Marine Pollution Bulletin 101 (2015) 539–548

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Marine Pollution Bulletinjournal homepage: www.elsevier.com/locate/marpolbul

Backwash process of marine macroplastics from a beach by nearshore
currents around a submerged breakwater
Tomoya Kataoka a, Hirofumi Hinata b,⁎, Shigeru Kato caCoastal Zone Systems Division, Coastal, Marine and Disaster Prevention Department, National Institute for Land and Infrastructure Management, 3-1-1 Nagase, Yokosuka, Kanagawa 239-0826,
Japanb
Department of Civil and Environmental Engineering, Faculty of Engineering, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japanc
Department of Architecture and Civil Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku, Toyohashi, Aichi 441-8580, Japana r t i c l e

i n f oArticle history:
Received 31 August 2015
Received in revised form 22 October 2015
Accepted 23 October 2015
Available online 11 November 2015
Keywords:
Marine macroplastics
Residence time
Submerged breakwater
Nearshore current
Mark-recapture experimenta b s t r a c t
A key factor for determining the residence time of macroplastics on a beach is the process by which the plastics
are backwashed offshore (backwash process). Here, we deduced the backwash process of plastic ﬁshing ﬂoats on
Wadahama Beach based on the analysis of two-year mark-recapture experiments as well as nearshore current
structures revealed by sequential images taken by za webcam installed at the edge of a cliff behind the beach.
The analysis results revealed the occurrence of a combination of offshore currents and convergence of alongshore
currents in the surf zone in storm events around a submerged breakwater off the northern part of the beach,where 48% of the backwashed ﬂoats were last found. We conclude that the majority of the ﬂoats on the beachwere transported alongshore and tended to concentrate in the convergence zone, from where they were
backwashed offshore by the nearshore currents generated in the events.
© 2015 Elsevier Ltd. All rights reserved.

1. Introduction
It is well known that the most likely sources for generating small
plastic fragments in the ocean are beaches because plastic debris lying
on a beach quickly undergoes photo-oxidative degradation through exposure to solar ultraviolet radiation and the heat of the sand (Andrady,2011). Also, lead stearate (Pb(C18H35O2)2) used as an additive for plastic
production could leach from the surface of a stranded PVC (polyvinyl
chloride) ﬁshing ﬂoat into the beach with the aid of rainfall (Nakashima
et al., 2012). Kataoka and Hinata (2015) recently demonstrated that
estimating the residence time of macroplastics (N 20 mm diameter;
see Barnes et al., 2009) on a beach allows us to evaluate the amount ofsmall plastic fragments generated on the beach and that of lead stearateleaching into the beach from the macroplastics, by applying a linear system analysis.
Conducting 20-month mark-recapture (MR) experiments using
plastic ﬂoats on Wadahama Beach, Nii-jima Island and considering thebeach as a linear black box describing the input–output behavior of
the ﬂoats, we successfully estimated the average residence time of theﬂoats on the beach as well as the overall responses of the beach toidealized ﬂoat inputs (Kataoka et al., 2013). The ﬂoats stranded on thebeach were eventually backwashed offshore into the coastal sea⁎ Corresponding author at: Department of Civil and Environmental Engineering, Facultyof Engineering, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan.
E-mail address: hinata@cee.ehime-u.ac.jp (H. Hinata).

http://dx.doi.org/10.1016/j.marpolbul.2015.10.060
0025-326X/© 2015 Elsevier Ltd. All rights reserved.

resulting in a residence time of 209 days. By understanding how theﬂoats disappear from the beach (hereinafter, “backwash process”), we
can grasp which factors determine the ﬂoats' residence time on thebeach. This comprehensive understanding will allow us to estimate
the residence time of the ﬂoats on other beaches without conducting
long-term, labor-intensive MR experiments. In our previous study, thebackwash process of the ﬂoats was not fully analyzed except for theestimation of the diffusion coefﬁcient, which determines the offshore
ﬂux of the ﬂoats from the entire beach to the coastal sea.
Several studies have investigated the accumulation of marine debris
on multiple beaches (e.g., Garrity and Levings, 1993; Bowman et al.,
1998; Williams and Tudor, 2001; Barnes et al., 2009; Ryan et al., 2014;
Smith et al., 2014). However, the behavior of plastic debris and its temporal variability on a beach are not well understood. In the present
study, we attempted to clarify the backwash process of the plastic ﬂoats
from Wadahama Beach by analyzing the long-term MR experimentdata, wind and wave statistics and nearshore current structures using
images taken by a webcam system installed at the edge of a cliff behindthe beach.
The purpose of this study is, in other words, to understand the
behavior of backwashed ﬂoats in high wave events. However, tracking
data on the backwashed ﬂoats when they were transported offshore
from the beach could not be directly obtained from our MR experiments. Therefore, we deduced the backwash process based on thealongshore movements of the remnant ﬂoats. First, we investigatedthe behavior of the ﬂoats on the beach based on the MR experiments,

