R. Periäfiez et al. 
Environmental Modelling and Software 122 (2019) 104523 
Water 
Phytoplankton 
Zooplankton 
Non- 
piscivorous 
fish 
Piscivorous 
fish 
Fig. 6. Scheme of radionuclide transfer (arrows) in a dynamic food chain model (from Maderich et al., 2014a). 
comprises two compartments describing fast and slow uptake and 
depuration rates, which allows a better description of the temporal 
variations of radionuclide concentrations after an accidental release. 
Physiologically-based pharmacokinetic multi-compartmental models 
(Thomann et al., 1997) have an interesting potential. In these models 
well-mixed compartments correspond to the fish organs/tissues or 
groups of organs/tissues according to specific metabolic functions. 
The kinetics of exchange is first order, and transport between com- 
partments is governed by blood flux. However, these models require 
many parameters, which should be calibrated from controlled ex- 
periments. Therefore, this approach was rarely used in radioecology 
"Garnier-Laplace et al., 2000). 
Dynamic food web models can be included within a marine disper- 
sion model in order to simulate radionuclide concentrations in biota at 
oceanic scales. Thus, previous equations must be included in the marine 
transport model. They are solved for each grid cell in the domain. 
From the calculated concentration in water, Eqs. (19) and (20) provide 
‚adionuclide concentrations in each grid cell, time and species. 
This work was recently carried out in MODARIA-II program (Per- 
läfiez et al., 2019): 137Cs concentrations in phytoplankton, zooplank- 
‘on, non-piscivorous and piscivorous fish were calculated over the 
Whole north Pacific Ocean up to two years after the Fukushima acci- 
dent. Several transport models with different models for biota uptake 
were applied and results compared with measurements in water, sedi- 
ment and biota (zooplankton and fish). Three types of biological uptake 
nodels were tested: an equilibrium model based on a concentration 
‚ratio, the dynamic model described here and an allometry method, 
Dynamic models provided the known patterns of delayed rise of activity 
zoncentration in biota, Details may be seen in the cited reference. 
A more complex model of 14C transfer in the marine trophic web 
was recently described by Tierney et al. (2018). However, advection 
was treated in a limited way and measurement data could not be 
‘‚eproduced in some areas. 
As a resume, a compilation of the basic characteristics of some 
radionuclide marine transport models are listed in Tables 4-6 for, re- 
spectively, transport models linked with hydrodynamic models, stand- 
alone radionuclide transport models which import water circulation, 
and box models; including all the previously cited characteristics. 
In general, equilibrium or dynamic models may be used to describe 
water/sediment interactions and biota uptake. The main advantages 
and disadvantages of each approach are discussed in Section 5.5. 
Fig. 7 presents a scheme of the modelling procedures, The hydrody- 
namic model provides water currents which are required by Eulerian 
and Lagrangian models for simulating physical transport (advection 
and diffusion). Box models need water fluxes which are deduced from 
>bservations and/or calculated from water currents. Bio-geochemical 
orocesses (water/sediment interactions and uptake of radionuclides by 
>iota) may be described by equilibrium or dynamic models, In general, 
‘he equilibrium approach is used in box models, since long temporal 
scales are simulated with them. In contrast, dynamic models are more 
frequently used in Eulerian and Lagrangian models. Suspended matter 
concentrations and sedimentation rates may also be required if radionu- 
elide interactions with suspended particulate matter are included. Mean 
values of these magnitudes, deduced from observations, are generally 
used in box models. Values calculated with a sediment transport mode] 
{which can be Eulerian or Lagrangian) are more often used in Eulerian 
and Lagrangian radionuclide transport models. The physical transport 
model, with the added bio-geochemical model, provides radionuclide 
concentrations in water, sediment and biota species. 
4. Models applied to simulate and estimate Fukushima releases in 
the Pacific Ocean 
Significant amounts of radioactive material were released to the 
environment from FDNPP as a consequence of the March 2011 earth- 
quake and tsunami. Radionuclides released to the atmosphere were 
transported eastwards by a jet stream, and they reached the coast of 
North America in four days (Takemura et al., 2011). Some of these 
tadionuclides were deposited on the Pacific Ocean surface by wet 
and dry processes. In addition, water used to cool a damaged nuclear 
reactor directly leaked into the ocean (Kobayashi et al., 2013). Since 
most of the recent efforts in modelling marine radionuclide dispersion 
were focused in Fukushima releases in the Pacific Ocean, a brief review 
of some of the models applied to this problem is included. A review on 
Aispersion patterns of!?7Cs released from Fukushima in the Pacific de- 
rived from field measurements (not models) may be seen in Kaeriyama 
2017). 
The first modelling studies into the dispersion of Fukushima releases 
in the Pacific Ocean were published soon after the accident. Thus, the 
spreading of !911 and !97Cs using the Lagrangian model SEA-GEARN, 
developed at JAEA, was simulated by Kawamura et al. (2011). A 
Lagrangian code was applied to simulate the dispersion of 137Cs and 
$4Cs in the world ocean up to 30 years after the accident (Nakano 
and Povinec, 2012). Annually averaged water circulation was used 
for this purpose. The dispersion of !97Cs, using a high resolution (1 
km) regional Eulerian model, during the first three months after the 
accident was simulated by Tsumune et al. (2012). Later, simulations 
were extended to one year in Tsumune et al. (2013). 
Ten year long simulations of !97Cs dispersion in the Pacific Ocean 
were also performed by Behrens et al. (2012). Water circulation of the 
past 10 years was used for this purpose. They found that the initial 
current field was relevant for !97Cs spreading in the first months after 
the aceident, but this relevance fades in the long-term. Also, these 
authors found that concentrations would be nearly homogeneous over 
the whole Pacific after some 10 years. Simulations finally indicated a 
fast mixing over the upper 500 m of the water column. Similar results 
were found by other authors (Kawamura et al., 2014): radioactive 
caesium concentration was efficiently diluted in the North Pacific 2.5 
years after the accident. The meso-scale eddies in the Kuroshio Exten- 
sion (see Fig. 4) played an important role in diluting the radioactive