Computational Water, Energy, and Environmental Engineering, 2013, 2, 61-68
doi:10.4236/cweee.2013.22B011 Published Online April 2013 (http://www.scirp.org/journal/cweee)
Atmospheric Dispersion and Deposition of Radionuclides
(137Cs and 131I) Released from the Fukushima Dai-ichi
Nuclear Power Plant
Soon-Ung Park, Anna Choe, Moon-Soo Park
Center for Atmospheric and Environmental Modeling, Seoul, Korea
Received 2013
ABSTRACT
The Lagrangian Particle Dispersion Model (LPDM) in the 594 km × 594 km model domain with the horizontal grid
scale of 3 km × 3 km centered at a po wer plant and the Eulerian Transport Model (ETM) modified from the Asian Dust
Aerosol Model 2 (ADAM2) in the domain of 70° LAT × 140° LON with the horizontal grid scale of 27 km × 27 km
have been developed. These models have been implemented to simulate the concentration and deposition of radionuc-
lides (137Cs and 131I) released from the accide nt of the Fukushi ma Dai-ic hi nuclear p ower plant. I t is found that both
models are able to simulate quite reasonably the observed concentrations of 137Cs and 131I near the power plant.
However, the LPDM model is more useful for the estimation of concentration near the power plant site in details whe-
reas the ETM model is good for the long-range transport processes of the radionuclide plume. T he estimated maximum
mean surface concentration, column integrated mean concentration and the total deposition (wet+dry) by LPDM for the
period from 12 March to 30 April 2011 are, respectively found to be 2.975 × 102 Bq m-3, 3.7 × 107 Bq m-2, and 1.78 ×
1014 Bq m-2 for 137Cs and 1.96 × 104 Bq m-3, 2.24 × 109 Bq m-2 and 5.96 × 1014 Bq m-2 for 131I. The radionuclide
plumes released from the accident power plant are found to spread wide regions not only the whole model domain of
downwind regions but the upwind regions of Russia, Mongolia, Korea, eastern China, Philippines and Vietnam within
the analysis period.
Keywords: Eulerian Transport Model; Fukushima Nuclear Power Plant; Lagrangian Particle Dispersion Model;
Radionuclides of 137Cs a nd 131I
1. Introduction
On 11 March 2011, an extraordinary magnitude 9.0
earthquake occurred off the Sanriku about 180 km off the
Pacific coast of Japan’s main island Honshu, at 38.3 °N,
142.4 °E and followed by a large tsunami [1]. These
events caused a station blackout at the Fukushima
Dai-ichi nuclear power plant. As a consequence, four of
the six Fukushima Dai-ichi nuclear power plants units
heavily damaged, and causing a massive discharge of
radionuclides into the air and into the ocean.
Fukushima Dai-ichi nuclear power plant consisted of
six boiling water reactors lined up directly along the
shore. The earthquake triggered the automatic shutdown
of the chain reaction in the units 1 to 3 at 05:46 UTC
(14:46 JST) on 11 March 2011. Outside power supply
was lost and the emergency diesel generators started up.
However, the tsunami arrived 50 minutes later and inun-
dated the reactor sites and their auxiliary buildings and
caused the total loss of AC power. Cooling of the reactor
cores was lost, water levels in the reactor pressure ves-
sels could not be maintained and the cores in all three
units that had been under operation, were degraded and
partially (or even completely) melted. The hydrogen
produced in this process caused major explosions that
massively damaged the upper parts of the reactor build-
ings of units 1 and 3. Damage to the upper parts of the
reactor building could be prevented in unit 2, however, a
hydrogen explosion were presumably damaged the sup-
pression chamber [2].
During the Fukushima accident period, massive ra-
dioactive materials were released to the environment.
Several studies have been devoted to estimate released
radioactive materials from this accident. Stohl et al.