540

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

in which the positions of the ﬂoats were recorded until their disappearance from the beach. Then we compared the behavior with the nearshore current structures visualized by the contrast in color between
turbid beach waters generated in high wave events and clean offshore
waters, and deduced the backwash process of the plastic ﬂoats fromthe beach.
2. Materials and methods(black circle in Fig. 1(a)), the high water level (HWL), mean waterlevel (MWL) and low water level (LWL) are, respectively, 67.9 cm,
18.8 cm and −84.2 cm relative to Tokyo Peil (mean sea level at Tokyo
Bay) (Fig. 1(b)). Approximately 100 m from the shoreline, at a depthof 6 m, there are four submerged breakwaters (SBs) of 150 m (SB1),
100 m (SB2), 250 m (SB3) and 250 m (SB4) in length (Fig. 1(b)). The
crest of the SBs is 35 m wide and 1.5 m below the MWL. SBs play an important role in determining nearshore current structure by breaking
waves above the SB (e.g., Ranasinghe and Turner, 2006).

2.1. Study site
2.2. Target items
Wadahama Beach is located on the west coast of Nii-jima Island, Japan(Fig. 1(a)). The beach is approximately 900 m long and 30–50 m widewith coarse sand having a mean sediment diameter of d50 = 1.43 mm;
a promontory and concrete blocks form the northern and southernboundaries, respectively (Fig. 1(b), (c)). The beach is classiﬁed as intermediate with a beach slope (tan β) ranging from 0.09 (β = 5°) to 0.18 (β =10°) (Wright and Short, 1984). An escarpment with an average angle ofabout 35° connects the beach to the coastal hinterland (Fig. 1(b)). This
steep escarpment blocks the migration of marine debris onto the hinterland except for lower-density debris such as plastic PET bottles, plastic
sheets and plastic bags.
From the analysis of tide levels recorded at the JMA tidal station on
Oshima Island, which is situated about 50 km north of Nii-jima Island

The target items for the MR experiments are three types of plasticﬁshing ﬂoats (Fig. 1(d)) as in our previous study (Kataoka et al.,2013). Dimensions and average weight of the ﬂoats measured in situ
are as follows: Type 1: 13.0 cm × ϕmax 2.4 cm, 38.8 g; Type 2:
13.1 cm × ϕmax 7.8 cm, 116.9 g; and Type 3: 11.0 cm × ϕmax 1.9 cm,
12.8 g. All three types of ﬂoats are distributed on beaches from thenorthernmost to southernmost ends of the Japanese Archipelago.
Thus, in the future, the backwash process of these ﬂoats on Wadahama
Beach can be compared with that on other beaches.
In the present study, we assumed that the behavior of the ﬂoats on
Wadahama Beach was hardly affected by winds. In actuality, we observed almost no wind-induced motion of the ﬂoats on the beachFig. 1. (a) Location of Nii-jima Island, wave observation (black triangles) and tide observation sites (black circles). On the enlarged map of Nii-jima Island, contour lines and gray-white
gradation denote the altitudes of Nii-jima Island. White circles and triangles indicate the location of surface wind observation and webcam sites, respectively. (b) Enlarged map ofWadahama Beach showing the altitudes relative to Tokyo Peil (contour lines and gray-white gradation). Note that the scale in the latitudinal direction is 3.2 times as large as that in
the longitudinal direction. The upper panel of (b) shows the cross-sectional beach topography along the red dash-dotted line in the lower panel. The black boxes in panel (b) denotesubmerged breakwaters (SBs). (c) View of Wadahama Beach from the south in a storm event. (d) Photos of target items.

