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Estuarine, Coastal and Shelf Science 134 (2013) 69e79

Contents lists available at ScienceDirect

Estuarine, Coastal and Shelf Sciencejournal homepage: www.elsevier.com/locate/ecss

Numerical estimation of inﬂow ﬂux of ﬂoating natural macro-debris
into Tokyo Bay
T. Kataoka a, *, H. Hinata a, 1, Y. Nihei b, 2
aCoastal 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 Engineering, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japana r t i c l e i n f o

a b s t r a c t

Article history:
Received 27 March 2013
Accepted 6 September 2013
Available online 19 September 2013

We numerically estimated the inﬂow ﬂux of terrestrial grass, which is the main ﬂoating macro-debris,
into Tokyo Bay from April 2008 to March 2009 based on a two-way particle-tracking model and an
inverse method applying a Lagrange multiplier. In the estimation, we used surface current velocities
derived by high-frequency ocean radar and the quantity of grass collected by clean-up vessels which areoperated daily in the bay. At least 2115 m3 yr1 of the grass ﬂowed into the bay annually, and thecontribution of a ﬂood event to the inﬂow ﬂux of grass was larger than that of the inﬂow ﬂux offreshwater. We show that 39% of the annual inﬂow ﬂux of grass into the bay was collected, and 61%
ﬂowed out of the bay or sank to the seabed. The numerical estimation in this study will be useful toestablish a system for predicting patches of ﬂoating macro-debris in the bay, and to evaluate the effectsof river development or clean-up along river banks and ﬂood plains in the upper reaches.
Ó 2013 Elsevier Ltd. All rights reserved.

Keywords:
debris ﬂow
Japan
Tokyo Bayradar
particle motion
inversions

1. Introduction
Estimating ﬂuxes of debris from the land into the ocean is
crucial in order to take measures, and to understand the impacts on
the marine environment. Most studies on marine debris havefocused on contamination of the marine and coastal environment
by anthropogenic debris (e.g., Moore et al., 2001; Ryan et al., 2009;Law et al., 2010). Although large quantities of natural debris ﬂowing
into the ocean from the land due to natural disasters affect humanactivities such as sailing and marine leisure activities in the coastal
zone, few studies have focused on natural debris (e.g., Moore andAllen, 2000). In addition, natural debris ﬂowing into the ocean
would contribute to the marine ecosystem, such as the oceaniccarbon cycle, because terrestrial organic matter like natural debris
represents a substantial source of terrestrial dissolved and particulate organic carbon (Hedges et al., 1997).
Tokyo Bay is located on the southeast coast of the main island ofJapan (Fig. 1(a)). The bay plays a key role for industry in Japan, withsome 600 freighters passing through the bay mouth each day, and* Corresponding author.
E-mail addresses: kataoka-t852a@ysk.nilim.go.jp (T. Kataoka), hinata-h92y2@
ysk.nilim.go.jp (H. Hinata), nihei@rs.noda.tus.ac.jp (Y. Nihei).
1Tel.: þ81 46 844 5025; fax: þ81 46 844 1145.
2
Tel.: þ81 4 7124 1501x4031; fax: þ81 4 7123 9766.
0272-7714/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ecss.2013.09.005

the bay is heavily eutrophicated due to terrestrial loads (Furukawa
and Okada, 2006). To ensure safety for users of the bay and toprotect its marine environment, the ﬁve port administrators ofTokyo, Kawasaki, Yokohama, Chiba, Kisarazu as well as the Ministryof Land, Infrastructure, Transport and Tourism (MLIT) have beencollecting both natural and anthropogenic debris drifting in thesurface layer (upper 2 m) using clean-up vessels since the 1970s(Furukawa and Okada, 2006). The collected debris is classiﬁed as
macro-debris (Ryan et al., 2009) because it is collected using askipper with slit widths of 2e6 cm (Fig. 2(a)). To identify the effectof the clean-ups, we need to assess, for instance, the ratio of theannual amount of collected debris to the annual inﬂow.
A common approach to quantify the inﬂow ﬂux is to sample
debris by various ﬁltering systems or customized nets at suspectedsources for ﬁxed periods (e.g. Durrum, 1997; Armitage andRooseboom, 2000; Nihei et al., 2010), and then to calculate aloading rate of the debris per unit catchment area per unit time, or
per unit volume of river discharge per unit time. Generally, theloading rate from a particular source shows a time dependency andincludes a history effect, such as “ﬁrst ﬂush” (Armitage andRooseboom, 2000). The loading rate also depends on the land use
pattern of the catchment area, such as urban area or forest area.
Thus, long-term sampling at multiple sources is required in order toestimate the inﬂow ﬂux by using the loading rates calculated fromdirect debris sampling.

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Fig. 1. (a) Map of Japan showing Tokyo Bay and ocean currents. (b) The catchment area of Tokyo Bay (area enclosed by thick chain line), the three large rivers ﬂowing into the bay(gray area), and the Tone River above Sekiyado (lateral line area). Squares and triangles show sampling sites of ﬂoating macro-debris by Nihei et al. (2010) and observation sites ofriver level by the MLIT, respectively. The broken line shows the boundaries between port areas (Tokyo (TO), Kawasaki (KA), Yokohama (YK), Yokosuka (YS), Chiba (CH), Kisarazu (Ki))
and the central bay. (c) Bathymetric map of Tokyo Bay showing also the residual current ﬁeld on 31 July 2008 measured by HF radar. The solid thin line and broken thin line in thebay show the western and eastern lines, respectively (see Fig. 8). The solid bold line and broken bold line show suspected sources of ﬂoating macro-debris and bay mouth,
respectively.

