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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

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1CEHIDRO Instituto Superior Técnico,

Technical University of Lisbon

1049-001 Portugal [email protected],

[email protected]



1049-001 Portugal [email protected]




4ICIST Instituto Superior Técnico,



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


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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.


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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.



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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.


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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.



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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.


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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



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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.


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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.

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