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Understanding cost distance analysis

Release 9.2
Last modified May 2, 2007

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"Distance analysis"

Understanding Euclidean distance analysis

Cost Distance algorithm

Least cost path and least cost corridor

Path Distance: adding more cost complexity

An overview of the Distance tools

Cost distance tools calculate for each cell the least accumulative cost to specified source
locations over a cost surface. A source and a cost must be created. Cost distance is the
prerequisite for finding the least cost path or corridor.

Learn how to calculate cost weighted distance, direction, and allocation using the Spatial
Analyst toolbar

Learn how to calculate cost weighted distance using the Cost Distance tool

Learn how to calculate cost weighted direction using the Cost Back Link tool

Learn how to calculate cost weighted allocation using the Cost Allocation tool

Finding the least-cost route for a road using the Cost Distance
function

In the following example, the Cost Distance functions are used to find the
least-cost path for a new road

The Cost Distance function is the prerequisite to the Cost Path function.
The Cost Path function determines the road's actual route.

To calculate the least accumulative cost from each cell to the nearest
source, the Cost Distance function needs a source and a cost raster

The source

The source is the starting point of your proposed feature for analysis. For
example, in the graphic below, you can see the starting point (in red) for the
proposed road.

The cost raster

The cost raster identifies the cost of traveling through each cell

To create this raster, you need

to identify the cost of constructing a road

through each cell

. Although the cost raster is a single dataset,

it is often

used to represent several criteria

In the following example, land use and

slope influence the construction costs. Each of these datasets is in a
different measurement system (land use type and percent slope), so they
cannot be compared to one another and must be reclassified to a
common scale

Creating a cost raster

Reclassifying your datasets to a common scale

In this example, slope and land use have been reclassified on a scale of 1
to 10.

The attributes of each dataset should be examined to determine their
contribution to the cost of building a road.

For example, it is more costly to traverse steep slopes, so steeper slopes
will be assigned higher costs when reclassifying this dataset. The graphics
below display the results.

Weighting datasets according to percent influence

The next step in producing the cost raster is to add the reclassified
datasets together.

The simplest approach is to just add them together.

However, some factors may be more important than others. For instance,
avoiding steep slopes may be twice as important as the land use type, so
you might give this dataset an influence of 66 percent and the land use

dataset an influence of 34 percent (to equal 100 percent). The following
diagram shows the conceptual process:

Combining the datasets

The final cost raster is the result of adding together the weighted datasets.

The following diagram shows the final cost raster, the result of
reclassifying the datasets of slope and land use; weighting each
by 0.66 and 0.34, respectively; then combining the weighted
datasets.

The Cost Distance function

Using the

cost raster

and the

source

, the Cost Distance function

produces

an output raster in which each cell is assigned a value that is the least
accumulative cost of getting back to the source.

Using the previous example, this function takes the cost raster and
calculates a value for each cell in the output cost-weighted raster that is
the accumulated least cost of getting from that cell to the nearest source.

Every cell in the cost-weighted raster is assigned a value representing the
sum of the minimum travel costs that would be incurred by traveling
back along the least-cost path to its nearest source.

In the example below, the accumulated least costly way of getting from
the cell colored dark orange to the school is 10.5.

Direction

The cost distance raster tells you the least accumulated cost of getting
from each cell to the nearest source, but it doesn't tell you how to get
there. The direction raster provides a road map, identifying the route to

take from any cell, along the least-cost path, back to the nearest source.

The algorithm for computing the direction raster assigns a code to each
cell that identifies which one of its neighboring cells is on the least-cost
path back to the nearest source

In the direction coding diagram above, 0 represents each processing cell in
the accumulative cost raster. Each cell is assigned a value representing the
direction of the nearest, cheapest cell on the route of the least costly path to
the nearest source.

For example, in the graphic above, the cheapest way to get from the cell
with a value of 10.5 to the source (the school site) is to go diagonally,
through the cell with a value of 5.7

The direction algorithm assigns a value of 4 to the cell with a value of 10.5,
and 4 to the cell with a value of 5.7, because (from the directional coding
described above) this is the direction of the least-cost path back to the source
from each of these cells. This process is done for all cells in the cost distance
raster, producing the direction raster, which tells you the direction to travel
from every cell in the cost distance raster back to the source.

Both the cost distance and direction rasters are

required if you want to

calculate the least-cost (shortest) path

between source locations and

destination locations.

Allocation

The cost allocation raster identifies the nearest source from each cell in
the cost distance raster. It is conceptually similar to the Euclidean