GIS model & modelingGIS model & modeling
ModelModel :: a simplified representation of a phenomenon or aa simplified representation of a phenomenon or a
systemsystem..
GIS modelingGIS modeling :: the use of GIS in the process of buildingthe use of GIS in the process of building
models with spatial datamodels with spatial data..
Basic requirement in modelingBasic requirement in modeling :: modelermodeler’’s interests interest &&
:: KnowledgeKnowledge of theof the systesystemsms
be modeledbe modeled..
e.g. environmente.g. environment Biologic (ecology)Biologic (ecology)
atmosphericatmospheric
hydrologichydrologic
Geologic (land surface/subsurface)Geologic (land surface/subsurface)
GIS model & modelingGIS model & modeling
GIS Model elementsGIS Model elements :: 1.1. a set of selected spatial variablesa set of selected spatial variables
:: 2.2. functionalfunctional // mathematical relationshipmathematical relationship
betweenbetween variablesvariables..
GIS Model can be related toGIS Model can be related to :: exploratory data analysisexploratory data analysis
: data visualization: data visualization
: DB management: DB management
GIS Model can work together withGIS Model can work together with // across GIS software packagesacross GIS software packages && otherother
computer programscomputer programs.. (( ee..gg.. exelexel ))
GIS Model can beGIS Model can be :: vectorvector –– basedbased
: raster: raster –– basedbased
: include both in one model / task: include both in one model / task ((usingusing conversionconversion )
Depends on nature of model ,data
source , computing algorithm
)
GIS Types of GIS modelsGIS Types of GIS models
Binary models
Index model
Regression models
Process models
Binary modelsBinary models
LogicalLogical modelmodel ((expressionsexpressions)) toto selectselect featuresfeatures fromfrom
compositecomposite mapmapss oror multiplemultiple gridsgrids
(features: point, line, polygon, cell)(features: point, line, polygon, cell)
OutputOutput 11 (( truetrue )) && øø (( fafalselse))
MapMap overlayoverlay combinecombine attributesattributes // variablesvariables
A commonA common example of this modelexample of this model isis sitingsiting [[ pointpoint,, polygonpolygon
((potentialpotential areaarea)) ]] analysisanalysis.. (( FigFig.. 14.1)14.1)
SpatialSpatial queryquery FigFig.. 14.214.2
comparecompare toto locallocal operationoperation of gridof grid
Binary modelsBinary models
( Chang, 2002 )( Chang, 2002 )
Index ModelsIndex Models:: WWeighteight--ratingrating SScorecore ModelsModels
Assign & standardize values to spatialAssign & standardize values to spatial elements(featureselements(features) of) of
each layer.each layer.
UseUse thethe indexindex valuevalue calculatedcalculated from afrom a compositecomposite mapmap oror
multiplemultiple grids togrids to produceproduce a ranka rank mapmap..
( ) ( )2211 AA xscoreweightxscoreweight +( ) ( )2211 AA xscoreweightxscoreweight +
Index value of aIndex value of a polygonpolygon // cellcell ==( ) ( )2211 AA scoreweightscoreweight ×+×
SeeSee FigFig.. 14.314.3 ((vectorvector--basedbased),), FigFig.14.4.14.4 (( rasterraster--basedbased ))
StepsSteps::
1.1. assignassign weightweight to each variableto each variable ((ww))
2.2. assignassign && standardizestandardize scorescoress to eachto each classclass ofof
eacheach variablevariable(data layer)(data layer)
IndexIndex ModelsModels :: WWeighteight--ratingrating SScorecore ModelsModels
( ) ( )2211 AA xscoreweightxscoreweight +( ) ( )2211 AA xscoreweightxscoreweight +
StepsSteps::
3. index value calculation
4. ranking index values of each polygon / cell.
Total Score / Index value = ∑=
n
i
ji sw1
i
th
j
th
Wi = weight of i
th
variable
Sj = score of class in the variable
Check !
( ) ( )2211 AA xscoreweightxscoreweight +( ) ( )2211 AA xscoreweightxscoreweight +
IndexIndex ModelsModels :: WWeighteight--ratingrating SScorecore ModelsModels
( Chang, 2002 )( Chang, 2002 )
IndexIndex ModelsModels :: WWeighteight--ratingrating SScorecore ModelsModels
( ) ( )2211 AA xscoreweightxscoreweight +( ) ( )2211 AA xscoreweightxscoreweight +
maxmax--XXii
maxmax--minmin
XXii--minmin
maxmax--minmin
77 2121
3232 4949
11 0.670.67
0.400.40 00
77 2121
3232 4949
00 0.330.33
0.590.59 11
Normalized/standardized cell values(scores) to be comparable.
