uncertainties associated with 223ra and 224ra measurements in water via a delayed coincidence...

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Marine Chemistry 109

Uncertainties associated with 223Ra and 224Ra measurements inwater via a Delayed Coincidence Counter (RaDeCC)

E. Garcia-Solsona a,b,⁎, J. Garcia-Orellana a,b, P. Masqué a,b, H. Dulaiova c

a Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spainb Institut de Ciència i Tecnologia Ambientals, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

c Department of Marine Chemistry and Geochemistry, Woods Hole Oceanographic Institution, Woods Hole, MA 02536, USA

Received 16 March 2007; received in revised form 16 November 2007; accepted 16 November 2007Available online 28 November 2007

Abstract

The short-lived radium isotopes, 223Ra (T1/2=11.4 days) and 224Ra (T1/2=3.66 days), have been successfully used as tracers ofseveral environmental processes, e.g., submarine groundwater discharge, coastal mixing processes, and water residence times. Inthis paper, the uncertainties associated with 223Ra and 224Ra measurements using a Radium Delayed Coincidence Counter aredetermined on a detailed error propagation basis with a confidence interval of 1σ. From the data analyses of several groups ofcoastal water samples, the calculated relative uncertainties averaged 12% for the 223Ra and 7% for the 224Ra. These uncertaintiescan decrease for radium-enriched groundwater samples although asymptotic limits have been found at 7% relative uncertainty for223Ra and 4% for 224Ra. In this paper, the influence of sampling and measurement parameters on the final radium uncertainties isevaluated in order to provide guidance to optimize these factors and obtain more reliable results.© 2007 Elsevier B.V. All rights reserved.

Keywords: Ra-223; Ra-224; Uncertainties propagation; Radium Delayed Coincidence Counting; Submarine groundwater discharge

1. Introduction

The four naturally occurring radium isotopes(223Ra, T1/2=11.4 days; 224Ra, T1/2=3.6 days; 226Ra,T1/2=1600 years and

228Ra, T1/2 =5.75 years, membersof the U and Th decay series) can be used as tracers of avariety of environmental processes. Among the variousapplications, this suite of isotopes can help withstudying the composition of a geological rock forma-

⁎ Corresponding author. Departament de Física, Universitat Autòn-oma de Barcelona, 08193 Bellaterra, Spain. Tel.: +34 935811191; fax:+34 93 581 2155.

E-mail address: [email protected] (E. Garcia-Solsona).

0304-4203/$ - see front matter © 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.marchem.2007.11.006

tion through which infiltrating rain-water has beenpercolated prior to surface run-off (223Ra and 228Ra;Al-Masri, 2006), estimating water residence times(223Ra and 224Ra; Moore, 2000a), determining theextent of river plumes in the ocean (223Ra and 224Ra;Moore and Krest, 2004) or evaluating resuspension andbioturbation events (223Ra and 224Ra; Sun andTorgersen, 2001). For the last decade, the DelayedCoincidence Counter (RaDeCC) system has becomethe instrument of choice to measure 223Ra and 224Raactivities in water samples (Moore and Arnold, 1996).Moreover, this system can also be used to determineconcentrations of their respective parents: 227Ac and231Pa (for 223Ra) and 228Ra and 228Th (for 224Ra),

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http://dx.doi.org/10.1016/j.marchem.2007.11.006

199E. Garcia-Solsona et al. / Marine Chemistry 109 (2008) 198–219

among others, allowing to study deep ocean mixingprocesses (Geibert et al., 2002; Nozaki, 1984; Shawand Moore, 2002).

