Probability and distribution of green water events and pressures

Abstract

This article proposes a method to quantify, first, the probability of occurrence of green water and, second, the expected maximum pressures during green water events using their statistical distribution for ships at forward speed. A large green water data set which represents 1945 hours of continuous sailing on full scale with different sea states, forward speeds and drafts was obtained with model test experiments in a wave–current tank. The data of the experiment are available as open data through https://doi.org/10.4121/21031981. With the large data set obtained, the distribution of the time between green water occurrences is identified as exponential, indicating that when green water occurs is independent of the time since the last occurrence. Two methods were compared to estimate the probability of green water occurrence. One method is based on the probability of water exceeding the deck and one on a ship’s freeboard and the significant wave height, the former being in better agreement with the data, the latter being more practical for designers. The maximum pressures caused by green water are distributed according to the Fréchet distribution, also called extreme value distribution II. With the newly identified distributions, finally, an equation to calculate the probability of a pressure limit being exceeded for a ship in operation is formulated.