Computation window for Terrain Ruggedness Index values

The ruggedness measures introduced here are based on the Terrain Ruggedness Index (TRI) developed by Riley et al. (A Terrain Ruggedness Index that Quantifies Topographic Heterogeneity (1999)). The TRI is calculated using data from a digital elevation model (DEM), a detailed representation of the Earth’s terrain at the scale of small, regularly spaced grid cells. A TRI value is computed for each grid cell by calculating "the sum change in elevation between [the given] grid cell and its eight neighbor cells," as illustrated. Lower values indicate less change in elevation within the 3-by-3 cell neighborhood, and higher values indicate areas with higher elevation differences. Two sets of TRI values were calculated, one including all territory (the Area TRI) and one including just those grid cells containing roads (the Road TRI). For the Area TRI, ruggedness values were calculated for all 255 million grid cells covering the United States. For the Roads TRI, ruggedness was measured using elevation data from the 44 million grid cells containing roads. Whereas the Area TRI value for a given grid cell was derived from a comparison with all eight neighbors (except on the edges of the grid), Road TRI values did not include values from a neighboring grid if that neighbor did not contain a road. We used all streets within the computation window, including highways, arterial, collector, local, and semi-private roads, when calculating the Road TRI, whether they intersect or not.