Reinterpreting the Bruun Rule in the Context of Equilibrium Shoreline Models

Abstract

Long-term (>decades) coastal recession due to sea-level rise (SLR) has been estimated using the Bruun Rule for nearly six decades. Equilibrium-based shoreline models have been shown to skillfully predict short-term wave-driven shoreline change on time scales of hours to decades. Both the Bruun Rule and equilibrium shoreline models rely on the equilibrium beach theory, which states that the beach profile shape equilibrates with its local wave and sea-level conditions. Integrating these two models into a unified framework can improve our understanding and predictive skill of future shoreline behavior. However, given that both models account for wave action, but over different time scales, a critical re-examination of the SLR-driven recession process is needed. We present a novel physical interpretation of the beach response to sea-level rise, identifying two main contributing processes: passive flooding and increased wave-driven erosion efficiency. Using this new concept, we analyze the integration of SLR-driven recession into equilibrium shoreline models and, with an idealized test case, show that the physical mechanisms underpinning the Bruun Rule are explicitly described within our integrated model. Finally, we discuss the possible advantages of integrating SLR-driven recession models within equilibrium-based models with dynamic feedbacks and the broader implications for coupling with hybrid shoreline models.

Effects of stochastic wave forcing on probabilistic equilibrium shoreline response across the 21st century including sea-level rise

“…Long-term shoreline retreat induced by SLR was modelled using the Bruun (1962) Rule. The wave-driven models and the Bruun Rule were run separately and then linearly combined in order to avoid spurious feedback mechanisms between the models (D'Anna et al, 2021b), in line with previous works (Vitousek et al, 2017).…”

“…We estimated tanβ = 0.023 using the beach profile reported in Figure 1c and the depth of closure calculated according to Hallermeier (1978). Although the generalized applicability of the Bruun model has been questioned due to its restricting assumptions (Cooper et al, 2020;Cooper and Pilkey, 2004;Ranasinghe et al, 2012), Truc Vert beach settings are in line with most of Bruun's underlying assumptions (D'Anna et al, 2021b).…”

“…Truc Vert beach is a cross-shore transport dominated, uninterrupted beach with large accommodation space most of the Bruun model assumptions are satisfied. However, alternative rule-based approaches (McCarroll et al, 2021), or dynamically coupled wave-driven and sea-level equilibrium approaches (D'Anna et al, 2021b) could be implemented for applications of this framework to a wider range of sites. In addition, here the Bruun Rule combined linearly with Y09 and SF with no feedbacks between wave-and SLR-driven modelled processes, preventing any interaction between wave forcing and SLR uncertainties.…”

Increase in the Erosion Rate Due to the Impact of Climate Change on Sea Level Rise: Victoria Beach, a Case Study

“…Bruun's model was developed to explain how SLR affects the shoreline retreat in the long-term, not considering other possible factors that influence erosion, such as the variability of waves, the supply of sediment from rivers, or onshore sediment transport due to overwash. Thus, the existence or absence of these factors should be considered when the Bruun Rule is applied to a particular beach [27].…”

“…Nevertheless, for the last 60 years, the Bruun Rule [26] has been the most commonly used method for estimating coastline retreat in the long term, due to SLR. The Bruun Rule is increasingly used in current coastal impact models, whether at a global scale or local scale, often without full consideration of its underlying physics [27]. Bruun (1962Bruun ( , 1988) [26,28] provided a simplistic method, assuming a closed material balance system so that the migrating beach has no net loss of sand volume and there is a uniform sandy shoreline with no outcrops or other obstacles that could cause nonuniform retreat rates [28][29][30].…”