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  <front>
    <journal-meta>
<journal-id journal-id-type="publisher">BG</journal-id>
<journal-title-group>
<journal-title>Biogeosciences</journal-title>
<abbrev-journal-title abbrev-type="publisher">BG</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Biogeosciences</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1726-4189</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>

    <article-meta>
      <article-id pub-id-type="doi">10.5194/bg-13-499-2016</article-id><title-group><article-title>Ecosystem model-based approach for modeling the dynamics of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
transfer to marine plankton populations: application to the western North
Pacific Ocean after the Fukushima nuclear power plant accident</article-title>
      </title-group><?xmltex \runningtitle{Ecosystem model-based approach for modeling the dynamics of ${}^{{137}}$Cs
transfer}?><?xmltex \runningauthor{M.~Belharet et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Belharet</surname><given-names>M.</given-names></name>
          <email>mokrane.belharet@gmail.com</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Estournel</surname><given-names>C.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Charmasson</surname><given-names>S.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Institut de Radioprotection et de Sûreté nucléaire,
ENV-PRP/SESURE/LERCM, 83507, CS20330,<?xmltex \hack{\newline}?> La Seyne-Sur-Mer, France</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Laboratoire d'aérologie (LA), UMR5560, CNRS – Université de
Toulouse, UPS, 14 avenue Edouard Belin,<?xmltex \hack{\newline}?> 31400 Toulouse, France</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">M. Belharet (mokrane.belharet@gmail.com)</corresp></author-notes><pub-date><day>25</day><month>January</month><year>2016</year></pub-date>
      
      <volume>13</volume>
      <issue>2</issue>
      <fpage>499</fpage><lpage>516</lpage>
      <history>
        <date date-type="received"><day>18</day><month>May</month><year>2015</year></date>
           <date date-type="rev-request"><day>26</day><month>June</month><year>2015</year></date>
           <date date-type="rev-recd"><day>20</day><month>December</month><year>2015</year></date>
           <date date-type="accepted"><day>27</day><month>December</month><year>2015</year></date>
      </history>
      <permissions>
<license license-type="open-access">
<license-p>This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/3.0/">http://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions><self-uri xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016.html">This article is available from https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016.html</self-uri>
<self-uri xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016.pdf</self-uri>


      <abstract>
    <p>Huge amounts of radionuclides, especially <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs, were released into the
western North Pacific Ocean after the Fukushima nuclear power plant (FNPP)
accident that occurred on 11 March 2011, resulting in contamination of the
marine biota. In this study we developed a radioecological model to estimate
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in phytoplankton and zooplankton populations
representing the lower levels of the pelagic trophic chain. We coupled this
model to a lower trophic level ecosystem model and an ocean circulation model
to take into account the site-specific environmental conditions in the area.
The different radioecological parameters of the model were estimated by
calibration, and a sensitivity analysis to parameter uncertainties was
carried out, showing a high sensitivity of the model results, especially to
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in seawater, to the rates of accumulation from
water and to the radionuclide assimilation efficiency for zooplankton. The
results of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in planktonic populations simulated
in this study were then validated through comparison with the data
available in the region after the accident. The model results have shown that
the maximum concentrations in plankton after the accident were about 2 to
4 orders of magnitude higher than those observed before the accident,
depending on the distance from FNPP. Finally, the maximum <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs absorbed
dose rate for phyto- and zooplankton populations was estimated to be about
5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and was, therefore, lower
than the predicted no-effect dose rate (PNEDR) value of
10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> defined in the ERICA assessment approach.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p>Huge amounts of radionuclides, especially <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs, were released into the
western North Pacific Ocean after the Fukushima nuclear power plant (FNPP)
accident that occurred on 11 March 2011 (UNSCEAR, 2014).</p>
      <p>Plankton populations, which play a prominent role in the input of many
pollutants into the aquatic food chain and are potentially important in the
biogeochemical cycling of various radionuclides in the ocean
(Fowler and Fisher, 2004), were contaminated by these releases.</p>
      <p>Data on <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs in phytoplankton are rare especially due to difficulties
in sampling. However, recently Baumann et al. (2015) reported <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs data
on suspended matter rich in marine phytoplankton sampled in June 2011 off the
Japanese coast (Buesseler et al., 2012) and suggested that phytoplankton
could have been a substantial source of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs for zooplankton after the
Fukushima accident.</p>
      <p>Within a few months following the accident, zooplankton collected at some
locations of the western North Pacific showed enhanced levels of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs,
even for the samples collected at the farthest locations from FNPP, such as
the S1 (47<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 160<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E, 1900 km from FNPP) and K1
(30<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 145<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> E, 900 km from FNPP) stations where the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs in zooplankton observed 1 month after the accident were 2
orders of magnitude higher than before 11 March. Three months after the
accident, Buesseler et al. (2012) reported that the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations
in zooplankton located at 300–600 km from FNPP were 2 to 3 orders of
magnitude higher than before the accident. Even 10 months after the accident,
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations observed in zooplankton, at 600–2100 km away
from FNPP, were still about 1 to 2 orders of magnitude higher than in the
pre-accident period (Kitamura et al., 2013).</p>
      <p>Although these field data provide a general overview of the plankton
contamination levels after the FNPP accident, the lack of information on the
contamination's temporal and spatial evolution and the need for
understanding the fate of radionuclides in the marine ecosystem, necessary
for the assessment of environmental and human health consequences, require
the adaptation of a modeling method.</p>
      <p>The simple linear method based on the bioconcentration factor, defined as the
ratio of the amount of radionuclide in the organism divided by the
concentration in the water, is the most commonly used method to assess the
radionuclide concentration in marine biota (IAEA, 2004). Despite its
simplicity, this method is not appropriate in an accident situation since the
main underlying hypothesis – i.e., an equilibrium state between the
radionuclide concentration in water and biota – is not reached.</p>
      <p>Rates of both radionuclide uptake and loss are known to be affected by
species metabolism, and it has been reported that a large part of the radionuclides
accumulated by heterotrophic marine biota comes from food
(Thomann, 1981; Kasamatsu and Ishikawa, 1997; Zhao et al., 2001; Rowan,
2013). Therefore, the characterization of the radionuclide distribution in
these components should be accompanied by ecological information such as
species composition in the ecosystem, population densities, rates of primary
and secondary production, food ingestion rate, etc. Such parameters are
generally influenced by various environmental factors (light, temperature,
salinity, food availability, marine hydrodynamics) that vary quickly from one
site to another according to geographic location and morphological
characteristics (bathymetry, distance from the shore). Moreover, movements of
radionuclides associated with planktonic material are subject to physical
transport processes, and are affected by bioaccumulation, retention and
subsequent food chain transfer, vertical migration of many species, and
passive sinking of biodetritus. It follows that the relative importance of
these biological transport mechanisms will be a function of the oceanic
biomass at any given location (Fowler and Fisher, 2004).</p>
      <p>Consequently, the effective consideration of all these factors implies that
the modeling approach of radionuclide transfer to marine biota should be
driven by an ecosystem model describing different ecological and physical
processes and transfers between organisms in the food web
(Erichsen
et al., 2013; Koulikov and Meili, 2003; Kryshev and Ryabov, 2000; Kumblad et
al., 2006; Sandberg et al., 2007).</p>
      <p>In this study, we developed a generic radioecological model to estimate the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in marine plankton populations. This model was
applied to study <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs transfer to plankton populations in the western
North Pacific after the FNPP accident and to compare it with the
pre-accident steady-state situation. The NEMURO ecosystem model
(Kishi et al., 2007) was used to
simulate the planktonic population dynamics in the area and to estimate
different ecological fluxes. It was coupled to the hydrodynamic SYMPHONIE
model (Marsaleix et al., 2008) in order to
account for the impact of hydrodynamic and hydrologic conditions on the
dynamics of organic and inorganic materials. The <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations
in seawater after the accident were obtained from dispersion numerical
simulations.</p>
</sec>
<sec id="Ch1.S2">
  <title>Material and methods</title>
      <p>The modeling method used in this study aims to estimate the activity
concentration of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs in different plankton populations, to analyze its
sensitivity to the model parameter uncertainties, and to understand the
transfer mechanism and its relation with the ecological functioning of the
living organisms. It is based on three different models: (1) a 3-D
hydrodynamic model simulating the movement of dissolved and particulate state
variables of the ecosystem model and estimating the physicochemical
characteristics of seawater (temperature, salinity), (2) an ecosystem model
simulating the plankton biomasses and their different metabolic rates and
fluxes (e.g., primary production, excretion, grazing, mortality, etc.), and
(3) a mechanistic radioecological model simulating the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentration in different plankton populations.</p>
<sec id="Ch1.S2.SS1">
  <title>Hydrodynamic modeling</title>
      <p>We used the 3-D SYMPHONIE ocean circulation model (Marsaleix et
al., 2009a, b, 2012). This model has been widely used in the Mediterranean
Sea to study different marine processes related to coastal circulation
(Estournel et al., 2003; Petrenko et al., 2008), sediment transport (Ulses et
al., 2008), larval dispersal (Guizien et al., 2012) and plankton population
dynamics (Auger et al., 2011; Herrmann et al., 2014). This model has also
been used, for the first time, in the western North Pacific Ocean to study
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs dispersion after the FNPP accident (Estournel et al., 2012).</p>
      <p>The numerical configuration used in this study was the same as the one
reported in detail by Estournel et al. (2012), with 30 vertical irregular
levels based on the sigma coordinate system and characterized by an increase
of resolution near the surface. The horizontal grid (Fig. 1) corresponds to
an orthogonal curvilinear system, with variable resolution increasing
linearly with the distance from FNPP (0.6 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 0.6 km near FNPP and
5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km at the open lateral boundaries off Japan).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><caption><p>Numerical domain and its bathymetry. The dashed lines indicate the
limits of the three regional areas: the subtropical region (latitude &lt; 35<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N), the transition region (35<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N &lt; latitude &lt; 39<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N), and the subarctic region
(latitude &gt;39<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N).</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f01.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS2">
  <title>Ecosystem modeling</title>
      <p>To properly represent the dynamics of the plankton populations exposed to
the radioactive contamination in our study area, the NEMURO (North-Pacific
Ecosystem Model for Understanding Regional Oceanography) biogeochemical
model (Kishi et al., 2007) was
applied. This model, which has been extensively used in the western North
Pacific region
(Aita
et al., 2003; Hashioka and Yamanaka, 2007; Komatsu et al., 2007), consists
of 11 state variables with two size classes of phytoplankton: small
phytoplankton (PS) representing small species such as coccolithophorids and
flagellates, and large phytoplankton (PL) representing diatoms. It includes
three size classes of zooplankton: small zooplankton (ZS) such as ciliates
and foraminifera, large zooplankton (ZL) (copepods) and predatory
zooplankton (ZP) such as krill and/or jellyfish. The other model state
variables are: nitrate (NO<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, ammonium (NH<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, silicate
(Si(OH)<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, particulate organic nitrogen (PON), biogenic silica (Opal)
and dissolved organic nitrogen (DON). The model structure and the different
parameter values are presented in detail in
Kishi et al. (2007).</p><?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Radioecological modeling</title>
<sec id="Ch1.S2.SS3.SSS1">
  <title>Phytoplankton</title>
      <p>The knowledge of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs accumulation mechanisms in aquatic primary
producers, mainly phytoplankton, is still vague. However, previous studies
underlined that it is mostly transported into the cell by active absorption
since it is an alkali metal analog of potassium
(Fukuda et al., 2014). Therefore, the dynamics of
radionuclide concentration in phytoplankton populations is determined by a
balance between radionuclide concentration in seawater, the biological
half-life of clearance, and different processes affecting the population
biomasses:

