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 and corridor analysis

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 and corridor analysis

The problem

• Have series of locations

- Habitat patches

- Firefighting headquarters

- Military installations

• Suitability model using Locate

Regions tool or known locations

• Need to connect them the most

effective way possible

• Cost distance analysis

Need a cost surface for movement

• Create a surface identifying the cost

to move through each cell location

• Similar to creating a suitability model

• Cost per map unit to move through

the cell

• The lower the cost the better

• Diagonal movement accounted for

How to create cost surface

• 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

• 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

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

Cost analysis 1 – Cost Connectivity

• Input regions

• Input cost

• Create a network of paths

- Output optimum paths

- Optional neighboring paths

Cost Connectivity – Optimum network

• Cost allocation identifies regions to

connect

• Cost path connects neighbors

- Base on cost not Euclidean distance

• Convert to graph theory

- Nodes – the regions

- Edges – the paths

- Weights – accumulative cost

• Maps back to paths

C

A

B

Cost Connectivity – Optimum network

DemoCreating the optimum network

Creating a cost surface

Cost Connectivity

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 and corridor analysis

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

Use cases for two-step process

• Know the specific start and end locations

• Have two locations to connect

• Add a path to the Cost Connectivity

network

• Connect location to several other locations

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

DemoCreating the least-cost path

Cost Distance

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 and corridor analysis

How cost distance analysis works

accum_cost = a1 + (cost2 + cost3)/2

Where

a1—The accumulative cost from cell 1 to cell 2

cost2—The cost of travel for cell 2

cost3—The cost of travel for cell 3

accum_cost—The accumulative cost to move into cell 3 from cell 1

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

DemoControlling the mover

Source Characteristics

Network Analyst

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 and corridor analysis

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

• Cost adjustment to overcome going

uphill and downhill

• Vertical factor

- Surface raster endure cost longer

- Vertical factor the additional cost to over

come the slope

Adding complexityAdding directionality with the Path Distance tool

• 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)

Creating a cost corridorThe Corridor tool

• Cost distance from source one

• Cost distance from source two

• Combine in the corridor tool

• Extract by Attribute tool to identify acceptable

threshold

Additional resource

• Two case studies in the Find locations section of the case studies in the online help

• Cost distance analysis

http://desktop.arcgis.com/en/analytics/case-studies/understanding-cost-distance-

analysis.htm

• Case study with 4 lessons with data (ArcGIS desktop and Pro

- Lesson 1: Creating a cost surface

- Lesson 2: Creating an optimal connectivity network

- Lesson 3: Creating a least cost path

- Lesson 4: Creating a corridor

Additional resource

• Suitability modeling:

http://desktop.arcgis.com/en/analytics/case-studies/understanding-the-suitability-modeling-

workflow.htm

• Case study and 4 lessons with data

- Lesson 1: Exploring and deriving data

- Lesson 2: Transforming data onto a common scale

- Lesson 3: Weighting and Combining Data

- Lesson 4: Locating and connecting regions

DemoDirectionality

Path Distance

Case studies and lessons

Cost distance analysis

Suitability modeling

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

Other Spatial Analyst sessions

• Spatial Analyst: An Introduction

- Tues 10:15 – 11:30

- Wed 10:15 – 11:30

• Finding the Best Locations Using Suitability Modeling

- Tues 1:30 – 2:45

- Thurs 8:30 – 9:45

• Identifying the Best Paths with Cost Distance

- Tues 3:15 – 4:30

- Wed 1:30 – 2:45

• Suitability Modeling and Cost Distance Analysis Integrated Workflow (Demo Theater)

- Wed 4:30 – 5:15

• Python: Raster Analysis

- Tues 8:30 – 9:45

• Getting Started With Map Algebra Using the Raster Calculator and Python (Demo

Theater)

- Thurs 9:30 – 10:159

Other Spatial Analyst sessions

• Modeling Renewable Energy Potential Using ArcGIS (Demo Theater)

- Tues 1:30 – 2:15

• Creating Watersheds and Stream Networks

- Wed 10:00 – 10:30

• Hydrologic and Hydraulic Modeling

- Wed 3:15 – 4:30

- Thurs 1:30 – 2:45

• GIS Techniques for Floodplain Delineation (Demo Theater)

- Tues 12:30 – 1:15

• Creating a Hydrologically Conditioned DEM (Demo Theater)

- Tues 10:30 – 11:15

• Creating Surfaces from Various Data Sources

- Tues 3:15 – 4:30

- Thurs 3:15 – 4:30

• Choosing the Best Kriging Model for Your Data (Demo Theater)

- Wed 11:30 – 12:15

Other Spatial Analyst sessions

• Surface Interpolation in ArcGIS (Demo Theater)

- Thurs 10:30 – 11:15

• Creating Watersheds and Stream Networks (Demo Theater)

- Wed 10:00 – 10:30

• Working with Elevation Services (Demo Theater)

- Tues 10:30 – 11:15

- Wed 9:30 – 10:15

• Building Python Raster Functions (Demo Theater)

- Tues 10:30 – 11:15

• Raster Analytics in Image Server: An Introduction

- Wed 3:15 – 4:30

• Raster Classification with ArcGIS Desktop (Demo Theater)

- Thurs 9:30 – 10:15

• Raster Function Processing (Demo Theater)

- Thurs 10:30 – 11:15

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