(2012) have made a first guess of released rates based on
fuel inventories and then subsequently improved by in-
verse modeling using the atmospheric transport model
and measurement data. The release duration and radioac-
tivity ratios of 131I/137Cs for the period between 05:00
JST on March 12 to 00:00 JST May 1 in 2011 have been
reported [1,3-5]. However, the estimated radionuclides

S.-U. PARK ET AL.
62
emis sion flu xes have b ee n rep or ted t o b e highl y sens iti ve
to the first guess of released rates. The estimated total
137Cs emission flux ranged from 9.1 PBq (JAEA, 2011)
for the period of 10-31 March to 36.6 PBq for the period
of 10 March to 20 April [2].
To assess air and water contamination levels resulting
from the Fukushima accident, as th is will be an important
consideratio n whe n e valuatin g the variou s app licatio ns to
the mitigation measures, the estimates of the dispersion
and deposition of radionuclides are required over the site
and o n the r egio nal sca le fo r a give n e missio n flu x. Si nce
the topography in the vicinity of the Fukushima Dai-ichi
plant is complex, the Eulerian transport model may not
be useful to simulate the detailed concentration and de-
position of radionuclides even though it may be reasona-
ble to be used for the simulation of them in a regional
scale.
For this purpose the Lagrangian Particle Dispersion
Model (LPDM) developed by Park (1998) [6] in the 594
km × 594 km model domain centered at a power plant
and the Eulerian transport model modified from the
Asian D ust Aerosol Model 2 (ADAM2) [7] in the model
domain of 140 degree longitudinal distance and 70 de-
gree latitudinal distance co-centered with LPDM have
been developed to estimate the concentration and deposi-
tion of radionuclides released from the nuclear power
plant. The LPDM model and the Eulerian Transport
Model (ETM) have, respectively, 3 km  3 km and 27
km  27 km grid spacing of a mesoscale meteorological
model with 25 vertical layers. The ETM uses the esti-
mated concentration by LPDM in the Lagrangian model
domain as the source for the long-range transport.
The purp ose of this study is to estimate co ncentrations
and depositions of radionuclides of 131I in the gas phase
and 137Cs in the aerosol phase released from the Fuku-
shima accident for the period from 05:00 JST 12 March
to 24:00 JST 30 April 2011 using both LPDM and ETM
not only in the eastern Japan but in the regional domain
including the Pacific Ocean and Asia.
2. Model Descri ption
2.1. Meteorological Model
The meteorological model used in this study is the
fift h-generation mesoscale model of non-hydrostatic ver-
sion ( MM5, P SU/NCAR ) in the x, y, a nd coordinates [8,
9].
The model domains include the LPDM domain (Fig-
ure 1(a)) and t he ETM domain (Figure 1(b)) centered by
the F ukushi ma Dai -ichi nclear po wer plant (Figure 1(b)).
The horizontal resolution of ETM is 27 km while that of
the LPDM is 3 km with both 25 vertical layers. The si-
mulations with both models have been conducted for the
period of 05:00 JST 12 March to 24:00 JST 30 April
2011. The 6 hourly reanalyzed National Center for Envi-
ronmental Program (NCEP) data are used for the initial
and boundary conditions for the MM5 model. The results
of the MM5 model are used for ETM. The nested MM5
model in the horizontal resolution of 3 km is used for the
LPDM model.
2.2. Eulerian Transport Model (ETM)
The Eulerian transport model (ETM) has been obtained
from the modification of the Asian Dust Aerosol Model 2
(ADAM2) [7]. The radionuclide concentrations esti-
mated by LPDM in its domain are used for the source of
ETM for the long-range transport of contaminants. The
ADAM2 used 11 particle-size bins with near the same
logarithmic intervals for the particles of 0.1 - 37 μm in
radius [10,11]. This has been changed to the logarithmic
size distribution with an aerodynamic mean diameter of
0.4 m and a logarithmic standard deviation of 0.3 for
137Cs [2], but for 131I, the ADAM2 model has been
chan ged to handle the gas p hase contami nants.
m
Figure 1. Domain for (a) the Langangian particle dispersion
model and (b) the Eulerian transport model with the to-
pography. Monitoring sites (A-C) and the Fukushima nuc-
lear power plant site (whit e star) are in dicated.

