Measuring and modelling temporal trends of 226Ra in waters of a Spanish estuary affected by the phosphate industry

Measu ing and modelling empo al ends o 226 Ra in wa e s o a Spanish es ua y affec ed by he phospha e indus y R. Pe ia ´n˜ez * Dp o. Fı ´sica Aplicada 1. EUITA, Uni e sidad de Se illa, C a U e a km 1, 41013-Se illa, Spain Recei ed in e ised o m 27 July 2004; accep ed 16 Augus 2004 Abs ac The p esence and empo al e olu ion (1990–2001) o 226 Ra in a idal es ua y affec ed by he phospha e indus y has been in es iga ed. Wa e samples collec ed in he cou se o ou sep- a a e sampling campaigns we e analysed o 226 Ra con en using a gas flow p opo ional coun- e ollowing Ba cop ecipi a ion. Two 226 Ra sou ces ha e been iden ified: di ec discha ges om he indus ial complex and un-off om a phosphogypsum pile. Al hough ac i i y le els a e simila , o e en highe , han hose ound in o he en i onmen s affec ed by he phospha e indus y, he e has been a gene al dec ease in con amina ion since di ec discha ges ceased in 1998 due o new egula ions om he EU. Howe e , sedimen s a e now ac ing as a sou ce o Ra o he wa e column due o edissolu ion p ocesses. A nume ical model o he es ua y has been de eloped o desc ibe quan i a i ely he expe imen al esul s. The model sol es he hyd odynamics and he dispe sion equa ion o 226 Ra including in e ac ions wi h sedimen s. Model esul s a e, in gene al, in good ag eemen wi h obse a ions. 2004 Else ie L d. All igh s ese ed. Keywo ds: Radium; Odiel-Tin o es ua y; Phosphogypsum; Nume ical modelling; Hyd odynamic; Sedimen 0141-1136/$ - see on ma e 2004 Else ie L d. All igh s ese ed. doi:10.1016/j.ma en es.2004.08.003 * Tel.: +34 954486474; ax: +34 954486436. E-mail add ess: [email p o ec ed]. Ma ine En i onmen al Resea ch 60 (2005) 35–49 www.else ie .com/loca e/ma en e MARINE ENVIRONMENTAL RESEARCH 1. In oduc ion The Odiel and Tin o i e s, in he sou hwes o Spain, o m a ully mixed idal es ua y which su ounds he own o Huel a (Fig. 1). Bo h i e s join a he Pun a del Sebo. F om his poin , hey flow oge he o he A lan ic Ocean. An indus ial complex, con aining a plan dedica ed o he p oduc ion o phos- pho ic acid and phospha e e ilize s, is loca ed by he Odiel i e . I is well known ha he phospha e ock used as a aw ma e ial by his indus y con ains significan amoun s o na u al adionuclides, mos ly U, Th and Ra. The indus ial p ocessing o he phospha e ock leads o a edis ibu ion o adioac i i y. Fo ins ance, du ing he we p ocess o phospho ic acid p oduc ion, 86% o U and 70% o Th p esen in he ock a e ans e ed o he phospho ic acid i sel , while 80% o he Ra con en ol- lows he so-called phosphogypsum pa h (Guimond & Ha din, 1989). This is a o m 10 20 30 40 50 60 10 20 30 40 50 60 70 80 01234 Canal del Bu o km Tin o Ri e Odiel Ri e N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 e ilize complex 16 P.Sebo HUELVA phosphogypsumpiles E D C B A Fig. 1. Map o he a ea o he es ua y co e ed by he model. Numbe ed ci cles indica e he poin s whe e wa e samples we e collec ed. Le e ed iangles indica e he poin s whe e cu en s measu emen s we e a ailable. Uni s on he axes gi e he g id cell numbe . The sea is app oxima ely 1 km o he sou h o poin 1. 