The behaviour of I-129 released from nuclear fuel reprocessing factories in the North Atlantic Ocean and transport to the Arctic assessed from numerical modelling

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.