The beha iou o
129
I eleased om nuclea uel ep ocessing
ac o ies in he No h A lan ic Ocean and anspo o he A c ic
assessed om nume ical modelling
M. Villa
a
, J.M. López-Gu ié ez
b
, Kyung-Suk Suh
c
, Byung-Il Min
c
, R. Pe iáñez
d,
⇑
a
Dp Física Aplicada II, ETSIE, Uni e si y o Se illa, Spain
b
Dp Física Aplicada I, EPS, Uni e si y o Se illa, Spain
c
KAERI, Daedeok-Dae o 989-111, Yuseong-Gu, Daejeon, Republic o Ko ea
d
Dp Física Aplicada I, ETSIA, Uni e sidad de Se illa, C a U e a km 1, 41013 Se illa, Spain
Keywo ds:
A lan ic Ocean
Iodine-129
Dispe sion
Lag angian model
A c ic Ocean
abs ac
A quan i a i e e alua ion o he a e o
129
I, eleased om he Eu opean ep ocessing plan s o Sellafield (UK) and La Hague
(F ance), has been made by means o a Lag angian dispe sion model. T anspo o adionuclides o he A c ic Ocean has been
de e mined. Thus, 5.1 and 16.6 TBq o
129
I ha e been in o-duced in he A c ic om Sellafield and La Hague espec i ely om 1966
o 2012. These figu es ep esen , espec i ely, 48% and 55% o he cumula i e discha ge o ha ime. In en o ies in he No h
A lan ic, including shel seas, a e 4.4 and 13.8 TBq coming om Sellafield and La Hague espec i ely. These figu es a e significan ly
di e en om p e ious es ima ions based on field da a. The dis ibu ion o hese in en- o ies among se e al shel seas and egions
has been e alua ed as well. Mean ages o ace s ha e been finally ob ained, making use o he age-a e aging hypo hesis. I has
been ound ha mean ages o Sellafield eleases a e abou 3.5 yea la ge han
o La Hague eleases.
1. In oduc ion
Nume ical models which simula e he dispe sion o adionuc-
lides in he ma ine en i onmen ha e been con inuously de el-
oped, since he pionee ing wo ks o P andle (1984) o he mos
sophis ica ed app oaches used, o ins ance, o p edic he ans-
po o Fukushima eleases in he Pacific Ocean (Masumo o e al.,
2012; Pe iáñez e al., 2014). Some models ha e also been de el-
oped o simula e he anspo o adionuclides eleased om he
Eu opean nuclea uel ep ocessing plan s o Sellafield (UK) and
La Hague (F ance) in A lan ic wa e s. These models ha e been
applied o a numbe o adionuclides like
137
Cs (P andle, 1984;
Gao e al., 2004),
90
S (Gao e al., 2004),
99
Tc (Ka che e al.,
2004) and
129
I(O e e al., 2009). We a e no men ioning he e
local-scale applica ions, o ins ance in he English Channel and
in he I ish Sea.
Among hese adionuclides,
129
I is a e y significan one since,
due o i s biophilic beha iou and e y long hal -li e
ð15:710
6
yea sÞ, can e en en e he ood chain and emain he e
much longe han o he sho -li ed iso opes. Thus, a numbe o
s udies conce ning he dis ibu ion and a e o
129
I eleases
om he Eu opean ep ocessing plan s in he No h A lan ic
ha e been published (Smi h e al., 2011; He e al., 2013; Michel
e al., 2012; Alfimo e al., 2004, 2013; Gómez-Guzman e al.,
2013).
