Grid-based Map Analysis Techniques and Grid-based Map Analysis Techniques and Modeling WorkshopModeling Workshop

Part 1 – Maps as DataPart 1 – Maps as DataPart 2– Surface ModelingPart 2– Surface Modeling

Part 3 – Spatial Data MiningPart 3 – Spatial Data Mining

Part 4 – Spatial AnalysisPart 4 – Spatial AnalysisSuitability mappingSuitability mapping

Measuring effective distance/connectivityMeasuring effective distance/connectivityVisual exposure analysisVisual exposure analysis

Analyzing landscape structureAnalyzing landscape structureCharacterizing terrain featuresCharacterizing terrain features

Part 5 – GIS ModelingPart 5 – GIS Modeling

Grid-Based Map AnalysisGrid-Based Map Analysis

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 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)

(Berry)(Berry)

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

Evaluating Habitat SuitabilityEvaluating Habitat Suitability

(Berry)

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

Manual Map Overlay Ranking Overlay Rating Overlay

CovertypeWaterMask

0= No, 1= Yes

HabitatRating

0= No, 1 to 9 Good

Constraint MapConstraint Map

HabitatRating

Bad 1 to 9 Good

WeightWeight

SolutionSolutionMapMap

gentle slopesgentle slopes

Interpreted Interpreted MapsMaps

CalibrateCalibrate

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

AlgorithmAlgorithm

Derived MapsDerived Maps

Conveying Suitability Model LogicConveying Suitability Model Logic

(Berry)

Elevation

Elevation

Elevation

Base MapsBase Maps

FactFact JudgmentJudgment

(See map Analysis, “Topic 22” for more information)(See map Analysis, “Topic 22” for more information)

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

Extending Model CriteriaExtending Model Criteria

(Berry)

Elevation

Elevation

Elevation

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

forestsforests

ForestPreference

Bad 1 to 9 Good

ForestProximity

Forests

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

waterwater

WaterPreference

Bad 1 to 9 Good

WaterProximity

Water

—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)

Establishing Distance and ConnectivityEstablishing Distance and Connectivity

(digital slide show (digital slide show DIST)

(Berry)(Berry)

Orthogonal distances are the same as calculated by Orthogonal distances are the same as calculated by the Pythagorean Theorem and align with a circle the Pythagorean Theorem and align with a circle of a given radius…of a given radius…

……other distances contain slight “rounding” errorsother distances contain slight “rounding” errors

PointPoint

Grid-based Simple Proximity SurfacesGrid-based Simple Proximity Surfaces

(Berry)(Berry)

Proximity Ripples for a large steps away Proximity Ripples for a large steps away from a starting location align fairly well from a starting location align fairly well with an exact circle… with an exact circle…

PointsPoints LinesLines PolygonsPolygons……an excellent technique for an excellent technique for

generating simple and effective generating simple and effective proximity surfaces respecting proximity surfaces respecting

absolute and relative barriers to absolute and relative barriers to movement from sets of points, movement from sets of points,

lines and polygonslines and polygons

(impossible to do with the (impossible to do with the Pythagorean Theorem )Pythagorean Theorem )

……but poorly align for but poorly align for small stepssmall steps

Simple ProximitySimple Proximity

……as the crow fliesas the crow flies

Calculating Effective Distance Calculating Effective Distance (Demo)(Demo)

(Berry)

Effective ProximityEffective Proximity

……as the crow walksas the crow walks

0= not able to cross0= not able to cross2= two min. to cross2= two min. to cross

7 = seven min. to cross7 = seven min. to cross

……the the Splash AlgorithmSplash Algorithm is like tossing a rock into a is like tossing a rock into a still pond with increasing distance rings that abut still pond with increasing distance rings that abut and bend around absolute and relative barriersand bend around absolute and relative barriers

Generating an Effective Travel-time BufferGenerating an Effective Travel-time Buffer

(Berry)

(a)(a) superimposition superimposition of an of an analysis analysis gridgrid over the over the area of interest area of interest

(b)(b) ““burns” the burns” the store location store location into its into its corresponding corresponding grid cell grid cell

(c)(c) ““burns” primary burns” primary and residential and residential streetsstreets are are identified identified

(d)(d) travel-timetravel-time buffer derived buffer derived from the two from the two grid layers grid layers

Travel-Time ConnectivityTravel-Time Connectivity

(Berry)(Berry)

……increasing distance from a increasing distance from a point forms bowl-shaped point forms bowl-shaped accumulation surfaceaccumulation surface

……steepest downhill path identifies steepest downhill path identifies the optimal paththe optimal path– wave front that – wave front that got there first.got there first.

