Analysis of a beach as a time-invariant linear input/output system of marine litter

The exponential decay of the amount of new litter on Wadahama Beach, Nii-jima Island, Japan revealed by 20-month mark-recapture experiments demonstrates a linear response of the beach to the input of target items. Here we show the amplitude and phase characteristics of the beach as a time-invariant linear input/output system and discuss the hydrodynamic and geomorphological factors that would determine the characteristics with the aid of a diffusion equation. The characteristics are fully determined by the residence time of the items (τr = 209 days) and can be described as functions of the ratio of τr to the period of input variability. The decay is reproduced well by the analytical solution of the equation with a constant diffusion coefficient (D), whose order was estimated by τr and the backshore width. Generally, D would depend on hydrodynamical statistics and beach geomorphology as well as the dimensions and density of the items.