Ocean dynamic processes causing spatially heterogeneous distribution of sedimentary caesium-137 massively released from the Fukushima Daiichi Nuclear Power Plant

Massive amounts of anthropogenic radiocaesium Cs that were released into the environment by the Fukushima Daiichi Nuclear Power Plant accident in March 2011 are widely known to have extensively migrated to Pacific Ocean sediment off of eastern Japan. Several recent reports have stated that the sedimentary Cs is now stable with a remarkably heterogeneous distribution. The present study elucidates ocean dynamic processes causing this heterogeneous sedimentary Cs distribution in and around the shelf off Fukushima and adjacent prefectures. We performed a numerical simulation of oceanic Cs behaviour for about 10 months after the accident, using a comprehensive dynamic model involving advection–diffusion transport in seawater, adsorption and desorption to and from particulate matter, sedimentation and suspension on and from the bottom, and vertical diffusion transport in the sediment. A notable simulated result was that the sedimentary Cs significantly accumulated in a swath just offshore of the shelf break (along the 50–100 m isobath) as in recent observations, although the seabed in the entire simulation domain was assumed to have ideal properties such as identical bulk density, uniform porosity, and aggregation of particles with a single grain diameter. This result indicated that the heterogeneous sedimentary Cs distribution was not necessarily a result of the spatial distribution of Cs sediment adsorptivity. The present simulation suggests that the shape of the swath is mainly associated with spatiotemporal variation between bottom shear stress in the shallow shelf (< 50 m depths) and that offshore of the shelf break. In a large part of the shallow shelf, the simulation indicated that strong bottom friction suspending particulate matter from the seabed frequently occurred via a periodic spring tide about every 2 weeks and via occasional strong wind. The sedimentary Cs thereby could hardly stay on the surface of the seabed with the result that the simulated sediment-surface Cs activity tended to decrease steadily for a long term after the initial Cs migration. By contrast, in the offshore region, neither the spring tide nor the strong wind caused bottom disturbance. Hence, the particulate matter incorporated with Cs, which was horizontally transported from the adjacent shallow shelf, readily settled and remained on the surface of the sediment just offshore of the shelf break.


Introduction
In March 2011, the Great East Japan Earthquake (moment magnitude M w 9.0) and subsequent huge tsunami caused a severe accident at the Fukushima Daiichi Nuclear Power Plant (1FNPP) operated by the Tokyo Electric Power Company (TEPCO).Massive anthropogenic radionuclides were thereby released from 1FNPP and extensively polluted the Pacific oceanic environment off of east Japan.The radiocaesium 137 Cs, one of the massively released radionuclides, was observed to reach a maximum O (10 5 ) Bq L −1 (we represent on the order of 10 n as O (10 n )) on the sea surface near 1FNPP just after the accident (early April 2011) (TEPCO, 2011).However, the seawater 137 Cs rapidly decreased down to less than O (10 2 ) Bq L −1 within a few months after the accident and finally O (10 −1 ) Bq L −1 as of the end of 2011 Published by Copernicus Publications on behalf of the European Geosciences Union.(TEPCO, 2011;MEXT, 2011;Buesseler et al., 2011Buesseler et al., , 2012)).By contrast, the sedimentary 137 Cs has been continuously detected with high activity (> O (10 2 ) Bq kg −1 ) in many sediment samples in the nearshore region off Fukushima and adjacent prefectures up to the present (e.g.Kusakabe et al., 2013;Thornton et al., 2013;Ambe et al., 2014;NRA, 2014a, b).There is no doubt that the 137 Cs remaining in the sediment is that which has migrated from the seawater to seabed.The total 137 Cs migration amount has been estimated as O (10 13 -10 14 ) Bq (Kusakabe et al., 2013;Ambe et al., 2014;Otosaka and Kato, 2014).Because 137 Cs has a very long half-life (30.2 years), we should fully understand the longterm oceanic behaviour of the massive sedimentary 137 Cs to predict its fate and future impact on the marine environment and ecosystem.
Recent measurements have made it clear that variation in the sedimentary 137 Cs is spatially heterogeneous and temporally slow.Thornton et al. (2013) made in situ measurements of continuous 137 Cs distributions on the seabed surface between November 2012 and February 2013 using a towed gamma-ray spectrometer.Their results revealed the following non-uniform sedimentary 137 Cs distribution.High 137 Cs activities (O (10 2 -10 3 ) Bq kg −1 ) on the sediment surface were detected in the nearshore region off 1FNPP (about 1-2 km east of the shore of 1FNPP) and offshore (beyond ∼ 12 km east of the shore), but low concentrations (O (10 1 ) Bq kg −1 ) were detected between those regions.Ambe et al. (2014) collected samples with high spatial resolution (5 latitude and longitude) in the nearshore region south of Fukushima in February and July 2012.They found a high-activity region in the shape of a swath with width ∼ 20 km along ∼ 100 m isobath (we call this region the "hotspot swath" hereinafter).Considering also more recent published and unpublished measurements (e.g.NRA, 2014a), the hotspot swath possibly extended along the shelf edge (50-100 m depths) from the coastal region off of southern Fukushima to northeastern Sendai Bay off of Miyagi Prefecture.These features of the sedimentary 137 Cs distribution could not be captured by sediment sampling with poor spatial resolution (e.g.MEXT, 2011;TEPCO, 2011;Kusakabe et al., 2013).
The seabed in the hotspot swath mainly consists of fine particulate matter such as silt and clay (Thornton et al., 2013;Ambe et al., 2014;NRA, 2014a).Caesium is widely known to be readily and almost irreversibly adsorbed on the surface of fine-grained particles.It is thereby understood that sediment in the swath readily accumulated the oceanic 137 Cs.In fact, many observational studies have reported that the sedimentary 137 Cs distribution is correlated with sediment properties, especially particle grain size (e.g.Otosaka and Kobayashi, 2013;Kusakabe et al., 2013;Otosaka and Kato, 2014).However, there have been few studies on accumulation mechanisms of the fine particulate matter and sedimentary 137 Cs in the hotspot swath.The future fate of sedimentary 137 Cs in this swath has not been predicted or discussed.
Our primary objective was to elucidate ocean dynamic processes causing the spatially heterogeneous sedimentary 137 Cs distribution, especially in the hotspot swath.The study was based on numerical simulation of oceanic 137 Cs behaviour in and around the shelf off Fukushima and adjacent prefectures during March and December 2011.
To achieve our objective, a numerical model of oceanic 137 Cs behaviour requires with the treatment of comprehensive dynamic processes such as advection-diffusion in seawater, adsorption and desorption on and from the particulate matter, and sedimentation and suspension to and from the seabed (e.g.Periáñez, 2003aPeriáñez, , b, 2004Periáñez, , 2008;;Kobayashi et al., 2007;Monte et al., 2009).Other numerical studies (Periáñez et al., 2012;Choi et al., 2013) simulated spatiotemporal variation in sedimentary 137 Cs after the 1FNPP accident using such comprehensive models.However, they did not discuss the hotspot swath.This may be because their simulations were limited to only the 4 months after the accident, probably because of insufficient observations.Misumi et al. (2014) developed a simulation model of 137 Cs transfer between bottom seawater and the seabed, focusing on sediment adsorptivity with caesium evaluated from sediment properties such as particle grain diameter, bulk density, and porosity.They thereby succeeded in reproducing major features of the observed heterogeneous distribution of sedimentary 137 Cs during the first year after the 1FNPP accident.However, their simulation treated only 137 Cs activity on the surface of the sediment, using bottom-seawater 137 Cs simulated by another model in advance (offline simulation, unlike the aforementioned two studies).In addition, the spatial distribution of sediment adsorptivity with 137 Cs as input data was used by the model.Hence, accumulation mechanisms of either the fine particulate matter or sedimentary 137 Cs in the hotspot swath could not be depicted by their simulations.
There is another issue to be addressed by the aforementioned earlier models.They did not take into account the vertical 137 Cs distribution in the sediment, i.e. model variable sedimentary 137 Cs was given in only one active layer of the seabed surface.The studies regarded the layer of sediment incorporated with 137 Cs as sufficiently thin (within a few centimetres).However, it has been reported that the vertical sedimentary 137 Cs distribution was not necessarily uniform and that there were sites where sedimentary 137 Cs activity in deeper sediment (> 10 cm) was higher than that in upper sediment (Otosaka and Kobayashi, 2013;Ambe et al., 2014;NRA, 2014a).These observations suggest that the vertical 137 Cs profile in the sediment should be considered in modelling sedimentation and suspension processes.For instance, suspension of the sediment (incorporating 137 Cs) occurs successively from its upper portions.Although numerical models of only sediment transport have been developed with consideration of the vertical profiles of sediment properties in the seabed (e.g.Reed et al., 1999;Lesser et al., 2004;Blaas et al., 2007), there have been few models for vertical movement of other substances intricately connected with those properties.
There is also a severe problem in that data on the sediment property spatial distribution immediately after the 1FNPP accident, necessary for such simulation, are extremely limited because of the huge tsunami.
Our previous study (Higashi et al., 2014) developed a comprehensive model for simulating oceanic 137 Cs behaviour in both seawater and seabed, with consideration of vertical 137 Cs transport in the sediment.We then roughly assumed that sediment matter in the entire simulation domain had ideal properties such as identical bulk density, uniform porosity, and particle aggregates of a single grain diameter.The reason why we used this assumption was not only because spatiotemporal variation of sediment properties just after the tsunami disturbance was unknown but also because the assumption enabled direct simulation of vertical 137 Cs behaviour in the sediment.This type of assumption has also been used in other models (Kobayashi et al., 2007;Choi et al., 2013), except for the 137 Cs behaviour in sediment.Our earlier simulations using the developed model agreed reasonably well with the sampling of 137 Cs activity in both seawater and sediment off eastern Japan in the Pacific during March and December 2011.However, we could not effectively simulate the heterogeneous sedimentary 137 Cs distribution mainly because of a lack of spatial resolution.
We performed a downscaling simulation of oceanic 137 Cs behaviour using the usual one-way nesting method to resolve the heterogeneous sedimentary 137 Cs distribution, especially in the hotspot swath.The present simulation also used the aforementioned assumption of ideal sediment properties in the entire domain, for the same reasons.The model and the numerical procedure are described in Sect. 2. Simulated results of the spatiotemporal 137 Cs distributions in seawater and sediment within the nested region are shown in Sect. 3 as compared with observations to evaluate model performance.In Sect.4, we discuss ocean dynamic processes causing the spatially heterogeneous distribution, especially in the hotspot swath, and include model uncertainties.

