonte, MG
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Modelos Estocásticos – DINAMICA
Funcionalidades
Estrutura aberta: suporta diferentes aplicações (floresta, urbano, águas, dispersão de fogo etc.).
Modelo aberto a diferentes parametrizações (pesos de evidência, regressão logística, redes neurais, MCE, árvore de decisão etc.).
Algoritmos de transição por expansão ou nucleação. Algoritmo genético para definição das melhores faixas de distância.
Módulo: construtor de estradas (temporalidade da variável de entrada) um modelo de CA embutido em um modelo de CA.
Modelo externo de probabilidades globais de transição permitem a geração de cenários variados.
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Método Bayesiano
Conceitos do método probabilidade a priori probabilidade a posteriori
Probabilidade a priori – o que sei quando tenho informação geral e não conheço os dados
Probabilidade a posteriori – o que sei a mais quando tenho informação adicional
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Teorema de Bayes
Chove 60 dias por ano em Campos do Jordão Será que vai chover amanhã? Probabilidade a priori = 60/360 = 0.15
Será que vai chover amanhã, dado que estamos no verão?
Sabemos que metade dos dias de chuva em Campos ocorrem no verão
Probabilidade a posteriori = (30/60) = 0.5
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Teorema de Bayes
Prob (chuva no verão) = (dias de chuva no verão)/(dias de verão)
)(
)()|(
VP
VCPVCP
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Dinâmica - Arquitetura
http://www.csr.ufmg.br/
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Área de Estudo, E
Evidência: Distancia, D = pres.
Evento: Floresta_Desmate, FD
Evidência: Distancia, ~D = aus.
Teorema de Bayes aplicado ao espaço
Usar evidências adicionais para aumentar a informação disponível
Quanto maior for a intersecção entre a área da evidência e o evento, maior será o peso da evidência
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Teorema de Bayes aplicado a uma evidência
)(
)|(log)|(
)(
)|(log)(log)|log(
)(
)|()()|(
1
11
1
11
1
11
EP
TEPETpot
EP
TEPTPET
EP
TEPTPETP
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Teorema de Bayes aplicado a duas evidências
)(
)|(log
)(
)|(log))|((
2
2
1
121 EP
TEP
EP
TEPEETPpot
)(
)|(
)(
)|()()|(
2
2
1
121 EP
TEP
EP
TEPTPEETP
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Teorema de Bayes aplicado a uma evidência e uma ausência
)(
)|(log
)(
)|(log))|((
2
2
1
121 EP
TEP
EP
TEPEETPpot
)(
)|(
)(
)|()()|(
2
2
1
121 EP
TEP
EP
TEPTPEETP
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Teorema de Bayes aplicado a duas evidências
)(
)|(log
)(
)|(log)|(
)(
)|(log
)(
)|(log)|(
)(
)|(log
)(
)|(log)|(
)(
)|(log
)(
)|(log)|(
2
2
1
121
2
2
1
121
2
2
1
121
2
2
1
121
EP
TEP
EP
TEPEETpot
EP
TEP
EP
TEPEETpot
EP
TEP
EP
TEPEETpot
EP
TEP
EP
TEPEETpot
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Como calcular as probabilidades (caso discreto)?
)(
)(
)(
)|(
/)()(
/)()|(
1
1
1
1
11
11
EN
TEN
EP
TEP
NENEP
NTENTEP
T
T
Influencia adicional de uma evidência = ocorrências conjuntas / total de ocorrências
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Como calcular as probabilidades (caso discreto)?
)(
)(
)(
)|(
/)()(
/)()|(
1
1
1
1
11
11
EN
TEN
EP
TEP
NENEP
NTENTEP
T
T
Influencia de ausência de evidência = eventos sem evidência / total de ausências
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Como calcular as probabilidades (caso contínuo)?
Caso mais simples – potencial baseado em distâncias
Considerar que P(E1) – probabilidade da evidência não condicionada é
uma distribuição normal P(E1| T) – probabilidade da evidência condicionada à
transição é uma distribuição fuzzy
)(
)|(log)|(
1
11
EP
TEPETpot
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Distribuição Fuzzy para o caso de distâncias
0
0,2
0,4
0,6
0,8
1
1,2
20 50 70 90 120
160
Distancia
Valor mínimo
Valor máximo
U(x) = 1 se x ,
U(x) = 1/[1+ (x )2], se x > .
= 1/(z0.5 )2
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Exercício Simples – Modelo Bayesiano
Vale do Anari 1995 projetado para 2000 Baseado nas transições 1985-1995 Três parâmetros
Distância à estrada principal Distância às estradas secundárias Distância às estradas vicinais
Usa as probabilidades bayesianas contínuas (não é pesos de evidência)
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Dados – Vale do Anari (1985)
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Vale do Anari (1995)
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Vale do Anari em 2000 (dado real)
Geométrico
Irregular
Linear
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Vale do Anari (1995 projetado para 2000) - Bayes
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Exercício 4 - Anari 1995 projetado para 2000 (estatístico)
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Comparação Bayes - estatístico
Uso de probabilidade bayesiana é promissor Resultados preliminares são encorajadores
Idéia – fazer mais experimentos