Some models ha e simula ed he dispe sion o
129
I in he no h-
e n A lan ic Ocean (O e e al., 2009), as commen ed abo e. How-
e e , only he anspo pa hways by he main cu en sys ems
ha e been desc ibed. Fu he mo e, a quan i a i e es ima ion o
he
129
I in en o ies in di e en sub-basins and shel seas has ne e
been pe o med. The objec i e o his pape consis s o p esen ing
such de ailed calcula ions by means o a Lag angian dispe sion
model. Due o he Lag angian na u e o he model, i is possible
o know i a gi en pa icle, loca ed anywhe e in he domain, is
coming om Sellafield o om La Hague. Thus, his allows o e al-
ua e independen ly he a e o adionuclides eleased om each
nuclea acili y and he con ibu ion o each plan o he in en o-
ies in he No h A lan ic. Also, he inpu o he A c ic Ocean
has been e alua ed, quan i a i ely de e mining he ac ions o
Sellafield and La Hague eleases which en e in o his ocean. Mean
age o wa e ace s ha e been calcula ed o eleases om
Sellafield, La Hague and conside ing bo h simul aneously. The
age-a e aging hypo hesis, desc ibed below, has been adop ed.
The model is b iefly desc ibed in Sec ion 2. Resul s a e p esen ed
and discussed in Sec ion 3.
⇑
Co esponding au ho . Tel.: +34 954486474; ax: +34 954486436.
E-mail add ess: [email p o ec ed] (R. Pe iáñez).
2. Model desc ip ion
The model is a Lag angian dispe sion model in which a adionu-
clide elease is simula ed by a numbe o pa icles, each o hem
equi alen o a numbe o uni s (a oms o Bq). Lag angian models
p esen wo ad an ages o e Eule ian models, in which an
ad ec ion/di usion equa ion o mass concen a ion is sol ed.
Fi s , a ificial nume ical di usion is no in oduced; second, spe-
cific p ope ies may be assigned o each pa icle. Fo ins ance, a
‘‘clock’’ may be a ached o each pa icle, which is use ul o ob ain
wa e ace ages (Mi ó e al., 2012).
The h ee-dimensional pa h ollowed by each pa icle is com-
pu ed, u bulen di usion being modelled as a h ee-dimensional
andom walk p ocess. The densi y o pa icles pe wa e olume
Fig. 1. Model domain wi h loca ion o sampling poin s whe e measu ed
129
I concen a ions ha e been compa ed wi h model esul s. Blue boxes define some egions whe e
adionuclide con en s ha e been e alua ed. (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.)
−50 −40 −30 −20 −10 010 20
50
55
60
65
70
75
Longi ude
La i ude
0.5 m/s
EGC
NCC
NAC
No h Sea
Cel ic Sea
Bal ic Sea
No h Cape
No wegian Sea
I mingue Sea
Fig. 2. Su ace cu en s calcula ed by JAMSTEC model o Janua y 2008 as an example. The main cu en s a e he Eas G eenland Cu en (EGC), No h A lan ic Cu en (NAC)
and he No wegian Coas al Cu en (NCC). Only one o each 25 ec o s is d awn.
uni is compu ed o ob ain adionuclide concen a ions o e he
domain a he desi ed imes and dep hs. Technical de ails may
be consul ed elsewhe e (Pe iáñez and Ellio , 2002; Pe iáñez and
Ca a aca, 2010), bu some indica ions a e gi en below.
Ad ec ion is compu ed sol ing he ollowing equa ion o each
pa icle:
d
d ¼qð1Þ
whe e is he posi ion ec o o he pa icle and qis he cu en
ec o a he pa icle posi ion and dep h, sol ed in componen s u
and
. T anspo due o e ical ad ec ion is masked by e ical
mixing due o u bulence, since e ical cu en s in he ocean a e
small. Thus, i is a common app oach o neglec e ical ad ec ion
in ma ine dispe sion modelling.
The maximum size o he ho izon al s ep gi en by he pa icle
due o u bulence, D
h
,is(P oc o e al., 1994; Hun e , 1987;
Pe iáñez and Ellio , 2002):
D
h
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
12K
h
D
pð2Þ
in he di ec ion h¼2
p
RAN, whe e RAN is a andom numbe
be ween 0 and 1. This equa ion gi es he maximum size o he s ep.
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 1012
Yea
Annual elease (Bq)
Sella ield
La Hague
Fig. 3. Annual
129
I eleases om Sellafield and La Hague ep ocessing plan s. This
in o ma ion has been compiled om López-Gu ié ez e al. (2004), Sellafield (2014),
A e a (2014).
