Terrain attributes (e.g. slope, rugosity) derived from digital terrain models are commonly used in environmentalstudies. The increasing availability of GIS tools that generate those attributes can lead users toselect a sub-optimal combination of terrain attributes for their applications. Our objectives were toidentify sets of terrain attributes that best capture terrain properties and to assess how they vary withsurface complexity. 230 tools from 11 software packages were used to derive terrain attributes from ninesurfaces of different topographic complexity levels. Covariation and independence of terrain attributeswere explored using three multivariate statistical methods. Distinct groups of correlated terrain attributeswere identified, and their importance in describing a surface varied with surface complexity.Terrain attributes were highly covarying and sometimes ambiguously defined within software documentation.We found that a combination of six to seven particular terrain attributes always capturesmore than 70% of the topographic structure of surfaces.