I have used the TRI (Terrain Ruggedness Index) function in QGIS>Raster>Analysis to develop TRI maps (see below). The maps are useful, but I am also trying to determine a single TRI value for the entire area covered by the DEM.

How can I do this?


  • 1
    Like an average value? Commented Jan 30, 2020 at 23:14
  • Given the range of potential TRI values in a dissected landscape a summary value would make very little sence and be very unstable across aggregations. It is unlikely that the underlying distribution would be normal so, the mean would not be representative of the central tendency. Commented Sep 24, 2020 at 23:48

2 Answers 2


TRI algorithm was made according to this science paper "Riley, S.J., De Gloria, S.D., Elliot, R. (1999): A Terrain Ruggedness that Quantifies Topographic Heterogeneity. Intermountain Journal of Science". First, you have to know which pixel size you have? If your pixel size 20x20 then you have some calculations. TRI Riley classification is based on 1km x 1km pixel size, and you have to customize your map. In SAGA GIS terrain ruggedness index algorithm, you should use "Search Radius = 25" (1000/20 = 50 = edge length; because a radius is: 50/2 = 25). (Better results are obtained with SAGA GIS software). After that, you have to convert Riley classification to yours. Each class, you should to reclassify like this: First class according to Riley is 0-80, and you should use calculation (80:1000=x:20), you will get 1,6 value which is discribed as "Level", and second is 2,32 ="Nearly Level" ect...

  • You have some mis-information here. The original approach collected observations from contours off of a paper topographic map for elk habitat modeling, then they released the 1999 paper. Then it was implemented in Workstation Arc/Info (AML) using sum of the squared deviations with in a 3 x3 window. I am the one that wrote the original AML so, there is some familiarity here. The TRI was not based on a 1km cell size and, in fact, is scale invariant. The classification ranges are from a 2001 USFS-RMRS technical report. Commented Sep 24, 2020 at 23:41
  • @Jeffrey Evans would you mind sharing the full citation for the 2001 paper? Thanks. Commented Sep 25, 2020 at 4:39
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    @DeccanTrap I will have to dig the GTR up but, it is the same author and quite similar to: Blaszczynski, J.S., (1997) Landform characterization with Geographic Information Systems. Photogrammetric Engineering and Remote Sensing, 63(2):183-191 In this paper Jacek defines landforms using a rule-based system but does also proposes breaks based on elevational deviations (eg., 240-497 moderately, 498-958 is highly, 959-5000 is extremely rugged). So, since it is not grey literature this is the more appropriate reference. Commented Sep 25, 2020 at 14:48

The answer to my question was to run Zonal Statistics for mean TRI. That would allow me to report a mean value for the entire sampled area.

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