## Main Article Content

## Abstract

The extreme significant wave heights and the corresponding mean wave periods were predicted for return periods of 12, 25, 50, 100 and 200 years for 38 different locations in the territorial and offshore locations of countries surrounding the Arabian Gulf. The input wave data for the study is hindcast waves obtained using a WAM model for a total period of 12 years, (1993 to 2004). The peak over threshold method (with 1.0 m as threshold value), is used for selecting the data for the extreme wave analysis. In general, a Weibull distribution is found to fit the data well compared to the Gumbel distribution for all these locations. From the joint probability of wave height and wave period, a simple polynomial relationship (Tmean = C3 (Hs)C4) is used to obtain the relationship between the significant wave height and mean wave period for all the 38 locations. The value of C3 is found to vary from 3.8 to 4.8 and the value of C4 is found to vary from 0.19 to 0.32. The mean wave period was found to be more sensitive to change in locations within the Gulf and it is less sensitive to change in return periods from 12 years to 200 years. The significant wave heights for 100 year return period varied from 3.0 to 4.5 for water depths of 9 to 16 m, whereas in the offshore sites (depths from 30 to 60 m) it varied from 5.0 to 7.0 m. A large number of coastal projects are in progress in the Arabian Gulf and many new projects are being planned in this region for the future. The results of the present study will be highly useful for optimal design of the ocean structures for these projects.

