Tomoya Kataoka, Hirofumi Hinata, Shigeru Kato, Analysis of a beach as a 
time-invariant linear input/output system of marine litter, Marine 
Pollution Bulletin, Volume 77, Issues 1–2, 15 December 2013, Pages 
266-273, ISSN 0025-326X, http://dx.doi.org/10.1016/j.marpolbul.2013.09.049.
(http://www.sciencedirect.com/science/article/pii/S0025326X13006000)
Abstract: 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.
Keywords: Nii-jima Island; Linear system analysis; Unit impulse 
response; Residence time; Diffusion equation; Mark-recapture experiment