# Energetic Potential Assessment of Wind-Driven Waves on the South-Southeastern Brazilian Shelf

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{s}), Mean Period (T

_{m}) and Mean Direction (D

_{m}) on the oceanic boundaries and the wind velocity on the free surface.

#### 2.1. Numerical Model

#### 2.2. Boundary Conditions and Computational Grid

_{s}, T

_{p}(peak period) and D

_{m}. The data were generated by WaveWatch III and have a spatial resolution of 30 arc minutes and a temporal resolution of 3 h. Bathymetric data were acquired from the Brazilian Navy Admiral Charts and from the GEBCO (General Bathymetric Chart of the Oceans) database.

#### 2.3. Validation

_{s}and T

_{p}from the Tomawac model with the time series measured by the wave buoys. The data used to validate the numerical model were obtained from PNBOIA on the coast of Rio Grande do Sul (31°34′ S 49°53′ W, 200 $\mathrm{m}$ depth), Santa Catarina (28°30′ S 47°22′ W, 200 $\mathrm{m}$ depth) and São Paulo (25°17′ S 44°56′ W, 200 $\mathrm{m}$ depth) (Figure 1). The datasets used had: 7749 data points at the buoy of Rio Grande do Sul, 8836 at the buoy of Santa Catarina, and 6988 data points at São Paulo.

_{s}.

_{s}is an average $0.5$ $\mathrm{m}$, a slightly lower value than values calculated in other calibration and validation studies [42,43,46,47].

_{p}is underestimated by Tomawac with a difference of approximately $0.9$ $\mathrm{s}$. The results obtained by Lalbeharry [42], Melo [43], and Santos [47] show approximately the same mean difference. Although the calibration and validation of wave models is primarily based on the H

_{s}parameter, due to the amount of errors in the T

_{p}data measured by the buoy, some filters can be applied to clean the data, and this often results in a robust correlation between the model and measured T

_{p}. The RMSE is approximately $2.0$ $\mathrm{s}$, which is comparable with aforementioned studies.

_{s}is between 0.88 and 0.91, the lowest value being found near the coast, indicating a less strong correlation at this region. For T

_{p}, the correlation coefficient is slightly higher than for H

_{s}(between 0.89 and 0.93) indicating the same level of correlation for both parameters.

_{s}calculated in deep regions is slightly more precise than H

_{s}calculated near the near shore. Additionally, the model output for T

_{p}approximates the measured data better than values of H

_{s}.

## 3. Results and Discussion

#### 3.1. Temporal Mean Analysis

_{s}(Figure 5) shows similar behaviour along all of the SSBS, with values approximately $1.6$ $\mathrm{m}$ over the continental shelf and reaching up $2.5$ $\mathrm{m}$ in the oceanic region.

_{s}surface shows a discontinuity on the Santos Basin, with a gap within 1.5$\mathrm{m}$ to 1.7$\mathrm{m}$, which begins at Farol Island (42° W, 23° S). This occurs because the island retains a part of the waves that propagate to the southwest, contributing to a decrease of H

_{s}in the Santos Basin.

_{s}of $1.3$ $\mathrm{m}$ near shore. Florianópolis (48.47° W, 27.70° S), a few kilometres to the north, has mean values lower than Laguna (approximately $1.1$ $\mathrm{m}$).

_{s}on the SSBS. The values are lower than $0.4$ $\mathrm{m}$, due to the extremely long continental shelf. In the middle part of the Santos Basin, near the São Paulo State, the Ilhabela island (45.21° W, 24° S) has the highest mean H

_{s}of approximately $1.2$ $\mathrm{m}$. This value likely stems from the projection of Ilhabela towards the ocean.

_{s}of all of the studied coastlines (up to $1.6$ $\mathrm{m}$), which is also due to its projection towards the ocean.

_{m}surface (Figure 6) shows that the main direction of propagation of the waves is 235° (waves going to southwest), with a deflection eastward in the direction of the ocean (180°) and another deflection to the northwest (315°), perpendicular to the shoreline. This latter deflection appears to be due to the refraction of the waves.

_{s}surface. The waves arrive at Farol Island with a mean D

_{m}of 230° and are blocked by the island, thereby reducing the H

_{s}of the waves that arrive at the Santos Basin.

_{m}(Figure 7) shows waves with periods between 8 s 9 $\mathrm{s}$ on the south and southeastern regions, respectively. These values are practically constant for the entire SSBS, except near the coastline, where it is possible to observe regions where the waves begin to be affected by the bottom. In these regions, the T

_{m}lowers to 5 $\mathrm{s}$, and wave height and length decrease.

