Wave Attenuation in the Shallows of San Francisco Bay

Waves propagating over broad, gently-sloped shallows decrease in height due to frictional dissipation at the bed. The rate of attenuation depends on bed roughness, which can be difficult to determine, and wave energy. Accurate characterization of wave evolution is critical both for modeling sediment transport and understanding of the role of mudflats in protecting the shoreline, a function threatened by sea-level rise. We quantified wave-height evolution across 7 km of mudflat in San Pablo Bay (northern San Francisco Bay), an environment where tidal mixing prevents the formation of fluid mud. Wave height was measured along a cross-shore transect from -2 m to +0.45 m MLLW in winter 2011 and summer 2012. Wave height decreased more than 50% across the transect. The exponential decay coefficient λ was inversely related to depth squared (λ = 6 x 10^-4 h^-2). We estimated the physical roughness length scale k_b to be m from near-bed turbulence measurements. The wave friction factor f_w determined from wave-height data was inversely related to wave Reynolds number Re_w. The empirical f_w was greater than the rough f_w (predicted from k_b/A, where A is near-bed wave amplitude) at low Re_w, when the wave boundary layer was classified transitional, and converged with the predicted rough f_w at high Re_w, when the boundary layer was rough. We predicted wave height at the inshore station using both the rough f_w and the analytical smooth f_w. Root-mean-square error between predicted and observed wave height was twice as great for the smooth as for the rough f_w. Researchers often assume that the wave boundary layer is smooth for settings with fine-grained sediments. At this site, the smooth f_w inadequately captures the effectiveness of the mudflats in protecting the shoreline through wave attenuation. In addition, use of a smooth f_w results in an underestimate of wave shear stress by a factor of approximately 3, which significantly decreases the potential for wave-driven resuspension and sediment transport.