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Here are some other general links regarding Tobler's Hiking Function. Be sure to check out this thread that points out problems with the CostPath function in ArcGIS v10. Reading through this thread, one will find mention of Nico Tripcevich's tutorial on Tobler's Hiking Function. For this lab, we will follow that tutorial. There are several important issues to consider when going through that lab. They are as follows:

  1. When making the SQL queries one will need to replace [] marks with "" marks. The brackets were used in an earlier version of ArcGIS. The quote marks are now used.
  2. Nico's original tutorial calculates distances from ArcID 675. We will use a different ArcID. We will use ArcID 607 as the location for calculating the Isotropic and PathDistance functions.
  3. When performing the Path Distance function, be sure that ArcID 607 was selected.

Data for the project can be downloaded at 2009_View_Cost.zip.

Isotropic Distance

In this part of the exercise, we will assume a walking speed of 4km/hr. This is slightly slower than a commonly assumed walking speed of 5 km/hr, but the terrain in the study area is very rough so a slightly slower travel speed is warranted.

  1. Unzip 2009_View_Cost.zip
  2. Add the following data sources
    1. Sites.shp
    1. hydro_lines100k
    1. cocla_aster
    2. coca_hs
  1. Open the Sites.shp attribute table and select the record that has an ArcID = 607.
  2. Open the Euclidean Distance tool and input the following parameters:
    1. Input Feature: Sites
    2. Output Dist Raster: EucDist_Site1
    3. Output cell size: 30
    4. Leave the other fields blank.
    5. Click Environments> General Settings>set Output Extent to "Same as layer colca_aster".
      1. For v10 click Environments > Processing Extent, and set as the same.
  3. Hit Ok
  4. The output raster is in units of distance, but we are interested in units of time. We will transform the distance raster into a time raster assuming a constant walking speed of 4 km/hr. Nico provides the following handy equation: 15 min / 1000 meters = 1 min / 66.66 meters.
  5. Using the Raster Calculator enter the following equation: EucDist_Site1/66.66
  6. Make the result permanent and remove the temporary calculation raster. Save the result as iso_min.
    1. v10 saves the raster calculation output in the Raster Calculator. 
  7. From here it is possible to generate isochrons, or contour lines of time. We want 15 minute isochrons. Do this using the contour tool and using the value of 15.

Anisotropic Distance

Here we will use a vertical factor table that was generated by Nico based on data published by Tobler and originally reported by Imhoff. Using this table we will implement the famous Tobler's hiking function. This function has been empirically tested in a number of ways. These tests have revealed some limitations, but it is sufficiently well supported to proceed.

  1. Open the Sites.shp attribute table and select the record that has an ArcID = 607. It is important that this site is selected because this becomes the point of origin for the Cost Path calculation.
  2. Open the Path Distance Tool and input the following parameters:
    1. Input: Sites
    2. Output: aniso_hrs1
    3. Input cost:<blank>
    4. Input surface: colca_aster
    5. Output Backlink raster: aniso1_bklk
    6. Open the "Vertical factor parameters" field
    7. Input Vertical Raster: colca_aster
    8. Vertical Factor: Table (it is at the bottom of the drop down list)
    9. browse to find "Tobler_away.txt" on your hard drive
      1. v10 will need to select colca_raster and the input vertical raster.
  3. Click OK
  4. Turn off aniso1_bklk so that aniso_hrs1 is visible.
  5. Note that the raster has values that range from 0-1.74. These are units of hours. To compare with the isotropic raster produced above, it is necessary to convert these into minutes. Use the raster calculator and multiply aniso_hrs1 by 60. Save the result as aniso_min.
  6. Now convert the resulting raster into 15 minute isochrons using the contour tool.
  7. Compare the results from Tobler's method with the results from isotropic distance mapping. It would be useful to use the raster calculator to perform the following calculation: aniso_min - iso_min.
  8. It can be helpful to symbolize the subtraction with a red-blue gradient fill.

Least Cost Paths

  1. Here we want to estimate the least cost paths from four sites (ArcID= 611, 811, 837, 926) to ArcID 607.
  2. Open the Sites.shp attribute table and open the Select by Attributes tool.
  3. In the SELECT * FROM Sites WHERE: window enter the following expression:
    1. "ARCHID" =611 OR "ARCHID" = 811 OR "ARCHID" = 837 OR "ARCHID" = 926
    2. Verify that for records are selected and close the attribute table.
  4. Open the Cost Path tool and enter the following parameters:
    1. Input Feature: Sites
    2. Destination Field: ArchID
    3. Input Cost Distance Raster: aniso_hours (use the hours not the minutes one)
    4. Input Cost Backlink Raster: aniso_bklk
  5. The output is a GRID. Convert this raster to a Polyline using the Raster to Polyline tool with the following parameters
    1. Input Raster: <the name of your cost paths file>
    2. Field: Value
    3. Geometry type: Polyline
  6. Explore the results with the following layers visible:
    1. aniso_minutes_isolines
    2. hydro_lines100k
    3. Sites.shp
    4. cocla_aster
    5. coca_hs

Lastly, given that several users are reporting differences between various versions of ArcGIS 9 and ArcGIS 10, include a screen shot of the Anisotropic cost distance raster and provide the statistics. We will then compare the results between the various versions of ArcGIS that are installed in the lab.

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