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

even in the beach surveys during the strong northwesterly winter monsoon conditions. Also, no ﬂoats were found on the coastal hinterland
over the steep escarpment. Thus, we consider that the ﬂoats disappeared from the beach by being backwashed offshore due to nearshore
currents (Fig. 1(c)).
2.3. Mark-recapture (MR) experiments and beach topographic
measurements
The MR experiments were conducted since September 2011 at oneto three-month intervals (Table 1). The average interval was 53 days.
The ﬁrst and second experiments were carried out in the northernmost
100- and 200-m-long areas, respectively (Fig. 1(b)), while the other experiments covered the whole beach. All three types of ﬂoats on thebeach were collected, numbered with a permanent marker and replaced where they were found. The marked number consisted of the experiment number and a sequential number allocated to each type of
ﬂoat (Fig. 1(d)). A thorough search for the ﬂoats was conducted until
no unnumbered target items could be found by repeated observations.
The position of each item was recorded by a handheld global positioning
system (GPS) receiver (GPSMAP® 60CSx, Garmin Ltd.) with a measurement error of about ±3 m.
For all analyses in the present study, we divided the beach into ninetransects measuring 100 m long in the alongshore direction as shownon the left side of Fig. 1(b). In addition, the ﬂoats were classiﬁed into
three states: newly washed ashore (immigrant), backwashed offshore(emigrant), or remaining on the beach surface (remnant) for the interval between the previous and present MR experiments (hereinafter,“experiment period”). In Table 1, the number of remnants includes
re-emerged ﬂoats that were not recovered in the previous surveys but
were found in the present survey. However, the ratio of re-emerged
ﬂoats to remnants is small (10% on average). The abundance of reemergence is added to the cohort population of the previous experiments.
The beach elevation was measured by using a real-time kinematic
GPS system (Trimble® 5800 II, Trimble Navigation Ltd.) with a horizontal and vertical measurement error of about ± 5 mm. The alongshore
and cross-shore distance between adjacent measurement points was
about 10 m and about 5 m, respectively. The raw measured data was interpolated to a grid point with both alongshore and cross-shore spacingof 5 m using a nearest-neighbor algorithm with a spline function(McKinley and Levine, 1998).
2.4. Observation of sea surface wind, waves and nearshore current structure
We analyzed the sea surface wind and wave data respectively observed by the Advanced Scatterometer (ASCAT) and by the GPS buoy(e.g., Kato et al., 2011) established at about 90 km west of Nii-jimaIsland (black triangle in Fig. 1(a)) by the Nationwide Ocean Wave Information Network for Ports and Harbours (NOWPHAS). The sea surface
wind data has been gridded using an optimal interpolation method
developed by Kako et al. (2011). We used the sea surface wind data ata grid point located in front of Wadahama Beach (white circle inFig. 1(a)). The wave runup height on Wadahama Beach was estimatedusing the wave statistics calculated from the data obtained by the GPS
buoy. Details of the estimation of the runup height are described in
the Appendix A.
The webcam system developed by Kataoka et al. (2012) has been
installed at the edge of the cliff behind the beach since December
2014 (white triangle in Fig. 1(a)). The webcam is programmed to operate for 15 min every 1 h from 7:00 to 17:00 (Japan standard time), thus
providing eleven 15-min videos every day. The videos are recorded on
an SDHC card installed in the webcam. From our analysis of the videos,
we understood the qualitative features of nearshore currents visualized
by the contrast in color between turbid beach waters and clear offshore
waters and its temporal evolution.

541

3. Results
3.1. Wave runup height on Wadahama BeachFig. 2 shows the temporal variability of sea surface wind (Fig. 2(a))
and wave runup height (Fig. 2(c)). In October to March (S1), southwesterly winds and waves prevailed when the runup height was greater than
2 m (Fig. 2(b) and (d)). Northwesterly winds intensiﬁed by the East Asian
Monsoon rarely developed longer-period wind waves under the small
fetch length from Honshu Island to the GPS buoy station (see Fig. 1(a)).
In April to September (S2), the sea surface wind was generally weakercompared with that in S1, while the estimated runup height was intermittently much greater than that in S1 because of the incidence of
longer-period waves (see Appendix A) mainly from the southsouthwest (Fig. 2(d)). These generally originated from low-pressure systems (e.g., typhoons) in the southern region of Nii-jima Island.
For the actual incident waves to Wadahama Beach as well, the smaller
fetch length between Honshu Island and Nii-jima Island (see Fig. 1(a))
basically limits the evolution of northerly wind waves. Thus, the wave
statistics and the estimated runup height based on the wave statistics at
the GPS station are considered useful for identifying storm events on
Wadahama Beach.
3.2. Re-estimation of ﬂoat residence time on the whole Wadahama Beach
The total number of remnant ﬂoats (hereinafter, “cohort population”) newly found at each MR experiment from September 30, 2011
to August 31, 2013 is shown in Table 1. The cohort population decreases
exponentially. We approximated the cohort population normalized by
the initial population as the exponential function (h(t) = exp.(−ft))
with a 95% conﬁdence level (n = 104, R2 = 0.852, P = 6.47 ×
10− 47 b 0.05) as follows:(hðt Þ ¼exp −4:471  10−3 t ;0;

t ≥ 0;
t b 0;

