Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography

Journal Article (Journal Article)

Seafloor topography affects a wide range of physical and biological processes; therefore, collapsing the three-dimensional structure of the bottom to roughness metrics is a common challenge in studies of marine systems. Here we assessed the properties captured by metrics previously proposed for the seafloor, as well as metrics developed to characterize other types of rough surfaces. We considered three classes of metrics: properties of the bottom elevation distribution (e.g., standard deviation), length scale ratios (e.g., rugosity), and metrics that describe how topography varies with spatial scale (e.g., Hölder exponents). The metrics were assessed using idealized topography and natural seafloor topography data from airborne lidar measurements of a coral reef. We illustrate that common roughness metrics (e.g., rugosity) can have the same value for topographies that are geometrically very different, limiting their utility. Application of the wavelet leaders technique to the reef data set demonstrates that the topography has a power law scaling behavior, but it is multifractal so a distribution of Hölder exponents is needed to describe its scaling behavior. Using principal component analysis, we identify three dominant modes of topographic variability, or ways metrics covary, among and within reef zones. Collectively, the results presented here show that coral reef topography is both multiscale and multifractal. While individual metrics that capture specific topography properties relevant to a given process may be suitable for some studies, many applications will require a set of metrics that includes statistics that capture how topography varies with spatial scale.

Full Text

Duke Authors

Cited Authors

  • Duvall, MS; Hench, JL; Rosman, JH

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 124 / 7

Start / End Page

  • 5021 - 5038

Electronic International Standard Serial Number (EISSN)

  • 2169-9291

International Standard Serial Number (ISSN)

  • 2169-9275

Digital Object Identifier (DOI)

  • 10.1029/2018JC014859

Citation Source

  • Scopus