Outline
The numerical model in the present study was online-coupled with a hydrodynamic model (Sect.2.2) and an oceanic 137 Cs behaviour model of seawater (Sect.2.3) and sediment (Sect.2.4) (Higashi et al., 2014).The function of the hydrodynamic model was to simulate three-dimensional oceanic currents, temperature, salinity, pressure, and others.The oceanic 137 Cs behaviour models of seawater and sediment dealt with spatiotemporal variations in concentrations of 137 Cs and particulate matter capable of adsorbing the 137 Cs. 137 Cs in our model was classified into two phases: dissolved 137 Cs and particulate 137 Cs, which was defined as 137 Cs adsorbing on the particulate matter.The oceanic 137 Cs behaviour model of seawater (hereinafter, "the seawater 137 Cs model") was used to simulate 137 Cs advectiondiffusion under ocean current conditions evaluated by the hydrodynamic model and simultaneous 137 Cs reactions such as adsorption/desorption on/from suspended particulate matter, settling, and radioactive decay (Fig. 1a).The oceanic 137 Cs behaviour model of the sediment (hereinafter, "the sediment 137 Cs model") simulated sedimentation/suspension of 137 Cs and particulate matter between bottom seawater and surface sediment and subsequent changes in the vertical 137 Cs distribution in the seabed (Fig. 1).To connect the seawater and sediment 137 Cs models through sedimentation/suspension at the bottom interface, we used the aforementioned assumption of ideal sediment (i.e.particle aggregates with a single grain diameter, identical density, and uniform porosity), whose properties were equivalent to silty clay over the entire simulation domain.In the model, 137 Cs migrates from seawater to sediment through the following sequential processes: suspension of particulate matter from the seabed caused by erosion, vertical mixing of both suspended particulate matter and dissolved 137 Cs, formation of particulate 137 Cs through adsorption of dissolved 137 Cs on the suspended particulate matter, and sedimentation of the particulate 137 Cs on the bottom (Fig. 1a).
We carried out a regional-scale simulation of oceanic behaviour of the 137 Cs released from 1FNPP during March and December 2011.To simulate the heterogeneous sedimentary 137 Cs distribution in and around the shelf off Fukushima and adjacent prefectures, a high-spatial-resolution analysis was needed.In addition, because our target area is within the Kuroshio-Oyashio Interfrontal Zone (Yasuda et al., 1996) where there are strong currents and mesoscale eddy circulations, the model domain had to be sufficiently wide to simulate these essential dynamics.We therefore used a one-way nesting method for downscale simulation from a large area of the northwestern Pacific (Region-1) to a fine-resolution area (Region-2) (Fig. 2a).Region-1 covered 138.0-148.0• E and 32.0-41.0• N with horizontal resolutions of 4.5 km in longitude and 4.4 km in latitude.Region-2 covered 140.4-144.0• E and 35.2-39.0• N with horizontal resolutions 1.5 km in both longitude and latitude.Vertical layers in both regions were set to 47 levels in the seawater, from the sea surface to 6000 m depth, with thickness between 2 m (near the sea surface) and 500 m (near 6000 m depth).There were 42 levels in the sediment from the seabed surface to 1 m depth, with thickness from 0.01 m (near the seabed surface) to 0.05 m (near 1 m depth).Bathymetry was obtained by spatially interpolating gridded water-depth data of JTOPO30, provided by the Marine Information Research Center (MIRC), Japan Hydrographic Association.

