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Duvall, Melissa S.; Rosman, Johanna H.; Hench, James L.
Journal of geophysical research. Oceans, June 2020, 2020-06-00, 20200601, Letnik: 125, Številka: 6Journal Article
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. Plain Language Summary Coral reefs depend on water motion for survival. At the same time, their complex structure exerts friction on the overlying flow and thereby affects water movement across reefs. Prediction of flow over reefs requires a model that captures the interaction between reef topography and the flow. This is typically done with a drag law that requires specification of the frontal area of topography perpendicular to the flow per unit horizontal area. Quantifying frontal area is problematic because reef topography has many length scales. Here we consider the effect that representing reefs either as discrete obstacle arrays (e.g., cylinders) or as continuous rough surfaces (e.g., represented by spectra) has on estimates of frontal area and drag. Our results show that the obstacle representation misses the contribution of small length scales while the surface approach captures all length scales, which contribute significantly to the total frontal area of natural reefs. This suggests that the many different topographic length scales should be considered in models of friction for flow across reefs. Key Points For reef topography, which is multiscale, a wide range of length scales contribute substantially to the frontal area per unit plan area Representing reef topography as an obstacle array does not capture the substantial contribution of small length scales to total frontal area Method is proposed for computing roughness density from local surface slopes that includes contributions from all topographic length scales
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