However, maybe one of the most prominent applica-tions of the so called radium-quartet is their use for theassessment of submarine groundwater discharge (SGD)in coastal areas, since brackish and salty groundwater isenriched in radium compared to offshore surficial watersand the excess radium signal is easily detected in thecoastal zone (Moore, 1996). There are several modelsthat can be used to determine SGD fluxes mostly basedon radium mass balance. To achieve a final estimate ofSGD with a certain accuracy, the uncertainties of theinput terms in the radium mass balance need to beassessed and cannot be too large, since each term'suncertainty contributes to the final error when solvingthe model. It is therefore important to determine theradium activities with the smallest possible uncertaintyin order to minimize the propagated uncertainty in thefinal calculated groundwater flux. The determination of223Ra and 224Ra uncertainties is also useful whenidentifying trends and variability in radium concentra-tions, or to clearly differentiate between groups ofsamples, i.e. different groundwater end-members.Although scientists are aware of the need for uncertaintypropagations through their analyses and models, inpractice, 223Ra and 224Ra uncertainties in the literatureare rarely quantified: when given, the uncertainties areestimated to be 10% of the radium values (Moore, 2003,2006; Moore and Krest, 2004) or only counting statisticsare considered (Hancock et al., 2000; Kim et al., 2003;Kraemer, 2005; Swarzenski et al., 2001).

It has long been recognized that most measurementsare subject to systematic and random errors which are notperfectly quantifiable and that there is uncertaintyassociatedwith the results of suchmeasurements.Withouta statement of the corresponding uncertainty, any value isof limited use in environmental research. In general, theknowledge of the uncertainty of a measurement isessential for any further use of the resulted value. Overall,a key step in performing any analyses is to identify whichsources contribute most to the overall uncertainty andoptimizing the analysis by suitable measures to reducethem. The ability to determine how much each inputparameter contributes to the output uncertainty isparticularly valuable. It allows exploring how much thequality of the output improves, given a reduction ofuncertainty in a particular input.When the uncertainty of aterm has a marginal effect on the output, then there is littleto be gained from optimizing it. In that case, extrasampling/measurement efforts can more effectively bedirected to an input term that has a larger contribution to

the output uncertainty. For instance, if a radium mixingmodel is sensitive to coastal seawater activities and less soto river radium activities, then it is more important tomeasure the former more accurately. Finally, uncertaintycalculation is also useful when one intends to comparedifferent measurement techniques.

In this paper, the relative uncertainties of 223Ra and224Ra measurements in water samples via a RaDeCCsystem are determined step-by-step through samplecollection, system calibration, counting and performingthe coincidence correction calculations. Different typesof water are analyzed and the influence of sampling andmeasurement parameters on the final radium uncertain-ties is evaluated. The paper is intended to serve as a guideto minimize propagated uncertainty in the Ra distribu-tion in a given environment to any further application,for instance, SGD determination.

2. Methods

2.1. Radium sampling and laboratory pretreatment

In the field, large volume water samples are collected andfiltered slowly (≤1.0 L·min−1) through a column loosely filledwith MnO2-impregnated acrylic fiber (~25 g dry, Mn-fiber). Atslow flow-rates the Mn-fiber quantitatively extracts radiumisotopes by adsorption onto the manganese oxide particles(Moore, 1976). If needed, the water sample can be pre-filteredusing 0.1–0.4 μm filters or raw fiber placed upstream from theMn-fiber in the column to act as a prefilter and avoid at least thelarger-sized particles to attach onto the Mn-fiber. Such particlescan have thorium (the parent of radium) or radium attachedwhich increase the measured radium values, alter the dissolvedradium isotope ratios, or decrease the active Mn-fiber surfacefrom radium adsorption.

Moore et al. (1995) checked for the efficiency of radiumuptake by pumping 500 L of groundwater through twoMn-fibercolumns connected in series. They concluded that a singlecolumn is adequate to extract at least 97% of the radium fromeither small or high volume samples. Kim et al. (2001) did asimilar experiment and confirmed quantitative radium adsorp-tion from 1000 L of groundwater. From our experience, we havechecked that out in a number of instances, including differentkind of waters, and complete radium uptake has been obtained(data not published).

