This document discusses comparisons between observed sea level data from tide gauges around the Mediterranean Sea in 2002 and predictions from two dynamical models - the barotropic Mog2D model and the ocean circulation Mercator PSY2 model. It finds that a combination of the low-pass filtered Mercator sea level and the Mog2D model most closely matches the observations. This combined prediction explains 10-20 square cm of the total sea level variance compared to the observations. While the individual models leave significant residuals, the composite prediction fits the tide gauge data remarkably well except for some events that neither model captured fully.

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Composite sea level prediction in the Mediterranean
Sea - comparisons with observations
By Florent Lyard and Laurent Roblou
1. Abstract
In this presentation, we focus on the sea level recorded and modelled in the Mediterranean Sea during the year
2002. Two dynamical models are made available to us, the first one designed to solve the ocean circulation
(Mercator Psy2-v1 (Newsletter Mercator N°8)) and the second one to solve the tide and storm surge processes
(Mog2D). We challenge the assumption that a combined use of those two models (i.e. through a full or partial
summation) should provide an optimal sea level predicting tool. By comparing with tide gauge measurements, the
predicting skills of models, alone and/or combined together, are estimated for different frequency ranges. The
two major conclusions that can be drawn from this study is that first a combination of low-pass filtered Mercator
plus Mog2D closely fits the recorded data, and second the Mog2D low frequency sea level signal is surprisingly
needed in this combination to obtain the best prediction (instead of the low-pass filtered Inverted Barometer
(IB)). Further investigations will be necessary to understand precisely the reasons of the latter finding.
2. Introduction
The sea level variations are one of the most measured
parameter of the physical oceanography. Beside the
classical tide gauge networks, the recent and present
satellite altimetry missions provide a constant flow of
data which continuity extends now for more than ten
years. Most of the sea level variability is due to the
tides and the meteorologically driven dynamic, but
ocean surface circulation or steric effects are clearly
depicted in sea surface measurements. Therefore the
sea level is an highly valuable observation, either for
ocean dynamic models validation or assimilation,
however its full and precise exploitation requests some
additional treatment, like horizontal and spatial scale
separation and de-aliasing.
Among other modelling efforts (Mathers [2000], Ponte
[1997], Ponte et al. [1991] and Ponte [1991]), the
global simulation of the ocean response to the
atmospheric forcing has been completed at the LEGOS
for the 1992-2003 period from the barotropic finite
element (FE) model Mog2D-G, on a medium resolution
mesh. The main objective of this simulation is to
provide the scientific community with improved high
frequency sea level corrections (compared to the
classical inverted barometer parameterisation; see
Wunsch et al., [1997], Woodworth et al., [1995]) in
the altimetric GDR in order to de-aliase the ocean
circulation signal (see e.g. Stammer et al., [2000],
Ponte and Gaspar, [1999], Gaspar and Ponte, [1997]).
In addition, a Mediterranean regional model has been
developed on a high resolution mesh for the Albicocca
project where altimetric and tide gauge measurements
are compared together for calibration and coastal
circulation observation purposes.
Due to the quasi-barotropic nature of the ocean
dynamical response to atmospheric forcing at periods
lower than about 30 days, Mog2D has most of the skills
needed to model the ocean high frequency dynamic.
For the larger time scales, the true ocean response to
the various forcing includes a significant baroclinic
contribution. Moreover, the ocean dilation due to the
heat content variation (steric effects) is a major
contributor to the sea level variability at the annual
and seasonal time scales. The OGCM models shows a
very complementary pattern, as most of the high
frequency dynamic (mostly barotropic) is filtered out,
while thermo-haline and low frequency wind-driven
dynamic is properly represented. Thus a simplistic idea
would be that the total sea level variation signal can be
predicted by a summation of a Mog2D prediction with
an OGCM sea surface. Nevertheless, two problems
need to be addressed: first, the barotropic model and
the OGCM have a common forcing term, namely the
low-frequency wind, and therefore may content some
redundant dynamic contributions. Secondly, the OGCM
assimilates sea level data where inverted barometer is
applied, thus a residual, dynamical aliased gravity
wave type signal is introduced in the simulation, but
possibly filtered later on by the model. To that point, it
is nearly impossible to quantify exactly what is the
OGCM high frequency content, and what is the Mog2D
low frequency content.
