Assessmen in ma ine en i onmen o a hypo he ic nuclea acciden
based on he da abase o idal ha monic cons an s
Byung-Il Min
a
, Raúl Pe iáñez
b
, Kihyun Pa k
a
, In-Gyu Kim
a
, Kyung-Suk Suh
a,
⇑
a
Nuclea En i onmen Sa e y Resea ch Di ision, Ko ea A omic Ene gy Resea ch Ins i u e, Daedeok-Dae o 989-111, Yuseong, Daejeon 305-600, Republic o Ko ea
b
Dp Fisica
Aplicada I, ETSIA, Uni e sidad de Se illa, C a. U e a, km 1, 41013 Se illa, Spain
Keywo ds:
Oceanic dispe sion assessmen
Tidal cu en
Real- ime o ecas ing
Nuclea acciden
abs ac
The ele en nuclea powe plan s in ope a ion, unde cons uc ion and a well-planned plan in he eas coas o China
gene ally use seawa e o eac o cooling. In his s udy, an oceanic dispe sion assessmen sys em based on a da abase
o idal ha monic cons an s is de eloped. This sys em can calcula e he idal cu en wi hou a la ge compu a ional
cos , and i is possible o calcula e eal- ime p edic ions o pollu- an dispe sions in he ocean.
Calcula ed ampli udes
and phases ha e maximum e o s o 10% and 20%wi h obse a ions, espec i ely. A numbe o hypo he ical
simula ions we e pe o med acco ding o a y-ing o he elease s a ing ime and du a ion o pollu an o he six
nuclea si es in China. The de eloped sys em equi es a compu a ional ime o one hou o one mon h o eal- ime
o ecas ing in Linux OS. Thus, i can use o e alua e apidly he dispe sion cha ac e is ics o he pollu an s
eleased in o he sea om a nuclea acciden .
1. In oduc ion
In ecen yea s, in a con ex o inc easing ene gy demand, many
coun ies ha e exp essed an in e es in including nuclea powe in
hei ene gy plans. In 2011, he Fukushima Daiichi nuclea disas e
occu ed in Japan, a e which all nuclea plan app o als we e o-
zen and ‘ ull sa e y checks’ o exis ing eac o s we e equi ed. The
cu en si ua ion in he eas coas o China is such ha he ele en
nuclea powe plan s a h ee si es a e in ope a ion (Hongyanhe,
Tianwan, Qinshan), unde cons uc ion (Hongshiding, Sanmen)
and a well-planned plan (Haiyang). These plan s a e loca ed in
he Yellow sea coas and gene ally use seawa e o eac o cooling
(Fig. 1).
The ma ine dispe sion o adionuclides om a nuclea acciden
has been an impo an issue since he Fukushima Daiichi acciden
in 2011 (Honda e al., 2012; Pe ianez e al., 2012; Tsumume e al.,
2012; Min e al., 2013). Release o he adioac i e ma e ials may
occu due o a majo acciden wi hin a NPP o o he easons, such
as spen uel anspo a ion o an acciden in ol ing a nuclea sub-
ma ine. An eme gency esponse sys em is necessa y o p ese e he
ma ine en i onmen in e ms o s abili y and public sa e y. In an
eme gency, hese sys ems de e mine he ange o e ec s o he
acciden , and hey can o e basic in o ma ion o a p o ec ion plan.
In his s udy, an oceanic dispe sion assessmen sys em based on
a da abase o idal ha monic cons an s has been de eloped o e al-
ua e he anspo cha ac e is ics o he pollu an o a hypo he i-
cal nuclea acciden loca ed in he eas coas o China. The
hyd ological cha ac e is ics in he Yellow Sea a e mainly go e ned
by ides, which a e dominan ly semidiu nal ( ising wice a day).
Ampli udes a y be ween 0.9 and 3 m along he coas o China.
Tides a e highe along he Ko ean Peninsula, ypically anging
be ween 4 and 8 m. The speed o he idal cu en is gene ally less
han 1.6 km/h in he middle o he Yellow Sea, bu i may inc ease
o mo e han 5 km/h nea he coas . Tidal p edic ions based on a
da abase o idal ha monic cons an s can calcula e he idal cu -
en s in as wi hou incu ing a la ge compu a ional cos , hus i
is also possible o calcula e eal- ime p edic ions o adioac i i y
in he ocean.
2. Tidal cu en o ecas sys em
Nume ical ci cula ion models p o ide a use ul and gene al iew
o ocean cu en s. A egional ci cula ion model was fi s ly de el-
oped by Ki k B yan and Michael Cox (B yan, 1969) and i was
expanded in a global scale, wi h a ho izon al esolu ion o wo
deg ees and wi h 12 le els in he e ical di ec ion (Cox, 1975).
