Spatial Dynamical Modeling with TerraME (part 2)

Gilberto 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)

tp - 20 tp - 10

tp

Calibration Calibration tp + 10

ForecastForecast

Dynamic Spatial Models

Source: Cláudia Almeida

Cell Spaces

A cell space is a raster-based spatial data structure where each cell can handle one or more types of attribute

Cell-spaces have several advantages over raster-based layers as a means of storing information about continuous spatial phenomena.

Using one-attribute raster structures, describing a complex spatial phenomenon requires information to be stored in different files

In a cell-space, such information is kept together in a single structure, with significant benefits in terms of visualization and interface.

Computational Modelling with Cell Spaces

Cell Spaces

Representation

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

2500 m 2.500 m e 500 m

Cellular Data Base Resolution

TerraME - overview

Model data in cell spaces

Read/write data from a database

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

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

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

TerraLib EnviromentalModeling Framework

C++ Signal Processing

librarys

C++ Mathematical

librarys

C++ Statistical

librarys

TerraME Virtual Machine

TerraME Compiler

TerraME Language

RondôniaModel DinamicaModel TROLLModel CLUEModel

TerraME architecture

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);

Types

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 Table

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

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

if (loc.distUrban > 1.5) then

Tables in LuaTables in Lua

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

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

Tables em Lua : functionsTables em Lua : functions

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

...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 Lua

function 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 librariesStandard libraries

Basic String Table Math IO OS Debug Coroutine

BasicBasic

Basic functionsprinttypesetmetatablepairs

StringString

String manipulationpattern matching

string.findstring.gsub

TableTable

Function for table manipulationtable.inserttable.removetable.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

My third Lua programMy third Lua program

4 6

2

8 97

1

5

3

30 30

50

15 1515

50

30

50

0.3 0.3

0.2

0.4 0.40.4

0.2

0.3

0.2

Cell number height absortioncapability

flow direction

TerraME extensions to LuaTerraME 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 SpaceCellular Space

A CellularSpace is a multivalued set of Cells. It consists of a geographical area of interest,

divided into a regular grid. Each cell in the grid has one or more

attributes.

CellularSpaces are stored and retrieved from a TerraLib database, so the modeller should specify the properties of the CellularSpace

Cellular SpaceCellular Space Usa o construtor de LUAcsCabecaDeBoi = CellularSpace {

dbType = "MySQL",host = "localhost",database = "CabecaDeBoi ",user = "",password = "",layer = "cells90x90",theme = "cells",select = { “height", “capInf" }where = "mask <> ‘noData’";

}

Loading DataLoading 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

Referencing cellsReferencing 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 spacec = csCabecaDeBoi.cells[ 7 ];-- Updating the attribute “infcap” from the

seventh cellc.infcap = 10;

print (csCabecaDeBoi.cells[7].infCap);

Database managementDatabase 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

The Cell typeThe 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 SpaceTraversing 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 SpaceTraversing 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 Isotropic neighbourhoods in cell spacesspaces

Traversing a NeighbourhoodTraversing 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

Synchronizing a cell spaceSynchronizing a cell space 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.

SynchronizationSynchronization

Always read from the pastAlways write to the present….csQ:syncronize();

ReferencesReferences 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.

Simulation of Physical Processes

- rain drainage in a terrain -

rainrain rain

N

Itacolomi do ItambéPeak Lobo’s Range

My first TerraME program

A simple 2D hydrological model(see example in “Gentle Introduction”)

Picture direction

Itacolomido Itambé Peak

Lobo’s Range

SimulationResult(36 min.)