# Connect locations with corridors

Connecting locations with a path in the most optimal way can be done using the Optimal Region Connections, Optimal Path As Line, and Optimal Path As Raster tools. However, you may want a result that is not limited to a narrow polyline or a one-cell wide path. You want a wider, two-dimensional area where the total cost of travel between locations is less than a particular threshold. This area is called a corridor.

It is possible to produce an area by buffering out an optimal path by a fixed distance. However, this approach may not properly capture what is important to the traveler. For example, a simple buffer around an optimal path might include an industrial park, which would not be suitable to include if you are planning a wildlife corridor. The width of the corridor that will connect the locations should be able to vary in accordance with the rate the actual accumulated cost varies from cell to cell between the locations. Since the industrial park would be a high cost for wildlife, that area would not be included in the corridor.

The corridor encompasses all the possible cost paths that are less than the specified accumulative cost. The Corridor tool calculates the sum of accumulated cost created between the sources. From that result, select the cells with values less than the cost threshold to define the corridor.

## Corridor application examples

Corridors can be used to solve analysis for various scenarios, such as the following:

• In a deer conservation plan, connect two patches of deer habitat with the optimal corridor.
• Identify the possible route for a proposed underground pipeline.
• Determine the feasible area that a proposed bike trail must stay within when connecting two parks.

## Corridor analysis

Distance analysis can be divided conceptually into the following related functional areas:

From the third functional area, locations are connected with corridors as illustrated in the examples below.

There is a bear population in a newly established park (light green polygon) and a second population in the surrounding area around one of the four ranger stations (the yellow point). A corridor will allow the bears to move between the two locations.

From the corridor map, a threshold is specified to define the width of the corridor.

## Create a corridor

The general process to identify a corridor between two sources is as follows:

• Calculate the accumulated distance from the first source location to every other cell in the study area.
• Calculate the accumulated distance from the second source location to every other cell in the study area.
• Calculate the sum of the accumulated distance between the two sources for each cell.
• Identify the cells whose total accumulated distance between the two sources falls within a defined threshold

To create a corridor result, complete the following steps:

Calculate the distance accumulation for the first source.

1. Open the Distance Accumulation tool.
2. Provide the first location to connect as a source (Source A) in the Input raster or feature source data parameter.
3. Name the output distance raster for Source A.
4. Identify the cost raster in the Input cost raster parameter.

The direction of the traveler cannot be incorporated in a corridor. Consequently, do not specify a vertical factor, a horizontal factor, or a value for the Travel Direction source characteristic parameter.

5. Click Run.
6. Calculate the distance accumulation for the second source.
7. Open the Distance Accumulation tool.
8. Provide the second location to connect as a source (Source B) in the Input raster or feature source data parameter.
9. Name the output distance raster for Source B.
10. Specify the same parameters as you did in step 4.
11. Click Run.
12. Calculate the sum of accumulative costs for the two sources.
13. Open the Corridor tool.
14. Identify the output for the first location (Source A) that was created in step 5 as the Input cost distance raster 1 parameter value.
15. Identify the output for the second location (Source B) that was created in step 10 as the Input cost distance raster 2 parameter value.
16. Name the output corridor raster
17. Click Run.
18. Select the cells whose sum accumulative cost falls under a defined threshold.
19. Open the Raster Calculator, the Extract by Attributes, or the Con tool.
20. Use the output raster created by the Corridor tool in step 15 as input.
21. Specify the threshold value.
22. Name the output raster.
23. Click Run.

## Connect locations with least-cost corridors

A corridor defines the least-cost geographic area that connects two source locations. It contains all nondirectional cost paths between the sources that are less than a specified accumulative cost. The corridor and paths within it are nondirectional because it does not matter which way you are traveling between the sources.

