Environmental Modelling and Software 122 (2019) 104523 
R. Peridfiez et al, 
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ig. 4. Example of water circulation obtained from an ocean model. It corresponds to the average surface circulation in March 2011. The model is FORA (Four-dimensional 
/ariational Ocean ReAnalysis model; (Usui et al., 2016). This type of velocity vectors are used in Eulerian and Lagrangian dispersion models to evaluate advective transport of 
-adionuclides in the water column, and often also diffusion coefficients. 
POM, Priceton Ocean Model. POM'? was first described by Blum- 
berg and Mellor (1987). It is a sigma coordinate (terrain- 
following), free surface ocean model with embedded turbulence 
and wave sub-models, as well as wet-dry capability. This model 
has been used since the 1980s, and continues with innovative 
new developments until today. 
ROMS.!? The 3D baroclinic free-surface, terrain-following, primitive 
equations (Haidvogel et al., 2000; Shchepetkin and McWilliams, 
2009) are solved. The model, widely used for different appli- 
sations, includes ice and sediment transport modules, and the 
two-way nesting package AGRIF. Model equations are evaluated 
using orthogonal curvilinear coordinates in the horizontal and 
terrain-following coordinates in the vertical. 
SELFE/SCHISM. The 3D primitive equation model SELFE (Zhang and 
Battista, 2008; Roland et al., 2012) renamed now as SCHISM'* 
is an open-source community supported modelling system with 
an embedded wave model and a sediment transport model as 
well. This model is based on unstructured grids and localized 
sigma coordinates with shaved cell (LSC?), designed for seamless 
simulation of 3D baroclinic circulation across the scales. 
These models were used in many radionuclide transport calculations 
’e.g. Kobayashi et al., 2007; Miyazawa et al., 2012; Tsumune et al,, 
2012, 2013; Periäfez et al., 2016b; Maderich et al., 2017). 
3.4. Water/sediment interactions and other processes 
Radionuclide exchange between the dissolved and solid phases is a 
significant process in the transport of non-conservative radionuclides in 
he marine environment. A good general review is given in the book by 
Duursma and Carroll (1996). Water-sediment interactions are schemat- 
jcally shown in Fig. 5 (Maderich et al., 2017). In the water column, 
12 http://www.ecepo.odu.edu/POMWEB/. 
13 https://www.myroms.org/ 
14 http://cerm.vims.edu/schism/. 
radionuclides in the dissolved and particulate phases are transported by 
currents (advection processes) and turbulent diffusion. Radionuclides 
in the dissolved phase interact with the particulate phase in suspended 
sediments and bottom deposits. Exchange of activity between the dis- 
solved and particulate phases is described by adsorption/desorption 
processes. Settling of contaminated suspended sediments and bottom 
erosion result in radionuclide exchanges between the bottom and sus- 
pended sediment. The transfer of activity between the water column 
and the pore water in the bottom sediment is governed by bottom 
boundary layer turbulence regulated diffusional processes (Maderich 
et al, 2017). The migration of activity in the sediments is due to 
molecular diffusion, diffusion driven by bioturbation, bioirrigation and 
also due to advection driven by surface waves and by subsurface 
groundwater flow (Maderich et al., 2017). A basic microscopy theory 
of radionuclide water/suspended sediment interactions was given by 
Abril (1998). 
Radionuclide transfers between water and sediments were initially 
described in models in terms of the equilibrium distribution coefficient, 
ky, of the considered radionuclide [as for instance in the models by 
Abril and Garcia-Le6n (1993)]. The marine distribution coefficient for 
a given radionuclide, k,, is defined (Carroll et al., 1999; Johansson 
et al., 2001; IAEA, 2004; Takata et al., 2016; Periäfez et al., 2018) 
as the ratio between the radionuclide concentration in the solid phase 
(suspended matter or bed sediment) and the concentration in water 
(dissolved phase): 
C; 
ka = Sr’ 
where C, and C,, are, respectively, radionuclide concentrations in the 
solid (Bq kg!) and dissolved (Bq m7®) phases. Such concentrations 
have to be at equilibrium, ie., after the partition of the radionuclide 
between phases has reached equilibrium. This k, is measured in SI units 
of m’kg-1, Table 1 summarizes recommended k, values (IAEA, 2004) 
for ocean margin and open ocean and for a number of elements, 
Thus, in the first models it was assumed that partition of the ra- 
dionuclide between the liquid and solid (suspended matter and/or bed 
sediments) achieves instantaneous equilibrium. From the radionuclide 
concentration in water, knowing the radionuclide k,, concentration in