Numerical modeling of waves for a tsunami early warning system

Numerical modeling of waves for a tsunami early warning system
Different validation tests have shown the capability of the model of
accurately reproduce the results of laboratory experiments on tsunamis. Two
methodologies are presented to generate waves inside the numerical domain:
with a wave-maker boundary condition or inside the field equation. The
model equation (MSE) has been derived with a source term which allows the
reproduction of the seafloor movements. The source term is calculated as the
time derivative of the water depth multiplied by a transfer function which
depends on the generated wave frequencies. It differs from other techniques
such that of Tinti et al. (2006b), who employ a transfer function based on
the landslide length. Since the model equations are solved in the frequency
domain, the inclusion of a frequency filter function in the source term appears
natural. Anyway it is important to notice that the same approach can be
easily applied to numerical models which work in the time domain, as those
based on the NLSWE or the BTE. The procedure in these cases requires
a previous filtering in the frequency domain of the source term, then antitransformation
in the time domain in order to provide the source term for
the equations. From a physical point of view, the transfer function has
the effect of a low-pass filter between the movements of the bottom and
the movements of the free surface. Translating the bottom deformations
directly to the free surface or by using a filter that has the same effect for
all the frequencies, introduces a large amount of spurious energy in the high
frequencies range, leading to unrealistic/wrong results. This effect is less
evident if non dispersive equations, NLSWE, are used to reproduce the wave
field, because the wave components propagate at the same celerity which
is not function of the wave frequency. It is worth to remember that the
technique used by Tinti et al. (2006b), although it does not consider the
wave frequency dependence, has always provided good results, because it
has been applied, since now, to models that do not reproduce the frequency
dispersion.
It is finally worth to remember that the inclusion of a source term in the
MSE has been here considered for submerged landslides. The extension of
the technique discussed to subaerial landslides is to be done carefully. When
a landslide enters the water it has a piston-like effect (especially if it has a
steep front), which induces a deformation of the shoreline not considered by
the source term used in the computations presented in this work.
A further important feature of the model is that it is suitable to be used
in early warning systems for tsunamis. It has been shown that the model
can be applied in two stages, in order to solve the heaviest computations in a
Università degli Studi di Roma Tre - DSIC 106