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Journal of Coastal Research (Edition) (Pg-pg) ICS (Country) (ISSN)
Journal of Coastal Research, (year)
1
Storm Surge Hydrodynamic Modelling
N.R.C. Marujo-Silva1, M.A.V.C. Araújo
2, A. Trigo-Teixeira
3 and A. P. Falcão
4
1CEHIDRO Instituto Superior Técnico,
Technical University of Lisbon
1049-001 Portugal [email protected],
2CEHIDRO Instituto Superior Técnico,
Technical University of Lisbon
1049-001 Portugal [email protected]
3CEHIDRO Instituto Superior Técnico,
Technical University of Lisbon
1049-001 Portugal [email protected]
4ICIST Instituto Superior Técnico,
Technical University of Lisbon
1049-001 Portugal [email protected]
ABSTRACT
Marujo-Silva, N.R.C., Araújo, M.A.V.C., Trigo-Teixeira, A. and Falcão, A. P., (year). Storm
surge hydrodynamic modelling. Journal of Coastal Research, (Issue designation), (pg-pg).
Location. ISSN.
In the present work a strong emphasis is given to the model calibration prior to the storm surge
phenomenon modelling. This event took place during the period of 14th
- 16th
October 1987.
Considering the two hydrodynamic scales existing in the interest area, the simulations considered
two different domains to account for different processes. A large domain including part of the
Atlantic Ocean was used to simulate the storm surge event along the Portuguese coast and a
second smaller domain to capture the Lima estuary storm surge response. Prior to simulations, a
field survey using Global Navigation Satellite System (GNSS) techniques was carried out to
build a local geoid undulation model (LGUM) and improve the existing bathymetry in the Lima
estuary. Both model setup were defined and calibrated for both domains using the astronomy
forcing and changing the friction coefficient, lateral viscosity, wave continuity and Coriolis
parameter. Thereafter the interaction between astronomy and meteorology was assessed
considering these jointly and separately. The river flow was also considered for the estuarine
domain simulations. The obtained results show a preponderance of the friction coefficient over
other parameters and the importance of considering a variable Coriolis parameter for large
domains in latitude. The best calibration results were obtained considering the 10 most important
tidal harmonic constituents: M2, S2, N2, O1, K1, K2, Q1, P1, NU2 and MU2. The meteorology
was found to have non linear interaction with the astronomy in both domains, even when
considering the river flow.
ADDITIONAL INDEX WORDS: ADCIRC model, Lima estuary, wetting/ drying, river flow,
inverted barometer effect, geoid undulation model
INTRODUCTION
Floods in coastal and estuarine areas are mainly caused
by the sea level rise due to strong winds, significant
pressure drops and the frequently associated
precipitation. The effects of these factors can be strongly
enhanced in case the storm hits the coast in a period with
high water levels. Significant material damage and
human loss may happen due to these phenomena.
Even though along the Portuguese coast these events are
not as extreme and critical as in other places, due to their
frequency and associated damages and losses, it is
considered of great importance to model and forecast the
impact of such events. Nonetheless, during storm surge
events, the sea level rise may cause flow rate changes of
the sewage systems, which are more severe than the
design scenarios, usually considering only the maximum
astronomic tide (MAT) instead of the maximum sea
surface elevation, which can be set as a linear
combination of the mean high water springs and a storm
surge height with a set return period.
Knowledge of the character of such events allows a
significant reduction in losses and damages in case
extreme storms hit the coast. The recurrence interval can
be increased and the impact of such events can be
mitigated if preventive measures are taken. Furthermore,
the risk can be assessed before damage occurs to coastal
and estuarines structures and lives are lost.
The European Union (EU) directive 2007/60/CE
concerning the assessment and risk management of
floods states that each member of the EU must assess the
flooding risk level, create risk charts and take adequate
measures in order to mitigate the risk wherever needed.
This directive, also known as “EU Flood Directive”,
considers, for the first time, three assessment stages:
flooding risk assessment, flooding risk charts and
flooding risk management. This directive explicitly
considers coastal and estuarine areas.
Storm surge hydrodynamic modelling
Journal of Coastal Research, (year)
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A detailed study as presented in this paper is justified
since there is little knowledge about the impact of storm
surges in estuaries and lagoons in Portugal. The fact that
few tidal gauges are present and limited data available
are two more reasons why this detailed study is justified.