ð1Þ

where t is elapsed time in days from the MR experiment day. From theintegral of this function from t = 0 to inﬁnity, the average residence
time of the ﬂoats on the whole beach is τr = 1/f = 224 days, that is,about 7.5 months. The margin of error of the coefﬁcient f was estimatedas 0.340 × 10− 3 (day− 1) by a t-distribution with a 95% conﬁdence
limit. Thus, the residence time has a 95% conﬁdence interval from
208 days (= 1 / (4.471 × 10 − 3 + 0.340 × 10− 3 )) to 242 days(= 1 / (4.471 × 10− 3 − 0.340 × 10− 3)). The exponential decay ofthe cohort population means that the cohort population decreased at aconstant rate of 0.5% day−1 determined as 1 − exp.(−1 / 224) = 0.005.
Kataoka et al. (2013) previously estimated the average residence
time on Wadahama Beach based on the 20-month exponential decay
from September 30, 2011 to May 8, 2013, which was 209 days with
the 95% conﬁdence interval from 192 to 230 days (n = 77, R2 =0.852, P = 4.97 × 10−35 b 0.05). The average residence time increasedslightly by adding the cohort population measured on June 27 andAugust 31, 2013. To estimate the “true” average residence time on
Wadahama Beach, it might be necessary to continuously conduct the
MR experiment. Nevertheless, the previously reported residence time
(209 days) is within the range of the 95% conﬁdence interval of there-estimated residence time in this study (i.e., 208 days b τr b 242
days). Hence, here we considered the average residence time of theﬂoats on Wadahama Beach as 224 days.
3.3. Spatial distribution and alongshore movement of the ﬂoats on thebeachFig. 3 shows the beach topography and the positions of the immigrant, remnant and emigrant ﬂoats measured at each MR experiment

542

Table 1
Number of ﬂoats recovered by the MR experiments and cohort population and abundance of re-emergence (within parentheses) in each MR experiment.
Experiment no.

1

2

3

4

5

6

7

Experiment date

2011/09/30

2011/10/27

2011/11/24

2011/11/26

2012/01/26

2012/03/23

2012/06/29

27

28

2

61

57

98

53

Number of storm events

1

2

1

3

3

16

4

Classiﬁcation of season

1

1

1

1

1

2

47

77

Remnant0 (0)

36 (0)

105 (1)163 (4)139 (7)112 (12)85 (22)

Total population

47

113

166

183

157

130

221

Emigrant

0

11

8

3

44

45

45

Cohort populationa
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
No. 9
No. 10No. 11
No. 12
No. 13
No. 1447 (0)
–
–
–
–
–
–
–
–
–
–
–
–
–

36 (0)b77 (0)
–
–
–
–
–
–
–
–
–
–
–
–

34 (1)
71 (0)
61 (0)
–
–
–
–
–
–
–
–
–
–
–

34 (2)
71 (2)
58 (0)
20 (0)
–
–
–
–
–
–
–
–
–
–

28 (2)
52 (5)
44 (0)
15 (0)
18 (0)
–
–
–
–
–
–
–
–
–

17 (0)
38 (2)
34 (6)
12 (4)
11 (0)
18 (0)
–
–
–
–
–
–
–
–

12 (3)
27 (8)
25 (7)
6 (1)
8 (3)
7 (0)
136 (0)
–
–
–
–
–
–
–

a
b

61

20

18

18

2

Immigrant

The abundance of reemergence is added to the cohort population of the previous experiments.
Cohort population of no. 1 in the second experiment is not used in the calculation of the residence time because the second experiment was carried out in the northernmost 200 m-long area.

136

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

Number of days

Table 1 (continued)
Experiment no.

8

Experiment date

2012/08/21

10

2012/11/08'11

2012/12/27

12

2013/02/27

13

2013/05/08

14

2013/06/27

2013/08/31

79

49

62

70

50

65

Number of storm events

20

3

3

3

1

4

Classiﬁcation of season

2

1

1

2

2

2

Immigrant

26

57

20

28

191

64

Remnant

188 (1)

97 (13)141 (12)137 (5)123 (60)

294 (6)21
305 (14)

Total population

214

154

161

165

314

358

326

Emigrant

33

117

13

24

42

20

53

Cohort populationa
No. 1
No. 2
No. 3
No. 4
No. 5
No. 6
No. 7
No. 8
No. 9
No. 10No. 11
No. 12
No. 13
No. 1410 (0)
23 (1)
21 (0)
5 (0)
7 (0)
6 (0)
116 (0)26 (0)
–
–
–
–
–
–