## Keywords

## Article Details

*How to Cite*

*The Journal of Engineering Research [TJER]*,

*6*(1), 21–36. https://doi.org/10.24200/tjer.vol6iss1pp21-36

* * References

- Al-Salem, K., Rakha, K., Sulisz, W. and Al-Nassar, W., 2005, "Verification of a WAM Model for the Arabian Gulf", Arabian Coast Conf., Dubai. UAE.
- Al-Yamani, F.Y., Bishop, J., Ramadhan, E., Al-Husaini, M. and A. Al-Ghadban, 2004, " Oceanographic Atlas of Kuwait's Waters," Kuwait Institute for Scientific Research, Kuwait. p. 203.
- Caires, S. and Sterl, A., 2005, "100-Year Return Value Estimates for Ocean Wind Speed and Significant Wave Height from the ERA-40 Data", J. of Climate, Vol. 18, pp. 1032-1048.
- Cardone, V.J., Pierson, W.J. and Ward, E.G., 1976, "Hindcasting the Directional Spectra of Hurricane Generated Waves", J. of Petrol. Tech., Vol. 28, pp. 385-394.
- Coles, S., 2001, “An Introduction to Statistical Modeling of Extreme Values”, Springer-Verlag, p. 208.
- Denis, M. St., 1969, "On Wind Generated Waves", In topics in Ocean Engineering, ed. C.L. Bretschneider, Gulf Publishing Co., Texas, Vol. I, pp. 37-41.
- Denis, M. St., 1973, "Some Cautions on the Employment of the Spectral Technique to Describe Waves of the Sea and the Response Thereto of Oceanic Systems", Proc. Offshore Technology Conference, Houston, Paper No. OTC 1819, pp. 827-837.
- El-Gindy, A. and Hegazi, M., 1996, “Atlas on Hydrographic Conditions in the Arabian Gulf and the Upper Layer of the Gulf of Oman”, University of Qatar, p. 170.
- Elshorbagy, W., Azam, M.H. and Taguchi, K., 2006, "Hydrodynamic Characterization and Modeling of the Arabian Gulf", J. of Waterway, Port, Coastal and Ocean Engineering, ASCE, Vol. 132(1), pp. 47-56.
- Emery, K.O., 1956, "Sediments and Water of the Persian Gulf", Bull. Amer. Ass. Petrol. Geol., Vol. 40(10), pp. 2354-2383.
- Ferreira, J.A. and Guedes Soares, C., 1998, "An Application of the Peaks Over Threshold Method to Predict Extremes of Significant Wave Height", J. Offshore Mech. Arct. Eng., Vol.120, pp. 165-176.
- Goda, Y., Hawkes, P., Mansard, E., Martin, M.J., Mathiesen, E., Peltier, E., Thompson, E. and Van Vledder, G., 1993, "Intercomparison of Extremal Wave Analysis Methods Using Numerically Simulated Data", Proc. 2nd Int. Symp. On Ocean Wave Measurement and Analysis, ASCE, New Orleans, pp. 963-977.
- Goda, Y., 1992, "Uncertainty of Design Parameters from Viewpoint of Extreme Statistics", J. of Offshore Mechanics and Arctic Engineering., ASME, Vol. 114, pp. 76-82.
- Gringorten, I.I., 1963, "A Plotting Rule for Extreme Probability Paper", J. of Geophys. Res., Vol. 68, pp. 813-814.
- Gumbel, E.J., 1958, “Statistics of Extremes”, Columbia University Press, New York.
- Jahns, H.O. and Wheeler, J.D., 1973, "Long-Term Wave Probabilities Based on Hindcasting of Severe Storms", J. of Petrol. Tech., Vol.25, pp. 473-486.
- Kamphuis, J.W., 2000, "Introduction to Coastal Engineering and Management," Advanced Series on Ocean Engineering, Vol. 16, World Scientific, Singapore, Chapter. 4. Long term Wave Analysis. pp. 81-102.
- Kimball, B.F., 1960, "On the Choice of Plotting Positions on Probability Paper", J. of Amer. Stat. Assn., Vol. 55, pp. 546-560.
- Leadbetter, M.R., 1991, "On a Basis for “Peak Over Threshold" Modeling", Stat. Prob. Lett., Vol. 12, pp. 357-362.
- Mathiesen, M., Hawkes, P., Martin, M.J., Thompson, E., Goda, Y., Mansard, E., Peltier, E. and Van Vledder, G., 1994, "Recommended Practice for Extreme Wave Analysis", J. Hydraulic Research., IAHR, Vol. 32, pp. 803-814.
- Neelamani, S., Al-Salem, K. and Rakha, K., 2006, "Extreme Waves for Kuwaiti Territorial Waters", Communicated to Ocean Engineering, Pergaman Press, UK.
- Nolte, K.G., 1973, "Statistical Methods for Determining Extreme Sea States", Proc. 2nd International Conference on Port and Ocean Engineering Under Arctic Conditions, Univ. of Iceland, pp. 705-742.
- Petrauskas, C. and Aagaard, P., 1971, "Extrapolation of Historical Storm Data for Estimating Design Wave Height", J. of Soc. Petrol. Eng., Vol. 11, pp. 23-37.
- Purser, B.H. and Seibold, E., 1973, "The Principal Environmental Factors Influencing Holocene Sedimentation and Diagenesis in the Persian Gulf", In: "Persian Gulf", Purser, B.H. (ed), Berlin, pp. 1-9.
- Rakha, K.A., Al-Salem, K. and Neelamani, S., 2007, "Hydrodynamic Atlas for Kuwaiti Territorial Waters", Kuwait Journal of Science and Engineering. Vol. 34 (1A), pp. 143-156
- Sarpkaya, T., de St. M. and Isaacson, Q., 1981, "Mechanics of Wave Forces on Offshore Structures”, Van Nostrand Reinhold Company, New York, USA.
- Simiu, E., Bietry, J. and Filliben, J.J., 1978, "Sampling Errors in Estimation of Extreme Winds," J. of the Structural Division, ASCE 104, pp. 491-501.

#### References

Al-Salem, K., Rakha, K., Sulisz, W. and Al-Nassar, W., 2005, "Verification of a WAM Model for the Arabian Gulf", Arabian Coast Conf., Dubai. UAE.

Al-Yamani, F.Y., Bishop, J., Ramadhan, E., Al-Husaini, M. and A. Al-Ghadban, 2004, " Oceanographic Atlas of Kuwait's Waters," Kuwait Institute for Scientific Research, Kuwait. p. 203.

Caires, S. and Sterl, A., 2005, "100-Year Return Value Estimates for Ocean Wind Speed and Significant Wave Height from the ERA-40 Data", J. of Climate, Vol. 18, pp. 1032-1048.

Cardone, V.J., Pierson, W.J. and Ward, E.G., 1976, "Hindcasting the Directional Spectra of Hurricane Generated Waves", J. of Petrol. Tech., Vol. 28, pp. 385-394.

Coles, S., 2001, “An Introduction to Statistical Modeling of Extreme Values”, Springer-Verlag, p. 208.

Denis, M. St., 1969, "On Wind Generated Waves", In topics in Ocean Engineering, ed. C.L. Bretschneider, Gulf Publishing Co., Texas, Vol. I, pp. 37-41.

Denis, M. St., 1973, "Some Cautions on the Employment of the Spectral Technique to Describe Waves of the Sea and the Response Thereto of Oceanic Systems", Proc. Offshore Technology Conference, Houston, Paper No. OTC 1819, pp. 827-837.

