Reinterpreting the Bruun Rule in the Context of Equilibrium Shoreline Models

Maurizio D’Anna,Sean Vitousek,Deborah Idier,Goneri Le Cozannet,Bruno Castelle

doi:10.3390/jmse9090974

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.

Highlights

Sandy beaches are dynamic environments, responding to a variety of complex processes interacting on different temporal and spatial scales [1]
These results show that, in the absence of feedback between the equilibrium-based shoreline models (ESMs) and the sea-level rise (SLR) impact model, the ESM reproduces the short-term shoreline fluctuations and the Bruun model reproduces the long-term SPF and SWR contributions
This suggests that introducing dSPF (PF model) into the ESM, the consequent disequilibrium increase, which reproduces the dSPF and the resulting wave reshaping (dSWR), explains the Bruun model’s results (Figure 8b)

Summary

Introduction

Sandy beaches are dynamic environments, responding to a variety of complex processes interacting on different temporal and spatial scales [1]. As sea-level rise (SLR) is accelerating due to climate change [2], reliable projections of shoreline change on long (decadal to centennial) time scales are critical for coastal managers and decision makers [3,4]. SLR-driven shoreline recession occurs on time scales from decades to centuries as a result of the interaction between short- and long-term processes (e.g., wave action and SLR). Integrating the SLR-driven erosion into more comprehensive shoreline change models is necessary to improve our understanding and the predictability of long-term shoreline evolution in the context of climate change. For the past 60 years, the Bruun [5] model (known as “Bruun Rule”) has been the most widely used method to estimate long-term beach recession due to SLR, and its use in contemporary applications keeps growing (Figure 1).

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Discussion

Conclusion