1. Spatial Dynamical Modeling with TerraME Tiago Carneiro Gilberto Câmara Pedro Andrade Licence: Creative Commons ̶̶̶̶ By Attribution ̶̶̶̶ Non Commercial ̶̶̶̶ Share Alike http://creativecommons.org/licenses/by-nc-sa/2.5/

2. f ( I t+n ). FF f (I t )f (I t+1 )f (I t+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)

3. Computational Modelling with Cell Spaces Cell Spaces Generalized Proximity Matriz – GPM Hybrid Automata model Nested scales Agents in space

4. TerraME - overview Model data in cell spaces Read/write data from a database

5. 2500 m2.500 m e 500 m Cellular Data Base Resolution

6. TerraME functionality

7. TerraLib TerraME C++ Framework C++ Signal Processing librarys C++ Mathematical librarys C++ Statistical librarys TerraML Virtual Machine TerraME: Software Architecture TerraMLCompiler TerraML Language Model 1Model 2 Model 3Model 4

8. TerraLib: spatio-temporal database as a basis for innovation Visualization (TerraView) Spatio-temporal Database (TerraLib) Modelling (TerraME) Data Mining(GeoDMA) Statistics (aRT) G. Câmara et al.“TerraLib: An open-source GIS library for large-scale environmental and socio-economic applications”. In: B. Hall, M. Leahy (eds.), “Open Source Approaches to Spatial Data Handling”. Berlin, Springer, 2008.

9. “GPM” Plugin TerraView 3.2.0 “FillCell” Plugin TerraView 3.2.0 TerraME integration with GIS (TerraView) TerraLib Database

10. Conversion from GIS data to cell spaces Vector geospatial data Cell space Real world

11. The mixed pixel problem How can you transform from vectors to cell attributes?

12. Using “FillCell” plugin to build Cell Spaces 1. Install the FillCell plugin: Copy the file "celulas.dll" to the directory "C: \ Program Files \ TerraView3.2.0 \ plugins". 2. Build the cell space with the desired resolution

13. Fill the attributes of the cell spaces For each data type to be transformed, there are appropriate operations

14. Filling Cells from vector data Numerical areas (polygons, cells) Categorical areas (polygons, cells) Lines and points Min, max, average, sum, standard dev Majority class (by number or by area) Percentage of each class, Percentage of majority class, area of majority class Average/Sum intersection- weighted Presence, minimum distance, count

15. Lua Roberto Ierusalimschy PUC-Rio, Brazil

16. What is Lua?  Yet Another Scripting Language  an “extension” language  implemented as a library in ANSI C Host Program Lua Interpreter -- a Lua script color = RED b = button { label = ‘OK’, x = 10, y = 20}

17. Why Lua?  Simple and flexible  “Simple things simple, complex things possible”  Small, Efficient, Portable  Whole library written in ANSI C, compiles the same source code in all platforms  Typical uses: MS-DOS, Windows (3.1, 95, NT), Unix (Linux, Solaris, IRIX, AIX, ULTRIX), Next, OS/2, Mac

18. Where is Lua?  Inside Brazil  Petrobras, the Brazilian Oil Company  Embratel (the main telecommunication company in Brazil)  many other companies  Outside Brazil  Lua is used in hundreds of projects, both commercial and academic  CGILua still in restricted use »until recently all documentation was in Portuguese

19. How is Lua?  Pascal-like Syntax.  Interpreter executes sequence of statements.  function definitions are also statements (see later)  Six types: numbers, tables, functions, strings, userdata, nil function fat (n) if n == 0 then return 1 else return n*fat(n-1) end

20. My first Lua program C = 2; -- rain/t K = 0.4; -- flow coefficient q = 0; -- RULES for time = 0, 20, 1 do -- soil water q = q + C - K*q; end print(“q = "..q);

21. Types

22. Type nil  Different from everything else  Default variable type  Also acts as false (boolean)

23. Type boolean  Comparison value  if (rain == true) then....

24. Type number  Unique native type for numbers  double (by default) a = 3 b = 3.5 c = 4.5e-8

25. Type string  Immutable  No size limit (read large files as strings)  No termination value (‘\0’)  Powerful Pattern-matching in standard library  myname = “Werner Kuhn”;

26. Tables  Implement associative arrays:  any value (including functions and other tables) can be used both for indices and values t = {} -- creates an empty table t[1] = "hello" t.x = print -- t.x is sugar for t[‘x’] t.x(t[1]) -- prints ‘hello’ t.next = t -- circular list

27. Table loc = { cover = "forest", distRoad = 0.3, distUrban = 2 }; loc.cover = “cerrado”; loc[“cover”] = “soja”; if (loc.distUrban > 1.5) then

28. Tables in Lua loc = { cover = "forest", distRoad = 0.3, distUrban = 2 }; loc.desfPot = loc.distRoad + loc.distUrban;

29. Constructors: Create and init tables  Record style  point={x=10,y=20}  print(point.y) --> 20  List style  days={ " Sun ", " Mon ", " Tue ", " Wed”, Sat " }  print(days[3]) --> Tue  Mixed style  points={{x=0,y=0}, point, n=2}  print(points[points.n].y) --> 20