Here, we numerically estimate the ﬂuxes of grass, which was themain type of ﬂoating macro-debris (see Section 2.1), into Tokyo Bay
from three large rivers (Edo River, Ara River and Tama River;
Fig. 1(c)) for ﬁscal 2008 (from April 2008 to March 2009; F2008)
based on a two-way particle-tracking model (two-way PTM)
developed by Isobe et al. (2009) and an “inverse method using a
Lagrange multiplier” (IMLM) developed by Kako et al. (2010) using
data on the grass collected in the bay by the MLIT (see Section 2.1)
and high-frequency (HF) ocean surface radar-derived surface current velocities (see Section 2.2). This numerical estimation allows
us to identify the sources and to estimate the inﬂow ﬂuxes withoutsampling debris at multiple sources. As the ﬁrst step to understandthe inﬂow ﬂux of macro-debris in Tokyo Bay, here we estimate theorder of magnitude of the inﬂow ﬂux of grass ﬂowing into the bay.
2. Data and method
2.1. Collection data of grass in Tokyo Bay
The MLIT collects macro-debris in central Tokyo Bay (Fig. 1(b))
during the daytime (9:00e16:00) on weekdays. Most of the debris
collected in F2008 was natural debris (Fig. 2(d)); only 4% wasanthropogenic debris such as plastic bags and sheets, bottles, cans,
styrofoam products, and electronic products. The daily volume ofthe debris is measured by placing it in containers with a scale at thehome port. In F2008, the maximum and the average of the dailycollected volume were 28.7 m3 and 4.6 m3, respectively. We
selected grass, which accounted for 29% (Fig. 2(d)), to facilitate theparticle-tracking experiments for the numerical estimation
because the advection process of grass is not strongly affected by

the wind. Since the collected grass contains voids, we conducted alaboratory experiment to estimate the net ratio (see Appendix A)
and hence compute the net volume of grass. The net volume wascomputed by multiplying the net ratio (0.3661) by the collectedvolume (Table 1).
The collection points and the volume of grass collected at eachpoint are not recorded. The speed of the vessel is reduced to 4 knots(2.06 m s1) or less during collection (Kataoka and Hinata, 2012).
Therefore, we identiﬁed the grass collection points by calculating
the vessel speed based on the track recorded every 4 s by the global
positioning system (GPS). Typically, a vessel goes back and forth
inside a patch of debris until no debris can be found during thecollection and its track also forms a patch (hereafter, “collection
patch”); the average position of the vessel track is taken as thecollection point. The collection patch is approximated as an ellipse,
and its average area in F2008 was approximately 0.765 km2(Kataoka and Hinata, 2012). The volume collected at each collection
point is calculated by allocating the daily collected volume of grassto each point in proportion to the duration of each collection. Tracks
were not recorded on some of the operation dates in F2008. In the
IMLM, only the net collected volume on the track recording date(value within parentheses in Table 1) was used.
The total volume of debris that was collected by the port administrators was recorded daily, but the collected volume of grass
and the tracks of the collection vessels are not available. We
assumed that the composition and the net ratio of grass collectedby the administrators are the same as those of grass collected by the
MLIT. The net volume of grass was calculated by multiplying thevolume collected by the administrators by the collection ratio ofgrass (29%) and the net ratio (0.3661) (Table 1).

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71

Fig. 2. Photographs of the MLIT clean-up vessel (a) and grass collected in the bay (b). (c) Quantity of ﬂoating macro-debris collected by the MLIT and the port administrators in thebay in F2008. (d) Composition of ﬂoating macro-debris collected by the MLIT (natural debris is shaded in gray) in F2008.

2.2. HF radar-derived surface current velocities
We use the HF radar-derived surface current velocity data set forF2008 produced by Kataoka and Hinata (2012). The speciﬁcationsof the HF radar system (Nagano Japan Radiowave Co., Ltd.) are
shown in Table 2. The estimated error of the radar system based on
a comparison between the velocities measured by the HF radarsystem and those measured by acoustic Doppler current proﬁlers(ADCP) is 6 cm s1 for both the EW and NS components (Yanagi
et al., 2003).
Dividing the bay into 347 grid points at 1.5-km intervals, thesurface velocity vectors at 250 of the 347 grid points can be obtained from two or three HF radar-derived radial velocities. At theother grid points where one or no radial velocity was measured, thevelocity vectors were estimated by extrapolating from the observed
velocity vectors around the grid points using the inverse distanceweighted method with a 1/d2 type of weight function and the velocity components at the grid points on the land being zero
(Kataoka and Hinata, 2012). The HF radar failed to obtain surface
velocities for 1 month from 28 January 2009 to 28 February 2009
because of a malfunction of the HF radar system.
2.3. Source identiﬁcation and inﬂow ﬂux estimation
Our numerical model consists of the two-way PTM to identify
the sources of grass (Isobe et al., 2009) and the IMLM to estimateinﬂow ﬂuxes of grass per unit time from each source identiﬁed by
the two-way PTM (Kako et al., 2010). To identify sources and to
estimate the inﬂow ﬂuxes, Kako et al. (2010) used accumulation
rates obtained by a bimonthly beach survey and modeled surface

current velocities on the East China Sea continental shelf. We usedthe volume of grass collected by the MLIT and the HF radar-derived
surface current velocities instead. The applicability of thesemethods to Tokyo Bay has already been conﬁrmed by Kataoka and
Hinata (2012), who found that the error of identifying sources by
the two-way PTM is within 10 km, and the error of estimating theinﬂow ﬂux is 0.9e1.6 times the true ﬂux.
2.3.1. Two-way PTM
Two-way PTM experiments were carried out to identify sourcesof grass by combining a “backward-in-time” PTM with a “forwardin-time” PTM. The details of the PTM are given in Appendix B. First,
backward-in-time PTM experiments were carried out to determine
the source candidates of grass. In these experiments, 5000 particles
placed at the collection points at the collection time were tracked
by the HF radar-derived surface currents with directions reversed
in sign for both horizontal current components in conjunction withrandom-walk processes. “Random-walk” means the trajectories ofsuccessive random steps computed by the last term of Eq. (B.1) inAppendix B. These particles were tracked until they reached the
1.5-km grid boxes of the western boundary covered by HF radar
near the mouths of the three large rivers and/or outfalls (bold line
in Fig. 1(c)). To determine the source candidates in the backwardin-time PTM experiments, the 1.5-km grid boxes were divided
into nine boxes of 500 m in size, and the 500-m boxes wereconsidered as source candidates. Multiple source candidates in a
1.5-km grid box were replaced with the candidate having the mostparticles. If the particles reached boundaries other than the bay
mouth (bold broken line in Fig. 1(c)) and the western boundary(bold line in Fig. 1(c)), we performed the re-drifting operation (seeAuthor's personal copy