A e ha , a ious nume ical models ha e been de eloped o
desc ibe coas al cu en s, ides, and s o m su ges. The models
ex end om he beach o he con inen al slope and hey included
⇑
Co esponding au ho . Tel.: +82 42 868 4788; ax: +82 42 868 8943.
E-mail add ess: [email p o ec ed] (K.-S. Suh).
.
a ee su ace, ealis ic coas s, bo om ea u es, i e uno and
a mosphe ic o cing da a. The coas al models ha e many di e en
goals and implemen a ions. Thus, i is impo an o selec o a
p ope ci cula ion model o unde s and he cha ac e is ics o he
dominan physical p ocesses in each pa icula a ea.
Nume ical s udies o idal cu en p edic ions use ci cula ion
models and ocus on s ong idally d i en sys ems. In his case,
he flow may be conside ed o obey wo-dimensional (2D) a e -
aged dynamics e ically (Panchang e al., 1997; Dudley e al.,
2000). Tides define wi h he pe iodic ise and all o sea le els
caused by he combined e ec s o he g a i a ional o ces exe ed
by he Moon and he Sun, and he o a ion o he Ea h. When pe i-
odic da a is analyzed, he s anda d app oach is o employ Fou ie
se ies wi h a o m o analysis ha uses sinusoidal unc ions ha ing
equencies ha a e ze o, one, wo, e c. imes he equency o a
pa icula undamen al cycle. These mul iples a e called wi h ‘ha -
monics’ o he undamen al equency and he p ocess is e med in
ha monic analysis. Doodson (1921) in oduced he Doodson Num-
be no a ion o o ganize hund eds o ha monics cons an s. This
app oach has been he in e na ional s anda d since hen. Real ides
can be explained by a sum o ha monics in he ollowing o m.
zð Þ¼X
N
i¼1
A
i
cosðw
i
þp
i
Þð1Þ
He e, zis he sea su ace displacemen o idal cu en o each U and
V componen s om he mean sea le el p oduced by he ide and N
is he numbe o ha monics ( idal cons i uen s). Fo each cons i u-
en , Ais he ampli ude, wis angula equency, pis he phase o se
wi h ega d o he as onomical s a e a ime = 0 and is ime
measu ed in hou s. The ampli ude (A) and phase o se (p) deno ed
as idal cons an s, a e no uni o m in space o each cons i uen .
The e a e se e al ways o ob ain hem. Fi s , a ha monic analysis
o di ec measu emen s o wa e le els in he egion o in e es is
he mos accu a e way, bu i is di ficul o ob ain idal cons an s
wi h spa ial con inui y. This me hod is mainly used o hyd o-
g aphic su eys, and has been used in na ional ins i u ions ( o
example, he NOAA o he USA, he POL o he UK and he KHOA
o he Republic o Ko ea). Second, sa elli e obse a ions ha e spa ial
con inui y bu he le el o accu acy is low. The sa elli e da a o
TOPEX/Poseidon (Smi h e al., 1997) and JASON-1 (A dalan and
Hashemi, 2008) can be used o his pu pose. Thi d, nume ical mod-
els can be used o calcula e hese ha monic cons an s. Bu nume i-
cal models and a ailable obse a ion da a a e gene ally applied o
complemen he disad an ages o each me hod.
In his s udy, he fi e-minu e in e al DB o Min e al. (2011) is
applied o ca y ou p edic ions o idal cu en s. The DB includes
ha monic cons an s o he sea su ace displacemen and idal cu -
en o each U and V componen s. De ails a e p esen ed by Min
Fig. 1. Map o he Yellow Sea. The loca ions o six nuclea si es, h ee cu en me e s and idal gauges a e indica ed. Ba hyme y (m) is also shown: IC:Incheon, DC:Daechun,
KS:Kunsan.
e al. (2011) o mo e in o ma ion like compu a ional domain,
desc ip ion and alida ion o he model. The idal cons an DB used
in his wo k is basically iden ical by Min e al. (2011), bu he new
p og am is de eloped o p edic idal cu en s. Fig. 2 shows he
ampli ude and phase esul ing om he DB compa ed wi h he
obse ed da a a all idal gauges in Fig. 1. The esul s o he M
2
,
S
2
,K
1
and O
1
cons i uen s a e shown whe e he co esponding
s a ion da a a e a ailable. The solid line, a a 45-deg angle, indica es
a one- o-one co espondence be ween he model esul s and he
obse ed da a. Ideally, he esul s o all idal cons i uen should all
along his line. Dashed lines indica e a 10 pe cen di e ence
be ween he DB esul s and he measu ed da a. Mos esul s om
he DB ha e e o s less han 10%, as seen in Fig. 2. Some unde -
p edic ion appea s o phases o wo diu nal cons i uen s (K
1
and
O
1
). This p oblem is caused by he open bounda y o cing used in
he global model (Min e al., 2011). Howe e , he e o o he phase
lag be ween he calcula ions and obse a ions is no la ge han 20%.
