Fig. 1. Effect of a poor resolution on the geometry of a strait. This one is widened by about 100%. Straits are of great importance because they control the exchange of water between ocean basins.

Fig. 2. Depending on the numerical scheme used, under-resolved channels in both finite element (below) and finite difference (above) schemes have problems representing simultaneously the depth and the cross-sectional area (center) leading to inaccurate determination of the transport.

Fig. 3. In the Arctic Archipelago, Kliem and Greenberg (2003) found significant transport through the minimally resolved Fury and Hecla Strait (bottom) and Hellgate (top) channels.

Fig. 4. Effect of the rotation on the discretization of a square domain. When the sides are not aligned with the axes, step-like features occur along the walls.

Fig. 5. Elevation field for the Kelvin retardation problem in the presence of steps along the walls at two different resolutions. α represents the rotation angle of the grid relative to the discretization axes. (a) 10 km, α=0; (b) 10 km, α=30; (c) 5 km, α=0; (d) 5 km, α=30. The dashed line is the contour, the solid lines are contours from 0.1 to 1.0 m with an increment of 0.1 m.

Fig. 6. Layer thickness in meters after a 6 year spin-up for 20 and 10 km resolution. Shown are results from the A and B combination (see text) with or without a 3.44 rotation angle of the basin. Note that the B case tends to resemble the A,B case with no rotation, but the A case does not.

Fig. 7. Convergence with resolution of the normalized elevation error for the second order C-grid FD, O-FDM4 and R-FDM4 models in a circular domain.

Fig. 8. Convergence with resolution of the normalized elevation error in a circular domain for three FE models (LW, HT, PZM) and the C-grid FD for comparison.

Fig. 9. The ADCIRC domain for tide and surge prediction. Approximate latitudinal range is 7–46N, and longitudinal range is 60–97W.

Fig. 10. Portion of ADCIRC mesh covering the city of New Orleans. This local resolution provides quality hurricane surge prediction when appended to the wide-area domain illustrated in Fig. 9. The horizontal scale of the figure is approximately 30 km per side.

Fig. 11. (Left) Bathymetry (m) south of Cape Cod, MA. The resolution is 0.1–1 km. The square zoom boxes shown are length 20 km. (Right) Computed M2 power density, [kw/m²].

Fig. 12. The barotropic Rossby radius (km) as calculated on the global FE mesh of Lyard et al. (2006). For most computations, this would not be a factor in determining model resolution.

Fig. 13. Contours of the baroclinic Rossby radius (km) from Chelton et al.'s (1998) values obtained from the web (see text) for the northern North Atlantic (left) and the Antarctic (right).

Fig. 14. Nearfield mesh resolving the ETIC, and data locations.

Fig. 15. Data-assimilative solution for nearfield M2 tidal amplitude (m) for the numbered areas identified in Fig. 16.

Fig. 16. Difference (m) between the ETIC-resolving and non-resolving solutions, following data assimilation. The results are plotted on the coarser mesh, which covers roughly 420 km along-shelf and 100 km cross-shelf. The difference is of order 20 cm over a significant portion of the shelf. The difference is vanishingly small at the data locations (green filled hexagons), as these points are fit to the model.

Fig. 17. Gulf of Mexico meshes from Hagen et al. (2001), (their Fig. 2 and Fig. 7, used with permission). The grid on the left was produced using a wavelength criterion and the grid on the right with LTEA (localized truncation error analysis). The meshes have approximately the same number of nodes and elements. Approximate latitudinal range is 18–30.5N, and longitudinal range is 81–97W.

Definition of variables in Eqs. (1) and (2)