Analysis of extreme waves with seasonal variation in the gulf of Mexico using a time-dependent GEV model F. Calderón-Vega a , A.O. Vázquez-Hernández b,n , A.D. García-Soto c a Universidad de Cantabria, Avda. de los Castros s/n, 39005 Santander, Spain b Instituto Mexicano del Petróleo, Deep Waters Explotation Department, Eje Central Lázaro Cárdenas Norte 152, Gustavo A. Madero, 07730 Mexico City, Mexico c Department of Applied Mechanics, Institute of Engineering, National Autonomous University of Mexico, Mexico City, Mexico article info Article history: Received 24 November 2012 Accepted 24 August 2013 Available online 19 September 2013 Keywords: Extreme wave statistics Extreme value distribution Significant wave height Seasonality GEV distribution abstract This paper considers a time-dependent GEV model to assess the extreme value of significant wave. The model incorporates the monthly seasonality of maximum values in a block of time of recorded events. The extreme value distribution parameters are fitted considering the seasonal behavior of the significant wave height using harmonic functions representing annual and semiannual cycles. The model is applied to the records in 10 buoys in the Gulf of Mexico. The obtained results are compared with some of the available results in the literature. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Correct characterization of the maritime climate is crucial for the design and operation of coastal and marine infrastructure. Seasonal variation of extreme values of waves influences the risk of flooding. It also affects the design, construction, installation and operation activities of structures such as breakwaters, ports, and oil rigs. Often the design and operation of the structures requires the estimation of the extreme wave height for specified return periods. The selection and assignment of an appropriate prob- ability distribution based on available statistical data is of para- mount importance for the estimation of the return period values of the wave height. According to the asymptotic theory, the maximum values of random sequences could be adequately modeled by the general- ized extreme value (GEV) distribution, which is a reformulation of the limiting distributions originally developed by Fisher and Tippet, and later systematized by Gumbel (Chakrabarti, 2001). It is important to note that, depending on the employed statistical method, the available records and the sample selection can significantly influence the assessment of the extreme values (Prpiĉ-Orsîc et al., 2007; Martucci et al., 2010). Several statistical models have been proposed to adequately represent the ocean behavior considering site conditions (Isaacson and Mackenzie, 1981; Muir and ElShaarawi, 1986; Prevosto et al., 2000; Stansell, 2005; Tayfun and Fedele, 2007; Jensen et al., 2011; Mazas and Hamm, 2011; Muraleedharan et al., 2012; Solari and Losada, 2012; Soares and Carvalho, 2012). However, only a few studies have focused on the seasonal variation. For example, Mietus (1998) carried out an analysis of the seasonal variation on the surface level wind speed in the Baltic Sea. Jönsson et al. (2002) showed that there is a large seasonal variation in maximum monthly wave heights in the Baltic Sea. Méndez et al. (2008) presented a statistical model to characterize the long-term extreme value distribution of significant wave height, conditioned to the duration of the storm and accounting for seasonality; they basically used a time-dependent version of the peak over thresh- old (POT) approach to build a model that considers the annual and semiannual cycles parameterized in terms of harmonic functions. Mackay et al. (2010) showed that estimates of extreme wave conditions from stationary models have a lower bias and variance than those from discrete seasonal models. They also showed that the estimations from discrete seasonal models tend to be highly biased. Räämet and Soomere (2010) estimated the seasonal varia- tion in wave climate in the Baltic Sea using a high-resolution version of a wave model. There are some studies for extreme wave heights in the Gulf of Mexico; most of them do not consider the seasonal variation. Although Jonathan and Ewans (2011) modeled the seasonality of extreme waves in the Gulf of Mexico using a non-homogeneous Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/oceaneng Ocean Engineering 0029-8018/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.oceaneng.2013.08.007 n Corresponding author. Tel.: þ52 55 9175 8228; fax: þ52 55 9175 8258. E-mail addresses: ovazquez@imp.mx, ovazquezmx@yahoo.com (A.O. Vázquez-Hernández). Ocean Engineering 73 (2013) 68–82