The DB-based p edic ed idal cu en s o e ime a e plo ed o
h ee s a ions in Fig. 3. DB-based idal cu en s a e in good ag ee-
men wi h obse a ions o all coas al s a ions. In pa icula ,
obse ed da a include he e ec s o wind, wind wa es and o he
a mosphe ic e ec s; none heless calcula ions a e in good ag ee-
men wi h hem in e ms o ebb and flood ide, as well as he
di ec ion and speed o idal cu en s. This means ha ides a e
p edominan in he Yellow and Eas China Seas. O he componen s
o he flow (densi y d i en cu en s, winds, wa es, e c...) a e
ela i ely small and may be neglec ed.
3. Ma ine dispe sion model
A e he Fukushima acciden , a la ge amoun o adioac i e
ma e ial was eleased o he ocean, as well as o he a mosphe e.
The e o e, i is necessa y o e alua e ma ine dispe sion o adio-
logical eme gency p epa edness agains a nuclea acciden . F om
his pe spec i e, an oceanic dispe sion model named LORAS
(Lag angian Oceanic Radiological Assessmen Sys em) has been
de eloped in Ko ea since 2011 (Min e al., 2013). The model was
designed o calcula e adionuclide concen a ions in seawa e , sus-
pended ma e and seabed sedimen s in ime and space using a
pa icle acking me hod. The dispe sion o eac i e and non- eac-
i e adionuclides may also be simula ed in he model. Th ee
dimensional u bulen di usion and he pollu an in e ac ions
be ween wa e , suspended ma e and bo om sedimen s a e sim-
ula ed using a s ochas ic me hod (Pe iáñez and Ellio , 2002). The
mo emen o he pa icle is ep esen ed by he sum o he mo e-
men s due o ad ec ion by he cu en and u bulence. The new
posi ion o a pa icle a e a ime s ep
D
is ep esen ed as ollows.
X
j
ð þ
D
Þ¼X
j
ð Þþ
j
ð Þ
D
þ
0
j
ð Þ
D
ð2Þ
whe e
j
a e he oceanic cu en s (j= 1,2,3) and
0
j
a e he u bulen
mo ion (j= 1,2,3). Th ee dimensional u bulen mixing is compu ed
by a andom walk me hod.
0
1;2
ð Þ
D
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
12K
1;2
D
qR;
0
3
ð Þ
D
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2K
3
D
pR;ð3Þ
whe e K
j
a e di usion coe ficien s in each co esponding di ec ion
o space and Ris a andom numbe .
A s ochas ic me hod is used o es ima e he dispe sion o non-
conse a i e adionuclides and p o ide concen a ions in wa e ,
suspended ma e and bo om sedimen s (Pe iáñez and Ellio ,
2002; Pe iáñez, 2011). The di e en ial equa ions which desc ibe
ans e s be ween he h ee phases a e exp essed he ollowing.
@C
w
@ ¼k
1m
C
w
k
1s
C
w
;@C
s
@ ¼k
2
C
s
;@C
b
@ ¼k
2
/C
b
ð4Þ
whe e C
w
,C
s
and C
b
a e adionuclide concen a ions in seawa e ,
suspend ma e and bo om sedimen s espec i ely. k
1m
is he
kine ic coe ficien desc ibing adionuclide ans e om wa e o
suspended ma e , k
1s
desc ibes he ans e om wa e o bo om
sedimen s and k
2
is he kine ic ans e coe ficien which desc ibes
adionuclide elease om suspended ma e o bo om sedimen s
o wa e . Finally /is a co ec ion ac o which akes in o accoun
ha some o he sedimen pa icle su ace may be hidden by o he
pa icles. Radioac i e decay is desc ibed by he ollowing equa ion.
cð þ
D
Þ
decay
¼cð Þ½1expðk
D
Þ ð5Þ
whe e cð Þis he concen a ion and kis he adioac i e decay a e.
Radionuclide concen a ions in seawa e (C
w
), suspended ma -
e (C
s
) and seabed sedimen s (C
b
) a e calcula ed in he domain
o in e es by coun ing he numbe o pa icles as ollows.