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>w</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced close=")" open="("><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>m</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msubsup><mml:mi>m</mml:mi><mml:mtext>p</mml:mtext><mml:mtext>G</mml:mtext></mml:msubsup></mml:mfenced><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E1"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>d</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>p</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>p B</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>p P</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>p</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where [Cs]<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>p</mml:mtext></mml:msub></mml:math></inline-formula> is the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in the phytoplankton
population (Bq g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight), <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>w</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>
is the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in the seawater (Bq L<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the phytoplankton biomass (<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>mol N L<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
the <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>m</mml:mi><mml:mtext>p</mml:mtext><mml:mtext>G</mml:mtext></mml:msubsup></mml:mrow></mml:math></inline-formula> are, respectively, the natural
mortality rate and the rate of mortality due to the grazing (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>p B</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>p P</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are, respectively, the
biological depuration rate of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs from phytoplankton and the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs physical decay rate (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs accumulation rate by the phytoplankton
(L g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p>In the NEMURO ecosystem model, the phytoplankton population growth rate is
given by
              <disp-formula id="Ch1.E2" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:msub><mml:mi>B</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mtext>exc</mml:mtext><mml:mtext>p</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mtext>p</mml:mtext><mml:mtext>G</mml:mtext></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mtext>exc</mml:mtext><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are, respectively, the
phytoplankton excretion and respiration rates (d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), and <inline-formula><mml:math display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> the gross
primary production rate (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. After rearrangement we obtain from
Eqs. (1) and (2):
              <disp-formula id="Ch1.E3" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mtext>p</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>w</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mfenced close=")" open="("><mml:mi>P</mml:mi><mml:mo>-</mml:mo><mml:mtext>exc</mml:mtext><mml:mo>-</mml:mo><mml:mi>R</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>p</mml:mtext></mml:msub><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S2.SS3.SSS2">
  <title>Zooplankton</title>
      <p>The dynamics of radionuclide concentration in consumers reflects the
variation over time of the radionuclide intake from both water and food.
Therefore, the differential equation describing the dynamics of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentration in the zooplankton populations can be written as

