Spatial Analyst – Identifying the Best

Paths with Cost Distance AnalysisKevin M. Johnston

Elizabeth Graham

Cost distance analysis - Outline

• What is cost distance analysis

• Creating a cost surface

• Cost Analysis 1

- Cost Connectivity

• Demo

• Cost Analysis 2

- Two step process – Cost Distance and Cost Path

• Demo

• Source characteristics and Network Analyst

• Demo

• Adding complexity

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

• Creating a cost surface

• Cost Analysis 1

- Cost Connectivity

• Demo

• Cost Analysis 2

- Two step process – Cost Distance and Cost Path

• Demo

• Source characteristics and Network Analyst

• Demo

• Adding complexity

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

• Creating a cost surface

• Cost Analysis 1

- Cost Connectivity

• Demo

• Cost Analysis 2

- Two step process – Cost Distance and Cost Path

• Demo

• Source characteristics and Network Analyst

• Demo

• Adding complexity

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 tool

• 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

Creating the least-

cost path

Cost distance analysis - Outline

• What is cost distance analysis

• Creating a cost surface

• Cost Analysis 1

- Cost Connectivity

• Demo

• Cost Analysis 2

- Two step process – Cost Distance and Cost Path

• Demo

• Source characteristics and Network Analyst

• Demo

• Adding complexity

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 (cont.)

• Travel direction (From source and To source)

- Bobcat, for security, prefer locations away from roads

- Bobcat prefer locations that are easiest to access streams

Travel from source

a5 = c1 + c2 (1+r) + c3 (1+r)2 + c4(1+r)3 + c5(1+r)4

Where

a5—The least accumulative cost for the first five cells

ci—The cell identifier

r—The resistance rate

Travel to source

a5 = c1 (1+r)4 + c2 (1+r)3 + c3 (1+r)2 + c4 (1+r) + c5

Cost Connectivity – Neighbor paths and Network Analyst

Source Characteristics

Network Analyst

Controlling the

mover

Cost distance analysis - Outline

• What is cost distance analysis

• Creating a cost surface

• Cost Analysis 1

- Cost Connectivity

• Demo

• Cost Analysis 2

- Two step process – Cost Distance and Cost Path

• Demo

• Source characteristics and Network Analyst

• Demo

• Adding complexity

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)

Path Distance

Case studies and lessons

Cost distance analysis

Suitability modeling

Directionality

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

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

• Creates the optimum least-cost solution

- Assumes memory

- Has visited all locations

Acknowledgements: The Vermont Center for Geographic Information 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

https://www.esri.com/arcgis-blog/products/arcgis-pro/analytics/spatial-analyst-

resources/

• Raster Analysis and Spatial Analyst Sessions at UC 2018

https://www.esri.com/arcgis-blog/products/spatial-analyst/announcements/uc2018-

spatial-analyst-raster-analysis/

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