C
w
¼I:N
w
D
x
D
y
D
z;C
s
¼I:N
s
m:
D
x
D
y
D
z;C
b
¼I:N
b
D
x
D
y:H:
q
b
ð6Þ
He e I=Q/NP, whe e Qis he sou ce e m and NP is he numbe o
pa icles used in he simula ion.
D
x
D
y
D
zis he olume o he each
cell, mis suspended ma e concen a ion, His he mixing dep h
in he bo om sedimen and q
b
is sedimen bulk densi y. Finally
N
w
,N
s
, and N
b
a e he numbe o pa icles in each phase.
(a) Ampli ude (b) Phase
Fig. 2. DB calcula ed e sus measu ed ha monic cons i uen s a all s a ions o Fig. 1.
4. Nume ical expe imen s and esul s
The oceanic dispe sion model based on he Lag angian pa icle-
acking me hod desc ibed abo e has been de eloped and es ed
o he Fukushima Daiichi nuclea disas e (Min e al., 2013). When
i needs o e alua e he dis ibu ion o adionuclides leaked in he
ocean, ull calcula ions using an oceanic ci cula ion model a e e y
ine ficien because o a la ge compu a ional ime and inpu da a.
The e o e, a compac ha monic p edic ion sys em consis ing o a
da abase o idal cons i uen s has been de eloped and is p esen ly
used o demons a e how eal- ime p edic ions a e gene a ed. The
coupled LORAS and idal p edic ion sys em ex ac s ha monic con-
s an s om he fi e-minu es DB based on he loca ion o adionuc-
lides, which a e ep esen ed by disc e e pa icles. Six y- wo
ha monic cons an s o he idal cu en we e ex ac ed. These al-
ues a e used o p edic eal- ime idal cu en s based on Eq. (1).
Each pa icle mo es by hese eal- ime idal cu en s, esul ing in
a new loca ion a he end o each compu a ional ime s ep.
I assumed ha a con amina ion sou ce, eleasing a hypo he i-
cal pollu an , was loca ed in he coas nea each nuclea powe
plan . The magni ude o he elease is a bi a y, since dilu ion o e
he sea is calcula ed. The idal signal oughly app oxima es a hal -
day cycle. Thus, we can assume he elease s a ing ime o be a
e e y h ee-hou in e al (Fig. 4). These hypo he ical elease si u-
a ions include flood and ebb idal cu en s, as well as slack wa e
condi ions. Also, he ollowing elease du a ions we e conside ed
wi h he 10, 20, 30 and 40 idal cycles. Thus, we ha e 16 hypo he -
ical pollu an elease cases o each NPP. A pe ec ly conse a i e
and long-li ed adionuclide was conside ed o he expe imen s.
In e ac ions wi h sedimen s educe he adionuclide mobili y, hus
wide dispe sion occu s i adionuclides emain dissol ed and he
adioac i e impac along he Yellow Sea coas s would be highe .
The e o e, adionuclide decay and in e ac ions wi h solid phases
a e neglec ed.
Fig. 5 shows he calcula ed dispe sion pa e ns eleased in o he
Yellow Sea om each NPP in China. These hypo he ical e en s
imply se e al assump ions, bu selec ed physical pa ame e s and
alues a e he same in he p e ious wo k (Min e al., 2013). The
esul s a e alid o a ange o conse a i e adionuclides. The
numbe o pa icles used in each simula ion is 2,000,000. Dilu ion
o e he sea is calcula ed o each expe imen , conside ing 1 dilu-
ion a each elease poin . Simula ion esul s in Fig. 5 a e p esen ed
wi h he la ges adionuclide dis ibu ion (i.e., la ges adionuclide
pa ch) wi hin he wa e column and he leading edge o he a e -
aged concen a ion o less han 10 m om he sea su ace, defined
as a 10
9
dilu ion (concen a ion he e would be 10
9
imes he
concen a ion in he elease poin ). A o al o 16 dis ibu ions ha e
been ob ained, co esponding o ou elease s a ing ime and ou
elease du a ion o each NPP. In gene al, he leading edges o he
pollu an s sp ead o 20 a c minu es on e e y 20 days. Hongshid-
ing, he nuclea powe plan closes o he Republic o Ko ea, is
abou h ee a c deg ees away. The e o e, eleased pollu an s can
heo e ically each he coas o he Ko ean Peninsula a e some
180 days.
Any e ec o an acciden occu ing om Qinshan and Hongyan-
he NPPs is unlikely in he Ko ean Peninsula due o hei geog aphic
loca ions. In con as , acciden s om Haiyang, Hongshiding and
Tianwan NPPs may easily a ec Ko ean ocean en i onmen . A
(a) Kunsan
(b) Daechun
(c) Incheon
Fig. 3. Tidal cu en imes se ies o DB ( ed) e sus obse a ions (blue) o he h ee
s a ions. (Fo in e p e a ion o he e e ences o colou in his figu e legend, he
eade is e e ed o he web e sion o his a icle.)
