On the deviation of extreme sea-cliff instabilities from the power-law frequency-volume distribution: practical implications for coastal management
Résumé
Predicting very large sea cliff instabilities (extremes) are of primary importance for coastal risk management. Numerous works have addressed this problem based on the same paradigm: if events exhibit the same statistical properties across a broad range of sizes, the probability of very large extreme events can be evaluated by extrapolating the frequency-size distribution (traditionally represented by a power law model). We address this issue with an inventory of >8,500 sea cliff failures collated from repeated terrestrial laser scanning (TLS) surveys along a coastal chalk cliff in Normandy (France). The largest recorded event, a fault-bounded compartment of >70,000 m3, stands out as an extreme event. We use our inventory to revisit the techniques used to fit power-law distribution with a statistically robust weighted maximum likelihood estimator, which is much less sensitive to outliers. The estimator assigns a weight between 0 and 1 to observations according to their representativeness and rank order. We show that the low weight assigned to the largest sea-cliff instability is statistically significant (with p-value <1 %). Notwithstanding observation errors through the use of TLS, such statistical departure is discussed regarding two possible explanations: the moderate time resolution of the survey (every 6 months), and the physical mechanisms generating this large event. This issue motivates future work in high resolution coastal cliff monitoring, because the physical explanation might have strong practical implications for risk management, either in terms of frequency prediction of such extreme events or of identification of an informative precursor.