R. Peridfiez et al 
Table 2 
<inetic rates (s-!) for several radionuclides, as derived from adsorption experiments: 
3erretzen and Salbu (2000) for 1°%Cd and °Co, Barretzen and Salbu (2002) for 194Cs 
and Nyffeler et al. (1984) for the rest of radionuclides. A zero rate means that such 
reaction is not relevant in the temporal frame of the experiment. 
2 
107* 
I 5,9 x 107% 
2.2 x 107? 
4,6 x 107? 
m 1.9 x 1072 
A 1.7 x 1071 
. 2.9 x 107* 
ae 1.7 x 107? 
En 4.5 x 10-3 
ee 2.1 x 1073 
on 4,1 x 107’ 
23Hg 
„1075 
2X 1073 
12x 1075 
1.2 x 10-5 
4.1 x 1077 
2,7 x 107 
1.2 x 1075 
5,8 x 10-6 
3.7 x 1076 
1.2 x 1075 
12x 1076 
x 1076 
LO>x 1076 
10x 10: 
6,9 x 10-8 
2.1x 107 
5.9 x 10-8 
0 
J 
3 
2,0x 10-7 
1.0x 1077 
4.0x 1078 
J 
and sediments, as those described in Berretzen and Salbu (2000, 2002) 
and Nyffeler et al. (1984). As an example, kinetic rates derived from 
hese experiments are shown in Table 2. It should be taken into account 
‘hat these values must be considered as tentative since kinetic rates are 
zite specific, depending on the water and sediment properties. Overall, 
information about kinetic rates is generally scarce in current literature, 
More complex water/sediment interaction models which involve 
parallel and consecutive reactions have been formulated as well (Barros 
and Abril, 2004; Benkdad et al., 2008), but they have not been yet 
mplemented in a marine radionuclide transport model. 
From our experience, it is also relevant to develop models of ra- 
ldionuclide migration in the seabed for heterogeneous environments 
where the sediment characteristics (sediment fractions, densities and 
porosity) vary in space (Aldridge et al., 2003; Higashi et al., 2015; 
Maderich et al., 2017): a few years after the Fukushima accident, 
jottom sediments on the Japan shelf have become the main source 
nf radionuclide remobilization to the water column due to the rapid 
dilution of radionuclides by intensive currents and eddies (Buesseler 
et al., 2017). Similarly, desorption from bottom sediments is the main 
source of dissolved!®7Cs in the Irish Sea following the reduction of rou- 
tine releases from Sellafield reprocessing plant (Mitchell et al., 1999). 
A detailed discussion on the water/sediment interaction problem can 
be found in Periäfez et al. (2018). 
Other processes may be included in marine transport models, if 
required. For instance, the behaviour of plutonium in aquatic systems 
is of considerable complexity due to the fact that it can exist in 
different oxidation states simultaneously and these change in time, 
Thus, Pu (Il) and Pu (IV) predominate as the reduced forms and Pu 
(V) and Pu (VD) as the oxidized forms (Mitchell et al., 1995). The 
reduced Pu is highly reactive with particles and possesses a distribution 
zoefficient that is two orders of magnitude higher than that of the 
more soluble oxidized Pu (Mitchell et al., 1995). Hence the k, values 
observed in field measurements represent the properties of the mixture 
of oxidation states that is present in the particular sample. Also, the 
oxidation state of Pu may change with time. For instance, Pu is released 
from Sellafield reprocessing plant in a reduced form, but after some 
days an equilibrium in the partition of Pu between the reduced and 
oxidized species is achieved. Redox reactions may be included in a 
model using kinetic rates, similarly to uptake/release reactions between 
water and sediments. Details may be seen in Perianez (2003b). A model 
‘or plutonium behaviour in the marine environment representing the 
oxidation state distribution and partitioning of plutonium between the 
soluble, colloidal, suspended particulate and seabed sediment fractions 
in the vicinity of the Sellafield plant was presented in Vives i Batlle 
st al. (2007). However, this model consisted of a single box in the 
Sellafield area and, in consequence, spatial distributions could not be 
obtained from it. 
Environmental Modelling and Software 122 (2019) 104523 
Table 3 
Generic parameters used in the dynamic biological uptake model (from Maderich et al. 
2014a) for 197Cs, The concentration factor for phytoplankton is CR,,,,, = 20 1/kg. 
BEE O0PENNL9L)ß 
Zooplankton Non-pisc, fish Pisc. fish 
Tos (day) 5 75 200 
0.2 0.5 0.7 
Y 0.001 0.001 0.001 
K, (day!) 1.0 0.035 0,0055 
Kı, (m’/kg day) 15 0.1 0.075 
3.5. Biological uptake models 
A further step is to integrate dynamic biota uptake models and 
turnover models within marine dispersion models, This was done in 
most box models using an equilibrium approximation based on a con- 
centration factor, CR, between water and biota, This CR, in analogy 
with the k,, is defined as the ratio between radionuclide concentration 
in a given species of biota and concentration in water: 
Cpio 
CR= To (18) 
Thus, concentration in biota, Cy, can be calculated from the CR 
and the calculated concentration in water, assuming equilibrium (Car- 
valho, 2018). 
In a recent model intercomparison carried out within the JAEA 
MODARIA programme (Vives i Batlle et al., 2016) it was shown that 
dynamic biota models, which handle situations out from equilibrium, 
perform better than equilibrium models. It was also demonstrated that 
a more correct description of radionuclide concentration in biota, by 
means of kinetic modelling, has a significant influence for radioecolog- 
ical dose assessment and, therefore, for decision-making, 
A basic dynamic model consists of four species (Heling et al., 
2002; Maderich et al., 2014a,b) : phytoplankton, zooplankton, non- 
piscivorous and piscivorous fish (Fig. 6, from (Maderich et al., 20143). 
The basic equation connecting concentration of activity in predator 
Cyred (Bq kg7 wet weight) with activity concentration in food C/ (Bq 
kg-1 wet weight) is: 
OCyred 
Fa = aKıCy + bKuCyw - Ko.5Copred» (19) 
where K, (s“!) is food uptake rate, a is the transfer coefficient through 
food, K,, is water uptake rate (s”!), b is the transfer coefficient from 
water and C,, is activity concentration in water (Bq m79). Kos is the 
radionuclide elimination rate from the body of the organism given 
by Kos = In27T;2, where Tos is the biological half-life of the ra- 
dionuclide(s). Thus, all organisms take radionuclides from water, phy- 
toplankton is the food for zooplankton, zooplankton is the food for 
non-piscivorous fish and this is the food for piscivorous fish (as sum- 
marized in Fig. 6). Phytoplankton exchanges radionuclides only with 
‘he water via adsorption and desorption processes, Due to the rapid 
uptake and short retention time of radioactivity, the concentration 
of radionuclides in phytoplankton is calculated using the equilibrium 
approach: 
Cppyto = CRypytoCws (20) 
where CRopo (m’kg-*, wet weight) is the concentration ratio for 
phytoplankton (see Eq. (18)). Standard literature values for all these 
parameters for the four considered species may be seen in Table 1 
in Maderich et al. (2014a), which is reproduced in Table 3. Further 
improvement of biota models includes the description of radionuclide 
transfer using metabolic rates of the marine organism, model which 
was developed by Konovalenko et al. (2014). The dynamic approach 
given by (19), combined with a model of spatial and temporal biomass 
dynamics, was applied by Walters and Christensen (2018). 
An organism is described as a single box in most dynamic biota 
models. In D-DAT model (Vives i Batlle et al., 2008) the organism