Testing the Sunamura et al. (2014) equations for wave attenuation over shore platforms

Modelling the geomorphologic evolution of rocky coasts over geological time requires estimating the attenuation of waves approaching cliffs and thus the forces of waves impacting lower cliff surfaces. Sunamura et al. (2014) proposed a set of equations for waves crossing horizontal shore platforms that are potentially useful for geomorphological modelling. Here, we use a compilation of wave measurements to test their equations on dipping platforms and in particular to evaluate the equation parameters. We select only those measurements made where waves approached coastlines nearly orthogonally, where tidal height variations are small and where satellite images show fewer complications from wave refraction, reefs, or coastal geomorphology causing reflected waves. For each dipping rock platform, we forward model the wave heights using the measured wave height at the most seaward location as the boundary condition and apply the Sunamura et al. (2014) equations in a series of small steps across the platform. Using the parameters provided by Sunamura et al. (2014), the model predicts wave heights with a global root-mean square error (RMSE) that is less than 0.08 m. We repeated the analysis varying parameters by factors of two and four (both smaller and larger), finding that the minimum RMSEs are achieved with exactly the same parameters proposed by Sunamura et al. (2014). This suggests the equations should reliably predict wave attenuation for one-dimensional geomorphologic modelling with those parameters.