Introduction to GIS ModelingIntroduction to GIS Modeling Week 3 — Reclassifying and Overlaying Maps Week 3 — Reclassifying and Overlaying Maps

GEOG 3110 –University of DenverGEOG 3110 –University of Denver

Suitability Modeling LogicSuitability Modeling LogicReclassifying Maps Reclassifying Maps (position, initial value, size, shape and contiguity)(position, initial value, size, shape and contiguity)

Overlaying Maps Overlaying Maps (point-by-point, region-wide and map-wide)(point-by-point, region-wide and map-wide)

Presented byPresented by Joseph K. BerryJoseph K. BerryW. M. Keck Scholar, Department of Geography, W. M. Keck Scholar, Department of Geography,

University of DenverUniversity of Denver

……but we but we didn’t finish didn’t finish last week’s last week’s material!!!material!!!

Display Settings for Grid-based MapsDisplay Settings for Grid-based Maps<Exercise 3 <Exercise 3 Question #1Question #1>>

Let’s look at some example displays in the Let’s look at some example displays in the Bighorn.rgsBighorn.rgs data base… data base…

(Berry)(Berry)

Reclassify and Overlay OperationsReclassify and Overlay Operations<Exercise 3 <Exercise 3 Question #2Question #2>>

<Exercise 3 <Exercise 3 Question #3Question #3>>

CovertypeCovertype(Input map)

Covertype_sizeCovertype_size(Output map)

SizeSize(Command)

SIZE Covertype FOR Covertype_sizeSIZE Covertype FOR Covertype_size …make sure your map display is “appropriate” –not simply the default

(Berry)(Berry)

Evaluating Habitat SuitabilityEvaluating Habitat Suitability

Manual Map OverlayManual Map Overlay(Binary)(Binary)

Ranking OverlayRanking Overlay(Binary Sum)(Binary Sum)

Rating OverlayRating Overlay(Rating Average)(Rating Average)

Generating maps of animal habitat…Generating maps of animal habitat…

(digital slide show Hugag)(digital slide show Hugag)

AssumptionsAssumptions – Hugags like…– Hugags like… gentle slopes, gentle slopes, southerly aspects, and southerly aspects, and lower elevationslower elevations

<Exercise 3 <Exercise 3 Question #4Question #4>>

(See Beyond Mapping III online book, “Topic 23” for more information)(See Beyond Mapping III online book, “Topic 23” for more information) (Berry)(Berry)

CovertypeWaterMask

0= No, 1= Yes

HabitatRating

0= No-go1 to 9 Good

Constraint MapConstraint Map

SolutionSolutionMapMap

HabitatRating

Bad 1 to 9 Good

(Times 1)(Times 1)

(1)(1)

(1)(1)

Conveying Suitability Model LogicConveying Suitability Model Logic

(See Beyond Mapping III online book, “Topic 22” for more information)(See Beyond Mapping III online book, “Topic 22” for more information)

Interpreted Interpreted MapsMaps

gentle slopesgentle slopes

SlopePreference

Bad 1 to 9 Good

AspectPreference

Bad 1 to 9 Good

ElevationPreference

Bad 1 to 9 Good

southerly aspectssoutherly aspects

lower elevationslower elevations

Derived MapsDerived Maps

Slope

Aspect

Base MapsBase Maps

Elevation

Elevation

Elevation

……while while ReclassifyReclassify and and OverlayOverlay commands are not very commands are not very exciting, they are some exciting, they are some of the most of the most frequently used frequently used operationsoperations

FactFact JudgmentJudgment

CalibrateCalibrateAlgorithmAlgorithm WeightWeight

RowsRows Model Criteria Model Criteria

ColumnsColumns Analysis Analysis LevelsLevels

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Reclassify

Reclassify

Reclassify

Reclassify

Overlay

Overlay

LinesLines

Processing StepsProcessing Steps (Commands)(Commands)

Extending Model CriteriaExtending Model Criteria

Additional criteria can be Additional criteria can be added…added…

forestsforests

ForestPreference

Bad 1 to 9 Good

ForestProximityForests

—Hugags would prefer to Hugags would prefer to bebe in/near forested areas in/near forested areas

waterwater

WaterPreference

Bad 1 to 9 Good

WaterProximityWater

—Hugags would prefer to Hugags would prefer to bebe near water near water—Hugags are Hugags are 10 times 10 times more concerned more concerned with slope, with slope, forest and water criteriaforest and water criteria than aspect and elevationthan aspect and elevation

