Estimating open-ocean barotropic tidal dissipation: The Hawaiian Ridge

The generalized inverse of a regional model is used to estimate barotropic tidal dissipation along the Hawaiian Ridge. The model, based on the linear shallow-water equations, incorporates parameterizations for the dissipation of energy via friction in the bottom boundary layer and form drag due to internal waves generated at topographic slopes. Sea surface height data from 364 orbit cycles of the Ocean Topography Experiment (TOPEX)/Poseidon satellite mission are used to perform inversions at eight diurnal and semidiurnal tidal frequencies. It is estimated that the barotropic M-2 tide loses energy at a rate of 19 GW, of which 88% is lost within 250 km of the ridge, presumably via conversion to the internal or baroclinic tide. Uncertainty in the assumed model error and wave drag in the forward model suggest that M-2 dissipation values from 18 to 25 GW are consistent with the altimetric observations. Other barotropic tidal constituents are estimated to lose a total of 5.7 GW. The spatial distribution of barotropic dissipation along the ridge is similar to that inferred from three-dimensional primitive equation models, and it is largely insensitive to details of assumed model and data errors. Dissipation at semidiurnal frequencies is most intense at the French Frigate Shoals with lesser, but significant, contributions at other sites. Diurnal tidal dissipation is concentrated to the east of the French Frigate Shoals, at the Gardner Pinnacles. Further work with three-dimensional models will be necessary to determine the fate of the energy that is removed from the barotropic tide.