A simplified geostatistical approach for characterizing key aspects of short-range roughness

Surface roughness, i.e. local variations in elevation which indicate less and less local smoothness, is an important concept for the analysis of solid earth/planetary surfaces and of the related surface processes. However, surface roughness is a general concept covering multiple aspects of the surface spatial variability structure, that can be characterized at different scales and with different metrics. Accordingly, it is not surprising the wide range of approaches and algorithms adopted for the analysis of surface roughness and the lack of an accepted standard for its evaluation. In this context, geostatistical-based roughness indexes are a valid solution, providing a good balance between flexibility of algorithms and interpretability of the results. However, despite the long record of applications and the well-known and robust theoretical framework, geostatistical-based surface roughness tools have still not gained momentum in the context of geomorphometric analysis. Many geomorphometric studies concerning with the evaluation of roughness indexes are based on popular approaches, such as the ones based on measures of dispersion of normal vectors to surface. Unfortunately, these indexes present some drawbacks in the capability to represent specific aspects of surface roughness and from the perspective of their interpretability. Accordingly, in this paper some of the key aspects and advantages of geostatistical-based approaches for roughness analysis are highlighted, including the relevance of roughness anisotropy. Then, a new approach tailored to the analysis of short-range roughness, requiring a minimum intervention by the user, is introduced discussing the advantages compared to the vector dispersion-based roughness. The new approach is implemented as open-source code both in R language using the functions of the “Terra” package as well as in Python for Esri ArcMap GIS. The methodological considerations and algorithms presented can be applied also in the broader context of image analysis.