2. 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

3. Upcoming Events Berry Midterm Study QuestionsMidterm Study Questions …posted now (class initiative to “group study” to collectively address the 50+ study questions) Midterm Study Questions Midterm Exam …you will download and take the 2-hour exam online (honor system) sometime between 8:00 am Friday February 15 and 5:00 pm Tuesday February 19 Exercise #6 Exercise #6 — you will form your own teams (2 to 3 members) and tackle one of eight projects; posted now but we will discuss all aspects of the project “opportunities” next week Exercise #6 …assigned Thursday, February 15 and final report due 5:00 pm Monday, February 25 …assigned Thursday, February 15 and final report due 5:00 pm Monday, February 25 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 No Exercise Week 7 (Example Real-World Projects; Introduction to Spatial Statistics (revisited); mini-Project Working Session) — pause …a moment for a group “dance of joy” Exercise #5 — normal report based on Exercise 5 questions; same teams as Exercise 4 report …yes or no? (you will choose” teams for the mini-project)

4. Simple Proximity surfaces can be generated for groups of points, lines or polygons …sets of Points LinesAreas Quick Review (Simple proximity) Berry Accumulation surfaces of ever-increasing distance away from a starting location(s)

5. Effective Proximity surfaces are generated by considering absolute and relative barriers to movement Quick Review (Effective proximity) …sets of Points Water Absolute Barrier Lines Slope Relative Barrier Areas Water & Slope Absolute & Relative Berry

6. Quick Review (Simple & Effective Proximity comparisons) Berry …sets of Points Water Absolute Barrier Lines Slope Relative Barrier Areas Water & Slope Absolute & Relative Simple Proximity Effective Proximity

7. Measuring Distance as “Waves” (Splash) (Berry) (See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion) Calculating Effective DistanceCalculating Effective Distance

8. Simple Proximity (Euclidean Distance) Starters S1Proximity S125,1 Close to S1 … a Starter location is selected … Proximity from the location to all other locations is computed Starters S2Proximity Close to S2 S21,25 …repeat for another starter location ShortestProximity Close to S2 Close to S1 … the computed Proximity values are compared to the current shortest proximity values … smaller values replace larger ones … repeat for next starter location ShortestProximityUpdated …compare proximity surfaces …store smallest value at each location Berry ShortestProximity Close Shortest Proximity Working Map

9. Effective Proximity (Overall) COMPARE— store Minimal Effective Distance …repeat for all other Starter locations Minimize (Effective Distance from different starters) Effective Proximity (S2) Effective Proximity (Intervening Conditions) Effective Proximity (S1) Minimize (Weight * 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) 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; values can be used to indicate movement weights (characteristics weight) S1 S2 Berry

10. Basic and Advanced Distance Operations Berry Basic Operations (Static) — Basic Operations (Static) — Simple Proximity as the crow “flies” counting cell lengths 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 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) Guiding Surface (Up/Down/Across) Stepped-accumulation (continuing distance) Stepped-accumulation (continuing distance) Gravity Model (movement weights) Gravity Model (movement weights) Back Link (starter ID# for identifying closest starter location) Back Link (starter ID# for identifying closest starter location) …based on differences in the intervening conditions (Dynamic): Accumulation (Total accumulation) Accumulation (Total accumulation) Momentum (Net accumulation) Momentum (Net accumulation) Direction (Look-up table) Direction (Look-up table) www.innovativegis.com/basis/MapAnalysis/Topic25/Topic25.htm

11. Connectivity Operations Berry Optimal Path Density counts the number of optimal paths passing through each map location (Drain) Optimal Path Density counts the number of optimal paths passing through each map location (Drain) 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) 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) 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) 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) Visual Prominence records the largest exposure angle to viewer cells (Degrees) Optimal Path Connectivity— 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) 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)

12. 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)) Cross-Reference (Berry)

13. 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)

14. Characterizing Neighborhoods (Berry)

15. 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. 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%.

16. 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 (Berry) …orientation of the fitted plane identifies the Aspect/Azimuth

17. 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 (Berry) …orientation of the fitted plane or direction of resultant vector identifies the Aspect/Azimuth

18. 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)

19. Neighborhood Techniques (Berry) Calculating Slope and Aspect… Use Slope to create maps of Slope_fitted, Slope_max, Slope_min and Slope_avg 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 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 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 (135-245 degrees azimuth) Develop a binary model that identifies map locations that are fairly steep (1-20 percent slope) AND southerly oriented (135-245 degrees azimuth) (Exercise 5, Part 1, Questions 1-3)

20. Classes of Neighborhood Operations Two broad classes of neighborhood analysis— Characterizing Surface Configuration Summarizing Map Values (Berry)

21. 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 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 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 Berry

22. # of Customers Customer Density Roving Window Total (Density Surface) Berry

23. Roving Window Average (Simple Average) Average = Total / #cells = 91 / 110 = 91 / 110 = 0.83 = 0.83Berry

24. 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

25. Example spatial filters depicting the fall-off of weights (Z) as a function of geographic distance (X,Y) Roving Window Decay Functions (Spatial Filters) Berry

26. Comparison of simple average (Uniform weights) and weighted average (Linear weights) smoothing results Roving Window Data Summary (Weighted Average) Berry

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

28. Creating a Housing Density Map The TOTAL number of houses within 500 meters is calculated for each map location (Berry) Note: Density Analysis and Spatial Interpolation are not the same thing

29. Iterative Smoothing The AVERAGE housing density value is successively calculated to smooth the Housing_density surface (seeking the geographic trend) (Berry)

30. Coefficient of Variation Map The COFFVAR of the elevation values within 500 meters is calculated. Coffvar= (Stdev/Mean) * 100 (Berry) What information do you think a Coffvar map of crop yield would contain? How might it be used?

31. 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)

32. 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)