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T. Kataoka et al. / Estuarine, Coastal and Shelf Science 134 (2013) 69e79

Table 1
The monthly freshwater ﬂux and the monthly collection of ﬂoating macro-debris by the MLIT and the port administrators.
2008

2009

Summation

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Jan

Feb

Mar

0.780

0.682

0.871

0.530

1.042

0.951

0.513

0.237

0.247

0.341

0.280

0.358

6.832

18 (16)40.46(40.01)19 (12)42.51(16.03)20 (17)17.82(14.31)20 (16)
7.99(6.69)

10 (8)
37.74(5.59)

18 (15)67.40(62.41)20 (15)38.28(28.73)17 (9)
27.01(20.33)18 (15)
8.03(6.87)

18 (16)
11.47(8.68)

4 (4)1.71(1.71)4 (1)1.22(0.42)

186 (144)
301.64(211.78)

12 (10)9.84(9.60)
3.60(3.51)
0.30

16 (11)
15.45(5.98)
5.66(2.19)
0.35

10 (8)
3.86(2.49)
1.41(0.91)
0.14

3 (3)
0.37
(0.37)
0.14(0.14)
0.05

9 (7)
16.32
(1.37)
5.97(0.50)
0.66

14 (12)
19.32(18.32)
7.07(6.71)
0.51

11 (7)
18.94(14.95)6.93(5.47)
0.63

10 (5)
3.74(2.74)
1.37(1.00)
0.14

0 (0)
0.00
(0.00)
0.00(0.00)
0.00

1 (1)
0.12
(0.12)
0.04(0.04)
0.04

1 (1)
0.25
(0.25)
0.09(0.09)
0.09

0 (0)
0.00
(0.00)
0.00(0.00)
0.00

87 (65)88.21(56.19)32.28(20.56)

Collection by the port administrators
All debris
681.34
Collected volume (m3)

850.71

549.14690.00745.211490.12529.57321.13353.88421.31486.18416.497535.08

Grass
Net collected volume (m3)

90.32

58.30

73.26

79.12

158.20

56.22

34.09

37.57

44.73

51.62

44.22

799.99Freshwater ﬂux of threerivers (109 m3)
Collection by the MLIT
All debris
Number of operation daysa
Collected volume (m3)b
Grass
Number of operation daysa
Collected volume (m3)b
Net collected volume (m3)b
Average daily collectedvolume (m3 d1)c

72.34

a

Value within parentheses means monthly number of days the tracks of the MLIT clean-up vessel were recorded.
b
Value within parentheses means monthly volume of debris that was collected on the days the tracks of the vessel were recorded.
c
Average daily collected volume was calculated by dividing the net collected volume by the number of operation days.

Appendix B). We terminated the backward-in-time PTM experiments at the time step when particles reached a grid box of the bay
mouth (bold broken line in Fig. 1(c)) or the corresponding monthly
residence time of the surface water masses (see Appendix B).
In general, source identiﬁcation using only backward-in-time
PTM is unreliable because the motion of an object includes irreversible random-walk processes. Therefore, forward-in-time PTM
experiments were carried out to examine whether each source
candidate was statistically signiﬁcant or not. In the experiments,
5000 particles were released from each source candidate identiﬁedin the foregoing backward-in-time PTM experiments, and werecarried by the HF radar-derived surface currents. Also, in theforward-in-time PTM, the particles that reached the boundaries
except the bay mouth continued to be tracked by the re-drifting
operation, and the tracking was terminated when they reached
the bay mouth. At each collection time, the particle distribution wasapproximated as an ellipse whose major axis length represented
twice the standard deviation of the distances between particle
positions and their averaged one. If the corresponding collection
point was located within the ellipse, the source candidate fromwhich these particles were released was considered to be signiﬁcant at the 95% conﬁdence level.
2.3.2. IMLM
The inﬂow ﬂuxes of grass at each source detected in the above
two-way PTM are computed using the IMLM. The relationship between the volume (z: a constant in each collection) which wascollected by the MLIT at each collection point and inﬂow ﬂux (f; arow vector) at various sources is given by:where the subscripts represent sources (N: the total number), thesuperscripts denote the hour in which the grass ﬂows into the bay
from each source, and M is the time when the MLIT collected grasscorresponding to z, and l is determined by the monthly residence
time (see Appendix B). Thus, the collected volume z is derived fromthe inﬂows up to l hours before. The column vector g denotes theweights of inﬂows from each source at each time in determining z,
and depends on the contribution of surface current to the behaviorof grass in Tokyo Bay. The weight vector g can be determined byforward-in-time PTM in conjunction with a random-walk process(i.e. the last term of Eq. (B.1)) in which the particles are released
from each source at each time from M to l, and according to thenumber of particles that reach the collection patch (see Section 2.1).
The inﬂow ﬂux f is calculated by solving the above equation using a
Lagrange multiplier. For a more thorough explanation of thedetermination of vector g and the solution of the inverse problem
for the above equation, refer to Kako et al. (2010).
2.4. River discharge at river mouth
In Tokyo Bay, rainwater falling in the catchment area of the bay
mainly ﬂows in the three large rivers: the total catchment area
(6571 km2) of these rivers (Edo River, 2391 km2; Ara River,
2940 km2; Tama River, 1240 km2; see Fig. 1(b) and (c)) accounts for
67% of the catchment area of Tokyo Bay (approximately 9800 km2).
Table 2
Speciﬁcations of the HF radar system.
Radar type

0


B
B
M
f1Ml ; f2Ml ; f3Ml ; .; fN1
; fNM B
B
@

g1
g2
g3
«
gNðlþ1Þ

1
CC
C ¼ z;CA(1)

Center frequency
Sweep bandwidth
Frequency sweep interval
Maximum transmission power
Range resolution
Velocity resolution

Frequency modulated interrupted
continuous wave (FMICW)
24.515 MHz
100 kHz (24.465e24.565 MHz)
0.5 s
200 W (peak)
1.5 km
<4.78 cm s1

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73

Fig. 4. The time series of river discharge (a) and inﬂow ﬂux estimated by this study (b).
The thick line in (b) is the cumulative curve of inﬂow ﬂux.

