Rugosity

Rugosity, fr, is a measure of small-scale variations of amplitude in the height of a surface, f_{\text{r}} = A_{\text{r}}/A_{\text{g}}

where Ar is the real (true, actual) surface area and Ag is the macroscopic geometric surface area. ==Utility== Rugosity calculations are commonly used in materials science to characterize surfaces, amongst others, in marine science to characterize seafloor habitats. A common technique to measure seafloor rugosity is Risk's chain-and-tape method but with the advent of underwater photography less invasive quantitative methods have been developed. Some examples include measuring small-scale seafloor bottom roughness from microtopographic laser scanning (Du Preez and Tunnicliffe 2012), and deriving multi-scale measures of rugosity, slope and aspect from benthic stereo image reconstructions (Friedman et al. 2012). ==Alternative== Despite the popularity of using rugosity for two- and three-dimensional surface analyses, methodological inconsistency has been problematic. Building off recent advances, the arc-chord ratio (ACR) rugosity index is capable of measuring the rugosity of two-dimensional profiles and three-dimensional surfaces using a single method (Du Preez 2015). The ACR rugosity index is defined as the contoured (real) surface area divided by the area of the surface orthogonally projected onto a plane of best fit (POBF), where the POBF is a function (linear interpolation) of the boundary data only. Using a POBF, instead of an arbitrary horizontal geometric plane, results in an important advantage of the ACR rugosity index: unlike most rugosity indices, ACR rugosity is not affected by slope.