A parametric model for barred equilibrium beach profiles: Two-dimensional implementation

Abstract

A method is proposed for estimating approximate 2DH bathymetry including longshore variable shoreline and sand bar systems. The method is based on, but extends, a previous 1DH model of Holman et al. (2014) by assuming that this 1DH equilibrium barred bathymetry can be applied for any offshore location if the corresponding mean shoreline orientation is taken to be the local average over a longshore span that is K times the offshore distance. Thus locations close to the beach are sensitive to shoreline and bar details while more seaward locations are steadily less sensitive.The model was tested against 14 ground truth surveys, collected over two years and under widely ranging environmental condition, spanning a 500 by 1000m region. Models inputs for the shoreline and sand bar positions were extracted from measured bathymetries for these tests (but would be derived from other sources in real applications) while deep-water inputs were found from a single deep-water survey. The model yielded complete 2DH bathymetry maps that were a very good approximation of ground truth. The mean bias and rms error over the full region and data set were 0.27m and 0.49m respectively and proxy bathymetries were visually very similar to ground truth. The largest source of error was occasional cross-shore misplacements of otherwise realistic looking sand bars. Results were only weakly dependent on the value of K when tested over a factor of four and the default value of 1.0 is recommended. Performance statistics using input locations for the shoreline and bar crest that were manually digitized from breaking patterns in rectified optical time exposure images were no worse than bathymetry-based inputs. Hydrodynamic predictions using these bathymetries would be a substantial improvement over those from monotonic or even barred 1DH equilibrium proxy bathymetries.