Extrapolation of historical coastal storm wave data with best-fit distribution function

Extreme or design wave heights are often extrapolated from historical storm wave data with an assigned "best-fit" probability distribution function. However, there is no detailed selection criterion on how to select a best-fit distribution from a pool of candidate distributions. This study is to develop this criterion. The 19-year wave data collected off the coast of Sydney in the Tasman Sea is used and analysed to obtain a large sample of peak storm wave heights with the peaks-of-threshold method. With the least-squares method, eight commonly-used candidate distributions, the lognormal, Weibull, FT-I, II and III from the generalised extreme value distribution, and GPD-I, II and III from the generalised Pareto distribution, are all fitted to the storm wave height data to determine the best-fit distribution. An extended least-squares method is also presented to estimate the shape parameter for the three-parameter distributions. It is found that the FT-III and GPD-III with the upper bounded end intend to underestimate extreme wave heights. The observed large storm wave heights are shown to be underestimated by the lognormal, but overestimated by the GPD-I or exponential. Both the FT-I and the Weibull are found to give an equally good fit to the storm wave data. Based on the findings of this study, the general selection criterion is then developed to be unboundedness, goodness of fit, simplicity and confidence level. According to this new criterion, the FT-I distribution of the eight candidates can be uniquely determined to be the best-fit distribution for extrapolation of the historical storm wave data. This general criterion can also be used to select a best-fit distribution for extrapolation of historical wave data collected at the other NSW coastal locations or at any other coasts.