Statistical modelling of extreme ocean climate with incorporation of storm clustering

Knowledge of extreme ocean climate is essential for the accurate assessment of coastal hazards to facilitate risk informed decision making in coastal planning and management. Clustered storm events, where two or more storms occur within a relatively short space of time, may induce disproportionately large coastal erosion compared to non-clustered storm events. Therefore this study aims to develop a statistical approach to modelling the frequency and intensity of storm events on the eastern and southern coast of Australia, with a focus on examining storm clustering. This paper presents the preliminary analysis of the recently developed methods and results when they are applied to a study site on the central coast of New South Wales, Australia. This study is a key component of the Bushfire and Natural Hazards CRC Project Resilience to clustered disaster events on the coast storm surge that aims to develop a new method to quantify the impact of coincident and clustered disaster events on the coast.
Extreme storm events at a given site can be described using multivariate summary statistics, including the events maximum significant wave height (Hsig), median wave period, median wave direction, duration, peak storm surge, and time of occurrence. This requires a definition of individual storm events, and so the current methodology firstly involves the extraction of independent storm events from a 30-year timeseries of observations. Events are initially defined using a peaks-over-threshold approach based on the significant wave height. The value of 95% exceedance quantiles (2.93 m) is adopted. Subsequently, these events are manually checked against sea-level pressure data to examine if closely spaced events are generated by the same meteorological system, and if so the events are combined. This means that the final event set is more likely to consist of statistically independent storm events.
Various statistical techniques are applied to model the magnitude and frequency of the extracted storm events. A number of variations on the non-homogenous Poisson process model are developed to estimate the event occurrence rate, duration and spacing. The models account for the sub-annual variations in the occurrence rate, temporal dependency between successive events, and the finite duration of events. The results indicate that in the current dataset, closely spaced events are more temporally spread out than would be expected if the event timings were independent, which we term anti-clustering. A particular marginal distribution is fitted to each variable, i.e. a Generalised Pareto (GP) distribution for Hsig, and Pearson type 3 (PE3) distributions for duration and tidal residual. Empirical marginal distributions are employed for wave period and direction. The joint cumulative distribution function of all storm magnitude statistics is modelled by constructing dependency structure using Copula functions. Two methods are tested: a t-copula and a combination of a Gumbel and Gaussian copulas. Comparison of modelled and observed scatterplots shows similar pattern, and the difference of using the two methods is marginal. The goodness-of-fit tests such as Komologorov-Smirnov (K-S) tests, Chi-square tests and AIC and BIC are used to quantitatively evaluate the fitting qualities and to assess model parsimony, along with graphical visualisations e.g. QQ plots.
Based on this approach, a set of long-term synthetic time-series of storm events (106) is generated using the event magnitude and timing suggested by the optimised models. These long-term synthetic events can be used to derive exceedance probabilities and to construct designed storm events to be applied to the beach erosion modelling.

极端海洋气候知识对于准确评估海岸灾害至关重要，可助力海岸规划与管理中基于风险的决策制定。集群风暴事件（clustered storm events）指在较短时间内发生两次或以上风暴的事件，与非集群风暴事件相比，其可能引发远超比例的海岸侵蚀。因此，本研究旨在开发一种统计方法，用于模拟澳大利亚东海岸和南海岸风暴事件的频率与强度，重点考察风暴集群现象（storm clustering）。本文介绍了近期开发的方法及其应用于澳大利亚新南威尔士州中海岸研究站点时的初步分析结果。本研究是澳大利亚丛林火灾与自然灾害合作研究中心（Bushfire and Natural Hazards CRC）“海岸集群灾害韧性——风暴潮”项目的核心组成部分，该项目旨在开发新方法以量化海岸重合及集群灾害事件的影响。

特定站点的极端风暴事件可通过多变量汇总统计描述，包括事件的最大有效波高（Hsig）、中位波周期、中位波方向、持续时间、峰值风暴潮及发生时间。这需要对单个风暴事件进行定义，因此当前方法首先从30年观测时间序列中提取独立风暴事件。事件最初基于有效波高采用阈值超额法（peaks-over-threshold approach）定义，采用95%超越分位数（2.93米）的值。随后，这些事件通过海平面气压数据进行人工核查，以确定紧密间隔的事件是否由同一气象系统产生，若如此则将其合并。这意味着最终事件集更可能由统计独立的风暴事件组成。

本研究应用多种统计技术对提取的风暴事件的强度与频率进行建模。针对非齐次泊松过程模型（non-homogenous Poisson process model）开发了若干变体，用于估计事件发生率、持续时间及间隔。这些模型考虑了发生率的年内变化、连续事件间的时间依赖性及事件的有限持续时间。结果表明，在当前数据集中，紧密间隔事件的时间分布比事件时序独立时的预期更为分散，我们称之为反集群现象（anti-clustering）。针对每个变量拟合特定的边缘分布：例如，Hsig采用广义帕累托（Generalised Pareto, GP）分布，持续时间和潮汐残差采用皮尔逊3型（Pearson type3, PE3）分布；波周期和方向则采用经验边缘分布。所有风暴强度统计量的联合累积分布函数通过Copula函数（Copula functions）构建依赖结构进行建模。本研究测试了两种方法：t-Copula及Gumbel与高斯Copula的组合。模型输出与观测值的散点图对比显示出相似模式，且两种方法的差异微小。拟合优度检验（如柯尔莫哥洛夫-斯米尔诺夫检验（Komologorov-Smirnov, K-S）、卡方检验、AIC及BIC）与图形可视化（如QQ图）共同用于定量评估拟合质量及模型简约性。

基于该方法，利用优化模型给出的事件强度及时序，生成了一组长期合成风暴事件时间序列（10⁶个事件）。这些长期合成事件可用于推导超越概率，并构建设计风暴事件以应用于海滩侵蚀建模。