36 R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 o impu e calcium sul a e emo ed as a p ecipi a e du ing he p ocess. Phosphogyp- sum is usually disposed in o piles in he open en i onmen o discha ged in o i e s o es ua ies, gi ing ise o a local adioac i e impac . The aw ma e ial used in he plan is phospha e ock om Senegal, Mo occo and Togo, which is ea ed by he we p ocess o ob ain phospho ic acid. Du ing 1990, o ins ance, 2 ·10 6 ons we e p ocessed and 3 ·10 6 ons o phosphogypsum we e p oduced. These was es we e pa ially eleased di ec ly in o he Odiel i e (20%), wi h he emaining 80% conduc ed wi h wa e h ough a pipeline o phosphogypsum piles loca ed by he Tin o i e (see Fig. 1), whe e such ma e ial is s o ed in he open ai . The gypsum piles co e some 12 km 2 o he Tin o i e ma gin. Since 1998, was es a e no eleased di ec ly in o he Odiel i e due o new egula ions om he EU, al hough phosphogypsum is s ill being disposed o in he piles by he Tin o i e . A numbe o ecen s udies ha e in es iga ed he adioac i e impac o he phos- pha e indus y in i s close en i onmen . Pa idaens and Vanma cke (2001) cha ed he 226 Ra con amina ion o he i e Laak (Belgium) and some a eas ha a e egula ly flooded by he i e . Ha idasan, Paul, and Desai (2001) ound ha he su ace un- off o wa e om a phosphogypsum pile placed by he Chi apuzha i e (India) ap- pea s o be he majo pa hway o anspo o Ra o he i e . McCa ney, Da idson, Howe, and Kea ing (2000) s udied he effec o a educ ion o he discha ges om a phospha e plan in he le els o U and Th iso opes along he Cumb ian coas (UK), while Poole, Alling on, and Denoon (1995) conduc ed a simila s udy bu o 226 Ra. The effec o he phospha e indus y in he Odiel and Tin o es ua y has also been in es iga ed. Ma ı ´nez-Agui e, Ga cı ´a-Leo ´n, and I ano ich (1994a) and Bolı ´ a , Ga cı ´a-Teno io, and Vaca (2000) s udied he p esence o U and Th iso opes o e di - e en a eas o he es ua y. The p esence o 226 Ra in wa e s o he es ua y was in es- iga ed by Pe ia ´n˜ez and Ga cı ´a-Leo ´n (1993), who de e mined 226 Ra ac i i y concen a ions in wa e s collec ed om he es ua y in wo diffe en sampling cam- paigns in July 1990 and Ma ch 1991. The objec i e o he p esen wo k is o p o ide a summa y o he wo k ca ied ou a he Uni e si y o Se ille conce ning he empo al e olu ion o he 226 Ra con am- ina ion o he es ua y, p esen ing esul s o sampling campaigns ca ied ou be o e and a e he change in he was e policy o he phospha e plan in 1998. To his effec , wo new sampling campaigns we e conduc ed; in Oc obe 1999 and Feb ua y 2001. Resul s ob ained o he ou campaigns a e p esen ed oge he . Al hough he esul s o he 1990 and 1991 samples ha e been published p e iously (Pe ia ´n˜ez & Ga cı ´a- Leo ´n, 1993), hey will also be included he e o ease o compa ison. I has o be poin ed ou ha sampling campaigns a e non-ideal o a empo al end s udy, since ha e been ca ied ou in diffe en mon hs du ing he ou yea s. Ne e heless, some in e es ing conclusions may be ob ained om hem, as will be shown. In e p e a ion o expe imen al esul s is no an easy ask since a numbe o p oc- esses affec concen a ions in he dissol ed phase. Cu en s due o idal oscilla ions p oduce ad ec i e anspo o dissol ed adionuclides along he es ua y. Fu he - mo e, u bulen diffusion is p esen and he e a e also ans e s o adionuclides be- ween he dissol ed and solid phases (suspended ma e pa