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mtext>z</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>z</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>w</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>+</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mtext>AE</mml:mtext><mml:mtext>z</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mtext>N</mml:mtext></mml:munderover><mml:msub><mml:mtext>IR</mml:mtext><mml:mrow><mml:mi>j</mml:mi><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced open="[" close="]"><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E4"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi>m</mml:mi><mml:mtext>z</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msubsup><mml:mi>m</mml:mi><mml:mtext>z</mml:mtext><mml:mtext>G</mml:mtext></mml:msubsup><mml:mo>+</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:msub><mml:mi>B</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>z</mml:mtext></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

              where <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mi>j</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>w</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> represent, respectively, the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in
zooplankton, in prey index <inline-formula><mml:math display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula> (Bq g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ww) and in seawater (Bq
L<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the zooplankton biomass (<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>mol N
L<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs accumulation rate by
zooplankton population (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, AE<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>z</mml:mtext></mml:msub></mml:math></inline-formula> is the assimilation
efficiency of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs by zooplankton, IR<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>j</mml:mi><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is the ingestion
rate of prey index <inline-formula><mml:math display="inline"><mml:mi>j</mml:mi></mml:math></inline-formula> by the zooplankton, <inline-formula><mml:math display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> represents the number of prey
populations present in the area that are available for the zooplankton,
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>z B</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>z P</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are, respectively, the
biological depuration rate (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs by the zooplankton
and the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs radioactive physical decay rate (d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>), and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:msubsup><mml:mi>m</mml:mi><mml:mtext>z</mml:mtext><mml:mtext>G</mml:mtext></mml:msubsup></mml:mrow></mml:math></inline-formula> are, respectively, the zooplankton
natural and grazing mortality rates (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p>The zooplankton population growth rate is modeled in the NEMURO model as
follows:
              <disp-formula id="Ch1.E5" content-type="numbered"><mml:math display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:msub><mml:mi>B</mml:mi><mml:mtext>z</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mfenced close=")" open="("><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mtext>N</mml:mtext></mml:munderover><mml:msub><mml:mtext>IR</mml:mtext><mml:mrow><mml:mi>j</mml:mi><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:mfenced><mml:mo>-</mml:mo><mml:msub><mml:mtext>exc</mml:mtext><mml:mtext>z</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mtext>ege</mml:mtext><mml:mtext>z</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mtext>z</mml:mtext></mml:msub><mml:mo>-</mml:mo><mml:msubsup><mml:mi>m</mml:mi><mml:mtext>z</mml:mtext><mml:mtext>G</mml:mtext></mml:msubsup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where exc<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>z</mml:mtext></mml:msub></mml:math></inline-formula> and ege<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>z</mml:mtext></mml:msub></mml:math></inline-formula> are, respectively, the excretion
and egestion rates (d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. After rearrangement of equations modeled in
the NEMURO model we obtain
              <disp-formula id="Ch1.E6" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mtext>exc</mml:mtext><mml:mtext>z</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mtext>ege</mml:mtext><mml:mtext>z</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mfenced close=")" open="("><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>b</mml:mi></mml:mfenced><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mtext>N</mml:mtext></mml:munderover><mml:msub><mml:mtext>IR</mml:mtext><mml:mrow><mml:mi>j</mml:mi><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
            where <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> is the growth efficiency of zooplankton (<italic>Beta</italic><inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>z</mml:mtext></mml:msub></mml:math></inline-formula>
in Kishi et al., 2007). By inserting Eq. (5) into Eq. (4), and considering
Eq. (6), we can write

