1. Grid-based Map Analysis: Utilizing Distance/Connectivity Operators in the Real-World
GIS Centroid Seminar – Colorado State University – April 18, 2011
Understanding…
1) Extending the Concept of Distance to Proximity
2) Calculating Simple Proximity
3) Extending the Concept of Simple Proximity to Movement
4) Calculating Effective Proximity/Connectivity
5) Utilizing Effective Proximity/Connectivity to Solve Real-World Problems
6) Where is Effective Proximity Headed
Presentation by Joseph K. Berry
W.M. Keck Scholar in Geosciences, University of Denver
Special Faculty in Natural Resources, Colorado State University Principal, Berry & Associates // Spatial Information Systems 2000 S. College Ave, Suite 300, Fort Collins, CO Phone: (970) Website at
Joseph K. Berry,

2. (Nanotechnology) Geotechnology (Biotechnology)
Keynote Address, ESRI SWUG 2009
(Nanotechnology) Geotechnology (Biotechnology)
Geotechnology is one of the three "mega technologies" for the 21st century and promises to forever change how we conceptualize, utilize and visualize
spatial relationships in scientific research and commercial applications (U.S. Department of Labor)
Global Positioning
System (location and navigation)
Geographic Information
Systems (map and analyze)
The Spatial Triad
Remote Sensing
(measure and classify)
GPS/GIS/RS is
Where What
GIS
Mapping involves precise placement (delineation) of physical features
(graphical inventory)
Descriptive
Mapping
Modeling involves analysis of spatial
relationships and patterns
(numerical analysis)
Prescriptive
Modeling
Why So What and What If
(Berry)

3. History/Evolution of Map Analysis
Geotechnology – one of the three “mega-technologies” for the 21st Century
(the other two are Nanotechnology and Biotechnology, U.S. Department of Labor)
Global Positioning System (Location and Navigation)
Remote Sensing (Measure and Classify)
Geographic Information Systems (Map and Analyze) 
70s Computer Mapping (Automated Cartography)
80s Spatial Database Management (Mapping and Geo-query)
90s Map Analysis (Investigates Spatial Relationships and Patterns)
00s Multimedia Mapping (Integration of GIS, Internet and Visualization)
Spatial Analysis (Geographical context)
Reclassify (single map layer; no new spatial information)
Overlay (coincidence of two or more map layers; new spatial information)
Proximity (simple/effective distance and connectivity; new spatial information)
Neighbors (roving window summaries of local vicinity; new spatial information)
Spatial Statistics (Numerical context)
Surface Modeling (point data to continuous spatial distributions
Spatial Data Mining (interrelationships within and among map layers)
Map Analysis
(Berry)

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. DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Discrete Buffers vs. Continuous Proximity
Continuous
Proximity
…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
Discrete
Buffer Rings
Discrete
Buffer
…all locations within
a specified distance
(Berry)
Joseph K. Berry, Keck Visiting Scholar

7. 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

8. 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—
This Optimal Path identifies the route the wave front to reach any location
(Berry)
Joseph K. Berry, Keck Visiting Scholar

9. 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

10. 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

11. 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

12. Calculating Effective Proximity (Intervening Conditions)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Starters Values on this map identify locations for measuring proximity (rocks tossed into still pond) 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

13. 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

14. On- and Off-road Emergency Response (Truck)
The left side of the figure below illustrates the on-road portion of a travel-time (TT) surface from headquarters along secondary backcountry roads. The grid-based solution uses friction values for each grid cell in a manner analogous to road segment vectors in network analysis. The difference being that each grid cell is calibrated for the time it takes to cross it (0.10 minute in this simplified example).
26.5 minutes
…farthest away by truck
Off-Road
HQ (start)
Emergency Response Surface
…travel-time by truck from HQ along roads
…each grid cell is calibrated by the time it takes to cross depending on the 1) type of movement and 2) the landscape conditions
Roads
Water
Slope
(Berry)

15. On- and Off-road Emergency Response (ATV)
The figure below identifies the shortest combined on- and off-road ATV travel-times. Note that the emergency response solution forms a bowl-like surface with the headquarters as the lowest point and the road proximities forming “valleys” of quick access. The sides of the valleys indicate ATV off-road travel with steeper rises for areas of steeper terrain slopes; the grey areas indicate locations that are too steep for ATV travel.
Emergency Response Surface
…travel-time by truck from HQ along roads and then by ATV until too steep (>40% slope)
HQ (start)
Too
Steep
52.1 minutes
…farthest away by truck and ATV
Slopemap
…draped over Elevation surface
Too Steep
For ATV use
ATV use
Steep canyon
area
(Berry)