S.-U. PARK ET AL.
63
2.3. Lagrangian Particle Dispersion Model
(LPDM)
The LPDM model [6,12-16] is based on conditioned par-
ticle concepts in which the conditioned particle is mov-
ing with the mean field velocity and the Lagrangian tur-
bulent velocity. The released particle is continuously
traced to find its position with time; that is
'
()()( ()())
ii ii
XttXtut utt+∆ =++∆
, i=1,2,3 (1)
where
i
X
is the positio n o f the Lagran gian pa rticle,
i
u
,
and
'
i
u
are the grid scale velocity component that are
resolved by the meteorological model and the subgrid
scale velocity component respectively, and
t∆
is the
integral time step.
The subgrid scale velocity component is
''1/2 "
,,
,3 ,
()( )()(1( ))()
(1( ))
iLi iLii
i Li d
uttR tutR tut
R tw
δ
+∆ =∆+−∆
+ −∆
(2)
where ,Li
R
is the Lagrangian auto correlation coeffi-
cient, ,3i δ
is the Kronecker delta,
"
i
u
is the random
turbulent velocity component and d W is the drift cor-
rec tion in vertica lly i n homo geneo us turb ulence [17 ]. All
necessary parameters and parameterizations are de-
scribed in details in Park (1998) [6].
The LPDM model takes into account deposition
processes; the dry deposition and wet deposition
processes. Dry deposition of radionuclides is estimated
with the dry deposition velocity,
d
V
multiplied by con-
centration of radionulides near the surface (
s
h
). T he dry
deposition velocity,
d
V
is parameterized with the use
of the inferential method [18,19] with taking into account
a gravitational settling velocity,
t
V
for the case of a
particle i n s uch a wa y that
1
dt
abc
VV
RRR
= +
++
(3)
where
a
R
is the aerodynamic resistance,
b
R
the quasi-
laminar sublayer resistance,
c
R
the surface or canopy
resistance and
t
V
the terminal velocity of a particle. The
terminal velocit y is given by
2
18
pp
t
gD
V
ρ
µ
=
(4)
where
p
ρ
is the density of a particle, g t he gra vity, p D
the diameter of a particle and
µ
the dynamic viscosity
of air.
In thi s st udy, 137Cs is assumed to be in a particle phase
with the density of 1,900 kg m-3 and a logarithmic size
distribution having an aerodynamic mean diameter of 0.4
μm and a logarithmic standard deviation of 0.3, while 131I
is assumed to be in a noble gas phase.
A Lagrangian particle with a hypothetical mass of Qk
positioned at (xk, yk, zk) produces the near surface con-
centration (he ight of hs) of
0.693 /
3
22 2
22 2
(,, )(2)
( )()()
exp[]
222
t
k
ks
kx ky kz
kk ks
kx kykz
Qe
C xyh
xxyy zh
τ
π σσσ
σσ σ
−
= ⋅
−−−
−− −
(5)
where σkx, σky, and σkz are, respectively the standard devi-
ation of the diffusio n distance in the x, y, a nd z dire ctions
associated with the k’s Largrangian particle, and τ is the
half life time of the radionuclide. hs is assumed to be 5 m
above the ground.