Hydrodynamic model
The hydrodynamic model was originally developed and applied to several fields in our previous studies (e.g.et al., 2011, 2013).This model was based on the threedimensional hydrostatic Boussinesq equations, solved by the finite difference method using a horizontal collocated and vertical z-level grid (e.g.Ushijima et al., 2002).A free seawater surface as a vertical moving boundary was traced by the volume-of-fluid (VOF) method (Hirt and Nichols, 1981).Vertical mixing was evaluated using the latest turbulenceclosure scheme (Furuichi et al., 2012;Furuichi and Hibiya, 2015), which was an improved version of the Nakanishi and Niino (2009) scheme.Horizontal eddy diffusion was calculated by the Smagorinsky (1963) formula.Momentum and heat exchanges between ocean and atmosphere, which were the seawater surface boundary conditions, were evaluated using the Kondo (1975) method.For these evaluations, we used the following meteorologi-cal data at/above the sea surface: hourly atmospheric pressure, wind velocity, air temperature, specific humidity, and precipitation from the Grid Point Value of Mesoscale Model (GPV/MSM) of the Japan Meteorological Agency (JMA).Six-hourly downward solar and long-wave radiation data were from the JMA Climate Data Assimilation System (JC-DAS).
In the Region-1 simulation, we specified daily-mean data of salinity and temperature at the lateral boundaries, reanalysed by FRA-JCOPE2 (the Japan Coastal Ocean Predictability Experiment 2 developed by Japan Agency for Marine-Earth Science and Technology in collaboration with Fisheries Research Agency) (Miyazawa et al., 2009).The FRA-JCOPE2 data were also used for simple threedimensional nudging of salinity and temperature to involve observed/assimilated features of geostrophic phenomena in our simulation.Reference data for the nudging were 10-day moving average time series of the FRA-JCOPE2 results.A parameter of nudging timescale was set to 20 days.The Region-2 simulation used the same methods for the lateral boundaries and nudging of temperature and salinity as in the Region-1 simulation, but the hourly Region-1 simulations provided the input data instead of FRA-JCOPE2.
Sea-surface elevation at the open boundaries in the Region-1 simulation was from a composite of mean level and tidal anomaly.The former was from the FRA-JCOPE2 daily data and the latter from hourly data produced by the ocean tide model NAO.99Jb (Matsumoto et al., 2000).Hourly seasurface height from the Region-1 simulation was used for the Region-2 boundary condition.To generate tidal current radiation through the boundaries, the Flather (1976) method was implemented in the simulations for both regions.Because the present simulations eventually indicated that the tide was an important factor in the heterogeneous sedimentary 137 Cs distribution (see discussion in Sect.4), we attempted to verify the simulated tidal amplitude by comparing to observations (Supplement Fig. S1).However, observations were very limited during the simulation period, because most tidal gauges offshore of east Japan were damaged by the tsunami.

Seawater 137 Cs model
The seawater 137 Cs model was used to simulate spatiotemporal variations in dissolved 137 Cs, particulate 137 Cs, and suspended particulate matter in the seawater.The model was based on the following advection-diffusion-reaction equations that were used in several studies (e.g.Kobayashi et al., 2007;Periáñez, 2008;Choi et al., 2013) with the same threedimensional grid as in the hydrodynamic model: where F represents the unsteady advection-diffusion terms, expressed as C d and C p are activities of the dissolved (Bq m −3 -water) and particulate 137 Cs (Bq kg −1 -dry) respectively; m is concentration of the suspended particulate matter (kg-dry m −3water); w p represents settling velocities of the suspended particulate matter and particulate 137 Cs (m s −1 ); k 1 m and k −1 are kinetic transfer coefficients of adsorption (s −1 ) and desorption (s −1 ) respectively; λ is a radioactive decay constant (s −1 ); u, v and w are three-dimensional seawater currents (m s −1 ); A x and A y are horizontal eddy-diffusion coefficients (m 2 s −1 ); K z is the vertical eddy-diffusion coefficient (m 2 s −1 ); φ is volumetric seawater content in a simulation grid, as a VOF function ranging from 0 (empty) to 1 (filled) (m 3 -water m −3 -grid); volumes of the suspended particulate matter and particulate-137 Cs are negligible in the seawater.
The first term on the right side in Eqs. ( 2) and (3) indicates settling of the particulate 137 Cs/suspended particulate matter in the seawater.The second/third terms in Eqs. ( 1) and ( 2) represent the rate of 137 Cs adsorption/desorption on/from the suspended particulate matter.Variables u, v, w, A x , A y , K z , and φ were evaluated over time by the hydrodynamic model.
Values of parameters k 1 m , k −1 , and w p are shown in Table 1.k 1 m and k −1 were derived from other simulations (Periáñez, 2008;Kobayashi et al., 2007).w p was confirmed as a sensitive parameter for the horizontal dispersion of sedimen-tary 137 Cs by our sensitivity analyses.Nevertheless, the value used in other studies (e.g.Kobayashi et al., 2007;Choi et al., 2013) had a wide range (O(10 −1 -10 2 ) m day −1 ).Although w p of the fine particulate matter is also known to be variable depending on its concentration (e.g.Sternberg et al., 1999), we treated it as a constant tuning parameter.
Inflow conditions of the dissolved 137 Cs, particulate 137 Cs, and suspended particulate matter must be given at the seasurface boundary in Eqs. ( 1)-( 3) respectively.We considered the 137 Cs inflow through two pathways: direct discharge from 1FNPP and atmospheric deposition.We treated inflow 137 Cs as in the dissolved phase.These source data were referred to Tsumune et al. (2012) for time series of direct discharge from 1FNPP (total of 3.5 PBq until the end of May 2011) and Morino et al. (2011) for spatiotemporal variation in atmospheric deposition, simulated by an atmospheric chemical-transport model (total 2.3/1.5 PBq in Region-1/2 through the end of April 2011).However, our preliminary experiments using these data indicated that simulated 137 Cs activities, especially in surface seawater, were much less than observed in all of Region-2, such that both sources were believed to be underestimated overall.In fact, these amounts were much smaller than a recent evaluation by Miyazawa et al. (2013) (direct discharge 5.5-5.9PBq through 6 May 2011, atmospheric deposition 5.5-9.7 PBq within 12-62 • N and 108-180 • E through 6 May 2011).Although their estimation was based on comparison between seawater surface 137 Cs in their ocean-atmosphere simulations and that of field observations, their oceanic 137  crease.Furthermore, spatiotemporal variation of atmospheric 137 Cs deposition over the ocean, which has been estimated by numerical simulation in several studies besides Miyazawa et al. (2013) and Morino et al. (2011), had relatively great uncertainty.These total depositions also had wide variation (e.g. 5 PBq within 30.5-48.0 • N, 127.0-154.5 • E through the end of April, Kawamura et al., 2011;7.6PBq in the North Pacific through the end of April, Kobayashi et al., 2013;28 PBq in the oceans through 20 April, Stohl et al., 2012).This difference may principally be caused by the source parameter of 137 Cs emission from 1FNPP to atmosphere (e.g.8.8 PBq, Terada et al., 2012;13 PBq, Chino et al., 2011, 35.9 PBq, Stohl et al., 2012) and wet/dry deposition schemes (e.g.Stohl et al., 2012).The present simulation used source data that were 1.65 times the direct discharge from 1FNPP of Tsumune et al. (2012) and 6.00 times the atmospheric deposition of Morino et al. (2011) (Fig. 3a).As a result, total direct discharge was 5.9 PBq through the end of May.Total atmospheric deposition on the sea surface was 13.8/9.2PBq in Region-1/2 through the end of April.Although this simple scaling reduced the discrepancy between observed and simulated seawater surface 137 Cs, we could not validate the 137 Cs inflow conditions in detail because neither the direct discharge nor the atmospheric deposition can be measured directly.
We ignored 137 Cs loading from the land as a source because its amount, which has been estimated at 0.0075 PBq of 134 Cs, is regarded as nearly equivalent to the 137 Cs amount through the end of October 2011 (Otosaka and Kato, 2014).This was much smaller than that of the direct discharge and atmospheric deposition.We also neglected particulate matter loading from the land because of a lack of available data.This may impose some limitation on our simulation, because the validity of that neglect is not well known.
At the bottom boundaries in the seawater 137 Cs simulation, diffusion flux of the dissolved 137 Cs and sedimentation/suspension fluxes of the particulate 137 Cs and suspended particulate matter, which were evaluated by the sediment 137 Cs model described in Sect.2.4, were specified.At the lateral boundaries, the three variables in the Region-1 simulation were set to 0. We used the hourly Region-1 results in the Region-2 domain.

