Introduction to GIS ModelingIntroduction to GIS Modeling Week 5 — Summarizing Neighborhoods Week 5 — Summarizing Neighborhoods

GEOG 3110 –University of DenverGEOG 3110 –University of Denver

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

of Denverof Denver

Calculating slope, aspect and profile maps Calculating slope, aspect and profile maps Applying spatial differentiation and integrationApplying spatial differentiation and integration

"Roving window" summary operations"Roving window" summary operationsCharacterizing edges and complexityCharacterizing edges and complexity

Upcoming EventsUpcoming Events

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Midterm Study QuestionsMidterm Study Questions ……posted nowposted now (class initiative to “group study” to (class initiative to “group study” to collectively address the 50+ study questions)collectively address the 50+ study questions)

Midterm Exam Midterm Exam ……you will download and take the 2-hour exam online (honor you will download and take the 2-hour exam online (honor system) sometime between system) sometime between 8:00 am Friday February 158:00 am Friday February 15 and and 5:00 pm Tuesday 5:00 pm Tuesday February 19 February 19

Exercise #6Exercise #6 — you will form — you will form your own teamsyour own teams (2 to 3 members) and tackle one of (2 to 3 members) and tackle one of eight projects; eight projects; posted nowposted now but we will discuss all aspects of the project but we will discuss all aspects of the project “opportunities” next week“opportunities” next week

… …assigned Thursday, February 15 and final report assigned Thursday, February 15 and final report due 5:00 pm Monday, February 25due 5:00 pm Monday, February 25

Exercises #8 and #9Exercises #8 and #9 — — to tailor your work to your interests, you can to tailor your work to your interests, you can choose to choose to not complete either or both not complete either or both of these standard exercises; in lieu of an exercise, of these standard exercises; in lieu of an exercise, however, you must submit a however, you must submit a short paper short paper (4-8 pages) on (4-8 pages) on a GIS modeling topic of a GIS modeling topic of your own choosingyour own choosing

No Exercise Week 7 No Exercise Week 7 ((Example Real-World Projects; Introduction to Spatial Statistics Example Real-World Projects; Introduction to Spatial Statistics

(revisited); mini-Project Working Session(revisited); mini-Project Working Session)) — — pause …a moment for a group “dance of joy”pause …a moment for a group “dance of joy”

Exercise #5 Exercise #5 — — normalnormal report based on Exercise 5 questions; report based on Exercise 5 questions; same teamssame teams as as Exercise 4 report …yes or no? Exercise 4 report …yes or no? (you will choose” teams for the mini-project)(you will choose” teams for the mini-project)

Simple ProximitySimple Proximity surfaces can be generated for groups surfaces can be generated for groups

of points, lines or polygonsof points, lines or polygons

……sets of Pointssets of Points LinesLines AreasAreas

Quick ReviewQuick Review (Simple proximity)(Simple proximity)

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AccumulationAccumulation surfaces of ever-increasing distance away from a starting location(s)surfaces of ever-increasing distance away from a starting location(s)

Effective ProximityEffective Proximity surfaces are generated by consideringsurfaces are generated by consideringabsolute and relative barriers to movementabsolute and relative barriers to movement

Quick ReviewQuick Review (Effective proximity)(Effective proximity)

……sets of Pointssets of Points

Water

Absolute BarrierAbsolute Barrier

LinesLines

Slope

Relative BarrierRelative Barrier

AreasAreas

Water& Slope

Absolute & RelativeAbsolute & Relative

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Quick ReviewQuick Review (Simple & Effective Proximity (Simple & Effective Proximity comparisonscomparisons))

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……sets of Pointssets of Points

Water

Absolute BarrierAbsolute Barrier

LinesLines

Slope

Relative BarrierRelative Barrier

AreasAreas

Water& Slope

Absolute & RelativeAbsolute & Relative

Simple ProximitySimple Proximity

Effective ProximityEffective Proximity

Measuring Distance as “Waves”Measuring Distance as “Waves” (Splash)(Splash)

(Berry)(See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion)(See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion)

Simple Proximity Simple Proximity (Euclidean Distance)(Euclidean Distance)

StartersStarters

S1S1ProximityProximity

S1S125,125,1

Close Close to S1to S1

… … a Starter location is selecteda Starter location is selected

… … Proximity from the location to all Proximity from the location to all other locations is computedother locations is computed