This information is needed in order to perform flood
frequency assessments and, at a second stage, create risk
charts. This phenomenon is well studied for river
systems upstream of the tidal influence but is less
understood in estuaries and lagoons with significant tidal
influence.
For the Lima River, which has an estuary where
mesotidal amplitudes are observed, the focus will be in
the zone where the storm surge impacts are expected to
be more severe. In this work, firstly the Digital Terrain
Model (DTM) built for the Lima Estuary is presented.
After the ADCIRC model setup is described, the
calibration process detailed and the model validation
results are presented.
DTM FOR THE LIMA ESTUARY
Considering the fact that one of the purposes of the
present study is the creation of a DTM for the Lima
estuary and a Local Geoid Undulation Model (LGUM), a
field survey was conducted to acquire the required
information to complement the already existent.
This survey was carried out in two parts: a high precision
position acquisition, in geodetic and levelling marks, and
position acquisition for several points in intertidal areas.
The survey was made using Global Navigation Satellite
System (GNSS) devices.
The first part was intended to provide the ellipsoidal
heights (h) in points where the orthometric heights (H)
were already known – geodetic and levelling marks.
According to Falcão (2010), Featherstone et al. (1998)
and Fotopoulos (2005), using expression (1) it is
possible to compute the geoid undulation (N).
(1)
Figure 1 – Local geoid undulation model for the Viana do Castelo
area (adapted from Falcão et al., 2011).
where, H(P) is the orthometric height of a point P, h(P)
is the ellipsoidal height of point P and N(P) is the geoid
undulation at point P.
With the geoid undulation for 10 points in the Viana do
Castelo area and using kriging techniques, according to
Falcão (2010), it was possible to define the LGUM for
this area. In figure 1, the obtained local geoid undulation
model for the Viana do Castelo area is presented.
The second part of the survey consisted in acquiring
bathymetry data in areas where information was lacking.
These areas were intertidal regions for which a GNSS
pedestrian campaign was performed. The recorded data
was post-processed and coupled to the other bathymetry
sources for the Lima estuary. These sources comprise
both altimetry and bathymetric datasets.
The altimetry dataset was obtained from the topographic
map at scale 1/25000 created by the Portuguese Army
Geographical Institute (IGEOE). The data was acquired
in 1997 and represented in the Hayford-Gauss coordinate
system Datum Lisboa Militar (SHGDDTLXMIL) with a
contour interval of 10 m. The bathymetric data can be
subdivided into three datasets: Lima, Eiffel and Estuary.
These were collected by the Hidrodata Company and
represented in the SHGDTLXMIL cartographic system.
The Lima river data was collected in 2006 with a spatial
resolution of approximately 20 m by 10 m. The Eiffel
data was collected in the vicinity of the Eiffel bridge in
2006 with a spatial resolution of approximately 2 m by 2
m and the data named Estuary were collected in 2006
with a spatial resolution of approximately 5 m by 5 m.
With the different datasets coupled, respecting the same
datum, according to Falcão (2011), the bathymetry DTM
was created for the Lima estuary. The information of this
DTM was used to extract a grid scatter set with 50 m by
50 m spacing, which was used as the bathymetry dataset
for the Lima estuary simulations. This is presented in
figure 2.
Figure 2 – Combined bathymetric DTM for the Lima estuary.
Marujo-Silva et al.
Journal of Coastal Research, (year)
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MODEL SETUP
ADCIRC numerical model description
The Advanced Circulation Model (ADCIRC) is a
numerical model based on the finite element approach
which allows the modelling of long period waves in 2D
or 3D. In this study the two dimensional depth integrated
(2DDI) version of the momentum and the continuity
equations was used. These equations consider the usual
approximations in coastal engineering applications:
incompressibility, Boussinesq and hydrostatic pressure.
The 2DDI equations are reproduced in equations (2), (3)
and (4) in geographical coordinates. The first is the
continuity equation and the following two the
momentum equations, respectively in the x and y
horizontal directions written considering the u and v
velocities (Luettich et al., 1992; Luettich and Westerink,
2004)).
