243
INFLUENCE OF THE ATMOSPHERIC WAVE VELOCITY IN THE COASTAL
AMPLIFICATION OF METEOTSUNAMIS
M. MARCOS1,2, S. MONSERRAT1,2, R. MEDINA3, C. VIDAL3
1
Grupo de Oceanografía Interdisciplinar/ Oceanografía Física, IMEDEA
(CSIC-UIB)
2
Departamento de Física, Universitat de les Illes Balears
3
Grupo de Ingeniería Oceanográfica y de Costas, Universidad de Cantabria,
E.T.S. Ingenieros de Caminos
Abstract
Extremely large seiche oscillations are regularly observed in some specific areas around the
world even in the absence of any seismic forcing. These seiches have been successfully
associated with strong atmospheric pressure perturbations inducing sea level oscillations at
the open ocean, before entering the inlet, which are in turn resonantly amplified by the
geometric characteristics of the inlet. The coastal behaviour of such waves, although of
different origin, is similar to tsunami waves behaviour and is sometimes referred to as
meteotsunamis. In some specific places, such as Ciutadella inlet, Balearic Islands, western
Mediterranean, these seiche oscillations are stronger than expected, even taking into
account the large amplification factor by resonance of the inlet. For these cases, some
external amplification, before entering the inlet, is necessary to explain the phenomenon. In
this paper, it is numerically shown how the phase speed of the atmospheric pressure
disturbance generating the surface waves is a critical factor in the energy transfer between
the atmosphere and the ocean.
1. Introduction
Large amplitude seiche oscillations with periods in the tsunami frequency range (several
minutes) are periodically observed in some specific areas around the world even in absence
of seismic forcing. These waves have been successfully related to atmospheric forcings
(mainly atmospheric pressure oscillations) and therefore referred to as meteotsunamis.
Strong seiche oscillations associated with atmospheric forcing have been reported in Japan
[1, 2], China [3], the Adriatic Sea [4], the Aegean Sea [5], etc.
Waves of this kind are periodically observed in Ciutadella harbour, located at the end of
an elongated inlet in Menorca Island, western Mediterranean (Fig. 1), where are locally
known as rissaga. It has been demonstrated that rissagas are due to the resonant
amplification of the inlet normal mode (10 min period) when this is externally forced by
open ocean long waves generated by rapid atmospheric pressure fluctuations [6, 7]. The
A. C. Yalçıner, E. Pelinovsky, E. Okal, C. E. Synolakis (eds.)
Submarine Landslides and Tsunamis 243-249.
@2003 Kluwer Academic Publishers. Printed in Netherlands
244
characteristics of these atmospheric waves are well established [8]. They are non-dispersive
waves, travelling from the SW to the NE and with a phase speed always ranging between
Figure 1. Situation of Ciutadella inlet in the western Mediterranean
20 and 30 m/s. The elongated dimensions of Ciutadella inlet (1 km long, 50 m wide) is a
key point conferring to this inlet a particularly high amplification factor by resonance.
However, the large sea level oscillations recorded at this site (up to 3 m wave height) can
only be explained if some amplification of the ocean long wave occurs prior to its arrival to
the inlet mouth. A finite difference 2D numerical model, able to simulate ocean long waves
generated by atmospheric pressure fluctuations, is used to show how the platform
characteristics allow this amplification and how the phase speed of the atmospheric
pressure waves is critical in this amplification.
2. Numerical model
The numerical model is a finite difference, 2D long wave model developed by the Ocean
and Coastal Research Group at the University of Cantabria. It has been modified to include
an atmospheric pressure term in the momentum equation. The model integrates the depthaveraged equations of continuity, momentum and diffusion over a finite difference grid.
The equations, in Cartesian coordinates have the form:
 Mass conservation:
 ( HU )  ( HV ) 


