Introduction to Spatial
Dynamical Modelling
Gilberto Câmara
Director, 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


Tuesday


Motivation, introduction to complexity and cellular automata,
examples from real-life problems
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?
Earth as a system
P h y s ic a l C lim a te S y s te m
C lim a te
Change
A tm ospheric P hysics/D ynam ics
O cean D yn am ics
T errestrial
E n erg y/M o istu re
H u m an
A ctivities
G lo b al M o istu re
M arin e
B io g eo ch em istry
T errestrial
E co system s
T ro p o s p h e ric C h e m is try
B io g e o c h e m ic a l C y c le s
(fro m E art h Syst em S cie nce : A n O ve rvie w , N A S A , 1 98 8 )
S o il
C O2
La nd
Use
C O2
P olluta nts
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 humanenvironment systems?
• How is the provision of
environmental goods and
services affected by changes
in terrestrial humanenvironment systems?
• What are the characteristics
and dynamics of vulnerability
in terrestrial humanenvironment 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 everyone
EO data: benefits to everyone
CBERS-2 image of Manaus
source: USGS
Aral Sea
Slides from LANDSAT
1973
1987
2000
1975
1992
2000
Bolivia
Can we avoid that this….
Source: Carlos Nobre (INPE)
Fire...
….becomes this?
Source: Carlos Nobre (INPE)
We might know the past….
Taxa
dedeforestation
Desmatamento
naAmazonia
Amazônia Legal
Yearly
rate Anual
in Legal
35000
Km2/ano
30000
25000
20000
15000
10000
5000
0
88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
(a)
(b) (b)
Ano
What’s coming next?
Total Deforestation up to 1997
Até 10%
10 - 20%
20 – 30%
30 – 40%
40 – 50%
50 – 60%
60 – 70%
70 – 80%
80 – 90%
90 – 100%
Increment – 1997 to 2000
Increment – 2000 to 2003
Até 3 %
3 - 6%
6 – 10%
10 – 13%
13 – 16%
16 – 20%
20 – 23%
23 – 26%
26 – 29%
29 – 33%
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)
Nome
UF
2005
2006
Variação
São Félix do Xingu
PA
1.406
764
-46%
Porto Velho
RO
646
382
-41%
Cumaru do Norte
PA
580
175
-70%
Altamira
PA
542
285
-47%
Colniza
MT
517
217
-58%
Total deforestation
Santana do Araguaia
PA
486
136
-72%
Juara
MT
403
200
-50%
2005 = 8.296 km2
2006 = 3.283 km2
Nova Maringá
MT
385
42
-89%
Aripuanã
MT
332
52
-84%
Nova Mamoré
RO
312
81
-74%
Paragominas
PA
303
75
-75%
Nova Bandeirantes
MT
294
128
-56%
Cotriguaçu
MT
292
61
-79%
Santa Maria das Barreiras
PA
280
81
-71%
Pacajá
PA
280
214
-24%
Vila Rica
MT
257
66
-74%
Nova Ubiratã
MT
255
73
-71%
Peixoto de Azevedo
MT
245
68
-72%
Machadinho D'Oeste
RO
242
116
-52%
Brasnorte
MT
239
65
-73%
Reduction: 60%
Deforestation classes per area
2000
2002
2003
2004
2005
2006
6%
8%
9%
9%
10%
10 a 25 ha
11%
6%
12%
14%
16%
20%
25%
25 a 50 ha
11%
5%
11%
11%
13%
