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Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography

Publication ,  Journal Article
Duvall, MS; Hench, JL; Rosman, JH
Published in: Journal of Geophysical Research: Oceans
January 1, 2019

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.

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Published In

Journal of Geophysical Research: Oceans

DOI

EISSN

2169-9291

ISSN

2169-9275

Publication Date

January 1, 2019

Volume

124

Issue

7

Start / End Page

5021 / 5038

Related Subject Headings

  • 3709 Physical geography and environmental geoscience
  • 3708 Oceanography
  • 3706 Geophysics
  • 0406 Physical Geography and Environmental Geoscience
  • 0405 Oceanography
  • 0404 Geophysics
 

Citation

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Duvall, M. S., Hench, J. L., & Rosman, J. H. (2019). Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography. Journal of Geophysical Research: Oceans, 124(7), 5021–5038. https://doi.org/10.1029/2018JC014859
Duvall, M. S., J. L. Hench, and J. H. Rosman. “Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography.” Journal of Geophysical Research: Oceans 124, no. 7 (January 1, 2019): 5021–38. https://doi.org/10.1029/2018JC014859.
Duvall MS, Hench JL, Rosman JH. Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography. Journal of Geophysical Research: Oceans. 2019 Jan 1;124(7):5021–38.
Duvall, M. S., et al. “Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography.” Journal of Geophysical Research: Oceans, vol. 124, no. 7, Jan. 2019, pp. 5021–38. Scopus, doi:10.1029/2018JC014859.
Duvall MS, Hench JL, Rosman JH. Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography. Journal of Geophysical Research: Oceans. 2019 Jan 1;124(7):5021–5038.

Published In

Journal of Geophysical Research: Oceans

DOI

EISSN

2169-9291

ISSN

2169-9275

Publication Date

January 1, 2019

Volume

124

Issue

7

Start / End Page

5021 / 5038

Related Subject Headings

  • 3709 Physical geography and environmental geoscience
  • 3708 Oceanography
  • 3706 Geophysics
  • 0406 Physical Geography and Environmental Geoscience
  • 0405 Oceanography
  • 0404 Geophysics