# Creating a Topographic Roughness Index for Pennsylvania

In the development of some data layers for a species distribution modeling project, I determined that one of the environmental drivers we might want to use was a measure of Topographic roughness. The topographic ruggedness index (TRI) appears to have been developed by Riley et al. (1999) to express the amount of elevation difference between adjacent cells of a digital elevation grid.

An excellent post by user ‘whuber’ gives a good workflow for creating a TRI:

Compute s = Focal sum (over 3 x 3 square neighborhoods) of [DEM]. Compute DEM2 = [DEM]*[DEM]. Compute t = Focal sum (over 3 x 3 square neighborhoods) of [DEM2]. Compute r2 = [t] + 9*[DEM2] - 2*[DEM]*[s]. Return r = Sqrt([r2]).

Using this as a guide, I created the a TRI layer in ArcGIS using these steps.

So starting with the standard 30-meter USGS DEM (we’ll call this layer “[DEM]”), we calculate the focal sum (over 3 x 3 square neighborhoods) of [DEM] using the Focal Statistics Tool in ArcGIS.

Next we’ll calculate the square of the DEM, naming it “[DEM2]” using the Square Tool in ArcGIS.

Next we calculate “t” which is the focal sum (over 3 x 3 square neighborhoods) of [DEM2].

I was half tempted to stop here as the map appeared to represent what I was going after for this particular species. But we had to complete the analysis, so we used Raster Calculator to compute r2 which is equal to the [t] + 9*[DEM2] – 2*[DEM]*[s]. Then we just take the square root of r2 and get this map, which represents topographic roughness for the state:

The darker the color, the more rough the area is. This appears to be true in the deep valleys section of northcentral PA, as well as the ridge and valley and lots of the Waynesburg Hills in the SW corner.

Although, we have a high resolution LiDAR-derived DEM for the state, this TRI developed from the 30-m dataset should be good enough for our needs, as the error in the DEM should be negligible especially given the modeling environment. Still, it would be fun to run at the finer scale.