Sediment 137 Cs model
The sediment 137 Cs model was used to simulate the vertical 137 Cs distribution in the seabed and sedimentation and/or suspension (erosion) at the bottom boundary.This model was based on the vertical one-dimensional transport equations for particulate and dissolved substances in the sediment (e.g.Fossing et al., 2004;Sohma et al., 2008).Lateral transport into the sediment was negligible.To solve the 137 Cs transport equations under the sedimentation/suspension conditions, it is necessary to trace the free boundary of the sediment surface, which changes with time on the basis of mass balance of the sedimentary particulate matter.If the usual finite difference method on a Cartesian coordinate (z axis in Fig. 1b) were used, its numerical procedure would be complicated in spite of the idealised sediment.To avoid such complication, we applied a relative vertical coordinate z , defined as distance from the sediment surface at any time (Fig. 1b).In addition, interaction between the bottom current and topological change of the sediment surface was ignored, and the ideal sediment assumption was used.The vertical transport equations were thus transformed into where m is dry sediment bulk density (kg-dry m −3sediment); γ is volumetric water content (m 3porewater m −3 -sediment), where (1-γ ) indicates volumetric solid content (m 3 -solid m −3 -sediment); ρ p is particle density (kg-dry m −3 -particle); C d is dissolved 137 Cs activity in porewater (Bq m −3 -porewater); C p is particulate 137 Cs activity (Bq kg −1 -dry) in the sediment; D d and D p are diffusion coefficients of the dissolved (m 2 s −1 ) and particulate 137 Cs (m 2 s −1 ) in the sediment respectively; and w s is vertical displacement of the sediment surface per unit time (m s −1 ).Equation ( 7) is a stationary solution of the partial-differential transport equation of the particulate matter satisfying the ideal sediment assumption.The second terms on the left side of Eqs. ( 5) and ( 6) represent parallel downward/upward translation of the vertical profiles of dissolved and particulate 137 Cs as much as the sedimentation/suspension thickness (Fig. 1b).Because sediment bulk density and porosity were defined as constant parameters by the ideal sediment assumption, the relationship between the rate of sedimentation/suspension and w s can be simply expressed by the following linear expression: where sus m and sed m are suspension (kg-dry m −2 s −1 ) and sedimentation (kg-dry m −2 s −1 ) fluxes of the particulate matter respectively.They are evaluated by where m b is suspended matter concentration in the bottom seawater (kg-dry m −3 -water), E is a suspension (erosion) coefficient (kg m −2 s −1 ), τ b is bottom friction (N m −2 ), and τ cr is critical shear stress (N m −2 ).τ b is calculated using "the law of the wall" from the bottom current (e.g.Deltares, 2012) in the hydrodynamic model, expressed as where ρ b is bottom seawater density (kg m −3 -water), κ is the von Kármán constant (= 0.4), z b is thickness of the seabottom grid (m), u b and v b are currents in the x and y directions on the sea-bottom grid (m s −1 ) respectively, and z 0 is roughness length of the seabed (m).Whereas Eqs. ( 9) and ( 10) are simple equations for sediment transport, they have generally been used in studies such as in coastal engineering (e.g.Blaas et al., 2007).Sedimentation and erosion of the particulate 137 Cs are similarly expressed by where sed mC p and sus mC p are sedimentation and suspension rates of the particulate 137 Cs (Bq m −2 s −1 ) respectively and C pb and C ps are particulate 137 Cs activity in the bottom seawater (Bq kg −1 -dry) and in surface sediment (Bq kg −1 -dry) respectively.
A list of parameters in the sediment 137 Cs model is also given in Table 1.We used k −1 and k 1 m in that model that were identical to those in the seawater 137 Cs model.These values were confirmed valid by the simulated sedimentary 137 Cs, which was consistent with little dissolution and nearly irreversible adsorption from and on the sediment in other studies (e.g.Otosaka and Kobayashi, 2013).The particulate phase (> 99 % of the sedimentary 137 Cs) dominated the dissolved phase in the sediment during the simulation term.Sediment physical properties such as particle density, volumetric water content, the suspension coefficient, and critical shear stress were selected as values representative of fine particulate matter (e.g.silt and clay).Sedimentary diffusion coefficients D m and D p usually consist of molecular diffusion and/or bioturbation (e.g.Fossing et al., 2004;Sohma et al., 2008).These coefficients were taken from the literature (Fossing et al., 2004), but their effects on the simulated result of sedimentary 137 Cs were found to be slight.
Net flux of particulate 137 Cs evaluated from Eqs. ( 12) and (13) was given as the surface seabed condition of Eq. ( 6) and bottom boundary of Eq. ( 2).Similarly, net flux of particulate matter from Eqs. ( 9) and ( 10) was specified at the bottom boundary in Eq. (3).Exchange of dissolved 137 Cs between bottom seawater (Eq. 1) and surface seabed (Eq.5) was calculated from the diffusion equation.The diffusion coefficient was derived from bottom seawater turbulent and sedimentary bioturbation.Adsorption of dissolved 137 Cs in bottom seawater on surface sediment may occur through the diffusion process in our model.At the bottom boundaries of Eqs. ( 5) and ( 6), we specified flux conditions as advection-outflow at the sedimentation or zero-inflow at the suspension if deeper 137 Cs activity was assumed 0. These fluxes were consistent with mass balance of the particulate matter expressed by the identical Eq. ( 7).However, there is an issue in the method, in that Eq. ( 7) cannot be restricted to the suspended amount of sediment matter; i.e. it is possible that the fine particulate matter is infinitely and endlessly supplied from deeper levels.Therefore, the present procedure using the relative verticalaxis z and uniform sediment assumption, which facilitates simulation of the vertical profile of sedimentary 137 Cs, probably overestimates the suspension in regions whose seabed does not actually have sufficient suspendible particulate matter.

