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. Class Logistics and Schedule Berry Midterm Study QuestionsMidterm Study Questions (and student answer outlines) …posted now and will be updated with group answers on Monday and Wednesday Midterm Study Questions Midterm Exam …you will download and take the 2-hour exam online (honor system) sometime between 8:00 am Friday February 12 and 5:00 pm Wednesday February 17 Exercise #6 (mini-project, example) — you will form your own teams (1 to 3 members) and tackle one of nine projects; posted now but we will discuss all aspects of the project “opportunities” next week mini-projectexamplemini-projectexample …assigned Thursday, February 11 and final report due 5:00 pm Sunday, February 21 …assigned Thursday, February 11 and final report due 5:00 pm Sunday, February 21 Exercises #7 and #8 — 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 New Teams for Exercise #5 Red Team, Kristina, Shelby and Luke Blue Team, Jason and Curtis Green Team, Jeremy V, Elizabeth and Sylvia Orange Team, Katie, Brenton and Eliot Violet Violet Team, Lia, Jason and Jeremy D

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. 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

8. Weighted Proximity (Mover Characteristics) S2 equal S1 equal Close to S2 Close to S1 Bisector Simple EqualInfluence Bisector Weighted Close to S2 Close to S1 S2 half S1 twice Twice the Influence …like gravity some locations have more influence therefore other locations are “effectively” closer Berry

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— Basic Operations— Simple Proximity as the crow “flies” in straight lines (Simple) Simple Proximity as the crow “flies” in straight lines (Simple) Weighted/Explicit Proximity recognizes differences in mover characteristics (Weighted and Explicitly) Weighted/Explicit Proximity recognizes differences in mover characteristics (Weighted and Explicitly) Guided Proximity uses guiding surface to determine Uphill and Downhill movements (Over) Guided Proximity uses guiding surface to determine Uphill and Downhill movements (Over) Effective Proximity as the crow “walks” in not necessarily straight lines that respect absolute/ relative barriers (Thru) Effective Proximity as the crow “walks” in not necessarily straight lines that respect absolute/ relative barriers (Thru) Advanced Operations— Directional Effects (bearing; up/across slope) Directional Effects (bearing; up/across slope) Accumulation Effects (wear and tear) Accumulation Effects (wear and tear) Momentum Effects (acceleration/deceleration with movement) Momentum Effects (acceleration/deceleration with movement) Stepped Movement (go until specified location then restart) Stepped Movement (go until specified location then restart) Back Azimuth (direction of travel) Back Azimuth (direction of travel) 1 st and 2 nd Derivative (speed and change in speed) 1 st and 2 nd Derivative (speed and change in speed)

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. Elevation Surface Overland Flow Model 1) The Pipeline is positioned on the Elevation surface 1) Pipeline 2) Flow from Spill Points along the pipeline are simulated X 2) Spill Point #1 3) High Consequence Areas (HCA) are identified 3) HCA 4) A Report is written identifying flow paths that cross HCA areas X HCA Impact 4) Report 5) Overland flow is halted when Flowing Water is encountered (Channel Flow Model) 5) Flowing Water Spill Migration Modeling (Berry)

13. Types of Surface Flows (Berry) Common sense suggests that “water flows downhill” however the corollary is “…but not always the same way” (See Beyond Mapping III online book, Topic 20 “Surface Flow Modeling” at www.innovativegis.com/basis) Beyond Mapping III Beyond Mapping III

14. Characterizing Overland Flow and Quantity (Berry) Intervening terrain and conditions form Flow Impedance and Quantity maps that are used to estimate flow time and retention Link to Spill1_animationSpill1_animation (Over) (Thru)

15. Simulating Different Product Types (Berry) Flow Velocity is a function of— Specific Gravity (p), Viscosity (n) and Depth (h) of product Slope Angle (spatial variable computed for each grid cell) Physical properties combine with terrain/conditions to model the flow of different product types

16. Characterizing Impacted Areas (Berry) Flows from spill 1, 2 and 3 The minimum time for flows from all spills… Drinking water HCA Impacted portion of the Drinking water HCA characterizes the impact for the High Consequence Areas characterizes the impact for the High Consequence Areas

17. Modeling Stream Channel Flow (Vector) (Berry) Channel Flow Model 1) Channel Flow Time 0 hr 7.3 hr 8.4 hr 9.6 hr 10.8 hr 10.1 hr 13.1 hr 11.2 hr 13.6 hr 1) Channel Flow times along stream network segments are added Base Point 2) Overland Flow time and quantity at entry is noted X.14.12.27.12.25.72.78 X Overland Flow (2.5 hours) 2) Overland Flow Entry Time X = 12.10 +.36 = 12.46 hr away from Base Point 11.2 hr 13.1 hr 3) Impacted High Consequence Areas (HCA) are identified In = 11.46 hr Out = 9.86 hr HCA 3) Impacted HCA Times HCA 4) Report is written identifying flow paths that cross HCA areas 4) Report of Impacted HCA’s 2.5 + (12.46 -11.46) = 3.5 hours total Overland Flow (Raster)

18. 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)

19. 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)

20. Characterizing Neighborhoods (Berry)

21. Calculating Slope (max, min, median, average) At a location, the eight individual slopes are 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)

22. 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

23. 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)

24. 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)

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

26. 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

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

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

29. 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

30. 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

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

32. 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)

33. 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

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

35. 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?

36. 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)

37. 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)

38. 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)