StartersStarters

S2S2ProximityProximityClose Close

to S2to S2

S2S21,251,25

……repeat for another starter locationrepeat for another starter location

ShortestShortestProximityProximity

Close Close to S2to S2

Close Close to S1to S1

… … the computed Proximity values are the computed Proximity values are compared to the current shortest compared to the current shortest

proximity valuesproximity values

… … smaller values replace larger onessmaller values replace larger ones

… … repeatrepeat for next starter location for next starter location

ShortestShortestProximityProximity

UpdatedUpdated

……compare proximity surfacescompare proximity surfaces

……store smallest value at each locationstore smallest value at each location

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ShortestShortestProximityProximityClose Close

Shortest ProximityShortest ProximityWorking MapWorking Map

Effective Proximity Effective Proximity (Overall)(Overall)

COMPARE— store COMPARE— store Minimal Effective DistanceMinimal Effective Distance

……repeat for all other Starter locationsrepeat for all other Starter locations

Minimize (Effective Distance from different starters)Minimize (Effective Distance from different starters)

Effective Proximity Effective Proximity (S2)(S2)

Effective Proximity Effective Proximity (Intervening Conditions)(Intervening Conditions)

Effective Proximity Effective Proximity (S1)(S1)

Minimize (Weight * Distance * Impedance)Minimize (Weight * Distance * Impedance)

FrictionFriction Relative ease of movement is Relative ease of movement is represented as Absolute and relative barriers; steps represented as Absolute and relative barriers; steps incur the relative impedance of the location it is incur the relative impedance of the location it is passing through (conditions passing through (conditions impedanceimpedance))

Movement TypeMovement Type Movement propagates Movement propagates from a starter location in waves; step distance can from a starter location in waves; step distance can be orthogonal or diagonal (geographic be orthogonal or diagonal (geographic distancedistance))

StartersStarters Values on this map identify locations Values on this map identify locations for measuring proximity; values can be used to for measuring proximity; values can be used to indicate movement weights (characteristics indicate movement weights (characteristics weightweight))

S1S1S2

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Basic and Advanced Distance OperationsBasic and Advanced Distance Operations

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BasicBasic Operations Operations (Static) (Static) ——

Simple ProximitySimple Proximity as the crow “flies” counting cell lengths as the crow “flies” counting cell lengths as it moves out as a wave front as it moves out as a wave front ((SimpleSimple– starts counting at 1)– starts counting at 1)

Effective ProximityEffective Proximity as the crow “walks” in not as the crow “walks” in not necessarily straight lines that respect absolute/ relative barriers necessarily straight lines that respect absolute/ relative barriers ((ThruThru– absolute and relative barriers)– absolute and relative barriers)

Advanced Operations— Advanced Operations—

……based on based on differences in the nature of the movementdifferences in the nature of the movement (Static): (Static): Guiding Surface Guiding Surface (Up/Down/Across) (Up/Down/Across)

Stepped-accumulationStepped-accumulation (continuing distance)(continuing distance) Gravity Model Gravity Model (movement weights)(movement weights) Back Link Back Link (starter ID# for identifying closest starter location)(starter ID# for identifying closest starter location)

……based on based on differences in the intervening conditionsdifferences in the intervening conditions (Dynamic): (Dynamic):

AccumulationAccumulation (Total accumulation) (Total accumulation)

MomentumMomentum (Net accumulation) (Net accumulation)

DirectionDirection (Look-up table) (Look-up table)

www.innovativegis.com/basis/MapAnalysis/Topic25/Topic25.htm www.innovativegis.com/basis/MapAnalysis/Topic25/Topic25.htm

Connectivity OperationsConnectivity Operations

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Optimal Path DensityOptimal Path Density counts the number of counts the number of optimal paths passing through each map location optimal paths passing through each map location ((DrainDrain))

Visual ConnectivityVisual Connectivity——

ViewshedViewshed results in a binary map identifying locations that are 1= seen results in a binary map identifying locations that are 1= seen

and 0= not seen from at least one viewer location and 0= not seen from at least one viewer location ((SimpleSimple)) Visual ExposureVisual Exposure counts the number of viewer cells connected to each counts the number of viewer cells connected to each

map location map location ((CompletelyCompletely)) Weighted Visual ExposureWeighted Visual Exposure weights the number of connections weights the number of connections based on viewer cell importance based on viewer cell importance ((WeightedWeighted))

Visual ProminenceVisual Prominence records the largest exposure angle to viewer cells records the largest exposure angle to viewer cells ((DegreesDegrees))

<ScreenHeights>

<TargetHeights>

<ViewerHeight>

Optimal Path ConnectivityOptimal Path Connectivity——

Optimal PathOptimal Path identifies the identifies the steepest downhill pathsteepest downhill path over a surface identifying the flow path if a terrain surface, over a surface identifying the flow path if a terrain surface, or the optimal path if a proximity surface or the optimal path if a proximity surface ((StreamStream))

Classes of Spatial Analysis OperatorsClasses of Spatial Analysis Operators ……all spatial analysis involves changing values (numbers) on a map(s) all spatial analysis involves changing values (numbers) on a map(s)

as a mathematical or statistical function of the values as a mathematical or statistical function of the values on that map or another map(s)on that map or another map(s)

(See MapCalc Applications, “Cross-Reference” for a cross reference of MapCalc operations and those of other systems))(See MapCalc Applications, “Cross-Reference” for a cross reference of MapCalc operations and those of other systems)) (Berry)

Neighborhood OperationsNeighborhood Operations

ORIENT -- Creates a map indicating aspect along a ORIENT -- Creates a map indicating aspect along a continuous surface. continuous surface.

PROFILE -- Creates a map indicating the cross-sectional PROFILE -- Creates a map indicating the cross-sectional profile along a continuous surface. profile along a continuous surface.

SCAN -- Creates a map summarizing the values that occur SCAN -- Creates a map summarizing the values that occur within the vicinity of each cell. within the vicinity of each cell.

SLOPE -- Creates a map indicating the slope (1st SLOPE -- Creates a map indicating the slope (1st derivative) along a continuous surface. derivative) along a continuous surface.

INTERPOLATE -- Creates a continuous surface from point INTERPOLATE -- Creates a continuous surface from point data (uses IDW or Nearest neighbor). data (uses IDW or Nearest neighbor).

(Berry)

Characterizing NeighborhoodsCharacterizing Neighborhoods

(Berry)

(Berry)

Calculating Slope Calculating Slope (max, min, median, average)(max, min, median, average)

At a location, the eight individual slopes can be calculated for the elevation values in a At a location, the eight individual slopes can be calculated for the elevation values in a 3x3 window… then summarized for the maximum, minimum, median and average slope. 3x3 window… then summarized for the maximum, minimum, median and average slope.

Slope = Rise/Run (*100 for %) ( ArcTan for Degrees)

The Maximum, Minimum, Median and Average slopes can be calculated using all eight individual slopes in the window or just the four corner slopes.

For example, the calculated Average slope using the four corners is 29%; using all eight is 59% .

Calculating Slope Calculating Slope (fitted using least squares & vector algebra)(fitted using least squares & vector algebra)

““Fitted slopeFitted slope” considers the overall slope within the window by ” considers the overall slope within the window by least square fitting a plane least square fitting a plane to the nine elevation valuesto the nine elevation values

(Berry)

……orientation of the fitted plane identifies the orientation of the fitted plane identifies the Aspect/AzimuthAspect/Azimuth

Calculating Slope Calculating Slope (fitted using least squares & vector algebra)(fitted using least squares & vector algebra)

““Fitted slopeFitted slope” considers the overall slope within the window by ” considers the overall slope within the window by least square fitting a plane least square fitting a plane to the nine elevation valuesto the nine elevation values or by the or by the

closure of the vector sum closure of the vector sum of the eight individual slopesof the eight individual slopes

(Berry)

……orientation of the fitted plane orientation of the fitted plane or direction of resultant vectoror direction of resultant vectoridentifies the identifies the Aspect/AzimuthAspect/Azimuth

Creating a Profile Map Creating a Profile Map (Set of cross-sections)(Set of cross-sections)

The value assigned to each cell identifies the profile The value assigned to each cell identifies the profile class of the side slope through the cell.class of the side slope through the cell.

(Berry)

Neighborhood TechniquesNeighborhood Techniques

(Berry)

Calculating Slope and Aspect…Calculating Slope and Aspect…

Use Use SlopeSlope to create maps of Slope_fitted, to create maps of Slope_fitted, Slope_max, Slope_min and Slope_avgSlope_max, Slope_min and Slope_avg

Use Use ComputeCompute to calculate difference surfaces to calculate difference surfaces between Slope_max minus Slope_min. and between Slope_max minus Slope_min. and Slope_max minus Slope_fittedSlope_max minus Slope_fitted

Use Use OrientOrient to create aspect maps in octants to create aspect maps in octants and degrees azimuthand degrees azimuth

Develop a binary modelDevelop a binary model that identifies that identifies map locations that are fairly steep (1-20 percent map locations that are fairly steep (1-20 percent slope) AND southerly oriented (135-245 degrees slope) AND southerly oriented (135-245 degrees azimuth)azimuth)

(Exercise 5, Part 1, Questions 1-3)(Exercise 5, Part 1, Questions 1-3)

Classes of Neighborhood OperationsClasses of Neighborhood Operations

Two broad classes of neighborhood analysis—Two broad classes of neighborhood analysis—

