1. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Introduction to GIS Modeling Week 4 — Measuring Distance and Connectivity GEOG 3110 –University of Denver
Presented by Joseph K. Berry
W. M. Keck Scholar, Department of Geography, University of Denver
Simple vs. weighted distance; Proximity and movement; Accumulation surfaces; Identifying optimal path(s); Narrowness; Viewsheds and visual exposure surfaces
Joseph K. Berry, Keck Visiting Scholar

2. 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

3. Concepts in GIS -- Topic #1
An Analytic Framework for GIS Modeling
Proximity operations involve measuring distance and connectivity among map locations
(GIS Modeling Framework paper)
(Berry)
Joseph K. Berry, BA_SIS, Inc. All Rights Reserved.

4. Distance and Connectivity Fundamentals
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance and Connectivity Fundamentals
S, SL, 2P
S route
(Berry)
Joseph K. Berry, Keck Visiting Scholar

5. Distance “Waves” (Simple and Effective Proximity)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance “Waves” (Simple and Effective Proximity)
(Linked slide show DIST)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

6. Variable-Width Buffers (Simple vs. Uphill Proximity)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Variable-Width Buffers (Simple vs. Uphill Proximity)
Simple Buffer– “as-the-crow-flies” proximity to the road; no absolute or relative barriers are considered; dark blue line indicates the full simple buffer reach (polygon)
Clipped Buffer– simple proximity for just the land areas
Downhill
Uphill Buffer– simple proximity to the road for just the areas that are uphill from the road; absolute barrier (uphill only– absolutely no downhill steps)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

7. Distance and Connectivity Operations
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance and Connectivity Operations
DRAIN -- Creates a map indicating the number of steepest paths (optimal path density) from a set of locations along a surface.
RADIATE -- Creates a map indicating areas that are visible from locations specified on the 'viewers map'.
SPAN -- Creates a map indicating the narrowness within all non-zero areas on a map.
SPREAD -- Creates a map indicating the shortest effective distance from specified cells to all other locations.
STREAM -- Creates a map identifying the steepest downhill route along a surface (optimal path).
(Berry)
Joseph K. Berry, Keck Visiting Scholar

8. Distance/Connectivity Techniques (Exercise 4, Q1)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance/Connectivity Techniques (Exercise 4, Q1)
Calculating Simple/Weighted Proximity …
SPREAD Roads TO 20 Simply FOR Roads_simpleprox
SPREAD Roads TO 20 OVER Elevation Uphill Only Simply FOR Roads_uphillprox
RENUMBER Covertype ASSIGNING 0 TO 1
ASSIGNING 3 TO 2 ASSIGNING 7 TO 3
FOR Hiking_friction
SPREAD Roads TO 60 THRU Hiking_friction Simply
FOR Roads_hikingprox
(Berry)
Joseph K. Berry, Keck Visiting Scholar

9. Customizing MapCalc Displays (Shading Manager)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Customizing MapCalc Displays (Shading Manager) 3)
3) Enter Range Breaks 4)
4) Set Color and Color Locks
1) Set “User Defined Ranges” 1) 2)
2) Set #Ranges = 14
(Berry)
Joseph K. Berry, Keck Visiting Scholar

10. Distance/Connectivity Techniques (Exercise 4, Q2)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance/Connectivity Techniques (Exercise 4, Q2)
Step 4) Isolate the starting
location (ranch)
RENUMBER
Step 5) Calculate the effective proximity from the ranch to everywhere
SPREAD
Locations
Ranch
1= Ranch
0= All else
Step 2) Establish on-road travel as 1= easiest with 0= all non-road areas
RENUMBER
Ranch_prox
Roads
Allroads
1= Any road
0= All else
Step 3) Combine the on- and off-road friction maps such that the on-road friction take precedent over the off-road friction
COVER
Bike_Hiking
_friction
Step 1) Establish off-road hiking friction that considers the relative ease of traveling through various cover types (done in Q1)
RENUMBER
Covertype
Hiking_friction
Boxes represent maps
Lines represent processing steps
(Berry)
Joseph K. Berry, Keck Visiting Scholar

11. Distance/Connectivity Techniques (Exercise 4, Q2)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance/Connectivity Techniques (Exercise 4, Q2)
Friction Map– identifies the relative ease of travel through each map location (grid cell)
Friction Map
…steps 1-3
Accumulation Surface
Accumulation Surface– identifies shortest distance (effective proximity steps)
83.0
…steps 4 and 5
(See Beyond Mapping III online book , “Topic 14” for more information)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