(Times 10)(Times 10)

(10)(10)

(10)(10)

(1)(1)

(1)(1)

(Berry)(Berry)

HabitatRating

Bad 1 to 9 Good

gentle slopesgentle slopes

SlopePreference

Bad 1 to 9 Good

AspectPreference

Bad 1 to 9 Good

ElevationPreference

Bad 1 to 9 Good

southerly aspectssoutherly aspects

lower elevationslower elevations

Slope

Aspect

Elevation

Elevation

Elevation

LinesLines

Processing StepsProcessing Steps (Commands)(Commands)

RowsRows Model Criteria Model Criteria

ColumnsColumns Analysis Analysis LevelsLevels

Optional QuestionsOptional Questions

3-1)3-1) Flowchart of Binary Habitat Model Flowchart of Binary Habitat Model

3-2) 3-2) “Simply” and “Completely” Crosstab Tables“Simply” and “Completely” Crosstab Tables

3-3)3-3) Average Suitability Rating for Average Suitability Rating for eacheach Covertype parcel Covertype parcel

Using PowerPoint as Using PowerPoint as

a “graphics package”a “graphics package”

3-4)3-4) Average and Coefficient of Variation maps for the Average and Coefficient of Variation maps for the 200 foot contour polygons of Elevation 200 foot contour polygons of Elevation (statistical model)(statistical model)

3-5)3-5) Average Wildfire Fuel Loading index for each Average Wildfire Fuel Loading index for each management District management District (mathematical model)(mathematical model)

(Berry)(Berry)

Creating a Flowchart Creating a Flowchart (using PowerPoint)(using PowerPoint)

Under the Under the HomeHome tab tab, 1) use the , 1) use the RectanglRectangle e drawing tool to create drawing tool to create and size a box to represent a map in the flowchart and 2) use the and size a box to represent a map in the flowchart and 2) use the TextText box drawing tool to enter the map name in the Rectangle. box drawing tool to enter the map name in the Rectangle. SelectSelect both and use both and use FormatFormat GroupGroup to group the two objects.to group the two objects.

Enter map titleEnter map title1122

Enter map titleEnter map title Enter other map Enter other map titletitle

Slop

e

Copy Copy andand Paste Paste the Rectangle to form other maps. the Rectangle to form other maps. Use theUse the LineLine drawing tool to connect the boxes. Use drawing tool to connect the boxes. Use the the TextText box drawing tool to enter the command, box drawing tool to enter the command, rotate and place over the Line.rotate and place over the Line.

Enter yet another Enter yet another map titlemap title

RepeatRepeat the process to add additional maps (boxes) the process to add additional maps (boxes) and processing steps (lines) to complete the and processing steps (lines) to complete the flowchart containing the logic of the GIS model.flowchart containing the logic of the GIS model.

There are a lot of other things you can do to make the graphic a bit more unique, such as There are a lot of other things you can do to make the graphic a bit more unique, such as borders, transparency, shadowing and animation (viewed as a slide show). Also, keep in mind borders, transparency, shadowing and animation (viewed as a slide show). Also, keep in mind that Formatthat Format Align can be used to align multiple graphic objects if things get out of whack. Align can be used to align multiple graphic objects if things get out of whack.

(Berry)(Berry)

Compound Graphic Compound Graphic (Campground model results)(Campground model results)

Use SnagIt to Use SnagIt to capturecapture one of the graphic elements, such as the S_Pref map then one of the graphic elements, such as the S_Pref map then Paste and Size Paste and Size at the appropriate location on the “canvas” (white background shape). at the appropriate location on the “canvas” (white background shape). Repeat Repeat for all of the for all of the

other graphic elements. Use the other graphic elements. Use the Text Box toolText Box tool to embed text as appropriate. to embed text as appropriate.

Group the figure elements in logical groupings and then use the Custom Animation tool to Group the figure elements in logical groupings and then use the Custom Animation tool to control their sequencing for display if you intend to present as a PowerPoint slide deck. control their sequencing for display if you intend to present as a PowerPoint slide deck.