30. Lua and the Web Constructors article{ author="F.P.Brooks", title="The Mythical Man-Month", year=1975, } news = { {text = "New version 2.0", date = "21/05/1997"}, {text = "New example", date = "21/05/1997"}, {text = "New version: 2.1",date = "17/06/1997"}, } calls function “article”

31. Functions in Lua function fat (n) if n == 0 then return 1 else return n*fat(n-1) end

32. Lua and the Web Functions in Lua  First class values function inc (x) return x+1 end inc = function (x) return x+1 end sugar clone = {} foreach(t, function (i,e) clone[i]=e end)  Example: cloning a table t

33. Functions and Tables w = { redraw = function ()... end, pick = function (x,y)... end, } if w.pick(x,y) then w.redraw() end

34. Tables x Objects  Tables are dynamically created objects. list value - v next - old list... list = {value=v, next=list}

35. Objects  First-class functions+ tables = almost OO  Tables can have functions as fields  Sugar for method definition and call  Implicit parameter self a.foo(a,x)a:foo(x) a.foo = function (self,x)... end function a:foo (x)... end sugar

36. My second Lua program C = 2; -- rain/t K = 0.4; -- flow coefficient q = 0; -- function rain (t) if (t < 10) then return 4 – 4*math.cos(math.pi*t/10); else return 4 – 4*math.cos(math.pi*(t-10)/10); end -- for time = 0, 20, 1 do -- soil water q = q + rain(time) - K*q; end -- report print(“q = "..q);

37. Standard libraries Basic String Table Math IO OS Debug Coroutine

38. Basic Basic functions print type setmetatable pairs

39. String String manipulation pattern matching string.find string.gsub

40. Table  Function for table manipulation – table.insert – table.remove – table.sort

41. rain N Itacolomi do Itambé Peak Lobo’s Range My third Lua program Define a two-dimensional grid Make it rain on the grid Let water flow downwards

42. TerraME: Vision An Earth´s environment can be represented as a synthetic environment where analytical entities (rules) change the space properties in time. Several interacting entities share the same spatiotemporal structure.

43. TerraLib TerraLib Enviromental Modeling Framework C++ Signal Processing librarys C++ Mathematical librarys C++ Statistical librarys TerraME Virtual Machine TerraME architecture & applications TerraME Compiler TerraME Language RondôniaModelDinamicaModelTROLLModelCLUEModel

44. TerraME Runtime Environment

45. The Scale Concept in TerraME Scale is a generic concept that includes the spatial, temporal, or analytical dimensions used to measure any phenomenon. Extent refers to the magnitude of measurement. Resolution refers to the granularity used in the measures. (Gibson et al. 2000)

46. TerraME allows nested scales

47. Nested scales are necessary for human- environment models Diverse space partitions can have different scales

48. TerraME extensions to Lua To build spatial dynamic models, TerraME includes new value types in LUA using the constructor mechanism. These values are: CellularSpace, Cell, Neighbourhood

49. Cellular Space A geographical area of interest, divided into a grid. Each cell in the grid has one or more attributes. Stored and retrieved from a TerraLib database

50. Loading Data -- Loads the TerraLib cellular space csCabecaDeBoi = CellularSpace { dbType = "ADO", host = “localhost", database = "c:\\cabecaDeBoi.mdb", user = "", password = "", layer = "cellsLobo90x90", theme = "cells", select = { “height", “soilWater", “capInf" } } csCabecaDeBoi:load(); csCabecaDeBoi:loadMooreNeighbourhood; GIS

51. Creating temporary cellular spaces game = CellularSpace { xdim = N, ydim = N }

52. Referencing cells A CellularSpace has a special attribute called cells. It is a one-dimensional table of references for each Cell in the CellularSpace -- c is the seventh cell in the cellular space c = csCabecaDeBoi.cells[ 7 ]; -- Updating the attribute “infcap” from the seventh cell c.infcap = 10; print (csCabecaDeBoi.cells[7].infCap);

53. Database management -- loads a cellular space csAmazonia:load() csAmazonia:loadNeighbourhood("Moore") -- save (time, themeName, attrTableName) -- for time = 1, 10,1 do csAmazonia:save(time, “sim", {"water"}) end

54. The Cell type A Cell value has two special attributes: latency and past. The latency attribute registers the period of time since the last change in a cell attribute value. The past attribute is a copy of all cell attribute values in the instant of the last change. if(cell.cover == "abandon" and cell.latency >= 10) then cell.cover = "secFor" end cell.water = cell.past.water + 2

55. Traversing a Cell Space " for...end" statement: "for i, cell in pairs (csQ.cells) do...end”. The i and cell variable in the statement are the index and the value of a cell inside the cells attribute from the cellular space csQ. for i, cell in pairs( csQ.cells ) do cell.water = cell.past.water + 2 end

56. Traversing a Cell Space forEachCell(cs, function()) Applies the chosen function to each cell of the cellular space. This function enables using different rules in a cellular space. forEachCell(csQ, function(cell) cell.Water = cell.past.Water + 2 return true end )

57. Von Neumann Neighborhood Moore Neighborhood Isotropic neighbourhoods in cell spaces

58. Traversing a Neighbourhood csq:loadNeighbourhood(“Moore”); forEachCell(csQ, function(cell) count = 0; forEachNeighbour(cell, 0, function(cell, neigh) if (neigh.past.value == 1 and neigh ~= cell) then count = count + 1; end end; ); -- for each neighbor

59. for i, cell ipairs( csValeDoAnary ) do end count = 0 ; print(“Number of deforested cells: ”.. count); if ( cell.past.sim_cover == 1 ) then cell.sim_cover = 0; count = count + 1 ; end cell.synchronize( ); Synchronizing a cell space tntn t n+1 rule ?

