Spatial Analyst – Identifying the Best

Paths with Cost Distance AnalysisKevin M. Johnston

Elizabeth Graham

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

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

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

Why do patches need to be connected?

• Fragmentation Metapopulation

- Logging Roads

- Supply routes for military locations

- Fire fighting routes

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

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

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

Cost analysis 1 – Cost Connectivity

• Input regions

• Input cost

• Create a network of paths

- Output optimum paths

- Optional neighboring paths

Cost Connectivity – Optimum network

C

A

B

Based on cost not Euclidean distance

Creating a cost surface

Cost Connectivity

Creating the

optimum network

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

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

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

Step 1: How to perform the cost distance analysisThe Cost Distance tool (continued)

• Back link

• Cost allocation

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

Cost Distance

Cost Path as Polyline

Creating the least-

cost path

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

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)

Source Characteristics

Controlling the

mover

Cost Connectivity – Neighbor paths and Network Analyst

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

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

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)

Directionality of the movement

Controlling the

mover

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

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

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

Euclidean Distance

Incorporating

barriers

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

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

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

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/

Please Share Your Feedback in the App

Download the Esri

Events app and find

your event

Select the session

you attended

Scroll down to

“Survey”

Log in to access the

survey

Complete the survey

and select “Submit”