_{w}field (Figure 8) exhibits the same behaviour as H

_{s}because the wave energy is proportional to the square of the amplitude and the period [1]. The mean P

_{w}in this oceanic region is approximately 22 $\mathrm{kW}$/$\mathrm{m}$ and reaches up to 30 $\mathrm{kW}$/$\mathrm{m}$ in the southern part of the domain. These elevated mean values in the southern region, for both P

_{w}and H

_{s}, are due to the wind fetch needed for the waves to develop in the Antarctic Ocean [1,17].

#### 3.2. Local Wave Power Analysis

_{w}available for conversion was conducted in the area of study. The selected locations are highlighted in Figure 8. A colormap of each location is presented in Figure 9.

_{s}of $1.2$ $\mathrm{m}$ (Figure 5), a relatively high value compared to other locations along the southern Brazilian coast.

_{w}spatial mean around Laguna (Figure 9a) exhibits an approximately linear behaviour parallel to the shoreline. This characteristic, combined with the bent geometry of the beach, contributes to the elevated mean P

_{w}of this location.

_{w}from the coastline towards the ocean, a substantial increase from $2.0$ $\mathrm{kW}$/$\mathrm{m}$ to $7.0$ $\mathrm{kW}$/$\mathrm{m}$ within the first 4 $\mathrm{km}$, and a subtle rise up to $10.0$ $\mathrm{kW}$/$\mathrm{m}$ within 20 $\mathrm{km}$.

_{w}is its temporal variability. Locations with smaller means and low variability are more efficient for energy conversion than locations with higher means and high variability. Neill and Hashemi [18], for instance, studied Great Britain, which has one of the highest P

_{w}in the world. in Great Britain is more than 60 $\mathrm{kW}$/$\mathrm{m}$, which is unevenly distributed between the winter (up to 110 $\mathrm{kW}$/$\mathrm{m}$ in average) and summer (close to zero).

_{w}as high as Great Britain but, in terms of variability, is far more stable. Temporal variability in Laguna is expressed in terms of standard deviation in Figure 10a. The general characteristics of the standard deviation are rather similar to those of the mean surface.

_{w}of $4.5$ $\mathrm{kW}$/$\mathrm{m}$ on the first 2 $\mathrm{km}$ off the coastline and does not show considerable growth further away. The standard deviation (Figure 10b) of this sector exhibits the same behaviour as the mean power, starting at 3 $\mathrm{kW}$/$\mathrm{m}$ but with slightly less growth advancing towards Santos Basin.

_{w}(Figure 9c) immediately south of the island is 15 $\mathrm{kW}$/$\mathrm{m}$, with an almost insignificant growth up to 17 $\mathrm{kW}$/$\mathrm{m}$, away from the island going south. At the eastern part of the island, the mean P

_{w}is reduced to 12 $\mathrm{kW}$/$\mathrm{m}$ at approximately 1 $\mathrm{km}$ off the coast. This value is constant further away into the sea. The behaviour is similar on the western side.

#### 3.3. Temporal Variability

_{w}with the wind intensity.

_{w}ranged from zero to $21.5$ $\mathrm{kW}$/$\mathrm{m}$ and the wind intensity ranged from $1.1$ $\mathrm{m}$/$\mathrm{s}$ to $8.1$ $\mathrm{m}$/$\mathrm{s}$. Figure 11b illustrates the Morlet local wavelet spectrum for Laguna: the most energetic frequencies are shown in dark red. The black outline encloses the parts of the spectrum that have 95% statistical confidence, while the regions below the dashed line are the regions where the border effects are present in the time series.

_{w}available on Laguna.

_{w}in the interval between zero and $24.6$ $\mathrm{kW}$/$\mathrm{m}$ and wind intensity from $1.0$ $\mathrm{m}$/$\mathrm{s}$ to $7.7$ $\mathrm{m}$/$\mathrm{s}$. The Morlet local wavelet spectrum (Figure 12b) shows a well-defined presence of an annual cycle along the entire time series associated with the largest part of the global spectrum (Figure 12c).

_{w}(Figure 13a), with common values up to $42.0$ $\mathrm{kW}$/$\mathrm{m}$, caused by the intense average winds in this region, between $1.7$ $\mathrm{m}$/$\mathrm{s}$ and $9.0$ $\mathrm{m}$/$\mathrm{s}$. The high intensity of winds appear to be due to the greater influence of the of south Atlantic Anticyclone at middle latitudes over this island [65,66], thereby making Farol Island have the highest values of P

_{w}in the study region.

