Topographic surface roughness: use, misuse and abuse in geomorphometry
Authors: Crema Stefano , Trevisani Sebastiano , Macchi Giorgia , Sarretta Alessandro , Marchi Lorenzo , Cavalli Marco 
Published: June 2022

&lt;p&gt;The concept of roughness is fundamental for the investigation of a wide variety of earth surface processes as every process acting over a surface either encounters or generates rough surfaces (Smith, 2014). Acknowledging the crucial role that roughness has across Earth sciences and recognizing the past and ongoing efforts carried out in roughness formulation, quantification and scaling properties, the present work wants to tackle a very specific roughness usage in geomorphometric investigations. In recent years the geomorphological community has indeed (re-)discovered the hydrological and sediment (dis-) connectivity paradigm as a valuable approach to better characterize sediment dynamics and effective sediment contributing area. This rediscovery is also being favored by quantitative methods and available software tools to carry out connectivity assessment considering diverse approaches such as DTM-based indices or graph description of sediment routes. For our purpose, we take here as an example an index of connectivity (Cavalli et al. 2013) as it represents a parsimonious approach (only requiring a DTM) and due to its numerous applications in contrasting physiographic contexts. In the above-mentioned index, surface roughness enters as a weighting factor to represent impedance to the fluxes and is computed as a detrended surface variability by deriving the standard deviation of residual topography over a desired window size. The convenience of having easy-to-use software tools for computing such an index might represent a tempting easy path to carry out connectivity assessment with the risk of avoiding a robust reasoning on the most appropriate moving window and cell size for our specific application. We show how the tested roughness index changes its hydraulic significance in relation to the scale of analysis, in terms of DTM resolution and window size. In a complex topographical setting, at fine resolution the index can be reasonably interpreted as a proxy of flow impedance; however, at larger scales, it provides information on long-range morphologies, therefore becoming a proxy of topographic gradient more than flow impedance. This behavior, apart from being expected, should trigger an alert especially when carrying out geomorphometric analyses such as the one herein reported. In fact, as we increase the cell size, we drift towards a metric that represents a proxy of slope and this in turn is actually favoring the flow, thus conceptually misusing the original formulation and introducing the opposite information in respect to the one intended.&lt;/p&gt;&lt;p&gt;Through such an example we would like to raise awareness over a known scale-related issues when using roughness metrics and to elicit some discussion on the topic for more robust approaches in geomorphometry. The mere availability of a DTM in fact should never be regarded as a green light for proceeding with processing techniques without a profound thinking on the most appropriate analyses.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;:&lt;/p&gt;&lt;ul&gt;&lt;li&gt;Cavalli, M., Trevisani, S., Comiti, F., Marchi, L., 2013. Geomorphometric assessment of spatial sediment connectivity in small Alpine catchments. Geomorphology, doi: 10.1016/j.geomorph.2012.05.007&lt;/li&gt;
&lt;li&gt;Smith, Mark W. (2014). Roughness in the Earth Sciences, Earth Science Reviews, doi: 10.1016/j.earscirev.2014.05.016&lt;/li&gt;
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