Surface texture analysis applied to high-resolution digital terrain models (HRDTMs) is a promising approach for extracting useful fine-scale morphological information. Surface roughness, considered here as a synonym of surface texture, can have a discriminant role in the detection of different geomorphic processes and factors. Very often, the local morphology presents, at different scales, anisotropic characteristics that could be taken into account when calculating or measuring surface roughness. The high morphological detail of HRDTMs permits the description of different aspects of surface roughness, beyond an evaluation limited to isotropic measures of surface roughness. The generalization of the concept of roughness implies the need to refer to a family of specific roughness indices capable of capturing specific multiscale and anisotropic aspects of surface morphology. An interesting set of roughness indices is represented by directional measures of roughness that can be meaningful in the context of analyzed and modeled flow processes. Accordingly, we test the application of a flow-oriented directional measure of roughness based on the geostatistical bivariate index MAD (median of absolute directional differences), which is computed considering surface gravity-driven flow direction. MAD is derived from a modification of a variogram and is specifically designed for the geomorphometric analysis of HRDTMs. The presented approach shows the potential impact of considering directionality in the calculation of roughness indices. The results demonstrate that the use of flow-directional roughness can improve geomorphometric modeling (e.g., sediment connectivity and surface texture modeling) and the interpretation of landscape morphology.