Characterizing Surface ConfigurationCharacterizing Surface ConfigurationSummarizing Map Values Summarizing Map Values

(Berry)

Crime Risk Map

ClassifiedCrime Risk

ClassifyClassify

Counts the number of Counts the number of incidences (points) incidences (points) within in each grid cellwithin in each grid cell

2D grid display of discrete incident counts

Creating a Crime Risk Density SurfaceCreating a Crime Risk Density Surface

Crime Incident Reports

Crime Incident

Locations

Grid IncidentCounts

Geo-CodingGeo-Coding Vector to RasterVector to Raster

Calculates the total number of reported crimes Calculates the total number of reported crimes

within a roving window– within a roving window– crime densitycrime density

DensitySurface Totals

Roving WindowRoving Window

2D perspective display of crime density contours

3D surface plot

9191

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# of Customers # of Customers

Customer Density Customer Density

Roving Window Total Roving Window Total (Density Surface)(Density Surface)

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Roving Window Average Roving Window Average (Simple Average)(Simple Average)

AverageAverage = Total / #cells = Total / #cells = 91 / 110 = 91 / 110 = 0.83 = 0.83

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Distance-Weighted Decay FunctionsDistance-Weighted Decay FunctionsWeighted Average Weighted Average of values in the “roving window”of values in the “roving window”

Standard mathematical Standard mathematical decay functionsdecay functions where weights (Y) decrease with increasing distance (X) where weights (Y) decrease with increasing distance (X)

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Example Example spatial filtersspatial filters depicting the fall-off depicting the fall-off of weights (Z) as a function of geographic distance (X,Y) of weights (Z) as a function of geographic distance (X,Y)

Roving Window Decay Functions Roving Window Decay Functions (Spatial Filters)(Spatial Filters)

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Comparison of Comparison of simple averagesimple average (Uniform weights) (Uniform weights) and and weighted averageweighted average (Linear weights) smoothing results (Linear weights) smoothing results

Roving Window Data Summary Roving Window Data Summary (Weighted Average)(Weighted Average)

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Neighborhood TechniquesNeighborhood Techniques

Roving Windows Data Summaries…Roving Windows Data Summaries…

Use Use ScanScan to create a map of to create a map of Housing Density Housing Density

Use Use ScanScan to create a map of the to create a map of the “ “coefficient of variation” in slopecoefficient of variation” in slope

Use Use ScanScan to create a map of to create a map of Covertype DiversityCovertype Diversity

Use Use ScanScan to identify the neighborhood proportion that has the to identify the neighborhood proportion that has the same cover typesame cover type

Develop a binary modelDevelop a binary model to identify locations that have high to identify locations that have high diversity diversity andand low proportion similar low proportion similar

(Berry)

(Exercise 5, Part 2, Questions 4-6)(Exercise 5, Part 2, Questions 4-6)

Creating a Housing Density MapCreating a Housing Density MapThe The TOTALTOTAL number of houses within 500 meters number of houses within 500 meters

is calculated for each map locationis calculated for each map location

(Berry)

NoteNote: Density Analysis and Spatial Interpolation : Density Analysis and Spatial Interpolation areare not not the same thingthe same thing

Iterative SmoothingIterative SmoothingThe The AVERAGEAVERAGE housing density value is successively calculated housing density value is successively calculated

to smooth the Housing_density surfaceto smooth the Housing_density surface (seeking the geographic trend) (seeking the geographic trend)

(Berry)

Coefficient of Variation MapCoefficient of Variation Map

The The COFFVARCOFFVAR of the elevation values within 500 meters of the elevation values within 500 meters is calculated. is calculated. Coffvar= (Stdev/Mean) * 100Coffvar= (Stdev/Mean) * 100

(Berry)

What information do you think a Coffvar map of crop yield would contain? What information do you think a Coffvar map of crop yield would contain? How might it be used?How might it be used?

Creating a Covertype Diversity MapCreating a Covertype Diversity Map

……a a DIVERSITYDIVERSITY map indicates the number of different map map indicates the number of different map values that occur within a window… e.g., cover types. values that occur within a window… e.g., cover types.

As the window is enlarged, the diversity increases. As the window is enlarged, the diversity increases.

(Berry)

Characterizing “Edginess”Characterizing “Edginess”

A simple “Edginess” model for the meadow involves assigning A simple “Edginess” model for the meadow involves assigning 1 to the meadow (Renumber) then calculating the total values 1 to the meadow (Renumber) then calculating the total values

within a 3x3 window for just the meadow area (Around)within a 3x3 window for just the meadow area (Around)

(Berry)