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 ( z 0 ); however, published C D 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 C D and assess the limitations of using C D and z 0 to parameterize drag on reefs. Using a formal framework based on the 3‐D spatially averaged momentum equations, we show that C D and z 0 are functions of canopy geometry and velocity profile shape. Using an idealized two‐layer model, we illustrate that C D 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 C D 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 z 0 determined from fits to point measurements of velocity profiles can be very different from z 0 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 z 0 values for coral reefs.