Spatial Dynamical Modeling with TerraME
Tiago CarneiroGilberto CâmaraPedro Andrade
Licence: Creative Commons ���� By Attribution ���� Non Commercial ���� Share Alikehttp://creativecommons.org/licenses/by-nc-sa/2.5/
What models are needed to describe human actions?
Modelling human-environment interactions
Clocks, clouds or ants?
Clocks: deterministic equations
Clouds: statistical distributions
Ants: emerging behaviour
f ( It+n )
. . FF
f (It) f (It+1) f (It+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)
Nature-society modelling with TerraME
Nature: Physical equations Describe processes
Society: Decisions on how to Use Earth´s resources
Nature-society modelling with TerraME
Nature: Physical equations Describe processes
Society: Decisions on how to Use Earth´s resources
Nature: Cellular space Society: Agents
Agen
t
Spa
ce
Space Agent
Benenson and Torrens, “Geographic Automata Systems”, IJGIS, 2005(but many questions remain...)
Modelling collective spatial actions
Computational Modelling with Cell SpacesCell Spaces
Generalized Proximity Matriz – GPM
Hybrid Automata model
Nested scales
Agents in space
TerraME - overview
Model data in cell spaces
Read/write data from a database
2500 m 2.500 m e 500 m
Cellular Data Base Resolution
Large farmer (25 cells)
500 m (all)
Small farmer (2 cells)
Spatial structure
Behavior is non-homogeneous in space and time
Phase transitions
Newly implanted
Deforesting
Slowing down
latency > 6 years
Deforestation > 80%
Iddle
Year of creation
Deforestation = 100%
Multi-scale modelling
Express anisotropy
y=a0 + a1x1 + a2x2 + ... +aixi +E
Statistics and agents
Tools for observing simulations
TerraME functionality
Eclipse & LUA plugin• model description• model highlight syntax
TerraView• data acquisition• data visualization• data management• data analysis
TerraLibdatabase
da
ta
Model source code
MODEL DATA
mod
el
• model syntax semantic checking• model execution
TerraME INTERPRETER
LUA interpreter
TerraME framework
TerraME/LUA interface
model d
ata
TerraLib: spatio-temporal database as a basis for innovation
Visualization (TerraView)
Spatio-temporalDatabase (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.
TerraLib
TerraME C++ Framework
C++ Signal Processing
librarys
C++ Mathematical
librarys
C++ Statistical
librarys
TerraML Virtual Machine
TerraME: Software Architecture
TerraMLCompiler
TerraML Language
Model 1 Model 2 Model 3 Model 4
Lua and the Web
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
TerraME Programming Language: Extension of Lua Lua is the language of choice for computer games
[Ierusalimschy et al, 1996]source: the Lua team
Lua
Roberto Ierusalimschy
PUC-Rio, Brazil
What is Lua?
4 Yet Another Scripting Language
4 an “extension” language
4 implemented as a library in ANSI C
HostProgram
LuaInterpreter
-- a Lua scriptcolor = REDb = button { label = ‘OK’, x = 10, y = 20}
Why Lua?
4 Simple and flexible 8“Simple things simple, complex things possible”
4 Small, Efficient, Portable 8Whole library written in ANSI C, compiles the same
source code in all platforms8Typical uses: MS-DOS, Windows (3.1, 95, NT), Unix (Linux,
Solaris, IRIX, AIX, ULTRIX), Next, OS/2, Mac
How is Lua?
4 Pascal-like Syntax.
4 Interpreter executes sequence of statements.8 function definitions are also statements (see later)
4 Six types: numbers, tables, functions, strings, userdata, nil
function fat (n) if n == 0 then return 1 else return n*fat(n-1) endend
Variables and Values Case sensitive
semicolon may optionally follow any statement
a = 1
b = a*2
print(a)
print(b)
Comments double hyphen (--) until the end of the line.
block comments start with --[[ and run until ]]
print("hello") -- my comment
-- print("hello”)
--[[
print(10) -- no action (comment)
--]]
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)
Types
Type nil
Different from everything else
Default variable type
Also acts as false (boolean)
Type boolean
4Comparison value
8if (rain == true) then ....
boolean false/true nil and false are false, everything else is true zero and the empty string are true operators and, or, and not
print(true and false)print(true and (false or true))print(false or (true and false) or (true and true))
number
the only type for numeric values double-precision floating-point number arithmetic operators: +, –, *, / exponent (^) and modulus (%) boolean operators (<, >, <=, >=, ~=, and ==)
A = 6 + 2.2 * 4e+3a = A ^ 2b = A % 7print(a > b)
print(b ~= 2)
ParenthesesAlways optional (except in the case of function call)
When in doubt, use parentheses
a+-i < b/2+1 <--> (a + (-i)) < ((b/2)+1)
5+x^2*8 <--> 5 + ( (x^2)*8 )
a < y and y <= z <--> (a < y) and (y <= z)
–x^y^z <--> –(x^(y^z))
Type string
4 Immutable
4 No size limit (read large files as strings)
4 No termination value (‘\0’)
4 Powerful Pattern-matching in standard library
8myname = “Werner Kuhn”;
if statement
An if statement tests condition and executes its then-part or its else-part (optional) accordingly
a = 6; b = 5
if a < b then print("a < b")
elseif a < b + 5 thenprint("b <= a < b+5")
elseprint("a > b+5")
end
for statementfor var = exp1, exp2, exp3 dosomething
end Execute something for each value of var from exp1 to exp2,
using exp3 as the step to increment var. This third expression is optional (default is 1).
