Topographic Ruggedness Index

Topographic Ruggedness Index (TRI)

General discussion of Roughness

The topographic ruggedness index (TRI) was developed by Riley et al. (1999) to express the amount of elevation difference between adjacent cells of a DEM. It calculates the difference in elevation values from a center cell and the eight cells immediately surrounding it. Then it squares each of the eight elevation difference values to make them all positive, sums them, and takes the square root.

Riley, S. J., S. D. DeGloria and R. Elliot (1999). A terrain ruggedness index that quantifies topographic heterogeneity, Intermountain Journal of Sciences, vol. 5, No. 1-4, pp.23-27.
Wilson et al 2007, Marine Geodesy 30:3-35: difference between a central cell and the mean of its eight neighbors

GDAL recommends the Riley method for terrestrial cases, and Wilson for bathymetric.

Can be done:

Using MICRODEM, with TPI and TRI both computed at the same time (Raster GIS, Create derivative grid). There are a number of ways to normalize distances, for the diagonals and geographic grids with dx and dy different. The improved SSR is a significant improvement.
Using GDAL, (Raster GIS, External tools) where there are 3 options
Using GRASS (Raster GIS, External tools) which has options for both TPI and TRI
Using SAGA
Using Whitebox Tools

Comparison of TRI with Various Programs

Improved parmeter SSR: Sebastiano Trevisani, Giordano Teza, & Peter L. Guth. (2023). Hacking the topographic ruggedness index. https://doi.org/10.5281/zenodo.7716785

See Rugosity, TPI,

Last revision 3/5/2023