Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography
Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography
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DOI：
10.1029/2018jc014859
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发表时间：
2019-07
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影响因子：
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通讯作者：
Melissa S. Duvall;James L. Hench;Johanna H. Rosman
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文献类型：
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作者：
Melissa S. Duvall;James L. Hench;Johanna H. Rosman
海底地形影响广泛的物理和生物过程;因此，将海底的三维结构分解为粗糙度指标是海洋系统研究中的一个常见挑战。在这里，我们评估了以前提出的海底度量所捕获的属性，以及为表征其他类型的粗糙表面而开发的度量。我们考虑了三类度量：底部高程分布的属性（例如，标准偏差），长度比例（例如，粗糙度），以及描述地形如何随空间尺度变化的度量（例如，Hölder指数）。使用理想化的地形和天然海底地形数据从机载激光雷达测量的珊瑚礁的指标进行了评估。我们说明了常见的粗糙度度量（例如，粗糙度）对于几何形状非常不同的地形可能具有相同的值，从而限制了它们的实用性。应用小波领导人技术的珊瑚礁数据集表明，地形具有幂律的标度行为，但它是多重分形的，所以需要一个分布的Hölder指数来描述其标度行为。使用主成分分析，我们确定了三种主导模式的地形变化，或度量协变的方式，珊瑚礁区之间和内。总的来说，这里提出的结果表明，珊瑚礁地形是多尺度和多重分形。虽然捕获与给定过程相关的特定地形特性的各个度量可能适合于某些研究，但许多应用将需要一组度量，其中包括捕获地形如何随空间尺度变化的统计数据。
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.