                  <disp-formula specific-use="align" content-type="numbered"><mml:math display="block"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mtext>d</mml:mtext><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mtext>z</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:mtext>d</mml:mtext><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>z</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mfenced open="[" close="]"><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>w</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>+</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mtext>AE</mml:mtext><mml:mtext>z</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced open="(" close=")"><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mtext>N</mml:mtext></mml:munderover><mml:msub><mml:mtext>IR</mml:mtext><mml:mrow><mml:mi>j</mml:mi><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mfenced close="]" open="["><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mi>j</mml:mi></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mlabeledtr id="Ch1.E7"><mml:mtd/><mml:mtd/><mml:mtd><mml:mrow><mml:mo>-</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mfenced close=")" open="("><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>z</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mtext>N</mml:mtext></mml:munderover><mml:msub><mml:mtext>IR</mml:mtext><mml:mrow><mml:mi>j</mml:mi><mml:mo>→</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mfenced><mml:msub><mml:mfenced open="[" close="]"><mml:mtext>Cs</mml:mtext></mml:mfenced><mml:mtext>z</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
</sec>
</sec>
<sec id="Ch1.S2.SS4">
  <title>Model simulation</title>
      <p>The ocean circulation model (OCM) was run from February 2010 to January 2013.
The currents, vertical diffusivities and temperature fields were then used to
force the ecosystem model and spun up for 3 years by repeating the same
forcing data for the first 2 years. For this study, we used the results of
the 2 last simulated years (February 2011 to December 2012), when a
quasi-steady state was reached.</p>
      <p>To assess the effect of the accident on the planktonic populations, two
different simulations were carried out: (1) the real (accidental) situation
with presence of contaminated waters due to the accident that occurred on
11 March 2011, and (2) a non-accidental situation by assuming homogeneous
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in seawater over the whole simulation period.</p>
      <p>Before the accident date (11 March 2011), the seawater <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentration for the western North Pacific Ocean ranged from 1 to
2 mBq L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Povinec et al., 2013). For the purposes of the
modeling, a constant <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in seawater of
2 mBq L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> is assumed throughout the study area. In the accidental
situation, we used, as of 11 March 2011, the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in
seawater obtained from the dispersion simulation carried out by Estournel et
al. (2012), in which the amount of atmospheric deposition included was
0.26 PBq within a radius of 80 km. The direct leakage was about 5.5 PBq
released between 12 March and 30 June 2011. The simulation was extended until
31 December 2012, and the inverse method described in Estournel et al. (2012) and
used to calculate the source term in the first three months after the
accident was applied to the whole period. After June 2011, the concentrations
at the two outlets of the nuclear power plant were simplified to a linear
decrease from 40 and 20 Bq L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> on 1 July 2011 to 8 Bq L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for
both outlets at the end of 2011 and then remained constant at this value for
2012. However, no other additional source (e.g., terrestrial runoff, rivers
flow, etc.) has been considered in this simulation.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <title>Model calibration and sensitivity analysis</title>
      <p>The radioecological parameters related to plankton are very scarce, and are
often associated with considerable uncertainties. In this study, a temporal
series of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in zooplankton collected at Sendai Bay
between June 2011 and December 2013 and reported in Kaeriyama et al. (2014)
was used to calibrate the model and estimate the different radioecological
parameters. However, because of non-indication of the zooplankton taxa
composition, we used for the purpose of modeling a weighted average of
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in the three zooplankton groups.</p>
      <p>To assess the sensitivity of the calibrated parameters, we investigated a
sensitivity analysis of the radioecological model using the classical
one-parameter-at-a-time analysis (OAT). The choice of this quantitative
method can be justified by its simplicity and by the absence of any
interactive effects among parameters. In this local approach, the single-parameter variation effect is estimated by increasing and decreasing each
parameter in Eqs. (3) and (7) by 10 %, while keeping all the others fixed
at their nominal values. The sensitivity <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> associated with each
parameter <inline-formula><mml:math display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> was computed as the percentage of change in activity
generated by the parameter variation:
            <disp-formula id="Ch1.E8" content-type="numbered"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="italic">%</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>E</mml:mi><mml:mfenced open="(" close=")"><mml:mi>p</mml:mi></mml:mfenced><mml:mo>-</mml:mo><mml:mi>E</mml:mi></mml:mrow><mml:mi>E</mml:mi></mml:mfrac></mml:mstyle><mml:mo>×</mml:mo><mml:mn>100</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mfenced close=")" open="("><mml:mi>p</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> is the prognostic variable value (here, the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in plankton populations) when the parameter <inline-formula><mml:math display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is
set to its changed value (10 % higher or lower than its calibrated
value), and <inline-formula><mml:math display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> is the value of the prognostic variable in the baseline run
(i.e., all parameters at their calibrated values).</p>
</sec>
<sec id="Ch1.S2.SS6">
  <title>Absorbed dose rate</title>
      <p>To assess the biological effects of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs ionizing radiation on the
plankton populations, we calculated the absorbed dose rate from internal and
external pathways using the ERICA graded approach (Brown et al., 2008). This
approach consists in converting the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in plankton
populations and in seawater to the internal and external absorbed dose rates,
respectively, using the so-called “Dose Conversion Coefficients”, which are
specific for each radionuclide–organism combination. The different dose rates
are calculated as follows, assuming that the organisms are freely floating in
the water column without any contact with sediment:
            <disp-formula id="Ch1.Ex4"><mml:math display="block"><mml:mrow><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mtext>int</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>D</mml:mi><mml:mtext>ext</mml:mtext></mml:msub></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.Ex5"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>int</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mtext>DCC</mml:mtext><mml:mtext>Cs-pk</mml:mtext></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>[</mml:mo><mml:mi mathvariant="normal">Cs</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mo>]</mml:mo><mml:mtext>pk</mml:mtext></mml:msub></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.Ex6"><mml:math display="block"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>ext</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mtext>DCC</mml:mtext><mml:mtext>Cs-w-pk</mml:mtext></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>[</mml:mo><mml:mtext>Cs</mml:mtext><mml:msub><mml:mo>]</mml:mo><mml:mtext>w</mml:mtext></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>int</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>D</mml:mi><mml:mtext>ext</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are, respectively, the total, the
internal and the external dose rates (<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the
<inline-formula><mml:math display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="normal">Cs</mml:mi><mml:msub><mml:mo>]</mml:mo><mml:mi mathvariant="normal">pk</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="normal">Cs</mml:mi><mml:msub><mml:mo>]</mml:mo><mml:mtext>w</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are,
respectively, the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in plankton population and
seawater (in Bq kg<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,the  <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mtext>DCC</mml:mtext><mml:mtext>Cs-pk</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the dose
conversion coefficient for the internal exposure, and
<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mtext>DCC</mml:mtext><mml:mtext>Cs-w-pk</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> represents the dose conversion coefficient for
external exposure (in <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> per Bq kg<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>.</p>
      <p>The DCC parameter values for phytoplankton and zooplankton used in this study
are obtained from the coastal aquatic ecosystem DCCs reported in Vives i
Batlle et al. (2004). The values of these parameters are summarized in
Table 1.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><caption><p>Parameter values used in the absorbed dose calculation. All units
are in <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> per Bq kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1">Parameter</oasis:entry>  
         <oasis:entry colname="col2">Definition</oasis:entry>  
         <oasis:entry colname="col3">Phytoplankton</oasis:entry>  
         <oasis:entry colname="col4">Zooplankton</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">DCC<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>Cs-pk</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Dose conversion</oasis:entry>  
         <oasis:entry colname="col3">4.7 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">4.6 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">coefficient for</oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">internal exposure</oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">DCC<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>Cs-w-pk</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Dose conversion</oasis:entry>  
         <oasis:entry colname="col3">1.1 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">3.6 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">coefficient for</oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"/>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2">external exposure</oasis:entry>  
         <oasis:entry colname="col3"/>  
         <oasis:entry colname="col4"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
</sec>
<sec id="Ch1.S3">
  <title>Results and discussions</title>
<sec id="Ch1.S3.SS1">
  <title>Validation of the ecosystem model, and zooplankton taxonomic
compositions</title>
      <p>The seasonal variations in phytoplankton and zooplankton biomasses were
presented for three different areas classified according to latitude: the
subtropical region (latitude &lt; 35<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N), the transition
region (35<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N &lt; latitude &lt; 39<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N), and
the subarctic region (latitude &gt; 39<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N) (Fig. 1). The
ecosystem model outputs are expressed in <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>mol N L<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, their
conversion to the chlorophyll-<inline-formula><mml:math display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> unit is carried out using a typical C : chlorophyll
ratio of 50, and a C : N ratio of <inline-formula><mml:math display="inline"><mml:mrow><mml:mn>133</mml:mn><mml:mo>/</mml:mo><mml:mn>17</mml:mn></mml:mrow></mml:math></inline-formula> (Kishi et al., 2007).</p>
      <p>The monthly medians of the spatial chlorophyll-<inline-formula><mml:math display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> concentration averaged over
a 50 m deep layer were used to compare model results for the period
(2011–2012) with the 20 years of climatology field data (1990–2010)
(Fig. 2a, c, e) derived from the Japan Oceanographic Data Center (JODC)
data set (available at: <uri>http://www.jodc.go.jp</uri>). In all areas, the
temporal evolution of the chlorophyll standing stocks showed a seasonal cycle
with higher median values in spring (April–May) and autumn
(October–November). This seasonal cycle is less marked in the subtropical
region than in the two other regions. The simulated chlorophyll-<inline-formula><mml:math display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>
concentration medians varied from less than 0.5 mg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in all regions
in winter to approximately 1, 1.5 and 3 mg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> in spring in the
subtropical, the transition and the subarctic regions, respectively. These
values of the chlorophyll-<inline-formula><mml:math display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> concentrations are in general consistent with the
field data, and show the same seasonal variability (Wilcoxon rank sum test
(<inline-formula><mml:math display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.05</mml:mn></mml:mrow></mml:math></inline-formula>): <inline-formula><mml:math display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>0.88</mml:mn></mml:mrow></mml:math></inline-formula>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><caption><p><bold>(a, c, e)</bold> Climatological seasonal cycle of integrated
chlorophyll from in situ data (in black) and model results (in red)
aggregated as monthly medians. In situ climatology data is derived from the
Japan Oceanographic Data Center (JODC) data set for the period (1990–2010).
Model outputs are monthly medians for the period 2011–2012 and represented
for the three regional areas described in Fig. 1. <bold>(b, d, f)</bold> Results
of the 2-year simulation of the total zooplankton biomass represented as
the spatial median (dark line) and its taxonomic composition in the three
regional areas described above: subtropical region <bold>(a, b)</bold>, transition region
<bold>(c, d)</bold>, subarctic region <bold>(e, f)</bold>.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f02.png"/>

