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Introduction to Spatial Dynamical Modelling

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					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
       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?
                           Earth as a system
                                   Physical Climate System

                                                                                      Climate
                         Atmospheric Physics/Dynamics                                 Change



                                                         Terrestrial
                           Ocean Dynamics
                                                       Energy/Moisture
                                                                                             Human
                                                                                            Activities
                                         Global Moisture          Soil   CO2



                               Marine                     Terrestrial          Land
                           Biogeochemistry               Ecosystems             Use



                                 Tropospheric Chemistry                               CO2

                                 Biogeochemical Cycles                         Pollutants

(from Earth System Science: An Overview, NASA, 1988)
     The fundamental question of our time




                          How is the Earth’s
                          environment changing,
                          and what are the
                          consequences for human
fonte: IGBP               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 everyone
EO data: benefits to everyone




                    CBERS-2 image of Manaus
Aral Sea                         source: USGS


    Slides from LANDSAT




           1973           1987          2000
Bolivia




           1975           1992          2000
  Can we avoid that this….




Source: Carlos Nobre (INPE)
Fire...



          ….becomes this?




                     Source: Carlos Nobre (INPE)
           We might know the past….

             Taxa de Desmatamento Anual na Amazônia Legal
              Yearly deforestation rate in Legal Amazonia
          35000

          30000
          25000
Km2/ano




          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%   2005 = 8.296 km2
Juara                       MT      403      200       -50%   2006 = 3.283 km2
Nova Maringá                MT      385       42       -89%
Aripuanã                    MT      332       52       -84%   Reduction: 60%
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%
                        Deforestation classes per area

                         2000         2001      2002        2003        2004       2005      2006
Less than 10 ha              5%         4%          6%          8%          9%         9%     10%




                                                                                                    Aumento
10 a 25 ha                  11%         6%        12%           14%       16%         20%     25%
25 a 50 ha                  11%         5%         11%          11%       13%         16%     19%




                                                                                                    Estável
50 a 100 ha                 12%         6%        13%           12%       13%         14%     16%
100 a 150 ha                 8%         3%          8%          7%          7%         7%      7%




                                                                                                    Redução
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
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
Altamira (Pará) – MODIS Image – 21 May 2004
                                      2004-05-21, com
                                      excesso de nuvens
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?
     Cattleranching?
     Small-scale setllers?
     Wood loggers?
     Land speculators?
     A mixture of the above?
photo source: Edson Sano (EMBRAPA)


                Large-Scale Agriculture




                           Agricultural Areas (ha)
                                     1970   1995/1996     %
       Legal Amazonia           5,375,165    32,932,158   513
       Brazil                  33,038,027    99,485,580   203

       Source: IBGE - Agrarian Census
photo source: Edson Sano (EMBRAPA)




                  Cattle in Amazonia and Brazil

       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

           Unidade                                   1992          2001         %

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

  Brasil                                       154,229,303       176,388,726   14,36%
Trends in deforestation and soya
prices
               40                                                                                                30.000


               35
                                                                                                                 25.000

               30

                                                                                                                 20.000




                                                                                                                          K2 desmatados
               25
 R$ ou IGP




               20                                                                                                15.000


               15
                                                                                                                 10.000

               10

                                                                                                                 5.000
                  5


              -                                                                                                  0
                      1994   1995   1996   1997   1998   1999   2000   2001   2002   2003   2004   2005   2006

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

                                                                                             Source: Paulo Barreto (IMAZON)
Trends in deforestation and meat
prices
               60                                                             30.000


               50                                                             25.000




                                                                                       K2 desmatados
               40                                                             20.000
  R$ ou IGP




               30                                                             15.000


               20                                                             10.000


               10                                                             5.000


              -                                                               0
                    199419951996 199719981999 2000200120022003 200420052006

              Preço boi (IGP) São Paulo           Km2 desmatado na Amazônia
                                                                  Source: Paulo Barreto (IMAZON)
                                      Deforestation classes per area




                         2000          2001        2002        2003        2004       2005      2006
Less than 10 ha              5%            4%          6%          8%          9%         9%     10%




                                                                                                       Aumento
10 a 25 ha                  11%            6%         12%          14%       16%         20%     25%
25 a 50 ha                  11%            5%         11%          11%       13%         16%     19%




                                                                                                       Estável
50 a 100 ha                 12%            6%         13%          12%       13%         14%     16%
100 a 150 ha                 8%            3%          8%          7%          7%         7%      7%




                                                                                                       Redução
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
   Deforested areas with more than 300ha em 2003
+ protected areas
Dynamic areas (current and future)




 New Frontiers
                                INPE 2003/2004:

 Intense Pressure                  Deforestation
                                   Forest
                                   Non-forest
 Future expansion
                                   Clouds/no data
  Challenge: How do people use space?



