An Introduction to TerraME Pedro Ribeiro de Andrade São José dos Campos,

Cell Spaces Fonte: (Carneiro, 2006) Hipótese: Nenhuma abordagem sozinha é suficiente para representar a complexidade das interações sociedade-natureza TerraME: Ambiente Computacional Multi-paradigma para o Desenvolvimento de Modelos Integrados Natureza-Sociedade

 CCST-INPE  Pedro Andrade, Gilberto Camara, Raian Maretto  TerraLab/UFOP  Tiago Carneiro  DPI/OBT-INPE  Miguel Monteiro, Time TerraLib Desenvolvimento do TerraME

TerraME

Visualization (TerraView) Spatio-temporal Database (TerraLib) Modelling (TerraME) Data Mining(GeoDMA)Statistics (R interface) Software: Open source GIS

Spatial structure 1:32:00Mens :32:10Mens :38:07Mens :42:00Mens return value true 1. Get first pair 2. Execute the ACTION 3. Timer =EVENT 4. timeToHappen += period Temporal structure Newly implanted Deforesting Slowing down latency > 6 years Iddle Year of creation Deforestation = 100% Rules of behaviour Spatial relations Source: [Carneiro, 2006] TerraME: Components

 Lua classes using the constructor mechanism: Cell, CellularSpace, Neighborhood, Timer, Event, Legend  A CellularSpace is a multivalued set of Cells. It consists of a geographical area of interest, divided into regular or irregular objects.  Each Cell has a set of attributes.  CellularSpaces can be stored and retrieved from TerraLib databases if the modeler specify where the data is. TerraME extensions to Lua

Example 1: Random cellular space

Cellular Space in memory and forEachCell DEAD = 0 ALIVE = 1 cs = CellularSpace { xdim = 30, ydim = 20 } function random (cs) forEachCell (cs, function (cell) v = math.random() -- a value between 0 and 1 if v > 0.5 then cell.state = ALIVE else cell.state = DEAD end end) end random(cs)

Legend and Observer lifeLeg = Legend{ type = TYPES.NUMBER, groupingMode = GROUPING.UNIQUEVALUE, slices = 2, maximum = ALIVE, minimum = DEAD, colorBar1 = { {BLACK, DEAD}, {WHITE, ALIVE} }, } cs:createObserver(OBSERVERS.MAP, {"state"}, {lifeLeg}) cs:notifyObservers()

Example 2: Game of life

Synchronizing a CellularSpace  TerraME keeps two copies of a cellular space in memory: one stores the past values of the cells, and another stores the current (present) values of the cells.  The model equations must read the past copy and write the values to the present copy of the cellular space.  At the correct moment, it will be necessary to synchronize the past copy with the current values of the cellular space.

Game of life source code DEAD = 0 ALIVE = 1 TURNS = 400 function random (cs) forEachCell (cs, function (cell) v = math.random() -- a value between 0 and 1 if v > 0.5 then cell.state = ALIVE else cell.state = DEAD end end) end

Cellular Space and neighborhood cs = CellularSpace { xdim = 50 } random(cs) createMooreNeighborhood(cs, "1", false) function countAlive(cell) count = 0 forEachNeighbor(cell, function(cell, neigh) if neigh.past.state == ALIVE then count = count + 1 end end) return count end

Updating the cellular space function updateSpace(mycs) forEachCell(mycs, function(cell) n = countAlive(cell) -- cells with one or no neighbors die (loneliness). if n < 2 then cell.state = DEAD -- cells with four or more neighbors die (overpopulation). elseif n > 3 then cell.state = DEAD -- cells with two neighbors survive. elseif n == 2 then cell.state = cell.past.state -- cells with three neighbors become populated. elseif n == 3 then cell.state = ALIVE end end) end

Running and synchronizing lifeLeg = Legend{ type = TYPES.NUMBER, groupingMode = GROUPING.UNIQUEVALUE, slices = 2, maximum = ALIVE, minimum = DEAD, colorBar1 = { {BLACK, ALIVE}, {WHITE, DEAD} } cs:createObserver(OBSERVERS.MAP, {"state"}, {lifeLeg}) cs:notifyObservers() for i = 1,TURNS do cs:synchronize() updateSpace(cs) cs:notifyObservers() end

Example 3: Runoff rain Itacolomi do Itambé Peak Lobo’s Range

CellularSpace from database and neighborhood -- input and output data paths TERRAME_PATH = "e:\\Programas\\TerraME\\" INPUT_PATH = TERRAME_PATH.."Database\\" -- retrieve the cell space from the database csQ = CellularSpace{ database = INPUT_PATH.."cabecaDeBoi.mdb", theme = "cells", select = { "height", "soilWater" } } csQ:load() function filter(cell, neigh) if cell.height >= neigh.height then return true end return false end create3x3Neighborhood(csQ, filter)

Observers using two attributes heightLeg = Legend{ type = TYPES.NUMBER, groupingMode = GROUPING.EQUALSTEPS, slices = 50, maximum = 255, minimum = 0, colorBar1 = { {BLACK, 0}, {WHITE, 1} } soilWaterLeg = Legend{ type = TYPES.NUMBER, groupingMode = GROUPING.EQUALSTEPS, slices = 100, maximum = 200, minimum = 0, colorBar1 = { {WHITE, 0}, {BLUE, 200} } csQ:createObserver(OBSERVERS.MAP, {"soilWater", "height"}, {soilWaterLeg, heightLeg})

Rain and runoff RAIN = 4 -- rain/t MIN_HEIGHT = 200 function rain(cs) forEachCell(cs, function(cell) if ANYWHERE or (cell.height > MIN_HEIGHT) then cell.soilWater = cell.soilWater + RAIN end end) end function runoff(cs) cs:synchronize("soilWater") forEachCell(cs, function(cell) cell.soilWater = 0 end) forEachCell(cs, function(cell) countNeigh = cell:getNeighborhood():size() if countNeigh > 0 then soilWater = cell.past.soilWater / countNeigh forEachNeighbor(cell, function(cell, neigh) neigh.soilWater = neigh.soilWater + soilWater end) else cell.soilWater = cell.soilWater + cell.past.soilWater end end) end

Timer RAINING_TIME = 5 FINAL_TIME = 50 t = Timer{ Event{message = function(event) rain(csQ) if event:getTime() > RAINING_TIME then return false end end}, Event{message = function(event) runoff(csQ) end}, Event{priority = 5, message = function(event) csQ:notifyObservers() end} } t:execute(FINAL_TIME)

Large 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 Different spatial resolutions

Generalized Proximity Matrices (GPM)

Models of Computation Agent based models Cellular automata models (Rosenschein and Kaelbling, 1995) (Wooldbridge, 1995) (von Neumann, 1966)(Minsky, 1967) (Aguiar et al, 2004) (Pedrosa et al, 2003) (Straatman et al, 2001)

Create pasture/ Deforest Speculator/ large/small bad land management money surplus Subsistence agriculture Diversify use Manage cattle Move towards the frontier Abandon/Sell the property Buy new land Settlement/ invaded land Sustainability path (alternative uses, technology) Sustainability path (technology) State machines

To Agent Cell a b a b c c Cell Agent From GPM as a graph

CellAgent forEachAgent forEachCell forEachRelativeforEachNeighbor forEachAgent CellularSpace Society GroupTrajectory DBMS Agent-based modelling relations

Prodes/INPE Nested environments

up-scaling Escala 1 Escala 2 pai filho down-scaling Nested environments

An Introduction to TerraME Pedro Ribeiro de Andrade São José dos Campos,