Therefore the usually recommended approach would be
to perform the model sea level combination by filtering
the low-frequency signal in the barotropic prediction,
and reversely the high frequency signal in the OGCM
simulation before adding them together. Doing so, the
low frequency inverted barometer needs to be added to
the combination as the atmospheric pressure loading
contribution is not insignificant in the low frequency
band and it is not present in the OGCM sea level. For
similar reasons, the combination of high-pass (20
days) filtered Mog2D simulation with low-pass filtered
inverted barometer is usually seen as the best guess
for altimetric data correction before their assimilation
in an OGCM. Although considered as very reasonable,
these assumptions need to be verified more closely.
The Mediterranean Mog2D and the Mercator PSY2
simulations, plus the existence of a large tide gauge
network, provide us the opportunity to scrutinise the
various hypotheses.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
3. The Mog2D model
Figure 1: Mid-resolution finite element mesh used.
Mog2D (2D Gravity Wave model) is a barotropic, non
linear and time stepping model, derived originally from
Lynch and Gray [1979] and developed since for coastal
to global tidal and atmospheric driven applications
(Greenberg and Lyard, personal communication).
Model governing equations are based on the classical
shallow water continuity and momentum equations.
These are solved through a non linear shallow-water
wave equation with a quasi-elliptic formulation which
improves numerical stability. The currents are derived
through the non conservative momentum equation. The
model capabilities include tidal and meteorological
forcing (atmospheric surface pressure and wind). Its
main originality is a finite element space discretisation
(FE), which allows to raise resolution in regions of
interest like high topographic gradient areas (showing
strong current variability and internal waves
generation) and shallow waters, where most of bottom
friction dissipation occurs. To improve the
computational efficiency, a reduced time-stepping
scheme is dedicated to care on unstable model nodes.
The bottom friction is taken from a Chezy-type
quadratic parameterisation. A novel parameterisation
of the barotropic to baroclinic energy transfer (through
the internal waves generation on topographic slopes) is
included in the model. The horizontal viscosity is
prescribed following the Smagorinsky viscosity scheme
(Smagorinsky [1963]) which allows to take into
account the varying FE mesh cells size. By essence, the
barotropic model does not include any vertical energy
dissipation (like ocean de-stratification processes or
vertical shear drag), which appears to be a problem
when the annual mean wind stress is kept in the
simulation forcing. In this case, some unrealistically
strong deep ocean circulations can appear. An
additional rough Raleigh-type dissipation term is
thus introduced in order to parameterise the
internal dissipation (Egbert and Ray [ 2000], Morozov
[2000]).
Boundary conditions have been extracted from the
Mog2D-G global simulation through a radiative
condition (characteristics method). For the present
study, only atmospheric forcing is applied to the model
(no tidal forcing, neither potential nor boundary
conditions). Surface pressure and 10 metres wind are
taken from the ARPEGE (Météo france) and ECMWF
fields (ECMWF [1991]) with a temporal resolution of 6
hours (which implies that frequencies lower than 12
hours are widely misrepresented). The wind stress is
derived from the classical formula of Rosati and
Miyakoda [1988] (with ocean surface and atmospheric
temperatures taken equal to zero in the present
application). At each time step, the atmospheric
pressure is corrected from its instantaneous global
mean, to guaranty the oceanic mass conservation and
thus be able to compare our simulations with the IB
approximation.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
4. Wind and pressure driven sea level overview
Computed on year 2002, the Mediterranean sea
surface shows a 10 centimetre gradient from East to
West (figure 2). This gradient is mainly due to the
atmospheric pressure mean gradient. Some regions
show local coastal gradient, linked generally with a
coastal mean transport (Adriatic Sea, Gulf of Gabes,
Lybian-egyptian coast) or local wind regime. On
average, the sea level variability due to the wind and
pressure forcing ranges from 5 to 10 centimetres
(figure 3), with maximum values observed on shallow
water regions. In most part of the Mediterranean Sea,
it is comparable to the tidal variability. The
atmospheric pressure driven sea level variations in the
Mediterranean Sea are well known to poorly fit the
inverted barometer parameterisation (Candela et
Lozano [1994], Candela [1991]). Adding the wind
effect, the departure is even greater, especially in the
Eastern basin (Gulf of Gabes and Adriatic Sea), with a
strong seasonal modulation. As shown on Figure 4, the
mean IB departure is of the order of 1 to 2 cm, nearly
uniform in the eastern and western basin, but showing
the signature of the coastal circulation mentioned
above. The model departure from IB standard
deviation (Figure 5) ranges from 6 to 9 centimetres,
which compares to 50% up to 100% of the sea level
variability itself. In the western basin, the Gulf of Lyon
shows the maximum IB departure, due to the presence
of the continental shelf and the intense wind regime.
