# Digital Terrain Analysis - Roughness Index [closed]

Currently I am working on a project dealing with terrain analysis based on a DEM. I came across the term "roughness index" using slope values from that specific DEM. On YouTube I found a video, which showed how to do it in ArcGIS using Focal Statistics:

1. Creating a slope map based on the DEM.
2. Using focal statistics to calculate mean, min and max within a 3x3 cell raster for the whole DEM.
3. Using raster caclulator with this expression:

``````(mean_elevation - min_elevation) / (max_elevation - min_elevation)
``````
4. The outcome is called Surface roughness index.

I don't understand why this formula is used.

Why do I have to subtract the minimum elevation from the mean and divide this by the minimum elevation subtracted from the maximum?

Has anyone another (scientific) reference for working with roughness values as standard deviations of slopes?

## closed as too broad by PolyGeo♦Jul 22 at 19:44

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• As per the Tour there should be only one question asked per question. Questions are more focused when only one of two software options are asked about in the same question. – PolyGeo Jul 22 at 19:48

If you look at the Raster > Analysis > Roughness index in QGIS 3.0, you will see the following (source https://docs.qgis.org/3.4/en/docs/user_manual/processing_algs/gdal/rasteranalysis.html#gdalroughness )

Outputs a single-band raster with values computed from the elevation. Roughness is the degree of irregularity of the surface. It’s calculated by the largest inter-cell difference of a central pixel and its surrounding cell. The determination of the roughness plays a role in the analysis of terrain elevation data, it’s useful for calculations of the river morphology, in climatology and physical geography in general.

This algorithm is derived from the GDAL DEM utility .

From GDAL DEM (https://gdal.org/programs/gdaldem.html):

TRI

This command outputs a single-band raster with values computed from the elevation. TRI stands for Terrain Ruggedness Index, which is defined as the mean difference between a central pixel and its surrounding cells (see Wilson et al 2007, Marine Geodesy 30:3-35).

...

roughness

This command outputs a single-band raster with values computed from the elevation. Roughness is the largest inter-cell difference of a central pixel and its surrounding cell, as defined in Wilson et al (2007, Marine Geodesy 30:3-35)