1. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Introduction to GIS Modeling Week 5 — Summarizing Neighborhoods GEOG 3110 –University of Denver
Presented by Joseph K. Berry
W. M. Keck Scholar, Department of Geography, University of Denver
Calculating slope, aspect and profile maps; Applying spatial differentiation and integration; "Roving window" summary operations; Characterizing edges and complexity
Joseph K. Berry, Keck Visiting Scholar

2. Class Logistics and Schedule
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Lessons Learned Grading Thoughts— … thoughts about the “red” …are any of the comments useful? …if so, which ones?
…also—distinction among Numerical, Geographical and Display Data Types
Teams for Exercise #5
New teams? …or same as Exercise #1&2 ...or, same as Exercises 3&4
Midterm Study Questions (and student answer outlines) …posted now ; if useful I will coordinate posting of group answers on Monday and Wednesday
Midterm Exam …you will download and take the 2-hour exam online (honor system) sometime between 8:00 am Friday February 11 and 5:00 pm Wednesday February 16
Exercise #6 (mini-project, example) — you will form your own teams (2 to 4 members) and tackle one of eight projects; posted now but we will discuss all aspects of the project “opportunities” next week
…assigned Thursday, February 11 and final report due 5:00 pm Sunday, February 21
No Exercise Week 7 — pause …a moment for a group “dance of joy”
Exercises #8 and #9 — to tailor your work to your interests, you can choose to not complete either or both of these standard exercises; in lieu of an exercise, however, you must submit a short paper (4-8 pages) on a GIS modeling topic of your own choosing
Berry
Joseph K. Berry, Keck Visiting Scholar

3. Quick Review (Simple proximity)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Quick Review (Simple proximity)
Simple Proximity surfaces can be generated for groups
of points, lines or polygons
…sets of Points
Lines
Areas
Accumulation surfaces of ever-increasing distance away from a starting location(s)
Berry
Joseph K. Berry, Keck Visiting Scholar

4. Quick Review (Effective proximity)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Quick Review (Effective proximity)
Effective Proximity surfaces are generated by considering
absolute and relative barriers to movement
…sets of Points
Water
Absolute Barrier
Lines
Slope
Relative Barrier
Areas
Water
& Slope
Absolute & Relative
Berry
Joseph K. Berry, Keck Visiting Scholar

5. Quick Review (Simple & Effective Proximity comparisons)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Quick Review (Simple & Effective Proximity comparisons)
Simple Proximity
…sets of Points
Water
Absolute Barrier
Lines
Slope
Relative Barrier
Areas
Water
& Slope
Absolute & Relative
Effective Proximity
Berry
Joseph K. Berry, Keck Visiting Scholar

6. Measuring Distance as “Waves” (Splash)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Measuring Distance as “Waves” (Splash)
(See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

7. Simple Proximity (Euclidean Distance)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Simple Proximity (Euclidean Distance)
Starters S1
Proximity
25,1
Close
to S1
… a Starter location is selected
… Proximity from the location to all other locations is computed
Starters S2
Proximity
Close
to S2
1,25
…repeat for another starter location
Shortest
Proximity
Close
Shortest Proximity
Working Map
Shortest
Proximity
Close
to S2
to S1
… the computed Proximity values are compared to the current shortest proximity values
… smaller values replace larger ones
… repeat for next starter location
Shortest
Proximity
Updated
…compare proximity surfaces
…store smallest value at each location
Berry
Joseph K. Berry, Keck Visiting Scholar

8. Effective Proximity (Intervening Conditions)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Starters Values on this map identify locations for measuring proximity; values can be used to indicate movement weights (characteristics weight) S1 S2
Movement Type Movement propagates from a starter location in waves; step distance can be orthogonal or diagonal (geographic distance)
Friction Relative ease of movement is represented as Absolute and relative barriers; steps incur the relative impedance of the location it is passing through (conditions impedance)
Effective Proximity (S1)
Minimize (Weight * Distance * Impedance)
Effective Proximity (S2)
Effective Proximity (Overall)
COMPARE— store Minimal Effective Distance
…repeat for all other Starter locations
Minimize (Effective Distance from different starters)
Berry
Joseph K. Berry, Keck Visiting Scholar

