Terrain (DEM)

TRI: Putting a Number on How Rugged the Terrain Is

Concept article · Updated · by Dr. Anant Kumar Pathak

Some ground is billiard-table smooth; some is a chaos of gullies and crags. The Terrain Ruggedness Index compresses that difference into a single value by measuring how much elevation jumps around each pixel.

How it reads the surface

TRI sums the elevation differences between a cell and its neighbours (Riley's formulation uses the square root of the summed squared differences). Level ground scores near zero; broken, dissected terrain scores high. It quantifies local heterogeneity rather than steepness itself.

The math behind it

TRI = √( Σ (Zi − Zcell)² ) over the neighbouring cells

How to interpret the output

Typical range: 0 upward (higher = rougher)

Near 0 = level ground · increasing values = progressively more rugged, dissected terrain.

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The data it needs

Derived fromDigital Elevation Model (SRTM / Copernicus, 30 m) — not an optical band index.

Real-world use

It is applied in wildlife-habitat modelling (ruggedness as refuge or barrier), military and access analysis, and geomorphological characterisation.

Watch out for

Confounds true roughness with DEM noise and, like TPI, depends on the window size.

TRI cannot tell true roughness from DEM noise, and like TPI it depends on window size — a jittery DEM will read as "rugged". Smooth or quality-check the DEM first if ruggedness is your headline result.

Compute TRI on your own study area

Skip the code. Draw or upload a boundary and Spatial Research Suite runs TRI on live data — with cloud masking, exports and citations built in.

Run this analysis in GISforus →

Frequently asked

What is the difference between TRI and slope?

Slope measures the overall gradient; TRI measures local variability — how much neighbouring elevations differ — so a uniform steep slope can be steep but not rugged.

Does DEM noise inflate TRI?

Yes — random elevation error reads as roughness, so noisy DEMs overstate ruggedness; clean the data first.

Primary reference: Riley, S.J., DeGloria, S.D. & Elliott, R. (1999). A terrain ruggedness index that quantifies topographic heterogeneity. Intermountain Journal of Sciences 5(1–4), 23–27.