16%
19%
50 a 100 ha
12%
6%
13%
12%
13%
14%
16%
100 a 150 ha
8%
3%
8%
7%
7%
7%
7%
150 a 300 ha
12%
6%
14%
12%
11%
11%
10%
More than 300 ha
38%
68%
31%
32%
27%
22%
13%
Tendência de Aumento
Aproxim. Estável
Tendência de Redução
Redução
4%
Estável
5%
Aumento
Less than 10 ha
2001
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
Altamira (Pará) – MODIS Image – 22 June 2004
6.000 hectares deforested in one month!
Altamira (Pará) – LANDSAT Image – 07 July 2004
What Drives Tropical Deforestation?
% of the cases
 5% 10% 50%
Underlying Factors
driving proximate causes
Causative interlinkages at
proximate/underlying levels
Internal drivers
*If less than 5%of cases,
not depicted here.
source:Geist &Lambin
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?
photo source: Edson Sano (EMBRAPA)
Large-Scale Agriculture
Agricultural Areas (ha)
1970
Legal Amazonia
Brazil
1995/1996
%
5,375,165
32,932,158
513
33,038,027
99,485,580
203
Source: IBGE - Agrarian Census
photo source: Edson Sano (EMBRAPA)
Cattle in Amazonia and Brazil
Unidade
Amazônia Legal
Brasil
Fonte: PAM - IBGE
1992
29915799
154,229,303
2001
51689061
176,388,726
%
72,78%
14,36%
Cattle in Amazonia and Brazil
Unidade
Amazônia Legal
Brasil
1992
2001
%
29,915,799
51,689,061
72,78%
154,229,303
176,388,726
14,36%
Trends in deforestation and soya
prices
40
30.000
35
25.000
20.000
R$ ou IGP
25
20
15.000
15
K2 desmatados
30
10.000
10
5.000
5
-
0
1994
1995
1996
1997
1998
1999
2000
2001
2002
Soja (Média anual) deflacionado R$/sc 60 kg - MT
2003
2004
2005
2006
Km2 desmatado na Amazônia
Source: Paulo Barreto (IMAZON)
60
30.000
50
25.000
40
20.000
30
15.000
20
10.000
10
5.000
-
K2 desmatados
R$ ou IGP
Trends in deforestation and meat
prices
0
199419951996 199719981999 2000200120022003 200420052006
Preço boi (IGP) São Paulo
Km2 desmatado na Amazônia
Source: Paulo Barreto (IMAZON)
Deforestation classes per area
2000
2002
2003
2004
2005
2006
6%
8%
9%
9%
10%
10 a 25 ha
11%
6%
12%
14%
16%
20%
25%
25 a 50 ha
11%
5%
11%
11%
13%
16%
19%
50 a 100 ha
12%
6%
13%
12%
13%
14%
16%
100 a 150 ha
8%
3%
8%
7%
7%
7%
7%
150 a 300 ha
12%
6%
14%
12%
11%
11%
10%
More than 300 ha
38%
68%
31%
32%
27%
22%
13%
Tendência de Aumento
Aproxim. Estável
Tendência de Redução
Redução
4%
Estável
5%
Aumento
Less than 10 ha
2001
Deforested areas with more than 300ha em 2003
+ protected areas
Dynamic areas (current and future)
New Frontiers
INPE 2003/2004:
Intense Pressure
Future expansion
Deforestation
Forest
Non-forest
Clouds/no data
Challenge: How do people use space?
Soybeans
Loggers
Competition for Space
Small-scale Farming
Source: Dan Nepstad (Woods Hole)
Ranchers
Field knowledge is fundamental!
Rondônia (Vale do Anari)
People changing the landscape
What is a Model?

