When assessing the joint-probability of significant wave height and peak period, (Hs,Tp) measured over years at a given site, it is customary to fit a log-normal distribution to assess Tp dependence on Hs. The parameters of this distribution are then used either to compute N-year return period design curves in order to compute extreme response by means of short-term analysis, or response distributions, by means of response-based analysis.

The main drawback of the Log-Normal distribution to represent the variability of Tp wrt. Hs is that its lower bound is zero, while physics tell us that wave steepness cannot be infinite, hence the lower bound, Tplim(Hs) should be greater than zero. If the distribution is kept unbounded, the resulting statistical fitting tends to predict occurrences of sea-states with (Hs,Tp) pairs having unphysical or unlikely steepness. This is particularly true in the range of 10–15s, where some ship-shaped units mooring systems responses are at their maximum.

Attempts have been made in the past to introduce a lower bound to the log-normal distribution, for instance by Drago et al, [1], by shifting it by a predefined value of limit steepness. By doing so, some points of the original dataset had to be discarded as they were falling below the lower bound. An evolution of their methodology is proposed in this paper, which uses the points of the dataset in a relevant region which will be defined hereafter, and then uses this limit to shift the Log-Normal distribution. The obtained environmental contours are then compared against observed data to check which one fits most accurately the original set of measured (Hs,Tp) pairs.

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