The role of roughness geometry in frictional wave dissipation

Quantifying the topographical structure of rocky and coral seabeds

“…From a qualitative view, the only site showing a clear anisotropy of the topographical structure is Socoa. A subset of four sites, namely Socoa, Banneg, Parlementia A and B have been documented both in cross-shore and alongshore directions (see Table 1 ) in order to test the ability of the directionality index proposed by [ 67 ] to quantify the level of roughness anisotropy.…”

“…For the sake of standardization and statistical robustness, we may recommend that STD should be preferentially used. Note however that experimental laboratory studies dedicated to bottom drag and wave dissipation [ 67 , 69 ] on idealized topography have identified a specific, but moderate, effect of effective slope on frictional dissipation, but this would require further confirmation on real terrain. Note also that the relationship between the spectral slope and the effective slope highlighted in the laboratory by [ 62 ] is not observed here, probably due to the non-perfect self affine spectra and Gaussian distribution of elevations.…”

“…It may still provide useful information at small (sub-metric scale) to characterize habitats [ 6 ]. The third and fourth statistical moments, namely the skewness and the excess kurtosis, should deserve attention owing to the fact that they both display also significant differences between sites and, at least for skewness, an effect on friction processes has already been identified [ 63 , 67 ]. For the studied sites, the solid fraction appears to be strongly correlated to the skewness.…”

“…Combining standard statistical moments and roughness estimators proposed in the literature [ 6 , 21 – 23 , 45 , 49 , 62 – 67 ], a series of metrics are computed for each transect and then transect-averaged to obtain the proposed values for each site. The only exception is the directionality index ( Eq 11 ) which is computed from transect-averaged metrics.…”

“…To our knowledge, very few direct estimators of topographical directionality have been proposed in the literature. We use here the directionality index Δ proposed by [ 67 ] based on the computation of directional standard deviations STD x and STD y , in cross-shore and along-shore directions, respectively: …”