Rating score
Benefit: The more, the better : rain index value probability Landslide
Cost: The less, the better: veg density index value LS prob
Regression ModelRegression Model
RelatesRelates a dependent variable to aa dependent variable to a numbernumber ofof independentindependent
variables invariables in anan equationequation -- used forused for predictionprediction // estimationestimation..
22 typestypes of regression modelof regression model (??(?? -- discussdiscuss??)??)
LinearLinear(?)(?) regressionregression :: whenwhen variables are allvariables are all numericnumeric..
LogisticLogistic regressionregression :: dependent variable is a binarydependent variable is a binary
phenomenonphenomenon(/probability?)(/probability?) & the& the independentindependent
variables arevariables are categoricalcategorical oror numericnumeric variablesvariables..
Regression ModelRegression Model
ExampleExample :: LinearLinear (?)(?) regressionregression
SWESWE == EastingEasting ++ southingsouthing ++ ELEVELEV
WhenWhen a,, ,, and are regression coefficientsand are regression coefficients
EastingEasting -- column nocolumn no.. of a grid cellof a grid cell
SouthingSouthing –– row norow no.. of a cellof a cell
ELEVELEV –– elevation values of a cellelevation values of a cell
SWESWE –– snow water equivalentsnow water equivalent -- a dependent variablea dependent variable
1ba + 2b 3b
1b 2b 3b
Regression ModelRegression Model
Logistic regressionLogistic regression
yy == 0.0020.002 ELEVELEV –– 0.2280.228 slopeslope ++ 0.6850.685 canopycanopy 11 ++ 0.4430.443 canopycanopy 22 ++
0.4810.481 canopycanopy 33 ++ 0.0090.009 aspect Easpect E--WW
yy == habitat suitability for red squirrel to be presenthabitat suitability for red squirrel to be present
where canopywhere canopy 1,2,31,2,3 -- categories of canopycategories of canopy
thenthen,,
ProbabilityProbability (( pp)) of squirrel presence for each cellof squirrel presence for each cell ::
PP == 11 // (( 1+1+ expexp ((--yy)) ))
y P
?? # Check relationship of regression models with ( i ) linear equation, nd
2 order polynomial, ‘best fit’ least square analysis ??#
mathematicsIn , especially as applied in
statistics,
the logit (pronounced with a long "o" and a soft
"g", IPA /loʊdʒɪt/) of a number p between 0 and 1
is
This function is used in logistic regression
Process ModelProcess Model
Integrate existing knowledge aboutIntegrate existing knowledge about envtenvt.. process in the realprocess in the real
world into a set of relationships and equation forworld into a set of relationships and equation for
quantifying the processquantifying the process..
Offer both a predicative capabilityOffer both a predicative capability && explanation processesexplanation processes
proposedproposed..
Examples: A = RKLSCPUSLE
A- av. soil loss in tons , R- rainfall intensity S – slope gradient , C – cultivation factor
K-soil erodibility , L- slope length P- supporting practice factor.
L & S – estimated from field measurement sometimes
combined to be a single topographic factor
Process ModelProcess Model
“AGNPS” (Agricultural nonpoint source)
SL = ( EI ) K LS C P (SSF)
- Used to estimate upland erosion for a single storm.
SL – soil loss
EI – product of the storm total kinetic energy and max – 30 minute intensity
K- soil erodibility , LS – topographic factor,
C- cultivation factor, P - supporting practice factor
SSF – a factor to adjust slope shape in a cell.
Process ModelProcess Model
“SWAT” (soil & water assessment tool )
a model predicts the impact of land management practices on
water Q & Q, sediment, and agricultural chemical yields in large
complex watersheds.
Inputs are Land management practice such as :
Crop rotation, irrigation, fertilizer use, pesticide application rates,
physical characteristics of the basin & subbasin
( precipitation, temperature, soil, vegetation, & topography )
Output :
simulated values of surface water flow, GW flow, crop growth,
sediment & chemical yields.