        </fig>

      <p>The total zooplankton biomass and its taxonomic composition are presented in
Fig. 2b, d, f for the three regional areas described above. The simulated
zooplankton biomasses showed an annual seasonality in the three regions, with
minimum values in winter and peaks in spring and autumn. The zooplankton
biomasses showed latitudinal variations with greater biomass in the subarctic
region (from 200 mg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight in winter to about
700 mg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight in late spring), followed by the transition
region (from 150 to about 500 mg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ww) and the subtropical region
(from 100 to about 300 mg m<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ww).</p>
      <p>In the subtropical region, the taxonomic composition of zooplankton biomass
was dominated by large zooplankton with about 40 %, followed by small and
predatory zooplankton each accounting for 30 % of the total biomass.</p>
      <p>In the transition region, the seasonal cycle of zooplankton composition was
more pronounced. In winter, the zooplankton was represented by 40 % of
large zooplankton, and 30 % of small and predatory zooplankton. In
spring, the zooplankton biomass was dominated by large zooplankton (60 %
ZL and 20 % for both ZS and ZP). From late spring until early autumn, the
zooplankton composition changed progressively with a decrease of the ZL
proportion, to be composed of 40 % ZP and 30 % of ZS and ZL in early
autumn.</p>
      <p>In the subarctic region, the proportions of small zooplankton, large
zooplankton and predatory zooplankton were, respectively, 25, 35 and 40 %
in winter, 10, 70 and 20 % in spring, and 20, 35 and 45 % in late
summer and early autumn.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <title>Model calibration</title>
      <p>The result of the calibration is shown in Fig. 3, and the final estimated
radioecological parameters are summarized in Table 2. The phytoplankton
elimination rates estimated from this calibration (0.5 d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
were very similar to that calculated using the allometric relationship
reported by Vives i Batlle et al. (2007) (0.58 d<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. For the
zooplankton, the obtained values ranged from 0.03 to 0.11 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and
are also in good agreement with the literature values (Thomann (1981): 0.03 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>; Vives i Batlle et al. (2007): 0.056 d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2" specific-use="star"><caption><p>Apparent radioecological parameters obtained from the model
calibration.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="4">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">  
         <oasis:entry namest="col1" nameend="col2" align="center">Parameter </oasis:entry>  
         <oasis:entry colname="col3">Unit</oasis:entry>  
         <oasis:entry colname="col4">Value</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>ps</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Accumulation rate from water for PS</oasis:entry>  
         <oasis:entry colname="col3">L  g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.015</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>pl</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Accumulation rate from water for PL</oasis:entry>  
         <oasis:entry colname="col3">L g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.015</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>zs</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Accumulation rate from water for ZS</oasis:entry>  
         <oasis:entry colname="col3">L  g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>zl</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Accumulation rate from water for ZL</oasis:entry>  
         <oasis:entry colname="col3">L  g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>zp</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Accumulation rate from water for ZP</oasis:entry>  
         <oasis:entry colname="col3">L  g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4"><inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mn>10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>ps</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Small phytoplankton elimination rate</oasis:entry>  
         <oasis:entry colname="col3">d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.5</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>pl</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Large phytoplankton elimination rate</oasis:entry>  
         <oasis:entry colname="col3">d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.5</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>zs</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Small zooplankton elimination rate</oasis:entry>  
         <oasis:entry colname="col3">d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.11</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>zl</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Large zooplankton elimination rate</oasis:entry>  
         <oasis:entry colname="col3">d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.07</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>zp</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">Predatory zooplankton elimination rate</oasis:entry>  
         <oasis:entry colname="col3">d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col4">0.03</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1"><inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mtext>AE</mml:mtext><mml:mtext>z</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2"><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs assimilation efficiency by zooplankton</oasis:entry>  
         <oasis:entry colname="col3">No dim</oasis:entry>  
         <oasis:entry colname="col4">0.75</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>The <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs assimilation efficiency by zooplankton calibrated in this
study was 0.75. This value is similar to that used by Brown et al. (2006),
and is slightly higher than the 0.63 observed by Mathews and Fisher (2008) for
the crustacean zooplankton <italic>Artemia salina</italic>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p>Results of the model calibration represented as the spatial median
of the weighted average of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in the three zooplankton
groups situated in  Sendai Bay. The red stars represent the field data of
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity in zooplankton in the same location (Kaeriyama et al.,
2014).</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f03.png"/>

        </fig>

      <p>The rates of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs direct accumulation from water by zooplankton found
in this study were about 5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> L g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for small and
large zooplankton, and about 0.001 L g<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> d<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for predatory
zooplankton. The accumulation rate corresponding to phytoplankton was 0.015
for both groups.</p>
      <p>However, for the calibration we used zooplankton data from coastal areas
presented in Kaeriyama et al. (2014). According
to these authors, zooplankton gut content in these areas may contain
particles with high <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs levels, which could affect the calibrated
values. Consequently, overestimations in <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in these
populations could be generated especially in the open ocean where the
particles contribution is generally negligible.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <title>Sensitivity analysis</title>
      <p>The sensitivity of the estimated <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity concentrations in
different plankton groups to uncertainty in the parameters of Eqs. (3) and
(7) calibrated to field data at Sendai Bay was tested using the OAT method,
and the results are shown in Fig. 4.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><caption><p>Sensitivity (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the estimated <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentrations in different plankton groups (PS, PL, ZS, ZL, ZP) to a
10 % change in the parameters of Eqs. (3) and (7).
The <inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mtext>p</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values are calculated using Eq. (8). Significance of parameters: <inline-formula><mml:math display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>_: primary production rate, <inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>_: phytoplankton
respiration rate, [Cs]_w: <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in seawater, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">λ</mml:mi></mml:math></inline-formula>_: depuration rate, <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">μ</mml:mi></mml:math></inline-formula>_: accumulation rate, AE_: Assimilation
efficiency, <inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>: growth efficiency of zooplankton.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f04.png"/>

        </fig>

      <p>For all plankton groups, the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity estimates showed a great
sensitivity to the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in seawater, with an activity
change of 10 % for a 10 % change in the seawater <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentration. The <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity in seawater used in this study was
obtained from the numerical simulations of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs dispersion using
the SYMPHONIE circulation model. One can imagine that all potential biases
associated with this simulation would generate the same ranges of error in
the results concerning the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in plankton. It is,
therefore, clearly important to take into consideration all these errors when
interpreting the results of the radioecological model.</p>
      <p>The <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity estimates in the phytoplankton groups are very
sensitive to the accumulation rate from water (10 % change for a 10 %
change in the parameter), and are moderately sensitive to the elimination and
primary production rates (5–7 % change in the opposite sense), whereas
the sensitivity to the daily respiration rate did not exceed 1 %. The
primary production rate is, therefore, the most important ecological
parameter in the estimation of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in phytoplankton. It
allows dilution of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in phytoplankton by
promoting the growth of its populations.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><caption><p>Spatial and temporal comparisons between the weighted average of
simulated <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in the three zooplankton groups
(Bq kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> ww) and the field observations (colored
rounds) reported by <bold>(a)</bold> Buesseler et al. (2012), <bold>(b, c, d, f)</bold> Kaeriyama et al. (2014) and <bold>(e)</bold> Kitamura et al. (2013).</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f05.png"/>

