NHESSNatural Hazards and Earth System ScienceNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus GmbHGöttingen, Germany10.5194/nhess-14-3195-2014Analysis of extreme wave events on the southern coast of BrazilGuimarãesP. V.pvguima@gmail.comFarinaL.Toldo Jr.E. E.Instituto de Geociências, Universidade Federal do Rio Grande do Sul, Campus do Vale Av. Bento Gonçalves 9500, Porto Alegre, RS, BrasilInstituto de Matemática, Universidade Federal do Rio Grande do Sul, Campus do Vale Av. Bento Gonçalves 9500, Porto Alegre, RS, BrasilBCAM, Basque Center for Applied Mathematics, Alameda de Mazarredo, 14, 48009, Bilbao, Basque Country, SpainP. V. Guimarães (pvguima@gmail.com)3December201414123195320514May201417June20149September201425October2014This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.nat-hazards-earth-syst-sci.net/14/3195/2014/nhess-14-3195-2014.htmlThe full text article is available as a PDF file from https://www.nat-hazards-earth-syst-sci.net/14/3195/2014/nhess-14-3195-2014.pdf
Using the wave model SWAN (simulating waves
nearshore), high waves on the southwestern Atlantic
generated by extra-tropical cyclones are simulated from 2000 to 2010,
and their impact on the Rio Grande do Sul (RS) coast is studied. The
modeled waves are compared with buoy data and good agreement is
found. The six extreme events in the period that presented
significant wave heights above 5 m, on a particular point of
interest, are investigated in detail. It is found that the
cyclogenetic pattern between the latitudes 31.5 and
34∘ S is the most favorable for developing high
waves. Hovmöller diagrams for deep water show that the region
between the south of Rio Grande do Sul up to a latitude of 31.5∘ S
is the most energetic during a cyclone's passage, although the event
of May 2008 indicates that the location of this region can vary,
depending on the cyclone's displacement. On the other hand, the
Hovmöller diagrams for shallow water show that the different
shoreface morphologies were responsible for focusing or dissipating
the waves' energy; the regions found are in agreement with the
observations of erosion and progradation regions. It can be concluded
that some of the urban areas of the beaches of Hermenegildo, Cidreira,
Pinhal, Tramandaí, Imbé and Torres have been more exposed during
the extreme wave events on the Rio Grande do Sul coast, and are more
vulnerable to this natural hazard.
Introduction
Storms are one of the most important natural hazards to nearshore
urban areas, resulting in property destruction and lives lost
(Almeida et al., ). The
strong winds over the ocean favor the air–sea momentum transfer that
is responsible for the ocean disturbances, which may lead to high sea
waves affecting navigation, and petroleum platforms, causing severe
shore erosion, flooding and other damages on the coast. Thus, the
understanding of the dynamics and climate of waves and winds is of
major relevance for preventing and mitigating the natural threats.
The mid-latitude cyclogenesis with low-pressure centers in the deep
ocean and along the coast increases the intensity of Mid-Atlantic
storms, causing extreme storm surges and storm waves (Calliari et al.,
). Storm surges are also the major geological
risk in low coastal areas. They are often associated with significant
losses of life and property. Additionally, sea level elevations at
the shore can be further amplified by the presence of shelf waves and
by the piling up of water due to wave breaking processes in the surf
zone (wave setup).
So, the impact of storms on sandy coasts are induced by different
morphodynamic responses, which significantly modify the coastal
landscape over short time periods. The magnitude of these processes,
such as beach and dune erosion, and the resulting changes are controlled by
the combination of storm characteristics and coastal geomorphology
(e.g., Morton, ).
A number of articles examine coastal storms by means of variables, such
as wave energy (Sénéchal et al., ), wave
height (Wright and Short, ), maximum water level
reached by waves (Sallenger, ), surge
level (Wright et al., ) and other inundation
parameters (Mendoza and Jimenez, ,
).
Data on waves and tidal level in the South Atlantic is very
scarce. Thus, numerical simulations of extreme events have been the
first approach to study the potential damage of storm events. On the
Rio Grande do Sul (RS) coast in Brazil, storm events have been
investigated by Calliari et al. (), Parise
et al. () and Machado
et al. ().
