The effect of serial correlation in environmental conditions on estimates of extreme events

In offshore engineering, it is common practice to estimate long-term extremes under the assumption that environmental conditions are independent. However, many environmental variables, such as winds and waves, exhibit correlation over several days. In this work, we consider the impact that this has on estimates of return values of metocean variables, environmental contours and long-term extreme responses. It is shown that methods which neglect serial correlation over-estimate the size of extreme events at a given return period. We introduce a new definition of a sub-asymptotic extremal index, and show how this can be used to quantify the effect of neglecting serial correlation. Simple examples are presented to illustrate why neglecting serial correlation leads to positive bias. We show how the size of the bias is related to the average shape of storm events and the shape of the tail of the distribution of storm peak values, with the latter having the dominant effect. Storm peak distributions with longer tails lead to larger biases when serial correlation is neglected. In the examples presented, neglecting serial correlation resulted in relative errors of over 50% in the 25-year extreme response estimates in some cases. The examples presented show that accounting for serial correlation in estimates of environmental contours and long-term extreme responses can reduce over-conservatism and result in more efficient designs.

Automated summary

This study investigates the impact of serial correlation on estimates of environmental extremes in offshore engineering, finding that neglecting serial correlation leads to overestimation of extreme event sizes. A new definition of a sub-asymptotic extremal index is introduced to quantify the effect of neglecting serial correlation, showing that considering serial correlation can reduce over-conservatism. The size of bias in estimates is related to storm event shapes and peak distribution tails, with longer tails leading to larger biases when serial correlation is neglected.