Figure 2: Mean sea level computed from Mog2D over
the year 2002. Units are centimetres.
Figure 3: Sea level standard deviation computed from
Mog2D over the year 2002. Units are centimetres.
Figure 4: Mean inverted barometer departure over the
year 2002. Units are centimetres.
Figure 5: Inverted barometer departure standard
deviation over the year 2002. Units are centimetres.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
5. Comparisons with tide gauge observations
As an illustration, we show the instantaneous sea level
(13th of February 2002 at noon) computed from
Mog2D (figure 6), deduced from Mercator surface
pressure (figure 7) and the summation of the two
maps (figure 8). Apart from the tides and the geoïd,
the latter represents probably the best approximation
of the true sea level at this date, if our assumption that
the two models are complementary is correct.
Figure 6: Mog2D instantaneous sea level at noon
13/02/2002. Units in centimetres.
Figure 7: Mercator instantaneous surface pressure at
noon 13/02/2002. Units in centimetres.
Figure 8: Composite (Mercator plus Mog2D)
instantaneous sea level at noon 13/02/2002. Units in
centimetres.
For the present study, focusing on year 2002, most of
available observations come from the SONEL
distribution and the Italian network (SIMN) (see Figure
9 and table 1). Only a subset of typical stations has
been chosen to avoid a tedious presentation. The
selected sites are marked in grey in table 1. The hourly
delivered time series are detided in a preliminary step
[Ponchaut et al., 2001]. The comparisons covers the
full year period to insure a reasonable statistical
significance. We compare three original predictions
(Mog2D, IB, and Mercator) and three composite
predictions (CP-1, Mog2D plus Mercator; CP-2, Mog2D
plus filtered Mercator; CP-3, IB plus Mercator) with the
observations. All models and observations are
corrected of an yearly average sea level to narrow the
curves (relative levels). Comparisons are detailed for a
set of different period range to investigate the model
prediction skill in the whole frequency spectrum range.
Figure 9: Available tide gauge observation sites for the
2002 period. The tide gauge presented in this paper
have been named. The map background indicates the
bathymetry (in metres), with colour interval's chosen
to highlight the shallower regions.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
On plate 1, we display the variance histograms for the
observed signal and the residuals signal (after model
correction). The first bar’s group shows the total
variance, the following are computed for specific
frequency bands. The total variance of the sea level
corrected by the composite model CP-2 ranges from 10
to 20 square centimetres over the tide gauge network,
which means roughly that the sea level CP-2 has a
typical 4 cm mean accuracy. On figures 10 to 18, we
have plotted the observed sea level versus the
Mercator and composite prediction CP-2. The
composite prediction has been built as the summation
of Mog2D seal level plus the low-pass filtered Mercator.
Cut-off frequencies (given in Table 2) has been chosen
so that the composite prediction shows the minimum
residual variance in each frequency band after
correcting the observed sea level. It is graphically clear
that for all locations the composite model fits much
better the observations than Mercator sea level alone.
