44 
physical knowledge of the boundary conditions for the North Sea area. Another weakness is 
the numerical formulation of these boundary conditions, a problem which is far from being 
solved, in spite of interesting attempts (e.g. van Joolen et al. 2005). In all of these models, 
the grid spacing has to be fitted to the shorter wave lengths. 
Fundamental changes in model physics, as proposed in section 6.2, have not been made for 
the model simulations discussed in this section. Analytical waves are prescribed at the model 
boundary. For the North Sea, the input wave height (5 m) was chosen to reflect the Storegga 
slope failure. The boundary condition for the North-East Atlantic model is rather arbitrary. 
Wave height (3 m) is chosen in such a way that potential boundary conditions for the North 
Sea model (Fig. 7.2.6) have about the same height as the wave prescribed as analytical 
boundary condition of the North Sea model. The boundary conditions were slightly modified 
numerically (cf. section 6.1.6), and problems were reduced by allowing signals to enter the 
model areas only perpendicular to the boundary. 
A major adjustment, compared to the operational models, has been made in the horizontal 
resolution. The simulations discussed in the following were run using a higher resolution of 
about 10 km in the North-East Atlantic model (future version of the BSFI using topographic 
data from the DMI version, 10.4: DMImo). The North Sea simulations were made using a 
high-resolution (about 2 km) two-dimensional, barotropic version of the BSFI model for the 
North and Baltic Seas. This version (North Sea 2 km) also covers an area extending 
somewhat farther to the north. The topography, especially that of the German Bight, was 
reconstructed completely using data from numerous sources (Fig. 7.01). 
With the fitted models, a coarse impression of the behaviour of a hypothetical tsunami with 
periods of 30 minutes or longer in the North-East Atlantic is obtained. On the shelf, using a 
realistic bottom topography, it is possible to adequately simulate the propagation of a 
tsunami with comparable periods up to the near-shore area (36 grid points/wave length at 
500 m depth, 20 at 50 m, and 9 at 10 m). Flydrostatic non-linear models like those used at 
the BSFI reproduce the modification of incoming signals by diffraction on coastline features, 
reflection in bays, reflection and refraction by bottom topography, shoaling of individual 
waves, and rear waves catching up with leading waves due to decreasing depth. (For a brief 
explanation of such processes, cf. e.g. section 5 and Masselink 2005). In particular, realistic 
travel times can be given for the shelf. Flowever, non-linear hydrostatic equations 
overestimate increases in energy density per area unit for a wave train in shallow water 
because they neglect dispersion. For a wide, shallow shelf sea like the North Sea, it is 
important that the models adequately simulate dissipation by bottom friction. In this way, the 
signals for the simulation of potentially devastating processes in the immediate near-shore 
area of the German Bight contain less energy than signals travelling across a narrow 
continental shelf before they reach the coast. Flowever, numerical methods almost always 
lead to an additional, artificial dissipation of energy. The BSFI models, and similar models of 
this type, cease to be valid near the coast, where wave lengths become so short that 
dispersion effects become relevant again. The applicability of the model assumptions 
(including the Boussinesq equations) is restricted more severely by the breaking criterion 
(H/h< 0.78 as h/L< 0.1). The water level elevations given for the individual coastal 
stations, therefore, have to be interpreted with caution. 
The following simulations were carried out: 
North-East Atlantic: wave train from the north (H3m, 71800 s, Fig. 7.2.1,7.2.4-6) 
North-East Atlantic: wave train from the south (H3m, 71800 s, Fig. 7.2.2, 7.2.4-6) 
North-East Atlantic: wave train from the west (H3m, 71800 s, Fig. 7.2.3, 7.2.4-6) 
North Sea 2 km: wave train from the west {H 5 m, 71800 s, Fig. 7.3.1-6) 
North Sea 2 km: wave train from the north (H5m, 71800 s, left Fig. 7.4.1-6, 7.4.7-9) 
North Sea 2 km (h=500 m): wave train from the north (H5 m, 7600 s, right Fig. 7.4.1-6) 
North Sea 2 km: wave train from the north (H 6, 7 and 8 m, 71800 s, Fig. 7.4.8-9)