Results
Here we show simulated variation of spatiotemporal 137 Cs in both seawater and sediment in Region-2 and describe model performance and uncertainty based on comparison to observation.To evaluate model performance, we used two statistical indexes: factor (FAn) and fractional bias (FB) (e.g.Draxler, 2006;Draxler et al., 2013) as described in Appendix A. FAn is defined as the percentage of number of simulated results within a certain factor n of a measured value (i.e.within a range from n −1 -to n-times the measurements).A larger value indicates better estimation.FB represents normalized model bias in a range from −2 to 2, with positive/negative values indicating overestimation/underestimation.Evaluation results of the statistical indexes for the sea-surface 137 Cs, sediment-surface 137 Cs, and vertical profile of sedimentary 137 Cs are summarised in Supplement Tables S1-S4.

Seawater 137 Cs dispersion
To investigate performance of the seawater 137 Cs model, simulated 137 Cs activities on the sea surface (= C d + mC p ; however, the sea-surface mC p was negligible) were compared with observed data.For this comparison, we used TEPCO monitoring data (TEPCO, 2011) at the nearshore sites shown in Fig. 4j, where time series were sufficient.Observations at stations W-1 and W-2 were within the same simulation grid (Fig. 4a and j), because they are very close.
Sea-surface 137 Cs simulated by the model largely agreed with observed data (Figs. 4 and S2).The average FA2 at all stations, which had a relatively large value of 52.2 %, also indicates good model performance (Table S1).This agreement was mainly attributable to adjustment of the amount of 137 Cs inflow through atmosphere deposition and direct discharge from 1FNPP (mentioned in Sect.2.3).However, all FB values in Table S1 became negative, indicating that the simulations still somewhat underestimated the sea-surface 137 Cs.In particular, relatively large discrepancies between the simulations and observations were found in the initial period between the end of March and mid-April (Fig. 4).These discrepancies would affect initial 137 Cs sedimentation in the simulation.The results imply that the amount of actual 137 Cs inflow exceeded that input to the simulation.
Spatiotemporal variation in sea-surface 137 Cs strongly depended on atmospheric deposition prior to the end of March and afterward on direct discharge from 1FNPP (Figs. 3 and  4).Early in April, seawater 137 Cs reached a peak O(10 3 -10 4 ) Bq L −1 along the coast near 1FNPP (Fig. 4a-c) and O( 102 ) Bq L −1 15 km offshore (Fig. 4d-i).There was a rapid decline of activity from mid-April to the beginning of May and a gradual decrease afterward (Fig. 4a-i).The decrease in seawater 137 Cs was caused by significant dispersion from the coastal region to the open ocean (Fig. S2).As mentioned in Sect. 1, many studies have discussed the spatiotemporal 137 Cs distribution and its detailed physical background on the basis of numerical simulations (Kawamura et al., 2011;Tsumune et al., 2012Tsumune et al., , 2013;;Masumoto et al., 2012;Choi et al., 2013;Miyazawa et al., 2012Miyazawa et al., , 2013)).Hence, we do not address the seawater 137 Cs in detail hereafter.It stands to reason that there was no earlier simulation that quantitatively agreed with our spatiotemporal distribution of seawater 137 Cs because of differences in numerical procedures and/or simulation conditions.Thus, we confirmed that our seawater 137 Cs dispersion (Figs. 4 and S2) had qualitative features similar to the earlier simulations.For instance, our simulation tended to underestimate sea-surface 137 Cs southeast of 1FNPP, such as at stations W-8 through W-10 (Fig. 4g-i and FB in Table S1) per the earlier simulations (Kawamura et al., 2011;Tsumune et al., 2012;Miyazawa et al., 2013).

Spatiotemporal 137 Cs distribution on surface of sediment
To evaluate the reproduction performance of the sediment 137 Cs model, simulated 137 Cs on the sediment surface was compared with observations (Figs.5-7 and Tables S2 and  S3).We mainly used sediment sampling data from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) and TEPCO.TEPCO sampling stations were near the shore of Fukushima Prefecture (Fig. 2c), and MEXT monitoring stations were offshore of Miyagi through Ibaraki Prefectures (Fig. 2b).Detailed information on MEXT measurements was given by Kusakabe et al. (2013).It was noted that TEPCO data were published in units Bq kg −1 -wet at the time, while others were in Bq kg −1 -dry.Spatiotemporal variations of the sediment-surface 137 Cs were comparable with the observations in both coastal and offshore regions (Figs.5-7).Station averages of FA2, which are 40.7 % for the offshore MEXT stations (Table S2) and 30.1 % for the coastal TEPCO stations (Table S3), indicate tolerable model performance.Simulated sediment-surface 137 Cs activities increased dramatically in the first 3 months at most of the stations (Figs. 6 and 7) but, unfortunately, this cannot be sufficiently verified because of a lack of observations during that period.Afterward, activities remained stable or decreased steadily.These temporal changes in sedimentsurface 137 Cs activities indicate that reproduction performance for the sediment-surface 137 Cs was largely determined by the initial 137 Cs migration from seawater to seabed.The simulation overestimated some sediment-surface 137 Cs activities, especially in the region northeast of 1FNPP such as at MEXT stations B1 and C1 (Fig. 6b and c) in Sendai Bay and TEPCO stations 5 and 6 (Fig. 7d) near the coast of northern Fukushima where even FA5 values were 0.0 % (Tables S2 and S3).It was believed that the main cause of these overestimations was the uniform application of the ideal sediment assumption to the entire simulation domain.As mentioned in Sect.2.4, our model possibly overestimated the amount of particulate matter suspended from the seabed, especially in regions whose sediment does not actually have sufficient suspendible particulate matter.The suspended particulate matter is important in 137 Cs migration from seawater to seabed in our model, because 137 Cs in seawater cannot sink toward the bottom unless it is transformed from dissolved to particulate phase by adsorbing on the suspended particulate matter (Fig. 1a).Hence, it is believed that the excess particulate matter suspended from the seabed resulted in overestimation of the sediment-surface 137 Cs.Indeed, the region where the simulation overestimated sediment-surface 137 Cs was dominated by coarse sand outcrops in surveys prior to the powerful tsunami (Aoyagi and Igarashi, 1999).In addition, sediment sampling after the tsunami indicated that the surface sediment had low water contents, which correspond to coarse particles at MEXT stations B1 and C1 (Kusakabe et al., 2013).
Despite the aforementioned limitation, our model succeeded in reasonably reproducing the hotspot swath (Fig. 5j), consistent with the recent observations (Thornton et al, 2013;Ambe et al., 2014) described in Sect. 1.The hotspot swath could not be captured by the sediment sampling with coarse spatial resolution, such as that of TEPCO (2011) and MEXT (2011), as mentioned in Sect.
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay    used the ideal sediment assumption over the entire simulation domain.That is, spatial distributions of sediment adsorptivity with caesium input data were not input to the model, in contrast to the simulation of Misumi et al. (2014).Sequential processes causing the hotspot swath simulated by our model are discussed in detail in Sect. 4.