……SPREADing from multiple SPREADing from multiple locations identifies locations identifies catchment catchment areasareas– locations closest to – locations closest to starting locationsstarting locations

……what do you think the what do you think the ridges ridges represent?represent?

Accumulation Surface AnalysisAccumulation Surface Analysis

(Berry)(Berry)(See (See Map Analysis, “Topic 5” and “Topic 17” for more information)

……increasing distance from a point forms bowl-shaped accumulation surfaceincreasing distance from a point forms bowl-shaped accumulation surface

Simple distance Simple distance – symmetrical bowl– symmetrical bowlAbsolute barrier Absolute barrier – abrupt pillars– abrupt pillarsRelative barrier Relative barrier – gradual humps– gradual humps

……subtracting two proximity subtracting two proximity surfaces identifies relative surfaces identifies relative advantageadvantage

ZeroZero – equidistant – equidistant SignSign – which has the advantage – which has the advantage MagnitudeMagnitude – strength of advantage – strength of advantage

……what would get if you what would get if you added the added the two surfaces?two surfaces?

Establishing Visual ConnectivityEstablishing Visual Connectivity

……like measuring proximity, it starts somewhere (starter cell) and moves through geographic space like measuring proximity, it starts somewhere (starter cell) and moves through geographic space by steps (wave front) evaluating whether the moving tangent is beat—by steps (wave front) evaluating whether the moving tangent is beat—

……if so, the location is marked as “seen” and its tangent is assigned as the one to beatif so, the location is marked as “seen” and its tangent is assigned as the one to beat

Seen ifSeen if new tangent exceeds all new tangent exceeds all previous tangents previous tangents along the line along the line of sight—of sight—

AtAt <Viewer_heightValue> <Viewer_heightValue> ThruThru <Screens_heightMap>) <Screens_heightMap>) Onto Onto <Target_heightMap><Target_heightMap>

(Berry)

RadiateRadiate – – visual visual exposure is calculated exposure is calculated bay a series of “waves” bay a series of “waves” that carry the tangent to that carry the tangent to beat.beat.

SimplySimply – viewshed – viewshedCompletelyCompletely – number of – number of “viewers” that see each location“viewers” that see each locationWeightedWeighted – viewer cell value is – viewer cell value is addedadded

Calculating Visual Exposure Calculating Visual Exposure (# Times Seen)(# Times Seen)

Visual exposure identifies how many times each map location is Visual exposure identifies how many times each map location is seen from a set of viewer locations seen from a set of viewer locations

(Berry)(Berry)

Visual Exposure from Extended FeaturesVisual Exposure from Extended Features

A visual exposure map identifies how many times each location is seen from an A visual exposure map identifies how many times each location is seen from an “extended eyeball” composed of numerous viewer locations (road network) “extended eyeball” composed of numerous viewer locations (road network)

(Berry)(Berry)

Weighted Visual Exposure Weighted Visual Exposure (Sum of Viewer Weights)(Sum of Viewer Weights)

Different road types are weighted by the relative number of cars per unit of time …the total Different road types are weighted by the relative number of cars per unit of time …the total “number of cars” replaces the “number of times seen” for each grid location“number of cars” replaces the “number of times seen” for each grid location

(See (See Map Analysis, Topic 15, “Deriving and Using Visual Exposure Maps” for more information) (Berry)(Berry)

ViewshedViewshed ……as the crow seesas the crow sees

(seen or not seen)(seen or not seen)

Calculating Visual Exposure Calculating Visual Exposure (Demo)(Demo)

(Berry)

Visual ExposureVisual Exposure ……as the flock seesas the flock sees

(# times seen)(# times seen)

