A mass conservation model to study the evolution of coastal soft cliffs driven by sea level rise over multi-century timescales

Soft cliffed coasts are particularly vulnerable to erosion and their retreat depends on environmental, geological and geomechanical factors. In this work, we use a mathematical modelling approach to understand effects of future global sea level rise on these coasts over multiple centuries. We develop a simple mass conservation model, equating mate rial eroded from a cliff to the sediment required for foreshore adaptation to sea level rise. The model considers geological differences between cliff and beach sediment, variable and uncertain rates of sea level rise, and the complex inland topography a cliff may erode through. The model is solved analytically, and long-term behaviours discussed, including conditions for an equilibrium recession rate or a change in coastal typology. Methods for obtaining estimates of model parameters are detailed and an application of the depth of closure concept to multi-century timescales proposed. The model is applied to the Holderness coast, United Kingdom. It predicts an acceleration of cliff retreat due to rising sea levels over the next centuries, though local topographical features may cause temporary deceleration. No long-term equilibrium behaviour is identified. The study also estimates that vulnerable locations along this coast will experience a change in coastal typology within the next few hundred years. These findings highlight the importance of inland topography in determining an eroding cliffed coast’s resilience to sea level rise. We propose that the relative sea level rise corresponding to typology change should be used as an indicator of cliff resilience to sea level rise, instead of current cliff height.