Cost distance analysis is one of the most common applications in Spatial Analyst. Similar to Euclidean tools, which calculate the shortest distance from one location to another, cost distance tools determine shortest weighted distance (or least accumulated travel cost) between two locations. Travel cost is measured in units of cost, such as:

 

• Preference
• Energy expended
• Time
• Dollars
• Risk

 

Cost distance analysis generally consists of two steps:

 

Step 1: Use the Cost Distance tool to calculate least accumulative cost for each cell.

 

Cost Distance has two input

• Sources (starting point)
• Cost surface (cost per map unit)

 

Cost Distance has two 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)

 

Step 2: Use the Cost Path tool to calculate the least-cost path between a source and destination.

 

Cost Path tool has three input

• Destination (ending point)
• Cost distance output raster from Cost Distance tool
• Back link output raster from Cost Distance tool

 

Cost Path tool has one output:

• Least-cost paths (the least cost path)

Creating the Cost Surface

Similar to creating a suitability model, a cost surface model can be thought of as a suitability model that measures cost. Data is transformed onto a common scale then weighted and combined. Each map unit contains a value indicating the cost to move through that cell. Locations with low cost are more suitable, whereas locations with high cost are least suitable. Recall that costs may be measured in:

 

• Preference
• Energy expended
• Time
• Dollars
• Risk

 

Cost distance analysis begins with the Cost Distance tool which requires two inputs: a source and a cost surface (Figure A). Source locations can be raster or feature data.

 

Figure A

 

Once a source has been identified and a cost surface has been created, the Cost Distance tool calculates the least accumulated cost for each cell from the source data set. This is an iterative process that expands outwards from each source (Figure B)

 

Figure B

 

Accumulative cost is determined by adding the cost of one cell to the average of the next two cells (Figure C). Cost of diagonal movement is accounted for by multiplying by the length of the hypotenuse between the cell center and cell corner.

 

Figure C

 

The output cost distance raster is a measure of the least accumulative cost from the source.

In addition to the output cost distance raster, the Cost Distance tool has an option to create an output cost back-link raster. The back-link raster contains values of 0 through 8, which define the direction to the next cell along the least accumulative cost path from a cell to a least cost source. Both the cost distance raster and back-link raster are then used in step two of cost distance analysis.

 

At this point in the workflow, a cost distance and cost back-link have been created. Both raster layers and a destination are required input for the Cost Path tool. Cost Path calculates the least-cost path from the destination to the source(s).

 

Sources and destinations can be connected in one of three ways:

 

Each cell: Least-cost paths are generated for each individual cell in the input destination data.

 

Each zone: For each zone in the input destination data, a least-cost path connecting to the source data is generated.

 

Best single: A sole least-cost path is calculated between input destination data and source data.

 

The Cost Distance/Cost Path workflow can be repeated to create multiple paths.

Cost Distance analysis is often used to create an optimum least-cost solution to an issue through a two-step workflow.

 

Step 1: The Cost Distance tool calculates a cost distance raster and a cost back-link raster from an input source data and input cost surface raster. The backlink raster is used to retrace the least costly route from the destination to the source over the cost distance surface.

 

Step 2: The Cost Path tool determines the least-cost path from a destination point to a source. The output cost distance and cost back-link rasters (from step one) and a specified destination are required input for the Cost Path tool.

 

Below are some items to keep in mind while performing cost distance analysis:

 

• Defining cost units can be difficult.
• Identifying which sources and destinations to connect can be difficult.
• Cost does not account for different modes of travel from a source, starting costs, or dynamic adjustments (such as getting tired).

 

 

Acknowledgements

We thank Steven Lamonde of Johnson State College and the Vermont Center for Geographic Information for their contributions.