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Mar Pollut Bull. 2013 Dec 15;77(1-2):266-73. doi: 10.1016/j.marpolbul.2013.09.049. Epub 2013 Oct 18.

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

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  • 1Coastal Zone Systems Division, Coastal, Marine and Disaster Prevention Department, National Institute for Land and Infrastructure Management, 3-1-1 Nagase, Yokosuka, Kanagawa 239-0826, Japan; Department of Architecture and Civil Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku, Toyohashi, Aichi 441-8580, Japan. Electronic address:


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 (τ(r)=209 days) and can be described as functions of the ratio of τ(r) 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 τ(r) and the backshore width. Generally, D would depend on hydrodynamical statistics and beach geomorphology as well as the dimensions and density of the items.

Copyright © 2013 Elsevier Ltd. All rights reserved.


Diffusion equation; Linear system analysis; Mark-recapture experiment; Nii-jima Island; Residence time; Unit impulse response

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