_{w}time series used on wavelet analysis. Corroborating previous results, all of the values calculated for the time series on Farol Island are substantially higher than those calculated for the other localities.

_{w}on Laguna and Ilhabela are similar, but P

_{w}on Farol Island is approximately 65% higher. The same behaviour was observed in the standard deviation, but with a difference of approximately 90%.

## 4. Conclusions

_{s}, T

_{m}, D

_{m}and P

_{w}on the oceanic region. As the waves approach the coastline, the H

_{s}, T

_{m}and P

_{w}values decrease due to bottom friction, while the D

_{m}undergoes the refraction effect and deflects towards the coast.

_{s}and P

_{w}parameters. The locations are Laguna, with a mean H

_{s}of $1.3$ $\mathrm{m}$ and P

_{w}, with a mean of 10 $\mathrm{kW}$/$\mathrm{m}$; Ilhabela, with mean H

_{s}and P

_{w}of $1.2$ $\mathrm{m}$ and 10 $\mathrm{kW}$/$\mathrm{m}$, respectively; and Farol Island, with means of $1.6$ $\mathrm{m}$ and 15 $\mathrm{kW}$/$\mathrm{m}$ for H

_{s}and P

_{w}, respectively.

_{w}and wind intensity to define the variability cycles for each location. The main variability cycle observed at the three locations is the annual cycle, which was present over the 18 years simulated, with a strong seasonal presence on Ilhabela. The synoptic cycles are, as expected, present at all localities but with little influence on Farol Island.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANP | Agência Nacional do Petróleo |

CAPES | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior |

CESUP-UFRGS | Supercomputing Center of the Federal University of Rio Grande do Sul |