Fig. 3. Comparison of the relationship between the LR and the SRD obtained by thisstudy and the net samplings of Nihei et al. (2010). The regression equation is shown in
the upper left, and a typical c-section of the large rivers ﬂowing into Tokyo Bay inlower reaches is shown in the lower right. The black arrow shows the maximum of the
SRD in F2008.

Thus, most of debris would ﬂow into Tokyo Bay through these threerivers. The catchment area of the Edo River is determined to be2391 km2 assuming that it diverges from the Tone River (Nihei
et al., 2007a).
To investigate the relationship between the inﬂow ﬂux of grass
and the river discharge of the three large rivers, we used a data setof river discharge at a river mouth established by Nihei et al.
(2007b). Brieﬂy, this method is as follows. First, the relationshipbetween the water level and the river discharge (i.e. rating curve) at
an observation site located in the upper reaches is determined; theobservation sites of the Edo River, Ara River and Tama River are
respectively “Noda” located 39 km upstream, “Akigase” located
34 km upstream and “Denenchofu” located 13 km upstream(Fig. 1(b)). The river discharge at each observation site was calculated by applying the water level which was continuously observedat the sites (Water Information System by the MLIT; http://www1.
river.go.jp/) to the rating curve at each site. Then, the riverdischarge at the river mouth was calculated by considering theinﬂow of other rivers and sewers, water from river branches andrainfall on the catchment of the lower reaches. The accuracy of theriver discharge calculated by this method was conﬁrmed bycomparing it with the river discharge observed at the river mouth.
3. Results
3.1. Estimation of inﬂow ﬂuxes of grass
Inﬂow ﬂuxes of grass from sources identiﬁed by the two-way
PTM every hour were numerically estimated by the IMLM in
F2008. However, it was difﬁcult to classify the inﬂow ﬂux from eachsource (or each river) because the errors of identifying debris
sources by the two-way PTM were within 10 km (Kataoka and
Hinata, 2012). Therefore, hourly inﬂow ﬂux was calculated fromthe summation of the inﬂow ﬂuxes from all sources every hour.
The estimated hourly inﬂow ﬂuxes were compared with thetotal river discharge of the three large rivers (Fig. 3). In Fig. 3,“loading rate (LR)” and “speciﬁc river discharge (SRD)” are calculated by respectively dividing the hourly inﬂow ﬂux and the total
river discharge by the total catchment area (i.e., 6571 km2).
The relationship between the ﬂux L of a substance in river waterand river discharge Q is frequently modeled as:

L ¼ aQ b ;(2)where a and b are constants (e.g. Ebise, 1985; Takada et al., 1992). In
this study, L is the LR (m3 h1 km2), Q is the SRD (m3 s1 km2),
and the LR is regressed against the SRD. We found a signiﬁcantrelationship between the LR and the SRD at the 95% conﬁdence
level (R2 ¼ 0.23, P < 0.01, see Fig. 3). The coefﬁcients a and b in Eq.
(2) were 2.123  103 and 1.326, respectively (black solid line in
Fig. 3), and the 95% conﬁdence interval of the coefﬁcient a ranged
from 8.699  105 to 5.181  102 (black broken line in Fig. 3).
Although the determination coefﬁcient was low due to the large
variability of the LR for the SRD of 0.02e0.3 m3 s1 km2, therelationship was statistically signiﬁcant. This means that the grassin the river channel was ﬂushed out downstream by ﬂood events.
The hourly inﬂow ﬂuxes were not estimated during some periods because grass was not collected by the MLIT at certain times,
namely outside of operating hours (9:00e16:00) on weekdays,
weekends, holidays, and days when the vessel was maintained. In
addition, surface velocities were not obtained from 28 January
2009 to 28 February 2009 (see Section 2.2). The unestimated hourly
inﬂow ﬂuxes were calculated by Eq. (2). In this calculation, weestablished a threshold value for the river discharge of each river tojudge whether the river was in a ﬂood or non-ﬂood condition
because most of the grass grows on the ﬂoodplain and the banks ofthe main channel, and would not ﬂow out into Tokyo Bay in the
non-ﬂood condition because of the lower water level and theweaker current (see lower right in Fig. 3).
It is difﬁcult to deﬁne a speciﬁc threshold value to judge theﬂood condition because it depends on the cross-section of the river
channel. We used 0.02 m3 s1 km2 as the threshold value of the
SRD because hourly inﬂow ﬂuxes were not estimated in the lower
SRD range (Fig. 3). If the SRD calculated from the total riverdischarge was higher than the threshold value, the hourly inﬂow
ﬂuxes were calculated by multiplying the total catchment area
(6571 km2) by the LR, which was computed by substituting its SRD
into Eq. (2).
Consequently, the daily inﬂow ﬂuxes were calculated by adding
the summation of the hourly inﬂow ﬂuxes to the daily net volumeof grass collected by the port administrators. The time series of theAuthor's personal copy

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T. Kataoka et al. / Estuarine, Coastal and Shelf Science 134 (2013) 69e79

