Terrain Ruggedness Index

Draft: written, not yet checked by a person Operation · terrain-ruggedness-index

How much each cell of an elevation raster differs in height from its eight neighbours.

Pitfall. Engines use different formulas under the same name (a square root of summed squares, a mean of absolute differences, a root mean square), which differ by a factor of 2 or more.

Pitfall. Cells on the raster's edge have incomplete neighbourhoods; engines leave them nodata or compute them differently.

About this operation
Also called	TRI, ruggedness index, Riley TRI, gdaldem TRI
Group	`raster/terrain`
Checks	`raster.nodata`
Pitfalls	2 listed above
Columbus tool	Not stated
Notes	Not stated
Status	active
Broader	Not stated
Narrower	Not stated
Related	`topographic-position-index` `roughness` `slope`

Parameters

Name	Type	Required	Default	Values	Note
`algorithm`	enum	no	`riley`	`riley, wilson, rmsd`	riley: square root of the sum of squared differences (Riley and others, 1999); wilson: mean absolute difference (Wilson and others, 2007); rmsd: root mean square difference.

Inputs and outputs

Direction	Name	Type	Geometry	Note
Input	`raster`	raster	Not stated	An elevation model.
Output	`output`	raster	Not stated	Not stated

In each engine

Engine	Tool	Parameters	Differences
`gdal`	`gdal raster tri`	`algorithm` → `algorithm` : riley = Riley; wilson = Wilson. not supported: rmsd `raster` → `input` `output` → `output`	Edge cells are computed from incomplete neighbourhoods unless --no-edges leaves them as nodata.
`postgis-raster`	`st_tri`	`algorithm` always wilson `raster` → `rast`	The mean of the absolute differences from the eight neighbours.
`qgis`	`gdal:triterrainruggednessindex`	`algorithm` always riley `raster` → `INPUT` `output` → `OUTPUT`	Cells on the raster's edge are left as nodata unless edges are computed (COMPUTE_EDGES).
`qgis`	`native:ruggednessindex`	`algorithm` always riley `raster` → `INPUT` `output` → `OUTPUT`	Z_FACTOR scales the elevations first; edge cells are computed from the neighbours that exist.
`terra`	`terra::terrain`	`algorithm` → `v` : riley = TRIriley; wilson = TRI; rmsd = TRIrmsd `raster` → `x`	v = 'TRI' is the mean absolute difference; 'TRIriley' Riley's index; 'TRIrmsd' the root mean square difference.
`whiteboxtools`	`RuggednessIndex`	`algorithm` always rmsd `raster` → `dem` `output` → `output`	Described as Riley's index, but computes the root mean square of the differences from the eight neighbours (Riley's value divided by the square root of 8).