Once the water samples have been passed through the Mn-fibers, the fibers are rinsed with radium-free deionized water.This is important in order to wash out any particles and sea saltthat may dry on the fiber and interfere with radon emanationduring the measurement (Moore, 2000b; Sun and Torgersen,1998). The Mn-fibers are then hand-squeezed or dried partiallyby flushing with compressed air. The net weight of the wet Mn-fiber is monitored until it reaches a water/fiber weight ratio in arange from 0.3 to 1 gH2O/gfiber. This ratio allows achievingoptimal radon emanation efficiency by having the ideal moisture

200 E. Garcia-Solsona et al. / Marine Chemistry 109 (2008) 198–219

content so that the maximum fraction of the produced radonenters the circulating gas stream that passes through the countingcell (Sun and Torgersen, 1998).

2.2. Measurement of radium using the Radium DelayedCoincidence Counter

2.2.1. Description of the detection technique

For the measurement of 223Ra (T1/2=11.43 days) and224Ra

(T1/2=3.66 days), the Mn-fibers are counted on a RadiumDelayed Coincidence Counter (RaDeCC). This system waspioneered by Giffin et al. (1963) and adapted for radiummeasurements byMoore andArnold (1996). The partially driedMn-fibers are placed in a closed helium-circulation loop. Thegas is pumped through a flow meter to the sample chambercontaining the Mn-fibers where the flux of helium strips theshort-lived radon daughters of 223Ra and 224Ra (219Rn and220Rn, respectively) from the fiber and carries them to a ZnScoated 1.1 L scintillation cell. By regulating the gas flow-rate at6 L min−1 (i.e. a helium flow of 3.4 L min−1; Moore, 2008-thisissue) we achieve an optimal residence time of the gas in thecounting system of 24.6 s (6 half-lives of 219Rn). Thereby, the220Rn–216Po and 219Rn–215Po pairs mostly decay in the celland they can be used to uniquely identify the radon isotope. Thealpha particles are registered using a photomultiplier tube(PMT) attached to the scintillation cell and the delayedcoincidence circuit sorts the signals generated by the decayof each of these radon isotopes to a short-lived poloniumisotope: the 219Rn isotope decays to 215Po (T1/2=1.8 ms) and220Rn decays to 216Po (T1/2=150 ms).

Any alpha particle detected in the scintillation cell produces asignal which is routed to a total count register and also to the 219and 220 circuits. The total channel records every decay event(total counts, cpm total). In the two other circuits, the 219 and220 channels, the signal is delayed to allow the circuit to stabilizeor filter any undesirable event (such as an electronic spike in thecircuit). The signal then opens an electronic gate in each channelthat will remain open for 5.6 ms (219 circuit) and 600 ms (220channel). Any second event occurred in these time intervals willbe counted in the respective circuit (219 counts and cpm 219;220 counts and cpm 220). The interferences between channelsare adequately subtracted. Also, random counts, i.e. “chance”events due to background counts and the decay of 222Rn, aresubtracted to obtain the correct events in each channel. Once thecorrected 219 and 220 counts are calculated, the activities of223Ra and 224Ra on the Mn-fiber can be determined.

Giffin et al. (1963) derived and verified the expressions tocalculate the fraction of chance coincidence events (events thatdo not originate from the isotope of which channel they wereregistered in) which are expected to occur in the 219 and 220channels (Y 219 CC and Y 220 CC). They are calculatedfollowing relationships given in Giffin et al. (1963) and Mooreand Arnold (1996) described in the Annex (Eqs. (1) and (2)).The chance coincidence contribution is then subtracted fromthe 220 cpm and the 219 cpm to obtain the corrected values(corr 220 and corr 219; Eqs. (3) and (4) in the Annex).

Cross-talk between the channels also needs to be corrected.For the 224Ra, the delay on the 220 circuit effectively prevents219Rn–215Po signals from registering in this circuit. However, afinal adjustment must be made to the 220 data due to 219Rn andits daughter. If two 219Rn decays occur while the 220 window isopen, the second 219Rn decay and the decay of 215Po will berecorded in the 220 channel (equations to account for thesecorrections are described in the Annex; final 220, Eq. (5)).