12. Establishing Optimal Paths (Exercise 4, Q3)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Stream (Optimal Path) – like a raindrop, the “steepest downhill path” identifies the optimal route. If the surface is a proximity map, the optimal path identifies the shortest (not necessarily straight) route between any location on the surface and the closest starting cell (point, line or polygon)
41.1
38.2
42.8
36.5
40.6
43.5
36.0
35.0
43.0
Col 22, Row 20
(36.5 – 41.1) uphill (N)
(36.5 – 38.2) uphill (NE)
(36.5 – 40.6) uphill (E)
(36.5 – 35.0) downhill (SE)
(36.5 – 36.0) downhill (S)
(36.5 – 43.0) uphill (SW)
(36.5 – 43.5) uphill (W)
(36.5 – 42.8) uphill (NW)
…move to SE cell
How STREAM works
RISE / run
35.0
41.1
38.2
42.8
36.5
40.6
43.5
36.0
50.0
Repeat for next step Col 23, Row 19
33.6
34.6
42.0
41.6
43.0
Accumulation Surface
and next, and next…
until no more downhill steps (bottom)
Drain (Optimal Path Density) – accumulates the optimal paths from many locations. Higher “Drain” values indicate locations that have numerous optimal paths passing through it (many uphill sources moving through).
(Q3a)
(Q3b)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

13. Measuring Narrowness (Connectivity to Edge)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Measuring Narrowness (Connectivity to Edge)
Narrowness is defined as the “shortest chord connecting opposing edges.”
The simple distance from a location to all edge (boundary) locations is computed. The minimum value of the sum of distances for opposing edge cells is assigned… narrowness.
To improve performance, the procedure is usually constrained to some maximum reach (e.g., all locations greater than 500 meters will be set to 500)
SPAN Meadow WITHIN 9 FOR Cover_narrow
…how would create a map that identifies Meadow locations that are “open” (narrowness >4)?
…then expand your investigation to identify the proximity to Open Water for each of the open meadow locations
(See MapCalc Applications, “Characterizing Narrowness” for more information)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

14. Establishing Visual Connectivity
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Seen if new tangent exceeds all previous tangents along the line of sight—
At <Viewer_heightValue>
Thru <Screens_heightMap>)
Onto <Target_heightMap>
…like proximity, Visual Connectivity starts somewhere (starter cell) and moves through geographic space by steps (wave front)– like a lighthouse beam…
Radiate – visual exposure is calculated by a series of “waves” that carry the tangent to beat.
Simply – Viewshed
Visual Exposure
Completely – number of “viewers” that see each location
Weighted – viewer cell value is added
(Berry)
Joseph K. Berry, Keck Visiting Scholar

15. Calculating Visual Exposure (# Times Seen)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Calculating Visual Exposure (# Times Seen)
Visual exposure identifies how many times (count) each map location is seen from a set of viewer locations
(Berry)
Joseph K. Berry, Keck Visiting Scholar

16. Visual Exposure from Extended Features
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Visual Exposure from Extended Features
A visual exposure map identifies how many times each location is seen from an “extended eyeball” composed of numerous viewer locations, such as a road network (simple sum)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

17. Weighted Visual Exposure (Sum of Viewer Weights)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Weighted Visual Exposure (Sum of Viewer Weights)
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 (weighted sum)
(See Beyond Mapping III, Topic 15, “Deriving and Using Visual Exposure Maps” for more information)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

18. Real-World Visual Analysis
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Real-World Visual Analysis
Weighted visual exposure map for an ongoing visual assessment in a national recreation area— the project developed visual vulnerability maps from the reservoir in the center of the park and a major highway running through the park. In addition, aesthetic maps were generated based on visual exposure to pretty and ugly places in the park
(Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

19. Variable-Width Buffers (Line-of-sight)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Variable-Width Buffers (Line-of-sight)
Line-of-Sight Buffer– identifies all land locations (clipped) within 250m that can be seen from the road…
250m “viewshed” of the road
Line-of-Sight Exposure– notes the number of times each location in the buffer is seen
Line-of-Sight Noise– locations hidden behind a ridge or farther away from a source (road) greatly decrease noise levels.
(Berry)
Joseph K. Berry, Keck Visiting Scholar