CNPq | Conselho Nacional de Desenvolvimento Científico e Tecnológico |

ECMWF | European Centre for Medium-Range Weather Forecasts |

EDF | Électricité de France |

ENSO | El Niño Southern Oscillation |

FAPERGS | Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul |

LNCC | Laboratório Nacional de Computação Científica |

NOAA | National Oceanic and Atmospheric Administration |

NCEP | National Centers for Environmental Prediction |

NCAR | National Center for Atmospheric Research |

PNBOIA | Programa Nacional de Boias |

PRH | Programa de Recursos Humanos |

RMSE | Root Mean Square Error |

SI | Scatter Index |

SSBS | South-Southeastern Brazilian Shelf |

Tomawac | Telemac-Based Operational Model Addressing Wave Action Computation |

WAM | WAve Model |

## References

- Clément, A.; McCullen, P.; Falcão, A.; Fiorentino, A.; Gardner, F.; Hammarlund, K.; Lemonis, G.; Lewis, T.; Nielsen, K.; Petroncini, S.; et al. Wave energy in Europe: Current status and perspectives. Renew. Sustain. Energy Rev.
**2002**, 6, 405–431. [Google Scholar] [CrossRef] - López, I.; Andreu, J.; Ceballos, S.; Alegría, I.M.D.; Kortabarria, I. Review of wave energy technologies and the necessary power-equipment. Renew. Sustain. Energy Rev.
**2013**, 27, 413–434. [Google Scholar] [CrossRef] - Jama, M.A.; Noura, H.; Wahyudie, A.; Assi, A. Enhancing the performance of heaving wave energy converters using model-free control approach. Renew. Energy
**2015**, 83, 931–941. [Google Scholar] [CrossRef] - Buccino, M.; Stagonas, D.; Vicinanza, D. Development of a composite sea wall wave energy converter system. Renew. Energy
**2015**, 81, 509–522. [Google Scholar] [CrossRef] - Bódai, T.; Srinil, N. Performance analysis and optimization of a box-hull wave energy converter concept. Renew. Energy
**2015**, 81, 551–565. [Google Scholar] [CrossRef] - Gaspar, J.F.; Calvário, M.; Kamarlouei, M.; Guedes Soares, C. Power take-off concept for wave energy converters based on oil-hydraulic transformer units. Renew. Energy
**2016**, 86, 1232–1246. [Google Scholar] [CrossRef] - Rusu, E. Evaluation of the wave energy conversion efficiency in various coastal environments. Energies
**2014**, 7, 4002–4018. [Google Scholar] [CrossRef] - Carballo, R.; Sánchez, M.; Ramos, V.; Fraguela, J.A.; Iglesias, G. Intra-annual wave resource characterization for energy exploitation: A new decision-aid tool. Energy Convers. Manag.
**2015**, 93, 1–8. [Google Scholar] [CrossRef] - Robertson, B.; Hiles, C.; Luczko, E.; Buckham, B. Quantifying wave power and wave energy converter array production potential. Int. J. Mar. Energy
**2016**, 14, 143–160. [Google Scholar] [CrossRef] - Cahill, B.G.; Lewis, T. Wave energy resource characterisation of the Atlantic Marine Energy Test Site. Int. J. Mar. Energy
**2013**, 1, 3–15. [Google Scholar] [CrossRef] - Kim, J.; Kweon, H.M.; Jeong, W.M.; Cho, I.H.; Cho, H.Y. Design of the dual-buoy wave energy converter based on actual wave data of east sea. Int. J. Naval Archit. Ocean Eng.
**2015**, 7, 739–749. [Google Scholar] [CrossRef] - Yaakob, O.; Hashim, F.E.; Mohd Omar, K.; Md Din, A.H.; Koh, K.K. Satellite-based wave data and wave energy resource assessment for South China Sea. Renew. Energy
**2016**, 88, 359–371. [Google Scholar] [CrossRef] - Isaacs, J.D.; Seymour, R.J. The Ocean as a Power Resource. Int. J. Environ. Stud.
**1973**, 4, 201–205. [Google Scholar] [CrossRef] - Krogstad, H.E.; Barstow, S.F. Satellite wave measurements for coastal engineering applications. Coast. Eng.
**1999**, 37, 283–307. [Google Scholar] [CrossRef] - Arinaga, R.A.; Cheung, K.F. Atlas of global wave energy from 10 years of reanalysis and hindcast data. Renew. Energy
**2012**, 39, 49–64. [Google Scholar] [CrossRef] - Reguero, B.G.; Losada, I.J.; Méndez, F.J. A global wave power resource and its seasonal, interannual and long-term variability. Appl. Energy
**2015**, 148, 366–380. [Google Scholar] [CrossRef] - Gunn, K.; Stock-Williams, C. Quantifying the global wave power resource. Renew. Energy
**2012**, 44, 296–304. [Google Scholar] [CrossRef] - Neill, S.P.; Hashemi, M.R. Wave power variability over the northwest European shelf seas. Appl. Energy
**2013**, 106, 31–46. [Google Scholar] [CrossRef] - Stopa, J.E.; Cheung, K.F.; Chen, Y.l. Assessment of wave energy resources in Hawaii. Renew. Energy
**2011**, 36, 554–567. [Google Scholar] [CrossRef] - Iglesias, G.; Carballo, R. Wave resource in El Hierro-an island towards energy self-sufficiency. Renew. Energy
**2011**, 36, 689–698. [Google