## 6 Conclusions  
In this study, a simplified methodology to compute maximum significant wave heights and companion wind velocities associated with given return periods, accounting for seasonality, is presented. Simultaneous data from a buoy in the Gulf of Mexico are used. The approach is developed from projected return levels of significant wave heights based on a time-dependent GEV model and classical regression of the two metocean variables. A time-dependent GEV model for the companion wind velocities is also developed, to assess the adequacy of the method to predict the wind velocity as a function of significant wave height for a given return period. It is found that the time window selected to estimate return period values of metocean variables can have an important impact in the predicted return levels for some seasons. It is concluded that correlation of significant weight height and companion wind velocity can be adequately represented by linear or power equations, which could be easily implemented for design purposes, with different parameters to account for seasonality, but with the same functional form. Results are not very dissimilar with predictions from simplified equations in the literature or guidelines; however, it is found that a single equation with given parameters cannot capture the seasonality effects. It is also found that the uncertainty in the predicted companion wind velocities as a function of significant wave height can be determined in a simplified way by using the root mean squared error from the regression analysis, expressed as a set of proposed equations to determine approximately (but closely)the 95% confidence intervals of future values. These same equations can be used to represent the envelope of the uncertainty estimated from the GEV models for different return periods. It is considered that the proposed approach is a simple but adequate method to determine concurrent metocean hazards associated with given return periods, which could be imposed on a system to estimate the demand for design purposes, while also providing measures of uncertainty. The proposed expressions do not differ substantially to those provided in guidelines; thus, they could be amenable to designers, while also incorporating the seasonality effects in a simpler way as compared to other methods available in the literature. To the authors' knowledge, some of the findings in the present study--like the simplified proposal to include the uncertainty in the correlated metocean variables--are not reported elsewhere. Conceptualization, F.C.-V., A.-D.G.-S. and C.M. ; Formal analysis, F.C.-V., A.-D.G.-S. and C.M. ; Funding acquisition, A.-D.G.-S. and C.M. ; Investigation, F.C.-V., A.-D.G.-S. and C.M. ; Methodology, F.C.-V., A.-D.G.-S and C.M. ; Project administration, C.M. ; Supervision, A.-D.G.-S. and C.M. All authors have read and agreed to the published version of the manuscript. The financial support from the Erasmus Mundus Coastal and Marine Engineering and Management (CoMEM) programme and support from Laboratori d'Enginyeria Martima, Universitat Politecnica de Catalunya and from Universidad de Guanajuato (CIIC 2020 Research Projects) is gratefully acknowledged. We thank two anonymous reviewers for their comments, suggestions and constructive criticism. We also thank guess Editor [PERSON] and the editorial team of _Applied Sciences_ for their help in the editorial process. The authors declare no conflict of interest. Appendix BFigure A4: Regression lines and confidence intervals including (solid and dashed lines, respectively) and excluding (dashed–dotted and dotted lines, respectively) \(T_{-yr}\) values for May; (**a**) and (**b**) for logarithmic space and linear space, respectively. Filled circles represent \(T_{-yr}\) values with embedded perpendicular lines indicating confidence intervals from GEV models.