Semidiurnal tides in the northeast Atlantic from a finite element numerical model

An in‐time spectral method is used to solve the complete nonlinear problem of tide propagation simultaneously over oceanic and coastal areas. For each constituent of the tidal spectrum, the corresponding elliptic modal problem is written under a variational form and solved by using a finite element technique. The model is applied to the computation of the dominant M 2 wave over the northeast Atlantic. The numerous in situ data over this domain and the large extent of the European continental shelf allow analysis of the gain of accuracy obtained by different components characterizing the model. To get a mean accuracy of less than 2 cm and 2° for the amplitudes and phases of the sea surface elevation, it is found that (1) the use of a refined mesh over the shallow areas and of a quasi‐linearized version of the quadratic Chezy friction law is essential; (2) loading effects computed by means of a Green integral have to be taken into account; and (3) accurate boundary conditions need to be prescribed at the entrances of dynamically active shallow water areas if they are not included in the investigated area (or it is necessary to extend the model over the whole neighboring coastal basin if these boundary conditions are not available). From the M 2 velocity field solution, bottom friction coefficients are derived for the secondary astronomical constituents of the tidal spectrum, and accurate charts of the S 2 and N 2 tides are produced over the modeled area.