On the other hand, some events due to 220Rn–216Po decay fallinto the 219 circuit because the time constant of the 219 gate islong enough for 2.55%of the 220Rn–216Po decays to occur in thiswindow. The final 219 cpm are then calculated based on Eq. (6)(Annex).

Once the final 219 and 220 cpm are calculated, they areconverted to activity (decay per minute, dpm) by dividingthem by the efficiencies of each channel (Eqs. (7) and (8) in theAnnex; see Section 2.2.3 for the efficiency calculation). Thecounts recorded in the total channel can also be used to cal-culate 224Ra by eliminating the total background and thecalculated 219 dpm from the total cpm, and using the totalchannel efficiency (E total) (Eq. (9), Annex). Ideally, the twodifferent 224Ra calculations (Eqs. (8) and (9) in the Annex)should result in the same number for the 224Ra but somediscrepancy commonly occurs because the total channel canregister more than the 219 plus the 220 and background counts(i.e. 222Rn when 226Ra on the fiber is very high). The criterionapplied when deciding between Eq. (8) (220 cpm) or Eq. (9)(total cpm) for the 224Ra quantification relies on the calculationof two indicators: a) [cpm 220 /Y220 CC] and b) [total cpm/total cpm bkg]. If the ratio between the recorded 220 cpm andthe chance coincidence cpm is lower than the total count ratedivided by the background cpm (i.e., a ratio being much lessthan b) it is better to use the total channel counts to calculate224Ra activities because the chance coincidence events mimica high background; this usually occurs when high activitysamples are measured, i.e. count rates in the total channelexceed 10 cpm (Moore, 2008-this issue), where the chancecoincidence correction for the 220 channel is too high andaffects the 224Ra activity.

The next step in the calculation is the correction for radiumradioactive decay that occurred between sampling and measure-ment (Eqs. (10), (11) and (12) in the Annex). The decaycorrected 219 and 220 dpm are then divided by the samplevolume filtered through the Mn-fiber to obtain the 223Ra and224Ra specific activities (Eqs. (16), (17) and (18) in the Annex).

2.2.2. RaDeCC counting

2.2.2.1. Background measurements. The RaDeCC systemhas the advantage of very low backgrounds: our detectors havetypical backgrounds of 0.03–0.07 cpm in the 220 channel and0.001–0.007 cpm in the 219 channel. However, by consecu-tively measuring samples in the same counter the subsequentbackgrounds may increase due to decay products remaining inthe counting cell. In order to clean the system of these residualisotopes, ambient air is circulated through the open system forat least 30 min. This procedure effectively prevents any





possible contamination of the system, especially the build-upof long-lived isotopes.

A background measurement is performed before everysample count and used for correction of the results and uncer-tainties. While no significant 219 and 220 background counts areusually detected, the total channel may record considerableamount of background counts hence introducing uncertaintieswhen calculating 224Ra activities via the total counts. Fig. 1shows counts recorded during flushing of the cell after counting asample with ~300 dpm 100 L−1 of 224Ra. It illustrates thatsometimes it is beneficial to wait several hours (or overnight) forthe Ra daughters remaining in the counting cell to decay.

2.2.2.2. Sample counting. Each sample is usually countedthree times in a 1-month period after sampling. The firstmeasurement (224Ra count) is usually carried out within 1–3 days after sampling in order to avoid significant 224Ra decay.Since the natural initial 224Ra activity is usually approximately10 to 20 times the 223Ra activity (Charette et al., 2001;Hancock et al., 2000), the initial interference of 220Rn–216Podecays falling into the 219 channel (a 2.55% of the total) canrepresent a high value compared to the 215Po decays in thischannel. Thus, only 224Ra activity is quantified from the firstmeasurement. The obtained 219, 220 and total counts (in 10-minute intervals) from a first measurement of a coastal watersample are presented against time in Fig. 2. The RaDeCCsoftware can integrate the registered counts in different timeintervals (from 1 to 60 min) that can be changed at will. By

Fig. 1. Background counts on the RaDeCC system: the open symbols correspoout after measuring a high radium activity sample. The high background in thfrom the active sample and is the highest in the total channel. The solid symbobefore the high activity sample measurement. The solid symbols on the right iafter the long background measurement.

grouping the counts in time intervals there is a gain in statisticswhen looking for outliers (e.g. applying Chauvenet's criterion;Taylor, 1997) and checking for trends caused by decay productin-growth in the counting cell. Based on our experience,typical samples can be counted for up to 3 h without significantdecay product or 222Rn in-growth.