16. On- and Off-road Emergency Response (Hiking)
The figure below completes the total on- and off-road travel-time to all locations by adding hiking time from where the wave front of the accumulated travel-time by truck and ATV stopped. Note the very steep rise in the surface (blue tones) resulting from the slow movement in the rugged and steep slopes of the canyon area.
HQ (start)
Emergency Response Surface
…travel-time by truck from HQ along roads, then by ATV until too steep and finally hiking
in the steep terrain
96.0 minutes
…farthest away by truck, ATV and hiking
Response Surface
…draped over Elevation surface
HQ (start)
Farthest
(end)
Optimal Path
(quickest route)
…accessing locations in the southern portions of the steep canyon require driving along the road, then proceeding via ATV and finally hiking nearly 45 minutes to the bottom of the canyon
Steep canyon
area
(Berry)

17. Emergency Response Model Logic (Flowchart)
Emergency Response Model (Travel-Time = fn(roads, elevation, water)
…1) the response team first travels by truck along secondary roads, then
Base Map
Derived Map
Interpreted Map
Modeled Map
Abstraction
Level: HQ
Roads
Renumber
Truck
Rfriction
HQ RoadProx
Spread
1) Travel-time from HQ to all road locations (by Truck)
2) continues using all-terrain vehicles (ATV) for off-road travel until open water or steep slopes are encountered, then
Spread
ATV
Prox
Slope
Renumber
Elevation
Slopemap
ATV Sfriction
Water
Absolute
ATV Friction
Calculate
2) Travel-time from HQ to all ATV accessible locations
(by Truck and ATV)
3) proceeds by hiking in the rugged terrain to reach all locations
Renumber
Slopemap
Hiking
Sfriction
Water
Absolute
Friction
Calculate
Spread
Prox
3) Travel-time from HQ to all locations
(by Truck, ATV & Hiking)
(Berry)

18. Where Is Effective Proximity Headed? (6 extensions)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Where Is Effective Proximity Headed? (6 extensions)
Starters Values on this map identify locations for measuring proximity.
Extensions include using the starter value to 1) indicate starting distance value 2) indicate movement weights, and 3) starter location ID#
Guiding Surface Extension considers 4) whether a step is uphill, downhill or across based on guiding surface configuration
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)
Dodecahedral
6) Hexagon
Effective Proximity
Minimize (Distance * Impedance)
Extension uses 5) a look-up table to update the friction surface based on the nature of the movement (direction, accumulation, momentum)
(Berry)
Joseph K. Berry, Keck Visiting Scholar

19. Where Is Connectivity Headed? (optimal path; visual exposure)
DU Mini-Workshops on GIS Modeling -- Surface Modeling/Analysis
Where Is Connectivity Headed? (optimal path; visual exposure)
Starters Map Extensions include using the starter value to indicate starting distance value ,
indicate movement weights, and starter location ID#
Friction Map Extension uses a look-up table to update the friction surface
based on the nature of the movement (direction, accumulation, momentum)
Guiding Surface Extension considers whether a step is uphill, downhill
or across based on guiding surface configuration
Movement Type Extension trades squares and cubes in the analysis grid
for Hexagons and Dodecahedrals
Effective Distance: movement respecting relative and absolute barriers
Optimal Path(s): steepest downhill path over a proximity or accumulation cost surface
Overland Flow Single Path or Optimal Path Density— Extension to Weighted Optimal Path Density
Corridor Analysis Best Route; Nth Optimal Path Density— Extension for Path Straightening/Centering and Feeder Networks
Topic 15, Deriving and Using Visual Exposure Maps
Topic 16, Routing and Optimal Paths
Beyond Mapping III book at
Visual Connectivity: location seen if new tangent exceeds all previous tangents
Viewshed visually connected at lease once— Extensions for Distance Effects, Target Height, Haze/Opacity, Degree of Exposure (prominence)
Visual Exposure Extension that counts #times seen
Weighted Visual Exposure Extension that sums the weights for all “viewer” locations
(Berry)
Joseph K. Berry, Keck Visiting Scholar

20. GIS Modeling -- Future Directions
Where From Here?
Joseph K. Berry
— Website:
Geospatial Centroid Seminar – Colorado State University
April, 2011
1) Extending the Concept of Distance to Proximity
2) Calculating Simple Proximity
3) Extending the Concept of Simple Proximity to Movement
4) Calculating Effective Proximity/Connectivity
5) Utilizing Effective Proximity/Connectivity to Solve
Real-World Problems
6) Where is Effective Proximity Headed
PowerPoint slide set is posted at
Graduate level GIS Modeling course materials are posted at
Additional Information:
Concepts, Considerations and Procedures in Applying Effective Distance Modeling, GeoTec Conference, Vancouver, British Columbia, Canada, February 11 – 16, 2005.  J.K. Berry.
 Calculating Effective Distance and Connectivity, online book Beyond Mapping III, Topic 25.  J.K. Berry.
(Berry)
Joseph K. Berry, Keck Visiting Scholar