icles and bo om R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 37 sedimen s). The solid phase may ac as a sink o as a sou ce o adionuclides o he wa e column, depending on he concen a ion o adionuclides in each phase and on he a es go e ning he adso p ion and elease eac ions. To accoun o hese p oc- esses, a nume ical model o he es ua y, including all hese ac o s, has been de el- oped. The model sol es he hyd odynamics o he es ua y and he dispe sion o 226 Ra, including he in e ac ions be ween he dissol ed and solid (bo om sedimen s) phases. The model applica ion allows ep oduc ion o he expe imen al esul s o he diffe en campaigns and an es ima e o be made o he inpu o 226 Ra om he phosphogypsum piles o he Tin o i e . De ails o he sampling and he expe imen al me hod o 226 Ra ex ac ion and measu emen a e p esen ed in he nex sec ion. This is ollowed by he p esen a ion and discussion o esul s. Finally, he model is desc ibed and applied. 2. Sampling and analysis Sampling campaigns we e ca ied ou on 19 h July 1990, 5 h Ma ch 1991, 27 h Oc obe 1999 and 14 h Feb ua y 2001, unde low wa e condi ions (1 h a e low wa e in he case o 1991). Samples (see Fig. 1 o posi ions o he sampling poin s) we e collec ed in 25 l plas ic bo les. The wa e was fil e ed soon a e sampling, using 0.45 lm po e size Nuclepo e fil e s o emo e suspended pa icles. Fil e ed samples we e acidified o pH 2–3 wi h HNO 3 o a oid he g ow h o mic oo ganisms and minimize wa e –wall in e ac ions du ing s o age. 226 Ra ac i i ies we e de e mined om 0.5 l aliquo s o he wa e samples. A e neu alisa ion o he fil a e using NH 4 OH, 5 mg o BaCl 2 and 20 ml o 1 M H 2 SO 4 we e added o he sample. Unde hese condi ions Ba–Ra sul a e p ecipi a es a e some 20 min o con inuous s i ing and mode a e hea ing. The p ecipi a e, con- aining he adium, was collec ed by fil a ion h ough a 0.45 lm Millipo e fil e . Ac i i y on he fil e was measu ed using a low backg ound gas flow p opo ional coun e p e iously calib a ed o o al efficiency s. p ecipi a e mass hickness. These p ocedu es ha e been widely alida ed and applied. Fu he de ails on he me hod can be ound in Mo o ´n, Ga cı ´a-Teno io, Ga cı ´a-Mon an˜o, Ga cı ´a-Leo ´n, and Madu ga (1986),Ma ı ´nez-Agui e and Ga cı ´a-Leo ´n (1994) and Pe ia ´n˜ez and Ga cı ´a-Leo ´n (1993). 3. Expe imen al esul s 226 Ra concen a ions o he ou campaigns a e p esen ed in Table 1. The le els measu ed in he fi s h ee campaigns a e b oadly simila (o somewha highe ) o hose ound in o he i e s affec ed by e ilise indus ies. In he Boben Ri e (Slo e- nia), o example, 226 Ra concen a ions o 40 mBq/l ha e been epo ed in wa e s om he mos affec ed a ea (Kobal, B ajnik, Kaluza, & Vengus , 1990), while alues in he ange 9–68 mBq/l ha e been epo ed o affec ed wa e s in he Schelde, Ne h- e lands (Kos e e al., 1991). Mo e ecen ly, 226 Ra concen a ions o 30 mBq/l ha e 38 R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 been measu ed downs eam a phosphogypsum pile in he Chi apuzha Ri e , India (Ha idasan e al., 2001). In he case o he 1990 samples, he e is an in ense peak o 670 mBq/l a poin 8, loca ed close o he pipeline h ough which di ec discha ges o he Odiel i e we e ca ied ou . This shows a clea local adioac i e impac in he es ua y due o he ope a ion o he e ilize plan . Fo