        </fig>

      <p>For all zooplankton groups, the activity estimates were most sensitive to the
change in the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs assimilation efficiency (AE), with an activity
change of about 9 % for both small and large zooplankton. For predatory
zooplankton, the activity change was slightly above 10 %, which can be
explained by the direct effect of the AE parameter on ZP and the indirect
effect due to the change in ZS and ZL that are preyed on by ZP.</p>
      <p>The sensitivity to the population growth efficiency (<inline-formula><mml:math display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>) was also
significant with about 7 % of change. This ecological parameter, which
affects the zooplankton population growth and consequently plays a role in
the dilution of their <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations, is associated with
substantial uncertainty. Sushchenya (1970) reported values ranging from 4.8
to 48.9 %. The value used in this study was 30 % (Kishi et al.,
2007). One can expect, therefore, an overestimation of up to 45 % or an
underestimation of up to 60 % in the estimates of zooplankton <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentrations.</p>
      <p>The sensitivity to the direct accumulation rate of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs from water by
zooplankton (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>z</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was relatively low (&lt; 4 % for the
three groups of zooplankton). This can be related to the lower proportion of
contamination coming from water compared to that coming from food. The
variation in the depuration rate induced a relatively moderate change of
5 %.</p>
      <p>The sensitivity of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity estimates in the three groups of
zooplankton to parameters related to their different preys is also not
negligible. The proportions of change varied from 1 to 9 % depending on
the zooplankton group and the parameter in question. For example, the
sensitivity of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in ZS to the PS accumulation rate
(<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">μ</mml:mi><mml:mtext>ps</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the elimination rate (<inline-formula><mml:math display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mtext>ps</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and the primary production rate (<inline-formula><mml:math display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>) were 9, 5 and
7 %, respectively.</p>
      <p>This sensitivity analysis showed that the parameters related to the two
groups of phytoplankton are very important for the estimation of the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in all plankton groups. Therefore, these parameters
are key determinants of the radionuclide concentration in all marine animals
of the pelagic food chain
(Mathews and Fisher,
2008). Consequently, the experimental determination of these parameters,
often neglected due to the difficulties characterizing the measurement of
radionuclides in phytoplankton, is of the greatest importance.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <title>Radioecological model validation</title>
      <p>The simulation results corresponding to the spatial distribution of the
weighted average of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in the three zooplankton groups
(ZS, ZL, ZP) are presented in Fig. 5. These results are shown for six different
dates from June 2011 to August 2012, and are compared to the few field
observations available in the area (Buesseler et al., 2012; Kaeriyama et al.,
2014; Kitamura et al., 2013). Some field data reported in the unit of Bq kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> dry weight are converted to Bq kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight using dry
to wet weight ratio of 0.2 (Buesseler et al., 2012).</p>
      <p>In general, these results illustrated the good agreement between measured and
simulated results, which is confirmed by the Wilcoxon rank-sum statistical
test (<inline-formula><mml:math display="inline"><mml:mrow><mml:mi>P</mml:mi><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn>0.05</mml:mn></mml:mrow></mml:math></inline-formula>, non-significant difference). Nevertheless,
some points showed significant discrepancies between measured and simulated
concentrations, as in the case of (36<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> N, 144<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W) in the period
3–18 June 2011 (Fig. 5a) where the observed concentration was 2 orders of
magnitude higher than the simulated one. A large part of this difference
could be due to a spatial shift of the contaminated plume in the dispersion
model. Indeed, the coastal waters off Japan are very energetic, especially
with the interaction between the cold Oyashio current moving southward and
the warm Northward Kuroshio current, generating very complex physical
structures (eddies, tidal forces, etc), which are generally less well
represented by the hydrodynamics models leading to some spatial shifts
between the simulated <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in seawater used in this
simulation and the real field concentrations.</p>
</sec>
<sec id="Ch1.S3.SS5">
  <?xmltex \opttitle{Amplification of the ${}^{{137}}$Cs concentration in plankton populations
following the FNPP accident}?><title>Amplification of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in plankton populations
following the FNPP accident</title>
      <p>To assess the contamination level of plankton populations in 2011, we
calculated a ratio (<inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) of the<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in phytoplankton (the
weighted average of PS and PL) and zooplankton (the weighted average of ZS,
ZL and ZP) in the accidental situation to its concentration in these
populations in the non-accidental situation. The results of the temporal
evolution of these ratios for different distances from FNPP are shown in
Fig. 6.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><caption><p>Calculated ratios (<inline-formula><mml:math display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in phytoplankton
and zooplankton in the accident situation to its concentration in the same
population in the no-accident situation. The ratio was calculated for
different sectors at various distances from FNPP.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f06.png"/>

        </fig>

      <p>The ratios for phytoplankton and zooplankton are very similar spatially and
temporally. After the accident, the ratio increased rapidly until reaching a
maximum, whose  value and the time required to reach it are variable
following the distance from FNPP. The results showed that the time,
calculated from the accident date, required to reach the maximum value
increased with distance from FNPP, going from about 1 month for the
populations located at less than 30 km from FNPP to about 6 months for those
located at 500 m from FNPP. The maximum value, in turn, decreased with the
distance from FNPP (about 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:math></inline-formula> at 0–30 km from FNPP to slightly lower
than 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula> at 400–500 km from FNPP).</p>
      <p>After reaching the peak, the ratios progressively decreased over time but
remained relatively high at the end of 2011 especially in the sectors
situated at less than 50 km from FNPP where the ratio was still higher than
10.</p>
      <p>The rapid decrease of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs in planktonic populations 1 year after
the accident in the major parts of the study area can be explained by the
different processes related to both population ecological functioning (cells
growth and death, biological elimination) and the surrounding environment
conditions, especially by the horizontal and vertical mixing due to the ocean
hydrodynamics. Indeed, FNPP is located in an area where the east-flowing
Kuroshio current and the southwest-flowing Oyashio current mix, generating
complicated nearshore currents and mesoscale eddies
(Buesseler, 2014), thereby favoring dispersion,
regeneration, and thus dilution, of the contaminated planktonic populations
in the area.</p>
      <p>Referring to the biogeochemical cycle in the pelagic environment, part of the
contaminated populations would be transferred to the pelagic higher trophic
levels (planktivorous fishes, squids, etc.) by predation, leading to transfer
of this contamination along various trophic chains. The other part will
generate, after dying, large aggregated particles, known collectively as
marine snow, which can reach the deep waters (Asper et al., 1992) and thus
contribute to the contamination of sediment and benthic organisms, especially
in the coastal area. This phenomenon was observed in the Mediterranean Sea a
few days after the Chernobyl accident, generating a rapid transport of some
radionuclides from surface waters to a depth of 200 m (Fowler et al., 1987).
This process could be expected in the Japanese coastal area characterized by
very high levels of contamination, especially around FNPP.</p>
</sec>
<sec id="Ch1.S3.SS6">
  <title>Apparent concentration ratio (aCR)</title>
      <p>The concentration ratio (L kg<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is defined as the ratio of
radionuclide in the organism (Bq kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight) divided by its
concentration in the water (Bq L<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The dynamics of the calculated
apparent concentration ratios (aCR) for small phytoplankton, small
zooplankton and predatory zooplankton populations throughout the study area
and for populations located within a radius of 30 km from FNPP over the year
2011 are shown in Fig. 7. These apparent concentration ratios are estimated
for the two different situations described above (see Sect. 2.4).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><caption><p>Results of concentration ratio estimated for small phytoplankton
(PS), small zooplankton (ZS) and predatory zooplankton (ZP) in the whole
study area (left) and for those populations located at less than 30 km from
FNPP (right). The blue vertical line separates the pre- and post-accident
periods.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f07.png"/>

        </fig>

      <p>The spatial median of the apparent concentration ratios in the non-accidental
situation (i.e., the steady-state situation) was between 20 and
30 L kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight for small phytoplankton and between 10 in
winter to slightly more than 30 L kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> during the rest of the year
for small zooplankton. In the case of predatory zooplankton, the
concentration ratio was a little higher, ranging from 10 to about
40 L kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight. These values are in good agreement with the
reported data on plankton concentration ratios in marine ecosystems, which
generally range from 6 to 40 L kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> wet weight in steady-state
conditions (Fowler, 1977; IAEA, 2004; Kaeriyama et al., 2008). In the sector
situated at less than 30 km from FNPP (Fig. 7), the concentration ratio was
almost constant and seasonal variability was very less pronounced, with about
25 L kg<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> for PS and 30–40 for ZS and ZP. This constancy in the
estimated concentration ratios for the populations located at less than
30 km compared to those estimated for the whole study area, where a
substantial decrease in the concentration ratio was observed during winter,
can be related to the clear differences in food ingestion rates observed in
this period between the two locations (Fig. 8). In winter, the zooplankton
ingestion rates estimated for the populations located at less than 30 km
were higher than those estimated for the whole study area, due essentially to
the spatial heterogeneity characterizing the whole study area in terms of
food availability, with the presence of some less productive regions such as the
subtropical zone where the planktonic biomasses were generally very low (see
Sect. 3.1).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><caption><p>Food ingestion rate associated with the diet composition for the
three groups of zooplankton in the areas located between 0 and 30 km (left) and
for the zooplankton of the whole study area (right).</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f08.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><caption><p>Relative fraction of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs accumulated from diet for the three
groups of zooplankton calculated as the spatial median and quantiles of the
whole study area (left) and in the sector located at less than 30 km from
FNPP (right). The vertical blue line separates the pre- and post-accident
periods.</p></caption>
          <?xmltex \igopts{width=369.885827pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f09.png"/>

