Reconciling Reef Representations: A Comparison of Obstacle and Surface Models, and Consequences for Drag

For many 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 as a continuous surface. Here, we assess the implications of using obstacle-based and surface-based representations to estimate geometric properties needed to parameterize drag. Using a high-resolution scanning multi-beam sonar, we collected topography data that resolved individual coral colonies, allowing us to quantify properties of discrete obstacles (dimensions, shapes) as well as properties of the surface elevation data (rms slope, spectral density). We then computed the roughness density, or frontal area per unit plan area, from both analysis approaches given its demonstrated effect on bottom friction. Our results show that for multi-scale coral topography, obstacle and surface-based estimates of roughness density do not agree. These results challenge the common conceptualization of shallow-water canopies as obstacle arrays, because this approach does not capture the significant contribution of high-wavenumber roughness to total frontal area. Instead, natural canopies are better represented as continuous surfaces. Parameterizations of bottom friction in hydrodynamic models should therefore consider the contribution of a range of length scales (e.g., colony-scale, polyp-scale) to the total frontal area and drag.