### Corridor creation process

To create a corridor raster, you need two datasets: one that defines the first set of source locations, and another that defines the second set of locations. You'll use the Distance Accumulation tool to create an accumulated cost raster for the first set of sources. Then use the same tool to create an accumulated cost raster for the second set of locations. Use these two results as input to the Corridor tool, which creates a sum of accumulated cost between the two sources. The last step is to identify an acceptable threshold and to select only those cells that fall within that threshold to create the final corridor raster result.

#### Corridor directionality and threshold

Corridors are nondirectional and moving from one source to the other has the same cost as moving from the second source back to the first. However, it is important to use the same settings for both runs of the Distance Accumulation tool.

You can use a cost surface and a surface raster to increase the level of complexity in how the distance is being modeled. You cannot, however, use a vertical factor, a horizontal factor, or the travel direction source characteristic since these parameters depend on the directionality of the movement.

The image below shows an example of a corridor that was created for a proposed powerline project. The only criteria for assessing cost for the corridor is the land acquisition cost. The final corridor (light red) contains all paths that are at most 10 percent more expensive than the least-cost path, which is also shown (dark red line). The width of the corridor varies along its length, and the corridor diverges noticeably in spots. This result is different than it would be if a fixed width buffer was generated around the least cost path.

If you select all cells with a total accumulative cost that are at most 10 percent greater than the least-cost path, the result can be considered a 10 percent cost corridor.

#### Corridor width

Narrow sections of a corridor typically identify areas where the corridor is most sensitive to the costs and there are fewer options for routes through those sections. In the powerline case, the narrower sections of the corridor may be the locations that should be purchased first because there is less latitude where powerlines can be placed in that section of the corridor. These areas are the most critical locations in the corridor.

When siting wildlife corridors, the narrow sections of the corridor might be where the animals are at most risk when they are moving through the landscape. These narrow areas may be the most important to preserve because wildlife will have fewer options when moving through them.

Another way to visualize the significance of corridor width is to think of a river moving through a valley. Where the valley is wide and flat, there may be many options for the river to pass through that section (taking the least resistance). During a flood, the river can overflow it banks and widen and even follow a different path. However, where the valley narrows into a canyon and has steep walls on both sides, there are few opportunities for the river to change course. The costs surrounding the narrow sections of the canyon can be considered as being much higher. See the Additional information section below for a visual illustration of this concept. In the visualization, the least-cost path is the river and the various cost thresholds are the contour lines.

#### Appropriate threshold

The threshold is dependent on the units of the cost surface. Cost in dollars is one of the easier units to define. For a wildlife corridor, however, if the cost units are preference, a threshold may be more challenging to determine. Associating a biologic threshold to subjective preference cost units will be more difficult to justify.

In this type of case, several thresholds are tried until the appropriate widths are obtained. Ideally, the specified threshold will be driven by objective measures.

#### Islands in the corridor

Depending on the specified threshold, islands can be created in the resulting corridor in areas where the corridor diverges and is not contiguous, such as in the powerline corridor example above. The island cells have higher accumulative costs, and the corridor will navigate around them.

#### Multiple source locations

The number of unique sources that can be used to create the input accumulative cost rasters is not limited to one. Multiple sources can be input to the Distance Accumulation tool. Depending on the accumulative-cost values between the sources and the specified threshold, multiple corridors can be produced between the sources, instead of one single corridor.

### Calculate corridors on a per-cell basis

The following diagrams show how a corridor is created for a single cell location. This process occurs for each cell in the input rasters, but for demonstration purposes, one cell will be shown.

To create a corridor, two cost accumulative rasters must be created using the Distance Accumulation tool: one from source A and one from source B.

The Corridor tool then adds the two accumulative cost surfaces together.

The output raster does not define a single least-cost path between the two sources; it identifies the range of accumulative costs between the sources. That is, the least accumulative cost to reach source A, plus the least accumulative cost to reach source B, equals the total accumulative cost of a path passing through a cell. It is the least accumulative cost if a path is routed through the cell between source A and source B.

A threshold is then specified to define the width of the corridor.

All cells with accumulative cost values that are less than the specified threshold are selected from the raster to create a corridor. Once the threshold is applied, the resultant output can be considered the least-cost corridor of cells, not the least-cost path (a single line).