The state of Rio Grande do Sul is characterized by an extensive
coastline with uniform NE–SW orientation and a light sinuosity along
its extension of 615 km (Fig. ), including on
Cassino Beach, one of the longest sandy beaches in the world (Dillenburg
et al., ). All this extension consists of
unconsolidated deposits from quaternary rivers that do not receive
contributions from modern sands. The continental shelf is part of
a broad and passive margin, more than 150 km long, with
maximum depths ranging between 100 and 140 m and a gentle
slope on the order of 0.06. The shoreface is extensive and shallow
with an outer boundary at a depth of 10 m, with predominantly
sandy deposits (Toldo et al., ).
Study field representation. Solid lines represent the the grid boundaries. Inside,
on the color scale, the grid bathymetry is between 0 and -60 m. The
points indicate reference beaches at Rio Grande do Sul. Tramandaí beach is
where the buoy was placed for the comparison analysis. The maps are plotted
over a Google Maps image.
A good regional geomorphological description is given by
Fachin (): according to this author, the shorefaces for
the northern and southern end of this region are totally different,
changing at the south of the Lagoa dos Patos inlet. The area near the
south of Lagoa dos Patos is described as more homogeneous, with
a gradually decreasing slope toward the sea. The northern and
southern ends of this area have two different standards for the
presence and orientation of sand ridges. To the north, there is a high
concentration of sand ridges with an orientation predominantly
parallel to the shoreline, with depths of 18 and 22 m and with
coastal distances from 8 to 10 km. At the southern end, there
are more complex morphologies, with sand ridges oblique to the coast,
directed predominantly from SE to NE, with depths between 12 and
30 m.
The water level is also affected by the South Atlantic circulation
responsible for short-term sea level variations. At Rio Grande do Sul,
the maximum values of storm surges were on the order of 1,
1.4 and 1.9 m, found by, Calliari
et al. (), Saraiva
et al. () and Parise
et al. (), respectively. As tidal range is small, the waves are
responsible for most sediment transport and deposition along the
coast. The average significant wave height at depths of around
17 m is found by Strauch () to be
1.5 m.
According to Speranski and Calliari (), the
convergence of wave rays due to refraction by small-scale bed slopes
focuses the wave with a period longer than 9 s at some coastal
areas. This is one of the probable causes of the local erosion under
wave storms in Rio Grande do Sul.
Hermenegildo Beach, at the southern end of Rio Grande do Sul, has been
studied often – e.g., by Calliari et al. ()
and Esteves et al. (, ) –
because of the severe erosion problem in this region. According to
Dillenburg et al. (), this problem involves
anthropic occupation too. Toldo et al. () have
analyzed the retreat and progradation zone identifying a high regional
coastal erosion along the middle coast between the Lagoa dos Patos
inlet until the Tramandaí region as a function of longshore
transport. The estimated potential of sediment transport predicts
a substantial variation of the energy flux into the surf zone, due to
little changes to shoreline alignments and consequently to the
transport potential along the coast. The net longshore sand transport
to the northeast is responsible for the increasing of coastal erosion
rates. On the other hand, the reduction of the sediment flux among the
alignments produce a jam in the longshore transport and the
progradation in these places.
Validation of the SWAN wave model with the directional buoy data. (a) The SWAN predictions are
shown in continuous lines and the buoy data are in circles. (b) Scatterplot of the linear
correlation; the colors of the dots represent the distance from the regression line.
The effects of waves have been shown to be the fundamental process for
coastal management, since it is the main forcing term in the dynamics,
composition and morphology of this coastline. Most of the incoming wave energy
incidents on this coastal zone are associated with gravity waves and the
most energetic events are associated with the extra-tropical
cyclones. These cyclones are very turbulent and unstable
meteorological phenomena, defined as low-pressure systems of synoptic
scale that occur in the mid-latitudes. They have a great influence
on the regional climate and constitute an important mechanism of
atmospheric circulation for the thermal equilibrium between the
regions of low and high latitudes.