for i = 1, 10 doprint(i)
endfor i = 1, 10, 2 doprint(i)
end
Tables
4 Implement associative arrays:8any value (including functions and other tables) can be
used both for indices and values
t = {} -- creates an empty tablet[1] = "hello"t.x = print -- t.x is sugar for t[‘x’]t.x(t[1]) -- prints ‘hello’t.next = t -- circular list
table Tables can be indexed not only with numbers, but also with
strings or any other value of the language, except nilloc = {cover = "forest",distRoad = 0.3,distUrban = 2
}
print(loc["cover"])print(loc.cover)loc.distRoad = loc.distRoad^2loc.distTotal = loc.distRoad + loc.distUrbanloc.deforestationPot = 1/loc.distTotal
Tables within tables
loc = { cover = "forest",
dist = {road = 0.3, urban = 2}
}
print(loc.dist.road)
loc.dist.total = loc.dist.road + loc.dist.urban
print(loc.dist.total)
Constructors: Create and init tables
4 Record style8point={x=10,y=20}8print(point.y) --> 20
4 List style8days={"Sun","Mon","Tue","Wed”, Sat"}8print(days[3]) --> Tue
4 Mixed style8points={{x=0,y=0}, point, n=2}8print(points[points.n].y) --> 20
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”
function
A function can carry out a specific task (commonly called procedure) or compute and return values.
A function is a first-class value in Lua. Functions can be stored in variables and in tables, can be
passed as arguments, and can be returned by other functions, giving great flexibility to the language.
myprint = printprint = nilmyprint(2)print = myprint
Functions in Luafunction fat (n)
if n == 0 then
return 1
else
return n*fat(n-1)
end
end
Higher-order Functions Functions can also be parameters to other functions. This kind
of function is what we call a higher-order function.
function foreach(tab, func)
for position, value in pairs(tab) dofunc(value, position)
endendx = {7, 3, 2, 6, 4}foreach(x, function(element)print(element)
end)foreach(x, function(value, position)print(position, value)
end)
Lua and the Web
Functions in Lua
4 First class values
function inc (x) return x+1end
inc = function (x) return x+1 end
sugar
clone = {}foreach(t, function (i,e) clone[i]=e end)
4 Example: cloning a table t
Functions and Tables
w = { redraw = function () ... end, pick = function (x,y) ... end,}
if w.pick(x,y) then w.redraw()end
Tables with functionsTables may have their own functions.
loc = {cover = "forest", distRoad = 0.3, distUrban = 2,deforestPot = function(myloc)
return 1/(myloc.distRoad + myloc.distUrban)
end}
print(loc.deforestPot(loc))print(loc:deforestPot())
Tables with functions4 We can declare a “class” in Lua by creating a function that
takes a table constructor as argument.
function MyLocation(locdata)locdata.covertype = "forest"locdata.deforPot = function(self) return 1/(self.distRoad + self.distUrban)endreturn locdata
end
loc = MyLocation({distRoad = 0.3, distUrban = 2})loc = MyLocation{distRoad = 0.3, distUrban = 2}print(loc.covertype)print(loc:deforPot())
Tables x Objects
4 Tables are dynamically created objects.
list
value - vnext -
old list...
list = {value=v, next=list}
Objects4 First-class functions+ tables = almost OO
8Tables can have functions as fields
4 Sugar for method definition and call8 Implicit parameter self
a.foo(a,x)a:foo(x)
a.foo = function (self,x) ...end
function a:foo (x) ...end
sugar
sugar
My second Lua programC = 2; -- rain/tK = 0.4; -- flow coefficientq = 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); endend--for time = 0, 20, 1 do
-- soil waterq = q + rain(time) - K*q;
end-- report
print(“q = "..q);
Standard libraries
BasicStringTableMathIOOSDebugCoroutine
TerraME: Vision
Nature: represented by a cellular space
Society: represented by agents
Several interacting entities share the same spatiotemporal structure.
