Equilibrium responses of cliffed coasts to changes in the rate of sea level rise

Abstract

Basic formulae have long been used to predict the effects of sea-level rise on coastal recession; for instance, the geometric ‘Bruun rule’ (and its modifications) has often been applied to sandy coasts, both low-lying and steep. However, the behavior of rocky coasts, whether strongly or poorly lithified, should be significantly different than that of sandy coasts given that rocky coast evolution depends upon the irreversible breakdown of rock, whereas sandy and depositional systems are controlled by the transport (and related transport gradients) of mobile sediment. Here, we investigate the basis of a modeled relationship which suggests (with a number of caveats) that the equilibrium soft-rock cliff recession rate can be estimated by the square root of the relative change in sea-level rise rate. Although this relationship was derived using the numerical model SCAPE (Soft Cliff And Platform Erosion), which simulates a broad soft-rock cliffed coastal system driven by stochastic environmental forces, here we show that a simplified modeling approach also reproduces the relationship. We then extend this approach to develop a general theoretical framework within which it is possible to consider the potential responses of the different types of cliffed coasts to changes in the rate of sea level rise. Although a wide variety of processes affect different coastal settings, this framework demonstrates how the strength and the nature of feedbacks within cliffed system control their response to sea-level rise. This suggests that cliffed environments controlled by different processes can still respond in similar ways to changes in the rate of sea-level rise. Most rocky coasts would be expected to respond as a damped, or ‘negative feedback’ system between the extremes of a ‘no feedback’ system that is unresponsive to sea-level rise rate and an ‘instant response’ system characterized by a linear response similar to the Bruun rule. This framework suggests that a potential ‘inverse feedback’ case could also exist, in which increased rates of sea-level rise reduce the rate of coastal recession. In almost all cases, it is apparent that cliffed coast response to sea-level rise depends not only upon the total elevation change of sea level, but on the rate of the sea-level rise. These theoretical investigations and the classifications presented provide a framework to understand the behavior of systems affected by a wide array of processes, and provide expectations that can be tested using more complex models of cliffed coast evolution in a variety of environments, whether sandy or rocky, hard or soft.