Applying copula to joint probability methods: a comparison of extreme sea-level estimation methods

Accurate evaluation of sea-level return levels is crucial for coastal planning. Two ubiquitous methods are the generalised Pareto distribution (GPD), favoured for its ease of access and cheap computational cost, and the skew surge joint probability method (SSJPM), which models deterministic tides and stochastic surges separately but does not consider tide–surge interaction. We propose a modification to the SSJPM, called the copula joint probability method (CJPM), where a copula is used to model the joint distribution of skew surges and peak tides, to account for correlation between tidal high water and skew surge. We compare the performance of the GPD, SSJPM and CJPM in estimating the 30-year return level using only ten years of training data. To validate the models, we require long observational records which can be provided by tide gauges with approximately 100 calendar years of records. For each tide gauge record, ten calendar years are randomly chosen to train the three models while the remaining years are used to validate model predictions. This procedure is repeated multiple times and the mean absolute error (MAE) of each model is estimated at each tide gauge site. The SSJPM and CJPM have lower MAE than the GPD at most tide gauges. The CJPM complements the SSJPM by accounting for correlation between tidal high water and skew surge, providing improved performance at many tide gauges.