Roughness in the Earth Sciences

Rough surfaces are ubiquitous in nature. Near-surface processes both encounter and create surface roughness. Recent advances in surveying have improved the resolution, extent and availability of topographic datasets. This broad review synthesises efforts to represent surface roughness in such datasets, drawing examples from a number of branches of Earth Science, with the aim of facilitating a more systematic exchange of roughness formulations. A number of issues surround the definition of roughness. The term ‘roughness’ has been applied variously to represent a property of a surface, a property of a flow and as a model tuning parameter; yet these distinctions are articulated rarely. There has been a proliferation of methods of quantifying surface roughness. Given the wide range of applications of roughness in the Earth Sciences, attempts to create a standardised parameter set will likely be problematic. Yet a standard protocol for reporting roughness calculation would be appropriate, especially considering the importance of the choice of partition scale in the distinction between roughness and topography. Applications of surface roughness treat it as a variable (in the mapping of landforms, for example), a surrogate for less measurable variables (as in the estimation of resistance to flows) or as an indicator of near-surface processes. Recent developments examining interactions between roughness elements (e.g. sheltering) highlight the need to consider the pattern of surface roughness (e.g. anisotropy, connectivity of peaks) if appropriate parameterisations are to be developed. Addressing these issues will maximise the exciting potential offered by advances in topographic surveys.