R. Perläfiez et al. 
be defined. If we are interested in solving transport induced by tides, 
temporal resolution must be much higher than the tidal period. Average 
circulation fields are used for longer range calculations, These fields 
can be daily averages, monthly averages, annual averages etc, again 
depending on the problem to be solved. Time step is also limited by 
numerical stability conditions (Kowalik and Murty, 1993). 
3.3, Water circulation 
The description of water circulation is a key factor in radionuclide 
'ransport modelling since, as commented before, water currents are 
he main vector in radionuclide transport in the sea. Even in box 
models, exchange rates between boxes are derived from water cir- 
culation patterns, as already mentioned. In addition, water currents 
and density stratification may also be used to derive the diffusion 
zoefficients describing turbulent mixing; for instance using the Richard- 
son number based schemes (Pacanowski and Philander, 1981), or the 
generic length-scale turbulence model (Umlauf and Burchard, 2003) for 
vertical diffusivity and the Smagorinsky’s scheme (Cushman-Roisin and 
Beckers, 2011) for horizontal diffusivity. Other methods exist to derive 
diffusivities (Kowalik and Murty, 1993) since turbulence is still an 
open problem in fluid dynamics and can only be parameterized. Most 
5f the circulation models are written in Boussinesq and hydrostatic 
approximations, Besides physical parameterizations (turbulent mixing, 
sxchange with atmosphere by heat and mass, ice cover), they differ in 
the vertical discretization (e.g. z-, @ and isopycnal coordinate systems) 
and horizontal discretization (structured and unstructured meshes). 
Reviews on physics and numerics of models and formulation of dif- 
‘usivities are given in James (2002) and Fox-Kemper et al. (2019). 
A description of equations, approaches and numerical methods used 
'n hydrodynamic models may be seen in the books by Kowalik and 
Murty (1993), Müller and von Storch (2004), Chassignet and Verron 
72006), Miller (2007), Kampf (2009, 2010), Cushman-Roisin and Beck- 
ars (2011) and Glover et al. (2011), among many others, Herzfeld 
et al. (2011) present an excellent review on the specification of open 
oundary conditions in ocean models. 
Generally speaking, there are two ways of obtaining water circu- 
lation for a radionuclide transport model: to use pre-computed fields 
[rom a global ocean forecasting system and to solve the fluid dynamic 
2quations in regional applications. These methods are briefly described 
ın the following subsections. 
3.3.1. Global models 
One option is to use pre-computed circulation by an operational 
global ocean forecasting system or reanalysis, in which past observation 
lata are assimilated by the circulation model. These circulation data 
may be downloaded from each model web page in binary format. For 
instance, a number of different ocean forecasting models were applied 
'o simulate the dispersion of FDNPP releases in the Pacific Ocean 
(Periäfiez et al., 2015a). Some examples of global models are: 
MOM, Modular Ocean Model. The model was developed and sup- 
ported by researchers at NOAA Geophysical Fluid Dynamics 
Laboratory (GFDL)®°. Initially it was developed by K. Bryan and 
M.Cox in 1960-1980s as a first global circulation model being 
permanently improved and extended. The model uses gener- 
alized orthogonal horizontal coordinates and variable vertical 
toordinates. 
HYCOM, Hybrid Coordinate Ocean Model. HYCOM® consortium is 
a multi-institutional effort sponsored by the National Ocean 
Partnership (NOPP) as a part of U.S, Global Ocean Data Assim- 
Jation Experiment (GODAE) (Bleck, 2001). HYCOM is a primi- 
ive equation general circulation model with vertical coordinates 
(hat remain isopycnic in the open, stratified ocean. 
$ https://www.gfdl.noaa.gov/mom-ocean-model/, 
& https://hycom.org/. 
Environmental Modelling and Software 122 (2019) 104523 
NEMO, Nucleus for European Modelling of the Ocean. NEMO’ is a 
framework of ocean related models for ocean dynamics and 
thermodynamics, for sea-ice dynamics and thermodynamics, 
and for tracer transport. The model uses a curvilinear orthogonal 
grid in the horizontal direction, and in the vertical direction it 
uses z—-coordinates, terrain-following coordinates, or a mixture 
of the two. The embedded zooms are created using the two-way 
nesting package AGRIF.* This is a package for the integration of 
adaptive mesh refinement features within a multidimensional 
model. The nesting capability allows resolution to be focused 
over a region of interest by introducing an additional grid. 
OFES, Ocean global circulation model For the Earth Simulator. 
OFES? was developed by the Japan Agency for Marine-Earth 
Science and Technology (JAMSTEC). Horizontal resolution is 
0.1°. and there are 54 vertical levels, with increasing thickness 
from the surface towards the sea bottom. A comparison of model 
performance with data in several regions of the global ocean 
may be seen in Masumoto et al. (2004). This model was used 
by Periäfiez et al. (2016a) to simulate historical releases from 
European nuclear fuel reprocessing plants in the North Atlantic. 
The reanalysis data can be downloaded from the Copernicus Marine 
Environment Monitoring Service (CMEMS)!, from the HYCOM web 
site or from several other databases, 
As an example, the surface circulation in the Pacific Ocean (aver- 
aged value for March 2011), as applied to simulate the transport of 
fukushima releases in the whole North Pacific (Periäfiez et al., 2019), 
is presented in Fig. 4. This water circulation was calculated in JAMSTEC 
(Japan Agency of Marine-Earth Science and Technology) with FORA! 
(Four-dimensional Variational Ocean ReAnalysis) model (Usui et al., 
2016). FORA is the first-ever dataset covering the western North Pacific 
Over the last three decades (1982-2014) at eddy-resolving resolution. 
This is a cooperative work of JAMSTEC and the Meteorological Re- 
search Institute, Japan Meteorological Agency (JMA/MRI) using the 
Earth Simulator. The domain extends 117° E-160° W, 15° N-65° N 
with horizontal resolution 1/10° in both longitude and latitude and 
54 vertical levels (0-6300 m). The general large scale circulation in 
the western Pacific Ocean is dominated by the interaction between the 
Kuroshio and Oyashio currents, The Kuroshio Current is the western 
voundary current in the north Pacific, which flows along the coast of 
Japan towards the north and curves to the central Pacific Ocean, then 
forming the so-called Kuroshio Extension, The Oyashio Current is a 
cold current which flows from the north. These two current systems 
converge in the coastal waters off Fukushima coast, which leads to the 
generation of unsteady eddies in the area, These features may be seen in 
Fig. 4. Transport calculations were carried out in the frame of the IJAFA 
MODARIA-II program (Periäfiez et al., 2019) with these hydrodynamic 
fields (monthly means from 2011 to 2014). 
3.3.2. Regional models 
Another option is to solve the fluid dynamic Navier-Stokes equa- 
tions to calculate water circulation (Kowalik and Murty, 1993) in the 
area of interest. This can be done either in on-line (water circulation 
and radionuclide transport calculated at the same time) or off-line 
(circulation is calculated in advance and stored) modes (Periänez, 
2005a). A numerical method is required and, as in the case with the 
transport model, the model structure must be selected according to 
the characteristics of the area (2D, 3D model etc.). Three well known 
regional models used in radionuclide transport studies are: 
7 http://www.nemo-ocean.eu/, 
3 http: //forge.ipsl.jussieu.fr/nemo/wiki/Users/SetupNewConfiguration/ 
AGRIF-nesting-tool. 
9 http://www.jamstec.go.jp/esc/research/AtmOcn/product/ofes,html#cite_ 
note-1. 
10 http://marine.copernicus.eu/. 
11 http://synthesis.jamstec.go.jp/FORA/e/index.html.