CampgroundSuitability

(Berry)(Berry)

Big Picture of Map Analysis and ModelingBig Picture of Map Analysis and ModelingNanotechnology Nanotechnology GEOTECHNOLOGYGEOTECHNOLOGY Biotechnology Biotechnology

Global Positioning System Global Positioning System GEOGRAPHIC INFORMATION SYSTEMSGEOGRAPHIC INFORMATION SYSTEMS Remote Sensing Remote Sensing

ANALYSIS ANALYSIS andand MODELINMODELINGG(Grid-based)(Grid-based)

Mapping Mapping andand Geo-query Geo-query(Vector-based)(Vector-based)

SPATIAL ANALYSISSPATIAL ANALYSIS(Geographic Relationships)(Geographic Relationships)

SPATIAL STATISTICSSPATIAL STATISTICS(Numeric Relationships)(Numeric Relationships)

Reclassify Reclassify andand Overlay OverlayDistance Distance andand Neighbors Neighbors

Surface ModelingSurface ModelingSpatial Data MiningSpatial Data Mining

GISer’s GISer’s PerspectivesPerspectivesWeek 3Week 3

Week 4Week 4 Week 5Week 5

GIS Modeling GIS Modeling Weeks 6 and 7Weeks 6 and 7

Week 8Week 8

Week 9Week 9

Future DirectionsFuture DirectionsWeek 10Week 10

Mathematician’s Perspective:Mathematician’s Perspective:Basic GridMath & Map AlgebraBasic GridMath & Map Algebra

Advanced GridMathAdvanced GridMathMap CalculusMap CalculusMap GeometryMap Geometry

Plane Geometry ConnectivityPlane Geometry ConnectivitySolid Geometry ConnectivitySolid Geometry Connectivity

Unique Map AnalyticsUnique Map Analytics

Math/StatMath/StatPerspectivesPerspectives((SpatialSTEMSpatialSTEM))

Statistician’s Perspective:Statistician’s Perspective:Basic Descriptive StatisticsBasic Descriptive Statistics

Basic ClassificationBasic ClassificationMap ComparisonMap Comparison

Unique Map StatisticsUnique Map StatisticsSurface ModelingSurface Modeling

Advanced ClassificationAdvanced ClassificationPredictive StatisticsPredictive Statistics

See Topic 30, Beyond Mapping III

(Berry)(Berry)

Grid-Based Map AnalysisGrid-Based Map Analysis

Spatial analysisSpatial analysis investigates the “contextual” relationships in mapped data…investigates the “contextual” relationships in mapped data…

ReclassifyReclassify— — reassigning map values (position; value; size, shape; contiguity) reassigning map values (position; value; size, shape; contiguity) OverlayOverlay— — map overlay (point-by-point; region-wide; map-wide)map overlay (point-by-point; region-wide; map-wide) DistanceDistance— proximity and connectivity (movement; optimal paths; visibility)— proximity and connectivity (movement; optimal paths; visibility) NeighborsNeighbors— — ”roving windows” (slope/aspect; diversity; anomaly)”roving windows” (slope/aspect; diversity; anomaly)

Data miningData mining investigates the “numerical” relationships in mapped data…investigates the “numerical” relationships in mapped data…

DescriptiveDescriptive— — aggregate statistics (e.g., average/stdev, similarity, clustering)aggregate statistics (e.g., average/stdev, similarity, clustering) PredictivePredictive— — relationships among maps (e.g., regression)relationships among maps (e.g., regression) PrescriptivePrescriptive— — appropriate actions (e.g., optimization) appropriate actions (e.g., optimization)

Surface modelingSurface modeling maps the spatial distribution and pattern of point data…maps the spatial distribution and pattern of point data…

Map GeneralizationMap Generalization— — characterizes spatial trends (e.g., titled plane)characterizes spatial trends (e.g., titled plane) Spatial InterpolationSpatial Interpolation— — deriving spatial distributions (e.g., IDW, Krig)deriving spatial distributions (e.g., IDW, Krig) OtherOther— — roving window/facets (e.g., density surface; tessellation) roving window/facets (e.g., density surface; tessellation)

Spatial statisticsSpatial statistics

Weeks 3,4,5Weeks 3,4,5

Weeks,8,9Weeks,8,9

(Berry)(Berry)

……recall Map Analysis organization and evolution discussion recall Map Analysis organization and evolution discussion from Week 1 class presentation/reading from Week 1 class presentation/reading (GIS Modeling Framework paper)(GIS Modeling Framework paper)

An Analytic Framework for GIS ModelingAn Analytic Framework for GIS Modeling

Reclassify operationsReclassify operations involve involve reassigning map values to reflect new reassigning map values to reflect new information about existing map featuresinformation about existing map features

(Berry)(Berry)

Reclassifying MapsReclassifying Maps

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Reclassifying MapsReclassifying Maps<Homework <Homework Question #2Question #2>>

CLUMP -- Assigns new values to contiguous groups of cells within each map category.