0
x
y
t
 Momentum conservation:
 0
 UH 
 U 2 H 
 UVH 
1 Pa

g


 fVH 

 gH

H2
t
x
y
ρ0
x
x
20
x

 h
  2U
g   
 2U 

 2H
h 
z  'dz dz   xz ( )   xz(  h )  H h  2 
2 
 0  x
y 
x

 x
 h  U
U
V 
H


x
y  y
x 
245
VH  V 2 H  UVH 
1 P
 g 2  0


  fUH   a  gH 
H
t
y
x
ρ 0 y
y 2  0
y


  2V  2V 
g  
 h V
  U V 
H h   
h  z  'dz dz   yz ( )   yz (  h )  H h  2  2   2 H
 0  y
y y
x  y x 

 x y 
 Diffusion equations for temperature, T and salinity, S (here both are denoted as C):
C
C
C 1  
C  1  
C 
U 
V 

 HDy 

 HDx 

t
x
y H x 
x  H y 
y 
where, x, y, z form the right-handed Cartesian coordinate system, U and V are the
depth-averaged velocity and H=h+, where  is the free surface and h is the depth. The
term f is the Coriolis parameter, P a is the atmospheric pressure, h, and z are, respectively,
the horizontal [9] and vertical [10] eddy viscosity coefficients, D x and Dy are the horizontal
diffusivity coefficients and  = 0+’ is the water density, with 0 being the reference
density. Density is obtained from the values of T and S using the UNESCO equation of
state, as adapted by Mellor [11].
Model equations are written on a staggered grid (Arakawa C) and are solved by means
of an implicit finite difference method, except for non-linear terms, which are treated
explicitly. The finite difference algorithm is a centered, two time levels scheme, resulting in
a second order approximation in space and time.
3. Model inputs
The actual bathymetry between Mallorca and Menorca islands (Fig 2a) may be
schematically modelled as shown in Fig. 2b, taking a platform depth of 60m bounded by a
1000m ocean. Both actual and simplified bathymetries are used in separate simulations. A
set of atmospheric perturbation propagating upwards with phase speeds ranging between 15
and 50 m/s has been used as the boundary condition along the lower boundary of the
computational domain. The atmospheric perturbation employed in simulations is the actual
record measured during 22-23 July, 1997, corresponding to a rissaga event In numerical
computations, the grid size is 0.5 km and the time step for all the simulations has been 5 s.
Boundary conditions in both bathymetry cases are radiation conditions in the upper and
lower boundaries and reflection condition on the left and right ones.
246
Figure 2. Actual (a) and idealized (b) bathymetries of Menorca Channel
Figure 3. Sea level spectra for 25 m/s atmospheric phase speed forcing for real (full line) and idealized
(dashed line) bathymetries (16 degrees of freedom) a). Spectral ratio between sea level (in cm) and
atmospheric pressure (in Pa) versus phase speed for real (full line) and idealised (dashed line)
bathymetries b.)
4. Results
Time series of modelled sea level height at a point close to the upper coast have been
analysed by means of spectral techniques and compared with in-situ measurements. A
Kaiser-Bessel window of 512 points has been used for segments of 2400 data,
corresponding to 40 hours of simulation, resulting in 16 degrees of freedom. In both
247
spectra, several peaks, probably associated with standing waves, are clearly identified (Fig.
3a). The spectral ratio between sea level height (cm) and atmospheric pressure (Pa) for
Figure 4. Atmospheric forcing and computed sea level at three different points a). Comparison between the
measured and computed spectra of the free surface at these three points (14 degrees of freedom): outside
Ciutadella inlet b),atthe end of line Ciutadella inlet c) and inside the neighbouring inlet of Platja Gran
d).
different values of the atmospheric perturbation phase speed and for both bathymetries are
shown in Fig. 3b.
248
These results suggest that the presence of the two islands in the wave track is a
favourable point to the generation of standing waves, whose periods are basically
controlled by the platform length and depth. However, their energy is deeply depending on
the atmospheric waves phase speed. The optimal energy transfer between the atmosphere
and the ocean occurs for phase speeds of about 25 m/s, value which is close to (gH)1/2 in
the ideal case (24.24 m/s) and coincides with the measured velocity of the atmospheric
waves when major events have been observed.
5. Sea level oscillations inside the inlet
The same numerical model, with a smaller grid of 10 m and corresponding time step of 0.5
s, has also been used to simulate the wave propagation inside Ciutadella and Platja Gran