Scholar] [CrossRef] - Liang, B.; Fan, F.; Yin, Z.; Shi, H.; Lee, D. Numerical modelling of the nearshore wave energy resources of Shandong peninsula, China. Renew. Energy
**2013**, 57, 330–338. [Google Scholar] [CrossRef] - Hiles, C.E.; Buckham, B.J.; Wild, P.; Robertson, B. Wave energy resources near Hot Springs Cove, Canada. Renew. Energy
**2014**, 71, 598–608. [Google Scholar] [CrossRef] - Robertson, B.R.D.; Hiles, C.E.; Buckham, B.J. Characterizing the near shore wave energy resource on the west coast of Vancouver Island, Canada. Renew. Energy
**2014**, 71, 665–678. [Google Scholar] [CrossRef] - Hemer, M.A.; Griffin, D.A. The wave energy resource along Australia’s Southern margin. J. Renew. Sustain. Energy
**2010**, 2, 1–15. [Google Scholar] [CrossRef] - Behrens, S.; Hayward, J.; Hemer, M.; Osman, P. Assessing the wave energy converter potential for Australian coastal regions. Renew. Energy
**2012**, 43, 210–217. [Google Scholar] [CrossRef] - Pianca, C.; Mazzini, P.L.F.; Siegle, E. Brazilian offshore wave climate based on NWW3 reanalysis. Braz. J. Oceanogr.
**2010**, 58, 53–70. [Google Scholar] [CrossRef] - Parise, C.K.; Farina, L. Ocean wave modes in the South Atlantic by a short-scale simulation. Tellus A
**2012**, 64, 1–14. [Google Scholar] [CrossRef] - Losada, I.J.; Reguero, B.G.; Méndez, F.J.; Castanedo, S.; Abascal, A.J.; Mínguez, R. Long-term changes in sea-level components in Latin America and the Caribbean. Glob. Planet. Chang.
**2013**, 104, 34–50. [Google Scholar] [CrossRef] - Guimarães, P.V.; Farina, L.; Toldo, E.E., Jr. Analysis of extreme wave events on the southern coast of Brazil. Nat. Hazards Earth Syst. Sci.
**2014**, 14, 3195–3205. [Google Scholar] [CrossRef] - Guimarães, P.V.; Farina, L.; Toldo, E.E., Jr.; Diaz-Hernandez, G.; Akhmatskaya, E. Numerical simulation of extreme wave runup during storm events in Tramandaí Beach, Rio Grande do Sul, Brazil. Coast. Eng.
**2015**, 95, 171–180. [Google Scholar] [CrossRef] - Cuchiara, D.; Fernandes, E.; Strauch, J.; Winterwerp, J.; Calliari, L. Determination of the wave climate for the southern Brazilian shelf. Cont. Shelf Res.
**2009**, 29, 545–555. [Google Scholar] [CrossRef] - Parente, C.E.; Nogueira, I.C.M.; Martins, R.P.; Ribeiro, E.O. Climatologia de Ondas. In Caracterização Ambiental Regional da Bacia de Campos, Atlântico Sudoeste: Meteorologia e Oceanografia. Habitats, 1st ed.; Martins, R.P., Santiago Grossmann-Matheson, G., Eds.; Elsevier: Rio de Janeiro, Brazil, 2015; Chapter 2; pp. 55–98. [Google Scholar]
- Green, D.A. A colour scheme for the display of astronomical intensity images. Bull. Astron. Soc. India
**2011**, 39, 289–295. [Google Scholar] - Tolman, H.L. A Third-Generation Model for Wind Waves on Slowly Varying, Unsteady, and Inhomogeneous Depths and Currents. J. Phys. Oceanogr.
**1991**, 21, 782–797. [Google Scholar] [CrossRef] - Komen, G.J.; Cavaleri, L.; Donelan, M.; Hasselmann, K.; Hasselmann, S.; Janssen, P.A.E.M. Dynamics and mOdelling of Ocean Waves; Cambridge University Press: Cambridge, UK, 1994; p. 532. [Google Scholar]
- Awk, T. Tomawac User Manual Version 7.2, Technical Report; The TELEMAC-Mascaret Consortium, Version 7.2.3. 2017.
- Tolman, H.L. User Manual and System Documentation of WAVEWATCH III Version 1.15; Technical Report; National Oceanic and Atmospheric Administration: Washington, DC, USA, 1997.
- Tolman, H.L. User Manual and System Documentation of WAVEWATCH III Version 1.18; Technical Report; National Oceanic and Atmospheric Administration: Washington, DC, USA, 1999.
- Tolman, H.L. User Manual and System Documentation of WAVEWATCH III Version 3.14; Technical Report; National Oceanic and Atmospheric Administration: Washington, DC, USA, 2009.
- Kalnay, E.; Kanamitsu, M.; Kistler, R.; Collins, W.; Deaven, D.; Gandin, L.; Iredell, M.; Saha, S.; White, G.; Woollen, J.; et al. The NCEP/NCAR 40-Year Reanalysis Project. Bull. Am. Meteorol. Soc.
**1996**, 77, 437–472. [Google Scholar] [CrossRef] - Janssen, P.A.E.M.; Hansen, B.; Bidlot, J.R. Verification of the ECMWF Wave Forecasting System against Buoy and Altimeter Data. Am. Meteorol. Soc.
**1997**, 12, 763–784. [Google Scholar] [CrossRef] - Lalbeharry, R. Evaluation of the CMC regional wave forecasting system against buoy data. Atmos. Ocean
**2002**, 40, 1–20. [Google Scholar] [CrossRef] - Melo, E.; Hammes, G.R.; Franco, D.; Romeu, M.A.R. Avaliação de desempenho do modelo WW3 em Santa Catarina. In Proceedings of the Anais do III SEMENGO: Seminário e Workshop em Engenharia Oceânica, Rio Grande, Brazil, 2008. [Google Scholar]
- Melo, E.; Romeu, M.; Hammes, G. Condições extremas de agitação marítima ao largo de Rio Grande a partir do modelo WW3. In Proceedings of the Anais do IV Seminário e Workshop em Engenharia Oceânica, Rio Grande, Brazil, 2010; pp. 1–20. [Google Scholar]
