A new method for calculating return periods of various level values from nonstationary time series data is presented. The keyidea of the method is a new definition of the return period, based on the Mean Number of Upcrossings of the level x (MENU method). The whole procedure is numerically implemented and applied to long-term measured time series of significant wave height. The method is compared with other more classical approaches that take into acount the time dependance for time series of

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... gnificant wave height. Estimates of the extremal index are given and for each method bootstrap confidence intervals are computed. The predictions obtained by means of MENU method are lower than the traditional predictions. This is in accordance with the results of other methods that take also into account the dependence structure of the examined time series. Copyright c 2006 by ASME ary. Recently, more advanced models for the representation of time series of wind and wave parameters have been proposed; see, e.g., [14] [15] [16] [17] [18] [19] . These more sophisticated time series models permit us to significantly improve stochastic predictions of extreme values. According to these, except for the stochastic character of the series, the dependence structure and the seasonality exhibited are appropriately modelled. Then, the theory of periodically correlated stochastic processes can be used for the extreme-value predictions; see, e.g., Middleton and Thompson [20]. Another interesting method is the so-called MENU method, according to which the H S return period for prespecified H S level values is the time period in which the MEan Number of Upcrossings of the level H S becomes equal to unity. The MENU method has been presented for the first time in [21] , where an application with Gaussian synthetic data is presented. A similar approach based on the characteristic function of the Gaussian process is shown in Naess [22] . A full account of MENU method can be found in [23] . In the present work, the MENU method is further developed, exploiting the nonstationary modelling of time series of H S presented in [14] , and the non-Gaussian modelling of the secondorder probability structure presented in [24] , to calculate return periods from nonstationary time series of H S . The results are also compared with results from traditional methods. In general, MENU method gives lower estimates of return values (design values) than the traditional methods do. This is in accordance with the findings of other works that take into account the dependence and seasonality features of the time series [10, 11, 25] . TRADITIONAL METHODS FOR RETURN PERIOD CAL-CULATIONS