Vertical 137 Cs profile in sediment
It is important to understand the performance and uncertainty of our sediment 137 Cs model by comparing observed and simulated vertical profiles of sedimentary 137 Cs.However, we could not accomplish this adequately, because there were only a few data available in the study area in 2011.Among those, we used observations of Otosaka and Kobayashi (2013) and Otosaka and Kato (2014).The for-  137 Cs profiles (red lines) and observed (black lines) by (a-t) Otosaka and Kobayashi (2013) and (u-x) Otosaka and Kato (2014).Values in parentheses show observed water depth.mer were from a narrow nearshore region (26-95 m depths) off Ibaraki Prefecture (Fig. 2c).Their samples were from the upper 10 cm of sediment and cut into two layers, upper (0-3 cm) and lower (3-10 cm).The latter sampling stations were offshore (105-1175 m depths) of Fukushima and Ibaraki prefectures, and samples were upper from 10 cm of sediment and cut into 1 cm thick sections.Although the latter survey was over a wider area than the former, we selected observations at only four stations (Fig. 2b) where sedimentary 137 Cs concentration m C p was considerably greater than 50 kBq m −3 .It is an issue that the above two observations covered only a small part of Region-2, not including notable regions such as the nearshore off 1FNPP and Sendai Bay.
The comparison in the nearshore region off Ibaraki Prefecture (Fig. 8a-t) indicates that simulated sedimentary 137 Cs in the upper 3 cm layer largely agreed with the observations within one order of magnitude.The station-average FA5 is 95.0 %, also showing good model performance, but the station-average FB is a positive value of 0.72, indicat-ing some overestimation (Table S4a).Discrepancy between simulated and observed sedimentary 137 Cs in the lower layer (3-10 cm) was less than that in the upper layer; station averages of FA2 and FB in the lower layer were superior to those in the upper layer (Table S4a).By contrast, results in the offshore region (Fig. 8u-x and Table S4b) show that our model clearly overestimated sedimentary 137 Cs in the lower layers (4-30 cm), although the simulated result in the upper layers (0-4 cm) agreed well with the observations.In particular, at the Otosaka and Kato (2014) stations O-K9 and O-K1, simulated sedimentary 137 Cs dispersion into the sediment reached about 20 cm depth, although observation was confined to 5 cm depth (Fig. 8u, x).Although these results imply that sedimentation of the suspended matter and particulate 137 Cs were somewhat overestimated in the offshore region by our model, this did not matter much because the sedimentary 137 Cs amounts were very small there.
Notably, the simulation successfully reproduced an observed feature of the vertical sedimentary 137 Cs profile, i.e.
Biogeosciences, 12, 7107-7128, 2015 activity in the deeper sediment was significantly higher than that in the upper in the nearshore region, such as at the Otosaka and Kobayashi (2013) station O-S4 (Fig. 8i).Processes causing such a vertical profile in the sediment are described in Sect.4.2.

Total amount of sedimentary 137 Cs and its uncertainty
The total 137 Cs amount rapidly increased at the beginning of April in our simulation because of atmospheric deposition and direct discharge from 1FNPP (Fig. 3).After that, it stabilised at ∼ 12 PBq by the end of May and strongly declined to 4.3 PBq at the end of 2011.The latter decrease was caused by the seawater 137 Cs dispersed from Region-2 to the open ocean.Sedimentary 137 Cs also increased steadily until onset of the significant seawater dispersion but suddenly declined at the end of May.This rapid decrease resulted from short but strong suspension induced by an extratropical cyclone that originated as typhoon 201102 (SONGDA) and passed over the southern part of Region-2.Afterward, the sedimentary 137 Cs rapidly recovered, indicating that the suspended 137 Cs returned to the sediment.Such behaviours of sedimentary 137 Cs before and after the cyclone were also simulated by Choi et al. (2013).
In our simulation, total sedimentary 137 Cs was 0.10 PBq (0.66 % of total 137 Cs inflow) in the upper 3 cm layer, 0.40 PBq (2.6 % of total 137 Cs inflow) in the upper 10 cm layer, and 3.2 PBq (21 % of total 137 Cs inflow) in the entire seabed over all of Region-2 (1.4 × 10 5 km 2 ) at the end of 2011.Kusakabe et al. (2013) estimated 0.042-0.052PBq of total sedimentary 137 Cs between September and December 2011 in the upper 3 cm seabed off Miyagi, Fukushima, and Ibaraki prefectures (2.2 × 10 4 km 2 domain) on the basis of the MEXT (2011) observations.Otosaka and Kato (2014) estimated total sedimentary 134 Cs.This was regarded as nearly equivalent to 137 Cs amount at 0.20 ± 0.06 PBq (decay corrected to 11 March 2011) within the region less than 200 m depth (1.5 × 10 4 km 2 domain) in October 2011, using their sampling data in upper 10 cm sediments and MEXT observations.Accounting for the difference in study area, our results of sedimentary 137 Cs amounts in the upper layers were almost comparable to the two studies above.However, the simulated amounts in the upper 3 and 10 cm layers were only 3 and 13 % of total sedimentary 137 Cs respectively; the remainder was present in deeper sediment.
We could not adequately validate the simulated result of large 137 Cs amount in the deeper layers.One of the reasons was a lack of observations in deeper sediment, necessary for validation after the accident, especially near 1FNPP where massive sedimentary 137 Cs remains even today (described in Sect.3.3).We described in Sect.3.2 that the simu-
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Sendai Bay
Another reason why we could not validate the sedimentary 137 Cs amount in the deeper layer was uncertainty related to our simulation conditions.As mentioned in Sect.2.4, because we used the ideal sediment assumption, our simulation would overestimate sedimentary suspension unless the actual seabed consisted mainly of fine particles.In fact, that simulation overestimated some sediment-surface 137 Cs activities to the northeast of 1FNPP and Sendai Bay, whose seabed was dominated by coarse sand (mentioned in Sect.3.2).The simulated amount of sedimentary 137 Cs in the 30 × 45 km rectangular region in Sendai Bay (141.03-141.37 • E, 37.71-38.11• N in Fig. 9) reached 0.52 PBq (16% of total sedimentary 137 Cs).Furthermore, our result included uncertainty of 137 Cs inflow conditions, especially the atmospheric depo-sition (Sect.2.2).Clearly, the total amount of sedimentary 137 Cs directly depends on that of 137 Cs inflow.