The deposition flux due to the k’s Lagrangian particle
is
0.693 /
3
22 2
22 2
(2)
( )()()
exp[ ]
222
t
kd
k
kx ky kz
k k ks
kx kykz
QVe
F
xx yy zh
τ
π σσσ
σσ σ
−
= ⋅
−−−
−− −
(6)
Therefore, the total mass depo sition of t he k’s Lagra n-
gian particle, Qd is
2
2
3
22
22
()
exp[ 0.693]exp[]
2
(2)
( )()
exp[ ]
22
ks
k
kz
d
kx ky kz
kk
d
kx ky
zh tt
Qt
Q
xx yy
V dxdy
τσ
π σσσ
σσ
∞∞
−∞ −∞
− +∆
∆− −
= ⋅
−−
−−
∫∫
(7)
Due to depo sition the k’s Lagrangian p article will lose
the mass of Qd after Δt time and results in a reduced mass
of k particle after time interval Δt is
'
k kd
QQQ= −
.
The k’s Lagrangian particle is assumed to be totally
deposited on the ground if zk is ne gative and
| |3
k kz
z σ ≥
,
otherwise it will be reflected from the ground with the
reduced mass of
'
k
Q
.
The wet deposition amounts of radionuclides are de-
termined by the precipitation rate and the averaged con-
centration in cloud water estimated by the sub-grid cloud
scheme followed by the diagnostic cloud model in
ADAM2 [6] and the Regional Acid Deposition Model
(RADM) version 2.6 [20-22]. The below cloud scaveng-
ing pr ocess is also inc l uded [6].
3. Simulation Results of 137Cs and 131I
Concentrations and Depositions
131I is assumed to be in the gas phase with the half-life
time of 8.07 days whereas 137Cs is to be in the aerosol
phase with the aerodynamic mean diameter of 0.4 m, a
logarithmic standard deviation of 0.3 and the half-life
time of 30.2 years.
The emission rate of 131I and 137Cs from the Fukushima
nuclear power plant accident estimated by [4,5,23] for
the period from 05:00 JST 12 March to 24:00 JST 30
April 2011 are used in t his study and given in Figure 2 .

S.-U. PARK ET AL.
64
The first emission peak of 834 GBq s-1 of 131I and 83.4
GBq s-1 of 137Cs from 15:30 JST to 16:00 JST 12 March
[1] was reported to be related to the hydrogen explosion
in reactor unit 1. The highest emission of up to 1,110
GBq s-1 of 131I and 110 GBq s-1 of 137Cs dur i ng t he p er io d
of 11:00 JST 14 March to 17:00 JST 15 March 2011 was
reported to be relate to the hydrogen explosion in unit 4
and together with the hydrogen explosion in unit 2.
3.1. Simulated 131I and 137Cs Concentrations
and Depositions by LPDM
The LPDM model has been employed to simulate radio-
nuclide concentrations and depositions in the domain in
Figure 1(a). The Lagrangian particles are released at the
rate of one particle per minute at the height of the first σ
level (about 18-20 m above the ground) with the appor-
tioned mass co ncentratio n equivale nt to the e mission rate
in Figure 2.
The particle is released starting at 09:00 JST (00:00
UTC) 12 March and ending at 09:00 JST 30 April 2011
for the whole emission period from the Fukushima
Dai-ichi nuclear power pla nt.
The concentration is calculated hourly at each level
with the horiz ontal d istanc e of 1 ,500 m. The hour ly total
deposition (wet and dry) is estimated at each grid with
the horizontal distance o f 1,500 m.
Figure 3 shows time variations of model simulated
daily mean concentrations of 137Cs and 131I with the
measured concentrations at 3 sites given in Figure 1(a).
Both nuclide s are quite well si mula te d at all site s.
Figure 2. Time variations of emission rate of I-131 (solid
line) and Cs-137 (dashed line) from Fukushima nuclear
pow e r plant from 12 M ar c h to 01 M ay 2011.
Fig ure 3 . T i me varia ti o ns of mode l s i mul at e d by LP DM dai ly mea n su rf ac e c o nce ntr a ti o n (B q m-3) of (1) Cs-137 and (2) I-131
at (a) site A, (b) site B, and (c) site C for the period from 12 March to 5 April 2011. Observed concentration at each site is
shown in wi th red bars .

