Estimating Geometric Properties of Coral Reef Topography Using Obstacle- and Surface-Based Approaches
©2020. American Geophysical Union. All Rights Reserved. In shallow water systems like coral reefs, bottom friction is an important term in the momentum balance. Parameterizations of bottom friction require a representation of canopy geometry, which can be conceptualized as an array of discrete obstacles or a continuous surface. Here, we assess the implications of using obstacle- and surface-based representations to estimate geometric properties needed to parameterize drag. We collected high-resolution reef topography data using a scanning multibeam sonar that resolved individual coral colonies within a set of 100-m2 reef patches primarily composed of mounding Porites corals. The topography measurements yielded 1-cm resolution continuous surfaces consisting of a single elevation value for each position in a regular horizontal grid. These surfaces were analyzed by (1) defining discrete obstacles and quantifying their properties (dimensions, shapes), and (2) computing properties of the elevation field (root mean square (rms) elevations, rms slopes, spectra). We then computed the roughness density (i.e., frontal area per unit plan area) using both analysis approaches. The obstacle and surface-based estimates of roughness density did not agree, largely because small-scale topographic variations contributed significantly to total frontal area. These results challenge the common conceptualization of shallow-water canopies as obstacle arrays, which may not capture significant contributions of high-wavenumber roughness to total frontal area. In contrast, the full range of roughness length scales present in natural reefs is captured by the continuous surface representation. Parameterizations of bottom friction over reef topography could potentially be improved by representing the contributions of all length scales to total frontal area and drag.
Duvall, MS; Rosman, JH; Hench, JL
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