The far-reaching back-effect of coastal tides upon open-ocean tides

As part of a study into various factors that impact the amplitudes of semidiurnal tides in the open and coastal ocean, we investigate the back-effect of coastal tides upon open-ocean tides. We use two tools for our study--a forward numerical model of the global ocean tides, and analytical solutions for a damped/driven non-rotating one-dimensional deep ocean basin of uniform depth coupled to a shelf of lesser uniform depth. The analytical model suggests that the presence of a resonant shelf can significantly alter the amplitudes of tides in the deep ocean, as shown by comparison of the coupled model to a simpler model in which the deep ocean basin stands by itself. Consistent with the analytical results, we find that if regions of known large coastal tides are blocked off, there is a very significant and far-reaching back-effect on the tides in a forward global numerical model. For instance, blocking off Hudson Strait leads to a global M2 tide with an rms amplitude 10 percent larger than is seen without the blocking. The disruptions in amplitude (and in phase) obtained by blocking Hudson Strait are largest near the Strait itself, but significant disruptions are seen as far away as the Indian Ocean. Blocking out the Northwest European Shelf, Gulf of Maine, Patagonian Shelf, East China Sea, or Northwest Australian Shelf also leads to significant and far-reaching changes to the global ocean tide. The conclusion is that shelf tides are not only forced by the deep ocean tide, but also have a substantial back effect on it. Implications for tides during the ice age, when sea levels were much lower and shelves were less extensive, will be briefly discussed.