According to Machado et al. (), the intense
cyclonic weather systems in southern Brazil generate ocean storms,
which can, on a temporal scale varying from a few hours to a day,
completely erode a beach profile from its maximum accretion
state. Mid-latitude cyclogenesis with low-pressure centers in the deep
ocean and along the coast increases the intensity of Mid-Atlantic
storms, causing storm surges and storm waves. During the event of
September 2006, it was observed that a great part of Cassino Beach was
flooded when the water reached the first avenue close to the beach.
Regarding the occurrence of extra-tropical cyclones in South America, Gan
and Rao (), analyzing 10 years of data (from
1979 to 1988), have found that the majority of them happen in winter
(eight events), followed by autumn (six events), spring (four events) and summer (three events). Gan and
Rao () identified two cyclogenesis regions in South
America: one in Argentina (42.5∘ S and 62.5∘ W),
related to the baroclinic instability of the westerly winds, and
another in Uruguay (31.5∘ S and 55∘ W), associated
with the baroclinic instability due to the presence of the
Andes. Recently, a third region between 20 and 35∘ S,
located in southern and southeastern Brazil, was identified (Reboita
et al., ).
Reboita et al. (), using the 10 m high
wind field to calculate the relative vorticity (ζ10),
classified all the systems with ζ10≤-1.5×10-5s-1 as extra-tropical cyclones and a lifetime greater than
or equal to 24 h, and they found a total of 2787 cyclogenesis in
10 years over the South Atlantic Ocean. However,
initially considering only the stronger systems with ζ10≤-2.5×10-5s-1, there is a well-characterized
high frequency of cyclogenesis. Parise et al. ()
and Machado et al. () also classified three
trajectory patterns over the southern Atlantic Ocean: the cyclogenesis
in the south of Argentina with an eastward displacement and
a trajectory between 47.5 and 57.5∘ S (RC1); the
cyclogenesis in the south of Uruguay with an eastward displacement and
a trajectory between 28 and 43∘ S (RC2); the
cyclogenesis in the south of Uruguay with a southeasterly displacement
and a trajectory between 35 and 57.5∘ S (RC3).
Machado et al. () include the high-pressure
center generating an easterly wind as a fourth pattern of those events.
The extra-tropical cyclone of September 2006 was well studied by
Parise et al. (), who shows that this particular
storm caused a surge of 1.827 m at Cassino Beach. Although the
surge was very high, these authors describe only a low level of beach
erosion. This event was equally well classified and discussed by
Machado et al. (), who included the regional
cyclogenesis pattern RC3.
So, regarding the potential problem of storm waves, the geological
history and the Mid-Atlantic cyclones, the aim of the present paper
is to describe the development of high waves during extreme events at
the coast of Rio Grande do Sul, and also to point to some places that
could be at potential risk during these events.
Materials and methods
To accomplish this, we analyzed the cases of extreme waves
that occurred between 2000 and 2010. To conduct this study, we
analyzed the global wave data from WW3 (WAVEWATCH III) (Tolman,
), and the nearshore waves were simulated
numerically with the spectral wave model SWAN (simulating waves
nearshore) nested in WW3. Intending to validate this methodology,
a computational simulation was run from December 2006 through May 2007.
The model was started from rest condition in December, and run
for 6 months, storing the results hourly. The results were compared
with the directional buoy measurements from a buoy installed from
November 2006 to May 2007, close to Tramandaí city (its location is
indicated in Fig. ), in 17 m intermediate waters
(Strauch et al., ). Waves above 5 m of
significant wave height by an offshore WW3 point were selected as the
most extreme wave events. The simulation of each of these events was
computed from the steady condition for 7 days before and 5 days
after the peak of the event.
Model description
SWAN is a nearshore spectral wave model, efficient when predicting
wave conditions for small scales, and for obtaining realistic estimates of
wave parameters in coastal areas, lakes and estuaries, for prescribed
wind, bottom and current conditions (Holthuijsen
et al., ; Booij
et al., ; Ris et al., ).
SWAN is based on the spectral action balance equation. Short-crested,
random wave fields propagating simultaneously from widely varying
directions can be simulated. The SWAN model accounts for shoaling,
refraction due to spatial variations in bottom and current,
diffraction, blocking and reflections, wave generation due to wind,
energy dissipation due to white-capping, bottom friction,
depth-induced breaking and nonlinear wave–wave interactions in both
deep and shallow water (quadruplets and triads). The SWAN version used
in these simulations is 40.72. A thorough description of the SWAN
package and its background is in Young () and
Booij et al. (). In addition, the wave-induced
setup of the mean sea surface was computed in SWAN.
We ran SWAN in nonstationary mode over a curvilinear grid, employing
a 5 min time step, updating wind input every 3 h, and
the tides were forced hourly.
The computational grids are better resolved close to the coast
area. The areas of low resolution are around 1.5 km in deep
water and those of high resolution are 0.5 km in the coastal
areas, rotated by 45∘. The final grid contains 275 200 cells,
corresponding to an area around 250 000 km2, covering all of
the coastal zone of Rio Grande do Sul, and part of Uruguay and the
state of Santa Catarina.
Every simulation was run over the same grid, considering the
ETOPO1
ETOPO1 is a 1 arcmin global relief model of the
Earth's surface that integrates land topography and ocean bathymetry.
For more information, see http://www.ngdc.noaa.gov/mgg/global/
bathymetry corrected with nautical charts provided by the
DHN/CHM
Brazil Marine through the Oceanographic Modeling and Observation
Network (REMO).
Boundary conditions and forcing
The wave boundary conditions and the wind surface used are from the
third generation wind wave model WAVEWATCH III (Tolman,
), operated by the wave modeling group at the
National Center for Environmental Prediction (the wave hindcast
database extends from 1999 to 2010 – see
http://polar.ncep.noaa.gov/waves). They cover the globe in the
domain 78–78∘ N with a grid resolution of 1∘ in
latitude and 1.25∘ in longitude. This model outputs the wind speed
and direction, as well as the integrated spectral parameters, such as
the significant wave height (Hs), the peak period (Tp) and the mean
direction at the peak period (Dp). The temporal data resolution is
every 3 h.
The data from WAVEWATCH III were nested in SWAN as boundary conditions
every 3 h. The intensity of the wind components (U and V)
were fit in a computational grid using linear interpolation based on
a Delaunay triangulation of the data, and then the wind
components were smoothed over the SWAN grid surface. The spectral wave boundary
conditions from WAVEWATCH III were defined with a nonstationary
distribution of Jonswap spectrum obtained by the waves' parameters Hs,
Tp, and Dp and the directional spreading. This wave information came from
the global results of WAVEWATCH III and was linearly interpolated to
60 equidistant points along the segments of the computational grid
boundaries.
Water level correlation
The sea level exchange can be understood as a combination of the
astronomical tide with the influence of the atmospheric level. To
better represent the waves in shallow water during the analyzed
events, the water levels were corrected by directly employing the data
measured by a tide gauge inside of the Tramandaí inlet from the
Brazilian Superintendency of Ports and Waterways
(29.977∘ S, 50.124∘ W). The water levels were
interpolated and included in the model each computational hour.
Cyclone trajectories
To analyze the cyclone trajectories that generated these waves, each
cyclone's track and intensity were identified employing its
relative vorticity (ζ10) at the cyclone
center given by
ζ10=∂v10∂x-∂u10∂yk^,
where u10 and v10 are the zonal and meridional wind
components from WW3 at a 10 m height. k^ is the
normal vector to the surface.
ResultsModel validation
As mentioned before, wave data measured on the South Atlantic is
extremely rare. For this study, we have carried out a simulation to
compare the model's results with one of the few available
observational data. Thus, the simulations were compared with
measurements made by a directional buoy moored from November 2006 to
May 2007 close to Tramandaí city (the location of which is indicated
in Fig. ) in 17 m of intermediate water (Strauch
et al., ). This means that the buoy that is located over
intermediate water depth could be measuring waves disturbed by the
local bathymetry and is therefore not representative of the large-scale
wave field. This analysis enabled the selection of the significant
wave hight, the peak period and the peak direction
(Fig. shows these two dates at the same period).
Table summarizes the statistical correlation between SWAN and
the directional buoy data for the same data presented in Fig. .
r represents the Pearson correlation coefficient, measuring the
degree of correlation, and a and b are the regression line
coefficients (y=ax+b). The Pearson correlation is +1 in the case
of a perfect positive (increasing) linear relationship (correlation),
and 0 when there is low linear correlation between the variables (closer to uncorrelated
or independent). According to Triola (), for
a normal Pearson distribution, where n=1175 is the number of
samples, the critical value for |r| to exceed the significance
levels of 99 and 95 % (i.e., that the data has
a chance of 1 or 5 % of not being correlated) is
0.2560 and 0.1960, respectively. For this case, a linear model, the
coefficient of determination r2 is Pearson's product-moment
coefficient.
Extreme wave events: the start time gives the time at which the waves of these
events started to appear in the computational domain. The end time indicates when the waves
leave the domain. The peak time gives the most energetic moment in each event,
and the duration is the time between the start and the end.
EventsStartEndPeakDurationE0130 Aug 2002, 15:004 Sep 2002, 00:002 Sep 2002, 15:004 days, 09:00 hE0226 Jun 2006, 12:0028 Jun 2006, 18:0027 Jun 2006, 03:002 days, 06:00 hE032 Sep 2006, 19:006 Sep 2006, 11:003 Sep 2006, 19:003 days, 16:00 hE0427 Jul 2007, 09:0030 Jul 2007, 06:0028 Jul 2007, 13:002 days, 21:00 hE053 May 2008, 04:006 May 2008, 11:003 May 2008, 23:003 days, 07:00 hE069 Jun 2008, 22:0011 Jun 2008, 02:0010 Jun 2008, 10:001 days, 04:00 h
Looking at Figs. a and b, it is possible to see
that the wave direction errors were near 10∘ and the r2 shows
that the SWAN could fit a coefficient of determination of 0.72.
But SWAN could not represent more than 53 % of the variance
for the peak wave periods; usually, the peaks of the swell period
were underestimated and the sea peak waves' periods were overestimated. The
significant wave heights were well represented by the model, with
r2=0.62. Usually the buoy registers were overestimated,
however, in some of the higher events, the model
underestimates on the order of 50 cm compared to that observed.
Overall, the model calibration results were reasonable and
satisfactory at intermediate water waves. The coefficients of
correlation between the model and the observed data were 0.79–0.85.
The error statistics showed that all three wave parameters analyzed
had a good match with reality in most of the SWAN cases. The model
slightly underestimated the significant wave heights. However, it
follows the variation pattern of wave oscillation very soon, although
small disagreements between the observed and the simulated data do exist.
Extreme wave events
The selected six events with waves higher than 5 m between
2000 and 2010 from WW3 point to coordinates 31∘ S and
50∘ W. Table shows some information about
these events. The start time represents the time point at which the
extreme significant wave height started to appear within the region of
the computational grid. The end time point represents the points at
which these wave events leave the computational grid. The peak time
represents the most energetic time point of each simulation. The difference
between the start and the end time point gives the duration of the
event. Table shows the maximum of significant wave
height simulated (Hsmax) observed in deep
water, Wlmax represents the highest water
level measured at the Tramandaí tide gauge during each event and
Tpfreq and Dpfreq give
the period of the most frequent peak waves and the direction of the
peak waves for each event in the whole computational domain.
Waves information for each events: Hsmax is the max of significant
wave height simulated at deep water, the Wlmax is the higher water level
at a Tramandaí coastal point and the Tpfreq and the Dpfreq
are the most frequently of the peak wave period and the peak wave direction in the computational domain.
Wave field maps for the event 02. (a) Significant wave height (Hs) in
meters and (b) peak wave period (Tp). The peak wave directions (Dp) are
presented in scale vectors.
From the colored lines, it is possible to identify each anticyclone track per
event, and the gray balls show the vorticity intensity.
Hovmöller diagram for deep water waves. The diagram displays the wave parameters
(Hs and Dp) for 50 m isobathymetry. The latitude
of the wave is displayed along the y axis, and the time is shown along the x axis. The
Hs are on a color scale and the Dp are shown as vectors.
The analysis of Tables and shows
that the event of 27 June 2006 might be one of most energetic that has
occurred in the Rio Grande do Sul coastal zone for the last 10 years;
this time, the waves surpassed 9 m in height at offshore
places. Figure shows a simulation of the most
energetic time point of this event. On a color scale, Figure a
exhibits the significant wave heights over the
computational grid, with the scale vector representing the peak wave
direction. During this event, the formation of long wave periods was also observed, as was shown in
Table ; Fig. b exemplifies one screen of the peak wave
period at this event.
Discussion
To closely analyze the selected cases, from the wind's vorticity
analysis, it was possible to identify the patterns of synoptic
situations for these event. Figure presents the
track of each event and the relative vorticity on a color
scale. Employing the authors' classifications and the observations in
Fig. , the majority of the events E01, E02,
E04, E05 and E06 could be classified in pattern as regional
RC2 with cyclogenesis in the south of Uruguay with an eastward
displacement and a trajectory between 28 and
42.5∘ S. Only the event E03 occurred at region RC3 with
cyclogenesis in the south of Uruguay with a southeasterly displacement
and a trajectory between 35 and 57.5∘ S.
While only waves over 5 m were analyzed, the high frequency of
events with pattern RC2 suggests that the eastward displacement of
Mid-Atlantic cyclones best develops the extreme wave events on the Rio
Grande do Sul coast. The extra-tropical cyclone of event E03 was
well studied by Parise et al. () and Machado
et al. (): in this case, the meteorological
scenario, due to a long wind fetch from S to SW and the association
between this wind pattern and the NE–SW orientation of the shoreline,
favored the extra high rise in sea level observed on the coast due to
the Coriolis effect. The events E04, E05 and E06 were the
stronger systems, characterized by a high frequency of cyclogenesis
with ζ10≤-2.5×10-5s-1.
To better understand how the waves developed during these events,
Fig. presents a Hovmöller diagram for
significant wave heights. The diagram plots the wave data on a color
scale, and the peak wave directions are displayed by vectors. This
diagram shows the time as the abscissa (x axis) and the latitude of
50 m isobathymetry as the ordinate (y axis).
From Fig. , it is possible to observe that,
during these events, the majority of wave energy at 50 m was
concentrated between the latitudes 31.5 and
34∘ S. Excluding the event E05, that concentrates the
energy to the north of the Rio Grande do Sul littoral. The explication
of this phenomenon is in the cyclogenic pattern. While most of the
cyclones had displacements closer to the south coast, the E05 was
the event that had the northernmost cyclogenic track. These
observations allow us to say that the energy of the deep waves in the
Rio Grande do Sul coastal zone during storm events are mostly
concentrated in the southern portion of the state, controlled by the
cyclone pattern RC2, with an eastward displacement between
28 and 43∘ S. But an event like E05 can cause
big waves at the northern region too, showing that the wave energy is
fully related to the intensity and direction of the cyclone's track.
Considering the recent cyclogenetic studies of Parise
et al. (), Machado
et al. () and Reboita
et al. () provide us with information to determine
that the south of the Rio Grande do Sul region collects most of the
waves' energy at 50 m deep water during extreme events.
The wave analysis of the 50 m deep water waves provides
important information for evaluating the risk for navigation and
offshore operations, but is insufficient for coastal zone studies. So,
Fig. presents the same Hovmöller analysis for
the waves at 6 m depth.
Hovmöller diagram for shallow water waves. The diagram displays the wave parameters
Hs and Dp for 6 m isobathymetry. The latitude of the
wave is displayed along the y axis, and the time is shown along the x axis. The Hs
are on a color scale and the Dp are shown as vectors.
Unlike the 50 m wave analysis, Fig.
shows that the waves' energy during these extreme events was
concentrated to the north of Rio Grande city and at the Hermenegildo
Beach region. The explanation of this fact is not just in the
cyclone's pattern, but also in the shoreface morphologies. The region
next to the lagoon's mouth (south) has a completely different
shoreface morphology compared to that at the northern and the southern end
of Rio Grande do Sul.
The region south of the mouth of the Lagoa dos Patos presents a wide
inner shelf, virtually homogeneous, with isobaths parallel to the
coastline until next to Hermenegildo Beach (seen also in
Fig. ). In this region, close to Hermenegildo Beach
(33.2∘ S), the subaqueous profile has remnants of sand ridges.
The region north of the Lagoa dos Patos inlet (32.2∘ S) is
characterized by a large concentration of sand ridges oriented at
shoreline oblique, predominantly in NE–SE directions, and between the
12 and 30 m isobaths. Also, along with a narrowing
of the region of the shoreface, where the largest profile
slopes occur, with is predominantly sandy sedimentology. So, these bottom
features corroborate the results obtained by the analysis of the waves
in shallow water. Due to the gentle and smooth slope in the region
south of the Lagoa dos Patos, most of the wave energy is dissipated at the
shoreface. The natural features in this region act like a natural
submerged barrier to the wave impact during these extreme events. In
contrast, the high bathymetric gradients and the different submerged
features observed north of the Lagoa dos Patos outflow showed
a tendency to concentrate the energy of the shallow water waves during
the analyzed events. In such cases, the phenomena of refraction and
friction with the background become more significant, due to the large
peak wave periods (seldom found in typical wave fields), more often
between 12 and 14 s.
To better understand the interaction between the Rio Grande do Sul
shallow water waves and the morphologies, Fig. shows
the nearshore bathymetry between 0 and -60 m. These
results support the results of the Hovmöller diagram for shallow
water waves (Fig. ), wherein the wave energy has
been concentrated by the high slope gradients.
Although the erosion problem in the further south of Rio Grande do Sul
at Hermenegildo has mainly been a problem of anthropic occupation,
this wave analysis shows that this problem can also be associated with
the cyclogenesis pattern and the wave transformation at the shoreface,
where the waves' energy has been concentrated in front of
Hermenegildo.
However, the trends of the shoreline are established by the extreme
erosive and depositional results of the complex interaction between
the rates of relative changes in the sea level, the rate of sediment
supply, the wave dynamics and the impacts produced by storm
waves. However, because of the large energy carried by the waves of 2
to 3 m in shallow water, combined with the sea leave rise of 0.7
to 1.3 m during extreme events, the sedimentary dynamics
during these high wave energy events are an important factor in the
sediment budget of the sand beaches.
The results of Toldo et al. () about a high
coastal retreat from the north of the Lagoa dos Patos inlet to the
Tramandaí region are also related to Fig. ,
where one can observe a trend in the waves' energy at this part of the
littoral. Toldo et al. () also classified the
sectors in front of Mostardas (31∘ S) and Dunas Altas (30.5∘ S) as
sediment sink areas. The region of lower wave energy between the Rio
Grande and about 33∘ S was classified by Toldo
et al. () as an area of progradation and moderate
retrogradation. Except for the event E05, which had a different
cyclonic trajectory from the others, the analysis of
Fig. also allows the observation of a small region of
lower wave energy just north of Tramandaí beach; at this area, the
progradation and moderate retrogradation rates were also checked by
Toldo et al. (). Therefore, these authors' results
conform to the shallow water wave analysis presented in this article,
thus showing that the high-energy wave events could be one of the
causes of somo beaches erosion along the coast of Rio Grande do Sul.
However, other factors, such as currents, beach profile, sea level,
grain size, etc., have been extremely important for the sediment
dynamics of the region. The morphological response and amplitude
caused by a storm are often defined as proportional to the intensity
of waves and the tidal level of high energy (as described by Wright
and Short, ; Wright et al., ;
Sénéchal et al., ). So, the results of
this study are directly in agreement with those found by Toldo
et al. () and Toldo et al. ()
after storm events, thus suggesting that the dynamics induced by
extreme wave events can be one of the determinants of sediment
transport in the region, being one of the major contributors to the
large volumes of sedimentary mobilization, moving the sediment from
areas of largest wave height toward offshore areas or towards areas
of lower wave energy. In addition, the waves that hit the
coast during these events were mainly affected by the regional shoreface morphology and
by the cyclone pattern that generated these events.
While most of Rio Grande do Sul is highly prone to coastal
erosion, much of the coast is still preserved with low
urbanization. Crossing the results of significant wave height with the
urbanization and use, it is possible to determine that
Hermenegildo Beach (33.2∘ S), Cidreira (30.2∘ S), Pinhal
(30.3∘ S), Tramandaí and Imbé (30.0∘ S) and Torres
(29.3∘ S) should pay more attention to the passage of extreme wave
events. The analysis of deep water waves suggests that more attention
should be given to the region next to Rio Grande (32.1∘ S),
where one of the most important ports of Brazil is located, and the
risks are directly related to navigation and offshore operations.
Summary and conclusions
Employing some of the studies and measured wave data for the Rio
Grande do Sul, this paper reviewed the extreme wave events there from
2000 to 2010. Spectral wave modeling with a good spatial resolution
(around 1 km) and nonstationary high-frequency time
resolution (5 min) allowed a good numerical representation of
the waves. The high grid resolution that was employed in the areas of interest
allowed a good simulation of the waves, where the buoy data were available
for validating this simulation. Overall, the comparison of the
measured buoy data with the model results showed that there was
a reasonable fit, and have been satisfactory for shallow water waves. The
statistical results showed that all three wave parameters analyzed had
a good match with reality in most of the SWAN cases, with correlation
coefficients between 0.79 and 0.85. It has to be emphasized that
comparison studies of this type are extremely rare and scarce in the
South Atlantic. Thus, the results here are new and relevant to future
works on the modeling and description of the wave fields in this
domain of the globe's oceans.
The direct analysis of deep water waves from WW3 identified six events
between 2000 and 2010, where the waves surpassed 5 m of
significant height on a point of interest. Employing the Mid-Atlantic cyclonic pattern classification, it was possible to detect
a high frequency of events of pattern RC2 among all events with high
wave energy. This suggests that the eastward displacement of Mid-Atlantic cyclones develop the extreme wave events
on the Rio Grande do Sul coast more intensively.
The pattern RC2 did better at developing highly energetic events
between the latitudes 31.5 and 34∘ S, but the
simple formation of these events at the north, as for event E05,
could change the deep water wave pattern. This shows that the highly
energetic wave patterns in deep water are mostly controlled by the
cyclonic track and intensity.
The Hovmöller diagram for shallow and deep water analysis allows
a good description of the time evolution for each event. The wave
analysis in 50 m deep water could provide important
information for navigation and offshore operations risk, while the
shallow water analysis, at 6 m deep, shows where most of the
waves' energy was dissipated or concentrated along the Rio Grande do
Sul shoreface.
These results agree with the Rio Grande do Sul geomorphological
description. The wave energy tends to be concentrated in areas of
higher gradients of bathymetry and with heterogeneous bottom
morphology, in front of Hermenegildo Beach and to the north of the
Lagoa dos Patos inlet. But, to the south of the Lagoa dos Patos inlet,
the gentle and smooth slope dissipates most of the wave energy at the
shoreface, acting as a natural submerged barrier to the waves' impact
during these extreme events. The wave pattern found during these
events in deep water showed a greater concentration of wave energy
south of 31.5∘ S, while, in shallow waters, this pattern was
inverted, with focus of the wave energy mainly to the north of 31∘ S.
The wave pattern in shallow water during these events is also in
accordance with the coastal progradation and retraction areas of this
coast, showing that the concentration and the dissipation of the
waves' energy at shoreface during extreme events could be one of the
main factors responsible for the sediment budget on the Rio Grande do
Sul coast.
Finally, another key aspect of this storm wave analysis involves the
assessment of the risk conditions for each examined beach. As
a consequence, this paper could determine the sensitive places during
storm wave occurrences for urban occupation, navigation and offshore
activities.
Acknowledgements
The first author would like to thank CAPES (Coordenação de Aperfeiçoamento de
Pessoal de Nível Superior) for a research fellowship
and financial support from CNPq. Pedro V. Guimarães and Leandro
Farina have done part of the research on this article at the Basque
Center for Applied Mathematics (BCAM), while members of the EU project
number FP7-295217-HPC-GA. The authors also would like to thank Brazil's
Superintendency of Ports and Waterways for making the water level data
available.
Edited by: I. Didenkulova
Reviewed by: two anonymous referees
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