Fig. 4. Hypo he ical pollu an elease ins an s along a idal cycle.
nuclea acciden will ha e a significan economic and sociologic
impac , since ma ine esou ces p oduced in he Yellow Sea ha e
a e y la ge p opo ion o he ood o Ko ea and a ound he
coun y.
Eme gency esponse sys ems a e ele an o suppo decision
making a e an acciden . An e alua ion o model esul sensi i i y
o he acciden cha ac e is ics should be ca ied ou . The Mon e
Ca lo me hod is gene ally conside ed o be he mos sui able
app oach o ca y ou a quan i a i e analysis o model sensi i i y
and p opaga ion o unce ain ies pe aining o adionuclide ans-
po codes. The sensi i i y analysis in his s udy was only applied
o e alua e he model esponse acco ding o he a ia ions in he
s a ing ime and du a ion o he pollu an elease. The e o e, we
used a simple sensi i i y analysis in ol ing a di ec compa ison
o he 16 simula ions which we e made o each NPP. Fig. 6 shows
he a ia ions in maximum concen a ions a 20 km o sho e om
(a) Haiyang (b) Hongshiding
(c) Hongyanhe (d) Qinshan
(e) Sanmen ( ) Tianwan
Fig. 5. Calcula ed maximum pollu an dis ibu ion o each NPP. The leading edge is defined by he 10
9
dilu ion con ou .

each powe plan . Concen a ions o Haiyang, Hongshiding, Tian-
wan and Hongyanhe dec ease as he elease du a ion inc eases,
since he elease a e is de e mined by he same o al emission ol-
ume bu di ided by a longe ime pe iod. This pa e n is no e i-
den o Qinshan and Sanmen, because cu en s a ound hem a e
s ongly influenced by i e s and islands. The elease s a ing ime
can also be seen as a ele an ac o , excep o Haiyang. In his
case idal cu en s a e e y uni o m, leading o a a he iso opic
dispe sion in space, as shown in Fig. 5. In o he egions, esul s
a e mo e sensi i e o he elease s a ing ime han o he elease
du a ion.
5. Conclusions
The eliabili y o p edic ions is a c ucial pe o mance c i e ion
o nume ical models. The da abase o ha monic cons an s can be
imp o ed by modi ying i s physical pa ame e s, nume ical scheme
and de ails o i s mesh sys em. In his pape , he o ecas e ficiency
and cu en o ecas s om an independen model sys em we e
e alua ed. The in oduced DB-based idal cu en o ecas sys em
is highly eliable. Ampli udes and phases om he compa isons o
calcula ion and obse a ion a e ob ained wi h e o s less han
10% and 20%, espec i ely. The calcula ed esul s o he idal cu -
en o ecas s showed gene ally good ag eemen s wi h obse a-
ions. The 16 hypo he ical simula ions we e pe o med depending
on he elease s a ing ime and du a ion o he pollu an emission
o each o he six NNPs o China. Con amina ion om Hongshiding
NPP a e a hypo he ical acciden is expec ed o each he coas o
he Ko ea Peninsula a e 180 days. Pollu an dispe sion pa e ns
a e e y sensi i e o he loca ion o he NPP, as well as o he elease
s a ing ime and du a ion. Thus, accu a e o ecas s o eal- ime
idal cu en s a e equi ed o eme gency esponse sys ems which
would suppo decision-making a e an acciden . The de eloped
sys em equi es one hou o compu a ional ime o one mon h o
eal- ime o ecas s in Linux OS. Thus, i is ela i ely easy o imple-
men i in o an eme gency esponse sys em.
Acknowledgemen s
This s udy was suppo ed by he Na ional Resea ch Founda ion
o Ko ea (NRF) g an unded by he Ko ea Go e nmen (MSIP)
(MSIP: No. 2012M2A8A4025912, NSSC: No. 2012M5A1A1029210).
R. Pe iáñez was pa ially unded by he EU FP7 EURATOM p ojec
PREPARE ‘‘Inno a i e in eg a i e ools and pla o ms o be p epa ed
(a) Haiyang (b) Hongshiding
(c) Hongyanhe (d) Qinshan
(e) Sanmen ( ) Tianwan
Fig. 6. Concen a ion sensi i i y o changes in 16 hypo he ical simula ion cases.
o adiological eme gencies and pos -acciden esponse in Eu ope’’,
p ojec numbe 323287.
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