rainrain rain
N
Itacolomi do ItambéPeak Lobo’s Range
My third Lua program
Define a two-dimensional gridMake it rain on the gridLet water flow downwards
TerraME Runtime Environment
Eclipse & LUA plugin• model description• model highlight syntax
TerraView• data acquisition• data visualization• data management• data analysis
TerraLibdatabase
da
ta
Model source code
MODEL DATA
mod
el
• model syntax semantic checking• model execution
TerraME INTERPRETER
LUA interpreter
TerraME framework
TerraME/LUA interface
model d
ata
TerraME allows nested scales
Nested scales are necessary for human-environment models
Diverse space partitions can have different scales
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
Loading Data
-- Loads the TerraLib cellular spacecsCabecaDeBoi = CellularSpace{
dbType = "ADO",host = “localhost",database = "c:\\cabecaDeBoi.mdb",user = "",password = "",layer = "cellsLobo90x90",theme = "cells",select = { “height", “soilWater", “capInf" }
}csCabecaDeBoi:load();
csCabecaDeBoi:loadMooreNeighbourhood;
GIS
Creating temporary cellular spaces
game = CellularSpace { xdim = N, ydim = N }
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);
Database management-- loads a cellular spacecsAmazonia:load()csAmazonia:loadNeighbourhood("Moore")-- save (time, themeName, attrTableName) -- for time = 1, 10,1 do csAmazonia:save(time, “sim", {"water"})end
Eclipse & LUA plugin• model description• model highlight syntax
TerraView• data acquisition• data visualization• data management• data analysis
TerraLibdatabase
Model source code
MODEL DATA
• model syntax semantic checking• model execution
TerraME INTERPRETER
LUA interpreter
TerraME framework
TerraME/LUA interface
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"
endcell.water = cell.past.water + 2
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 trueend
)
Von Neumann Neighborhood
Moore Neighborhood
Isotropic neighbourhoods in cell spaces
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
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+1
rule
?
Synchronizing a cell space
tntn+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
Synchronization
Always read from the pastAlways write to the present….csQ:syncronize();
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}
Which objects are nearest to each other?
Using Generalized Proximity Matrices (GPM)
Consolidated area Emergent area
TerraME neighborhoods are graphs
Euclidean space Open network Closed network
D2
D1
[Aguiar et al., 2003]
Create or load neighborhoods-- Create a Moore neighborhoodcreateMooreNeighborhood( myCellSpace, “neighName” )
-- Create a 3x3 neighborhoodcreate3x3Neighborhood(myCellSpace, filterF() , weightF(),
name )
-- Create a MxN neighborhoodcreateMxNNeighborhood( M, N, myCellSpace,filterF(),
weightF(), name )
-- Load neighborhood from TerraLib databasemyCellSpace: loadTerraLibGPM(“myGPM");-- Load neighborhood from TerraLib GAL filesmyCellSpace:loadGALNeighborhood("c:\\myNeigh.gal")
Building neighborhoods between cell spaces
spatialCoupling( M, N, cs1,cs2, filterF, weightF, name )
filterF(cell, neigh) Boolean
wheighF(cell, neigh) Real
Example: neighborhood to simulate rain
-- Creates a 3x3 Neighborhood based on the cell "slope"-- only lower neighbors are consideredcreate3x3Neighborhood(
csQ,function(cell,neigh)
return neigh.altimetry < cell.altimetryend,function(cell, neigh)
return (cell.altimetry - neigh.altimetry)/(cell.altimetry + neigh.altimetry)
end,"slope"
);
“GPM” PluginTerraView 3.2.0
“FillCell” PluginTerraView 3.2.0
TerraME integration with GIS (TerraView)
TerraLib Database
Conversion from GIS data to cell spaces
Vector geospatial data
Cell space
Real world
The mixed pixel problem
How can you transform from vectors to cell attributes?
Fill the attributes of the cell spaces
For each data type to be transformed, there are appropriate operations
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
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
rainrain rain
N
Itacolomi do ItambéPeak Lobo’s Range
Picture direction
Itacolomido Itambé Peak
Lobo’s Range
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
SimulationResult(36 min.)
Demo: Fire propagation
Database: c:\\TerraME\\Database\\db_emas.mdbModel: c:\\TerraME\\Modelos\\demo6_FireSpreadModel.lua
CA 1 CA 2 CA 3 CA 4 CA 5
CA 1CA 1 0.1000.100 0.2500.250 0.2610.261 0.2730.273 0.2850.285
CA 2CA 2 0.1130.113 0.2530.253 0.2640.264 0.2760.276 0.2880.288
CA 3CA 3 0.1160.116 0.2560.256 0.2670.267 0.2790.279 0.2910.291
CA 4CA 4 0.1190.119 0.2590.259 0.2700.270 0.2820.282 0.2940.294
CA 5CA 5 0.1220.122 0.2620.262 0.2730.273 0.2850.285 0.2970.297
QUEIMANDO
INER
TE
Demo: Amazon deforestation
Database: c:\\TerraME\\Database\\amazonia.mdbModel: c:\\TerraME\\Modelos\\demo3_desflorestamento_save.lua
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 (2nd edition). Rio de Janeiro, Lua.Org.
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