(2)
(3)
(4)
where, is the time, and are, respectively, the
longitude (positive East of Greenwich) and latitude
(positive North of Equator (degrees), is the water
surface elevation, and are the depth-averaged
horizontal velocities, is the total water
column height, is the bathymetric depth, is the
Coriolis parameter, is the Earth radius, is the
reference density, is the gravitational acceleration, is
the Earth elasticity factor, is the Newtonian
equilibrium tidal potential, Ps is the atmospheric pressure
at the sea surface, sx and sy are the imposed surface
stresses in x and y direction, respectively, bx and by are
the bottom stress components in x and y direction,
respectively.
From Reid (1990) the Newtonian equilibrium tidal
potential is presented in expression (4.4).
(5)
where, Cjn is a constant characterizing the amplitude of
tidal constituent n of species j, fjn is the time-dependant
nodal factor, vjn is the time-dependent astronomical
argument, j=0, 1, 2 are the tidal species (j=0 -
declinational; j=1 - diurnal; j=2 - semidiurnal),
, , , t0 is the
reference time and Tjn is the period of constituent n of
species j.
The presented equations will be solved based upon the
spatial discretization using the Finite Element Method
(FEM) and in time using the Finite Differences Method
(FDM). The 2DDI equations are discretized in space
using Garlekin Finite Elements (GFE) and in time using
Three Level Finite Differences (TLFD). The model
discretization in space is based on a finite element
method approach, materialized by an unstructured mesh
with triangular elements, whereas in time is based on a
chosen time step .
Figure 3 – Oceanic domain mesh (M0) and the location of the 8 considered tidal gauges along the Portuguese coast.
Storm surge hydrodynamic modelling
Journal of Coastal Research, (year)
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Figure 4 – Estuarine mesh and the location of the five recording
stations considered in the study of the storm surge in the Lima
estuary.
Computational domain
In this paper, two domains were considered: an oceanic
domain and an estuarine domain. These were defined at
two different stages of the storm surge modelling to
account for different effects.
The boundaries of the oceanic domain are the meridians
8ºW and 34ºW and the 36.5ºN latitude line and parallel
48ºN. Where the meridian 8ºW intersects land the
boundary is changed and materialized by the 4m
bathymetric depth contour. This depth contour was
chosen in order to avoid using the wet and dry option in
this initial stage of the project. This is considered
conservative since the tidal amplitude for this region is
smaller than 4 m.
The estuarine domain was defined in such a way that the
estuary tidal flats and the ebb/ flow channels are
considered. While setting up the model several factors
were taken into account such as the inclusion of
mudflats, channels and avoiding complex features such
as bridge columns and breakwaters. The ocean boundary
was created considering an arc of circumference with a
radius of approximately 8 km and the domain extended
approximately 9 km upstream of the river mouth. The
north and south boundaries were defined to coincide
with the river banks.
The meshes used in both the oceanic and estuarine
domain simulations are represented in figure 3 and 4,
respectively.
Bathymetry
The bathymetry used in the present study has different
sources. Near the Portuguese coast up to a depth of 4000
m, nautical Portuguese charts scaled 1:150 000 and 1:1
000 000 were digitalized. For deep water, the bathymetry
was obtained from the world database of the Institute of
Geophysics and Planetary Physics with a grid resolution
of 1 minute (Smith and Sandwell, 1997).
For the estuarine domain, as previously mentioned, the
built DTM provided a scatter with a grid cell size of 50
m by 50 m, which was merged with the bathymetry data
for the Atlantic Ocean.
Data sources
Following the research work of Araújo et al. (2011) most
of the data sources presented herein are the same.
The observed hourly water surface elevations, used for
the model calibration, were obtained from the Viana do
Castelo tidal gauge.
Values of amplitude and phase of the tidal harmonic
constituents, which were used as forcing and potential
constituents, were obtained from the Le Provost’s global
tidal model based upon satellite altimetry (Le Provost et
al.., 1998).
The meteorological input, sea level pressure and wind
field at 10 m above the sea surface, was obtained from
the US National Center for Environmental Prediction –
NCEP/NCAR reanalysis (Kalnay et al.., 1996) at the
National Oceanic and Atmospheric Administration
(NOAA) website. These datasets are available in 6 hour
intervals, linearly interpolated in space and time, from
the global T62 Gaussian grid with 192x94 points (1.875º
x 1.875º) for the wind fields and from the 144x73 global
grid (2.5º x 2.5º) for the pressure, to the finite element
mesh.