S.-U. PARK ET AL.
65
Figure 4 shows the horizontal distributions at model
simulated mean surface concentration, column integrated
mean concentration and total deposition (wet+dry) of
137Cs for the period from 12 March to 30 April 2011. The
zone of the mean surface 137Cs concentration exceeding
50 Bq m-3 extends northward from the power plant to
38.5N and southward to 35.5N with relative high 137Cs
concentrations along the coastline. The maximum surface
mean 137Cs concentration of 2.975  102 Bq m-3 occurs
near the power plant (Figure 4(a)). The horizontal dis-
tribution pattern of the column integrated mean 137Cs
concentration (Figure 4(b)) is quite similar to that of the
surface mean concentration (Figure 4(a)) with the max-
imum value of 3.7  107 Bq m-2 near the power plant. A
similar horizontal distribution pattern is also seen in the
horizontal distribution of the total deposition of 137Cs.
The maximum deposition of 1.78  1014 Bq m-2 occurs
near the power plant (Figure 4(c)).
Figure 5 shows the horizontal distributions of the
model simulated surface mean concentration, the column
integrated mean co ncentr ation , and the to tal deposition of
131I for the period from 12 March to 30 April 2011. The
horizontal distribution pattern of the mean surface 131I
concentration (Figure 5(a)) is quite similar to that of
137Cs (Figure 4(a)) but 131I c oncentra tion i s much hi gher
than 137Cs due to high emission rate of 131I (Figure 2).
The area enclosed by the isoline of surface mean 131I
concentratio n of 100 Bq m-2 is nearly the same as that of
the surface mean 137Cs concentration of 50 Bq m-2 (Fig-
ure 4(a)). The maximum surface mean 131I concentration,
and the maximum mean column integrated 131I concen-
tration (Fig ure 5(b)) are, r espectively 1.96  107 Bq m-3
and 2.44  109 Bq m-2 tha t ar e 1 00 times hi ghe r tha n t he
corresponding values of 137Cs (Figures 4(a) and (b)).
However, the total deposition of 131I with the maximum
value of 5.96  1014 Bq m-2 (Figure 5(c)) is 4 times
greater than that of 137Cs, suggesting more effectiveness
of the aerosol than the gas for the deposition.
3.2. Simulated 131I and 137Cs Concentrations
and Depositions by the Eulerian Transport
Model (ETM)
Figure 6 shows the model (ET M) simulated surface mean
concentration, the column integrated mean concentration
and the total dep osition (wet+dry) of 137Cs for the period
from 12 March to 30 April 2011.
The emitted 137Cs from the power plant affects all the
downwind region of the model domain with some exten-
sion to ward the up wind regi on dur ing the anal ysis per iod
(12 March to 20 April). The high surface mean 137Cs
conc ent ra tion r e gio n e xtend s s o uth we st war d from Alas ka
to Philippines with the surface mean maximum concen-
tration of 20 Bq m-3 near the power plant (Figure 7(a)).
The further upwind extension up to 100°E of the at-
mospheric loading of 137Cs is seen in Figure 7(b) with
the maximum column integrated mean 137Cs concentra-
tion of 2.78  104 Bq m-2 near the po wer plant.
Figure 4. Horizontal distributions of (a) the near surface
mean concentration (Bq m-3), (b) the column integrated
mean concentration (Bq m-2), and the total deposition (Bq
m-2) of 137Cs for the period from 12 March to 30 April 2011.
Figure 5 . The same as in Figure 4 except for I-131.
Figure 6. Horizontal distributions of (a) the near surface
mean concentration (Bq m-3), (b) column integrated mean
concentration, and (c) total deposition of Cs-137 for the
period from 12 to 20 April 2011.

S.-U. PARK ET AL.
66
Figure 7 shows the model (ETM) simulated surface
mean concentration, column integrated mean concentra-
tion and total deposition (wet+dry) of 131I for the period
from 12 March to 30 April 2011.