daily inﬂow ﬂux ﬂuctuated as the river discharge swelled, and inparticular, greatly increased on August 29 and 30 (Fig. 4(a) and (b)).
The annual inﬂow ﬂux was calculated by the summation of thedaily inﬂow ﬂuxes, and was 2115 m3 yr1. The inﬂow ﬂux(506 m3 10 day1) in the largest ﬂood event (for the 10 days from 25
August to 3 September) accounted for 24% of the annual inﬂow ﬂux.
On the other hand, the inﬂow ﬂux of freshwater for the same 10days (7.219  108 m3 10 day1) corresponds to 11% of the annual
freshwater ﬂux (6.832  109 m3 yr1). This indicates that the inﬂow
ﬂux of grass is greatly increased by ﬂood events compared with the
freshwater ﬂux.
3.2. Comparison with loading rates obtained by net samplings
The low determination coefﬁcient for the regression equation
was due to the large variability of the LR for the SRD of 0.02e
0.3 m3 s1 km2 (Fig. 3). To conﬁrm the variability of the LR in thisrange of the SRD, we compared the relationship between the LR
and the SRD obtained by the IMLM with that observed by a net
sampling that was conducted at the Noda Bridge across the Edo
River (Nihei et al., 2010). Details of this net sampling have alreadybeen published by Nihei et al. (2010), so the observation design is
explained only brieﬂy in Appendix C. The LR and the SRD were
calculated by respectively dividing the hourly inﬂow ﬂux measured
by the net sampling and the river discharge at each observation site,
by the catchment area that was taken from the start of the Edo
River to the Noda Bridge (2223.5 km2). The relationship between
the LR and the SRD obtained by the net sampling is shown in Fig. 3.
Consequently, the large variability of the LR for the SRD of 0.02e
0.3 m3 s1 km2 is reasonable because the LRs observed by the net
sampling were included within the 95% conﬁdence interval of theregression residuals, and also largely varied in the same range of
the SRD (Fig. 3). We consider that the large variability of the LR wascaused by the difference of the LR between the rising stage and thesubsiding stage, various cross sections of river channel in thecatchment area of the rivers and seasonal variations of the relationship between LR and SRD (e.g. ﬁrst ﬂush) (see Section 4.1).
3.3. Validation of hourly inﬂow ﬂuxes by a hindcast experiment
To validate the hourly inﬂow ﬂuxes, the net collected volume ofgrass was simulated based on the forward-in-time PTM. In thehindcast experiment, to also investigate the fate of grass on thesurface in the bay, monthly residual volume (i.e. volume of grassstaying in the bay) and monthly outﬂow (i.e. volume of grass
ﬂowed out of the bay) were computed. In this experiment, the netcollected volume by the port administrators was subtracted fromthe hourly inﬂow ﬂuxes because the MLIT cannot collect grass thathas already been collected by the port administrators. The numberof particles was determined by multiplying the hourly inﬂow ﬂuxes
by one hundred (i.e. the weight of a single particle is 0.01 m3).
The sources for the hindcast experiment were the grid points
along the western boundary of the HF radar coverage where theriver mouths of the three large rivers and/or outfalls are locatednearby (bold line in Fig. 1(c)), and the interval between the sources
is 500 m. The particles were homogeneously released into the bay
from each source on the hour. The particles released from eachsource were tracked until they were collected by the vessel or
ﬂowed out of the bay through the bay mouth (bold broken line in
Fig. 1(c)). The hindcasted volume was calculated by multiplying theweight per particle (i.e., 0.01 m3 per particle) by the number ofparticles located in the collection patch (see Section 2.1). Thus thehindcasted volume corresponds to the net volume of grass that wascollected on the date on which the tracks were recorded (i.e. values
within parentheses in Table 1).

Fig. 5. (a) Comparison of hindcasted volume of grass collected by the MLIT with theactual volume. (b) Time series of the monthly inﬂow ﬂux, the residual volume in thebay at the end of the month and the monthly outﬂow from the bay mouth. In January
and February 2009, the hindcast experiment could not be carried out because of
malfunction of the HF radar system (shaded in gray).

The monthly residual volume and the monthly outﬂow were
calculated by multiplying the weight per particle by the number ofresidual particles at the end of each month in the bay and the total
number of particles reaching the boundary along the bay mouth(bold broken line in Fig. 1(c)) during each month, respectively. In
the experiments, if some particles reached the boundaries of HF
radar coverage except the bay mouth, the re-drifting operation was
performed (see Appendix B).
The monthly hindcasted volume was compared with themonthly net volume actually collected by the MLIT (Fig. 5(a)).
Fig. 5(a) demonstrates that the monthly hindcasted volume indeed
varies consistently with the monthly actual volume except in June
2008. The deviation in June between the monthly hindcasted volume and the monthly actual volume is 13.3 m3. This overestimation
is caused by the daily hindcasted volume on 2 June 2008 (9.6 m3).
On this date, the many particles that accumulated along theboundaries of HF radar coverage in the Yokohama port area were
temporarily returned offshore by the northeastward tidal current
and were collected by the vessel near the boundaries of the
Yokohama port area in the hindcast experiments (star in Fig. 6(a)).
The re-drifting operation performed near the boundaries would be
one of the reasons for the overestimation. This paper does notfurther discuss the overestimation because the present PTM is
unable to track drifting particles out of the HF radar coverage.
Nevertheless, the monthly hindcasted volumes are reasonably
consistent with the monthly actual volume (Fig. 5(a)). Fig. 5(a) indicates that the hourly inﬂow ﬂuxes of grass are successfully estimated by the IMLM and the regression equation (i.e. upper left in
Fig. 3).
The time series of the monthly residual volume, the monthly
outﬂow and the monthly inﬂow ﬂux from the three large rivers (i.e.
the summation of the hourly inﬂow ﬂuxes during each month) are
shown in Fig. 5(b). The hindcast experiment revealed a seasonalvariation of the monthly residual volume in the bay: the volume
increased from April to August 2008, reaching 355 m3 at the end of
August. This corresponds to 36% of the ﬁve-month inﬂow (990 m3)
until the end of August. Conversely, residual grass (64% of the ﬁve-

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75

Fig. 6. Snapshot of the distribution of grass in the hindcast experiment and surface current pattern on 2 June (a) and 3 June (b). The gray shading and star show the quantity of grass
per unit area and collection point by the MLIT, respectively. The broken lines show the boundaries between the port area and the central bay.

month inﬂow) ﬂowed out of the bay until this month. It greatly
decreased in September 2008 and did not increase after October
2008 because of small inﬂow ﬂuxes. We consider that the seasonalvariation of the residual volume reﬂects that of the residual current
in Tokyo Bay (see Section 4.2).
3.4. Annual ﬂow of grass in Tokyo Bay
We consider the annual ﬂow of grass in Tokyo Bay as a simple,
one-dimensional ﬂow (Fig. 7). Fig. 7 shows the annual ﬂow
described based on the hindcast experiment. 39% of the annualinﬂow ﬂux was collected by the port administrators and the MLIT,
and the remaining grass (61% of the annual inﬂow ﬂux) would ﬂow
out of the bay during one year (Fig. 7). The true inﬂow ﬂux would belarger than our estimation which depends on the effort of clearance
services. If the MLIT could not completely clear the debris patches
due to missing grass and/or an overﬂow of the built-in bucket withthe grass (Fig. 2(a)), the estimation is underestimated. Nevertheless, the order of magnitude of the estimation is considered to bereasonable because of the following reasons: the vessel went backand forth inside a debris patch until no grass could be found; thedaily collected volume did not exceed the volume of the bucket(30 m3, see Section 2.1). In addition, the average daily collectedvolume in each month was signiﬁcantly related to theFig. 7. Schematic ﬂow diagram of grass in Tokyo Bay. The broken arrows show unknown ﬂow in this study.

