32 
dispersion and subsequent dissipation of the short-wave components of the signal and the 
resultant weakening of the leading signal. The difference between hydrostatic and non 
hydrostatic computations may be less problematic in three-dimensional simulations of 
pointlike initial distributions (10.5: PEDpT) or slow bottom changes (Androsov et al. 2005) 
than in simulations of long faults or impulse-type bottom changes. 
The influence of advection in the horizontal momentum equation and in the surface boundary 
conditions is low, like that of turbulent, horizontal momentum exchange. Nevertheless, both 
may significantly change the shape of a tsunami propagating in the deep ocean. Therefore, it 
is advisable to use the full non-hydrostatic, non-linear equations in this area. However, this is 
done only in research simulations. 
In section 3, causes of possible North Sea tsunami have been compiled. The near field of 
such tsunami would be located outside the North Sea. Adequate simulation of the tsunami 
near-field in the North-East Atlantic would require major changes to the BSH model concept. 
However, the BSH is not planning to carry out such near field studies. 
6.1.3 Deep ocean propagation 
As a tsunami travels across the deep ocean, dispersion only plays a major role if an 
equilibrium signal (e.g. a soliton) of short and long waves has formed in the near field. 
Otherwise the short waves have dissipated, and propagation of the remaining long-period 
signal is simulated well with the hydrostatic assumption. In MOST (Titov et al. 1997), a 
hydrostatic model is used both for the simulation of near-field and deep-ocean propagation. 
However, dispersion is deliberately re-introduced in this case via the numerical method 
chosen. Gjevik et al., 1997, in a tsunami simulation, studied numerical dispersion caused by 
finite differences using an Arakawa-C-grid, a grid which is also used in the BSH models. 
They found that numerical dispersion did not always behave in a way that was consistent 
with physical law. The results of hydrostatic models are nevertheless useful (Horrillo et al. 
2006). Good knowledge of the bottom topography is essential for modelling the propagation 
of long waves. In particular, a good approximation to travel times is obtained by integration of 
the distance covered at local speed -Jgh (Annunziato et al. 2005). Such computations are 
very fast and, provided that a suitable resolution of topography covering also the coastal 
waters is available, they give reasonable results, especially if corrections are made to include 
diffraction on islands and coastal spits. The authors, Annunziato et al. (2005), announced 
that their model would be extended to provide an equally fast estimation of energy. Following 
a comparison of such computations with exemplary simulations using more complex models, 
and by including the bottom topography of the BSH models, an adaptation of this type of 
model might lead to the development of a suitable warning instrument for the North Sea. The 
report (Buch et al. 2005) of the Danish Meteorological Institute (DMI) on tsunami risks 
includes this type of travel time computations for the starting points Cape Farvel (Greenland), 
Faeroe Islands, and Hanstholm (Denmark). Nirupama et al. (2006) computed travel times for 
118 starting points around the Atlantic Ocean. The bottom topography used was ET0P02 
(available at 10.4: GFDL), which has a resolution of 2 minutes of arc, i.e. about 3.3 km near 
the equator and about 2 km in the North Sea region. 
6.1.4 Modification on the continental slope 
A tsunami undergoes a substantial modification on the continental slope. Here, not only a 
good resolution is needed but also a non-hydrostatic simulation (Rubino 1998). Although the 
North-East Atlantic model of the BSH, in its new resolution of about 10 km, in fact shows 
expected alterations of wave height and length in this area (cf. section 7.2), this mainly 
reflects the influence of bottom topography on *Jgh . The influence of non-linear effects is 
low, dispersion only takes place as numerical dispersion, and the explicit turbulent 
momentum exchange has a lower boundary due to the numerical scheme used. To arrive at