he emainde o he es ua y, ac i i y concen a ions ange om 64 o 106 mBq/l, also sugges ing a clea con amina ion i hey a e compa ed wi h alues epo ed abo e. Fo samples collec ed in 1991, he peak in he icini y o he plan ou le is no appa en . Howe e , ac i i ies anging om 21 o 66 mBq/l a e indica i e o con amina ion s ill being p esen , al hough he inpu om he plan o he Odiel i e seems less han du ing he 1990 sampling. I is in e es ing o no e ha he e is an ac i i y peak in sample 15, collec ed in he Tin o i e close o he phosphogypsum pile. I seems ha some un-off om he phosphogypsum pile o he i e is occu ing and, as a consequence, 226 Ra is being anspo ed o he i e , as has been ound in o he en i onmen s (Ha idasan e al., 2001). This is ela ed o he ac ha he phos- phogypsum s o age a ea is c ossed by a numbe o small s eams o na u al and a ificial o igin (Pe ia ´n˜ez & Ga cı ´a-Leo ´n, 1993). Some o hese may be pos- sible emnan s o he we lands o ally in eg a ed in he es ua ine sys em o he i e s only 40 yea s ago, be o e indus ial ac i i y s a ed in he a ea (Bo ego & Pendo ´n, 1988). P esumably, hese s eams a e capable o anspo ing ac i i y om he s o age a ea o he main i e . This effec was also p obably aking place in 1990, al hough i may ha e been masked by he high con amina ion p o- duced by he la ge discha ges ha we e eleased in o he Odiel. This poin will be in es iga ed la e wi h he nume ical model o he es ua y. Table 1 226 Ra ac i i ies (mBq/l) in wa e samples o he Odiel and Tin o i e s Sample 1990 1991 1999 2001 1 3.6 ± 0.6 9.3 ± 1.2 2 19.1 ± 1.5 8.9 ± 1.4 3 16.4 ± 1.8 9.2 ± 1.2 4 71 ± 2 54.2 ± 1.8 19.6 ± 2.1 5 82 ± 1 46.6 ± 1.6 16.4 ± 1.6 12.5 ± 1.9 6 13.0 ± 0.6 9.4 ± 1.7 7 106 ± 3 46.5 ± 1.6 17.9 ± 2.2 8.9 ± 2.1 8 670 ± 13 53 ± 2 11.0 ± 0.6 9.4 ± 1.1 9 106 ± 2 25.3 ± 1.2 11.3 ± 1.0 6.6 ± 0.6 10 86 ± 2 21.3 ± 1.4 6.8 ± 0.6 7.2 ± 0.5 11 15.9 ± 1.7 9.7 ± 0.9 12 64 ± 2 33.6 ± 1.5 45 ± 5 10 ± 4 13 69.3 ± 1.9 36.0 ± 1.4 35.3 ± 1.8 8.4 ± 0.6 14 29 ± 4 9.7 ± 1.0 15 67 ± 1 65.6 ± 1.9 25.1 ± 2.3 8.6 ± 0.9 16 14.0 ± 0.9 8.6 ± 1.0 Unce ain ies (1 ) a e due o coun ing s a is ics in sample measu emen s and in de ec o calib a ion. Emp y spaces mean ha such samples we e no collec ed. R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 39 Ac i i y le els de ec ed in he 1999 campaign, anging om 3.6 o 45 mBq/l, a e lowe han hose ob ained in 1990 and 1991. This is likely o be ela ed o he in o- duc ion o s ic e was e policies in 1998, which esul ed in he cessa ion o di ec dis- cha ges in o he Odiel Ri e . As a consequence, he main sou ce o 226 Ra o he es ua y ha yea mus ha e been un-off om he phosphogypsum pile. Tha his is he case is e idenced by he highe concen a ions obse ed along he Tin o Ri e in compa ison o he Odiel Ri e , and by he ela i e uni o mi y o measu ed con- cen a ions in he la e . The pa e n is e y diffe en om ha obse ed in p e ious yea s, when di ec discha ges we e aking place. Ne e heless, concen a ions along he Odiel Ri e a e s ill highe han hose ound in non-pe u bed i e s, which a e ypically in he ange 0.09–3.4 mBq/l (Bha & K ishnaswamy, 1969; Rona & U y, 1952). The enhanced concen a ions can be a ibu ed o he edissolu ion o 226 Ra om a pool o unde lying con amina ed sedimen s. Indeed, he e is now s ong e idence o sugges ha con amina