The horizontal distribution patterns of these quantities
of 131I are quite resemble to those corresponding quanti-
ties of 137Cs (Figure 6) but the maximum values are
much higher than tho se of 137Cs; The ma ximum va lue of
the surface mean concentration (Figure 7(a)) the column
integrated concentration (Figure 7(b)) and the total de-
position (wet+dry) (Figure 7(c)) for 131I is 851 Bq m-3,
1.4 × 106 Bq m-2 and 8.88 × 105 Bq m-2, respectively.
To understand the long-range transport process of the
radionuclide plume, the daily averaged column integrated
131I concentration is calculated and presented in Figure 8
at other day interval from 12 March to 12 April 2011.
The radionuclide plume emitted from the power plant
is transported to the downwind region of Alaska and the
eastern boundary of the model domain within 4 days (on
15 March).
A well developed low pressure center located at the
Bering Sea on 17 March makes the plume to be con-
verge d to ward the lo w pre ssur e c enter and then pus hs t he
plume toward westward over Russia in association with
the circulation (21 March). Thereafter the northerlies in
association with the developing high pressure system
over Siberia push the plume south and southeastward to
Mongolia, East China and Korea (23-27 March).
On the mean time a high pressure system located to
the south of the power plant on 19 March makes the
emitted radionuclide plume from the power plant to be
diverged toward southward to the easterly zone of the
subtropical high pressure results in high atmospheric
loading of the radionuclide (131I) zone the along the
northern boundary of the subtropical high pressure sys-
tem that extends southwestward from the northwestern
Pacific Ocean to Philippines and Vietnam (19-31
March).
Figure 7 . The same as in Figure 6 except for I-131.
Figure 8. Horizontal distributions of the model si mulated dail y mean colu mn integr ated concentr ation (B q m-2) of I-131 for
every two days starting from 12 UTC 12 March to 12 UTC 12 April 2011.

S.-U. PARK ET AL.
67
4. Conclusions
The Lagrangian Particle Dispersion Model (LPDM) in
the 594 km × 594 km model domain centered at a power
plant with the horizontal grid distance of 3 × 3 km2 for
meteorological fields and the Eulerian Transport Model
(ETM) modified from the Asian Dust Aerosol Model 2
(ADAM2) in the model domain of 140° LON × 70° LAT
with the horizontal grid distance of 27 × 27 km2
co-centered with LPDM have been developed.
It is found that both models are able to produce the
observed concentrations of 137Cs and 131I near the power
plant reasonably. The LPDM model yields better results
than those of ETM near the power plant. However, the
long-range transport processes of the radionuclides are
well simulated by the ETM model. Therefore, the pre-
sently developed two models are found to be useful for
the concentration estimation in the near power plant area
by the LP DM model and i n the wid e regi on by the ETM
model.
The estimated maximum mean surface concentration,
mean column integrated concentration and the total de-
position by LPDM for the period from 12 March to 30
April are, respectively found to be 2.975 × 102 Bq m-3,
3.7 × 107 Bq m-2 and 1.78 × 1014 Bq m-2 for 137Cs and
1.96 × 104 Bq m-3, 2.24 × 109 Bq m-2 and 5.96 × 1014 Bq
m-2 for 131I. The ETM model result indicates that the ra-
dionuclide plume released from the Dai-ichi power plant
can affect wide regions not only the whole downwind
regio n of the p ower p lant but the up wind reg ions incl ud-
ing Russia, Mongolia, Korea, the eastern part of China,
Philippines and the parts of South East Asia.
The present study mainly pertains to the development
of the emergency response modeling system that will be
used for the operational model for the accidental releases.
Further verification of the model with measured data is
required to be used as an operational model.
5. Acknowledgements
This work was funded by the Korea Meteorological Ad-
ministration Research and Development program uder
Grant CATER 2012-2050.
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