Influences of tide and strong wind on sedimentary 137 Cs on shallow shelf
Suspension of particulate matter from the seabed was important in determining spatiotemporal variation of sedimentary 137 Cs in our model, as mentioned in Sect.3.2.This significant suspension is generally induced by strong bottom friction, caused by ocean currents, tides, wind waves, and others.
From linear long-wave theory, current velocity is in inverse proportion to the square root of water depth; thus, influences such as tide and wind on bottom shear stress tend to increase with water depth (but also depend on local bottom topography of course).Our simulation confirmed that strong bottom friction exceeding the critical shear stress (0.10 N m −2 in the simulation) in the shallow region (< 50 m depths) tended to occur more frequently than offshore (50-200 m depths) (Fig. 10).Extremely strong bottom friction is also found in the deep region (> 800 m depths) (Fig. 10).This is caused by the strong Kuroshio Current.As a result, sediment suspension occurred there at all times in our simulation (Fig. 11).This simulated result was probably in disagreement with actual suspension there.However, the direct effect of this on the simulated 137 Cs behaviour in and around the shelf re- The simulation indicates that the tide caused significant suspension and sedimentation of the particulate matter in the nearshore region from Sendai Bay to 1FNPP and off southern Ibaraki (Figs. 10a and b and 11a and b).Bottom friction in the nearshore region varied periodically, and the variation period of strong bottom friction exceeding the critical shear stress was approximately 2 weeks, corresponding to the spring-neap tidal variation (Fig. 12a).The same periodic changes were found in temporal variations of the vertical profiles of suspended matter concentration and particulate 137 Cs activity in seawater above the seabed (Fig. 12c  and d).The simulated results revealed that this tidal bottom disturbance caused suspension during spring tide and sedimentation during neap tide (Fig. 11a and b).Particulate matter and particulate 137 Cs suspended from the seabed were not believed to be transported over a large horizontal scale, because they rapidly settled on the bottom for several days (Fig. 12c and d).However, the long-term periodic tidal disturbance made the suspension/sedimentation distribution heterogeneous (Fig. 11d).We also found similar periodic changes in simulated sediment-surface 137 Cs activities at some nearshore TEPCO stations (Figs.7a, b and c and  12e).It is believed that these temporal changes -perhaps including observed ones as at TEPCO station 22 (Fig. 7a) -resulted from the periodic tidal disturbance.In addition, this long-term tidal influence steadily and strongly reduced sediment-surface 137 Cs activities (Figs. 7a,b,c,f,and 12a), whose rate of decrease tended to be greater in the shallower region.Periáñez et al. (2012) indicated little tidal effects on the initial 137 Cs dispersion and sedimentation on the basis of their numerical experiments, but our simulation suggests that this finding should be confined to the initial 3 months after the accident, and that the tide is very important for long-term sedimentary 137 Cs behaviour in the shallow region.
Strong wind also had considerable but occasional impacts on the bottom in the shallow region.In particular, the extratropical cyclone at the end of May increased the bottom shear stress to well beyond the critical value (Fig. 10c).As a result, simulated sediment-surface 137 Cs activities at many stations near 1FNPP (e.g.TEPCO stations 1, 2, 4, 11, 14, and 20-23 in Fig. 7) suddenly decreased about an order of magnitude.As mentioned in Sect.3.1, the suspended 137 Cs rapidly returned to the seabed afterward, across all of Region-2 (Fig. 3).However, the sediment-surface 137 Cs activities did not necessarily return to levels before the strong wind event (TEPCO stations 1, 2, and 4 in Fig. 7).On the contrary, we found that the latter sediment-surface 137 Cs be-came much greater than before at some sites (TEPCO stations 18 and 29 in Fig. 7).These results suggest that the strong wind event considerably enhanced horizontal transport of sedimentary 137 Cs and bottom suspension.
The bottom disturbance caused by the tide or strong wind did not occur in every shallow region (< 50 m depths) because of the seabed topography and other factors.In the narrow nearshore region from south Fukushima to north Ibaraki, bottom friction did not increase even during extratropical cyclone passage (Fig. 10c).The Otosaka and Kobayashi (2013) station O-S4, where apparent downward movement of sedimentary 137 Cs was found in both observation and simulation (Fig. 8i), was located just in that region.This area was where the bottom disturbance rarely occurred; if anything, the sedimentation slightly dominated the suspension over a long period (Fig. 11d).This indicates that the apparent vertical transport of sedimentary 137 Cs found at station O-S4 was caused by relatively fresh suspended particulate matter settling on earlier sediment containing substantial 137 Cs.It is inconceivable that the amount of sedimentation over only several months became so large under the stable seabed condition.Although this is probably caused by the uncertainty related to the ideal sediment assumption as mentioned in Sect.4.1, this may have been possible in the unstable seabed state just after the extraordinary disturbance of the tsunami.

Sedimentary 137 Cs behaviour in offshore region
In contrast to the shallow region, in the offshore region along the shelf break (50-200 m depths), impacts of the tide and strong wind on the bottom disturbance were much weaker (< 50 m depths).Even the extratropical cyclone that caused the strong bottom disturbance in the shallow region at the end of May could not increase bottom friction beyond the critical shear stress (Figs.10c and 12f), so little sediment was suspended (Figs.11c and 12h).Although strong vertical mixing then occurred in seawater, dissolved 137 Cs activity in bottom seawater did not increase (Fig. 12g), in contrast to the shallow result (Fig. 12b).Nevertheless, sedimentary 137 Cs activities in the offshore region began to increase significantly just after that strong wind event (MEXT stations C3, E1, D1, G0, G1, I0, I1, J1 in Fig. 6, and E1 in Fig. 12j).This increase in sedimentary 137 Cs resulted from sedimentation of particulate 137 Cs (Fig. 12i), which was suspended and horizontally transported into and from the adjacent shallow shelf by the wind event.This horizontal transport is supported by the fact that both concentrations of suspended matter and particulate 137 Cs suddenly increased in the upper seawater, without bottom suspension or upward diffusion (Fig. 12h and i).
The bottom friction barely exceeded the critical shear stress caused by the spring-neap tidal variation in the offshore region as well (Figs. 10 and 12f).Hence, the particulate 137 Cs, once settled on the seabed, was rarely moved horizontally over a long period.This result is consistent with the fact that both simulated and observed sediment-surface

Hotspot swath
The hotspot swath in our simulation was just offshore of the shelf break (along the 50-100 m isobath) off southern Fukushima Prefecture through northern Sendai Bay at the end of 2011 (Fig. 5j).After the 1FNPP accident, the region of high sedimentary 137 Cs activity gradually expanded from south of 1FNPP to north in and around the shelf (< 100 m depths) by June (Fig. 5a-e).Afterward, in the shallow shelf (< 50 m depths), the sediment-surface 137 Cs significantly decreased because of the periodic tidal disturbance causing sediment suspension, horizontal transport in the seawater, and/or apparent downward movement in the seabed.Meanwhile, in the offshore region (50-100 m depths), the sedimentary 137 Cs that settled after being horizontally transported from the shallow region during the extratropical cyclone at the end of May remained largely stable because of rare bottom disturbance.The present simulation suggests that these were the sequential processes causing the hotspot swath and that its shape is closely related to spatiotemporal variation between bottom shear stress on the shallow shelf and that offshore of the shelf break.Although our simulation includes quantitative uncertainty as mentioned in Sect.4.1, these processes are at least qualitatively reasonable.This is because 137 Cs accumulation in the hotspot swath is governed mainly by ocean dynamics, i.e. spatiotemporal variation of bottom shear stress.That is, the quantitative uncertainty in simulation conditions would affect amounts of suspension and subsequent horizontal transport of sedimentary 137 Cs on the shallow shelf but not the 137 Cs accumulation location offshore.
As mentioned in Sect. 1, Misumi et al. (2014) developed a sediment-surface 137 Cs model by considering the spatial distribution of sedimentary adsorptivity with caesium.They thereby reproduced the spatially heterogeneous distribution in sediment-surface 137 Cs, as in our simulation.Although the processes causing this distribution in their simulation appeared distinct from those in ours, they were not unrelated.This was because the ease/difficulty of sedimentation and accumulation of suspended particulate matter with high adsorptivity were related to the rare/frequent occurrence of strong bottom friction (Figs. 10 and 11).It is believed that our successful reproduction of the hotspot swath resulted from rough consistency between the actual distribution of seabed properties (e.g.Aoyagi and Igarashi, 1999) and the simulated spatial variation of bottom friction.

