Modeling tides in the western North Atlantic using unstructured graded grids

This paper describes grid convergence studies for a finite-element-based tidal model of the western North Atlantic, Gulf of Mexico and Caribbean. The very large computational domain used for this tidal model encompasses both the coastal and the deep ocean and facilitates the specification of boundary conditions. Due to the large variability in depths as well as scale content of the tides within the model domain, an optimal unstructured graded grid with highly variable finite element areas is developed which significantly reduces the size of the discrete problem while improving the accuracy of the computations. The convergence studies include computations for a sequence of regularly discretized grids ranging from a very coarse 1.6° × 1.6° mesh to a very fine 6’ × 6’ to 12’ × 12’ mesh as well as unstructured graded grids with resolutions varying between 1.6° and 5’ within each mesh. Resolution requirements are related to depth, gradients in topography as well as the resolution of the coastal boundary. The final optimal graded grid has a tidal response which is comparable to that of the finest regular grid in most regions. The optimal graded grid is then forced with Schwiderski’s (1979, 1980, 1981a—g) global model on the open ocean boundary and tidal potential forcing functions within the interior domain. The structure of the tides is examined, computed co-tidal charts are presented and comparisons are made between the computed results and field data at 77 stations within the model domain.