R. Periäfiez et al. 
of the advantages of Lagrangian models is that they do not introduce 
*his numerical diffusion). In particular, some numerical experiments 
with a Fukushima Eulerian advection-diffusion model were performed 
and effective diffusivities along time were evaluated (Dietze and Kriest, 
2012). High initial values were attributed to numerical diffusion in 
‘he initial release phase, due to the high concentrations gradients. 
After, effective diffusivities decreased and finally increased again once 
radionuclides entered the high-eddying Kuroshio system. 
Effective diffusivity increases with the model cell size, since a larger 
cell size implies that larger eddies are not solved, and thus have to be 
accounted for as sub-grid mixing. Eddy and non-resolving eddy models 
were compared in Behrens et al. (2012) for instance. They found that 
the non-eddy model underestimated lateral dispersion of the Fukushima 
plume in the Pacific. Eddy and non-resolving eddy models were also 
compared in Simonsen et al. (2017) for the North Atlantic Ocean, 
where transport of 9”Tc released from Sellafield reprocessing plant was 
simulated. 
Constructing an accurate Lagrangian numerical scheme for simul- 
taneous simulation of advection and diffusion is also a challenging 
problem. In the general case of diffusion in a complex flow field, the 
centre of mass of the particle distribution may not follow the stream- 
lines of the flow field, whereas the random distribution of particle 
locations due to diffusion can depend on the flow field. 
Finally, the radionuclide release area size has to be considered. In 
Eulerian models, radionuclides are homogeneously distributed into the 
telease cell where the accident occurs; this would be the initial patch 
minimum size, Thus, the initial patch size depends on the model spatial 
zesolution. In contrast, a real point source can be used in a Lagrangian 
nodel. 
5.3. Uncertainties in water circulation models 
Existing state-of-the-art marine dispersion models are robust tools 
in our opinion, providing consistent results (Periänez et al., 2016b). 
However there are problems with the predictions of hydrodynamic 
nodels in energetic regions characterized by strong current variability, 
like Fukushima waters and the North Western Pacific region, charac- 
terized by the very strong and fluctuating Kuroshio current and its 
extension (Masumoto et al., 2012) -a map of currents may be seen in 
3ig. 4. In the frame of IAEA MODARIA program it was shown that 
the energetics of the considered system (magnitude and variability of 
currents) control the agreement between different dispersion models 
(Perläfiez et al., 2016b). Good agreement could be achieved between 
models of very different type in environments characterized by weak 
zurrents, However, even similar models led to significantly different 
results in highly dynamic systems characterized by strong and variable 
currents, Two marine environments were studied: a highly dynamic 
system (Fukushima coastal waters) and a semi-enclosed basin (Baltic 
5ea). The models applied to the Baltic Sea included two box models, a 
{ull three dimensional model including water and ice thermodynamics 
and a depth-averaged two dimensional model forced with mean annual 
winds, Thus, very different approaches were used (details may be seen 
in Periäfiez et al., 2015b), In the case of the Baltic Sea results of 
models were in good agreement despite of the different approaches 
and simplifications applied by models. On the contrary, in the case 
of FDNPP accident, even similar hydrodynamic models led to differ- 
ent current fields which, in turn, led to very different radionuclide 
dispersion patterns. Given the intensity and variability of currents 
in this area, as well as the presence of unsteady eddies due to the 
instability of currents, small differences in the hydrodynamics may 
5aroduce different dispersion patterns. These differences tend to be 
amplified with time, For highly dynamic environments, the dispersion 
model output is extremely sensitive to the ocean model which is used to 
>btain circulation. Simulation results from a single oceanic advection- 
liffusion model and multiple oceanic general circulation models were 
compared in Kawamura et al. (2017), arriving at similar conclusions. 
Environmental Modelling and Software 122 (2019) 104523 
Thus, we may state that the ocean model should be selected with 
great care and after a detailed comparison with local measurements 
of currents. 
In this sense, the spatio/temporal scale of interest is also relevant. 
When simulating the transport of Fukushima releases in the Pacific 
Ocean, it was found that the initial current field is relevant for 137Cs 
spreading in the first months after the accident. However, this relevance 
fades in the long-term (Behrens et al., 2012). 
Additionally, it can be pointed out that, if measurements of radioac- 
Hvity concentration are available, then assimilation of observations is 
a powerful tool to improve the predictive capabilities of radionuclide 
transport models (Yuschenko et al., 2005). 
5.4. Emergency modelling 
One of the main applications of marine dispersion models is their 
use as predictive tools to assess radionuclide concentrations after an 
accident in order to support decision making. Three stages after a nu- 
clear accident in a coastal facility were defined by our group (Periäfiez 
et al., 2016b): emergency phase, post-emergency phase and long term 
phase. They are characterized by increasing spatio-temporal scales, and 
each one requires a specific kind of model to give response to decision 
makers. It must be noted that an ideal model which could be applied for 
all spatio-temporal scales does not exist. Of course physical-chemical 
processes are the same, but depending on the scales in which we are 
interested the numerical realization and involved simplifications are 
different. This leads to the different modelling approaches defined in 
Section 3.1. 
The prediction of radioactivity dispersion in the emergency phase 
days-weeks) should be carried out using robust models and numerical 
tools. Two approaches can be used, The first consists of the use of 
local forecasts of marine circulation linked to the transport and biota 
models (e.g. Duffa et al., 2016) when this local model is operational. 
However, such local forecasts are often unavailable or result in large 
computational burdens, Therefore, in several decision-support systems 
(DSS) another approach is used: the forecast of marine circulation from 
operational ocean models, In the JRODOS DSS (Maderich et al., 2016) 
the dispersion of radioactivity was calculated using velocity fields from 
pperational ocean models (Copernicus Marine Environment Monitoring 
Service‘®), It covers the European seas with 3-6 km resolution and the 
global ocean with resolution about 10 km. A similar approach was used 
by Kobayashi et al. (2017): the Short-Term Emergency Assessment sys- 
tem of Marine Environmental Radioactivity (STEAMER) was developed 
:o predict radionuclide migration for a nuclear accident in the ocean 
around Japan at 8 and 30 days using operational ocean models, 
An interesting modelling study was carried out by Kauler et al. 
(2016). The model was used to determine the areas where a nuclear 
accident (involving a nuclear powered vessel) would affect a sensitive 
point (in this case a fishery zone). Thus, the model was not used to 
deal with an emergency; instead it was used as a prevention tool since 
traffic of nuclear vessels could be banned across given areas. 
Although global ocean models produce realistic pictures of the 
general circulation in the ocean, their outputs differ in the local scale in 
dynamic environments, This may be, at least in part, attributed to their 
relatively coarse spatial resolution. The problem is then to assess the 
best way to develop a reliable model to support decision-making after 
an emergency, A multi-model approach, as described by Monte et al, 
(2008), may be of interest when environmental processes are complex. 
Through this approach, the conclusions that obtain the greatest degree 
of consensus among modellers are made evident and the aspects that 
are subject to dispute and which should therefore be handled carefully 
also become clear. Nevertheless, a multi model application is not the 
perfect choice when an emergency is involved and a rapid response 
15 http://marine.copernicus.eu/web/69-interactive-catalogue.php.