# Rugosity

Rugosity, fr, is a measure of small-scale variations or amplitude in the height of a surface,

$f_r = A_r/A_g$

where Ar is the real (true, actual) surface area and Ag is the geometric surface area.[1]

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[2] 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),[3] and deriving multi-scale measures of rugosity, slope and aspect from benthic stereo image reconstructions (Friedman et al. 2012).[4]

Ecology: As a measure of complexity, rugosity is presumed to be an indicator of the amount of available habitat available for colonization by benthic organisms (those attached to the seafloor), and shelter and foraging area for mobile organisms.

Geology: For marine geologists and geomorphologists, rugosity is a useful characteristic in distinguishing different types of seafloors in remote sensing applications (e.g., sonar and laser altimetry, based from ships, planes or satellites).

Oceanography: Among oceanographers, rugosity is recognized to influence small-scale hydrodynamics by converting organized laminar or oscillatory flow into energy-dissipating turbulence.

Coral biology: High rugosity is often an indication of the presence of coral, which creates a complex surface as it grows. A rugose seafloor's tendency to generate turbulence is understood to promote the growth of coral and coralline algae by delivering nutrient-rich water after the organisms have depleted the nutrients from the envelope of water immediately surrounding their tissues.