inlets. The finer grid model has been fed through the lower boundary with the sea level
results obtained from the outer model which was forced with the 25 m/s atmospheric wave.
The radiation condition is used in the open boundaries.
Figure 4a shows the atmospheric pressure record and the modelled sea level records at
the mouth (outside Ciutadella inlet) in approximately 30 m water depth, in the upper end of
Ciutadella inlet and in a neighbouring inlet, Platja Gran (see Fig. 1). Time series of 36
hours have been analysed as described above, now resulting in 14 degrees of freedom. The
measured and computed spectra at these points are shown in figures 4b, c and d. It can be
seen that outside the inlet (Fig. 4b), the oscillation is very weak, peaking at 24min, both in
the numerical and in the measured spectra. Other smaller peaks, appearing both in higher
and lower frequencies, have poorer match due to the limitations of the grid (for lower
frequencies) and the definition of the boundaries. The disagreement for periods larger than
1 hour is explained by the fact that the used domain is too small. Figure 4c shows the
spectra of the oscillations inside Ciutadella, in its upper end, where the oscillations are
maximal. In this case, the peak corresponds to the resonant period of the inlet fundamental
mode of 10.5 minutes. The matching between the measured and the computed spectral
density is excellent. Also the first mode, of about 5 minutes, shows an almost perfect
match. Finally, figure 4d shows the spectra of the oscillations inside the neighbouring cove
Platja Gran. In this case, the major peak corresponds to the resonant period of this smaller
cove, 5.1 minutes. Again, the matching between the measured and computed spectra is very
good.
6. Conclusions
Atmospherically generated large amplitude seiche oscillations (meteotsunamis) observed in
Ciutadella inlet (Balearic Islands) are numerically simulated. It is shown that travelling
atmospheric pressure fluctuations generate standing waves in the platform between the two
islands. Their periods are basically controlled by the platform length and depth, but their
energy depends on the atmospheric waves phase speed. The optimal energy transfer
between the atmosphere and the ocean occurs for phase speeds of about 25 m/s, value
which coincides with the measured velocity of the atmospheric waves when major events
have been observed. Finally, the complete process inside the inlet is simulated by using a
fine grid model with boundary forcing obtained from the coarse grid model on the shelf.
The simulated sea level oscillations inside the inlets compare very well with observed data.
249
References
1. Honda, K., Terada, T., Yoshida, Y. and Isitani, D. (1908) An investigation on the secondary undulations of
oceanic tides, J. College Sci., Imp. Univ. Tokyo, 108 p.
2. Hibiya, T. and Kajiura, K. (1982) Origin of `Abiki' phenomenon (a kind of seiches) in Nagasaki Bay, J.
Oceanogr. Soc. Japan, 38, 172-182.
3. Wang, X., Li, K., Yu, Z. and Wu, J. (1987) Statistical characteristics of seiches in Longkou Harbour, J. Phys.
Oceanogr., 17,1063-1065.
4. Hodvzic, M. (1979) Exceptional oscillations in the Bay of Vela Luka and meteorological situation on the
Adriatic, International School of Meteorology of the Mediterranean, 1 Course, Erice, Italy.
5. Papadopoulos, G. A. (1993) Some exceptional seismic (?) sea-waves in the Greek Archipelago, Science of
Tsunami Hazards, 11, 25-34.
6. Gomis, D., S. Monserrat, J. Tintoré (1993) Pressure-forced seiches of large amplitude in inlets of the Balearic
Islands, J. Geophys. Res., 98, 14437-14445
7. Monserrat, S., A.B. Rabinovich, B. Casas (1998) On the Reconstruction of the Transfer Function for
Atmospherically Generated Seiches, Geophys. Res. Let.,25, 2197-2205
8. Monserrat, S., A.J. Thorpe (1992) Gravity wave observations using an array of microbarographs in the Balearic
Islands, Q. J. R. Meteor. Soc., 118, 259-282.
9. Smagorinsky, J. (1963) General circulation experiments with the primitive equations, Mon. Weather Rev., 91,
99-165
10. Jin, X., Kronenburg, C. (1993) Quasi-3D numerical modelling of shallow water circulation, Journal of
Hydraulic Engineering, Vol 119, 4, 458-472
11. Mellor, G.L. (1991) An equation of state for numerical models of oceans and estuaries, J. Atmos. Oceanic.
Technol., 8, 601-611
250