A new empirical distribution for the design wave heights under the impact of typhoons

Abstract

In the South China Sea, where storm surges are frequent, accurate calculation of the design wave heights is crucial to the coastal structures and subsequent disaster prevention and relief. The data sampling methods have developed from annual extreme value sampling to over threshold value sampling to use the precious observed wave heights more effectively. However, the problems still exist, resulting in "sharp peak" and "thick tail" for the over threshold data. And traditional design wave heights estimation models cannot fully fit the tail of the data. The strong typhoon also makes the variation patterns of associated wave height factors highly uncertain. To address these issues, this study proposes a Poisson—Gumbel-Pareto distribution model based on the cumulative distribution functions and the combined extreme value distribution theory. The new model not only takes the impacts of typhoon frequency on wave heights into consideration when the wave heights are over the threshold, it can better represent the peak of the data, and also makes the tail of the probability density function curves gradually descend, that is, the tail data can be fully utilized and fitted using this new method. Taking the measured wave and typhoon data from the Naozhou Ocean Observatory in the South China Sea from 1990 to 2016, the design wave heights in the western Guangdong waters have been calculated on the level of once-in-many-years, the design wave heights for 100-year and 200-year are 9.51m and 10.11m respectively. The analysis shows that the new empirical distribution improves the previous extreme value models' disadvantages, with reasonable and stable projections in the high return periods, which is especially favorable when dealing with extreme sea conditions.