spatial dynamical modeling with terrame

Spatial Dynamical Modeling with TerraME

Tiago CarneiroGilberto Câmara

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)

Computational Modelling with Cell SpacesCell Spaces

Representation

Cell Spaces Generalized Proximity Matriz – GPM Hybrid Automata model Nested scales

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

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

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

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

“GPM” PluginTerraView 3.2.0

“FillCell” PluginTerraView 3.2.0

TerraME integration with GIS (TerraView)

TerraLib Databse

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?

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

Fill the attributes of the cell spaces

For each data type to be transformed, there are appropriate operations

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

Lua and the Web

Lua

Roberto Ierusalimschy

PUC-Rio, Brazil

Lua and the Web

What is Lua?

Yet Another Scripting Language

an “extension” language

implemented as a library in ANSI C

HostProgram

LuaInterpreter

-- a Lua scriptcolor = REDb = button { label = ‘OK’, x = 10, y = 20}

Lua and the Web

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

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

Lua and the Web

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) endend

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);

Type nil

Different from everything else

Default variable type

Also acts as false (boolean)

Type boolean

Comparison value

if (rain == true) then ....

Type number

Unique native type for numbersdouble (by default)

a = 3b = 3.5c = 4.5e-8

Type string

Immutable

No size limit (read large files as strings)

No termination value (‘\0’)

Powerful Pattern-matching in standard library

myname = “Werner Kuhn”;

Lua and the Web

Tables

Implement associative arrays: any 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

Lua and the Web

Constructors Expressions to create and initialize tables

Record style point={x=10,y=20} print(point.y) --> 20

List style days={"Sun","Mon","Tue","Wed","Thu","Fri","Sat"} print(days[3]) --> Tue

Mixed style points={{x=0,y=0}, point, n=2} print(points[points.n].y) --> 20

Table

loc = { cover = "forest", distRoad = 0.3, distUrban = 2 };

loc.cover = “cerrado”;loc[“cover”] = “soja”;

if (loc.distUrban > 1.5) then

Tables in Lua


loc.desfPot = loc.distRoad + loc.distUrban;

Tables em Lua : functions


...loc.reset = function( self )

self.cover = ""; self.distRoad = 0.0; self.distUrban = 0.0;

end

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”

Functions in Luafunction fat (n)

if n == 0 then

return 1

else

return n*fat(n-1)

end

end

Lua and the Web

Functions in Lua

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)

Example: cloning a table t

Lua and the Web

Upvalues

Mechanism to allow functions to access non-local variables

An upvalue is a variable expression whose value is computed when the enclosing function is instantiated (and not when the function is executed)

function add (x) return function (y) return y+%x endend

add1 = add(1)print(add1(10)) --> 11

upvalue

Functions and Tables

w = { redraw = function () ... end, pick = function (x,y) ... end,}

if w.pick(x,y) then w.redraw()end

Lua and the Web

Tables x Objects

Tables are dynamically created objects. in the sense of Hoare

list

value - vnext -

old list...

list = {value=v, next=list}

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

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

Basic

Basic functionsprinttypesetmetatablepairs

String

String manipulationpattern matching

string.findstring.gsub

Table

Function for table manipulation table.insert table.remove table.sort

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: 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.

TerraLib

TerraLib EnviromentalModeling Framework

C++ Signal Processing

librarys

C++ Mathematical

librarys

C++ Statisticallibrarys

TerraME Virtual Machine

TerraME architecture & applications

TerraME Compiler

TerraME Language

RondôniaModel DinamicaModel TROLLModel CLUEModel

TerraME Runtime Environment



TerraLibdatabase

da

ta

Model source code

MODEL DATA

mod

el


TerraME INTERPRETER

LUA interpreter

TerraME framework


model d

ata

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)

TerraME allows nested scales

Nested scales are necessary for human-environmental models

Diverse space partitions can have different scales

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

Cellular SpaceA geographical area of interest, divided into a grid. Each cell in the grid has one or more attributes. CellularSpaces are 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

myCellSpace = CellularSpace{ database = "", theme = "“ }

for i = 1, 2, 1 dofor j = 1, 2, 1 do

c = Cell{ soilType = “latosolo” }c.x = i;c.y = j; myCellSpace :add( c );

endend

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



TerraLibdatabase

Model source code

MODEL DATA


TerraME INTERPRETER

LUA interpreter

TerraME framework


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 == "abandoned" and cell.latency >= 10 ) then cell.cover = "secFor"; end

cell.water = cell.past.water + 2;

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 ) docell.water = cell.past.water + 2;

end

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);

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

?


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.


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}

Quais objetos são mais proximos?

Which objects are NEAR 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"

);

Saving cell spaces as images-- attribute used to generate the imageattr_name = "estado"-- values that the attribute can haveattr_value = {0,1,2}-- color palleteattr_color = {{0,255,0},{255,0,0},{0,0,0}}-- directory where images will be savedpath = "c:\\TerraME\\Results“-- size of the cell in pixelscellSize = 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

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: Desflorestamento na Amazônia

Banco de dados: c:\\TerraME\\Database\\amazonia.mdb Modelo: 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.

spatial dynamical modeling with terrame

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