  Soybeans


                                                    Loggers

                            Competition for Space




      Small-scale Farming                                     Ranchers


Source: Dan Nepstad (Woods Hole)
       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


    Farmer            deforest
               E0
                         owns            space
                                   E4
    • income
                                        • 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
     Requiresa 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 (It+2)            f ( It+n )

          F              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         Calibration         tp + 10
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     Money          Culture
(Geography)   (Economy)     (Antropology)


               Modelling
              (GIScience)
Modelling and Public Policy


             External
            Influences

System
                                    Desired
 Ecology                 Decision   System
Economy      Scenarios    Maker      State
 Politics


             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
               Netwon’s laws (mechanistic, cause-effect
     Paradigms:
      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                                         Variables
Demographic          Population Density
                     Proportion of urban population
                     Proportion of migrant population (before 1991, from 1991 to 1996)
Technology           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
Political            Percentage cover of protected areas (National Forests, Reserves,
                     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:        R² = .86
  Variables                   Description                      stb      p-level
                Percentage of large farms, in terms of
PORC3_AR        area                                             0,27       0,00

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

PRECIPIT        Avarege precipitation                           -0,32       0,00
                Percentage of small farms, in terms of
LOG_NR1         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 two-
    dimensional grid of cells, each of which is either alive or
    dead. Cells interact with their eight neighbors.
Most important neighborhoods




    Von Neumann         Moore Neighborhood
    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
     Isotropicspace
     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_road
                C34L18          01/01/1985    31/12/1985
     C34L181985-01-0100:00:001985-12-3123:59:59            forest                        7068.90              669.22
                C34L18          01/01/1988    31/12/1988
     C34L181988-01-0100:00:001988-12-3123:59:59            forest                        7068.90              669.22
                C34L18          01/01/1991    31/12/1991
     C34L181991-01-0100:00:001991-12-3123:59:59            forest                        7068.90              669.22
                C34L18          01/01/1994    31/12/1994
     C34L181994-01-0100:00:001994-12-3123:59:59            deforested                    7068.90              669.22
                C34L18          01/01/1997    31/12/1997
     C34L181997-01-0100:00:001997-12-3123:59:59            deforested                    7068.90              669.22
                C34L18          01/01/2000    31/12/2000
     C34L182000-01-0100:00:002000-12-3123:59:59            deforested                    7068.90              669.22
                C34L19          01/01/1985    31/12/1985
     C34L191985-01-0100:00:001985-12-3123:59:59            forest                        7087.29              269.24
                C34L19          01/01/1988    31/12/1988
     C34L191988-01-0100:00:001988-12-3123:59:59            deforested                    7087.29              269.24
                C34L19          01/01/1991    31/12/1991
     C34L191991-01-0100:00:001991-12-3123:59:59            deforested                    7087.29              269.24
                C34L19          01/01/1994    31/12/1994
     C34L191994-01-0100:00:001994-12-3123:59:59            deforested                    7087.29              269.24
                C34L19          01/01/1997    31/12/1997
     C34L191997-01-0100:00:001997-12-3123:59:59            deforested                    7087.29              269.24
                C34L19          01/01/2000    31/12/2000
     C34L192000-01-0100:00:002000-12-3123:59:59            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

            Demands                   Requirements
   Locations change due to          discretization of space in cells
    external forces

   Realistic representation of      generalization of CA
    landscape

   Elements of dynamic              discrete and continous
    models                            processes

   Geographical space is            Flexible neighborhood
    inhomogeneous                     definitions
                                     Extensibility to include user-
   Different types of models         defined 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          discretization of space in cells
    external forces

   Realistic representation of      generalization of CA
    landscape

   Elements of dynamic              discrete and continous
    models                            processes