        </fig>

      <p>At the time of the releases and immediately after the accident, the
concentration ratio decreased rapidly for all plankton groups. This is mainly
due to the sudden arrival of highly contaminated waters in these areas where
the living plankton populations were not yet contaminated. This phase was
less marked for small phytoplankton compared to the groups of zooplankton,
due to the fact that phytoplankton accumulates <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs only from water
whereas in the case of zooplankton an important part of the contamination
arises from food, a process requiring some time. For the populations located
at less than 30 km from FNPP the dramatic decrease in the concentration
ratio in March was even more intense and longer. The estimated time needed
for these populations to regain the equilibrium was about 5–10 days for PS,
30 days for ZS and about 50 days for ZP. The decreasing phase in
concentration ratio was directly followed by an increasing phase reflecting
the progressive accumulation of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs by plankton organisms.</p>
</sec>
<sec id="Ch1.S3.SS7">
  <?xmltex \opttitle{Relative accumulation of ${}^{{137}}$Cs from diet by zooplankton}?><title>Relative accumulation of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs from diet by zooplankton</title>
      <p>The dynamics of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs fraction accumulated from diet by zooplankton
populations is estimated for both accidental and non-accidental situations
and in the two spatial scales (Fig. 9). This fraction remained stable in the
case of zooplankton living at less than 30 km from FNPP and represented more
than 80 % in the case of ZS, 90 % in the case of ZL and 98 % in
the case of ZP. These results indicated that the major part of accumulated
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs by these populations is coming from food, which is consistent with
the research conducted by Baumann et al. (2015), who postulated that the
dietary route could be largely responsible for the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs bioaccumulated
by the zooplankton collected off Japan 3 months after the accident.</p>
      <p>The accident effect was only briefly apparent with a slight decrease of this
proportion.</p>
      <p>Conversely, the proportion estimated for zooplankton populations living in
the whole area revealed a decline in winter, especially in the case of ZS for
which this proportion decreased to 30 %. Because of the non-decrease in
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in PS during this period (Fig. 10), the decrease
in the relative accumulation by ZS from diet could be related to the decrease
in the food ingestion rate (Fig. 8). No apparent effect of the accident on
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs fraction accumulated from diet was observed at this large
spatial scale.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><caption><p>Dynamics of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in all plankton groups in
the no-accident situation.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f10.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS8">
  <title>Trophic transfer factor</title>
      <p>The trophic transfer factor (TTF), defined as the ratio of radionuclide
concentration in the predator to its concentration in prey, was calculated
for each zooplankton group. The small zooplankton (ZS) has only one prey
(small phytoplankton), therefore the TTF was calculated directly by dividing
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentration in the ZS by its concentration in the PS. In
the case of large and predatory zooplankton that have more than one prey (three
for each one), we considered the weighted average of the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentration in preys related to each zooplankton group.</p>
      <p>Boxplots of predicted TTFs over 2011 for the three zooplankton groups in the
accident and steady-state situations are shown in Fig. 11 for the two spatial
scales described above.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><caption><p>Boxplots of the Trophic Transfer Factor (TTF) calculated over
2011 for the three groups of zooplankton and for the two different spatial
scales. The dark color represents the accident situation and the blue
color represents the no-accident situation. On each box, the central mark
is the median, the edges of the box are the 25th and 75th percentiles, the
whiskers extend to the most extreme data points not considered outliers, and
outliers are plotted individually (the red marks).</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f11.png"/>

        </fig>

      <p>The predicted TTF medians in the steady-state situation for ZS, ZL and ZP
were, respectively, about 1.5, 1.7 and 1.2 in the sector 0–30 km from FNPP,
and about 1.2, 1.45 and 1.1 in the whole study area. The TTF values
calculated for the whole study area were slightly lower than those of the
0–30 km sector, reflecting the variability in ingestion rate and diet
composition between the two spatial scales (Fig. 8). The lower values of ZP
TTFs compared to the two other zooplankton groups may also be due to
differences in their respective ingestion rate values. The correlation
coefficient <inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> between the modeled TTF related to each zooplankton group
in the steady-state conditions and their corresponding ingestion rates showed
a good correlation for the three groups of zooplankton and in both considered
spatial scales (Table 3).</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T3" specific-use="star"><caption><p>Correlation coefficients (<inline-formula><mml:math display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula>) between the ingestion rates and the
TTF of different zooplankton groups.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:thead>
       <oasis:row>  
         <oasis:entry colname="col1">Parameter</oasis:entry>  
         <oasis:entry colname="col2">TTF</oasis:entry>  
         <oasis:entry namest="col3" nameend="col4" align="center">Non-accidental </oasis:entry>  
         <oasis:entry namest="col5" nameend="col6" align="center">Accidental </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">  
         <oasis:entry colname="col1"/>  
         <oasis:entry colname="col2"/>  
         <oasis:entry colname="col3">Whole area</oasis:entry>  
         <oasis:entry colname="col4">0–30 km</oasis:entry>  
         <oasis:entry colname="col5">Whole area</oasis:entry>  
         <oasis:entry colname="col6">0–30 km</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>  
         <oasis:entry colname="col1">IR<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>ZS</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">ZS</oasis:entry>  
         <oasis:entry colname="col3">0.94</oasis:entry>  
         <oasis:entry colname="col4">0.91</oasis:entry>  
         <oasis:entry colname="col5">0.88</oasis:entry>  
         <oasis:entry colname="col6">0.68</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">IR<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>ZL</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">ZL</oasis:entry>  
         <oasis:entry colname="col3">0.85</oasis:entry>  
         <oasis:entry colname="col4">0.84</oasis:entry>  
         <oasis:entry colname="col5">0.77</oasis:entry>  
         <oasis:entry colname="col6">0.46</oasis:entry>
       </oasis:row>
       <oasis:row>  
         <oasis:entry colname="col1">IR<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mtext>ZP</mml:mtext></mml:msub></mml:math></inline-formula></oasis:entry>  
         <oasis:entry colname="col2">ZP</oasis:entry>  
         <oasis:entry colname="col3">0.83</oasis:entry>  
         <oasis:entry colname="col4">0.79</oasis:entry>  
         <oasis:entry colname="col5">0.76</oasis:entry>  
         <oasis:entry colname="col6">0.37</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p>The predicted TTFs in the accident situation were similar to those predicted
in the steady-state situation when considering the whole study area. This is
due to the fact that, in the farthest sites from FNPP, where the
contamination was not very high, the return to equilibrium occurred more
rapidly, leading to TTFs similar to those observed before the accident
although the concentrations in the predator and its preys were higher than
during the pre-accident period. In the sector 0–30 km from FNPP, the
predicted TTFs in the accidental situation were lower than those predicted in
the steady-state situation (non-accidental situation). This is due to the
persistence of the non-equilibrium state and the high <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
concentrations in seawater in this area, and to the fact that zooplankton
accumulates <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs mainly from food leading to a delay in its
contamination compared to its preys.</p>
      <p>In turn, the correlation coefficients between predicted TTFs and ingestion
rates in the accident situation showed a very slight decrease when
considering the whole study area, and a considerable decrease when
considering only the sector 0–30 km from FNPP. This means that the
instability and the non-steady-state conditions characterizing the
post-accident period had significant effects on this correlation.</p>
      <p>Previous works suggested that radiocesium is the only trace element apart
from Hg that may be potentially biomagnified along food chains
(Harmelin-Vivien
et al., 2012; Heldal et al., 2003; Zhao et al., 2001). In our study, the
modeled TTFs were generally higher than the unity for all zooplankton
groups, showing evidence of biomagnification potential at this trophic level.
Mathews and Fisher (2008) reached the same
general conclusion for the crustacean zooplankton <italic>Artemia salina</italic> feeding on phytoplankton,
and reported that TTFs are directly related to the food ingestion rates, and
that a consistent capacity for biomagnification exists when the food
ingestion rate is high.</p>
</sec>
<sec id="Ch1.S3.SS9">
  <title>Absorbed dose</title>
      <p>The estimation of the absorbed dose rate (<inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>G h<inline-formula><mml:math display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is an
essential step enabling media/biota activity concentrations to be interpreted
in terms of potential effect (Beresford et al., 2007) .</p>
      <p>The calculated dose rates received by phytoplankton and zooplankton
populations located at less than 30 km from FNPP over 2011 are shown in
Fig. 12. The external dose rate was about 7 times higher than the internal
dose rate for phytoplankton, and about 5 times higher than the internal dose
rate in the case of zooplankton, resulting in similarity between the total
and the external dose rates. The total dose rates for phyto- and zooplankton
were also very similar, whereas the internal dose was higher for zooplankton
than for phytoplankton.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12" specific-use="star"><caption><p><inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs dose rates received by plankton populations located at
less than 30 km from FNPP.</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://bg.copernicus.org/articles/13/499/2016/bg-13-499-2016-f12.png"/>