20. Distance/Connectivity Techniques (Exercise 4, Q4)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Distance/Connectivity Techniques (Exercise 4, Q4)
Determining
visual connectivity from roads and houses…
Radiate Roads
over Elevation
to 100 completely
for Ve_roads
Slice Ve_roads
into 5
for Ve_roads_sliced
Radiate Housing over Elevation to 100 weighted for Ve_housing
Slice Ve_housing into 5 for Ve_housing_sliced
Analyze average ve_roads_sliced with ve_housing_sliced for Vexposure 
(Berry)
Joseph K. Berry, Keck Visiting Scholar

21. On Your Own (Exercise 4, Q5)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Screen grab the important maps and briefly describe your solution as a narrative flowchart. Must do three (other 2 Optional extra credit)…
5-1) Using the Tutor25 database, determine the average visual exposure (Vexposure map) for each of the administrative districts (Districts map).
5-2) Using the Tutor25 database, identify the visual exposure (Vexposure map from question #4) for a 300m simple buffer (3 cells) around roads (Roads map).
5-3) Using the Tutor25 database, create a map (not just a display) that shows the locations that have the highest (top 10%) visual exposure to houses (Housing map).
5-4) Using the Island database, create a map that identifies locations that are fairly steep (15% or more on the Slope map) and are westerly oriented (SW, W and NW on the Aspect map) and are within 1500 feet inland from the ocean (hint: the analysis frame cell size is a “property” of any map display).
5-5) Using the Agdata database, create a map that locates areas that have unusually high phosphorous levels (one standard deviation above the mean on the 1997_Fall_P map) and are within 300 feet of a “high yield pocket” (top 10% on the 1997_Yield_Volume map).
(Berry)
Joseph K. Berry, Keck Visiting Scholar

22. Optional Questions Extended “Problems with No Guidance”
Weighted Visual Exposure Density Surface
“Draining Forests”
for What?
(Berry)

23. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Discrete vs. Continuous Buffers
Continuous
Buffer
Discrete
Buffer
…all locations within
a specified distance
…Proximity is formed by a series of continuous concentric rings– like throwing a rock into a pond …each “step” is a one cell (orthogonal/diagonal) movement away
(Berry)
Joseph K. Berry, Keck Visiting Scholar

24. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Calculating Effective Proximity (Travel-time)
Superimposed Analysis Grid
100c x 100r = 10,000 cells
Street Type as Barriers
Streets are calibrated…
…for ease of travel…
…“burn” the Roads
into the analysis grid
(Vector to Raster)
Effective Proximity
…”proximity waves” ripple out along the streets as if they were canals
…minutes away
TTime_animation.ppt
Starting Location
…splash…
…”burn” the Starting
location into the
analysis grid
(Vector to Raster)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

25. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Transferring Travel-Time Information
…the Proximity Waves propagate throughout the entire street pattern assigning the travel-time values
to each location
(farthest location is 26 minutes away in the upper-left corner)
...farthest
Raster (MapCalc)
…the proximity information is easily transferred to a desktop mapping system
…using Pseudo-Grid format
(Raster to Vector)
...farthest
Vector (MapInfo)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

26. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Utilizing Travel-Time Information
…a Spatial Join appends the travel-time information to the customer data table
Universal Key is cell position
(Row, Col )
…and is retrievable by clicking on any customer location or through a geo-query request
(families with 2 children that are more than 15 minutes—
80 base cells away)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

27. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Optimal Path Connectivity
…the “steepest” downhill path along the Travel-Time surface identifies the quickest route
(optimal path)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

28. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Identifying Catchment Areas (Optimal Path Density)
…the set of all optimal paths from all locations identify Catchment Areas characterized by travel-time to nearest ATM location
(Berry)
Joseph K. Berry, Keck Visiting Scholar

29. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Working with Travel-Time Surfaces
…a travel-time map forms an Accumulation Surface whose values are continuously increasing from the starting location
(increasingly farther away)
…the result is a bowl-like surface with estimated time to travel for every location
…not a perfect bowl but warped and twisted based on the Relative and Absolute barriers
to movement
(Berry)
Joseph K. Berry, Keck Visiting Scholar

30. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Competition Analysis (Relative Travel-time Position)
…subtracting the two surfaces derives relative travel-time advantage
…locations that are the same travel distance from both stores result in zero–
Positive values favor Colossal; Negative favor Kent
(Berry)
Joseph K. Berry, Keck Visiting Scholar