Surface Roughness in Geomorphometry: From Basic Metrics Toward a Coherent Framework

Surface roughness (SR), most often computed from a digital elevation model (DEM), is a fundamental concept in geomorphometry, with significant applications across the earth sciences and ecology. However, its analysis remains fragmented, lacking a unified conceptual and methodological framework within geomorphometry. This review synthesizes the current state of surface roughness research, highlighting persistent challenges that stem from this disunity. Key issues include a pervasive lack of consensus on terminology and definitions, frequent misuse of standardized indices, and difficulty in selecting appropriate analytical scales and metrics for specific landscapes and research questions. A major impediment to progress is the absence of benchmark datasets, which are crucial for the rigorous evaluation and comparison of both established and novel roughness metrics. Furthermore, we argue that in geomorphometry, roughness is best conceptualized as surface texture (ST), encompassing a multitude of terrain patterns across scales. Consequently, effective analysis often requires multiscale approaches and the development of new indices capable of quantifying specific textural features. We emphasize, for instance, the need for metrics based on robust statistical estimators, such as MAD or the Radial Roughness Index (RRI), to reliably characterize complex, heterogeneous terrain derived from high-resolution DEMs. These arguments are substantiated with computational examples comparing a range of metrics, from popular basic indices to more complex alternatives. This review aims to consolidate discourse on surface roughness and chart a path toward more robust, standardized, and interpretative analytical practices.