A parametric model for dry beach equilibrium profiles

Abstract

Predictions of dry beach morphologies are extensively required in coastal research for multiple purposes -e.g., dune erosion forecasting, inundation heights determination and beach fill design optimization. In this paper, we introduce and test a parametric model that describes the equilibrium shape of the dry beach in the cross-shore direction, i.e., an equation for the dry beach equilibrium profile. The model consists of a three-parameter equation formed by two terms: an exponential that defines the foreshore and berm morphology, plus a linear term that defines the slope from the berm to the landward limit as a planar far field behaviour. The three morphological parameters that shape the equation are related to the nearshore wave climate (H-s, and T-p) and the sediment characteristics (d(50)) in a form which is consistent with previous knowledge of dry beach morphodynamics, thus proposing the runup driver (HL)(1/2) and the dimensionless fall velocity 0 as the fundamental variables defining the equation parameters. We tested the predictive capacity of the model against an independent data set from Narrabeen Beach, which, depending on longshore location and the time of year, offers beach modal states ranging from dissipative to reflective. The exponential term of the equation correctly explains the foreshore and berm morphology under mean wave climate, and the linear term predicts the slope of the asymptotic-planar segment, all with good correlation coefficients(similar to 0.95) between modelled cross-shore transects and observations. The proposed model helps in defining the main shapes of subaerial beach profiles over the long term and it may also be useful as a coastal management tool for predicting dry beach morphologies.