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Spatial Analyst – Identifying the Best
Paths with Cost Distance AnalysisKevin M. Johnston
Elizabeth Graham
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Cost distance analysis - Outline
• What is cost distance analysis
• Cost Analysis 1 - Cost Connectivity (and creating a cost surface) - Demo
• Cost Analysis 2 - Two step process – Cost Distance and Cost Path - Demo
• Source characteristics - Demo
• Directionality of the movement - Demo
• Incorporating barriers - Demo
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What is cost distance analysis
• One of the most common applications in Spatial Analyst
• Euclidean distance – as the crow flies
• Cost distance – as the phenomenon moves across the landscape
• Euclidean is how far while cost analysis is a total amount
• Cost can be:
- Preference
- Energy expended
- Time
- Dollars
- Risk
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Problems addressed by cost distance analysis
• Constructing a road to a proposed shopping center
• Conserving wildlife corridors between habitat patches
• Supplying and reinforcing military troops in a deployment
• Providing movement paths for fire fighters between posts
• Locating a pipeline to connect energy fields to a refinery
• Siting electrical lines
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Why do patches need to be connected?
• Fragmentation Metapopulation
- Logging Roads
- Supply routes for military locations
- Fire fighting routes
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Cost distance analysis - Outline
• What is cost distance analysis
• Cost Analysis 1 - Cost Connectivity (and creating a cost surface) - Demo
• Cost Analysis 2 - Two step process – Cost Distance and Cost Path - Demo
• Source characteristics - Demo
• Directionality of the movement - Demo
• Incorporating barriers - Demo
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The input to cost distance analysis
• Define the problem (which includes creating submodels)
• Identify and derive the criteria
• Transform values to a common scale
• Weight the criteria relative to one another and combine.
• Analyze the results
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How to create cost surface
• Similar to creating a suitability
model
• Cost per map unit to move through
the cell
• The lower the cost the better
• Diagonal accounted for
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Cost analysis 1 – Cost Connectivity
• Input regions
• Input cost
• Create a network of paths
- Output optimum paths
- Optional neighboring paths
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Cost Connectivity – Optimum network
C
A
B
Based on cost not Euclidean distance
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Creating a cost surface
Cost Connectivity
Creating the
optimum network
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Cost distance analysis - Outline
• What is cost distance analysis
• Cost Analysis 1 - Cost Connectivity (and creating a cost surface) - Demo
• Cost Analysis 2 - Two step process – Cost Distance and Cost Path - Demo
• Source characteristics - Demo
• Directionality of the movement - Demo
• Incorporating barriers - Demo
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Two step process for performing cost distance analysis
• Cost Distance tool
- Input
- Sources – starting point
- Cost surface – cost per map unit for travel
- Output
- Cost distance – total accumulative least-cost for
each cell to reach a source
- Back link – direction to move from each cell to
reach a source
- Cost allocation – for each cell, which is the least-
cost source
• Cost Path tool
- Input
- Destination – ending point
- Cost distance and Back link output rasters from
Cost Distance tool
- Output
- Least-cost paths – the least-cost paths
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Step 1: How to perform the cost distance analysisThe Cost Distance tool
• Sources
• Cost surface
• Output distance raster – for each cell, the
lowest total accumulative cost to reach a source
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Step 1: How to perform the cost distance analysisThe Cost Distance tool (continued)
• Back link
• Cost allocation
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Step 2: How to create the least-cost pathThe Cost Path as Polyline and Cost Path tools
• Destination and the cost distance and back link output from
the Cost Distance tool
• Creates the least cost path from the destination to the sources
- Best single path
- Each zone
- Each cell
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Cost Distance
Cost Path as Polyline
Creating the least-
cost path
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Cost distance analysis - Outline
• What is cost distance analysis
• Cost Analysis 1 - Cost Connectivity (and creating a cost surface) - Demo
• Cost Analysis 2 - Two step process – Cost Distance and Cost Path - Demo
• Source characteristics - Demo
• Directionality of the movement - Demo
• Incorporating barriers - Demo
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Source characteristics
• Multiplier
- Different modes of travel from each source - an ATV versus walking
- Different magnitudes at each source – number of firefighters at each headquarter