WeightedWeightedVisual ExposureVisual Exposure ……as the flock seesas the flock sees

(not all in the flock are the same)(not all in the flock are the same)

Real-World Visual AnalysisReal-World Visual Analysis

Weighted visual Weighted visual exposure mapexposure map for an for an

ongoing visual ongoing visual assessment in a assessment in a

national recreation national recreation area— the project area— the project developed visual developed visual

vulnerability maps vulnerability maps from the reservoir in from the reservoir in the center of the park the center of the park and a major highway and a major highway running through the running through the

park. In addition, park. In addition, aesthetic mapsaesthetic maps were were generated based on generated based on visual exposure to visual exposure to

pretty and ugly pretty and ugly places in the parkplaces in the park

(Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003)(Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003)

(Berry)(Berry)

Neighborhood Techniques Neighborhood Techniques (Covertype Diversity Map)(Covertype Diversity Map)

……a DIVERSITY map indicates the a DIVERSITY map indicates the number of different map valuesnumber of different map values (categories) that occur within a window… e.g., cover types (categories) that occur within a window… e.g., cover types

As the window is enlarged, the diversity generally increasesAs the window is enlarged, the diversity generally increases

(Berry)

Neighbor Techniques Neighbor Techniques (Demo)(Demo)

Housing Density Housing Density by Districtsby Districts

Average housing density Average housing density for each districtfor each district

–SCANSCAN Covertype diversity within 3 for Cover_diversity3 Covertype diversity within 3 for Cover_diversity3

–SCANSCAN Slope coffvar with 2 for Roughness Slope coffvar with 2 for Roughness

–SCANSCAN Housing total with 5 for Housing_density Housing total with 5 for Housing_density

–RENUMBERRENUMBER Housing_density for High_hdensity Housing_density for High_hdensity

assign 0 to 0 thru 15 assign 1 to 15 thru 50assign 0 to 0 thru 15 assign 1 to 15 thru 50

–COMPOSITECOMPOSITE Districts with Housing_density average Districts with Housing_density average

for Districts_HDavgfor Districts_HDavg

(Berry)

Neighborhood VariabilityNeighborhood Variability

(Berry)(Berry)(See MapCalc Applications, “Assessing Cover Type Diversity and Delineating Core Area” and “Assessing Covertype Diversity” for more information)(See MapCalc Applications, “Assessing Cover Type Diversity and Delineating Core Area” and “Assessing Covertype Diversity” for more information)

Spatial Analysis of Landscape StructureSpatial Analysis of Landscape StructureAreaArea Metrics (6), Metrics (6), Patch Density, Size and VariabilityPatch Density, Size and Variability Metrics (5), Metrics (5), EdgeEdge Metrics (8), Metrics (8),

ShapeShape Metrics (8), Metrics (8), Core AreaCore Area Metrics (15), Metrics (15), Nearest NeighborNearest Neighbor Metrics (6), Metrics (6),

DiversityDiversity Metrics (9), Metrics (9), Contagion and InterspersionContagion and Interspersion Metrics (2) Metrics (2) ……59 individual indices59 individual indices (US Forest Service 1995 Report PNW-GTR-351)(US Forest Service 1995 Report PNW-GTR-351)

For example,For example,

Area MetricsArea Metrics … …AreaArea per per patchpatch

Shape MetricsShape Metrics … …Shape IndexShape Index per per patchpatch

Edge MetricsEdge Metrics……Edge ContrastEdge Contrast per per patchpatch

Size Size of individual patches is an of individual patches is an important first-order assessment of important first-order assessment of landscape structurelandscape structure

The amount and The amount and type of type of edge edge tracks tracks the nature of the the nature of the patch interfacepatch interface

P/A ratio P/A ratio tracks patchtracks patchshapeshape… … boundary boundary irregularityirregularity

(Berry)(Berry)See http://www.innovativegis.com/products/fragstatsarc/index.html for more informationSee http://www.innovativegis.com/products/fragstatsarc/index.html for more information

(digital slide show FRAG)(digital slide show FRAG)(digital slide show NN_statistics)(digital slide show NN_statistics)

Grid-Based Map AnalysisGrid-Based Map Analysis

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 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)

(Berry)(Berry)