Estimating extreme sea levels using a copula joint probability method

Abstract. Extreme sea levels pose significant risks to coastal communities and infrastructure. Joint probability methods are widely used to estimate return levels of extreme sea levels by combining tidal and non-tidal components, but most implementations assume independence between tide and surge. This assumption is not always valid, and neglecting correlation can affect the estimation of return levels and their associated uncertainties. Here, we introduce a Copula Joint Probability Method (CJPM) that explicitly accounts for non-linear correlation between peak tides and skew surges, generalising the Skew Surge Joint Probability Method (SSJPM). Using long tide gauge records (≥100 years) from 23 locations, we assess how incorporating correlation affects both central estimates and confidence intervals of estimated return levels. We find that accounting for this correlation can shift estimated return levels by up to approximately 10 cm at some locations. Importantly, uncertainty in the peak tide–skew surge correlation can be a statistically significant contributor to the width of confidence intervals, in some cases exceeding the contribution from uncertainty in the extreme skew surge distribution. At other locations, correlation has a negligible effect, and CJPM and SSJPM estimates are indistinguishable. These results demonstrate that explicitly representing correlation and its uncertainty provides a more complete quantification of return levels and their associated confidence intervals, and helps determine whether correlation materially affects return level estimation. The CJPM provides a flexible framework that can be applied across a wide range of settings without requiring assumptions about the strength or cause of any correlation.