60. Synchronizing a cell space tntn t n+1 rule TerraME keeps two copies of a cellular space in memory: one stores the past values of the cell attributes, and another stores the current (present) values of the cell attributes. The model equations must read (the right side of the equation rules) the past copy, and must write (the left side of the equation rules) the values to the present copy of the cellular space. At the correct moment, it will be necessary to synchronize the two copies of the cellular space, copying the current attribute values to the past copy of the cellular space

61. Synchronization Always read from the past Always write to the present …. csQ:syncronize();

62. Trajectories: spatial patterns of change modeller defined functions which map indexes (atributtes) to geo-objects (cells). it = Trajectory{ myCellSpace, function(cell) return cell.cover == "forest“ end, function( c1, c2 ) return c1.dist_roads < c2.dist_roads end }

63. Which objects are nearest to each other?

64. Using Generalized Proximity Matrices (GPM) Consolidated areaEmergent area

65. TerraME neighborhoods are graphs Euclidean space Open network Closed network D2 D1 [Aguiar et al., 2003]

66. Create or load neighborhoods -- Create a Moore neighborhood createMooreNeighborhood( myCellSpace, “neighName” ) -- Create a 3x3 neighborhood create3x3Neighborhood(myCellSpace, filterF(), weightF(), name ) -- Create a MxN neighborhood createMxNNeighborhood( M, N, myCellSpace,filterF(), weightF(), name ) -- Load neighborhood from TerraLib database myCellSpace: loadTerraLibGPM(“myGPM"); -- Load neighborhood from TerraLib GAL files myCellSpace:loadGALNeighborhood("c:\\myNeigh.gal")

67. Building neighborhoods between cell spaces spatialCoupling( M, N, cs1,cs2, filterF, weightF, name ) filterF(cell, neigh)  Boolean wheighF(cell, neigh)  Real

68. Example: neighborhood to simulate rain -- Creates a 3x3 Neighborhood based on the cell "slope" -- only lower neighbors are considered create3x3Neighborhood( csQ, function(cell,neigh) return neigh.altimetry < cell.altimetry end, function(cell, neigh) return (cell.altimetry - neigh.altimetry)/ (cell.altimetry + neigh.altimetry) end, "slope" );

69. Saving cell spaces as images -- attribute used to generate the image attr_name = "estado" -- values that the attribute can have attr_value = {0,1,2} -- color pallete attr_color = {{0,255,0},{255,0,0},{0,0,0}} -- directory where images will be saved path = "c:\\TerraME\\Results“ -- size of the cell in pixels cellSize = 2 -- load the o espaco celular do banco de dados TerraLib........................ for t = 1, 100 do CStoPNG(myCellSpace, attr_name,t,path,cellSize,attr_value,attr_color) end

70. rain N Itacolomi do Itambé Peak Lobo’s Range

71. Picture direction Itacolomi do Itambé Peak Lobo’s Range

72. Demo: Rain Drainage Model Database: c:\\TerraME\\Database\\CabecadeBoi.mdb Model: c:\\TerraME\\Modelos\\demo4_chuva_geoBD.lua Model: c:\\TerraME\\Modelos\\demo7_chuva_geoBD.lua

73. Simulation Result (36 min.)

74. Demo: Fire propagation Database: c:\\TerraME\\Database\\db_emas.mdb Model: c:\\TerraME\\Modelos\\demo6_FireSpreadModel.lua CA 1CA 2CA 3CA 4CA 5 CA 1 0.1000.2500.2610.2730.285 CA 2 0.1130.2530.2640.2760.288 CA 3 0.1160.2560.2670.2790.291 CA 4 0.1190.2590.2700.2820.294 CA 5 0.1220.2620.2730.2850.297 QUEIMANDO INERTE

75. Demo: Amazon deforestation Database: c:\\TerraME\\Database\\amazonia.mdb Model: c:\\TerraME\\Modelos\\demo3_desflorestamento_save.lua

76. References Carneiro, T., 2006. Nested-CA: a foundation for multiscale modeling of land use and land change., in PhD Thesis in Computer Science. National Institute of Space Research: São José dos Campos, Brazil. Carneiro, T.; Câmara, G., 2007. A Gentle Introduction to TerraME. INPE Report, 2007. Ierusalimschy, R. 2006. Programming in Lua (2 nd edition). Rio de Janeiro, Lua.Org.