An atlas of the main components of the tides has been produced on the basis of a finite element hydrodynamic model, with the aim of offering the scientific community, using satellite altimetric data, a prediction of the tidal contribution to sea surface height variations under the ground tracks of the satellites that is totally independent of altimetric measurements. The geographic coverage of the simulations only excludes, temporarily, some marginal seas like the Bay of Fundy. But the design of the model, based on a nonlinear formulation of the shallow water equations, could enable the simulations to be extended to these very singular areas. On the other hand, the Arctic Basin and the Antarctic Circumpolar Basin have been fully resolved, including the under-ice shelf areas of the Weddell Sea and the Ross Sea. Eight constituents, M(2), S-2, N-2, K-2, 2N(2), K-1, O-1, and Q(1) have been simulated. Five secondary constituents: Mu(2), Nu(2), L(2), T-2, and P-1, required to insure a priori correct predictions, have been deduced by admittance. The accuracy and precision of these solutions have been estimated by reference to the harmonic constituents data set available from analysis of the entire collection of pelagic, plateau and coastal observations made to date, and archived by International Association for Physical Sciences of the Oceans and International Hydrographic Bureau. Over the deep oceans, these solutions fit the observations to within a few centimeters for the larger components: M(2), S-2, K-1, O-1, and a few millimeters for the others, in RMS maximum difference to a standard set of 78 ground truth stations. Over the shelves, the differences are larger, because of the increase in amplitude of the tidal waves, but the flexibility offered by the finite element technique to refine the discretization mesh of the model over the shallow seas enables detailed cotidal maps to be produced along the coasts. One zoom on South Georgia Island, in the South Atlantic Ocean, is presented as an illustration. Finally, the performances of the tidal predictions made on the basis of this new set of solutions was tested by looking at the residual RMS differences at the crossover points of sea level measurements supplied by the TOPEX/POSEIDON mission, when using these predictions. This test provided confirmation of most of the conclusions already drawn on the basis of the previous comparisons with in situ tide gauge data.