- Chawla, A.; Spindler, D.M.; Tolman, H.L. Validation of a thirty year wave hindcast using the Climate Forecast System Reanalysis winds. Ocean Model.
**2013**, 70, 189–206. [Google Scholar] [CrossRef] - Edwards, E.; Cradden, L.; Ingram, D.; Kalogeri, C. Verification within wave resource assessments. Part 1: Statistical analysis. Int. J. Mar. Energy
**2014**, 8, 50–69. [Google Scholar] [CrossRef] - Dos Santos, R.B. Estudo Do Potencial Energético de Ondas Geradas pelo Vento para a Plataforma Continental sul do Brasil. Ph.D. Thesis, Universidade Federal do Rio Grande, Porto Alegre, Brazil, 2009. [Google Scholar]
- Iuppa, C.; Cavallaro, L.; Vicinanza, D.; Foti, E. Investigation of suitable sites for wave energy converters around Sicily (Italy). Ocean Sci.
**2015**, 11, 543–557. [Google Scholar] [CrossRef] - Cavaleri, L. Wave Modeling—Missing the Peaks. Mar. Sci.
**2009**, 39, 2757–2778. [Google Scholar] [CrossRef] - Torrence, C.; Compo, G.C. A Practical Guide to Wavelet Analysis. Bull. Am. Meteorol. Soc.
**1998**, 79, 61–78. [Google Scholar] [CrossRef] - Liu, Y.; Liang, X.S.; Weisberg, R.H. Rectification of the bias in the wavelet power spectrum. J. Atmos. Ocean. Technol.
**2007**, 24, 2093–2102. [Google Scholar] [CrossRef] - Martins, L.R.; Coutinho, P.N. The Brazilian continental margin. Earth-Sci. Rev.
**1981**, 17, 87–107. [Google Scholar] [CrossRef] - Garcia-Herrera, R.; Barriopedro, D.; Hernández, E.; Diaz, H.F.; Garcia, R.R.; Prieto, M.R.; Moyano, R. A Chronology of El Niño Events from Primary Documentary Sources in Northern Peru. J. Clim.
**2008**, 21, 1948–1962. [Google Scholar] [CrossRef] - Xu, K.M.; Wong, T.; Wielicki, B.A.; Parker, L. Statistical Analyses of Satellite Cloud Object Data from CERES. Part IV: Boundary Layer Cloud Objects 1998 El Niño. J. Clim.
**2008**, 21, 6668–6688. [Google Scholar] [CrossRef] - Marques, W.; Fernandes, E.; Monteiro, I.; Möller, O. Numerical modeling of the Patos Lagoon coastal plume, Brazil. Cont. Shelf Res.
**2009**, 29, 556–571. [Google Scholar] [CrossRef] - Marques, W.C.; Fernandes, E.H.L.; Moraes, B.C.; Möller, O.O.; Malcherek, A. Dynamics of the Patos Lagoon coastal plume and its contribution to the deposition pattern of the southern Brazilian inner shelf. J. Geophys. Res. Oceans
**2010**, 115, C10045. [Google Scholar] [CrossRef] - Marques, W.C.; Fernandes, E.H.L.; Moller, O.O. Straining and advection contributions to the mixing process of the Patos Lagoon coastal plume, Brazil. J. Geophys. Res.
**2010**, 115, C06019. [Google Scholar] [CrossRef] - Marques, W.C.; Fernandes, E.H.L.; Rocha, L.A.O. Straining and advection contributions to the mixing process in the Patos Lagoon estuary, Brazil. J. Geophys. Res.
**2011**, 116, C03016. [Google Scholar] [CrossRef] - McPhaden, M.J. Evolution of the 2002/03 El Niño. Bull. Am. Meteorol. Soc.
**2004**, 85, 677–695. [Google Scholar] [CrossRef] - Goddard, L.; Kumar, A.; Hoerling, P.P.; Barnston, A.G. Diagnosis of Anomalous Winter Temperatures over the Eastern United States during the 2002 / 03 El Niño. J. Clim.
**2006**, 19, 5624–5636. [Google Scholar] [CrossRef] - Okumura, Y.M.; Deser, C. Asymmetry in the Duration of El Niño and La Niña. J. Clim.
**2010**, 23, 5826–5843. [Google Scholar] [CrossRef] - Robinson, C.J.; Gómez-Gutiérrez, J.; Markaida, U.; Gilly, W.F. Prolonged decline of jumbo squid (Dosidicus gigas) landings in the Gulf of California is associated with chronically low wind stress and decreased chlorophyll a after El Niño 2009–2010. Fish. Res.
**2015**, 173, 128–138. [Google Scholar] [CrossRef] - Busalacchi, A.J.; Picaut, J. Seasonal Variability from a Model of the Tropical Atlantic Ocean. J. Phys. Oceanogr.
**1983**, 13, 1564–1588. [Google Scholar] [CrossRef] - Gan, M.A.; Rao, V.B. Surface Cyclogenesis over South America. Mon. Weather Rev.
**1991**, 119, 1293–1302. [Google Scholar] [CrossRef] - Venegas, S.A.; Mysak, L.A.; Straub, D.N. Atmosphere-ocean coupled variability in the south atlantic. J. Clim.
**1997**, 10, 2904–2920. [Google Scholar] [CrossRef] - Liebmann, B.; Kiladis, G.N.; Marengo, J.A.; Ambrizzi, T.; Glick, J.D. Submonthly convective variability over South America and the South Atlantic convergence zone. J. Clim.
**1999**, 12, 1877–1891. [Google Scholar] [CrossRef]