   Geographical space is            Flexible neighborhood
    inhomogeneous                     definitions
                                     Extensibility to include user-
   Different types of models         defined models
Agents and CA: Humans as ants
Identify different actors and try to model their
actions



                  Farms




                                                 Settlements
                                                 10 to 20 anos




      Recent
   Settlements                                                       Old
   (less than 4                                                  Settlements
                          Source: Escada, 2003
      years)                                                     (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:
                        1997          1997
2500 m resolution

Continuous variable:
% deforested

Two alternative neighborhood
 relations:
•connection through roads
• farm limits proximity
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


                                 Quantum                         Social and Economic
Uncertainty on basic equations




                                 Gravity                         Systems



                                   Particle
                                   Physics             Living
                                                       Systems
                                                                            Global
                                                                            Change
                                    Chemical      Hydrological
                                    Reactions       Models


                                                                             Meteorology
                                                 Solar System Dynamics


                                              Complexity of the phenomenon
                                                                                       source: John Barrow
                                                                                       (after David Ruelle)
Spatial        Dynamical
Modeling with TerraME

Tiago Garcia de Senna Carneiro
Antônio Miguel Vieira Monteiro
Gilberto Câmara
 Dynamic Spatial Models


f (It)        f (It+1)       f (It+2)            f ( It+n )

          F              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             Calibration         tp + 10
Source: Cláudia Almeida
    TerraME - overview

   TerraME is an enviroment for spatial dynamical
    modelling

   Model development in cell spaces

   Data input/output from spatial database

   Results visualisation
TerraLib: the support for TerraME

   Open source library for GIS
   Data management
       object-relational DBMS
            raster + vector geometries
            ORACLE, Postgres, mySQL, Access
   Environment for customized GIS applications
   Web-based cooperative development
       http://www.terralib.org
    TerraLib conception

   TerraLib kernel
      handles the different types of
       geographic data
      Interfaces with spatial DBMS


   Terralib algorithms
      use the kernel structures
      spatial analysis
      query and simulation
       languages,
      data conversion procedures


   New functions
        Implemented on top of the
         kernel
TerraME architecture


  RondôniaModel     DinamicaModel      TROLLModel    CLUEModel

                        TerraME Language

                        TerraME Compiler

                   TerraME Virtual Machine

                        C++ Signal        C++           C++
TerraLib Enviromental
                        Processing    Mathematical   Statistical
Modeling Framework        librarys      librarys      librarys




                           TerraLib
TerraME functionality


                                    TerraME INTERPRETER

                                    • model syntax semantic checking
                                    • model execution


 Eclipse & LUA plugin                                                            TerraView
                                             LUA interpreter
 • model description                                                             • data acquisition
 • model highlight syntax                                                        • data visualization
                                                                                 • data management
                                         TerraME/LUA interface                   • data analysis
             model




                                           TerraME framework
                            model




                                                                                       data
                                                                          data
 MODEL DATA




                       Model                                           TerraLib
                     source code                                       database
    Requirements for Spatio-Temporal
    Models

   Dealing with Data
        Storage and retrieval of large-scale datasets
        Inclusion of data from external source
   Representation of Space
        Spaces of places + spaces of networks (anisotropy)
        Cells as autonomously evolving entities
   Extensibility of Models
        Algorithms should be independent of data structures
        Different Models have different rules (CA, Markov chain,
         regression)
   Dealing with Modellers
        Cognitively meaningful interfaces (language?, data-flow?)
        Suitable visualization enviroments
      Computational Modelling with Cell
      Spaces
Cell Spaces
                               Representation
                                    Cell Spaces
                                    Generalized Proximity Matriz – GPM
                                    Hybrid Automata model
                                    Nested scales
Basic concepts

A dynamical model…




 is represented as a synthetic environment…
 … where rules change the space properties in time.
 Several interacting entities share the same spatiotemporal
 structure.
    What is a spatial dynamical model?

   A closed microworld with
        Spatial and temporal structure
                                           What is
        Entities
                                          changing?
        Rules of behaviour
                                           When?
                                           Where?
                                            Why?
Cyclical Model Development Process




TerraME provides support for all phases of the development of a multiple
                              LUCC model.

				
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