6 (3)
12 (4)
13 (2)
4 (1)
4 (0)
2 (0)
48 (3)8 (0)
57 (0)
–
–
–
–
–

6 (0)
10 (2)
11 (2)
4 (3)
4 (2)
2 (1)
46 (2)8 (0)
50 (0)
20 (0)
–
–
–
–

6 (1)
8 (0)
10 (0)
4 (0)
2 (0)
2 (0)
38 (1)7 (0)
44 (3)
16 (0)
28 (0)
–
–
–

6 (3)
7 (2)
7 (4)
1 (0)
2 (1)
1 (0)
35 (22)6 (3)31 (18)14 (7)
13 (0)
191 (0)
–
–

5 (0)
7 (0)
7 (0)
1 (1)
2 (0)
1 (1)
34 (1)5 (1)
29 (2)
11 (0)
13 (0)
179 (0)64 (0)
–

5 (0)
4 (1)
6 (2)
1 (0)
2 (0)
1 (0)
27 (2)4 (0)
29 (0)
11 (1)
12 (1)
158 (7)45 (0)
21 (0)

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

Number of days

9

543

544

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

Fig. 2. Time series of (a) wind component speeds observed by ASCAT and (c) wave runup height estimated based on the daily wave statistics observed at about 90 km west of Nii-jimaIsland (black triangle in Fig. 1(a)). The meanings of lines and their colors are shown in the top box. Light-gray bars in panels (a) and (c) indicate the duration of storm events, which is when
the runup height was higher than 2 m. Gray arrow indicates the MR experiment date as described in Table 1. Rose diagrams of wind and wave directions in storm events are shown inpanels (b) and (d), respectively. The wind and wave directions are expressed in degrees clockwise from the north; for instance, a wave and wind coming from the south are given as
180°. Blue (red) plane indicates the frequencies of wind and wave direction in S1 (S2).

from November 24, 2011 to August 31, 2013. Note that the positions of
the ﬂoats recorded in the experiments on September 30 and October 31,
2011 are not shown because these two experiments were conducted
only in the northernmost area (see Section 2.3). The positions of emigrant ﬂoats denote the positions of those found at the previous MR experiment. The shoreline of the beach consistently advanced seaward(i.e., salient) in the central area ranging from 500 to 700 m and in thenorthern area ranging from 900 to 1100 m, suggesting the generationof a consistent nearshore current structure in the surf zone off thebeach, which was probably controlled by the SBs.
The ﬂoats were consistently distributed at a beach elevation higher
than 2 m (Fig. 3). This indicates that the ﬂoats were moved by swash
waves reaching a beach elevation higher than 2 m, and conversely,
were hardly moved by tidal ﬂuctuations because the ﬂoats were washed
up at much higher elevations than the HWL (bold broken line in Fig. 3).
In the present study, we deﬁne the duration when the runup height was
higher than 2 m as a storm event (light-gray bars in Fig. 2(a) and (c)).
The total number of events that occurred in S2 (48 times) is threetimes greater than that in S1 (16 times) because of the longer-period
wave incidence to the beach in S2 (Table 1).
We summed up the number of immigrant, remnant and emigrant
ﬂoats in each 100-m-long transect obtained at every MR experimentand calculated the immigrant (In), remnant (Rn) and emigrant (En) ratios by dividing the three totals for each transect by the corresponding
totals for the whole beach. Note that we calculated In (Rn and En) byusing the data from the third (fourth) to fourteenth (fourteenth) MR experiments. Here, n denotes the transect number (n = 1, 2, …, 9). The
immigrant, remnant and emigrant ratios and their spatial distribution
are shown in Table 2 and Fig. 4(a), respectively. Looking at the seventhtransect, for instance, 29% (24%) of all remnant (immigrant) ﬂoats were(newly) found in this transect at the present MR experiment; 25% of all
ﬂoats backwashed offshore during the previous and present experiments were last found in this transect.
Overall, the distribution patterns of the three ratios were similar inreference to the local maxima of the fourth and seventh transects. Nevertheless, the sum of the remnant and emigrant ratios in the northernarea from 800 to 1100 m of alongshore distance (65% and 70%, respectively) was even higher than that of the immigrant ratio (52%) in thesame area (Table 2). The difference suggests that the ﬂoats were likely
to concentrate in the northern area in the backwash process, since theremnant and emigrant ﬂoats had stayed on the beach for a longer
time and had more chances to be transported by waves and coastal currents in the storm events than the immigrant ﬂoats, and thus the difference reﬂects the movement of the ﬂoats during the storm events.
Fig. 5 shows the temporal change of the alongshore position of theremnant ﬂoats of each cohort, that is, the alongshore movement of theﬂoats. It is noted that the ﬂoats did not move directly in the alongshore
direction on the beach by the winds as mentioned in Section 2.2. Whenthe ﬂoats that backwashed to the sea returned onto the beach, their new
positions were different from their original ones before backwashing.
The remnant ﬂoats tended to converge mainly in the seventh transectwith the cohort population decreasing in the backwash process. This resulted in the difference in the distribution between the ratios in thenorthern area as mentioned above. Dividing the alongshore transportdistance of the remnant ﬂoats by the total duration of the storm eventsin each experiment period, we calculated the temporal mean alongshore movement velocities of the remnant ﬂoats in the events (hereinafter, “transport velocity”) and found that the transport velocity was inT. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