The mean daily flow record for the Lima river was
obtained from the Portuguese SNIRH (Sistema Nacional
de Informação de Recursos Hídricos) website for the
Forno da Cal hydrometric station and extracted for the
period 12th
-18th
October 1987.
Hidrodata (2006) obtained water surface elevations and
current field, for 3 points inside the Lima estuary, during
the period 05th
– 15th
October 2006.
Atmospheric pressure data (Uppala et al., 2005) obtained
from the European Centre for Medium-range Weather
Forecast (ECMWF) website, was compared to the same
data from NOAA and IH. It was concluded that, for the
storm surge event of 14th
– 16th
October 1987, NOAA
data was likely to provide better hindcast results.
Marujo-Silva et al.
Journal of Coastal Research, (year)
5
Figure 5 – Comparison between water surface elevation observed values and modelled before and after calibration.
RESULTS AND DISCUSSION
Model calibration
Considering the two meshes used, it was necessary to
carry out two calibration sequences. Even though these
are based on the same assumptions, a brief description of
each is presented. In the present work, the model was
calibrated using the astronomy forcing and compared to
the observed water surface elevations.
It should be mentioned the need to consider the
wetting/drying algorithm when modelling the Lima
estuary (Rebordão and Trigo-Teixeira, 2009).
For the oceanic domain model (M0), this water surface
elevation record was the obtained from the Viana do
Castelo tidal gauge after it was analysed using the
T_TIDE software package (Pawlowicz et al., 2002).
For the estuarine domain the model was calibrated using
the water surface elevation and velocity field data from
the Hidrodata survey in 2006.
The model was calibrated by setting several
combinations of the friction coefficient, wave continuity
and lateral viscosity and choosing the one leading to best
model predictive skill. It was found that the friction
coefficient is responsible for the largest differences in
the obtained water surface elevations. An extremely high
friction coefficient of 0.30 and 0.10 was the best
calibration value for the oceanic and the estuarine
domain, respectively.
The results of the model calibration for the oceanic
domain are presented in figure 5, which shows a nearly
perfect fit. The statistical parameters for this calibration
are presented in table 1. After this calibration procedure
a different number of tidal constituents was tested being
noticeable a model accuracy improvement from 1.92 cm
to 1.71 cm and also in the model skill from 0.9977 to
0.9981.
Table 1 – Statistical parameters obtained during the calibration
procedure for the oceanic domain
Indicator Initial Final Differences
Bias (cm) -0.019 0.055 n.a.
Accuracy (cm)* 2.538 1.919 24.4 %
Skill* 0.9956 0.9977 -0.2 %
Maximum difference (cm)* 6.478 4.298 33.7 %
Minimum difference (cm)* -7.470 -4.576 38.7 %
RMSE (cm)* 3.099 2.221 28.3 %
*Improvement percentage
For the estuarine domain the model showed also a good
agreement with the predicted water surface elevations,
but consistently under predicted the velocity magnitudes.
The statistical parameters for this calibration are
presented in table 2. After this calibration procedure a
different number of tidal constituents was tested being
noticeable a model accuracy improvement from 9.86 cm
to 7.62 cm and also in the model skill from 0.9748 to
0.9858. Furthermore, analysing figures 6 and 7 it can be
stated that the model predictive skill is higher for the u
velocity component, aligned with most of the channels,
than the v component
It should be noted that these indicators are considered
reasonable but not as good as for the estuarine. One
reason for this fact might be the oceanic boundary being
close to shore not allowing adequate tidal wave
propagation. Nonetheless the obtained results are
satisfactory and the calibration process finished.
Storm surge hydrodynamic modelling
Journal of Coastal Research, (year)
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Figure 6 - Comparison between the observed and the
modelled U and V velocity components.
Table 2 – Statistical parameters obtained during the calibration
procedure for the estuarine domain
Indicator Initial Final Differences
Bias (cm) -7.608 -6.963 8.5
Accuracy (cm)* 9.857 7.616 22.7
Skill* 0.9748 0.9858 -1.1
Maximum difference (cm)* 12.207 4.752 61.1
Minimum difference (cm)* -35.569 -22.925 35.5
RMSE (cm)* 12.194 9.16 24.9
*Improvement percentage
Model validation
Once the model was calibrated, validation was
performed. For the oceanic domain this was done by
comparing the obtained results for several tidal gauges
along the Portuguese coast: Viana do Castelo, Leixões,
Aveiro, Figueira da Foz, Peniche, Cascais, Sines and
Lagos.