ed sedimen s can become a sou ce o emobilised adionuclides when he ex e nal inpu is educed and deso p ion eac- ions domina e o e adso p ion (Cook, MacKenzie, McDonald, & Jones, 1997; McCa ney e al., 2000). This hypo hesis will be s udied in mo e de ail wi h he help o he nume ical model desc ibed below. Ac i i y le els de ec ed in samples collec ed in 2001 a e a he uni o m o e all he es ua y, anging om 6.6 o 12.5 mBq/l. Unlike he 1999 da a, he e is no e idence o un-off o 226 Ra om he phosphogypsum pile o he Tin o Ri e . This is no unex- pec ed, gi en ha ea h dikes we e buil a ound he piles o p e en un-off in he pe - iod be ween he wo sampling campaigns. I may, he e o e, be assumed ha he only impo an sou ce o 226 Ra o he wa e s o he es ua y a he ime o his las cam- paign is emobilisa ion o his adionuclide om p e iously con amina ed sedimen s. 4. Model desc ip ion The sys em unde s udy is di ided in o a numbe o g id cells o compa men s. Two phases a e p esen in each g id cell: dissol ed and ac i e bo om sedimen s (pa - icles wi h a diame e <62.5 lm). The ac i e sedimen s co espond o muddy sedi- men s, ollowing he Wen wo h scale o sedimen g ain size (see o ins ance Pugh, 1987). La ge g ain sizes a e no conside ed since i has been shown ha i - ually all he adioac i i y is associa ed wi h he muddy sedimen (As on, Assinde , & Kelly, 1985). Suspended ma e pa icles ha e no been conside ed in he model, and hus dep- osi ion p ocesses and e osion o he sedimen ha e been neglec ed. This app oxima- ion is used since p e ious calcula ions ha e shown ha he adionuclide adso p ion capaci y o suspended ma e , gi en he ypical suspended ma e concen a ions in he es ua y (maximum concen a ions o he o de o 50 ppm) is e y small com- pa ed wi h ha o he sedimen (Pe ia ´n˜ez, Ab il, & Ga cı ´a-Leo ´n, 1996a). Mo eo e , he e osion-deposi ion a es, ob ained om a suspended ma e model o he es ua y (Pe ia ´n˜ez e al., 1996a), a e also small (10 2 g/cm 2 /yea ). Thus, as an app oxima- ion, i has been conside ed ha he mos impo an phases con olling adionuclide 40 R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 anspo a e he dissol ed phase and he bo om sedimen . This app oxima ion seems ealis ic gi en he gene ally good ag eemen be ween model esul s and obse - a ions (see below). Adso p ion and deso p ion eac ions a e desc ibed in e ms o kine ic ans e coefficien s. Thus, he adso p ion p ocess ( ans e o adionuclides om wa e o he sedimen ) will be go e ned by a coefficien k 1 and he in e se p ocess (deso p ion o he dissol ed phase) by a coefficien k 2 . The adso p ion p ocess is a su ace phenomenon ha depends on he su ace o pa icles pe wa e olume uni in o he g id cell. Following he no a ion o Pe ia ´n˜ez, Ab il, and Ga cı ´a-Leo ´n (1996b), he adso p ion coefficien is w i en as: k1¼ 1SE;ð1Þ whe e S E is he exchange su ace and 1 is a pa ame e wi h dimensions o eloci y, deno ed as he exchange eloci y. As a fi s app oach, assuming sphe ical sedimen pa icles and a s ep unc ion o he g ain size dis ibu ion o pa icles, i can be shown (Pe ia ´n˜ez e al., 1996b) ha SE¼3L /  H ;ð2Þ whe e  is he mean adius o sedimen pa icles, His he o al wa e dep h, Lis he a e age mixing dep h ( he dis ance o which he dissol ed phase pene a es he sedi- men ), gi es he ac ion o ac i e sedimen and /is a co ec ion ac o ha akes in o accoun ha no all he exchange su ace o he sedimen pa icle is in con ac wi h wa e since pa o i can be hidden by o he pa icles ( hus, i is also ela ed o sedimen po osi y). Consequen ly, i is implici ly assumed ha adionuclide con- cen a ions in sedimen po e wa e s, conside ing a sedimen laye o hickness Linside which he sedimen is homogeneous, a e equal o hose in he wa e column. On he o he hand, diffusion o adionuclides o deepe sedimen laye s has been neglec ed gi en he ime scale o he simula ions ca ied ou . The ans e coefficien k 2 is con- side ed cons an . O cou se, dissol ed adionuclides will be anspo ed along he es ua y by ad ec i e and diffusi e p ocesses. The e o e, he hyd odynamic equa ions mus be sol ed oo. 4.1. Hyd odynamic equa ions and physical cha ac e is ics o he es ua y The 2D shallow wa e hyd odynamic equa ions a e (see o ins ance Pugh, 1987): oz o þo ox½ðDþzÞuþo oy½ðDþzÞ ¼0;ð3Þ ou o þuou oxþ ou oyþgoz oxX þKuffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2þ 2 p Dþz¼0;ð4Þ o o þuo oxþ o oyþgoz oyþXuþK ffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2þ 2 p Dþz¼0;ð5Þ R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 41 whe e uand a e he dep h a e aged wa e eloci ies along he xand yaxis, Dis he dep h o wa e below he mean sea le el, zis he displacemen o he wa e su ace abo e he mean sea le el measu ed upwa ds, Xis he Co iolis pa ame e (X=2wsinb, whe e wis he ea h o a ional angula eloci y and bis la i ude), g is accele a ion due o g a i y and Kis he bed ic ion coefficien . The use o a 2D model is jus ified since he es ua y is e y shallow (maximum dep h a ound 19 m) and well mixed e ically. Mo eo e , he i e flows a e e y low and a as dispe - sion o esh wa e in o a much la ge olume o sal wa e occu s (Bo ego & Pen- do ´n, 1988). The Odiel Ri e flows usually ange om less han 1 m 3 /s du ing he summe o some 70 m 3 /s in No embe . In he case o he Tin o i e he co espond- ing flows a e e en smalle , wi h some 3 m 3 /s in No embe and no flow du ing he summe mon hs. This mixing be ween i e and sea wa e akes place ups eam o he s udied a ea, and o his eason ho izon al g adien s o salini y a e no consid- e ed he e. Indeed, elec ical conduc i i y along he es ua y is cons an and ypical o sea wa e , wi h an a e age alue o 37.1 ± 0.5 mS/cm (Bolı ´ a e al., 2000). The solu ion o hese equa ions p o ides he ins an aneous alues o he wo com- ponen s o he cu en and he wa e ele a ion o e he model domain, in o ma ion equi ed o sol e he ad ec ion–diffusion dispe sion equa ion o dissol ed adionuclides. 4.2. Radionuclide equa ions The equa ion ha gi es he empo al e olu ion o ac i i y concen a ions in he dissol ed phase, C d (Bq/m 3 ), is: oðHCdÞ o þoðuHCdÞ oxþoð HCdÞ oy¼o oxHKD oCd ox  þo oyHKD oCd oy  k1CdHþk2AsLqs /;ð6Þ whe e k 1 is gi en by Eqs. (1) and (2), o al dep h is H=D+z,K D is he diffusion coefficien , A s (Bq/kg) is ac i i y concen a ion in he ac i e sedimen and q s is he sedimen bulk densi y exp essed in kg/m 3 . The ex e nal sou ce o adionuclides should be added o his equa ion whe e necessa y. The equa ion o he empo al e olu ion o ac i i y concen a ion in he ac i e sedimen ac ion is: oAs o ¼k1 CdH Lqs k2As/:ð7Þ 4.3. Compu a ional scheme The hyd odynamic equa ions a e sol ed using an explici