Many coasts around the world experience coastal erosion as a result of climate change, lack of sediment supply or human interventions. In the coming decades, coasts will be exposed to increased natural forcing because of climate change and sea level rise, leading to increased risks of coastal flooding and erosion. As sandy coasts are highly dynamic systems, it is difficult to assess the impact of these risks. Long-term coastal evolution is evaluated on large temporal and spatial scales, which introduce uncertainty. Hence, probabilistic estimates are required rather than single, deterministic values. Complex, process-based models have been developed to simulate morphological changes in coastal zones, but these come at large computational expense. As probabilistic approaches require a large number of simulations, it is necessary to reduce computational times as much as possible.

Variability in coastline position is induced by both cross-shore and longshore processes, which occur perpendicular and parallel to the coastline, respectively. Extreme storm events and sea level rise are responsible for the long-term cross-shore coastal dynamics, while gradients in longshore sediment transport act as the main driver for the longshore coastline changes. This study focuses on developing a framework to combine predictions of long-term cross-shore and longshore processes in a probabilistic way. The framework combines probabilistic predictions of cross-shore effects with deterministic estimates of longshore-induced coastline change. Two separate models are studied for the cross-shore and longshore component, namely the Probabilistic Coastline Recession (PCR) model and the ShorelineS model. Both models are computationally efficient due to the use of reduced complexity sediment transport formulations and a simplified representation of the beach profile.

The developed framework is validated by a case study of the IJmuiden coastline, the Netherlands, to assess the effects of the blockage of longshore sediment transport by the breakwaters between 1967 and 2007. Consequently, projections of coastline development are determined for the period of 2023 to 2100, for a range of IPCC sea level rise scenarios. To model storm erosion with the PCR model, a synthetic time series of storm events is simulated by establishing joint probabilities of wave forcing variates. Moreover, the PCR model provides stochastic estimates of coastline recession, enabled by the large number of simulations. Regarding ShorelineS, a representative wave climate based on data of local wave conditions was used to compute the longshore sediment transport.

The ShorelineS simulation over the hindcasted period clearly resulted in accretion on both sides of the breakwaters in the order of 100 to 900 meters, in accordance with field observations. This outcome indicates that limited threats of coastal erosion are currently present. However, when analysing the projections for 2023-2100, the PCR model predicted that a combination of storm impact and sea level rise can definitely lead to coastline recession, with a median retreat of 18 meters and 32 meters for the RCP2.6 and RCP8.5 sea level rise scenario, respectively. Moreover, the PCR model indicated that at some point the coastline erosion might be larger than 100 meters with a probability of 1.5% for RCP2.6 and 4% for RCP8.5. The combined projections confirm the importance of accounting for both cross-shore and longshore impacts on long-term coastline evolution and show that the developed framework is a useful method for this purpose.

For further research it is recommended to study long-term coastline evolution while including interaction between cross-shore and longshore processes, to analyse its contribution to long-term coastline changes. It is also advised to further investigate how to obtain stochastic projections of coastline development induced by longshore processes, as this study only presents the cross-shore component in a probabilistic way. Furthermore, stochastic projections of sea level rise and beach recovery can be studied as well.