Considering this study is strongly intended for the Lima
estuary area, in table 3 it is presented the tidal
constituents obtained after a 90 days simulation for the
Viana do Castelo recording station. From the same table,
it is possible to see a highly satisfactory agreement
between the modelled tidal constituents amplitude and
phase and the obtained from a T_TIDE analysis and the
published in tide table by IH.
Additionally, for the model validation a different number
of harmonic constituents were considered: 6 and 10. In
figure 8, a comparison between the differences between
modelling with 6 or 10 harmonic constituents is
presented. From this graph it is possible to conclude that
when simulating using 10 harmonic constituents the
model skill is larger, producing also more accurate
results.
According to Blain et al. (1994) recommendations, the
influence of the domain size was studied by extending
the model boundaries to include the Bay of Biscay but
no advantages were found in considering such a large
domain.
Figure 7 - Comparison between the observed and the modelled velocity
amplitude.
Figure 9 – Observed and modelled water surface elevations using the two different meshes: oceanic and estuarine.
Marujo-Silva et al.
Journal of Coastal Research, (year)
7
Table 3 – Amplitude and phase of the 6 main harmonic constituents at Viana do Castelo from different sources.
IH Tide table T_TIDE harmonic analysis
(year 1999)
ADCIRC harmonic analysis
(90 days)
Constituents Amplitude (cm) Phase (º) Amplitude (cm) Phase (º) Amplitude (cm) Phase (º)
M2 104.4 75.9 104.3 75.6 105.2 76.9
S2 36.4 104.1 36.2 104.6 36.5 102.0
K1 7.1 61.3 7.1 61.6 6.5 63.9
O1 6.2 319.0 6.5 316.3 6.0 314.8
N2 n.a n.a 22.3 57.1 23.4 60.4
K2 n.a n.a 10.2 102.8 9.3 95.7
Figure 8 - Comparison between the observed and the modelling water
surface elevation differences while using the 6 and 10 harmonic
constituents from T_TIDE analysis.
According to Blain et al. (1998) recommendations, the
oceanic domain mesh convergence was analysed for the
tidal propagation, and it was concluded that satisfactory
convergence was achieved, even though it came at a cost
of a smaller time step.
This option was considered to solve numerical stability
issues that had arisen after refinement and bathymetry
interpolation.
For the estuarine domain, the model was validated by
comparing the model output with the observed water
surface elevation and the obtained using the oceanic
domain mesh. As can be seen in figure 9, the water
surface level elevation for the oceanic and the estuarine
domain are coincident and an almost perfect agreement
between the observed and modelled values observed.
Astronomy and meteorology forcing interaction
assessment
The method used to assess the type of interaction
between astronomy and meteorology is based on the
used by Fanjul et al. (2001). This consisted of simulating
the astronomy and meteorology forcings jointly and also
each one separately.
Figure 10 – Comparison between observed water surface elevation and the hindcasted by considering astronomy and meteorology forcing jointly and
separately using the oceanic domain mesh (M0) at the Viana do Castelo tidal gauge
Storm surge hydrodynamic modelling
Journal of Coastal Research, (year)
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Figure 11 – Comparison between observed water surface elevation and the hindcasted by considering astronomy and meteorology forcing jointly for
the oceanic (M0) and estuarine domain meshes at the Viana do Castelo tidal gauge
The results, obtained from both forcing mechanisms
acting together, were directly extracted from the model
output file. For the separate forcing, the results from
simulating only astronomy and only meteorology were
extracted separately and added up to obtain the expected
water surface elevation.
In figure 10 it is possible to observe the difference
between simulating the astronomy and meteorology
jointly or separately for the large oceanic domain and in
figure 11 for the estuarine domain, including the river
flow.
From figure 11, it can be concluded that the river flow is
responsible for a significant increase in the non linear
interaction between the meteorology and the astronomy.
This is thought to be due to the interaction between the
tidal wave and the currents resulting from the
meteorology forcing.