CONFIGURE -- Assigns new values characterizing the shape of the area associated with each category.

RENUMBER -- Assigns new values to the categories of a map. SIZE -- Assigns new values according to the size of the area associated with each map category.

SLICE -- Assigns new values by dividing the range of values on a map into specified intervals (contouring).

The most frequently used map analysis operation…and one of the most dangerous!!!

ContiguityContiguity

ShapeShape

InitialInitialValueValue

SizeSize

InitialInitialValueValue

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Renumber OperationRenumber OperationRenumberRenumber— assigns new values to the categories of a map.— assigns new values to the categories of a map.

RENUMBER Elevation RENUMBER Elevation ASSIGNING ASSIGNING 11 TO 500 THRU 1800 TO 500 THRU 1800 ASSIGNING ASSIGNING 00 TO 1800 THRU 2500 TO 1800 THRU 2500 FOR E_PrefFOR E_Pref

… …context context HelpHelp provides information provides information on function and use on function and use

of operationsof operations<more info in the MapCalc Manual><more info in the MapCalc Manual>

……any real number from -3.4Eany real number from -3.4E3838 to + 3.4E to + 3.4E3838 can can be assigned to any existing value on a mapbe assigned to any existing value on a map

……often integer values are assigned based on user often integer values are assigned based on user reasoning (as in this example)reasoning (as in this example)

NoteNote: : PMAP_NULLPMAP_NULL is a special value that can is a special value that can be assigned indicating “no data” and the grid be assigned indicating “no data” and the grid location will be ignored in processing and displaylocation will be ignored in processing and display

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Slice OperationSlice OperationSliceSlice— assigns new values by dividing the range of values — assigns new values by dividing the range of values

on a map into specified intervals on a map into specified intervals (“Equal Ranges” contouring)(“Equal Ranges” contouring)

……Slice <mapName>Slice <mapName> is often used to is often used to collapse a map with a large set of map values collapse a map with a large set of map values to just a few intervals for a quick view of the to just a few intervals for a quick view of the pattern of the spatial data distributionpattern of the spatial data distribution

……a user can specify the minimum a user can specify the minimum and maximum values and maximum values of the range– of the range– SLICE Elevation INTO 20 SLICE Elevation INTO 20 FROM 1000 THRU 1200 ZeroFill FROM 1000 THRU 1200 ZeroFill FOR Relief_10ftFOR Relief_10ft

……Map RangeMap Range = Max_Value – Min_Value = Max_Value – Min_Value = 2500 – 500= = 2500 – 500= 20002000 feet feet

……Contour IntervalContour Interval = Map Range / # ranges = Map Range / # ranges = 2000 / = 2000 / 2020 = 100 feet = 100 feet

SLICE Elevation into 20 FOR Relief_100ftSLICE Elevation into 20 FOR Relief_100ft

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Size OperationSize Operation

……the Size operation assigns the the Size operation assigns the number of cellsnumber of cells comprising each comprising each map regionmap region (category/value) (category/value)

……in this instance there are three map regions in this instance there are three map regions (Open Water= 1, Meadow= 2, Forest= 3)– note (Open Water= 1, Meadow= 2, Forest= 3)– note that Water occurs at two different places.that Water occurs at two different places.

……to calculate the actual area to calculate the actual area of each map region of each map region multiplymultiply the size map times the area the size map times the area per grid cell– 10,000 mper grid cell– 10,000 m22 or 1 ha in this caseor 1 ha in this case

……to calculate the size/area of each occurrence to calculate the size/area of each occurrence you must you must first Clumpfirst Clump the map “regions”, then the map “regions”, then use the Size commanduse the Size command

SizeSize— assigns new values according to the size of the area — assigns new values according to the size of the area associated with each map category.associated with each map category.