El-Gindy, A. and Hegazi, M., 1996, “Atlas on Hydrographic Conditions in the Arabian Gulf and the Upper Layer of the Gulf of Oman”, University of Qatar, p. 170.

Elshorbagy, W., Azam, M.H. and Taguchi, K., 2006, "Hydrodynamic Characterization and Modeling of the Arabian Gulf", J. of Waterway, Port, Coastal and Ocean Engineering, ASCE, Vol. 132(1), pp. 47-56.

Emery, K.O., 1956, "Sediments and Water of the Persian Gulf", Bull. Amer. Ass. Petrol. Geol., Vol. 40(10), pp. 2354-2383.

Ferreira, J.A. and Guedes Soares, C., 1998, "An Application of the Peaks Over Threshold Method to Predict Extremes of Significant Wave Height", J. Offshore Mech. Arct. Eng., Vol.120, pp. 165-176.

Goda, Y., Hawkes, P., Mansard, E., Martin, M.J., Mathiesen, E., Peltier, E., Thompson, E. and Van Vledder, G., 1993, "Intercomparison of Extremal Wave Analysis Methods Using Numerically Simulated Data", Proc. 2nd Int. Symp. On Ocean Wave Measurement and Analysis, ASCE, New Orleans, pp. 963-977.

Goda, Y., 1992, "Uncertainty of Design Parameters from Viewpoint of Extreme Statistics", J. of Offshore Mechanics and Arctic Engineering., ASME, Vol. 114, pp. 76-82.

Gringorten, I.I., 1963, "A Plotting Rule for Extreme Probability Paper", J. of Geophys. Res., Vol. 68, pp. 813-814.

Gumbel, E.J., 1958, “Statistics of Extremes”, Columbia University Press, New York.

Jahns, H.O. and Wheeler, J.D., 1973, "Long-Term Wave Probabilities Based on Hindcasting of Severe Storms", J. of Petrol. Tech., Vol.25, pp. 473-486.

Kamphuis, J.W., 2000, "Introduction to Coastal Engineering and Management," Advanced Series on Ocean Engineering, Vol. 16, World Scientific, Singapore, Chapter. 4. Long term Wave Analysis. pp. 81-102.

Kimball, B.F., 1960, "On the Choice of Plotting Positions on Probability Paper", J. of Amer. Stat. Assn., Vol. 55, pp. 546-560.

Leadbetter, M.R., 1991, "On a Basis for “Peak Over Threshold" Modeling", Stat. Prob. Lett., Vol. 12, pp. 357-362.

Mathiesen, M., Hawkes, P., Martin, M.J., Thompson, E., Goda, Y., Mansard, E., Peltier, E. and Van Vledder, G., 1994, "Recommended Practice for Extreme Wave Analysis", J. Hydraulic Research., IAHR, Vol. 32, pp. 803-814.

Neelamani, S., Al-Salem, K. and Rakha, K., 2006, "Extreme Waves for Kuwaiti Territorial Waters", Communicated to Ocean Engineering, Pergaman Press, UK.

Nolte, K.G., 1973, "Statistical Methods for Determining Extreme Sea States", Proc. 2nd International Conference on Port and Ocean Engineering Under Arctic Conditions, Univ. of Iceland, pp. 705-742.

Petrauskas, C. and Aagaard, P., 1971, "Extrapolation of Historical Storm Data for Estimating Design Wave Height", J. of Soc. Petrol. Eng., Vol. 11, pp. 23-37.

Purser, B.H. and Seibold, E., 1973, "The Principal Environmental Factors Influencing Holocene Sedimentation and Diagenesis in the Persian Gulf", In: "Persian Gulf", Purser, B.H. (ed), Berlin, pp. 1-9.

Rakha, K.A., Al-Salem, K. and Neelamani, S., 2007, "Hydrodynamic Atlas for Kuwaiti Territorial Waters", Kuwait Journal of Science and Engineering. Vol. 34 (1A), pp. 143-156

Sarpkaya, T., de St. M. and Isaacson, Q., 1981, "Mechanics of Wave Forces on Offshore Structures”, Van Nostrand Reinhold Company, New York, USA.

Simiu, E., Bietry, J. and Filliben, J.J., 1978, "Sampling Errors in Estimation of Extreme Winds," J. of the Structural Division, ASCE 104, pp. 491-501.