Apart from some very high frequency oscillations and
some abnormal peaks in the observations, most of the
observed signal is well simulated by the composite
model. The very high frequency left in the observations
after detiding can be true signal (local resonance like
seiches, for instance in the Adriatic Sea, diurnal wind
excitation, intermittent internal waves) mis-
represented by the models or observation errors (in
particular tides can not be properly removed in case of
a problem with the tide gauge clock, thus leaving a
large high frequency signal in the ill detided
observations). The agreement with the observations
are quite spectacular at Nice and Genova tide gauge,
apart during September (CNES day 19236 up to
19266). During this month, both tide gauge record a
quasi-linear sea level rise of about 20 centimetres. In
fact, this event can be seen in all north western tide
gauge records. Neither Mercator nor Mog2D show a
similar pattern. The most likely explanation of such a
sea level rise is that the Liguro-provencal current has
intensified and/or got closer to the coast during this
period. Because of the proximity with the shorelines
and the narrowness of the current main jet, it might be
plausible that the hydrodynamic modelling could not
capture this event nor the assimilation correct the
forecast. Additional investigations (possibly within
MFSTEP and Albicocca projects) are needed to
understand exactly the nature of the September 2002
event and the reasons of its absence in the models.
Table 1: Tide gauges locations.
Table 2: Cut-off period for CP-2 construction.
Code Station marégraphique Longtitude Latitude
1 Ajaccio 8,767 41,917
2 Ancona-1 13,502 43,625
3 Bari 16,867 41,137
4 Cagliari 9,108 39,207
5 Carloforte 8,305 39,14
6 Catania-1 15,09 37,492
7 Civitavecchia 11,783 42,087
8 Crotone 17,135 39,073
9 Genova 8,922 44,405
10 Imperia-1 8,018 43,873
11 Lampedusa 12,617 35,483
12 Livorno 10,293 43,54
13 Marseille 5,35 43,283
14 Monaco 7,417 43,733
15 Messina-1 15,558 38,187
16 Nice 7,267 43,267
17 Napoli-1 14,268 40,837
18 Ortona 14,41 42,353
19 Otranto 18,492 40,142
20 Palermo 13,368 38,285
21 Palinuro 15,272 40,025
22 Porto-Empedocle-1 13,522 37,287
23 Porto-Torres 8,403 40,838
24 Ravenna 12,275 44,492
25 Reggio-Calabria 15,643 38,118
26 Salerno 14,742 40,675
27 Toulon 5,917 43,117
28 Taranto 17,222 40,472
29 Trieste 13,753 45,653
30 Venezia 12,422 45,42
31 Vieste 16,172 41,888
32 Senetosa-MX 8,813 41,55
33 San-Antonio 1,3 38,967
Station marégraphique Période de coupure
Bari 30 jours
Cagliari 60 jours
Crotone 30 jours
Genova 10 jours
Lampedusa 30 jours
Nice 60 jours
Salerno 10 jours
Trieste 60 jours
San Antonio 60 jours

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
Plate 1 :
Sea level variance for observed sea level corrected
from models and models combinations. Units are cm².
The first bar's group shows the total variance. The
following are computed for specific frequency bands.
The period intervals (T) are given in days. As
mentioned in the text, PSY2v1 + IB corrected is the
composite prediction CP3, PSY2v1 +MOG2D corrected
is CP1 and PSY2v1/MOD2D composite corrected is CP2.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
Figure 10: Bari tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus low-
pass filtered Mercator) sea level (right). Series start February the first 2002
Figure 11: Cagliari tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus
low-pass filtered Mercator) sea level (right). Series start February the first 2002.
Figure 12: Crotone tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus
low-pass filtered Mercator) sea level (right). Series start February the first 2002.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
Figure 13: Genova tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus
low-pass filtered Mercator) sea level (right). Series start February the first 2002.
Figure 14: Lampedusa tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus
low-pass filtered Mercator) sea level (right). Series start February the first 2002.
Figure 15: Nice tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus low-
pass filtered Mercator) sea level (right). Series start February the first 2002.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
Figure 16: Salerno tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus
low-pass filtered Mercator) sea level (right). Series start February the first 2002.
Figure 17: San Antonio tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D
plus low-pass filtered Mercator) sea level (right). Series start February the first 2002.
Figure 18: Trieste tide gauge: observed sea level versus Mercator (left), versus composite (CP-2; Mog2D plus
low-pass filtered Mercator) sea level (right). Series start February the first 2002.

