Terrain complexity index: a novel metric for estimating multiscale three-dimensional terrain structure of montane areas based on digital elevation model

Terrain complexity for describing the heterogenicity of terrains plays a key role in many disciplines, including geographic information science, atmospheric boundary layer meteorology, and ecology. However, due to the intrinsic relationships between terrain structure and the size or scale of the terrains, quantifying the terrain complexity faces the challenges in adequately capturing the intricate three-dimensional and multiscale features. Here, we developed a novel terrain complexity index ( TCI ) based on digital elevation models (DEMs), integrating fractal dimension ( D f ), entropy of terrain elements ( H ), rugosity ( R ), volume filling ratio ( V ), and slope ( α ) as T C I = ( D f + sin α ) H − 1 / R + V . The results showed a substantial variability in D f , H , R , and V with elevations and terrain unit sizes, which was related to feature specific and scale dependent. The terrain features ( D f , H , R , and V ) increased with the terrain unit size and tended to approach a constant value as the terrain unit size grew larger. It was found that the minimum terrain unit size for these terrain features increased with decreasing DEM resolutions (from 0.5 m to 120 m, ten levels), being well expressed as a power function of the DEM resolution ( R 2 ≥ 0.97). The minimum terrain unit size was uniquely determined using the change point detection. For example, the minimum terrain unit sizes were 140 m × 140 m and 7.56 km × 7.56 km at 0.5 m and 120 m DEM resolutions, respectively. These terrain features, based on the 30 m resolution DEM, explained 7–21 % of the variance in annual soil water erosion (ASWE) and 9–24 % of vascular plant diversity. The TCI exhibited superior predictive capabilities, outperforming individual terrain features by 2–10 % for both ASWE and vascular plant diversity. Our TCI emerges as an effective metric for quantifying the intricate three-dimensional structures of mountainous terrains, providing new insights into its influence on mountainous ecosystem structure and function. • Terrain complexity index integrates multiple terrain features. • Terrain features stabilize with increasing size, defining practical terrain structure thresholds. • Minimum terrain size scales power-law with DEM resolution. • Terrain complexity index outperforms single metrics in ecological predictions.