Intermediate Wave Scale Rocky Bottom Variability for the Nearshore Along California

Approximately 75% of the world's and California's shores are rocky. Rocky shores are of biological interest owing to their diverse and productive species assemblages, where waves and currents play a critical role in larval dispersal and recruitment. Surface variability for nearshore $\left(5⪅depth⪅60m\right)$ rocky bottoms at intermediate wave scale is described for the first time using existing high-resolution bathymetric surveys extending the length of California. The vertical variability of rocky shores is three times larger than measured coral reefs at the reef scale of . The ensemble-averaged, normalized, wavenumber elevation spectra are self-similar, with at least two negative power-law slope regions of 1.3 indicating rough bottoms and 2.75 at high wavenumbers indicating smoother-filled depressions. The ensemble statistics for rocky bottoms appear isotropic based on their cross-shore and alongshore variances and wave number slope spectra being statistically equal. Isotropy is attributed to wave erosion over time that only occurs in the nearshore ocean region. A Fourier spectral representation of the bottom boundary condition, ${\bar{G}}_{z^{\prime }}$, is developed for wave and current-driven hydrodynamic models along rocky coasts. The model has an error of less than 2% relative to the observed spectral data for reconstructive profiles and surfaces.