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Environmental Modelling and Software 122 (2019) 104523 
BB: Bothnian Bay 
BS: Bothnian Sea 
F: Finland Bay 
R: Gulf of Riga 
BW: Baltic Sea West (deep 
and surface) 
BE: Baltic Sea East (deep 
and surface) 
B: Belt Sea (deep and 
surface) 
K: Kattegatt (deep and 
surface) 
N 
WM 
AO 
vap 
AM 
TR 
Ya 
m 
&: 
ar 
Fig. 3. POSEIDON (Lepicard et al., 2004) and NRPA (losjpe et al., 2002) model box structures for the Baltic Sea. Pink lines define NRPA model boxes and numbered boxes 
torrespond to POSEIDON. Biue boxes are those divided into two water layers (surface and deep). A grid suitable for an Eulerian model covering the Gulf of Finland is also shown. 
it was used in the model described in Periäfez et al. (2015b), The colorbar indicates water depths in m, which are specified for each grid cell. A similar grid is required in 
Lagrangian models to derive radionuclide concentrations from the number of particles per volume. 
where d, is mean water depth in box 7. If radioactive decay is also 
considered, then i would be added to the q; above, which is the 
radioactive decay constant of the considered radionuclide. Similarly, 
activity in the bottom deposit is partitioned between pore water and 
sediment particles using the distribution coefficient. The equation for 
the temporal evolution of combined aqueous and adsorbed activity in 
:he bottom deposit is derived taking into account molecular diffusion, 
oturbation and burial processes, 
As an example, two different box structures adopted for simulating 
‘he transport of radionuclides in the Baltic Sea (Periäfiez et al., 2015b) 
are presented in Fig. 3, 
Although in box models water/sediment interactions are described 
9y equilibrium distribution coefficients, as commented above, the 
present trend is to apply kinetic rates. Thus, water/sediment interac- 
dons are described dynamically. This dynamic description is presented 
in Section 3.4. 
3.1.2. Eulerlan models 
In Eulerian models the differential equations giving temporal and 
spatial evolution of the radionuclide concentrations in different states 
(e.g. dissolved in water column and pore water in sediments, fixed 
on the suspended and bottom sediment etc.) are solved. The general 
compact form of these equations for concentration of radioactivity C, 
in state a per unit of volume (Bq m-°3) or per unit of mass (Bq kg-1) 
are written in Cartesian coordinates as: 
(a) 
2 (x, 5) + X knC +5, - 4C, 
where (x, y, z) are Cartesian coordinates, U, Ux and w, are components 
of flow field for the radionuclide in the state a. In general, velocity can 
differ for different states (e.g. due the presence of settling velocity for 
suspended sediment or it may be zero in the bottom deposit). K, and 
K, are turbulent or molecular diffusivities in the horizontal and vertical 
directions respectively, and/or biodiffusivity in the bottom deposit, 
which are variable in time and space. The term Xo=1 KaxCg describes 
first order reactions between the radionuclides in different states, where 
Cox are kinetic transfer coefficients (they are defined in Section 3.4) 
and X%_, kg = 0 for each a; S, is the source term (defined as in the 
box models) and 4 is the radionuclide decay constant. Equations for 
the water column and bottom sediment layer are linked by fluxes of 
activity. A numerical solution of these equations is required; usually 
applying finite differences (Periäfiez, 2005a), An example of a Compu- 
tational grid which may be used to apply a finite difference techniaue