fini e diffe ence scheme. The g id cell size is Dx=Dy= 125 m and he ime s ep is fixed as D = 6 s. The CFL c i e ion is sa isfied wi h hese selec ions. Wa e ele a ions a e specified o each ime s ep along he sou he n bounda y om obse a ions. A adia ion condi ion is ap- 42 R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 plied along he no he n and eas e n open bounda ies. Along he coas , he cu en componen ha is no mal o he bounda y is se o ze o. Wa e dep hs we e in o- duced o each g id cell om ba hyme ic maps. Ins ead o sol ing he hyd odynamic equa ions simul aneously wi h he dispe - sion equa ions, he hyd odynamic model is calib a ed and alida ed in ad ance o speed up simula ions. Once he hyd odynamics ha e been alida ed, s anda d idal analysis is used o de e mine he idal cons an s (ampli ude and phase) o each g id cell. These cons an s a e e alua ed o bo h componen s o he flow (uand ) and o he wa e ele a ion (z), and o all he idal cons i uen s included in he model. Once he idal cons an s a e known, compu a ion o flow and wa e ele- a ion jus in ol es he calcula ion and addi ion o a ew cosine e ms since he cons an s a e s o ed in files ha a e ead by he dispe sion model. The ne esidual flow o e he es ua y mus also be calcula ed by he hyd odynamic model and added o he ins an aneous flow ob ained om he idal cons an s, since a esidual anspo canno be gene a ed wi h he pu e ha monic cu en s ha a e gi en by he idal analysis. The Mono onic Second O de Ups eam (MSOU) explici scheme is used o sol e he ad ec i e anspo in he dispe sion equa ion o dissol ed adionuclides. A sec- ond o de accu acy scheme has also been used o sol e he diffusion e ms. I is con- side ed ha he e is no flux o adionuclides h ough land bounda ies. Along open bounda ies, he bounda y condi ion desc ibed in Pe ia ´n˜ez (1998) is applied. 5. Model esul s Only he wo main idal cons i uen s, M 2 and S 2 , ha e been included. As will be shown below, his is enough o ha e a ealis ic ep esen a ion o he dispe sion pa - e ns o 226 Ra. The calib a ion o he hyd odynamic model consis ed o selec ing he op imum alue o he bed ic ion coefficien K. A e some model uns, i was selec ed as K= 0.040 o he Tin o i e and K= 0.005 o he es o he es ua y. Wi h hese selec ions, a easonable ag eemen be ween obse ed and compu ed cu en s has been achie ed. A compa ison be ween obse ed and compu ed magni ude and di ec- ion o he maximum cu en s o se e al loca ions in he es ua y (see Fig. 1)isp e- sen ed in Table 2 o a si ua ion o medium ides (coefficien 74.4). Once ha wa e ci cula ion is ep oduced by he hyd odynamic model, esul s a e ea ed wi h s and- a d idal analysis o calcula e he idal cons an s o be used by he dispe sion model o compu e cu en and wa e ele a ion a any posi ion and ins an o ime, as dis- cussed p e iously. A alue ha depends on a ho izon al leng h scale (se as he g id spacing) is cho- sen o he diffusion coefficien . Indeed, ollowing B e on and Salomon (1995) such coefficien was aken as 0.61 m 2 /s. Since he dispe sion model is no es ic ed by he CFL s abili y c i e ion, he ime s ep in he dispe sion model has been inc eased o 30 s. Howe e , s abili y condi ions imposed by he dispe sion equa ion a e sa isfied wi h his alue. R. Pe ia ´n˜ez / Ma ine En i onmen al Resea ch 60 (2005) 35–49 43