SIZE Covertype FOR Coverype_sizeSIZE Covertype FOR Coverype_size

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Clump OperationClump Operation

……a map “a map “categorycategory” identifies all locations with ” identifies all locations with the same characteristic or condition– e.g., Open the same characteristic or condition– e.g., Open Water, Meadow, Forest Water, Meadow, Forest

……a “a “clumpclump” is a ” is a contiguous groupcontiguous group (individual (individual spatial instance of a map “category”)–e.g., five spatial instance of a map “category”)–e.g., five cover type clumps with two instances of Open cover type clumps with two instances of Open Water Water

ClumpClump— assigns new values to contiguous groups of cells — assigns new values to contiguous groups of cells within each map category.within each map category.

CLUMP Covertype AT 1 DIAGONALLY CLUMP Covertype AT 1 DIAGONALLY FOR Coverype_clumpsFOR Coverype_clumps

““AtAt” identifies how ” identifies how far to far to reachreach in in defining clumpsdefining clumps

““OrthogonallyOrthogonally” reaches ” reaches horizontally and vertically horizontally and vertically only; “only; “DiagonallyDiagonally” includes ” includes off angles off angles

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Configure OperationConfigure Operation

Spatial IntegritySpatial Integrity

ConfigureConfigure— assigns new values characterizing the shape — assigns new values characterizing the shape and integrity of the area associated with each map category.and integrity of the area associated with each map category.

Boundary ConfigurationBoundary Configuration

Edge cellsCONFIGURE Covertype Edges CONFIGURE Covertype Edges FOR Covertype_edgesFOR Covertype_edges

Convexity Convexity is the is the ratio of the Edge ratio of the Edge to the Areato the Area (Size) and normalized (Size) and normalized to that of a circle of the same areato that of a circle of the same area

EulerEuler = (# Holes) – (1-#Fragments) = (# Holes) – (1-#Fragments)(Berry)(Berry)

Some Reclassifying Things to Keep in MindSome Reclassifying Things to Keep in Mind

The Covertype map contains The Covertype map contains NominalNominal data that is data that is Discretely Discretely (Choropleth) (Choropleth) distributed in geographic space. As such, it is best displayed in distributed in geographic space. As such, it is best displayed in 2D2D using using cells (cells (GridGrid) and with layer mesh on as the stored values do not form ) and with layer mesh on as the stored values do not form gradients in either numerical or geographic space. gradients in either numerical or geographic space.

The Size command assigns new values according to the The Size command assigns new values according to the size size of the area (# of cells) associated with each map categoryof the area (# of cells) associated with each map category. In . In this instance the input map is Covertype (Nominal/Discrete this instance the input map is Covertype (Nominal/Discrete data) and the output map is Covertype_size (Ratio/Discrete data) and the output map is Covertype_size (Ratio/Discrete data). The size algorithm data). The size algorithm “counts” the number of cells for “counts” the number of cells for each map category each map category (stored map value). (stored map value).

……identifies that “one cell in size” elevation values occur in identifies that “one cell in size” elevation values occur in 64% of the map area (384/1= 384 times; each value is 64% of the map area (384/1= 384 times; each value is unique). “Three cells in size” areas occur in 2.88% of the unique). “Three cells in size” areas occur in 2.88% of the analysis window (18/3= 6 times; six sets of the same value). analysis window (18/3= 6 times; six sets of the same value).

Size works on Size works on Nominal dataNominal data (Categorical) but usually is not (Categorical) but usually is not appropriate for ratio data as far to many values (decimal appropriate for ratio data as far to many values (decimal places); results in most of the map being assigned the cell places); results in most of the map being assigned the cell size value of 1 because elevation values with decimal points size value of 1 because elevation values with decimal points rarely are the same. For example, sizing the Elevation rarely are the same. For example, sizing the Elevation map… map…

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An Analytic Framework for GIS ModelingAn Analytic Framework for GIS Modeling

Overlay operationsOverlay operations involve characterizing involve characterizing the spatial coincidence of mapped datathe spatial coincidence of mapped data

……recall Map Analysis organization and evolution discussion recall Map Analysis organization and evolution discussion from Week 1 class presentation/reading from Week 1 class presentation/reading (GIS Modeling Framework paper)(GIS Modeling Framework paper)

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Overlaying Maps Overlaying Maps (conceptual approaches)(conceptual approaches)

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Overlaying Maps Overlaying Maps (accessing the data)(accessing the data)

Overlaying maps involves one of four basic techniques for accessing/organizing geo-registered data for analysis—

(Tomlin’s organizational framework)