In figure 12 it is possible to observe the increasing
influence of the river flow as the recording station is
located further upstream. The results presented in this
figure were obtained directly using only meteorology
forcing.
Figure 12 – Qualitative comparison between observed residuals at the Viana do Castelo tidal gauge and the hindcasted storm surge height in the 5
recording stations in the estuarine domain.
Marujo-Silva et al.
Journal of Coastal Research, (year)
9
CONCLUSIONS
After the present work was made several aspects must be
emphasized. Following the modelling sequence and
regarding mesh generation, it must be mentioned the
need to create size functions which are able to account
for significant bathymetry changes such as the existing
in the vicinity of the continental slope. The defined size
function must be capable of accounting for these
significant gradients, which will compromise the mesh
quality.
Respecting atmospheric pressure data, it must be stated
that the IH records may be used, when simulating
periods with available data, as a complement to the
hindcasted by NOAA and ECMRF.
A high importance was attributed to the calibration
sequence since the final results and conclusions are
heavily driven by the chosen parameters. After
concluding the present work, it is clearly the much
higher requirements and modeller experience and skill
required when considering spatial features with temporal
and spatial scales with orders of magnitude smaller than
the general physical processes to be modelled.
The nonlinear interaction between astronomy and
meteorology forcings for the considered scenarios and
implemented modelling strategies should also be
emphasized. Considering this fact, it is the author’s
recommendation to simulate both phenomena separately
and add the obtained water surface elevations. This is
based on the possibility of interference from the physical
nature of the process, but also numerical issues resulting
from the model setup.
After the present document has been elaborated, several
aspects still remain unaddressed. Among these, it should
be mentioned the hypothesis of considering an
interpolating grid with a higher resolution than 50 m x
50 m to extract the bathymetry data from the Lima
estuary DTM. Another aspect that may be interesting to
investigate is the definition of more efficient size
functions such that the element area transition is not very
abrupt in the continental slope. This may, for instance,
consist of defining a size function based not only in the
wavelength, but by adding a function with values that
succeed in smoothing locally the previous ones, thus
achieving a more gently varying element size. As an
example a two-dimensional Gaussian function might be
used. This might be combined with the Local Truncation
Error Analysis toolbox for the oceanic domain. Inside
the estuary, due to shallower areas (tidal flats) with wet
and dry processes, this option is not recommended since
it was tested and no satisfactory results were obtained
due to the assumptions inherent to this methodology.
Considering that, due to time constraints and steering
model incompatibilities, the wave set-up influence, via
the radiation stresses, was not considered for the surge
reproduction. This aspect was not considered, but it will
certainly improve the results if accounted for. With this
forcing mechanism the surge height is expected to be
incremented by ~15 cm at its peak based in the results
obtained by Araújo et al. (2011).
Concerning the recorded time series, stationarity must be
assessed such that no uncertainties remain about long
term variations. Furthermore, since the present paper is
inserted in a long-term project to create a risk chart for
the Lima estuary, a more careful analysis of the model
boundaries should be performed such that places
sheltered by walls, breakwaters and other structures are
considered. Another aspect that remained was the
necessity of considering a large friction coefficient,
which implies lower velocities than expected in reality.
This issue was not considered to be predominant over
other concerns since the water level has a much weaker
influence of this parameter and the main purpose of the
present paper was simulating storm surge heights.
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ACKNOWLEDGEMENTS
The first author would like to offer his sincere thanks to
his supervisor Prof. Dr. António Trigo-Teixeira for his
guidance, availability to answer and clarify all questions
that emerged during the elaboration of the MSc thesis on
which this document is based and all the knowledge
transmitted. Also his sincere thanks to Dr. Amélia
Araújo for her co-supervision, guidance and readiness to
explain some of the details of previous research on this
topic. Assistance was also provided on many issues that
emerged during the investigation of this subject.
Andrea Mazzolari must also be thanked for his support
and all the advice given from his previous experience
and research on this topic, which were consistently
accurate and useful, and has helped setting the course to
some solution presented in this paper.
Furthermore, his sincere thanks Prof. Alexandre
Gonçalves for the support and for taking part in the field
work and to Eng. Nádia Braz, representing the LNEC,
for taking part in this project and loaning very precise
GNSS instruments.