Conclusions
To clarify ocean dynamic processes causing the massive heterogeneous sedimentary 137 Cs distribution that persists in and around the shelf off Fukushima and adjacent prefectures, we numerically simulated oceanic 137 Cs behaviour for about 10 months after the 1FNPP accident.We succeeded in simulating that distribution, especially the hotspot swath just offshore of the shelf break (along the 50-100 m isobath) shown by recent observations (Thornton et al., 2013;Ambe et al., 2014;NRA, 2014a).However, quantitative validation of sedimentary 137 Cs amount was inadequate.The result suggests that several spatiotemporal characteristics of the sedimentary 137 Cs are produced by ocean dynamics.
The simulation provided new and meaningful findings to help predict the sedimentary 137 Cs fate.The most important suggestion is that the shape of the hotspot swath is largely due to spatiotemporal variation between bottom shear stress in the shallow shelf and that offshore of the shelf break, corresponding to regional-scale bathymetry.Although sediment in the hotspot swath consists of fine particulate matter with high caesium adsorptivity (Thornton et al., 2013;Ambe et al., 2014;NRA, 2014a), the shape of the swath is not directly attributable to that caesium adsorptivity of the sediment.Our simulation indicated that sediment with sufficient fine particulate matter resulted only from the fact that this matter was horizontally transported from the adjacent shelf and readily settled there.It was also found that the accumulation process of sedimentary 137 Cs in the hotspot swath was the same as that of the particulate matter.These results indicate that this swath was where the particulate matter (incorporated with 137 Cs) was readily accumulated, because it was in a boundary region between frequent and rare occurrence of bottom disturbance caused by tides and/or strong wind.It is therefore predicted that large amounts of sedimentary 137 Cs that are currently in the hotspot swath will remain stable or be submerged by additional sedimentation of fresh particulate matter.
Our simulation also produced significant findings regarding sedimentary 137 Cs behaviour on the shallow shelf.There, the simulated bottom disturbance tended to occur frequently because of the periodic spring tide and occasional strong winds, steadily decreasing simulated sediment-surface 137 Cs per several observations.The simulation indicated that repeated bottom disturbances reducing sediment-surface 137 Cs over the long term caused sedimentary 137 Cs to not only be horizontally transported to the offshore region but also vertically toward deeper sediment.Consequently, in our simulation, relatively large amounts of 137 Cs in deeper sediment remained on the shallow shelf, especially near 1FNPP, even about 10 months after the 1FNPP accident.Hence, total sedimentary 137 Cs at the end of 2011 reached 3.2 PBq, and 87 % of that was present below the 10 cm layer.If our simulation is correct, 137 Cs in deeper sediment would be much greater than in upper sediment and would remain stable over a long period.However, the simulated sedimentary 137 Cs amount in the deeper layers would include relatively large uncertainty at present.In future work, we will improve the model for quantitative simulation of the spatiotemporal variation of fine particulate matter in both seawater and sediment.We will perform long-term simulations including the tsunami disturbance to validate the model, using recent observations of vertical sedimentary 137 Cs distribution.
The Supplement related to this article is available online at doi:10.5194/bg-12-7107-2015-supplement.

Figure 3 .
Figure 3.Time series of (a) 137 Cs inflow rates of atmospheric deposition and direct discharge from 1FNNP and of (b) total amounts of 137 Cs in seawater and sediment over entire simulation domain of Region-2.Both time series are denoted by stacked graph.
Figure 4. (a)-(i) Time series of observed and simulated seawater-surface 137 Cs at TEPCO (2011) stations W-1 through W-10.(j) Location of the stations and an example of spatial distributions in observed (colour square plot) and simulated 137 Cs (colour shading) on sea surface (11 April 2011).Arrows show daily-mean current on sea surface.Black star indicates location of 1FNPP.Black square plots indicate observations of non-detected seawater 137 Cs activities.

1 .
The ability to simulate such a heterogeneous distribution of sedimentary137 Cs was very interesting and valuable, because the simulation www

Figure 5 .
Figure 5. Spatiotemporal variations of observed (colour plots of squares, circles, triangles, and rhombi) and simulated (colour shading) sediment-surface 137 Cs.Dates of simulated/observed results are denoted by bold/normal characters.Observed activities of MEXT (2011) (squares), TEPCO (2011) (circles), Otosaka and Kato (2013) (triangles), and Ministry of the Environment (MOE, 2011) (rhombi) are indicated using same colour table as the simulated result.Black star indicates location of 1FNPP.Contours show water depth (m) according to JTOPO30 (MIRC).Units of TEPCO observations are Bq kg −1 -wet, whereas those of the others including the simulation are Bq kg −1 -dry.

Figure 6 .
Figure 6.Time series of observed (circular plots) and simulated (lines) sediment-surface 137 Cs at MEXT (2011) stations.Locations of observations are shown in Fig. 1b.Water depths are according to Kusakabe et al. (2013).

Figure 7 .
Figure 7. Time series of observed (circular plots) and simulated (lines) sediment-surface 137 Cs at TEPCO (2011) stations.Locations of observations are shown in Fig. 1c.Longitude axis has units Bq kg −1 -wet.Water depths are according to JTOPO30 (MIRC).

www.biogeosciences.net/12/7107/2015/ Biogeosciences, 12, 7107-7128, 2015 gion
(< 200 m depths), such as sedimentary 137 Cs activity, was slight.This was because particulate matter suspended from the deep sediment had difficulty being transported upward beyond several tens of metres above the seabed by vertical mixing.Therefore, this suspended matter rapidly settled on the seabed within the deep region or dispersed to the open ocean because of the Kuroshio Current in our simulation (no figure shown).

Biogeosciences, 12, 7107-7128, 2015 www.biogeosciences.net/12/7107/2015/ H. Higashi et al.: Ocean dynamics causing heterogeneous sedimentary 137 Cs 7123 137
Cs at many offshore stations remained stable or slightly decreased after the strong sedimentation during extratropical cyclone passage (Figs.6 and 12j).Although there were considerable changes in sediment-surface 137 Cs at MEXT offshore stations J3 and L3 (Fig.6j and l), this was because of seasonal variation in strong bottom disturbance caused by the Kuroshio Current.