Multivariate return periods of sea storms for coastal erosion risk assessment

The erosion of a beach depends on various storm characteristics. Ideally, the risk associated with a storm would be described by a single multivariate return period that is also representative of the erosion risk, i.e. a 100 yr multivariate storm return period would cause a 100 yr erosion return period. Unfortunately, a specific probability level may be associated with numerous combinations of storm characteristics. These combinations, despite having the same multivariate probability, may cause very different erosion outcomes. This paper explores this ambiguity problem in the context of copula based multivariate return periods and using a case study at Durban on the east coast of South Africa. Simulations were used to correlate multivariate return periods of historical events to return periods of estimated storm induced erosion volumes. In addition, the relationship of the most-likely design event (Salvadori et al., 2011) to coastal erosion was investigated. It was found that the multivariate return periods for wave height and duration had the highest correlation to erosion return periods. The most-likely design event was found to be an inadequate design method in its current form. We explore the inclusion of conditions based on the physical realizability of wave events and the use of multivariate linear regression to relate storm parameters to erosion computed from a process based model. Establishing a link between storm statistics and erosion consequences can resolve the ambiguity between multivariate storm return periods and associated erosion return periods.