Mathematical modelling of global interaction between ocean tides and earth tides

Abstract

Solid Earth deformation due to ocean tides gives rise to an essential interaction between ocean tides and Earth tides. A hydrodynamical-numerical 4°-ocean tide model has been generalized by including this interaction, which depends on gravitational attraction and loading effects. The resulting integro-differential equation system has been solved numerically for semidiurnal and diurnal tides. In this way global maps have been obtained for both the ocean tide, and the tidal surface displacement of the solid Earth, the former reflecting the global interaction effect, and the latter being due to it. The computed ocean tide is compared with measurements from coastal and island stations, deep-sea instrument capsules and with earlier comparable ocean tide computational results which were obtained without considering the additional effects. The significant dynamical interaction effects which are recognized from the computed global maps of ocean-surface displacement and ocean current velocity are discussed and generally found to lead to a more realistic computed ocean tide. The contributions to the energy equation belonging to the tidal integro-differential equation system are evaluated. In particular, the quantities having reference to the angular momentum transfer between the ocean and the Moon, and to the angular momentum transfer between the solid Earth and the ocean are presented in view of the interaction considered.