The design wave method is frequently adopted for determining the design values concerning wave-induced response. For most purposes the wave height is taken to be the 100-year height, while a reasonable range is given for the corresponding wave period. In order to predict the ?100-year wave? for a given area, data on the long-term wave conditions are needed, either as measurements or in terms of reliable hindcast data. Subsequently, we will consider hindcast data from the central North Sea. The data are not calibrated against measurements, but for the present study this represents no problem since the extremes obtained by different methods are merely considered relative to each other.
The marginal distribution estimated from all six-hourly hindcast values is shown in Fig. 1. It is seen that the upper tail (h>5m) can be very well fitted by two-parameter Weibull distribution, i.e.
By defining the 100-year value as the value which is expected to be exceeded for d hours (accumulated duration) during 100 years, one has
Fig. 1 Marginal distribution for the significant wave height: hindcast data, Central North Sea(available in full paper)
The duration associated with the 100-year event does not necessarily correspond to only one exceedance. It expresses the expected cumulated duration above the level during a 100-year period. This is in contrast to various ‘severe storm’ consideration where we essentially predict the characteristic largest storm peak during a 100 year period. The duration of the storm peak is most probably comparable to the time of averaging associated with the input data. When predicting extreme individual waves (or load effects) this should be kept in mind, since it is the cumulated duration of exceedances which governs the extremes.
The 100-year values for the significant wave height are frequently also estimated by considering only the most severe storms. The first problem in this approach is the formulation of a proper storm selection criterion. This is crucial if a hindcast is to be carried out only for the selected cases. However, in the present study, continuous hindcast data are available and we can easily identify the most severe storm simply by introducing a certain threshold level. The peak values for the storm exceeding 7 m are given in Table 1. For two years, no storms above this limit occurred and for these years the yearly maxima are give.
The storm consideration may be formulated in two different ways:
Include all storms above the given threshold and fit a probabilistic model to the sample of peak values. The probability level corresponding to the 100-year event is given by where ñh is the expected annual number of storms exceeding the threshold level, h (Formula available in full paper)
Include only the largest storm during specified time periods, e.g. annual maxima. It is reasonable to believe that an extreme value distribution of Type.
Table 1 Peak value for storms exceeding 7 m (available in full paper)