### Interpret corridors

The width of a corridor can vary significantly along its length. It is not a fixed distance buffer around a least-cost path. You can define a minimum required width and determine if a set of least-cost paths forms an acceptable corridor.

Another way to think about a corridor is that it shows the uncertainty in the location of a least-cost path. The 10 percent corridor around a given least-cost path is a good visual summary of all paths that are no more than 10 percent more costly than the least-cost path.

A corridor can show where the least-cost path is sensitive to changes in its location. In the powerline example above, the wider area at the top of the corridor is on less expensive land, so there are more options for changing the path’s location in that area without significantly impacting its cost. In contrast, in the narrow middle section of the corridor, the alternative least-cost paths are spatially constricted with few options.

The following sections provide additional information regarding connecting locations with corridors.

### Alternative tools for defining the corridor threshold

There are several tools you can use to specify a threshold that defines the width of a corridor using conditional clauses. Three are described below. A threshold of 100 accumulative cost is used.

#### Con tool

Use the Con tool (from the Conditional toolset) with the following settings:

1. Open the Con tool.
2. Provide the output from the Corridor tool as the Input conditional raster parameter.
3. Build the statement "Value < 100" in the Expression parameter.
4. Specify 100 as the Input true raster or constant value parameter value.
5. Leave the Input false raster or constant value parameter empty.
6. Name the output raster.
7. Click Run.

#### Extract By Attributes tool

Use the Extract by Attributes tool with the following settings:

1. Open the Extract By Attributes tool.
2. Provide the output from the Corridor tool as the Input raster parameter value.
3. Build the "Value < 100" in the Where clause parameter.
4. Name the output raster.
5. Click Run.

#### Test tool

Use the Test tool with the following settings:

1. Open the Test tool.
2. Provide the output from the Corridor tool as the Input raster parameter value.
3. Build the statement "Value < 100" in the Where clause parameter.
4. Name the output raster.
5. Click Run.

### Understand corridors

To understand why adding the two distance accumulation rasters and setting a threshold creates a corridor, start with the simplest geometric case. A straight line is the least-cost path between two points in the plane. If point C is on that line, then AC + CB = AB. Using the corridor terminology, the sum of the accumulative costs from C to A and from C to B is constant and is also the minimum (the length of the line AB). As a result, a straight line is the 0 percent corridor between A and B. This is also another way of creating least-cost paths, one where you don’t need a back-direction raster.

If C is moved off the line (away from the least-cost path), AC is the new least-cost path from C to A and CB is the least cost path from C to B. As a result, AC + CB > AB. All points with that same summed cost form an ellipse around the original least-cost path. All least-cost paths connecting C to A and B are contained in the corridor. In corridor terminology, an ellipse is the x percent corridor around the least cost path. As with the powerline example, at the start of the corridor, a least-cost corridor around a least-cost path is different than a fixed width buffer around that path.

These facts are also true when dealing with more general least cost paths. The 0 percent corridor is identical to the least-cost path and higher threshold corridors form contour loops that contain all cells and all paths in that corridor.

If the direction of motion is not important in your least-cost path analysis, you can use corridors to visualize the uncertainty in the least-cost path or all the locations where alterative nondirectional paths could be located that are within an acceptable cost threshold around the least-cost path.

### Visualize corridors

You can gain insight and perspective when viewing corridors in 3D. The least-cost path becomes the relatively level floor of a canyon constructed from the summed accumulative cost input surfaces and the various x percent corridors form contour lines on the canyon walls. From any point on a canyon wall, you must head downhill to get to a source, which means you need to stay below the contour line that indicates you are within that percent’s corridor.

The wider sections of the corridor in the powerline example are contained in the wider, flatter bowl in the image above. If you are willing to spend additional accumulative cost, you can increase the threshold. The wider bowls are where you gain more options for routing the path since the width of the corridor increases significantly. The canyon walls show where that investment will be less successful.