• Start cost
- Time it takes to prepare before leaving the source
a1 = starting_cost + (((cost1 + cost2) / 2) * cost_multiplier)
• Resistance rate
- A hiker getting tired
• Capacity
- Identify potential locations for refueling stations for military tanks
accum_cost = (a1 * (1 + resistance_rate)) + ((((cost2 * HF(2)) + (cost3 * HF(3)))/2) *
Surface_distance(23) * VF(23) * cost_multiplier)
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Source Characteristics
Controlling the
mover
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Cost Connectivity – Neighbor paths and Network Analyst
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Cost distance analysis - Outline
• What is cost distance analysis
• Cost Analysis 1 - Cost Connectivity (and creating a cost surface) - Demo
• Cost Analysis 2 - Two step process – Cost Distance and Cost Path - Demo
• Source characteristics - Demo
• Directionality of the movement - Demo
• Incorporating barriers - Demo
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Adding complexity Adding surface distance with the Path Distance tool
• Actual distance traveled
• Endure the cost longer because going uphill
or downhill
• Surface raster
• The Path Distance tool
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Adding complexityAdding directionality with the Path Distance tool
• Adjustment to overcome going uphill and
downhill
• Vertical factor
- Surface raster endure cost longer
- Vertical factor the additional cost to over come the
slope
• Horizontal factor
- Additional cost to overcome a horizontal factor such
as wind
Accum_cost_distance = a1 + (((Cost_Surface(b) * Horizontal_factor(b)) +
(Cost_surface(c) * Horizontal_factor(c)))/2) * Surface_distance(bc) * Vertical_factor(bc)
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Directionality of the movement
Controlling the
mover
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Cost distance analysis - Outline
• What is cost distance analysis
• Cost Analysis 1 - Cost Connectivity (and creating a cost surface) - Demo
• Cost Analysis 2 - Two step process – Cost Distance and Cost Path - Demo
• Source characteristics - Demo
• Directionality of the movement - Demo
• Incorporating barriers - Demo
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Incorporating barriers in Cost Distance
• Locations that are barriers are set to
NoData in the cost surface through the
Environment mask
• Cost Distance and Backlink are
calculated around the barrier locations
• Cost Path and Cost Path As Polyline
are determined from the Backlink
therefore the paths do not pass
through the barriers
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Incorporating barriers in Euclidean Distance (new capability)
• Barriers are specified by an
input dataset
• Diagonal cracks are resolved
• Distance and Direction rasters
created (0 – 360 not 1 – 8)
• Paths from back direction raster
• Differs from Cost Distance with
constant cost surface
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Euclidean Distance
Incorporating
barriers
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Additional capability
• Distance tools are parallelized and
distributed
• Raster Analytic tools have been created for
the distance tools to work on large data in
the server environment
• Euclidean distance supports both planar and
geodesic calculations
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The road ahead – the near future
• Break from the constraints of processing cell
centers in a lattice
- “Raster is faster but vector more accurate” no
longer true – implement level set methods for
evolving boundaries (costs, fire, water)
• Resulting cost rasters will not have octagon
artifact and back direction 0 – 360 (not 1 – 8)
• Add barriers, address cracks, and implement
geodesic to cost analysis
• Simplify distance analysis
- Distance can now be a matter of whether you
have cost surface or barriers
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Conclusion
• Defining the cost units can be difficult
• Can create the optimum network of paths – Cost Connectivity
- Compatible with Network Analyst
• Two step process – Cost Distance and Cost Path
- When source and destination known
• Source Characteristics
- Difference modes of travel from a source
- Starting costs
- Dynamic adjustment – getting tired
• Directionality – Path Distance
• Barriers can be incorporated in Cost and Euclidean Distance
• Creates the optimum least-cost solution
- Assumes memory
- Has visited all locations
Acknowledgements: The Vermont Center for Geographic Information and British Columbia for the use of their data in this presentation
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Additional resource
• Cost distance analysis case study
http://desktop.arcgis.com/en/analytics/case-studies/understanding-cost-distance-
analysis.htm
• Suitability modeling case study
http://desktop.arcgis.com/en/analytics/case-studies/understanding-the-suitability-
modeling-workflow.htm
• Spatial Analyst Resources
http://esriurl.com/spatialAnalystResources
• We need your feedback, please take the Raster survey
https://www.esri.com/arcgis-blog/products/arcgis-pro/analytics/arcgis-spatial-analyst-
survey/
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