Microseismic measurement of wave-energy delivery to a rocky coast

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Abstract
Rocky coasts are attacked by waves that drive sea-cliff retreat and etch promontories and embayments into the coastline. Understanding the evolution of such coastlines requires knowledge of the energy supplied by waves, which should depend upon both the deep-water waves and the coastal bathymetry they cross. We employ microseismic measurements of the wave-induced shaking of sea cliffs near Santa Cruz, California, as a proxy for the temporal pattern of wave-energy delivery to the coast during much of the winter 2001 storm season. Visual inspection of the time series suggests that both deep-water wave heights and tide levels exert considerable control on the energy delivered. We test this concept quantitatively with two models in which synthetic time series of wave power at the coast are compared with the shaking data. In the first model, deep-water wave power is linearly scaled by a fitting parameter; because this model fails to account for the strong tidal signal, it fits poorly. In the second model, the wave transformation associated with shoaling and refraction diminishes the nearshore wave power, and dissipation associated with bottom drag and wave breaking is parameterized by exponential dependencies on two length scales; this model reduces the variance by 32%–45% and captures the essence of the full signal. Shoaling and refraction greatly modulate the wave power delivered to the coast. Energy dissipated by bottom drag across the shelf is relatively small; the dissipation length scale is many times the path length across the shelf. In contrast, much energy is dissipated in the surf zone; the tidal-dissipation depth scale is of the same order as the tidal range (1–2 m), which accounts for the strong dependence of the cliff shaking on the tide.

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