Local diagnostics to estimate density-induced sea level variations over topography and along coastlines

In the open ocean, sea level variability is primarily steric in origin. Steric sea level is given by the depth integral of the density field, raising the question of how tide gauges, which are situated in very shallow water, feel deep ocean variability. Here this question is examined in a high-resolution global ocean model. By considering a series of assumptions we show that if we wish to reconstruct coastal sea level using only local density information, then the best assumption we can make is one of no horizontal pressure gradient, and therefore no geostrophic flow, at the seafloor. Coastal sea level can then be determined using density at the ocean\textquoterights floor. When attempting to discriminate between mass and volume components of sea level measured by tide gauges, the conventional approach is to take steric height at deep-ocean sites close to the tide gauges as an estimate of the steric component. We find that with steric height computed at 3000 m this approach only works well in the equatorial band of the Atlantic and Pacific eastern boundaries. In most cases the steric correction can be improved by calculating steric height closer to shore, with the best results obtained in the depth range 500\textendash1000 m. Yet, for western boundaries, large discrepancies remain. Our results therefore suggest that on time scales up to about 5 years, and perhaps longer, the presence of boundary currents means that the conventional steric correction to tide gauges may not be valid in many places.