corresponding monthly freshwater ﬂux (R ¼ 0.69, P < 0.05, see
Table 1), which indicates that larger parts of the debris patches
were collected.
On the other hand, in reality, the remaining grass in the central
bay is assumed to have three major fates other than ﬂowing out of
the bay (broken line in Fig. 7): (1) washing ashore; (2) ﬂowing backto the port areas and then being collected by the administrators; or(3) sinking to the seabed. Fate (1) would not be critical in the annual
ﬂow because the coastline of the bay is highly developed and mostof the natural coast has disappeared (Furukawa and Okada, 2006).
In addition, beached grass is eventually returned to the bay by tides
and/or waves during one year because almost the entire natural
coast is a tidal ﬂat.
Ignoring fate (2) would result in overestimation of the inﬂow
and outﬂow ﬂuxes. However, we assume that the collected volumeof grass ﬂowing back to the port areas was relatively small because
the time series of the daily volume collected by the port administrators (not shown) was signiﬁcantly correlated with that of theriver discharge of the three major rivers (R ¼ 0.73, P < 0.01). This
indicates that the port administrators have been collecting thegrass directly after it ﬂows into the bay from the rivers. Thus theoverestimated volume by ignoring fate (2) would be relatively
small.
At present, we do not have data for discussing the contributionof fate (3) (i.e. sinking process) to the annual ﬂow. We assume thatthe portion of grass ﬂowing in from rivers sinks because terrestrial
vegetation has been found by a trawl survey on the seabed of theSouthern California Bight (Moore and Allen, 2000). If grass is storedby sinking in the bay, it might contribute to the oceanic carbon
cycle just like terrestrial dissolved and particulate organic carbon(Hedges et al., 1997). To determine the contribution of terrestrial
natural debris to the marine ecosystem, we will estimate the ﬂux ofthe natural debris sinking to the seabed in a future work.
Although the volume collected by the MLIT and the port administrators accounts for 39% of the annual inﬂow ﬂux, we consider
that they could perform clean-up operations more effectively. For
example, grass was dense near the bay mouth on 3 June when the
MLIT collected grass near the bay head (Fig. 6(b)). If information onpatches of grass could be informed to the captain of the MLIT cleanup vessel, a larger amount of grass could be collected. Surface

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Fig. 8. (a) The time series of wind speed observed at Umihotaru by the Japan Coast Guard (diamond in Fig. 1(c)), (b) surface velocity measured by HF radar on the western line (solid
thin line in Fig. 1(c)) and (c) eastern line (broken thin line in Fig. 1(c)). Wind speed and surface velocity are the 14-day moving averages. The top and bottom of the vertical axis ofboth (b) and (c) are the bay head and the bay mouth, respectively.

current velocities are available from HF radar systems in quasi-realtime (Tokyo Bay Environmental Information Center; http://www.
tbeic.go.jp/radar_tbeic/index.asp). River levels used to calculate
the river discharge at the river mouth (see Section 2.4 or Nihei et al.
(2007b)) are also measured by the MLIT in quasi-real time (Water
Information System by the MLIT; http://www1.river.go.jp/). In the
future, we will construct a prediction system by applying the PTM
using quasi-real time surface current velocities and hourly inﬂow
ﬂuxes calculated by substituting the quasi-real time river discharge
in Eq. (2) developed in this study.
In this study, to facilitate the particle-tracking experiments, weselected grass that has low windage (i.e. the ratio of the sail area ofdebris to its subsurface depth) as target natural debris (see Section
2.1). In the future, we will develop a PTM that takes the windage
into account. The PTM with the windage effect would enable us topredict the movement of other natural debris with higher windage(e.g. wood and bamboo).

4. Discussion
4.1. Relationship between grass inﬂow ﬂux and river discharge
Although the determination coefﬁcient for the regression
equation established by the IMLM was low because of the large
variability of the LR for the SRD of 0.02e0.3 m3 s1 km2, a signiﬁcant relationship was found between the LR and the SRD (seeSections 3.1 and 3.2). The variability would be caused by: (1) adifference of the LR between the rising stage and the subsiding
stage, (2) various cross sections of river channel in the catchment