Local

…collects data on a cell-by-cell basis

and reports a single value on a

cell-by-cell basis

“Spearing”

Map1

Map2

Focal

…collects data on a neighborhood basis and reports a single

value on a cell-by-cell basis

“Funneling”

Map1

Map2

Global

…collects data on a map-wide basis and reports results on a

map-wide or cell-by-cell basis

“Plunging”

Map1

Map2

EntireArea

Zonal

…collects data on a region-wide basis

and reports summary on a

region-wide basis

“Lacing”

Map1

Map2

TemplateMap

(Berry)(Berry)

Overlaying MapsOverlaying Maps

COMPOSITE -- Creates a map summarizing values from one map which coincide with the categories of another.

CALCULATE and COMPUTE -- Creates a map as the mathematical or statistical function of two or more maps.

COVER -- Creates a new map where nonzero values of the top map replace the values on the previous (bottom) map, or stack of maps.

CROSSTAB -- Generates a spatial coincidence table of two maps.

INTERSECT -- Creates a map that assigns new values to pair-wise combinations of values on two maps.

<Homework <Homework Question #3Question #3>>

…true “map-ematics”

Region-Region-widewide

Point-by-Point-by-PointPoint

Point-by-Point-by-PointPoint

Point-by-Point-by-PointPoint

Point-by-Point-by-PointPoint

……Map-wide overlay involves spatial statistics (spatial data mining)Map-wide overlay involves spatial statistics (spatial data mining)(Berry)(Berry)

Compute/Calculate OperationCompute/Calculate Operation

All of the All of the basicbasic mathematical operations on a typical pocket mathematical operations on a typical pocket calculator can be performed on grid maps…calculator can be performed on grid maps…

……including including Add, Subtract, Multiply, Add, Subtract, Multiply, DivideDivide, Exponentiation, Square, , Exponentiation, Square, Square Root, Max, Min, And, Or, & Trig functions Square Root, Max, Min, And, Or, & Trig functions … …other math operations?other math operations?

……in this example in this example one map is one map is multiplied by 10 then added to multiplied by 10 then added to another mapanother map, thereby creating, thereby creatinga a 2-digit code2-digit code indicating the indicating the first map’s categories as the tens digit followed first map’s categories as the tens digit followed by the second map’s categories as the one’s digitby the second map’s categories as the one’s digit

Compute/CalculateCompute/Calculate— creates a new map as the mathematical — creates a new map as the mathematical function of two or more maps.function of two or more maps.

COMPUTE Covertype TIMES 10 COMPUTE Covertype TIMES 10 Plus Water FOR Coverype_WaterPlus Water FOR Coverype_Water

CALCULATE ((Covertype * 10) CALCULATE ((Covertype * 10) + Water) FOR Covertype_Water+ Water) FOR Covertype_Water

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CrosstabCrosstab— generates a spatial coincidence — generates a spatial coincidence tabletable of two of two maps.maps.

Map1 = Districts

Map2 = Covertype

Crosstab OperationCrosstab Operation

……the maps are compared “cell-by-cell” and the maps are compared “cell-by-cell” and the number of joint occurrencesthe number of joint occurrencesbetween the map categories are between the map categories are summarized in a tablesummarized in a table

CROSSTAB Districts WITH Covertype CROSSTAB Districts WITH Covertype Simply TO Newtextfile.txtSimply TO Newtextfile.txt

In this example there are… In this example there are… • 58 cells 58 cells classified as classified as District 1District 1 on the on the Districts map Districts map • 82 cells 82 cells classified as classified as Open WaterOpen Water on the on the Covertype map Covertype map • 58 cells 58 cells identified as having the joint identified as having the joint condition of condition of District 1 and Open WaterDistrict 1 and Open Water representing 9.28 percent of the entire map representing 9.28 percent of the entire map area. area. NoteNote: all of the District 1 cells are in Open Water: all of the District 1 cells are in Open Water

Optional Question 3-2

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Intersect OperationIntersect Operation

……if “if “completelycompletely” is specified all ” is specified all combinations are automatically combinations are automatically identified using unique sequential identified using unique sequential numbering for map valuesnumbering for map values

NoteNote: Intersect is similar to : Intersect is similar to geo-querygeo-query operations in desktop mapping packages by operations in desktop mapping packages by identifying all locations having specified identifying all locations having specified category (map-value) combinations category (map-value) combinations

…“…“zerofillzerofill” assigns 0 to all ” assigns 0 to all combinations that are not specifiedcombinations that are not specified

… “… “oldfilloldfill” retains 1” retains 1stst map values map values for non-specified combinations for non-specified combinations

IntersectIntersect— creates a — creates a mapmap that assigns new values to pair- that assigns new values to pair-wise combinations of values on two maps.wise combinations of values on two maps.

