# Using Tobler's Function Equation in QGIS (Creating Friction Surface)

I'm struggling to get an equation working in QGIS that I've seen posted for ArcGIS. This article has a full description. Long story short, the author modifies the original Tobler's Hiking Function for use in ArcGIS, but it won't work in QGIS Raster Calculator. I've spent a few hours working on this with no luck.

The original formula is as follows:

``````(your_res /1000)/(6 * Exp(-3.5 * Abs(Tan(("your_slope" * 3.14159)/180) + .05)))
``````

"your_res" = resolution/pixel size of DEM (in this case, ASTER) "your_slope" equals slope raster (calculated using Raster -> Analysis -> Slope).

Here's how I modified the equation for QGIS Raster Calculator:

``````(your_res / 1000) / (6 * 2.71828 ^ (-3.5 * abs ( Tan ( ( "your_slope" * 3.14159)/180) + .05)))
``````

The resulting raster returns few values and basically flattens the image out. Only the most severe slope changes show any variation. I don't have ArcGIS at home to test, but that article is fairly well known to archaeologists and I suspect it works.

• Tobler function has maximum at about minus 3 degrees. Your slope raster doesn't have negative values, so it's wrong path. In arcgis it's doable using vertical factor which takes direction into account. Feb 8 at 1:44
• Any ideas on creating a friction raster using this method - this equation - in QGIS?
– user176999
Feb 8 at 2:27
• It is not doable mate, no matter the syntax of your expression. Perhaps read my first comment again or documentation on path distance in ArcGis help Feb 8 at 3:25
• "Load the DEM into the application and make note of its spatial resolution (cell size) by right-clicking on it in the Layers list, selecting Properties, and left-clicking on the Source tab. If the values are significantly smaller than 1.0 (e.g., .00027), the DEM has a Geographic Latitude/Longitude projection. To estimate cell size in meters for this case, a general rule of thumb is to multiply the values by 100,000. " Feb 8 at 6:09