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area of rivers and (3) seasonal variations of the relationship between the LR and the SRD. We consider each of these in turn.
(1) The LRs obtained by the net sampling (Nihei et al., 2010)
were classiﬁed into two groups (i.e. the LRs in the rising stage andthose in the subsiding stage). The rising (subsiding) stage is deﬁned
when the SRD increases (decreases) during the net sampling. The
net sampling data indicates that the LRs in the rising stage were oneorder of magnitude larger than those in the subsiding stage (Fig. 3).
(2) The catchment area of the large rivers ﬂowing into the bay isvery large, and the river channels have been developed in the lower
reaches (a typical cross-section is shown in the lower-right diagramof Fig. 3), and not developed in the upper reaches (i.e. a simple
parabolic cross-section). The variability of the LR with the developed cross-section would temporally differ from that with a simple
parabolic cross-section (Nihei et al., 2010). (3) The abundance ofgrass in the river channel would depend on the season; grass ismore abundant in summer than in winter. These are important
issues when estimating inﬂow ﬂuxes of grass precisely. Thus the LR
does not consistently increase in proportion to the river discharge.
At present, we do not obtain LRs for SRD values larger than
0.57 m3 s1 km2 by the net sampling. It would be difﬁcult to obtain
LRs by the net sampling continuously because the personnel andcost required, especially during large ﬂood events as the SRD islarger than 0.57 m3 s1 km2. On the other hand, the IMLM canallow us to estimate LRs more easily than the net sampling because
data collected systematically by the MLIT and HF radar-derived
surface velocities are available. Thus, we can obtain LRs in large
ﬂood events and in every season on the SRDeLR diagram andimprove the coefﬁcient values (i.e. a and b in Eq. (2)) in the
regression equation. In a future work, we will establish an inﬂow
model that considers the seasonal variation (e.g. ﬁrst ﬂush) and the
response to large ﬂood events by obtaining the LRs through estimations by the IMLM in various years.
Long-term estimations of the LR will be useful for evaluating theeffects of river development or clean-up along river banks and ﬂood
plains in the upper reaches. The LRs would gradually decrease as aresult of taking such measures along river channels. And the IMLM
enables us to conduct the long-term monitoring of the LRs.
4.2. Seasonal variation of residual volume
In the hindcast experiment, we found a seasonal variation of themonthly residual volume: it gradually increased from April toAugust 2008, and then greatly decreased in September 2008. The
main cause of this variation would be a seasonal residual current in
the bay. Fig. 8 shows the time series of the 14-day moving averagesurface velocity along the western line (solid thin line in Fig. 1(c))
and the eastern line (broken thin line in Fig. 1(c)) along the axis ofTokyo Bay. The southwestward current is positive in Fig. 8. The
northeastward (southwestward) residual current along the western (eastern) line was generated in the range between 10 km and
20 km away from the bay head from the end of April to mid August(Fig. 8). This ﬁgure indicates that this current ﬁeld consisted of ananti-cyclonic circulation near the bay head, and the northeastward(southwestward) residual current was strong (weak) in the period
when a southwesterly wind was blowing (i.e. from June to mid
August). A snapshot of the residual velocity ﬁeld on 31 July is shownin Fig. 1(c) and indicates that the anti-cyclonic circulation iscentered on the eastern side of the bay. On the other hand, thesouthwestward residual current was consistently generated when anortheasterly wind was blowing (i.e. from mid August to
September).
The mechanism of generation of this residual current ﬁeld is
examined based on the balance between an anti-cyclonic circulation formed by the estuarine circulation (Fujiwara et al., 1997) and a77

wind-driven current (Hinata et al., 2010). According to Fujiwara
et al. (1997), the anti-cyclonic circulation is generated in the upper layer near the bay head by the horizontal divergence associatedwith upward entrainment, which is part of the estuarine
circulation.
The dependence of the wind-driven current was theoreticallyinvestigated using a linear steady-state analytical model based on
Ekman solutions by Hinata et al. (2010). Their theory is applicableto Tokyo Bay because the bathymetry of the bay is approximated bya triangular cross-section as the basin axis shifts westward(Fig. 1(c)). The magnitude of the vertical diffusivity coefﬁcient inTokyo Bay is estimated to be 104 m2 s1 (Guo and Yanagi, 1996).
When estimating the Ekman number (E) using the diffusivity coefﬁcient (K ¼ 104 m2 s1), the Coriolis parameter(f ¼ 8.44  105 s1) corresponding to the latitude of 35.5 and the
maximum water depth (h ¼ 20 m) in the central bay, the magnitudeis 102 (i.e. E ¼ K/fh2 ¼ 0.03). With this magnitude of Ekman
number, when the wind is blowing in the direction of the basin
axis, the surface wind-driven currents in the shallower area (i.e.
both coasts of the bay) and the deeper area (i.e. around the basinaxis) are the strong current and the weak current for the downwind
direction, respectively (see Fig. 10 in Hinata et al. (2010)).
Thus, the anti-cyclonic circulation was frequently generated by
the estuarine circulation from the end of April to mid August. In
particular, the northeastward (southwestward) current on thewestern (eastern) side became strong (weak) from June to mid
August due to the wind-driven current formed by the southwesterly wind (i.e. wind toward the bay head along the bay axis), and its
center shifted to the eastern side. On the other hand, the southwestward density-driven current intensiﬁed from mid August to
September because of the large inﬂow ﬂux of freshwater during aﬂood event (see Fig. 4(a)). During this event, the southwestward
residual current prevailed consistently in the whole bay due to thenortheasterly wind (i.e. wind toward the bay mouth along the bayaxis).
Consequently, the monthly residual volume increased from
April to August because grass was trapped in the bay due to theanti-cyclonic circulation. In particular, grass was easily trapped in
the bay because the northeastward residual current of the circulation became strong due to the southwesterly wind blowing from
June to mid August. The monthly residual volume greatly decreasedin September because most of the grass immediately ﬂowed out of
the bay from mid August to September due to the southwestward
residual current, which consisted of the density-driven current andthe wind-driven current generated by the freshwater inﬂow andnortheasterly wind, respectively.
5. Conclusions
We numerically estimated the inﬂow ﬂux of terrestrial grass,which accounted for 29% of ﬂoating macro-debris collected by the
Ministry of Land, Infrastructure, Transport and Tourism (MLIT), into
Tokyo Bay from April 2008 to March 2009 (F2008) based on an“inverse method using a Lagrange multiplier” (IMLM) in conjunction with a two-way particle-tracking model (two-way PTM). In the
numerical estimation, we used the high-frequency (HF) ocean
surface radar-derived surface current velocities and the amount ofgrass collected by the MLIT using clean-up vessels.
The estimated hourly inﬂow ﬂux was compared with the total
river discharge of the three large rivers ﬂowing into Tokyo Bay (EdoRiver, Ara River and Tama River). A signiﬁcant relationship between
the estimated loading rate (i.e. hourly inﬂow ﬂux/total catchment
area of the three large rivers (6571 km2); LR) and the speciﬁc riverdischarge (i.e. river discharge/total catchment area; SRD) was foundby regressing the LR against the SRD using Eq. (2) (R2 ¼ 0.23,

