Collapsing complexity: metrics to quantify multi-scale properties of reef topography.


Duvall, M. S.Hench, J. L.Rosman, J. H.


Journal of Geophysical Research (Oceans)


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 dataset demonstrates that thetopography has a power law scaling behavior but it is multi-fractal 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 co-vary, among and within reef zones. Collectively, the results presented here show that coral reef topography is both multi-scale and multi-fractal. 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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Journal Article

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