Model = a simplified description of a complex
entity or process
Deforestation
deforest
Farmer
E0
• income
owns
E4
space
• land use
• soil type
Model = entities + relations + attributes + rules
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
Dynamic Spatial Models
f (It)
f (It+1)
F
f (It+2)
f ( It+n )
F
..
“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)
Dynamic Spatial Models
Forecast
tp - 20
tp - 10
tp
Calibration
Source: Cláudia Almeida
Calibration
tp + 10
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)
Modelling
(GIScience)
Culture
(Antropology)
Modelling and Public Policy
External
Influences
System
Ecology
Economy
Politics
Scenarios
Policy
Options
Decision
Maker
Desired
System
State
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 simpleminded”
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
y=a0 + a1x1 + a2x2 + ... +aixi +E



Establishes statistical relationship with variables
that are related to the phenomena under study
Basic hypothesis: stationary processes
Exemples: CLUE Model (University of
Wageningen)
Factors Affecting Deforestation
Category
Demographic
Technology
Variables
Population Density
Proportion of urban population
Proportion of migrant population (before 1991, from 1991 to 1996)
Number of tractors per number of farms
Percentage of farms with technical assistance
Agrarian strutucture Percentage of small, medium and large properties in terms of area
Percentage of small, medium and large properties in terms of number
Infra-structure
Distance to paved and non-paved roads
Distance to urban centers
Distance to ports
Economy
Distance to wood extraction poles
Distance to mining activities in operation (*)
Connection index to national markets
Percentage cover of protected areas (National Forests, Reserves,
Political
Presence of INCRA settlements
Number of families settled (*)
Environmental
Soils (classes of fertility, texture, slope)
Climatic (avarage precipitation, temperature*, relative umidity*)
Statistics: Humans as clouds
MODEL 7:
Variables
R² = .86
PORC3_AR
Description
Percentage of large farms, in terms of
area
LOG_DENS
Population density (log 10)
PRECIPIT
stb
p-level
0,27
0,00
0,38
0,00
-0,32
0,00
LOG_NR1
Avarege precipitation
Percentage 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
•Análise de tendências
•Modelos econômicos
Coarse: 100 km x 100 km grid
Fine: 25 km x 25 km grid
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)
From galaxies….
Source: John Finnigan (CSIRO)
…to cyclones
~ 100 km
CSIRO)
Gene expression and cell interaction
Source: John Finnigan (CSIRO)
Amoeba
Ribosome
Root
Tip
E
Coli
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
Neighbourhood
Rules
Space and Time
t
States
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 twodimensional grid of cells, each of which is either alive or
dead. Cells interact with their eight neighbors.
Most important neighborhoods
Von Neumann
Neighborhood
Moore Neighborhood
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
Event
Event
Jump condition
Control Mode A
Control Mode B
Flow Condition
Flow Condition
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
C34L181985-01-0100:00:001985-12-3123:59:59
C34L18
01/01/1985
31/12/1985
C34L181988-01-0100:00:001988-12-3123:59:59
C34L18
01/01/1988
31/12/1988
C34L181991-01-0100:00:001991-12-3123:59:59
C34L18
01/01/1991
31/12/1991
C34L181994-01-0100:00:001994-12-3123:59:59
C34L18
01/01/1994
31/12/1994
C34L181997-01-0100:00:001997-12-3123:59:59
C34L18
01/01/1997
31/12/1997
C34L182000-01-0100:00:002000-12-3123:59:59
C34L18
01/01/2000
31/12/2000
C34L191985-01-0100:00:001985-12-3123:59:59
C34L19
01/01/1985
31/12/1985
C34L191988-01-0100:00:001988-12-3123:59:59
C34L19
01/01/1988
31/12/1988
C34L191991-01-0100:00:001991-12-3123:59:59
C34L19
01/01/1991
31/12/1991
C34L191994-01-0100:00:001994-12-3123:59:59
C34L19
01/01/1994
31/12/1994
C34L191997-01-0100:00:001997-12-3123:59:59
C34L19
01/01/1997
31/12/1997
C34L192000-01-0100:00:002000-12-3123:59:59
C34L19
01/01/2000
31/12/2000
land_cover
forest
forest
forest
deforested
deforested
deforested
forest
deforested
deforested
deforested
deforested
deforested
dist_primary_road
dist_secondary_road
7068.90
669.22
7068.90
669.22
7068.90
669.22
7068.90
669.22
7068.90
669.22
7068.90
669.22
7087.29
269.24
7087.29
269.24
7087.29
269.24
7087.29
269.24
7087.29
269.24
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
Demands
Requirements

Locations change due to
external forces

discretization of space in cells

Realistic representation of
landscape

generalization of CA

Elements of dynamic
models

discrete and continous
processes

Geographical space is
inhomogeneous


Different types of models
Flexible neighborhood
definitions
Extensibility to include userdefined models

What Drives Tropical Deforestation?
% of the cases
 5% 10% 50%
Underlying Factors
driving proximate causes
Causative interlinkages at
proximate/underlying levels
Internal drivers
*If less than 5%of cases,
not depicted here.
source:Geist &Lambin
Spatial dynamic modeling
Demands
Requirements

Locations change due to
external forces

discretization of space in cells

Realistic representation of
landscape

generalization of CA

Elements of dynamic
models

discrete and continous
processes

Geographical space is
inhomogeneous


Different types of models
Flexible neighborhood
definitions
Extensibility to include userdefined models

Agents and CA: Humans as ants
Identify different actors and try to model their
actions
Farms
Settlements
10 to 20 anos
Recent
Settlements
(less than 4
years)
Source: Escada, 2003
Old
Settlements
(more than
20 years)
Agent model using Cellular Automata
1985
Small farms environments:
500 m resolution
Categorical variable:
deforested or forest
One neighborhood relation:
•connection through roads
Large farm environments:
2500 m resolution
1997
Continuous variable:
% deforested
Two alternative neighborhood
relations:
•connection through roads
• farm limits proximity
1997
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
Uncertainty on basic equations
Limits for Models
Social and Economic
Systems
Quantum
Gravity
Particle
Physics
Living
Systems
Global
Change
Chemical
Reactions
Hydrological
Models
Solar System Dynamics
Meteorology
Complexity of the phenomenon
source: John Barrow
(after David Ruelle)
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Introduction to Spatial Dynamical Modelling