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
6. Discussion
7. Conclusion
This preliminary comparisons of Mercator simulations to the sea level observed along the Mediterranean coast is
an additional contribution to the validation of this model. From this study, it is clear that the Mog2D simulations is
needed to reconstruct a synthetic sea level that can be more easily compared with tide gauge observations. In
fact, the combination of Mercator and Mog2D simulation can be seen as a valuable valorisation product for sea
level analysis or prediction, even in coastal regions.
Nevertheless, the pertinence of Mog2D low frequency signal rises many theorical and practical questions, like the
role of non-linearities due to high frequency dynamic in the low frequency sea level changes, and the definition of
an optimal approach to perform either Mercator’s sea level validation from tide gauge and satellite altimetry data
or data correction for assimilation in Mercator’s model.
As expected, the Mog2D prediction does explains much
of the high frequency sea level signal, and a much
smaller part of the signal for periods larger than 30 or
60 days. Similar conclusions can be drawn from the IB
prediction, except that it does not perform as well as
the numerical model does. On the reverse, the
Mercator prediction does explain a large amount of low
frequency signal, and shows poor performances for
periods less than 30 days.
The composite signals, i.e. Mercator plus IB and
Mercator plus Mog2D, show expected numbers in the
high frequency band, which is that adding Mercator
deteriorate the sea level prediction compared to Mog2D
or IB prediction alone. The reason being that Mercator
signal is not relevant and adds noise in this frequency
band. More surprisingly, the examination of the low
frequency band does not fit our preliminary view. We
would have expected that the optimal combination for
the low frequencies would have been Mercator plus the
inverted barometer, because first the barotropic
numerical model is not appropriate for ocean low
frequency dynamic, and second, part of the wind
forced signal may be redundant. But what we see is
that the best fitting to observations composite is
systematically Mercator plus Mog2D composite, which
might mean that Mog2D simulation contains a relevant
low frequency signal that is not present or partially
present in the Mercator simulation.
Of course, Mercator PSY2-v1 can not be considered as
a proper coastal model, mainly because the filtering of
the gravity waves, the lack of tidal and atmospheric
pressure forcing and its spatial resolution. Comparing
Mercator sea surface with coastal tide gauges
observations is somehow unfair to the model,
especially if the tide gauges are locating on a large
continental shelf. Nevertheless, there is no systematic
trend in the model low frequency misfit’s magnitude if
one considers a shelf tide gauge (like Trieste or
Lampedusa), and more pelagic-like one (like San
Antonio or Nice). So, except perhaps in the case of a
coastal jet, the Mercator sea surface low frequency
component extrapolates quite well to the shorelines. To
complete the picture, it is necessary to extend the sea
level comparisons with altimetric data, and to consider
in addition a coastal circulation model (possibly forced
at its boundary by Mercator’s simulations; note that
the POC, Pôle d’Océanographie Côtière de Toulouse, is
already investigating these topics for coastal circulation
modelling applications and for coastal altimetry
products development, in collaboration with the Groupe
Mission Mercator).

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Composite sea level prediction in the Mediterranean Sea - comparisons with observations (continued)
8. References
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Mathers, E.L., Sea level response to atmospheric pressure and wind forcing in the global deep ocean, PhD Thesis,
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Morozov, Semidiurnal internal wave global field, DSR 1, 42, 135-148, 1995.
Ponchaut, F., Lyard, F., Le Provost, C., An analysis of the tidal signal in the WOCE sea level dataset , J. Atmos.
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Ponte, R.M., Salstein, D.A., Rosen, R.D., Sea level response to pressure forcing in a barotropic numerical model,
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Ponte, R.M., Gaspar, P., Regional analysis of the inverted barometer effect over the global ocean using
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Smagorinsky, J., General circulation experiments with the primitive equations, Monthly Weather Review, 1963.
Stammer, D., Wunsch, C., Ponte, R.M., De-aliasing of global high frequency barotropic motions in altimeter
observations, Geophys. Res. Letters, 27 (8), pp 1175, 2000.
Woodworth, P.L., Windle, S.A., Vassie, J.M., Departures from the local inverse barometer model at periods of 5
days in the central South Atlantic, JGR, 100 (C9), 18281-18290, 1995.
Wunsch, C., Stammer, D., Atmospheric loading and the oceanic inverted barometer effect, Reviews of
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