Abstract. This paper presents a methodology that uses site-specific topographic and cosmogenic 10Be data to perform multi-objective model optimisation of a coupled coastal evolution and cosmogenic radionuclide production model. Optimal parameter estimation of the coupled model minimises discrepancies between model simulations and measured data to reveal the most likely history of rock coast development. This new capability allows a time series of cliff retreat rates to be quantified for rock coast sites over millennial timescales. Without such methods, long-term cliff retreat cannot be understood well, as historical records only cover the past ∼150 years. This is the first study that has (1) applied a process-based coastal evolution model to quantify long-term cliff retreat rates for real rock coast sites and (2) coupled cosmogenic radionuclide analysis with a process-based model. The Dakota optimisation software toolkit is used as an interface between the coupled coastal evolution and cosmogenic radionuclide production model and optimisation libraries. This framework enables future applications of datasets associated with a range of rock coast settings to be explored. Process-based coastal evolution models simplify erosional processes and, as a result, often have equifinality properties, for example that similar topography develops via different evolutionary trajectories. Our results show that coupling modelled topography with modelled 10Be concentrations can reduce equifinality in model outputs. Furthermore, our results reveal that multi-objective optimisation is essential in limiting model equifinality caused by parameter correlation to constrain best-fit model results for real-world sites. Results from two UK sites indicate that the rates of cliff retreat over millennial timescales are primarily driven by the rates of relative sea level rise. These findings provide strong motivation for further studies that investigate the effect of past and future relative sea level rise on cliff retreat at other rock coast sites globally.

Coastal response to anthropogenic climate change is of central importance to the infrastructure and inhabitants in these areas. Despite being globally ubiquitous, the stability of rock coasts has been largely neglected, and the expected acceleration of cliff erosion following sea-level rise has not been tested with empirical data, until now. We have optimised a coastal evolution model to topographic and cosmogenic radionuclide data to quantify cliff retreat rates for the past 8000 years and forecast rates for the next century. Here we show that rates of cliff retreat will increase by up to an order of magnitude by 2100 according to current predictions of sea-level rise: an increase much greater than previously predicted. This study challenges conventional coastal management practices by revealing that even historically stable rock coasts are highly sensitive to sea-level rise and should be included in future planning for global climate change response.

Abstract. This paper presents a methodology that uses site-specific topographic and cosmogenic 10Be data to perform multi-objective model optimisation of a coupled coastal evolution and cosmogenic radionuclide production model. Optimal parameter estimation of the coupled model minimises discrepancies between model simulations and measured data to reveal the most likely history of rock coast development. This new capability allows for a time-series of cliff retreat rates to be quantified for rock coast sites over millennial timescales. This is the first study that has 1) applied a process-based coastal evolution model to quantify long-term cliff retreat rates for real, rock coast sites, and 2) coupled cosmogenic radionuclide analysis with a process-based model. The Dakota optimisation software toolkit is used as an interface between the coupled coastal evolution and cosmogenic radionuclide production model and optimisation libraries. This framework enables future applications of datasets associated with a range of rock coast settings to be explored. Process-based coastal evolution models simplify erosional processes and, as a result, often have equifinality properties, for example, that similar topography develops via different evolutionary trajectories. Our results show that coupling modelled topography with modelled 10Be concentrations can reduce equifinality in model outputs. Furthermore, our results reveal that multi-objective optimisation is essential in limiting model equifinality caused by parameter correlation to constrain best-fit model results for real-world sites. Results from two UK sites indicate that the rates of cliff retreat over millennial timescales are primarily driven by the rates of relative sea level rise. These findings provide strong motivation for further studies that investigate the effect of past and future relative sea level rise on cliff retreat at other rock coast sites globally.

Rocky coast cliff retreat presents a hazard to coastal communities and infrastructure that is potentially amplified under rising sea level conditions, among other factors. Unfortunately, constraints on retreat rates are typically limited to those derived from imagery and maps spanning the last ∼100 years. Here, we use a newly developed coupled model of shore platform profile evolution and cosmogenic radionuclide production that considers the influence of relative sea level (RSL) rise, weathering, material resistance, and wave height decay to model cliff retreat over millennial timescales and its potential drivers in Del Mar, California. We demonstrate the ability to use topographic and bathymetric measurements from a narrow shore platform along with a limited data set of nine cosmogenic 10Be concentrations extending ∼125 m from the cliff base to obtain modeled cliff retreat rates that steadily range from 5.0 to 12.5 cm yr−1 over the last two millennia until 100 years before present. These rates are consistent with modern retreat rates of about 2–19 cm yr−1 here. RSL rise in Southern California remained relatively constant during the late Holocene, potentially explaining the relatively stable modeled cliff retreat rate over this time. We also explore the relative influence of weathering, material resistance, and wave erosion efficacy and find that both weathering and wave‐driven erosion are necessary to replicate the measured data at this location, with the latter exerting a stronger control on model acceptance, suggesting that waves may provide a possible mechanism by which RSL rise may influence coastal cliff erosion in southern California.

Abstract. The white chalk cliffs on the south coast of England are one of the most iconic coastlines in the world. Rock coasts located in a weak lithology, such as chalk, are likely to be most vulnerable to climate change-triggered accelerations in cliff retreat rates. In order to make future forecasts of cliff retreat rates as a response to climate change, we need to look beyond individual erosion events to quantify the long-term trends in cliff retreat rates. Exposure dating of shore platforms using cosmogenic radionuclide analysis and numerical modelling allows us to study past cliff retreat rate across the late-Holocene for these chalk coastlines. Here, we conduct a multi-objective optimisation of a coastal evolution model to both high-precision topographic data and 10Be concentrations at four chalk rock coast sites to reveal a link between cliff retreat rates and the rate of sea level rise. Furthermore, our results strengthen evidence for a recent acceleration in cliff retreat rates at the chalk cliffs on the south coast of England. Our optimised model results suggest that the relatively rapid historical cliff retreat rates observed at these sites spanning the last 150 years last occurred between 5300 and 6800 years ago when the rate of relative sea level rise was a factor of 5–9 times more rapid than during the recent observable record. However, results for these chalk sites also indicate that current process-based models of rock coast development are overlooking key processes that were not previously identified at sandstone rock coast sites. Interpretation of results suggest that beaches and heterogenous lithology play an important but poorly understood role in the long-term evolution of these chalk rock coast sites. Despite these limitations, our results reveal significant differences in intertidal weathering rates between sandstone and chalk rock coast sites, which helps to inform the long-standing debate of ‘wave versus weathering’ as the primary control on shore platform development. At the sandstone sites, subaerial weathering has been negligible during the Holocene. In contrast, for the chalk sites, intertidal weathering plays an active role in the long-term development of the shore platform and cliff system. Overall, our results demonstrate how an abstract, process-based model, when optimised with a rigorous optimisation routine, can not only capture long-term trends in transient cliff retreat rates but also distinguish key erosion processes active in millennial-scale rock coast evolution at real-world sites with contrasting rock types.

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Be concentration (atoms g -1 ) 10 Be concentration error (± atoms g -1 ) CB0228.2 4482 CB03 46.

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