Parameterizing wave runup with an effective peak frequency

Total wave runup is a combination of steady (wave setup) and oscillating (swash) components. The oscillating component is often parameterized as a function of beach slope β, deep water significant wave height H_0, and wavelength L₀ = g f_p^-2/(2pi),where f_p is the frequency for which the energy spectrum E(f) is maximum. However, f_p is unstable when E(f) contains sea and swell peaks of approximately equal energy, and the parameterized runup can jump by a nonphysical factor of 4, depending on which peak is dominant. Here, different definitions of effective frequency f_e, based on integrals of E(f) rather than the peak, are developed and tested with two unique data sets. Wave runup was measured with pressure sensors and a scanning lidar on a low-slope (1:80) dissipative beach and steep (1:8) reflective beach. Incident deep water wave heights ranged from 0.3 m -7.5 m, with peak periods between 5-20 s. Preliminary results show the magnitude of runup (composed of both infragravity and incident band waves) is most highly correlated with an f_e that weights low frequency swell more heavily than high frequency sea. For a sharp uni-modal incident wave spectrum, f_e = f_p.