        </fig>

      <p>For both phyto- and zooplankton, in the steady-state conditions before the
accident, the dose rates were about 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The
maximum value was reached 1 month after the accident with about
0.05 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. From this date, the dose rates decreased
progressively to reach about 5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
at the end of 2011. The calculated internal dose rates for zooplankton in
June 2011 were about 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and were,
therefore, about 5 times greater than those reported by Fisher et al. (2013)
for copepods and euphausiids collected 30–600 km off Japan. This difference
is mainly due to the fact that in this study the dose rates were calculated
for the populations located at 0–30 km from FNPP, where the activity level
of <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mspace width="0.125em" linebreak="nobreak"/></mml:msup></mml:math></inline-formula>was higher.</p>
      <p>The maximum dose rates calculated here were very low relative to the
benchmark value corresponding to 10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> as suggested by
the ERICA approach (Beresford et al., 2007), signifying that the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs
levels were too low to cause a measurable effect on these plankton
populations. However, this conclusion concerns only <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs – we ignore
whether the ionizing radiation doses due to the other radionuclides released
in high quantities following the FNPP accident, such as short-lived nuclides
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>132</mml:mn></mml:msup></mml:math></inline-formula>Te, <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>131</mml:mn></mml:msup></mml:math></inline-formula>I and <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>90</mml:mn></mml:msup></mml:math></inline-formula>Sr, can generate any effect on these
populations. Finally, it is important to note that this finding may be
representative of the average conditions characterizing the area located up
to 30 km from FNPP, however in close vicinity to the FNPP (e.g., FNPP Port),
the planktonic populations could have been exposed to more intense and more
persistent doses that could generate higher deleterious effects on these
populations.</p>
</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <title>Conclusions</title>
      <p>We presented a modeling approach based on an ecosystem model to estimate
the <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs activity in marine plankton populations following the
Fukushima nuclear power plant (FNPP) accident, and to understand the effect
of this accident on the different processes related to the radiocesium
transfer in the planktonic trophic levels. This kind of model enables
calculation of the non-equilibrium dynamic processes of radionuclide
transfer for the biological compartments taking into account the dynamics of
the biomass and the spatiotemporal variability in the ecological parameters
and environmental conditions (Sazykina, 2000).</p>
      <p>The radioecological parameters were estimated by calibration, and the model
was validated with observed <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs data in zooplankton after the accident. This study showed that the maximum values of the
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in phytoplankton and zooplankton populations were
mainly reached 1 month after the accident and were about 2 to 4 orders
of magnitude higher than those observed before the accident depending on the
distance from FNPP. On the other hand, it should be noted that
although the model results indicate that the spatiotemporal dynamics of
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs concentrations in zooplankton populations in non-accidental
conditions  mainly depend on the food availability (i.e., phytoplankton
biomasses in the area), with an apparent decrease of cesium concentrations in
these populations during the limited-food conditions (e.g., winter), this
finding has to be verified and validated by multi-years field observations
once these data are available.</p>
      <p>Contrary to Baumann et al. (2015) who did not observe any biomagnification
between phytoplankton and zooplankton collected 3 months after the
accident, our study highlighted a modest biomagnification potential between
the zooplankton groups, since the calculated trophic transfer factors were
slightly higher than unity. The result obtained by Baumann et al. (2015)
could be due to the fact that, 3 months after the accident, the
equilibrium has not been reached (Kaeriyama et al., 2014) resulting in some
delay in predator (zooplankton) contamination compared to its preys
(phytoplankton) since the major part of the bioaccumulated <inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs by
zooplankton is coming from food. Further analysis covering a longer time
series of contamination levels in zooplankton and phytoplankton are therefore
required to better understand the biomagnification potential of these
species. In our study, the TTF has been calculated over the full year 2011,
but one has to be careful in interpretation of this result since has not yet been
validated using the field data.</p>
      <p>Although the contamination degrees characterizing the seawater and the
plankton populations following the FNPP accident were high, the maximum
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs dose rates calculated for both phyto- and zooplankton were about
5 <inline-formula><mml:math display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 10<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and they remained lower than
the benchmark value considered in this study, which corresponds to the
incremental screening dose rate of 10 <inline-formula><mml:math display="inline"><mml:mi mathvariant="normal">µ</mml:mi></mml:math></inline-formula>Gy h<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> defined in
the ERICA assessment approach (Beresford et al., 2007). However, it is
important to note that the dose rate calculated in this study concerns only
<inline-formula><mml:math display="inline"><mml:msup><mml:mi/><mml:mn>137</mml:mn></mml:msup></mml:math></inline-formula>Cs, and that we ignore, at this stage, whether the ionizing radiation
doses due to the other radionuclides released in high quantities following
the FNPP accident can generate any effect on these populations, although
all previous studies have shown that the radioactivity levels in marine biota
have generally been below the levels necessary to cause a measurable effect
on populations (e.g., Vives i Batlle, 2016).</p>
</sec>

      
      </body>
    <back><ack><title>Acknowledgements</title><p>We warmly thank Caroline Ulses, Thomas Duhaut, Cyril Nguyen and Patrick Marsaleix of the Laboratoire d'Aérologie (CNRS and Toulouse University)
for their continuous assistance. This work was carried out in the frame of
the AMORAD project (French state financial support managed by the National
Agency for Research allocated in the “Investments for the Future”
framework programme under reference ANR-11-RSNR-0002). This work is also
part of the EC 7th Framework project COMET (Coordination and
iMplementation of a pan-Europe instrumenT for radioecology).
<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?>
Edited by: G. Herndl</p></ack><ref-list>
    <title>References</title>

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<abstract-html><p class="p">Huge amounts of radionuclides, especially <sup>137</sup>Cs, were released into the
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