1. | |

2. | |

3. | |

4. |

**Figure 1.**Study region on the south-southeastern Brazilian Shelf (

**a**); and location of the wave buoys (

**b**). Colour bars represent the bathymetry varying from 0 to 5000 $\mathrm{m}$ depth. Cube Helix color scheme developed by Green [33]. Satellite images from maps.google.com.

**Figure 2.**Representation of the numerical grid used for the simulations. Satellite images from

`maps.google.com`.

**Figure 3.**H

_{s}time series from Tomawac (black lines) and measured data (coloured dots) from the wave buoy located off the coast of: (

**top**) Rio Grande do Sul; (

**middle**) Santa Catarina; and (

**bottom**) São Paulo (sampled at a three-hourly interval).

**Figure 4.**Scatter plots of the buoy data (horizontal axis) vs. Tomawac’s result (vertical axis): (

**a**) Rio Grande do Sul; (

**b**) Santa Catarina; (

**c**) São Paulo. The colour represents the number of data points in each bin. The solid line shows the linear regression of the data set and the dotted 45° line represents an ideal regression for comparison.

**Figure 8.**Mean value of wave power rate P

_{w}($\mathrm{k}\mathrm{W}/\mathrm{m}$) over 18 years. Selected regions are highlighted using a black rectangle (Laguna), white rectangle (Ilhabela) and red rectangle (Farol Island).

**Figure 9.**Mean value of wave power rate P

_{w}($\mathrm{k}\mathrm{W}/\mathrm{m}$) over the 18 years simulated. The “X” marks the position where the time series were extracted for the wavelet analysis in Section 3.3: (

**a**) Laguna; (

**b**) Ilhabela; and (

**c**) Farol Island.

**Figure 10.**Standard deviation of wave power rate P

_{w}($\mathrm{k}\mathrm{W}/\mathrm{m}$) over the 18 years simulated. The “X” marks the position where the time series were extracted for the wavelet analysis in Section 3.3: (

**a**) Laguna; (

**b**) Ilhabela; and (

**c**) Farol Island.

**Figure 11.**(

**a**) Time series of wind intensity (blue) and P

_{w}(green) used for the cross-wavelet analysis. (

**b**) Local Morlet wavelet power spectrum. Thick contour lines enclose regions of greater than 95% confidence for a red noise process with a lag 1 coefficient of 0.7. Cross-hatched regions indicate the cone of influence where edge effects become important. (

**c**) Global Morlet power spectrum of the time series and the dotted line indicate the 95% confidence level. (

**d**) Mexican Hat local wavelet power spectrum. Thick contour lines enclose regions of greater than 95% confidence for a red noise process with a lag 1 coefficient of 0.1. Cross-hatched regions indicate the cone of influence where edge effects become important and. (

**e**) Global Mexican Hat power spectrum of the time series and the dotted line indicate the 95% confidence level on the coastal zone of Laguna. Cube Helix color scheme developed by Green [33].

**Figure 12.**(

**a**) Time series of wind intensity (blue) and P

_{w}(green) used for the cross-wavelet analysis. (

**b**) Local Morlet wavelet power spectrum. Thick contour lines enclose regions of greater than 95% confidence for a red noise process with a lag 1 coefficient of 0.7. Cross-hatched regions indicate the cone of influence where edge effects become important. (

**c**) Global Morlet power spectrum of the time series and the dotted line indicate the 95% confidence level. (

**d**) Mexican Hat local wavelet power spectrum. Thick contour lines enclose regions of greater than 95% confidence for a red noise process with a lag 1 coefficient of 0.1. Cross-hatched regions indicate the cone of influence where edge effects become important and. (

**e**) Global Mexican Hat power spectrum of the time series and the dotted line indicate the 95% confidence level on the coastal zone of Ilhabela. Cube Helix color scheme developed by Green [33].