Fig. 4. Measu ed
129
I concen a ions (mBq/m
3
) in su ace wa e s. No h Sea samples we e collec ed in 2005. The smalle numbe s a e sampling s a ion numbe s and he
la ge ones he co esponding measu ed concen a ions ( aken om Michel e al., 2012).
In p ac ice, i is mul iplied by RAN o ob ain he eal size a a gi en
ime and o a gi en pa icle. Simila ly, he maximum size o he
e ical s ep is (P oc o e al., 1994; Hun e , 1987; Pe iáñez and
Ellio , 2002):
D
¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2K
D
pð3Þ
gi en ei he owa ds he sea su ace o he sea bo om. K
h
and K
a e he ho izon al and e ical di usion coe ficien s espec i ely
and
D
is ime s ep. A cons an ypical alue o 1:010
3
m
2
=s
(Ellio e al., 2001) has been used o K
. I has been es ed ha
model esul s a e li le sensi i e o his pa ame e . Ac ually, mos
o he
129
I emains in he su ace laye , as has been ound in o he
modelling s udies (O e e al., 2009). The Smago insky’s scheme
(Cushman-Roisin and Becke s, 2011) has been adop ed o desc ibe
he ho izon al di usi i y.
Radioac i e decay can also be simula ed by a s ochas ic me hod
(Pe iáñez and Ellio , 2002), al hough his p ocess is neglec ed
gi en he e y long hal -li e o
129
I (1.6 10
7
yea s) in compa ison
wi h simula ed imes (47 yea s). Al hough adionuclide adso p-
ion/deso p ion eac ions be ween wa e and sedimen s can also
be simula ed using a s ochas ic me hod (Pe iáñez and Ellio ,
2002), hese p ocesses a e also neglec ed he e since iodine is con-
se a i e in seawa e , hus emaining in solu ion.
The conside ed domain in he no h A lan ic ex ends om 50°W
o 25°E in longi ude and om 45.1°N o 75.1°N in la i ude (Fig. 1).
Wa e ci cula ion o he pe iod o in e es has been ob ained om
JAMSTEC (Japan Agency o Ma ine-Ea h Science and Technology)
global ocean model. I is OFES (Ocean global ci cula ion model Fo
he Ea h Simula o ).
1
A compa ison o model pe o mance wi h
da a in se e al egions o he global ocean (including he No h
A lan ic) may be seen in Masumo o e al. (2004) Ho izon al esolu-
ion is 0.1°and he e a e 54 e ical le els, wi h inc easing hickness
om he su ace owa ds he sea bo om. Mon hly mean ci cula ion
has been used. As an example, he su ace wa e ci cula ion o Jan-
ua y 2008 is p esen ed in Fig. 2. The No wegian Coas al Cu en
(NCC), flowing along he No wegian coas o he no h, is clea ly
seen. The Eas G eenland Cu en (EGC) flows sou hwa ds along
he eas G eenland coas . Finally, he No h A lan ic Cu en (NAC),
de i ing om he Gul S eam, is appa en in he cen al A lan ic
wi h a numbe o eddies and meande s.
Annual
129
I eleases om Sellafield and La Hague, p esen ed in
Fig. 3, a e in oduced om 1966 o 2012, which is he simula ion
pe iod. These eleases define he numbe o Bq (o a oms) co e-
sponding o each eleased pa icle.
3. Resul s and discussion
Model esul s ha e been fi s compa ed wi h a ailable mea-
su emen s o es i s pe o mance. Michel e al. (2012) p esen a
map wi h
129
I concen a ions in he su ace wa e s o he No h
Sea and English Channel o samples collec ed in 2005 (Fig. 3 in
hei pape , which is ep oduced in Fig. 4). The au ho s do no gi e
he exac loca ion o sampling poin s. Thus, a de ailed compa ison
canno be done. Howe e , he o e all calcula ed dis ibu ion
Fig. 5. Calcula ed
129
I concen a ions (mBq/m
3
) in su ace wa e s (mean alue o e
a su ace laye wi h hickness 100 m) o he No h Sea o yea 2005.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
0
1
2
3
4
5
6
129I (mBq/m3)
129I (mBq/m3)
Sample numbe
Measu emen s
Calcula ions
19 20 21 22 23 24 25 26 27 28 29 30 31
0
50
100
150
200
250
300
Sample numbe
Measu emen s
Calcula ions
Fig. 6. Calcula ed (o e a 100 m hick laye ) and measu ed
129
I concen a ions
(mBq/m
3
) in su ace wa e s a poin s indica ed in Fig. 1 o samples collec ed in
2010 and 2012 (1–18; op panel. F om Gómez-Guzman e al. (2013) and López-
Gu ié ez e al. (2013)) and 1999 (19–31; bo om panel. F om Alfimo e al. (2004)).
1
h p://www.jams ec.go.jp/esc/ esea ch/A mOcn/p oduc /o es.h ml#ci e_no e-1.
pa e n o
129
I is in ag eemen wi h obse a ions. This calcula ed
dis ibu ion is p esen ed in Fig. 5. Su ace concen a ions a e
calcula ed as he mean alue o e a 100 hick su ace laye . The
hickness o he su ace mixed laye in he ocean ypically anges
om 25 o 200 m (Picka d and Eme y, 1982). Thus, we p o ide
concen a ions in he su ace as an a e age o e a 100 m hick
laye , which may be ep esen a i e o he mean alue o he
su ace mixed laye hickness.
Concen a ions abou 500 mBq/m
3
a e ob ained in he English
Channel, in ag eemen wi h Michel e al. (2012). A s ong concen-
a ion g adien is appa en in Denma k, wi h quickly dec easing
concen a ions as mo ing o sho e in o he No h Sea. This e ec
is also ound in Michel e al. (2012), al hough calcula ed concen a-
ions a e sligh ly o e es ima ed by he model. A simila pa e n is
ob ained along he UK eas e n coas . Howe e , his canno be seen
in he measu emen s o Michel e al. (2012) because samples we e
no collec ed close o he coas , bu ens o km o sho e. Since con-
cen a ions dec ease e y as as mo ing o sho e, p obably hese
high concen a ions calcula ed by he model along he B i ish coas
canno be app ecia ed in Michel e al. (2012). In he cen al No h
Sea, measu ed concen a ions gene ally a e o he o de o
10
1
mBq=m
3
. Model calcula ions a e in ag eemen wi h his
(Fig. 5). Measu ed
129
I concen a ions wi hin he I ish Sea a e no
o ally ep oduced by he model, which mus be due o he ela-
i ely low esolu ion o JAMSTEC cu en s. Spa ial s uc u e o cu -
en s may no be adequa ely ep esen ed in semi-enclosed basins
wi h na ow connec ions wi h he open ocean. The same si ua ion
occu s in he Danish S ai s, as will be shown below. Ne e heless,
he ocus o his pape is he open A lan ic Ocean, no shel seas.
Mo eo e , he I ish Sea is e y sensi i e o he discha ge iming.
Thus, modelled and measu ed esul s can be e y di e en he e,
depending o he sampling da e. Also, i mus be conside ed ha
mean annual discha ges a e being used in he model, which a ec s
model accu acy in he nea field.
Wa e samples ha e also been collec ed a ound Iceland, in he
I minge Sea and in a ansec om Sco land o Iceland (Fig. 1)in
2010 (Gómez-Guzman e al., 2013) and 2012 (López-Gu ié ez
e al., 2013). A compa ison be ween measu ed and calcula ed
129
I
su ace concen a ions is p esen ed in Fig. 6. Gene ally speaking,
calcula ed concen a ions in he UK-Iceland ansec a e in good
ag eemen wi h obse a ions. The model unde es ima es concen-
a ions in some sampling poin s in he a ea o Iceland (poin s
13, 14 and 15). Salini y and empe a u e measu emen s indica e
ha No h A lan ic Wa e is p esen he e (Gómez-Guzman e al.,
2013). Thus, he o igin o his
129
I canno be a ibu ed o he
EGC, which e en ually could be anspo ing adionuclides om
he A c ic back o he A lan ic. Ins ead, some eddies o episodic
cu en s which a e no ep oduced by he mean mon hly wa e ci -
cula ion could be anspo ing pa ches o Sellafield eleases o his
a ea.
An o e es ima ion abou one o de o magni ude is appa en in
he I ish Sea sample, which may be due o easons men ioned
abo e. Howe e , model esul s ag ee wi h measu emen s in he
Cel ic Sea a ea.
Some p ofiles in he wa e column we e also measu ed in he
a ea o Iceland (Gómez-Guzman e al., 2013), showing dec easing
concen a ions wi h wa e dep h. The model does no calcula e sig-
nifican concen a ions down he wa e column. As commen ed
abo e, i has been ound in o he modelling s udies (O e e al.,
2009) ha mos o he
129
I eleased om Sellafield and La Hague
emains in he su ace laye . Thus,
129
I measu ed in deep wa e s
in he a ea o Iceland could be coming om he A c ic. The model
canno simula e his anspo om he A c ic back o he A lan ic
since he o me is no wi hin he conside ed domain ( he A c ic is
no included in JAMSTEC hyd odynamic calcula ions).
Samples we e also collec ed in a ansec om he No h A lan ic
o he Bal ic Sea in 1999 (Alfimo e al., 2004). A compa ison o
model esul s wi h measu emen s is also p esen ed in Fig. 6. The
model is o e es ima ing concen a ions in he Danish S ai s.
This may be due o he ela i ely coa se esolu ion o he model,
which does no ep oduce adequa ely he na ow s ai s and
passages in hese wa e s. This makes pa icles o emain apped
in he a ea. Ne e heless, he o e es ima ion is no la ge han a
ac o 5.
As an example, he calcula ed
129
I concen a ion in su ace
wa e o yea 2000 is p esen ed in Fig. 7. Radionuclides ollow
Fig. 7. Calcula ed
129
I concen a ions (mBq/m
3
) in su ace wa e s (100 m laye ) in yea 2000. The maximum o he colou scale has been se o 500 mBq/m
3
. (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.)

he well known anspo pa hways (O e e al., 2009; Po inec
e al., 2003). Thus, Sellafield eleases a el a ound Sco land and
en e he No h Sea. He e hey join La Hague eleases and hen
a el along No way coas wi h he NCC. Pa o he ac i i y p e-
iously en e s he Bal ic Sea. S ong g adien s a e ob ained ac oss
he NCC, which has al eady been ound in he case o
137
Cs, and is
also in ag eemen wi h p e ious
129
I simula ions (O e e al.,
2009). In addi ion, some o he Sellafield eleased adionuclides
a e anspo ed o he sou h, as has been ound o
137
Cs
(Po inec e al., 2003). Then pa o his ac i i y en e s he English
Channel and, om he e, he No h Sea.
A main con ibu ion o his wo k is o p o ide a quan i a i e
analysis on he a e o
129
I eleased om Sellafield and La Hague.
Fi s , he ac i i y in en o y in he A c ic Ocean has been e alua ed.
Pa icles in he A c ic a e defined as hose which lea e he model
h ough he no h and no h-eas open bounda ies. As commen ed
be o e, anspo o adionuclides back om he A c ic o he A lan-
ic canno be simula ed. Thus, esul s should be conside ed as an
uppe limi . Model esul s a e p esen ed in Figs. 8–10 o adionuc-
lides espec i ely eleased om Sellafield, La Hague, and conside -
ing bo h sou ces. No e ha , gi en he Lag angian na u e o he
model, di e en labels can be assigned o pa icles eleased om
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
2
4
6
8
10
12 x 1012
Bq
Ac i i y in A c ic Ocean
Cumula i e discha ge
In en o y in domain
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
20
40
60
80
100
120
% in he A c ic
Yea
Respec o cumula i e discha ge
Respec o in en o y in domain
Fig. 8. Top: o al in en o y o
129
I in he A c ic, Sellafield cumula i e discha ge and in en o y in he model domain o eleases om Sellafield. Bo om: ac ion o he A c ic
in en o y wi h espec o he cumula i e discha ge and o he in en o y in he domain.
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
0.5
1
1.5
2
2.5
3
3.5 x 1013
Bq
Ac i i y in A c ic Ocean
Cumula i e discha ge
In en o y in domain
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
20
40
60
80
100
120
140
% in he A c ic
Yea
Respec o cumula i e discha ge
Respec o in en o y in domain
Fig. 9. Same as Fig. 8 bu o eleases om La Hague.
La Hague and Sellafield. Thus, a de ailed analysis may be ca ied
ou since he o igin o each pa icle in he compu a ional domain
is known.
Radionuclide in en o y in he A c ic inc eases mono onically
along he simula ion pe iod. Abou 48% o he o al eleases om
Sellafield a e wi hin he A c ic Ocean a he end o he simula ion
(2012). In he case o La Hague eleases his ac ion is sligh ly
highe (55%) since mos o he ac i i y is anspo ed o he eas ,
owa ds he No h Sea. Howe e , pa o Sellafield eleases a e
anspo ed sou h, o he Cel ic Sea. The e is a highe ac i i y inpu
o he A c ic Ocean han he ac i i y p esen wi hin he model
domain (abou 120%), as may be seen in Figs. 8–10. I can be con-
cluded ha 5.1 and 16.6 TBq o
129
I ha e been in oduced in he A c ic
om Sellafield and La Hague espec i ely un il 2012 (Figs. 8 and 9).
The o al supply o
129
I om bo h plan s o he A c ic in 1993 was
es ima ed o be P7 TBq (Ke shaw and Bax e , 1995). Bu his
figu e essen ially ep esen s 100% o he cumula i e discha ge o
ha ime, and seems o be la gely o e es ima ed. The calcula ed
in en o y in he A c ic o ha ime wi h he p esen model esul s
2.1 TBq (Fig. 10), which is 31% o he cumula i e discha ge om
bo h plan s un il hen. In he case o
90
S , which is also conse a i e
in seawa e , i was es ima ed ha 30% o he Sellafield elease was
anspo ed in o he Ba en s Sea (Ke shaw and Bax e , 1995).
In en o ies in he No h A lan ic, including shel seas (i.e., he
model domain), a e 4.4 and 13.8 TBq, coming om Sellafield and
La Hague espec i ely, in 2012 (Figs. 8 and 9).
The ac ions o adionuclides in di e en egions o he No h
A lan ic (wi h espec o he cumula i e discha ges) a e p esen ed
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
1
2
3
4
5x 1013
Bq
Ac i i y in A c ic Ocean
Cumula i e discha ge
In en o y in domain
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
20
40
60
80
100
120
% in he A c ic
Yea
Respec o cumula i e discha ge
Respec o in en o y in domain
Fig. 10. Same as Fig. 8 bu o eleases om Sellafield and La Hague oge he .
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
2
4
6
8
10
%
Cel ic Sea
English Channel
A lan ic
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
10
20
30
40
50
60
%
No way Sea
No h Sea
Bal ic Sea
Fig. 11. F ac ions o
129
I in se e al basins wi h espec o he cumula i e discha ge o eleases om Sellafield.
M. Villa e al. / Ma ine Pollu ion Bulle in 90 (2015) 15–24 21
in Figs. 11 and 12 o Sellafield and La Hague eleases espec i ely.
These egions a e indica ed in he map o Fig. 1. A ecen imes,
be ween 10% and 15% o he eleases a e p esen in he No h
Sea, Bal ic Sea and No way Sea, o bo h Sellafield and La Hague
eleases. In he case o La Hague, he in en o y in he English Chan-
nel is abou 3% o he discha ge, and in he Cel ic Sea and open
A lan ic i is negligible (Fig. 12). In he case o Sellafield, abou
2% o he discha ge is in he Cel ic Sea in 2012 and less han 1%
is p esen in bo h he English Channel and open A lan ic. This is
simila o p e ious esul s o
137
Cs: i has been ound (Po inec
e al., 2003) ha , on a e age, 1% o Sellafield eleases go h ough
he English Channel.
The model has been applied o calcula e he mean age o he
adioac i i y con en in he model domain. The concep o age is
widely used in ocean sciences o highligh he inhe en ime scales
o a sys em associa ed wi h he ad ec ion and di usion o ma e .
I has been used o wo main pu poses: o es ima e he en ila ion
a e o ocean basins and o in e ho izon al ci cula ion om ace
dispe sion. In he las case he age is defined as he ime elapsed
since a ace was eleased in he sea om a poin sou ce. As
desc ibed in de ail by Delee snijde e al. (2001), he age is a
Lag angian concep : one jus needs o a ach a ‘‘clock’’ o each pa -
icle. In ou case, he clock is ini ialized when he pa icle is
eleased om Sellafield o La Hague plan s. A he end o he sim-
ula ion, he ages indica ed by he clocks a ached o he pa icles in
he ocean a e ead. The ‘‘age-a e aging hypo hesis’’ (Delee snijde
e al., 2001) is applied o e alua e he mean age, which eads ha
he mean age o a se o pa icles (in ou case, pa icles which a e
wi hin each g id cell) is defined as he mass-weigh ed a i hme ic
a e age o he ages o he pa icles conside ed. The mass o each
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
10
20
30
40
50
60
%
Cel ic Sea
English Channel
A lan ic
1970 1975 1980 1985 1990 1995 2000 2005 2010
0
10
20
30
40
50
60
%
No way Sea
No h Sea
Bal ic Sea
Fig. 12. F ac ions o
129
I in se e al basins wi h espec o he cumula i e discha ge o eleases om La Hague.
Fig. 13. Calcula ed
129
I mean ages (yea s) o e he model domain.
pa icle co esponds o i s adioac i i y con en in he p esen
applica ion. I mus be poin ed ou ha age is a di e en concep
om ansi ime, which a e well defined o his a ea [ o ins ance
in Po inec e al., 2003)] and a e no calcula ed again in his wo k.
Calcula ed mean ages o e he model domain a e p esen ed in
Fig. 13. Ob iously, ace age inc eases wi h inc easing dis ance
om he sou ce (Sellafield and La Hague). Mean age o ace s in
he No h Sea is abou 5 yea s, while i is la ge in he Cel ic Sea
(app oaching o some 10 yea s in he sou h). Mean age in he Bal ic
is significan ly longe (mo e han 20 yea s). This is due o he ac
ha pa icles, once hey en e he Bal ic, emain he e o a signi -
ican ime due o he limi ed wa e exchange wi h he No h Sea.
Ac ually, esidence imes es ima ed o he Bal ic ange om 11
o 30 yea s (Leppa an a and My be g, 2009). Mean age inc eases
along he NCC, eaching mo e han 10 yea s in he a ea o No h
Cape. In he open A lan ic Ocean, ace ages a e o he o de o
20 yea s.
Gi en he Lag angian na u e in he model, he o igin o each
pa icle is known. Thus, mean ages o eleases coming om
Sellafield and La Hague can be calcula ed sepa a ely. These a e
shown in Fig. 14. These pic u es a e also use ul o see in de ail
he di e en a es o Sellafield and La Hague eleases, al eady
ou lined in Fig. 7. The las s ollow a e y s aigh pa h owa ds
he NCC, al hough some is los in o he Bal ic Sea. Some o he
Sellafield eleases en e he No h Sea om he English Channel
and some om he no h (a ound Sco land). These wo ac ions
con ibu e di e en ly o he mean ages o Sellafield eleases in
he No h Sea. Pa icles coming om he English Channel ha e
mean ages a ound 8 yea s, while pa icles coming om Sco land
ha e mean ages abou 2 yea s. As a esul o he mixing o hese
wo ac ions o pa icles, mean ages in he sou he n NCC (a
60°N la i ude) is abou 9 yea s. On he o he hand, mean age in his
a ea o pa icles coming om La Hague is abou 5.5 yea s.
Consequen ly, mean ages o Sellafield eleases a e abou 3.5 yea s
Fig. 14. Calcula ed
129
I mean ages (yea s) o e he model domain. Top: Sellafield eleases. Bo om: La Hague eleases.