Finite-Element Modeling of the Global Ocean Tides and Currents in the Time Domain

The problem of numerical modeling of tides and currents in the global oceans over an elastic Earth with realistic continental boundaries and bathymetries that are driven by the tidal generating forces of the Moon and the Sun has ever challenged numerical modelers. All the numerical models for the global ocean tides have been restricted to the finite difference method and to solving the Laplace's Tide Equations in the frequency domain. Schwiderski, however, was able to improve Zahel's tidal model by tide-gauge observational constraints, and to yield one of the best global tidal models available today. We have taken an entirely different approach toward the objective of solving the problem of the global ocean tides and currents. We solve solely the vertically integrated hydrodynamic (or so called shallow-water) equations in the time domain without resorting to any tide-gauge observational constraints. We use the semi-implicit finite element method that (1) provides the flexibility in variable element size and shape to adequately discretize highly irregular continental boundaries, particularly around reentrant corners and rapidly varying bathymetries in trenches and continental margins, and (2) achieves numerical stability and convergence for large time steps in the time integration. Moreover, for tidal generating forces, we make use of the precise ephemerides of the Moon and the Sun, instead of using the harmonic development of tidal species. Finite element results of the global ocean tides so obtained are compared favorably with the SEASAT altimeter data, as a first test, in the Pacific Ocean, and are comparable to the relative precision of Schwiderski's tidal model. They are better than Schwiderski's tidal model in the region where tide-gauge observations are lacking, for instance, in the northeastern Pacific Ocean and Gulf of Alaska.