Magnitude-frequency of sea cliff instabilities

The magnitude-frequency relationship of sea cliff failures in strong, low retreat rate cliffs, was studied using systematic historical inventories carried out in the coasts of Portugal and Morocco, in different geological and geomorphological settings, covering a wide size scale, from small to comparatively large rockslides, topples and rockfalls, at different time and spatial scales. The magnitude-frequency expressed in terms of volume displaced and of horizontal area lost at the cliff top showed good fit by inverse power laws of the type p=a.x(-b), with a values from 0.2 to 0.3, and exponents b close to 1.0, similar to those proposed for rockfall inventories. The proposed power laws address the magnitude-frequency for sea cliff failures, which is an important component of hazard assessment, to be completed with adequate models for space and time hazard components. Maximum local retreat at the cliff top provided acceptable fitting to inverse power laws only for failures wider than 2m, with a=4.0, and exponent b=2.3, which may be useful to assess the cliff retreat hazard for the use of areas located near the cliff top.