Map 1 = Districts

Map 2 = Covertype

The maps are compared “The maps are compared “cell-by-cellcell-by-cell” and a user ” and a user specified number is assigned to designated category specified number is assigned to designated category combinations…combinations…

INTERSECT Districts WITH Covertype INTERSECT Districts WITH Covertype ASSIGN 1 to 1, 1 Zerofill FOR Districts1_Cover1ASSIGN 1 to 1, 1 Zerofill FOR Districts1_Cover1

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CoverCover— creates a new map where the non-zero values of the top map — creates a new map where the non-zero values of the top map replace the values on the previous (bottom) map, or stack of maps.replace the values on the previous (bottom) map, or stack of maps.

4Water 4

Cover 1

Water

Covertype

0

31

4

Cover OperationCover Operation

……in the example coincidence in the example coincidence 4,14,1 4 4 because 4 is non-zero because 4 is non-zero and replaces what is beneath itand replaces what is beneath it

……0,30,3 3 3 because zero is ignored and does not because zero is ignored and does not replace the previous value in the map stackreplace the previous value in the map stack

……the maps are compared “cell-by-cell” and the the maps are compared “cell-by-cell” and the value in the top-most cell value in the top-most cell replacesreplaces the previous the previous values unless that value is zerovalues unless that value is zero, then the top most , then the top most non-zero value in the map stack is retainednon-zero value in the map stack is retained

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Composite OperationComposite Operation

……data summary data summary proceduresprocedures include include

Average, Standard deviation, Average, Standard deviation, Coefficient of variation, Total, Coefficient of variation, Total, Maximum, Minimum, MedianMaximum, Minimum, Median

Majority, Minority, Diversity,Majority, Minority, Diversity, Deviation Deviation andand Proportion Proportion

“Cookie-cutter”

Template Map

Data Map

CompositeComposite— creates a map summarizing values from one map that — creates a map summarizing values from one map that coincide with the categories (termed regions) identified on another mapcoincide with the categories (termed regions) identified on another map

……the regions identified by category values the regions identified by category values on one map serve as cookie-cutter shapes on one map serve as cookie-cutter shapes ((Template mapTemplate map) for summarizing data ) for summarizing data contained on another map (contained on another map (Data mapData map))

COMPOSITE Districts WITH Slope Average COMPOSITE Districts WITH Slope Average IGNORE PMAP_NULL FOR Districts_avgSlopeIGNORE PMAP_NULL FOR Districts_avgSlope

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Thematic Mapping Thematic Mapping (Average elevation by district)(Average elevation by district)

Best

Worst

500500 15391539 21762176

65365310991099

1779177910801080

Average Elevationof Districts

“Thematic Mapping”(Discrete Spatial Object)

(0)(0) (39)(39) (9)(9)

(29)(29)(21)(21)

(9)(9)

(24)(24)

…include Coffvar in Thematic Mapping results

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Map Accuracy Map Accuracy (Error Propagation– simple overlay)(Error Propagation– simple overlay)

Soil TypeSoil TypeForest TypeForest Type

Joint ProbabilityJoint Probability — — likelihood of likelihood of two  conditions occurring together…two  conditions occurring together…

VectorVector

RasterRaster

P(x,y) = P(x) * P(y)P(x,y) = P(x) * P(y)

……evaluated evaluated cell-by-cellcell-by-cell

P(x)P(x)

P(y)P(y)

P(x,y)P(x,y) Joint

Probability

(See Beyond Mapping II, “Topic 4, “Toward and Honest GIS”)(See Beyond Mapping II, “Topic 4, “Toward and Honest GIS”)

Topological OverlayTopological Overlay

Coincidence SearchCoincidence Search100% certain everywhere 100% certain everywhere in the derived polygon?in the derived polygon?

Intersect Intersect PolygonsPolygons

Spatial TableSpatial Table

Attribute TableAttribute TableJoinJoinDataData

Believable?Believable?(digital slide show Honest)(digital slide show Honest)

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