545

Fig. 3. Beach topography measured by RTK-GPS (white-gray gradation) and alongshore distribution of ﬂoats at each experiment date from November 24, 2011 to August 31, 2013. The boldbroken line denotes the HWL (high water level). The meanings of the colors of circles are shown in the upper right box.

the order of 10−4 to 10−3 ms−1. This is much smaller than the nearshore current velocities in the surf zones (10−1 to 100 ms−1) reported
in previous studies (e.g., Sonu, 1972; Kuriyama and Nakatsukasa, 2000).

were likely to be transported from the original transect, where they
were ﬁrst found as immigrant ﬂoats, to other transects and/or backwashed offshore in each experiment period, the average residence
time in the original transect is shorter than that in other transects.
Here, we estimated two types of average residence time of the ﬂoats
stranded in a 100-m-long transect (transect residence time; hereinafter,“TRT”), that is, the average residence time until the ﬂoats disappear
from the original transect by being moved to other transects or
backwashed offshore (TRT1), and the residence time until the ﬂoats disappear from the beach by being backwashed offshore (TRT2). Transects

3.4. Residence time of ﬂoats originating in a 100-m-long alongshoretransect
The ﬂoats stranded in each transect had three possible fates in eachexperiment period: backwashing offshore, moving to other transects inthe alongshore direction, or staying in the same transect. If the ﬂoats

Table 2
Immigrant, remnant and emigrant ratios, TRT1, TRT2 and the difference between TRT1 and TRT2 with respect to horizontal position.
Alongshore
distance [m]TransectnumberDistribution of the ﬂoats
Immigrant ratio[%]

Remnant ratio[%]

TRT1 [days]
Emigrant ratio
[%]

Ave.

TRT2 [days]

95% conf.
interval
Min.

Max.

R2

Ave.

95% conf.
interval
Min.

Max.

R2

Difference of TRTs
[days]

1100
9

12

14

22

136

116

163

0.72

260

217

325

0.35

125

8

16

22

23

143

128

163

0.76

222

199

251

0.76

79

7

24

29

25

198

182

216

0.86

264

241

291

0.84

66

6

13

12

7

124

104

153

0.76

300

247

384

0.58

176

5

5

3

4

–

–

–

–

518

373

849

0.18

–

4

14

11

8

154

125

201

0.64

348

300

414

0.67

194

3

8

5

5

185

146

251

0.58

313

250

421

0.38

129

2

6

2

4

57

51

65

0.97

213

153

349

0.50

156

1

3

1

2

–

–

–

–

403

270

791

0.46

–

1000
900
800
700
600
500
400
300
200

546

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

having a shorter TRT2 and a smaller difference between TRT1 and TRT2
are possible transects where the ﬂoats were backwashed offshore,because the combination of a shorter TRT2 and smaller differencemeans that the ﬂoats tend to be backwashed offshore rather than be
moved to other transects.
In the same way as the estimation of the average residence time on
the whole beach (see Section 3.1), the average TRTs can be estimatedby approximating the decrease in the population of remnant ﬂoats originating in each transect as an exponential function:hn ðt Þ ¼

Fig. 4. Alongshore distributions of immigrant ratio (In), remnant ratio (Rn), emigrant ratio(En) (a) and transect residence times (TRTs) (b). The meanings of symbols and their colors
are shown in the bottom box. Light-gray area indicates the alongshore position of the SB.
The transect numbers are shown on the right side of panel (b).

P n ðt k þ t Þ¼
P n ðt k Þexpð f n t Þ; t ≥ 0;0;
t b 0;

ð2Þ

where Pn(tk) is the number of immigrant ﬂoats stranded in the n-thtransect at the k-th MR experiment conducted at tk (transect cohort
population). Pn(tk + t) is the transect cohort population at tk + t in
the n-th transect (on the whole beach) for calculating TRT1 (TRT2). t
is the elapsed time in days from tk. From the population decay of thetransect cohorts with respect to t, we deﬁned the exponential function.
TRTs of the n-th transect are deﬁned as 1/fn.
TRT1 and TRT2 are shown in Table 2 and Fig. 4(b). TRT1 of the ﬁrst
and ﬁfth transects having a much smaller cohort population could not
be calculated because the population decay was not signiﬁcantly approximated as an exponential function. Overall, TRT1 was shorter than
the average residence time of all ﬂoats on the whole beach (i.e., 224days), because the transect cohort population decreased by moving toother transects as well as being backwashed offshore. On the other
hand, TRT2 ranged widely from 213 to 518 days and was longer at thecenter of the beach and became shorter in the northern and southern

Fig. 5. Alongshore movements of the ﬂoats on the beach from when they were newly found to August 31, 2013. Light-gray area indicates the alongshore position of the SB.

