A framework for understanding drag parameterizations for coral reefs

In a hydrodynamic sense, a coral reef is a complex array of obstacles that exerts a net drag force on water moving over the reef. This drag is typically parameterized in ocean circulation models using drag coefficients (C D) or roughness length scales (z0); however, published CD for coral reefs span two orders of magnitude, posing a challenge to predictive modeling. Here we examine the reasons for the large range in reported CD and assess the limitations of using CD and z0 to parameterize drag on reefs. Using a formal framework based on the 3-D spatially averaged momentum equations, we show that CD and z0 are functions of canopy geometry and velocity profile shape. Using an idealized two-layer model, we illustrate that CD can vary by more than an order of magnitude for the same geometry and flow depending on the reference velocity selected and that differences in definition account for much of the range in reported CD values. Roughness length scales z 0 are typically used in 3-D circulation models to adjust C D for reference height, but this relies on spatially averaged near-bottom velocity profiles being logarithmic. Measurements from a shallow backreef indicate that z0 determined from fits to point measurements of velocity profiles can be very different from z0 required to parameterize spatially averaged drag. More sophisticated parameterizations for drag and shear stresses are required to simulate 3-D velocity fields over shallow reefs; in the meantime, we urge caution when using published C D and z0 values for coral reefs

Estimating Geometric Properties of Coral Reef Topography Using Obstacle- and Surface-Based Approaches

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

Interaction of Waves with Idealized High-Relief Bottom Roughness

Considerable uncertainty exists about how to represent wave bottom friction in coastal systems like reefs where orbital excursions are similar to roughness element size. Here, interactions between waves and large bottom roughness were investigated using Large Eddy Simulations of oscillatory flow over infinite hemisphere arrays. Wave amplitude, period, and hemisphere spacing were varied to investigate the dependence of kinematics and dynamics on dimensionless parameters. The net effect of topography on the oscillatory flow was assessed using a spatially and phase-averaged Navier-Stokes framework. Dynamics depended strongly on Keulegan-Carpenter number (KC), the ratio of wave orbital excursion to roughness element size. For 1 < KC < 10, flow separation was weak, form drag was small, stress gradients were negligible, and the main effect of topography on the flow was the inertial force associated with acceleration around roughness elements. For 10 < KC < 20, strong flow separation occurred, and both drag and inertial forces were important. Phase-dependent dispersive stresses were the main mechanism for vertical momentum transfer between the canopy layer and the overlying water column. Friction factors based on the drag force increased with KC for 1 < KC < 20, different from previously proposed empirical curves, but approached these curves for high KC. Friction factors based on the total force decreased with increasing KC and were consistent with previously proposed curves. These results highlight the importance of distinguishing the total force on the bottom, the drag force that removes energy from the flow, and the shear stress above the canopy layer, which were very different for the parameter range in this study

Boundary layer dynamics and bottom friction in combined wave-current flows over large roughness elements

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter D), in which current (Uc), wave velocity (Uw) and period (T) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as Uw/Uc increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number KC = UwT/D and Uc/Uw increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on Uc/Uw and KC. For large roughness elements, bottom friction is well represented by a friction factor(fw) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with KC and Uc/Uw

Collapsing Complexity: Quantifying Multiscale Properties of Reef Topography

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

Extracting Reynolds stresses from acoustic Doppler current profiler measurements in wave-dominated environments

Surface waves introduce velocity correlations that bias and often dominate Reynolds stress estimates made using the traditional variance method for acoustic Doppler current profilers (ADCPs). This analysis shows that the wave bias is the sum of a real wave stress and an error due to instrument tilt, both of which have a large uncertainty. Three alternative extensions to the variance method for calculating Reynolds stress profiles from ADCP measurements in wavy conditions are analyzed. The previously proposed variance fitting method (Variance Fit) is evaluated and two more general methods that use along- and between-beam velocity differencing with adaptive filtering (Vertical AF and Horizontal AF) are derived. The three methods are tested on datasets containing long-period monochromatic swell (Moorea, French Polynesia) and shorter-period mixed swell (Santa Barbara, California). The Variance Fit method leaves a residual wave bias in beam velocity variances, especially for intermediate waves, but gives physically reasonable Reynolds stress estimates because most of the residual wave bias cancels when the variance method is applied. The new Vertical AF method does not produce inherent wave bias in beam velocity variances, but yields comparable Reynolds stresses to the Variance Fit method. The Horizontal AF method performs poorly for all but monochromatic waves. Error remaining after one of the above methods is applied can be attributed to residual wave error, correlation of turbulence between points chosen for differencing, or correlation between waves and turbulence. A simple procedure is provided for determining the minimum bin separation that can be used

Increasing comparability among coral bleaching experiments

Coral bleaching is the single largest global threat to coral reefs worldwide. Integrating the diverse body of work on coral bleaching is critical to understanding and combating this global problem. Yet investigating the drivers, patterns, and processes of coral bleaching poses a major challenge. A recent review of published experiments revealed a wide range of experimental variables used across studies. Such a wide range of approaches enhances discovery, but without full transparency in the experimental and analytical methods used, can also make comparisons among studies challenging. To increase comparability but not stifle innovation, we propose a common framework for coral bleaching experiments that includes consideration of coral provenance, experimental conditions, and husbandry. For example, reporting the number of genets used, collection site conditions, the experimental temperature offset(s) from the maximum monthly mean (MMM) of the collection site, experimental light conditions, flow, and the feeding regime will greatly facilitate comparability across studies. Similarly, quantifying common response variables of endosymbiont (Symbiodiniaceae) and holobiont phenotypes (i.e., color, chlorophyll, endosymbiont cell density, mortality, and skeletal growth) could further facilitate cross-study comparisons. While no single bleaching experiment can provide the data necessary to determine global coral responses of all corals to current and future ocean warming, linking studies through a common framework as outlined here, would help increase comparability among experiments, facilitate synthetic insights into the causes and underlying mechanisms of coral bleaching, and reveal unique bleaching responses among genets, species, and regions. Such a collaborative framework that fosters transparency in methods used would strengthen comparisons among studies that can help inform coral reef management and facilitate conservation strategies to mitigate coral bleaching worldwide

Effect of Fe O /ZnO on two glass compositions for solidification of Swedish nuclear wastes

SIGLEAvailable from CEN Saclay, Service de Documentation, 91191 - Gif-sur-Yvette Cedex (France) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc