Analysis of Extreme Wave Events in the Southern Coast of Brazil

icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Nat. Hazards Earth Syst. Sci. Discuss., 2, 4363–4391, 2014 www.nat-hazards-earth-syst-sci-discuss.net/2/4363/2014/ doi:10.5194/nhessd-2-4363-2014 NHESSD © Author(s) 2014. CC Attribution 3.0 License. 2, 4363–4391, 2014

This discussion paper is/has been under review for the journal Natural Hazards and Earth Analysis of extreme System Sciences (NHESS). Please refer to the corresponding ﬁnal paper in NHESS if available. wave events in the southern coast of Analysis of extreme wave events in the Brazil southern coast of Brazil P. V. Guimarães et al.

P. V. Guimarães1,3, L. Farina2,3, and E. Toldo1 Title Page 1Instituto de Geociências, Universidade Federal do Rio Grande do Sul, Campus do Vale Av. Abstract Introduction Bento Gonçalves 9500,Porto Alegre, RS, Brasil 2 Instituto de Matemática, Universidade Federal do Rio Grande do Sul, Campus do Vale Av. Conclusions References Bento Gonçalves 9500, Porto Alegre, RS, Brasil 3BCAM, Basque Center for Applied Mathematics, Alameda de Mazarredo, 14, 48009, Bilbao, Tables Figures Basque Country, Spain J I Received: 14 May 2014 – Accepted: 4 June 2014 – Published: 17 June 2014 Correspondence to: P. V. Guimarães ([email protected]) J I Published by Copernicus Publications on behalf of the European Geosciences Union. Back Close Full Screen / Esc

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4363 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract NHESSD Using the model SWAN, high waves on the Southwestern Atlantic generated by extra- tropical cyclones are simulated from 2000 to 2010 and their impact on the Rio Grande 2, 4363–4391, 2014 do Sul coast is studied. The modeled waves are compared with buoy data and good 5 agreement is found. The six extreme events in the period which presented signiﬁcant Analysis of extreme wave heights above 5 m, on a particular point of interest, are investigated in detail. It is wave events in the ◦ found that the cyclogenetic pattern between the latitudes 31.5 and 34 S, is the most southern coast of favorable for developing high waves. Hovmöller diagrams for deep water show that the Brazil region between the south of Rio Grande do Sul up to latitude 31.5◦ S is the most en- 10 ergetic during a cyclone’s passage, although the event of May 2008 indicate that the P. V. Guimarães et al. location of this region can vary, depending on the cyclone’s displacement. On the oher hand, the Hovmöller diagrams for shallow water show that the diﬀerent shoreface morphologies were responsable for focusing or dissipating the waves’ energy; the regions Title Page found are in agreement with the observations of erosion and progradation regions. Abstract Introduction 15 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 ex- Conclusions References treme wave events at Rio Grande do Sul coast, and are more vulnerable to this natural Tables Figures hazard.

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1 Introduction J I

Back Close 20 Storms are one of the most important natural hazards to nearshore urban areas, re-

sulting in property destruction and lives lost. The strong winds over the ocean favor the Full Screen / Esc air-sea momentum transfer that is responsible for the ocean disturbances which may

lead to high sea waves affecting navigation, petroleum platforms, and causing severe Printer-friendly Version shore erosion, flooding and other damages on the coast. Thus, the understanding of Interactive Discussion 25 the dynamics and climate of waves and winds are of major relevance for preventing and mitigating the natural threats. 4364 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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 NHESSD and storm waves (Calliari et al., 1998b). Storm surges are also the major geological 2, 4363–4391, 2014 risk in low coastal areas. They are often associated with significant losses of life and 5 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 Analysis of extreme in the surf zone (wave run-up). wave events in the So, the impact of storms on sandy coasts are induced by different morphodynamic southern coast of responses which significantly modify the coastal landscape over short time periods. Brazil 10 The magnitude of these processes, such as beach and dune erosion, and resulting changes is controlled by the combination of storm characteristics and coastal geomor- P. V. Guimarães et al. phology (e.g. Morton, 2002). A number of articles examine coastal storms by means of variables such as wave Title Page energy (Sénéchal et al., 2009), wave height (Wright and Short, 1984), maximum water 15 level reached by waves (Sallenger, 2000), and surge level (Wright et al., 1985) and Abstract Introduction other inundation parameters (Mendoza and Jimenez, 2006, 2009). Conclusions References Data on waves and tidal level on the South Atlantic is very scarce. Thus, numerical simulations of extreme events have been the first approach to study the potential Tables Figures damage of storm events. At the Rio Grande do Sul (RS) coast in Brazil, storm events 20 have been investigated by Calliari et al. (1998b), Parise et al. (2009) and Machado J I et al. (2010). The state of Rio Grande do Sul is characterized by an extensive coastline with uni- J I form orientation NE–SW and light sinuosity along its extension of 615 km (Fig. 1), in- Back Close cludin Cassino, one of the longest sandy beaches in the world (Dillenburg et al., 2004). Full Screen / Esc 25 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 Printer-friendly Version 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 Interactive Discussion

4365 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion shallow with an outer boundary at a depth of 10 m, with predominantly sandy deposits (Toldo et al., 2006). NHESSD A good regional geomorphological description is given by Fachin (1998): according 2, 4363–4391, 2014 to this author, the shorefaces for the northern and southern end of this region are 5 totally different, changing at the south of the Lagoa dos Patos inlet. The area near and south of Lagoa dos Patos is described as more homogeneous, with a gradually Analysis of extreme decreasing slope toward the sea. The northern and southern ends of this area have wave events in the two different standards for the presence and orientation of sand ridges. To the north southern coast of there is a high concentration of sand ridges with an orientation predominantly parallel Brazil 10 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 P. V. Guimarães et al. the coast, directed predominantly SE–NE, with depths between 12 and 30 m. The water level is also affected by the South Atlantic circulation responsible for short- Title Page term sea level variations. At Rio Grande do Sul, the maximum values of storm surges 15 were on the order of 1, 1.4 and 1.9 m, found by, respectively, Calliari et al. (1998b), Abstract Introduction Saraiva et al. (2003) and Parise et al. (2009). As tidal rage is small, the waves are Conclusions References responsable for most sediments transport and deposition along the coast. The average significant wave height at depths of around 17 m is found by Strauch (2009) to be 1.5 m. Tables Figures According to Speranski and Calliari (2001), the convergence of wave rays due to 20 refraction by small-scale bed slopes focus the wave with period longer than 9 s at some J I coastal areas. This is one of the probable causes of the local erosion under waves storms in Rio Grande do Sul. J I Hermenegildo beach at the southern end of Rio Grande do Sul has been much Back Close studied, e.g., Calliari et al. (1998a), Esteves et al. (2002, 2003), because of the se- Full Screen / Esc 25 vere erosion problem in this region. According to Dillenburg et al. (2004), this problem involves anthropic occupation too. Toldo et al. (2006) have analyzed the retreat and Printer-friendly Version 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 long- Interactive Discussion shore transport. The estimated potential of sediment transport predicts a substantial

4366 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion variation of the energy flux into the surf zone, due to little changes in shoreline alignments and consequently on the transport potential along the coast. The net longshore NHESSD sand transport to northeast are responsible for the increase the coastal erosion rates. 2, 4363–4391, 2014 On the other hand, the reduction of the sediment flux among the alignments produce 5 a jam in the longshore transport and the progradation in these places. The effects of waves have been shown to be the fundamental process for coastal Analysis of extreme management, since it is the main forcing term in the dynamics, composition, and mor- wave events in the phology of this coastline. Most of the energy incident on this coastal zone is associated southern coast of with gravity waves and the most energetic events are associated with the extra-tropical Brazil 10 cyclones. These cyclones are very turbulent and unstable meteorological phenomena, defined as low pressure systems of synoptic scale that occur in the middle latitudes. P. V. Guimarães et al. They have a great influence on the regional climate and constitute an important mech- anism of atmospheric circulation for the thermal equilibrium between the regions of low Title Page and high latitudes. 15 According to Machado et al. (2010), the intense cyclonic weather systems in south- Abstract Introduction ern Brazil generate ocean storms which can, on a temporal scale varying from a few Conclusions References 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 Tables Figures increases the intensity of Mid-Atlantic storms, causing storm surges and storm waves. 20 During the a event of September 2006, it was observed that a great part of Cassino J I beach was flooded when the water reached the first avenue close to the beach. Regarding the occurrence of South America extra-tropical cyclones, Gan and Rao J I (1991), analyzing 10 years of data (from 1979 to 1988), has found that the majority of Back Close them happen in winter (8 events), followed by autumn (6), spring (4) and summer (3). Full Screen / Esc 25 Gan and Rao (1991) identified two cyclogenesis regions in South America: one in Ar- gentina (42.5◦ S and 62.5◦ W) related to the baroclinic instability of the westerly winds, Printer-friendly Version 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, lo- Interactive Discussion cated in southern and south-eastern Brazil, was identified (Reboita et al., 2010).

4367 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Reboita et al. (2010), using the 10 m height wind field to calculate the relative vortic- −5 −1 ity (ζ 10), classified as extra-tropical cyclones all the systems with ζ 10 ≤ −1.5×10 s NHESSD and a lifetime greater than or equal to 24 h, and they found 2787 cyclogenesis in 2, 4363–4391, 2014 10 years in total over the South Atlantic Ocean. However, initially considering only the −5 −1 5 stronger systems with ζ 10 ≤ −2.5 × 10 s , there is a well characterized high frequency of cyclogenesis. Parise et al. (2009) and Machado et al. (2010) also classified Analysis of extreme three trajectory patterns over the southern Atlantic Ocean: the cyclogenesis in the wave events in the south of Argentina with an eastward displacement and a trajectory between 47.5 and southern coast of 57.5◦ S (RC1), the cyclogenesis in the south of Uruguay with an eastward displace- Brazil ◦ 10 ment and a trajectory between 28 and 43 S (RC2), and the cyclogenesis in the south of Uruguay with a southeasterly displacement and a trajectory between 35 and 57.5◦ S P. V. Guimarães et al. (RC3). Machado et al. (2010) include the high-pressure center generating an easterly wind as a fourth patter of those events. Title Page The extra-tropical cyclone of September 2006 was well studied by Parise 15 et al. (2009), who shows that this particular storm caused a surge of 1.827 m at Cassino Abstract Introduction Beach. Although the surge was very high, these authors describe only a low level Conclusions References of beach erosion. This event was equally well classified and discussed by Machado et al. (2010), who included the regional cyclogenesis pattern RC3. Tables Figures So, regarding the potential problem of storm waves, the geological history and the 20 Middle Atlantic Cyclones, the aim of the present paper is to describe the development J I of high waves during extreme events at the coast of Rio Grande do Sul, and also point to some places that could be at potential risk during these events. J I Back Close

2 Materials and methods Full Screen / Esc

To accomplish this, there were analyzed the cases of extreme waves that occurred be- Printer-friendly Version 25 tween 2000 and 2010. To conduct this study, we analyzed the global wave data from Interactive Discussion WW3 (WAVEWATCH III, Tolman, 2009) and the nearshore waves were simulated nu- merically with the spectral wave model SWAN (Simulating Waves Nearshore) nested 4368 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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 NHESSD December, and run for six months, storing the result hourly. The results were compared 2, 4363–4391, 2014 with the directional buoy measurements from a buoy installed from November 2006 to 5 May 2007 close to Tramandaí city, (its location is indicated in Fig. 1) in 17 m intermediate waters (Strauch et al., 2009). Waves above 5 m of significant wave height by an Analysis of extreme offshore WW3 point were selected as the most extreme wave events. The simulation wave events in the of each of these events was computed from the steady condition for seven days before southern coast of and five days after the peak of the event. Brazil

10 2.1 Model description P. V. Guimarães et al.

SWAN is a nearshore spectral wave model, efficient when predicting wave conditions for small scales, for obtaining realistic estimates of wave parameters in coastal areas, Title Page lakes and estuaries, for prescribed wind, bottom and current conditions (Holthuijsen Abstract Introduction et al., 1993; Booij et al., 1999; Ris et al., 1999). 15 SWAN is based on the spectral action balance equation. Short-crested, random Conclusions References wave fields propagating simultaneously from widely varying directions can be simu- Tables Figures lated. The SWAN model accounts for shoaling, refraction due to spatial variations in bottom and current, diffraction, blocking and reflections, wave generation due to wind, J I energy dissipation due to white-capping, bottom friction, depth-induced breaking and 20 non-linear wave-wave interactions in both deep and shallow water (quadruplets and J I triads). The SWAN version used in these simulations is 40.72. A thorough description Back Close of the SWAN package and its background are in Young (1999) and Booij et al. (1999). In addition, the wave-induced setup of the mean sea surface was computed in SWAN. Full Screen / Esc We ran SWAN in non-stationary mode over a curvilinear grid, employing a 5 min time 25 step, updating wind input every three hours, and the tides was corrected hourly. Printer-friendly Version The computational grids are better resolved close to the coast area. The areas of Interactive Discussion 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 contain 275 200 cells, corresponding 4369 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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. NHESSD 1 Every simulation was run over the same grid, considering the ETOPO1 bathymetry 2, 4363–4391, 2014 corrected with nautical charts provided by the DHN/CHM 2 Brazil Marine through the 5 Oceanographic Modeling and Observation Network (REMO). Analysis of extreme 2.2 Boundary conditions and forcing wave events in the southern coast of The wave boundary conditions and the wind surface used are from the third generation Brazil wind wave model WAVEWATCH III (Tolman, 2009), operated by the wave modeling group at the National Center for Environmental Prediction (the wave hindcast database P. V. Guimarães et al. 10 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 Title Page parameters such as the significant wave height (Hs), the peak period (Tp), and the mean Abstract Introduction direction at the peak period (Dp). The temporal data resolution is every three hours. Conclusions References 15 The data from WAVEWATCH III were nested in SWAN as boundary conditions every three hours. The intensity of the wind components (U and V ) were fit in a computa- Tables Figures tional grid using linear interpolation based on a Delaunay triangulation of the data,

then smoothing the wind components over the SWAN grid surface. The spectral waves J I boundary conditions from WAVEWATCH III were deﬁned with a nonstationary distri- J I 20 bution of Jonswap spectrum obtained by the waves’ parameters Hs, Tp, Dp and the directional spreading. This wave information came from the global results of WAVE- Back Close WATCH III and were linearly interpolated to 60 equidistant points along the segments of the computational grid boundaries. Full Screen / Esc

1 ETOPO1 is a 1 arcmin global relief model of the Earth’s surface that integrates land topog- Printer-friendly Version raphy and ocean bathymetry, for more information see http://www.ngdc.noaa.gov/mgg/global/ 2http://www.mar.mil.br/dhn/chm/box-cartas-nauticas/cartas.html Interactive Discussion

4370 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2.3 Water level correlation NHESSD 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 wa- 2, 4363–4391, 2014 ter during the analyzed events, the water levels were corrected by directly employing 5 the data measured by a tide gauge on side of the Tramandaí inlet from the Brazilian Su- Analysis of extreme ◦ ◦ perintendency of Ports and Waterways (29.977 S, 50.124 W). The water levels were wave events in the interpolated and included in the model each computational hour. southern coast of Brazil 2.4 Cyclone trajectories P. V. Guimarães et al. To analyze the cyclone trajectories that generated these waves, each cyclone’s track 10 and intensity were identiﬁed employing the its relative vorticity (ζ 10) at the cyclone center given by Title Page

∂v ∂u Abstract Introduction ζ = 10 − 10 kˆ (1) 10 ∂x ∂y Conclusions References where u and v are the zonal and meridional wind components from WW3 at 10 m 10 10 Tables Figures 15 height. The kˆ is the versor normal to the surface.

J I 3 Results J I

3.1 Model validation Back Close

As mentioned before, wave data measured on the South Atlantic is extremely rare. Full Screen / Esc For this study, we have carried out a simulation to compare the model’s results with Printer-friendly Version 20 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 Interactive Discussion close to Tramandaí city (the location of which is indicated in Fig. 1) in 17 m intermediate water (Strauch et al., 2009). This means that the buoy located over intermediate water 4371 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion depth could be measuring waves disturbed by the local bathymetry and therefore not representative of the large-scale wave field. This analysis enabled the selection of the NHESSD significant wave hight, the pick period, and the pick direction (Fig. 2 shows these two 2, 4363–4391, 2014 dates at the same period). 5 Table 1 summarizes the statistical correlation between SWAN and the directional buoy data for the same data presented in Fig. 2. Analysis of extreme r represents the Pearson correlation coefficient, measuring the degree of correlation, wave events in the a and b are the regression line coefficients (y = ax + b). The Pearson correlation is +1 southern coast of in the case of a perfect positive (increasing) linear relationship (correlation), and zero Brazil 10 when there is less of a relationship (closer to uncorrelated or independent). According to Triola (2006), for a normal Pearson distribution where n = 1175 is the number of P. V. Guimarães et al. 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, are 0.2560 and Title Page 0.1960, respectively. For this case, a linear model, the coefficient of determination r2 is 15 Pearson’s product-moment coefficient. Abstract Introduction Looking at Fig. 2a and b, it is possible to see that the wave direction errors were near Conclusions References 10o and the r2 shows that the SWAN could fit the direction in 72 % of the cases. But SWAN could not represent more than 53 % of the cases of peak wave periods: usually Tables Figures the peaks of the swell period were underestimated and the sea peak waves’ periods 20 were overestimated. The significant wave heights were well represented by the model J I 62 % of the time, usually the buoy registers were overestimated, however in some of the higher events, the model predicts something less by 50 cm than that observed. J I Overall, the model calibration results were reasonable and satisfactory at intermedi- Back Close ate water waves. The coefficients of correlation between the model and the observed Full Screen / Esc 25 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 Printer-friendly Version underestimated the significant wave heights. However, it caught the variation pattern of wave oscillation very soon, although small disagreements between the observed and Interactive Discussion the simulated data exist.

4372 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 3.2 Extreme wave events NHESSD 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 2 show some information about these 2, 4363–4391, 2014 events. The start time represent the time-point where the extreme significant wave 5 height started to appear within the region of the computational grid. The end time- Analysis of extreme point represents the points where these wave events left the computational grid. The wave events in the peak time represent the most energetic time-point of each simulation. The difference southern coast of between the start and the end time-point gives the duration of the event. Table 3 shows Brazil the max of significant wave height simulated ( H ) observed at deep water, W smax lmax 10 represents the highest water level measured at the Tramandaí coastal point during P. V. Guimarães et al. each event, T and D give the period of the most frequent peak waves and the pfreq pfreq direction of the peak waves for each event in the whole computational domain. The analysis of Tables 2 and 3 shows that the event of 27 June 2006 might be one Title Page of most energetic that has acted on the Rio Grande do Sul coastal zone for the last Abstract Introduction 15 ten years: this time, the waves surpassed 9 m in height at offshore places. Figure 3 shows a simulation of the most energetic time point of this event. Figure 3a exhibits in Conclusions References a color scale the significant wave heights over the computational grid, the scale vector Tables Figures representing the peak waves direction. During this event, there was also observed the formation of long wave periods, as was shown in Table 3, Fig. 3b exemplifies one J I 20 screen of the peak wave period at these event. J I

Back Close 4 Discussion Full Screen / Esc 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 4 presents the Printer-friendly Version track of each event and the relative vorticity in a color scale. Employing those authors’ Interactive Discussion 25 classification and the observations in Fig. 4, the majority of the events E01, E02, E04, E05 and E06 could be classified in pattern as regional (RC2) with cyclogenesis in the 4373 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion south of Uruguay with an eastward displacement and a trajectory between 28◦ S and 42.5◦ S. Only the event E03 occurred at region (RC3) with cyclogenesis in the south of NHESSD Uruguay with a southeasterly displacement and a trajectory between 35◦ S and 57.5◦ S. 2, 4363–4391, 2014 While only waves over 5 m were analyzed, the high frequency of events with pattern 5 RC2 suggests that the eastward displacement of Middle Atlantic cyclones best devel- ops the extreme wave events at Rio Grande do Sul coast. The extra-tropical cyclone Analysis of extreme of event E03 was well studied by Parise et al. (2009) and Machado et al. (2010): in wave events in the this case, the meteorological scenario, due to a long wind fetch from S to SW and the southern coast of association between this wind pattern and the NE–SW orientation of the shoreline, fa- Brazil 10 vored the extra high rise in sea level observed on the coast due to the Coriolis effect. P. V. Guimarães et al. The events E04, E05 and E06 were the stronger systems, characterized by a high −5 −1 frequency of cyclogenesis with ζ 10 ≤ −2.5 × 10 s . To better understand how the waves developed during these events, Fig. 5 presents Title Page a Hovmöller diagram for significant wave heights. The diagram plots the wave data 15 in a color scale and the peak wave directions are displayed by vectors. This diagram Abstract Introduction shows the time as the abscissa (x axis) and the latitude of 50 m isobathymetry as the Conclusions References ordinate (y axis). From Fig. 5, it is possible to observe that during these events, the majority of waves Tables Figures energy at 50 m was concentrated between the latitudes 31.5 and 34◦ S. Except for 20 the event E05, that concentrates the energy to the north of the Rio Grande do Sul J I 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 J I had the northernmost cyclogenic track. These observations allow us to say that the Back Close energy of the deep waves at the Rio Grande do Sul coastal zone during storm events Full Screen / Esc 25 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 Printer-friendly Version E05 can grow 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 Interactive Discussion cyclogenetic studies of Parise et al. (2009), Machado et al. (2010) and Reboita et al.

4374 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion (2012) provide us 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. NHESSD The wave analysis of the 50 m deep water waves provides important information for 2, 4363–4391, 2014 evaluating the risk for navigation and offshore operations. But is insufficient for coastal 5 zone studies. So Fig. 6 presents the same Hovmöller analysis for the waves at 6 m depth. Analysis of extreme Unlike the 50 m wave analysis, Fig. 6 shows that the waves’ energy during these ex- wave events in the treme events was concentrated to the north of Rio Grande city and at the Hermenegildo southern coast of beach region. The explanation of this fact is not just in the cyclone’s pattern, but also in Brazil 10 the shoreface morphologies. The region next to the lagoon’s mouth (south) has a completely different shoreface morphology as compared to the northern and the southern P. V. Guimarães et al. end of Rio Grande do Sul. The region south of the mouth of the Lagoa dos Patos presents a wide inner shelf, vir- Title Page tually homogeneous, with isobaths parallel to the coastline until next to Hermenegildo ◦ 15 beach (seen also in Fig. 1). At this region, close to the Hermenegildo beach (33.2 S), Abstract Introduction the sub-aqueous profile has remnants of sand ridges. Conclusions References 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 Tables Figures directions, and between the 12 and 30 m isobaths. Also, along with a narrowing of the 20 region of the shoreface where there occur the largest profile slopes, with a predomi- J I nantly 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 J I the region south of the Lagoa dos Patos, most of wave energy is dissipated at the Back Close shoreface. The natural features in this region act like a natural submerged barrier to Full Screen / Esc 25 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 Printer-friendly Version 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 Interactive Discussion

4375 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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. NHESSD To better understand the interaction between the Rio Grande do Sul shallow water 2, 4363–4391, 2014 waves and the morphologies, Fig. 1 shows the nearshore bathymetry between 0 and 5 −60 m. These results support the results of the Hovmöller diagram for shallow water waves (Fig. 6), wherein the wave energy has been concentrated by the high slope Analysis of extreme gradients. wave events in the Although the erosion problem in the further south of Rio Grande do Sul at southern coast of Hermenegildo has been mainly a problem of anthropic occupation, this wave analy- Brazil 10 sis shows that this problem also can be associated to the cyclogenesis pattern and the wave transformation at the shoreface, where the waves’ energy has been concentrated P. V. Guimarães et al. in front of Hermenegildo. However, the trends of the shoreline are established by the extreme erosive and Title Page depositional results of the complex interaction between the rates of relative changes 15 in the sea level, the rate of sediment supply, the wave dynamics, and the impacts Abstract Introduction produced by storm waves. However, because of the large energy carried by the waves Conclusions References of 2 to 3 m in shalow water, combined com a sea leave rise of 0.7 to 1.3 m during extreme events, the sedimentary dynamics during these high wave energy events are Tables Figures an important factor in the sediment budget of the sand beaches. 20 The results of Toldo et al. (2006) about a high coastal retreat from the north of the J I Lagoa dos Patos inlet to the Tramandaí region are also related in Fig. 6, where one can observe a trend in the waves’ energy at this part of the littoral. Toldo et al. (2013) J I ◦ ◦ also classified the sectors in front of Mostardas (31 S) and Dunas Altas (30.5 S) as Back Close sediment sink areas. The region of lower wave energy between the Rio Grande and ◦ Full Screen / Esc 25 about 33 S was classified by Toldo et al. (2006) as an area of progradation and moderate retrogradation. Except for the event E05, with had a different cyclonic trajectory Printer-friendly Version from the others, the analysis of Fig. 6 also allows observing a small region of lower wave energy just north of Tramandaí beach: at this area the progradation and mod- Interactive Discussion erate retrogradation rates were also checked by Toldo et al. (2006). Therefore these

4376 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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 some NHESSD beaches along the coast of Rio Grande do Sul. 2, 4363–4391, 2014 However, other factors such as currents, beach profile, sea level, grain size, and 5 others, have been extremely important for the sediment dynamics of the region. The morphological response and amplitude caused by a storm are often defined as pro- Analysis of extreme portional to the intensity of waves and the tidal level of high energy (as described by wave events in the Wright and Short, 1984; Wright et al., 1985 and Sénéchal et al., 2009). So, the results southern coast of of this study are directly in agreement with those found by Toldo et al. (2006) and Toldo Brazil 10 et al. (2013) 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, be- P. V. Guimarães et al. ing one of the major contributors to the large volumes of sedimentary mobilization, moving the sediment from areas of largeset wave height toward offshore areas or to- Title Page wards areas of lesser wave energy. But the waves in these events that hit the coast 15 are mainly controlled by the regional shoreface morphology and by the cyclone pattern Abstract Introduction that generated these events. Conclusions References While most of the Rio Grande do Sul has a high tendency to coastal erosion, much of the coast is still preserved with low urbanization. Crossing the results of sig- Tables Figures nificant wave height with the urbanization and use, it is possible to determine that ◦ ◦ ◦ 20 the Hermenegildo beach (33.2 S), Cidreira (30.2 S), Pinhal (30.3 S), Tramandaí and J I Imbé (30.0◦ S) and Torres (29.3◦ S) should give more attention to the passage of extreme wave events. The analysis of deep water waves suggests that more attention J I ◦ should be given to the region next to Rio Grande (32.1 S), where is located one of Back Close the most important ports of Brazil, and the risks are directly related to navigation and Full Screen / Esc 25 offshore operations.

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4377 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 5 Summary and conclusions NHESSD 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 mod- 2, 4363–4391, 2014 eling with a good spatial resolution (around 1 km) and non-stationary high frequency 5 time resolution (5 min) allowed a good numerical representation of the waves. The high Analysis of extreme grid resolution employed in the areas of interest allowed well simulating the waves wave events in the where the buoy data was available for validating this simulation. Overall, the compari- southern coast of son of the measured buoy data with the model results showed there was a reasonable Brazil fit, and satisfactory for shallow water waves. The statistical results showed that all three 10 wave parameters analyzed had a good match with reality in most of the SWAN cases, P. V. Guimarães et al. 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 Title Page of the wave fields on this domain of the globe’s oceans. Abstract Introduction 15 The direct analysis of deep water waves from WW3 identified six events between 2000 and 2010 where the waves surpassed five meters of significant height, on a point Conclusions References of interest. Employing the Middle Atlantic Cyclonic pattern classification, it was possible Tables Figures to detect a high frequency of events of pattern RC2 among all events with high wave

energy. This suggests that the eastward displacement of Middle Atlantic Cyclones de- J I 20 velop more intensively the extreme wave events at the Rio Grande do Sul coast. The pattern RC2 did better at developing highly energetic events between the lati- J I ◦ tudes 31.5 and 34 S, but the simple formation of these events at the north, as for event Back Close E05, could change the deep water wave pattern. This shows that the highly energetic wave patterns at deep water are mostly controlled by the cyclonic track and intensity. Full Screen / Esc 25 The Hovmöller diagram for shallow and deep water analysis allows a good description of the time evolution for each event. The wave analysis at 50 m deep water could Printer-friendly Version provide important information for navigation and oﬀshore operations risk, while the Interactive Discussion

4378 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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. NHESSD These results agree with the Rio Grande do Sul geomorphological description. The 2, 4363–4391, 2014 wave energy tends to be concentrated in areas of higher gradients of bathymetry and 5 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 Analysis of extreme gentle and smooth slope dissipates most of the wave energy at the shoreface, acting wave events in the as a natural submerged barrier to the waves’ impact during these extreme events. The southern coast of wave pattern found during these events in deep water showed a greater concentration Brazil ◦ 10 of wave energy south of 31.5 S, while in shallow waters, this pattern was inverted, with foci of wave energy mainly to the north of 31◦ S. P. V. Guimarães et al. 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 Title Page and the dissipation of the waves’ energy at shoreface during extreme events could be 15 one of the main factors responsible for the sediment budget at the Rio Grande do Sul Abstract Introduction coast. Conclusions References Finally, another key aspect of this storm wave analysis involves the assessment of the risk conditions for each of beaches examined. As a consequence, this paper could Tables Figures determine the sensitive places during storm wave occurrences for urban occupation, 20 navigation and oﬀshore activities. J I

Acknowledgements. The ﬁrst author would like to thank CAPES for a research fellowship and J I ﬁnantial support from CNPq. Pedro V. Guimarães and Leandro Farina have done part of the Back Close research on this article at the Basque Center for Applied Mathematics (BCAM), while members of the EU project FP7-295217-HPC-GA. The authors also would like to thank Brazil’s Superin- Full Screen / Esc 25 tendency of Ports and Waterways for making the water level data available.

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4379 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion References NHESSD Booij, N., Ris, R. C., and Holthuijsen, L. H.: A third-generation wave model for coastal regions: 1. Model description and validation, J. Geophys. Res., 104, 7649, doi:10.1029/98JC02622, 2, 4363–4391, 2014 1999. 4369 5 Calliari, L. J., Speranski, N., and Boukareva, I.: Stable focus of waves rays as a reason of local erosion at southern Brazil coast., J. Coastal Res., 26, 19–23, 1998a. 4366 Analysis of extreme Calliari, L. J., Tozzi, H. A. M., and Klein, A. H. F.: Beach morphology and coastline erosion wave events in the associated with storm surges, An. Acad. Bras. Ciênc., 70, 232–247, 1998b. 4365, 4366 southern coast of Dillenburg, S. R., Esteves, L. S., and Tomazelli, L. J.: A critical evaluation of coastal erosion in Brazil 10 Rio Grande do Sul, Southern Brazil, Ann. Brazil. Acad. Sci., 76, 611–623, 2004. 4365, 4366 Esteves, L. S., Toldo, E. E., Dillenburg, S. R., and Tomazelli, L. J.: Long- and short-term coastal P. V. Guimarães et al. erosion in Southern Brazil, J. Coastal Res., 282, 273–282, 2002. 4366 Esteves, L. S., da Silva, A. R. P., Arejano, T. B., Pivel, M. A. G., and Vranjac, M. P.: Coastal development and human impacts along the Rio Grande do Sul Beaches, Brazil, J. Coastal Title Page 15 Res., 35, 548–556, 2003. 4366 Fachin, S.: Caracterização do Perﬁl de Equilíbrio da Antepraia na Costa do Rio Grande do Sul, Abstract Introduction Ph.D. thesis, Universidade Federal do Rio Grande do Sul, 1998. 4366 Gan, M. A. and Rao, B. V.: Surface ciclogenesis over South America., Mon. Weather Rev., 119, Conclusions References 293–302, 1991. 4367 Tables Figures 20 Holthuijsen, L. H., Booij, N., and Ris, R. C.: A spectral wave model for the coastal zone, Pro- ceedings 2nd International Symposium on Ocean Wave Measurement and Analysis, New Orleans, Louisiana, 25–28 July, New York, 630–641, 1993. 4369 J I Machado, A. A., Calliari, L. J., Melo, E., and Klein, A. H. F.: Historical assessment of extreme J I coastal sea state conditions in southern Brazil and their relation to erosion episodes, Pan- 25 American J. Aquatic Sci., 5, 105–114, 2010. 4365, 4367, 4368, 4374 Back Close Mendoza, E. and Jimenez, J.: Storm-induced beach erosion potential on the Catalonian Coast., J. Coastal Res., SI 48, 81–88, 2006. 4365 Full Screen / Esc Mendoza, E. and Jimenez, J.: Regional geomorphic vulnerability analysis to storms for Catalan beaches., P. I. Civil Eng.-Mar. En., 162, 127–135, 2009. 4365 Printer-friendly Version 30 Morton, R.: Factors controlling storm impacts on coastal barriers and beaches: a preliminary basis for near real-time forecasting, J. Coastal Res., 18, 486–51, 2002. 4365 Interactive Discussion

4380 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Parise, C. K., Calliari, L. J., and Krusche, N.: Extreme storm surges in the south of brazil: atmospheric conditions and shore erosion, Braz. J. Oceanogr., 57, 175–188, 2009. 4365, NHESSD 4366, 4368, 4374 Reboita, M. S., Rocha, R. P., and Ambrizzi, T.: Dynamic and climatological features of cyclonic 2, 4363–4391, 2014 5 developments over Southwestern South Atlantic Ocean, in: Horizons in Earth Science Re- search., vol. 6, chap. 4, Nova Science Publishers, São Paulo, 135–160, 2012. 4375 Reboita, M. S. O., da Rocha, R. P., Ambrizzi, T., and Sugahara, S.: South Atlantic Ocean Analysis of extreme cyclogenesis climatology simulated by regional climate model (RegCM3), Clim. Dynam., 35, wave events in the 1331–1347, 2010. 4367, 4368 southern coast of 10 Ris, R. C., Holthuijsen, L. H., and Booij, N.: A third-generation wave model for coastal regions: Brazil 2. Veriﬁcation, J. Geophys. Res., 104, 7667, doi:10.1029/1998JC900123, 1999. 4369 Sallenger, A.: Storm impact scale for barrier islands., J. Coastal Res., 16, 890–895, 2000. 4365 P. V. Guimarães et al. Saraiva, J. M. B., Bedran, C., and Carneiro, C.: Monitoring of storm surges at Cassino Beach., J. Coastal Res., SI 35, 323–331, 2003. 4366 15 Sénéchal, N., Gouriou, T., Castelle, B., Parisot, J., Capo, S., and Bujan, S., H. H.: Morphody- Title Page namic response of a meso- to macro-tidal intermediate beach based on a long-term data set, Geomorphology, 107, 263–274, 2009. 4365, 4377 Abstract Introduction Speranski, N. and Calliari, L.: Bathymetric lenses and localized coastal erosion in Southern Brazil, J. Coastal Res., 34, 209–215, 2001. 4366 Conclusions References 20 Strauch, J. a. C., Cuchiara, D. C., Júnior, E. E. T., and de Almeida, L. E. S. B.: O Padrão das Tables Figures Ondas de Verão e Outono no Litoral Sul e Norte do Rio Grande do Sul, RBRH – Revista Brasileira de Recursos Hídricos, 14, 29–37, 2009. 4366, 4369, 4371 Toldo, E., Nicolodi, J., Almeida, L., Corrêa, I., and Esteves, L.: Coastal dunes and shoreface J I width as a function of longshore transport, J. Coastal Res., 39, 390–394, 2006. 4366, 4376, J I 25 4377 Toldo, E. E., da Motta, L. M., de Almeida, L. E. d. S. B., and Nunes, J. C. R.: Large morphological Back Close change linked to the sediment budget in the Rio Grande do Sul Coast, Coast. Dynam., 7th International Conference on Coastal Dynamics., 1687–1696, 2013. 4376, 4377 Full Screen / Esc Tolman, H. L.: User manual and system documentation of WAVEWATCH-III, Tech. rep., 30 NOAA/NWS/NCEP/OMB, 2009. 4368, 4370 Printer-friendly Version Triola, M.: Elementary Statistics, 10 edn., Pearson Education, Boston, 2006. 4372 Wright, L. and Short, A.: Morphodynamic variability of surf zones and beaches: a synthesis., Interactive Discussion Mar. Geol., 56, 93–118, 1984. 4365, 4377 4381 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Wright, L., Short, A., and Green, M.: Short-term changes in the morphodynamic states of beaches and surf zones: an empirical predictive model., Mar. Geol., 62, 339–364, 1985. NHESSD 4365, 4377 Young, I.: Wind Generated Ocean Waves, 1st edn., Elsevier, University of Adelaide, Australia, 2, 4363–4391, 2014 5 1999. 4369 Analysis of extreme wave events in the southern coast of Brazil

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Analysis of extreme wave events in the southern coast of Brazil

P. V. Guimarães et al. Table 1. Model and buoy data statistics.

H T D s p p Title Page Adjust equation y = 0.87x + 0.13 y = 0.96x + 0.38 y = 1.00x − 10.58 b 0.1271 0.3751 −10.5758 Abstract Introduction a 0.8734 0.9618 1.0009 Conclusions References r2 0.6178 0.5388 0.7242 r 0.7860 0.7340 0.8510 Tables Figures

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Analysis of extreme wave events in the southern coast of Brazil Table 2. Extreme wave events: The Start time gives the time where the waves of these events started to appear in the computational domain. End indicates when the waves leave the do- P. V. Guimarães et al. main. The Peak time gives the most energetic moment in each event, and Duration is the time between End and Start.

Title Page Events Start End Peak Duration E01 30 Aug 2002, 15:00 4 Sep 2002, 00:00 2 Sep 2002, 15:00 4 days, 09:00 h Abstract Introduction E 02 26 Jun 2006, 12:00 28 Jun 200,6 18:00 27 Jun 2006, 03:00 2 days, 06:00 h Conclusions References E03 2 Sep 2006, 19:00 6 Sep 2006, 11:00 3 Sep 2006, 19:00 3 days, 16:00 h E04 27 Jul 2007, 09:00 30 Jul 2007, 06:00 28 Jul 2007, 13:00 2 days, 21:00 h Tables Figures E05 3 May 2008, 04:00 6 May 2008, 11:00 3 May 2008, 23:00 3 days, 07:00 h E06 9 Jun 2008, 22:00 11 Jun 2008, 02:00 10 Jun 2008, 10:00 1 days, 04:00 h J I

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Analysis of extreme wave events in the southern coast of Brazil Table 3. Waves informations for each events: H is the max of signiﬁcant wave height sim- smax ulated at deep watter, the W is the higher water level in a Tramandaí coastal point, the T lmax pfreq P. V. Guimarães et al. and the D are the most frequently of the peak waves period and the peak waves direction in pfreq the computational domain.

Title Page Events H [m] W [m] T [s] D smax lmax pfreq pfreq Abstract Introduction E01 7.254 0.83 12–14 SE E02 8.982 0.84 12–14 E–SE Conclusions References E03 8.423 1.38 12–14 E E04 8.351 0.90 12–14 E Tables Figures E05 7.991 0.76 10–12 S–SE E06 7.875 0.71 8–10 NE J I

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4385 2 P. V. Guimaraes:˜ Msc.

The state of Rio Grande do Sul is characterized by an ex- directed predominantly SE–NE, with depths between 12 and tensive coastline with uniform orientation NE–SW and light 30 m. sinuosity along its extension of 615 km (Fig. 1), includin The water level is also affected by the South Atlantic circu- Cassino, one of the longest sandy beaches in the world (Dil- lation responsible for short-term sea level variations. At Rio 70 lenburg et al., 2004). All this extension consists of uncon- 95 Grande do Sul, the maximum values of storm surges were on solidated deposits from quaternary rivers that do not receive the order of 1 m, 1.4 m and 1.9 m, found by, respectively, contributions from modern sands. The Continental Shelf is Calliari et al. (1998b), Saraiva et al. (2003) and Parise et al. part of a broad and passive margin, more than 150 km long, (2009). As tidal rage is small, the waves are responsable for with maximum depths ranging between 100 and 140 meters most sediments transport and deposition along the coast. The 75 and a gentle slope on the order of 0.06. The shoreface is ex- 100 average significant wave height at depths of around 17 m is tensive and shallow with an outer boundary at a depth of 10 found by Strauch, 2009 to be 1.5 m. m, with predominantly sandy deposits (Toldo et al. 2006). According to Speranski and Calliari (2001), the conver- icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion gence of wave rays due to refraction by small-scale bed slopes focus the wave withNHESSD period longer than 9 s at some 105 coastal areas. This is one of the probable causes of the local 2, 4363–4391, 2014 erosion under waves storms in Rio Grande do Sul. Hermenegildo beach at the southern end of Rio Grande do Sul has been much studied,Analysis e.g., Calliari of extremeet al. 1998a, Esteves et al. 2002 and 2003, becausewave eventsof the severe in the erosion problem 110 in this region. Accordingsouthern to Dillenburg coastet of al. (2004) , this problem involves anthropic occupationBrazil too. Toldo et al. 2006 have analyzed the retreat and progradation zone identifying a high regional coastalP. erosion V. Guimarães along the et al. middle coast between the Lagoa dos Patos inlet until the Tramanda´ı region, 115 as a function of longshore transport. The estimated potential of sediment transport predictsTitle a substantial Page variation of the energy flux into the surf zone,Abstract due toIntroduction little changes in shoreline alignments and consequently on the transport potential along the coast. The netConclusions longshore sandReferences transport to north- 120 east are responsible for theTables increase theFigures coastal erosion rates. On the other hand, the reduction of the sediment flux among

the alignments produce a jamJ in the longshoreI transport and the progradation in these places. The effects of waves haveJ been shownI to be the funda- 125 mental process for coastalBack management,Close since it is the main forcing term in the dynamics, composition, and morphology of this coastline. Most of theFull energy Screen incident/ Esc on this coastal Figure 1. StudyFig. field 1. Study representation. field representation. Solid lines Solid represent lines represent the the the grid the boundaries. grid Inside, in boundaries. Inside, in color scale, the grid bathymetry is between 0 zone is associated with gravity waves and the most energetic color scale, the grid bathymetry is between 0 and −60 m. The points indicate reference beaches Printer-friendly Version at Rio Grandeand do -60 Sul. m. Tramandaí The points indicatebeach is reference where thebeaches buoy at was Rio Grande placed do for theevents comparison are associated with the extra-tropical cyclones. These analysis. The mapsSul. Tramanda are plotted´ı beach over is a where Google the Maps buoy was image. placed for the compar- 130 cyclones are very turbulentInteractive and unstable Discussion meteorological phe- ison analysis. The maps are plotted over a Google Maps image. nomena, defined as low pressure systems of synoptic scale that occur in the middle latitudes. They have a great influence A good regional geomorphological4386 description is given by on the regional climate and constitute an important mecha- Fachin (1998): according to this author, the shorefaces for nism of atmospheric circulation for the thermal equilibrium 80 the northern and southern end of this region are totally dif- 135 between the regions of low and high latitudes. ferent, changing at the south of the Lagoa dos Patos inlet. According to Machado et al. (2010), the intense cyclonic The area near and south of Lagoa dos Patos is described as weather systems in southern Brazil generate ocean storms more homogeneous, with a gradually decreasing slope to- which can, on a temporal scale varying from a few hours to ward the sea. The northern and southern ends of this area a day, completely erode a beach profile from its maximum 85 have two different standards for the presence and orientation 140 accretion state. Mid-latitude cyclogenesis with low pressure of sand ridges. To the north there is a high concentration of centers in the deep ocean and along the coast increases the sand ridges with an orientation predominantly parallel to the intensity of Mid-Atlantic storms, causing storm surges and shoreline with depths of 18 and 22 m and with coastal dis- storm waves. During the a event of September 2006, it was tances from 8 to 10 km. At the southern end there are more observed that a great part of Cassino beach was flooded when 90 complex morphologies, with sand ridges oblique to the coast, 145 the water reached the first avenue close to the beach. icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion NHESSD 2, 4363–4391, 2014

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Figure 2. Validation of the SWAN wave model with the directional buoy data. (a) The SWAN Printer-friendly Version predictions are shown in continuous lines and the buoy data are in circles. (b) Scatter plot of the linear correlation, the colors of the dots represent the distance from the regression line. Interactive Discussion

4387 P. V. Guimaraes:˜ Msc. 7

Table 2. Extreme wave events: The Start time gives the time where the waves of these events started to appear in the computational domain. End indicates when the waves leave the domain. The P eak time gives the most energetic moment in each event, and Duration is the time between End and Start.

Events Start End Peak Duration E01 30-Aug-2002 15:00 04-Sep-2002 00:00 02-Sep-2002 15:00 4 days 09:00 h

E02 26-Jun-2006 12:00 28-Jun-2006 18:00 27-Jun-2006 03:00 2 days | 06:00 Paper Discussion h | Paper Discussion | Paper Discussion | Paper Discussion E03 02-Sep-2006 19:00 06-Sep-2006 11:00 03-Sep-2006 19:00 3 days 16:00 h E04 27-Jul-2007 09:00 30-Jul-2007 06:00 28-Jul-2007 13:00 2 days 21:00 h E05 03-May-2008 04:00 06-May-2008 11:00 03-May-2008 23:00 3 days 07:00 h NHESSD E06 09-Jun-2008 22:00 11-Jun-2008 02:00 10-Jun-2008 10:00 1 days 04:00 h 2, 4363–4391, 2014

Analysis of extreme wave events in the southern coast of Brazil

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J I a) Hs and Dp of EVENT 02 (b) T p and Dp of EVENT 02 Back Close Fig. 3. Surface of Hs and T p in color scale, the Dp are presented in scale vectors. Figure 3. Surface of H and T in color scale, the D are presented in scale vectors. s p p Full Screen / Esc

445 occur the largest profile slopes, with a predominantly sandy 460 To better understand the interaction between the Rio sedimentology. So these bottom features corroborate the re- Grande do Sul shallow water waves and the morphologies, Printer-friendly Version sults obtained by the analysis of the waves in shallow water. Figure 1 shows the nearshore bathymetry between 0 and −60 Due to the gentle and smooth slope in the region south of m. These results support the results of the Hovmoller¨ dia- Interactive Discussion the Lagoa dos Patos, most of wave energy is dissipated at gram for shallow water waves (Fig. 6), wherein the wave en- 450 the shoreface. The natural features in this region act like a 465 ergy has been concentrated by the high slope gradients. natural submerged barrier to the wave impact during these Although the erosion problem in the further south of extreme events. In contrast, the high bathymetric gradients4388Rio Grande do Sul at Hermenegildo has been mainly a and the different submerged features observed north of the problem of anthropic occupation, this wave analysis shows Lagoa dos Patos outflow showed a tendency to concentrate that this problem also can be associated to the cyclogen- 455 the energy of the shallow water waves during the analyzed 470 esis pattern and the wave transformation at the shoreface, events. In such cases, the phenomena of refraction and fric- where the waves’ energy has been concentrated in front of tion with the background become more significant, due to Hermenegildo. the large peak wave periods (seldom found in typical wave However, the trends of the shoreline are established by fields), more often between 12 and 14 s. the extreme erosive and depositional results of the complex 8 P. V. Guimaraes:˜ Msc.

Table 3. Waves informations for each events: Hsmax is the max of sink areas. The region of lower wave energy between the Rio ◦ significant wave height simulated at deep watter, the W lmax is the 490 Grande and about 33 S was classified by Toldo et al. 2006 higher water level in a Tramanda´ı coastal point, the T pfreq and the as an area of progradation and moderate retrogradation. Ex- Dpfreq are the most frequently of the peak waves period and the cept for the event E05, with had a different cyclonic trajec- peak waves direction in the computational domain. tory from the others, the analysis of Figure 6 also allows observing a small region of lower wave energy just north of 495 Tramanda´ı beach: at this area the progradation and moderate Events Hsmax [m] W lmax [m] T pfreq [s] Dpfreq E01 7.254 0.83 12-14 SE retrogradation rates were also checked by Toldo et al. 2006. E02 8.982 0.84 12-14 E–SE Therefore these authors’ results conform to the shallow water E03 8.423 1.38 12-14 E wave analysis presented in this article, thus showing that the E04 8.351 0.90 12-14 E high energy wave events could be one of the causes of some E05 7.991 0.76 10-12 S–SE 500 beaches along the coast of Rio Grande do Sul. E06 7.875 0.71 8-10 NE However, other factors such as currents, beach profile, sea icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | level, Paper Discussion | grain Paper Discussion size, and others, have been extremely important for the sediment dynamicsNHESSD of the region. The morphological response and amplitude caused by a storm are often de- 2, 4363–4391, 2014 505 fined as proportional to the intensity of waves and the tidal −20 track E01 level of high energy (as described by Wright and Short, 1984, Analysis of extreme −25 track E02 Wright et al., 1985 and Sen´ echal´ et al., 2009). So, the results track E03 of this study arewave directly events in agreement in the with those found by track E04 southern coast of −30 Toldo et al. 2006 and Toldo et al. 2013 after storm events, track E05 Brazil track E06 510 thus suggesting that the dynamics induced by extreme wave −35 events can be oneP. V. of Guimarães the determinants et al. of sediment transport in the region, being one of the major contributors to the large −40

Latitude volumes of sedimentary mobilization, moving the sediment from areas of largesetTitle wave Page height toward offshore areas or −45 515 towards areas ofAbstract lesser waveIntroduction energy. But the waves in these events that hit the coast are mainly controlled by the regional −50 shoreface morphologyConclusions andReferences by the cyclone pattern that gener- Tables Figures −55 ated these events. While most of the Rio Grande do Sul has a high ten- 520 dency to coastal erosion,J muchI of the coast is still preserved −60 −55 −50 −45 −40 −35 −30 −25 −20 −15 −10 Longitude with low urbanization.J CrossingI the results of signiﬁcant wave height with the urbanization and use, it is possible to −2.5 −2 −1.5 −1 −0.5 0 Back Close 33.2o −5 determine that the Hermenegildo beach ( S), Cidreira vorticity [1/s] x 10 (30.2oS), Pinhal (30.3Full◦ ScreenS), Tramanda / Esc ´ı and Imbe´ (30.0oS) and o Figure 4. In color lines it is possible to identify each anticyclone track per event and the525 coloredTorres (29.3 S) should give more attention to the passage of balls show the vorticityFig. 4. In intensity. color lines it is possible to identify each anticyclone track extreme wave events.Printer-friendly The analysis Version of deep water waves sug- per event and the colored balls show the vorticity intensity. gests that more attentionInteractive Discussion should be given to the region next to Rio Grande (32.1◦S), where is located one of the most important ports of Brazil, and the risks are directly related to 4389 475 interaction between the rates of relative changes in the sea 530 navigation and offshore operations. 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 metres in 5 Summary and conclusions shalow water, combined com a sea leave rise of 0.7 to 1.3 480 m during extreme events, the sedimentary dynamics during Employing some of the studies and measured wave data for these high wave energy events are an important factor in the the Rio Grande do Sul, this paper reviewed the extreme wave sediment budget of the sand beaches. events there from 2000 to 2010. Spectral wave modeling with The results of Toldo et al. 2006 about a high coastal re- 535 a good spatial resolution (around 1 km) and non-stationary treat from the north of the Lagoa dos Patos inlet to the Tra- high frequency time resolution (5 min) allowed a good nu- 485 manda´ı region are also related in Figure 6, where one can merical representation of the waves. The high grid resolution observe a trend in the waves’ energy at this part of the lit- employed in the areas of interest allowed well simulating the toral. Toldo et al. 2013 also classiﬁed the sectors in front waves where the buoy data was available for validating this o o of Mostardas (31 S) and Dunas Altas (30.5 S) as sediment 540 simulation. Overall, the comparison of the measured buoy icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion NHESSD P. V. Guimaraes:˜ Msc. 9 2, 4363–4391, 2014

Analysis of extreme wave events in the southern coast of Brazil

P. V. Guimarães et al.

Title Page

Abstract Introduction

Conclusions References

Tables Figures

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Back Close Figure 5. HovmöllerFig. 5. Hovmoller¨ diagram diagram for deep for water deep waves. The water diagram displaywaves. the wave The parameters diagram (Hs and Dp display) for 50 m isobathymetry. the wave The parameters latitude of the wave is displayed along the y-axis, and the time is along the x-axis. The Hs are in a color scale and the Dp as vectors. (Hs and Dp) for 50 m isobathymetry. The latitude of the wave is displayed along the y-axis, and Full Screen / Esc the time is alongdata with the model x-axis. results showed The thereHs wasare a reasonable in a colorsuggests scale that and the eastward the D displacementp as vectors. of Middle Atlantic fit, and satisfactory for shallow water waves. The statisti- Cyclones develop more intensively the extreme wave events cal results showed that all three wave parameters analyzed at the Rio Grande do Sul coast. Printer-friendly Version had a good match with reality in most of the SWAN cases, 560 The pattern RC2 did better at developing highly energetic ◦ ◦ 545 with correlation coefficients between 0.79 and 0.85. It has to events between the latitudes 31.5 S and 34 S, but the sim- Interactive Discussion be emphasized that comparison studies of this type are ex- ple formation of these events at the north, as for event E05, tremely rare and scarce in the South Atlantic. Thus the re- could change the deep water wave pattern. This shows that sults here are new and relevant to future works on the mod- the highly energetic wave patterns at deep water are mostly eling and description of the wave fields on this domain of the 565 controlled by the cyclonic track and intensity. 550 globe’s oceans. The Hovmoller¨ diagram for shallow and deep water anal- The direct analysis of deep water waves from WW3 iden-4390ysis allows a good description of the time evolution for each tified six events between 2000 and 2010 where the waves sur- event. The wave analysis at 50 m deep water could provide passed five meters of significant height, on a point of interest. important information for navigation and offshore operations Employing the Middle Atlantic Cyclonic pattern classifica- 570 risk, while the shallow water analysis, at 6 m deep, shows 555 tion, it was possible to detect a high frequency of events of where most of the waves’ energy was dissipated or concen- pattern RC2 among all events with high wave energy. This trated along the Rio Grande do Sul shoreface. icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion NHESSD 10 P. V. Guimaraes:˜ Msc. 2, 4363–4391, 2014

Analysis of extreme wave events in the southern coast of Brazil

P. V. Guimarães et al.

Title Page

Abstract Introduction

Conclusions References

Tables Figures

J I

Back Close Fig. 6. Hovmoller¨ diagram for shallow water waves. The diagram displays the wave parameters Hs and Dp for 6 m isobathymetry. The Figure 6. Hovmöllerlatitude of the wave diagram is displayed along for the y shallow-axis, and the time water is along waves.the x-axis. The TheHs are indiagram a color scale and displays the Dp as vectors. the wave param- Full Screen / Esc eters Hs and Dp for 6 m isobathymetry. The latitude of the wave is displayed along the y axis, These results agree with the Rio Grande do Sul geomor- the dissipation of the waves’ energy at shoreface during ex- and the time is along the x axis. The Hs are in a color scale and the Dp as vectors. phological description. The wave energy tends to be concen- 590 treme events could be one of the main factors responsible for 575 trated in areas of higher gradients of bathymetry and with the sediment budget at the Rio Grande do Sul coast. Printer-friendly Version heterogeneous bottom morphology, in front of Hermenegildo Finally, another key aspect of this storm wave analysis Beach and to the north of the Lagoa dos Patos inlet. But to involves the assessment of the risk conditions for each of the south of the Lagoa dos Patos inlet, the gentle and smooth beaches examined. As a consequence, this paper could de- Interactive Discussion slope dissipates most of the wave energy at the shoreface, 595 termine the sensitive places during storm wave occurrences 580 acting as a natural submerged barrier to the waves’ impact for urban occupation, navigation and offshore activities. during these extreme events. The wave pattern found during these events in deep water showed a greater concentration of o wave energy south of 31.5 S, while in shallow waters, this4391Acknowledgements. The ﬁrst author would like to thank CAPES pattern was inverted, with foci of wave energy mainly to the for a research fellowship and ﬁnantial support from CNPq. Pedro o 585 north of 31 S. V. Guimaraes˜ and Leandro Farina have done part of the research on The wave pattern in shallow water during these events is 600 this article at the Basque Center for Applied Mathematics (BCAM), also in accordance with the coastal progradation and retrac- while members of the EU project FP7-295217 - HPC-GA. The au- tion areas of this coast, showing that the concentration and thors also would like to thank Brazil’s Superintendency of Ports and Waterways for making the water level data available.