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P < 0.01, see Fig. 3). The hourly inﬂow ﬂuxes in certain periods that
could not be estimated by the IMLM because either the MLIT cleanup vessels did not operate or the HF radar malfunctioned, were
estimated using the regression equation between the LR and the
SRD. Consequently, at least 2115 m3 yr1 of the grass ﬂowed into
the bay annually, and the contribution of ﬂood events to the inﬂow
ﬂux of grass was larger than that of the inﬂow ﬂux of freshwater. In
the course of one year, 39% of grass ﬂowing into Tokyo Bay wascollected by the clean-up vessels in the bay, and 61% ﬂowed out of
the bay or sank to the seabed.
The low determination coefﬁcient for the regression equation
was due to the large variability of the LR for the SRD of 0.02e
0.3 m3 s1 km2 (Fig. 3). However, the large variability wasreasonable because the LRs observed by the net sampling conducted by Nihei et al. (2010) were included within the 95% conﬁdence interval of the regression residuals, and also largely varied in
the same range of the SRD (Fig. 3). We consider that one of thereasons for the large variability is seasonal variation of the LR (seeSection 4.1). At present, LRs in large ﬂood events (i.e. SRD larger
than 0.57 m3 s1 km2) have not been obtained. The IMLM will be
useful for establishing an inﬂow model that considers the seasonalvariation (e.g. ﬁrst ﬂush) and the response to large ﬂood events,
because the LRs are systematically estimated by the IMLM using HF
radar derived surface currents and data on debris collected by the
MLIT (see Section 4.1).
To validate our estimation, we carried out a hindcast experimentand showed that the monthly net volume of grass actually collectedby the MLIT was successfully reproduced by the experiment. This
indicates that, in general, the hourly inﬂow ﬂuxes of grass are
successfully estimated in this study. In addition, we demonstrated
the monthly residual volume in the bay and the monthly outﬂow
from the bay mouth through the hindcast experiment, and foundthat the volume varied seasonally: it gradually increased from April
to August 2008 and greatly decreased in September 2008. Thisseasonal variation depends on the surface residual current.
In the future, we will establish a prediction system to enablegrass to be collected more effectively by the MLIT and the port
administrators using HF radar-derived surface currents and theinﬂow model. In addition, we will estimate the sinking ﬂux ofnatural debris to help understand the role of natural debris inmarine ecosystems.
Acknowledgments
The authors thank Dr. S. Kako of Kagoshima University, Dr. S.
Kato of Toyohashi University of Technology and Dr. S. Aoki of Osaka
University for their valuable comments, the Chiba Port Ofﬁce of the
Ministry of Land, Infrastructure, Transport and Tourism and thePort Administrators for providing the collected data on ﬂoating
macro-debris, and Dr. A. Kuwae and Mr. E. Miyoshi for helping withthe laboratory experiments. We also thank Dr. E. Wolanski, editor ofthis paper, and anonymous reviewers; their detailed and instructive comments improved this paper considerably. This research was
supported by the Environment Research and Technology Development Fund (B-1007) of the Ministry of the Environment, Japanand by a Grant-in-Aid for Scientiﬁc Research (KAKENHI)(23656309, 25820234).
Appendix A
The voids between pieces of grass are included in the volume ofgrass measured at the home port. Therefore, to estimate the net
volume of grass, a “net ratio” (i.e., net volume/total volume
including the void volume) was measured by a simple experimentin our laboratory. These experiments were conducted using

approximately 30 L of sample grass that the MLIT collected invarious seasons. In the experiment, 10 L of sample grass wereplaced in a 15-L cylinder, then the cylinder was ﬁlled with water.
The volume of water that drained from the cylinder was measured
using a beaker with a scale. The net volume was then obtained bysubtracting the volume of drained water from the total volume. We
conducted this experiment three times using the same sample
grass, and determined the average net ratio as 0.3661.
Appendix B
Before identifying the source and estimating the inﬂow ﬂux, we
conducted particle-tracking experiments to calculate the monthly
residence time of the surface water masses; this time is used as thelongest time duration for the backward-in-time PTM experiments.
The particles were uniformly deployed at a spacing of 100 m in thearea covered by HF radar at 00:00 every day and were carried by
the HF radar-derived surface current. Speciﬁcally, the location (x, y)of particle X at time t þ Dt, where Dt is the time increment (300 s),
is given byXtþDt ¼ Xt þ UDt þqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
1vU
Dt 2 þ R 2Kh Dt ði; jÞ;
U$VH U þ
2
vt
(B.1)

where U [¼(u, v)] is the HF radar-derived surface current vector, Kh
is the horizontal diffusivity which is modeled with the Smagorinsky
formula for diffusion, i and j are unit vectors in the x (eastewest)
and y (northesouth) directions, respectively, and R is a random
number generated at each time step with an average and standard
deviation of 0.0 and 1.0.
We assumed that the particles reaching the bay mouth gridboxes (bold broken line in Fig. 1(c)) within each time step ﬂowed
out of the bay. If the particles reach other boundaries of HF radar
coverage, they are returned to their location in the previous time
step. This operation is repeatedly conducted until the particles return to offshore, and is referred to as “re-drifting operation”. The
particle tracking was performed daily until 90% of the deployedparticles ﬂowed out, and the daily residence time was determinedas the time until 90% of the particles ﬂowed out. The maximum of
the daily residence times in the month was used as the monthly
residence time. The monthly residence time ranged from 19 to 60
days. The particles deployed from June to July showed the longest
monthly residence time (60 days), and those deployed in
September showed the shortest residence time (19 days).
Appendix C
Nihei et al. (2010) conducted a net sampling at the Noda Bridge(black square in Fig. 1(b)) across the Edo River on 10e12 August
2009 and 8e9 October 2009. They collected debris on each river bysuspending a 2.5-cm mesh net with a mouth measuring 1 m  1 m
for 1e5 min, and measured the ﬂuxes of debris per unit widthcollected by the net. In the sampling, more than 94% of the collected
debris was grass. The net sampling was conducted at only thecenter point on the lateral cross section of the river because of the
difﬁculty of sampling at multiple positions on the bridge. To deﬁnea lateral distribution function of the ﬂux per unit width on eachobservation, video images were taken simultaneously at multiple
points on the bridges including the center point. The number ofclearly identiﬁable debris pixels in sequential images was counted
by eye. The ﬂuxes per unit width were linearly correlated with thenumber of pixels at the same point. The unit-width ﬂuxes at otherpoints except the center point were calculated using the linear

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T. Kataoka et al. / Estuarine, Coastal and Shelf Science 134 (2013) 69e79

correlation and the numbers of pixels at those points. The lateral
distribution function was then determined by linearly interpolating
the unit-width ﬂuxes for the in-between points. The hourly inﬂow
ﬂuxes were calculated by integrating the function for the riverwidth at the observation site (90 m).
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