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

transects. TRT2s of the second and eighth transects were shorter than224 days. The difference in TRTs of the seventh and eighth transects,
where 48% of the total emigrant ﬂoats were last found (Table 2), wassigniﬁcantly smaller than that of the other transects. These results
suggest that the seventh and eighth transects were the most likely backwash transects. In other words, in terms of nearshore hydrodynamics,
offshore currents would occur in the surf zone near these transects inthe storm events. In addition, the alongshore ﬂoat movements (Fig. 5)
indicate that alongshore current convergence mainly occurred off theseventh transect.
3.5. Nearshore current structures around SB4
Fig. 6(a) and (b) shows snapshots of the nearshore current structures off the ﬁfth to ninth transects in storm events, as recorded by
the webcam at 12:19 on December 21, 2014 (corresponding to S1)and at 14:11 on July 26, 2015 (corresponding to S2), respectively.
Also, 15-min animations made from the images taken every 5 s can beviewed online in the electronic version of this article (Appendix B).
From the wave and surface wind records, the mean surface wind andwave directions were respectively 311° and 238° measured clockwisefrom the north on December 21, 2014. The estimated runup height was
3.2 m. Regarding the wave directions observed in storm events in S1 during the MR experiment period, the waves propagated from the southwest,
while the northwesterly wind prevailed on this day. However, based on
the images, the waves propagated nearly normal to the beach probably
due to wave refraction and diffraction. The incident waves were broken
above SB4 resulting in the onshore mass transport and the turbid beachwaters ﬂowed offshore mainly from the seventh and eighth transects
through the gap between SB4 and SB3 and along the promontory. This
combination of onshore–offshore currents around SB4 is expected to induce northward and southward alongshore currents in the lee of SB4(broken arrows in Fig. 6(a)), resulting in the generation of horizontal convergence off the seventh transect. Off SB4, the turbid beach waters originating in the surf zone were advected southward due to offshore current,
which was presumably driven by wind. However, we cannot exclude thepossibility of tidal currents and/or the Kuroshio ﬁlaments. It is interesting
to note that offshore clear waters intruded into the surf zone through thegaps between SB4 and the promontory and between SB3 and SB4.
On July 26, 2015, the estimated runup height was 4.1 m and the mean
wind and wave directions were respectively 263° and 215° as observed instorm events in S2 during the MR experiment period. The nearshore current structure was similar to that generated on December 21, 2014 exceptthat no offshore water intrusion occurred in the gap between SB4 and thepromontory. Off SB4, northward current was dominant on that day.
Overall current structure in the surf zone on the two days corresponds well with that generated behind a submerged breakwater

547

under normal wave incidence conditions described in previous studies(e.g., Ranasinghe and Turner, 2006). This suggests that the wavedriven currents dominated over the currents driven by other forces inthe surf zone, whereas the currents driven by other forces were dominant off SB4 in the storm events.
4. Discussion and conclusions
The images and animations of the nearshore current structure off thenorthern part of the beach (Fig. 6) conﬁrmed the occurrence of the combination of offshore currents in the lee of SB4 and alongshore current
convergence mainly off the seventh transect deduced from the MR experiment results (Figs. 4, 5). The current structure corresponds wellwith that generated around a SB as described in previous studies(e.g., Ranasinghe and Turner, 2006). The conﬁrmation allows us to conclude that the majority of remnant ﬂoats on the beach were transported
alongshore and tended to concentrate in the convergence zone andwere backwashed offshore by the wave-driven nearshore currents.
The backwash process speculated in our previous study (Fig. 7 in
Kataoka et al., 2013) has been improved as illustrated in Fig. 7 except
for the process in the central–southern area of the beach because of
the limited coverage of the webcam. Although a southwesterly wind
generally prevails in a storm event, current off SB4 transports the turbid
water from the surf zone southward when a northwesterly wind prevails as on December 21, 2014. The backwash process in the central–southern part of the beach is also expected to be determined by thenearshore current structure, which is probably controlled by the distribution of SBs. The consistent shoreline with the salient in the central
and northern areas suggests the generation of a consistent nearshore
current structure in the surf zone off the beach. The large remnant
ratio in the northern corner (Fig. 4a) would result from the overall
northward transfer of the ﬂoats on the beach under the northward
winds and waves prevailing during the storm events (Fig. 2b and d).
The transport velocities of the remnant ﬂoats were much smaller
than those of the nearshore currents (see Section 3.3). The transport velocities were evaluated based on the remnant ﬂoat movements, but notby the emigrant ﬂoat movements, which might be of the same order ofmagnitude as the nearshore current velocities. From all the remnant
ﬂoat movements during November 24, 2011 and August 31, 2013, it
was found that 89% of the recaptured ﬂoats were transported within adistance of less than 100 m, while 11% of the ﬂoats were greatly
transported over a longer distance than 100 m during one experimentperiod. This suggests that the majority of the remnant ﬂoats aretransported into the surf zone and washed ashore onto the same transect by swash waves repeatedly and intermittently in the storm events.
In this process, on average, they would be gradually transported in thealongshore direction by the alongshore wind- and wave-driven

