A unifying framework for shoreline migration: 2. Application to wave‐dominated coasts

TLDR

The Bruun rule, commonly used to predict shoreline transgression from sea‑level rise, ignores inland topography and lithology, producing unrealistic predictions over long timescales. This study aims to develop a shoreline Exner equation framework to model transgression on wave‑dominated coasts across decades to millennia. The framework couples nearshore sediment dynamics with inland topography and lithology, yielding analytical solutions that capture interactions between coastal processes and landscape slope. Results show that while short‑term retreat may align with the Bruun rule, long‑term transgression follows inland topography slope, with steep landscapes forming cliff‑backed beaches and gentle slopes forming barrier‑island lagoons, though compositional differences can modify this pattern.

Abstract

The Bruun rule, widely used to predict transgression due to sea level rise on decade to century timescales based on a fixed nearshore profile, neglects the influence of inland topography and substrate lithology, leading to physically unreasonable predictions on longer timescales. We use a new approach, the shoreline Exner equation, to model shoreline transgression on wave‐dominated coasts over timescales of decades to millennia. Our results show that interactions between nearshore processes and inland topography, neglected by Bruun‐style models, drive morphologic evolution which modulates shoreline retreat. Analytical solutions suggest that while short‐term shoreline retreat will sometimes follow the Bruun rule, long‐term transgression will always follow the slope of the inland topography. Moreover, our results show that the slope of the inland landscape, relative to the nearshore slope, exerts a first‐order control on coastal morphology, such that steep coasts tend to form cliff‐backed beaches while gentle coasts tend to form barrier island‐lagoon systems. However compositional variations between the inland landscape and nearshore system can alter this pattern.