9. Basic and Advanced Distance Operations
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Basic and Advanced Distance Operations
Basic Operations (Static) —
Simple Proximity as the crow “flies” counting cell lengths
as it moves out as a wave front (Simple– starts counting at 1)
Effective Proximity as the crow “walks” in not
necessarily straight lines that respect absolute/ relative barriers
(Thru– absolute and relative barriers)
Advanced Operations—
…based on differences in the nature of the movement (Static):
Guiding Surface (Up/Down/Across)
Stepped-accumulation (continuing distance)
Gravity Model (movement weights)
Back Link (starter ID# for identifying closest starter location)
…based on differences in the intervening conditions (Dynamic):
Accumulation (Total accumulation)
Momentum (Net accumulation)
Direction (Look-up table)
Berry
Joseph K. Berry, Keck Visiting Scholar

10. Basic and Advanced Distance Operations
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Basic and Advanced Distance Operations
Effective Proximity
Minimize (Distance * Impedance)
Friction Relative ease of movement is represented as Absolute and relative barriers; steps incur the relative impedance of the location it is passing through (Conditions Impedance)
Extension uses 5) a look-up table to update the friction surface based on the nature of the movement (direction, accumulation, momentum)
Movement Type Movement propagates from a starter location in waves; step distance can be orthogonal or diagonal (Geographic Distance)
Starters Values on this map identify locations for measuring proximity. Extensions include using the starter value to 1) indicate movement weights, 2) indicate starting distance value and 3) starter location ID#
Guiding Surface Extension considers 4) whether a step is uphill, downhill or across based on guiding surface configuration
Berry
Joseph K. Berry, Keck Visiting Scholar

11. Connectivity Operations
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Connectivity Operations
Optimal Path Density counts the number of optimal paths passing through each map location (Drain)
Optimal Path Connectivity—
Optimal Path identifies the steepest downhill path over a surface identifying the flow path if a terrain surface, or the optimal path if a proximity surface (Stream)
Visual Connectivity—
Viewshed results in a binary map identifying locations that are 1= seen and 0= not seen from at least one viewer location (Simple)
Visual Exposure counts the number of viewer cells connected to each map location (Completely)
Weighted Visual Exposure weights the number of connections based on viewer cell importance (Weighted)
Visual Prominence records the largest exposure angle to viewer cells (Degrees)
<ScreenHeights>
<TargetHeights>
<ViewerHeight>
Berry
Joseph K. Berry, Keck Visiting Scholar

12. Classes of Spatial Analysis Operators
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Classes of Spatial Analysis Operators
…all spatial analysis involves changing values (numbers) on a map(s)
as a mathematical or statistical function of the values
on that map or another map(s)
(See MapCalc Applications, “Cross-Reference” for a cross reference of MapCalc operations and those of other systems))
(Berry)
Joseph K. Berry, Keck Visiting Scholar

13. Neighborhood Operations
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Neighborhood Operations
ORIENT -- Creates a map indicating aspect along a continuous surface.
PROFILE -- Creates a map indicating the cross-sectional profile along a continuous surface.
SCAN -- Creates a map summarizing the values that occur within the vicinity of each cell.
SLOPE -- Creates a map indicating the slope (1st derivative) along a continuous surface.
INTERPOLATE -- Creates a continuous surface from point data (uses IDW or Nearest neighbor).
(Berry)
Joseph K. Berry, Keck Visiting Scholar

14. Characterizing Neighborhoods
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Characterizing Neighborhoods
(Berry)
Joseph K. Berry, Keck Visiting Scholar

15. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Calculating Slope (max, min, median, average)
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.
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% .
Slope = Rise/Run (*100 for %) ( ArcTan for Degrees)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

16. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Calculating Slope (fitted using least squares & vector algebra)
“Fitted slope” considers the overall slope within the window by least square fitting a plane to the nine elevation values
…orientation of the fitted plane identifies the Aspect/Azimuth
(Berry)
Joseph K. Berry, Keck Visiting Scholar

17. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Calculating Slope (fitted using least squares & vector algebra)
“Fitted slope” considers the overall slope within the window by least square fitting a plane to the nine elevation values or by the closure of the vector sum of the eight individual slopes
…orientation of the fitted plane or direction of resultant vector
identifies the Aspect/Azimuth
(Berry)
Joseph K. Berry, Keck Visiting Scholar

18. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Creating a Profile Map (Set of cross-sections)
The value assigned to each cell identifies the profile class of the side slope through the cell.
(Berry)
Joseph K. Berry, Keck Visiting Scholar

19. Neighborhood Techniques
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Neighborhood Techniques
Calculating Slope and Aspect…
Use Slope to create maps of Slope_fitted, Slope_max, Slope_min and Slope_avg
Use Compute to calculate difference surfaces between Slope_max minus Slope_min. and Slope_max minus Slope_fitted
Use Orient to create aspect maps in octants and degrees azimuth
Develop a binary model that identifies map locations that are fairly steep (1-20 percent slope) AND southerly oriented ( degrees azimuth)
(Exercise 5, Part 1, Questions 1-3)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

20. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Classes of Neighborhood Operations
Two broad classes of neighborhood analysis—
Characterizing Surface Configuration
Summarizing Map Values
(Berry)
Joseph K. Berry, Keck Visiting Scholar

21. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Creating a Crime Risk Density Surface
Crime Incident Reports
Crime Incident Locations
Grid
Incident
Counts
Geo-Coding
Vector to Raster
Calculates the total number of reported crimes within a roving window– crime density
Density
Surface Totals
Roving Window
2D perspective display
of crime density contours
3D surface plot 91
Crime Risk Map
Classified
Crime
Risk
Classify
Counts the number of incidences (points) within in each grid cell
2D grid display of discrete incident counts
Berry
Joseph K. Berry, Keck Visiting Scholar

22. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Roving Window Total (Density Surface)
# of Customers
Customer Density
Berry
Joseph K. Berry, Keck Visiting Scholar

23. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Roving Window Average (Simple Average)
Average = Total / #cells
= 91 / 110
= 0.83
Berry
Joseph K. Berry, Keck Visiting Scholar

24. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance-Weighted Decay Functions
Weighted Average of values in the “roving window”
Standard mathematical decay functions
where weights (Y) decrease with increasing distance (X)
Berry
Joseph K. Berry, Keck Visiting Scholar

25. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Roving Window Decay Functions (Spatial Filters)
Example spatial filters depicting the fall-off
of weights (Z) as a function of geographic distance (X,Y)
Berry
Joseph K. Berry, Keck Visiting Scholar

26. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Roving Window Data Summary (Weighted Average)
Comparison of simple average (Uniform weights)
and weighted average (Linear weights) smoothing results
Berry
Joseph K. Berry, Keck Visiting Scholar

27. Neighborhood Techniques
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Neighborhood Techniques
Roving Windows Data Summaries…
Use Scan to create a map of
Housing Density
Use Scan to create a map of the
“coefficient of variation” in slope
Covertype Diversity
Use Scan to identify the neighborhood proportion that has the same cover type
Develop a binary model to identify locations that have high diversity and low proportion similar
(Exercise 5, Part 2, Questions 4-6)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

28. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Creating a Housing Density Map
The TOTAL number of houses within 500 meters
is calculated for each map location
Note: Density Analysis and Spatial Interpolation are not the same thing
(Berry)
Joseph K. Berry, Keck Visiting Scholar

29. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Iterative Smoothing
The AVERAGE housing density value is successively calculated to smooth the Housing_density surface (seeking the geographic trend)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

30. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Coefficient of Variation Map
The COFFVAR of the elevation values within 500 meters
is calculated. Coffvar= (Stdev/Mean) * 100
What information do you think a Coffvar map of crop yield would contain? How might it be used?
(Berry)
Joseph K. Berry, Keck Visiting Scholar

31. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Creating a Covertype Diversity Map
…a DIVERSITY map indicates the number of different map values that occur within a window… e.g., cover types.
As the window is enlarged, the diversity increases.
(Berry)
Joseph K. Berry, Keck Visiting Scholar

32. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Characterizing “Edginess”
A simple “Edginess” model for the meadow involves assigning 1 to the meadow (Renumber) then calculating the total values within a 3x3 window for just the meadow area (Around)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

33. …questions cover Class/Lab material and Reading assignments to date
Pop Quiz Possibility
…questions cover Class/Lab material
and Reading assignments to date
— you reviewed the previous class material and did the required reading for this class as well as, right?
(Berry)