Fig. 6. Snapshot of nearshore currents taken by the webcam at 12:19 on December 21, 2014 (a) and at 14:11 on July 26, 2015 (b) visualized by the contrast in color of turbid beach waters
and clear offshore waters and its temporal evolution (solid arrows). Broken arrows are deduced currents. 15-min animations made from the images taken every 5 s are also available online
in the electronic version of this article (Appendix B).

548

T. Kataoka et al. / Marine Pollution Bulletin 101 (2015) 539–548

height was calculated using the daily signiﬁcant wave height and period
as follows
R
¼ ξ;
H0

ðA1Þ

where R is the runup height from MWL and H0 is the deep-water signiﬁcant wave height (Hunt, 1959). ξ is the Iribarren number, which isdeﬁned as (Battjes, 1974):
ξ¼

tan β
ðH 0 =L0 Þ1=2

;

ðA2Þ

where tanβ is the beach slope, L0 is the deep-water wave length given
by L0 = (g/2π)T20 where g is the acceleration due to gravity and T0 is
the signiﬁcant wave period. The beach slope was determined astanβ = 0.14 based on measurements of the beach topography. The
Iribarren number can be interpreted as the dynamic beach steepness,comparing the beach slope to the square root of the deep-water wave
steepness.
Appendix B. Supplementary data
Fig. 7. Schematic image of nearshore current structure and associated backwash process ofthe ﬂoats from Wadahama Beach. Black (red) broken arrow indicates deduced nearshore
current (backwash process). Horizontal convergence of alongshore current mainly occurs
in the shaded area.

currents. In addition, we assumed that the remnant ﬂoats had been
moving during the storm events and calculated the transport velocity
by dividing the alongshore transport distance of the remnant ﬂoats by
the duration of the storm events (see Section 3.3), whereas in actuality
they would be intermittently moved in the alongshore direction by the
combination of swash waves and alongshore currents. Therefore, although the transport velocities were much smaller than the nearshore
current velocities, we believe that the movements of the remnant ﬂoats
reﬂect the alongshore current structure.
The ﬁnal goal of this study is to establish a mathematical model toestimate the average residence time of marine plastics on the beach.
Considering that the backwash process was controlled by the nearshore
currents in the storm events, the average residence time on the beach is
expected to be determined by the frequency of the storm event occurrence and nearshore current structures, that is, the scales of the horizontal length and velocity of the currents. We can understand the frequency
and qualitative features of the nearshore currents based on the webcam
images, as demonstrated in this study. In the near future, we will measure the scales of the nearshore current structures using the tracking
data of small buoys equipped with the GPS receiver distributed in thesurf zone in the storm events. An understanding of the scales and thefrequency will enable us to estimate the diffusion coefﬁcient of the plastic
ﬂoats, which determines the offshore ﬂux of the ﬂoats from the beach andthus the residence time of the ﬂoats on the whole beach.
Acknowledgments
This research was supported by the Environment Research andTechnology Development Fund (B-1007 and 4-1502) of the Ministryof the Environment, Japan and by JSPS KAKENHI Grant Numbers
23656309, 25820234 and 26630231.
Appendix A. Estimation of wave runup height on Wadahama Beach
Waves are monitored by a NOWPHAS GPS buoy located about 90 km
west of Nii-jima Island (black triangle in Fig. 1(a)). Data is available at
http://www.mlit.go.jp/kowan/nowphas/index_eng.html. The runup

Supplementary data to this article can be found online at http://dx.
doi.org/10.1016/j.marpolbul.2015.10.060.
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