With the increasing accessibility of terrestrial light detection and ranging scanners (LiDAR), generating tools to elicit meaningful information from high-density point cloud data has become of paramount importance. Surface roughness is one metric that has gained popularity, largely due to the accuracy and density of LiDAR-derived point cloud data. Surface roughness is typically defined as a spread of point distances from a reference datum, the standard deviation of point distances from a model surface being a commonly employed model. Unfortunately, a recent literature review has found that existing surface roughness models are far from standardized and may be prone to error resulting from underlying surface topography. In the research presented here, we develop a surface roughness model that is robust to underlying topographic variability by segmenting the point cloud with a three-dimensional regular grid, establishing local (grid cell) reference planes by orthogonal distance regression, and estimating the surface roughness of each grid cell as the standard deviation of orthogonal point-to-plane distances. This surface roughness model is employed to identify fracture and rubble zone distributions within a terrestrial LiDAR scan from a basalt outcrop in southeast Idaho, and the results are compared to a more common model based on ordinary least-squares plane fitting. Results indicate that the orthogonal regression model is robust to outcrop orientation and that the ordinary least-squares model systematically overestimates surface roughness by contaminating estimates with spatially correlated errors that increase with decreasing grid size.