R. Peridfiez et al. 
from the model is required. In any case, it may help to select the 
most adequate characterization of water circulation to be used in the 
»perational dispersion model in the development stage. However, there 
may be cases when an “outlier model" is closer to observations than 
"he “consensus", An example is provided in IAEA (1995) -pages 26- 
28. Care should be taken with these cases. In our opinion, site specific 
-ools should be carefully developed, tested and then made available for 
any marine area potentially exposed to a radionuclide release. In other 
words, we cannot be a priori confident in generic models which import 
ocean forecasts of currents if a highly dynamic environment is involved. 
The source term information is an important but not solved issue 
in emergency modelling. Usually, it cannot be directly obtained and 
it is necessary to solve the inverse problem of source determination 
using marine monitoring data, as already commented. If these data are 
not available in the emergency phase, then an automatic prediction 
mode can be used assuming a unit release rate directly to the ocean 
and/or in the atmosphere (Kobayashi et al., 2017). These predictions 
can be useful for prohibiting fishing and sailing over given sea areas 
and setting up an emergency Ocean monitoring corresponding to a 
realistic marine pollution area. At the post-emergency phase an inverse 
modelling, as described in Section 4, could be used. 
5,5. Selecting a radionuclide transport model 
The most significant processes governing the transport of radionu- 
‚Jides in the marine environment are advection by currents, turbulent 
nixing, water/sediment interactions and biota uptake. The different 
'ormulations and numerical treatments of these processes lead to the 
lifferent modelling approaches which have been discussed in the paper. 
Thus, advection and mixing may be solved using a box, an Eulerian or 
a Lagrangian model. Water/sediment interaction and biota uptake may 
be described, essentially, using an equilibrium or a dynamic model. But, 
as commented before there is not a model which can be applied to all 
situations, Le., to all spatio-temporal scales. 
The basic assumptions in box models (uniform and instantaneous 
mixing of radionuclides within each box) make these models well suited 
to long-term assessments over large spatial scales. Thus, they are useful 
‚ools in the long-term phase of an emergency (Section 5.4), as well 
as for the environmental assessment of chronic releases from nuclear 
facilities, In addition, involved mathematics are relatively simple and 
these models are easy to program or to adapt to specific cases. Finally, 
detailed water circulation patterns are not required since the only 
needed parameterization is water fluxes between boxes. 
Eulerian and Lagrangian models make use of detailed water circu- 
lation fields, changing in time and space. Thus, these models provide 
Jistributions of radionuclides in space and time, which make them 
appropriate for the emergency and post-emergency phases of an ac- 
zident (Section 5.4). The mathematical formulation and solution on 
hese models are more complex than in box models and therefore 
‘hey are more difficult to program or to customize. Moreover, these 
nodels require the mentioned water circulation fields as input data; 
information which is not always easy to obtain and accurate enough, 
as already discussed (Section 5.3). 
Lagrangian models are specially well suited to the emergency phase 
of an accident, since they do not introduce numerical diffusion (Sec- 
jon 5.2) and thus can handle the very high concentration gradients 
between contaminated and clean water which would be expected after 
an acute radionuclide release into the sea. In addition, computation can 
be significantly faster than in Eulerian models when the contaminated 
area initially is a small part of the whole computational domain and 
ıf the number of particles in the simulation is reasonable (typically 
a few tens of thousands). This is another advantage to be considered 
in emergency modelling, when a fast response must be forwarded 
to decision-makers. Finally, a real point source may be defined in 
Lagrangian models (Section 5.2); in Eulerian models the initial patch 
Environmental Modelling and Software 122 (2019) 104523 
size is defined by the grid spatial resolution. Consequently, lower peak 
concentrations are expected from Eulerian models. 
Eulerian models present the advantage, over Lagrangian ones, that 
the inclusion of additional processes is simpler since only the addition 
of new terms to the transport differential equations is required. For 
instance, including multi-stage water/sediment interactions and/or re- 
dox reactions can be done in an easier way in Eulerian models. Also, 
the number of particles required in a Lagrangian simulation increases 
as the number of sub-compartments (i.e., different oxidation states in 
water, different speciation states in sediments) increases. Consequently, 
an Eulerian model may be more efficient than a Lagrangian one if these 
processes are the main focus of the simulations. Eulerian models are 
also more appropriate for simulating spatially extended radionuclide 
sources (for instance due to atmospheric fallout) over large areas since 
many particles would be required in a Lagrangian simulation, which 
would be computationally more expensive. 
Regarding water/sediment interactions and biota uptake, they can 
be described using equilibrium or dynamic models, as commented. 
Again, each approach has advantages and disadvantages, The obvious 
advantage of equilibrium models is their simplicity and the fact that few 
parameters are required; only water/sediment distribution coefficients 
and biota concentration ratios. The equilibrium assumption implies that 
these models may be applied in long-term assessments over wide spatial 
scales; thus they are well suited to be included within box transport 
nodels. In contrast, these models should not be used for emergency 
purposes and for assessments of chronic releases near the radionuclide 
source, since equilibrium is not achieved. Dynamic models should be 
used in these cases; but the main difficulty with these models, in 
addition to their more complicated formulation, is that a significant 
ıumber of parameters are required, These parameters are radionuclide 
and site specific; information about them is generally scarce and only 
tentative values can be used in many cases, 
Thus, all model types are useful tools for assessments of marine 
radionuclide transport, provided that each model is applied to suitable 
spatio-temporal scales. A model which can be applied in all situations 
does not exist because of practical computational limitations. 
6. Conclusions 
Significant advances in techniques for simulating the transport of 
radionuclides in the marine environment have taken place in the last 
years. Currently, most models do not only solve the transport in the 
dissolved phase (advection and turbulent mixing), but also include in- 
teractions with sediments and biota, There is a general trend consisting 
of describing sediment processes in a dynamic way, by means of kinetic 
transfer coefficients; instead of using an equilibrium approach based 
upon distribution coefficients, k,s, since an equilibrium approach leads 
»o significant errors in the near field, both in the cases of chronic and 
accidental releases. More detailed processes, such as redox reactions 
“which are relevant in the case of plutonium) may be also described in 
dynamic models. The most recent efforts are directed to include bio- 
logical uptake models within the marine dispersion model. It has been 
‘gund that biological uptake is also better described using dynamic than 
equilibrium models, 
Generally speaking, three kinds of models exist: box models, Eule- 
rian and Lagrangian models. Models also differ in structure (from one- 
dimensional to full three-dimensional models) and resolution, ie., the 
same physico-chemical processes are described in different ways. A 
universal model which is able to describe all the spatial and temporal 
scales in a marine dispersion problem does not exist because of practical 
computational limitations. Thus, it is essential to have the different 
implementations mentioned in this paper. 
Recently, it was found that the main source of uncertainty in 
marine transport models is due to water circulation in highly dynamic 
environments characterized by strong and variable currents. Thus, 
narine transport models are robust tools, providing consistent results.