**Figure 13.**(

**a**) Time series of wind intensity (blue) and P

_{w}(green) used for the cross-wavelet analysis. (

**b**) Local Morlet wavelet power spectrum. Thick contour lines enclose regions of greater than 95% confidence for a red noise process with a lag 1 coefficient of 0.7. Cross-hatched regions indicate the cone of influence where edge effects become important. (

**c**) Global Morlet power spectrum of the time series and the dotted line indicate the 95% confidence level. (

**d**) Mexican Hat local wavelet power spectrum. Thick contour lines enclose regions of greater than 95% confidence for a red noise process with a lag 1 coefficient of 0.1. Cross-hatched regions indicate the cone of influence where edge effects become important. (

**e**) Global Mexican Hat power spectrum of the time series and the dotted line indicates the 95% confidence level on the coastal zone of Farol Island. Cube Helix color scheme developed by Green [33].

Root Mean Square Error | $\mathrm{RMSE}=\sqrt{\frac{\sum {{T}_{i}-{B}_{i}}^{2}}{n}}$ |

Scatter Index | $SI=\frac{\mathrm{RMSE}}{\overline{B}}$ |

Correlation Coefficient | $r=\frac{\sum {T}_{i}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{B}_{i}-n\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\overline{T}\overline{B}}{\sqrt{\sum {T}_{i}^{2}-n\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\overline{T}}^{2}}\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}\sqrt{\sum {B}_{i}^{2}-n\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\overline{B}}^{2}}}$ |

**Table 2.**Statistical parameters calculated using the measured buoy data (B) and the Tomawac output (T).

Parameter | Rio Grande Do Sul | Santa Catarina | São Paulo | ||||
---|---|---|---|---|---|---|---|

B | T | B | T | B | T | ||

H_{s} | Average [$\mathrm{m}$] | 2,06 | 1,80 | 1,94 | 1,77 | 2,01 | 1,81 |

Root Mean Square Error [$\mathrm{m}$] | 0,58 | 0,50 | 0,61 | ||||

Correlation Coefficient | 0,91 | 0,89 | 0,91 | ||||

Scatter Index | 0,28 | 0,26 | 0,30 | ||||

T_{p} | Average [$\mathrm{s}$] | 9,51 | 8,63 | 9,82 | 9,11 | 9,77 | 8,79 |

Root Mean Square Error [$\mathrm{s}$] | 2,07 | 2,00 | 2,10 | ||||

Correlation Coefficient | 0,93 | 0,92 | 0,93 | ||||

Scatter Index | 0,22 | 0,20 | 0,22 |

**Table 3.**Statistical parameters calculated using the time series of each studied point over 18 years.

Laguna | Ilhabela | Farol Island | |
---|---|---|---|

Mean [$\mathrm{kW}/\mathrm{m}$] | 9,08 | 10,01 | 15,93 |

Standard Deviation [$\mathrm{kW}/\mathrm{m}$] | 6,47 | 7,59 | 13,51 |

Maximum [$\mathrm{kW}/\mathrm{m}$] | 79,88 | 112,13 | 140,70 |

Integrated [$\mathrm{MW}/\mathrm{m}$] | 119,36 | 131,66 | 209,50 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Oleinik, P.H.; Kirinus, E.d.P.; Fragassa, C.; Marques, W.C.; Costi, J.
Energetic Potential Assessment of Wind-Driven Waves on the South-Southeastern Brazilian Shelf. *J. Mar. Sci. Eng.* **2019**, *7*, 25.
https://doi.org/10.3390/jmse7020025

**AMA Style**

Oleinik PH, Kirinus EdP, Fragassa C, Marques WC, Costi J.
Energetic Potential Assessment of Wind-Driven Waves on the South-Southeastern Brazilian Shelf. *Journal of Marine Science and Engineering*. 2019; 7(2):25.
https://doi.org/10.3390/jmse7020025

**Chicago/Turabian Style**

Oleinik, Phelype Haron, Eduardo de Paula Kirinus, Cristiano Fragassa, Wiliam Correa Marques, and Juliana Costi.
2019. "Energetic Potential Assessment of Wind-Driven Waves on the South-Southeastern Brazilian Shelf" *Journal of Marine Science and Engineering* 7, no. 2: 25.
https://doi.org/10.3390/jmse7020025