A second measurement (223Ra count) is performed afterseveral days (typically 7 to 12 days) and provides a measure of223Ra. By this time, much of the 224Ra has decayed thus theinterference of 216Po in the 219 channel is less significant. Thissecond measurement requires longer counting times (usuallyseveral hours) to obtain good statistics for the less abundant223Ra isotope. Even though a long measurement can result inan excessive background building up, it mostly affects the 220and total channels (Fig. 3). By plotting the recorded countsversus counting time, any outliers or trends in the counts areeasily detected, they can be corrected and the new count ratesfor every channel recalculated. Unexpected electronic spikesin the system would show up as outliers of very high counts(mostly in the 219 and total channels), which can be easilydiscarded. Moreover, if any increasing trend is observed it canbe corrected for by discarding the data collected after the pointat which the increasing (or decreasing) trend is statisticallyidentified. Again, the correct count rate based on the revisedcounts and times have to be recalculated for each channel.When counting typical coastal and groundwater samples(n=50), we found that the corrections in the second count(223Ra measurement) from outliers and trends may change the

nd to a 500-minute background count in the respective channels carriede system is due to the accumulation of 224Ra and 222Rn decay productsls on the left indicate counts per minute of the background counted justndicate the values of a subsequent background count carried out the day

Fig. 2. Counts in the three channels collected in 10-minute intervals plotted against total counting time of the 224Ra count (first measurement) of a coastalwater sample that is enriched in radium from SGD. A linear regression (least squares fitting technique) gave no outliers at a confidence level of 95%.


final count rate as much as 1–6% for the 219 channel, 1–10 %for the 220 and 1–10% for the total channel.

After the 223Ra and 224Ra measurements are completed, theMn-fiber samples are aged for 3–5 weeks to allow the excess224Ra to decay and the supported 224Ra to equilibrate with its

Fig. 3. Counts per minute in the 219, 220 and total channels versus counting tan increase in the total channel is typically observed due to decay product ashow up in the 220 channel, but the 219 channel is basically not affected.

parent 228Th also collected onto the Mn-fiber. The measured228Th (i.e. supported 224Ra) is subtracted from the total 224Rato obtain excess 224Ra activities. This third measurement(228Th count) is carried out for a period of several hours toobtain good counting statistics. Although 228Th counts in the

ime for the 223Ra count of a coastal water sample. After 100 to 180 min,nd radon accumulation in the counting cell. Some of these counts also

Table 1Average activities of coastal water samples from three study sites

# samples 224Raex(dpm 100 L−1)

Relative uncertaintyin 224Ra (%)

223Ra(dpm 100 L−1)

Relative uncertaintyin 223Ra (%)

220 228Th(dpm L−1)

219

Venice Lagoon (northern sector), Italy a

n=22 68 6 7 11 10 0.020±0.005Maestrat coastal area, east Spain b

n=30 72 6 5 12 15 0.030±0.006Minorca Island (southern region), Spain c

n=26 14 9 2 14 9 0.010±0.003Averages

n=78 7 12 11 0.020±0.010

The initial 220/219 count ratios and the measured 228Th activities are also given. The collected sample volumes are 50 L and the counting times rangefrom 80 to 180 min for the first count and from 250 to 500 for the second count. All samples were measured within 0.5–3.5 days (1st count) and 8–18 days (2nd count) after collection.a Data from Garcia-Solsona et al. (submitted to Marine Chemistry, 2008-this issue).b Data from Mejías et al. (2007), Garcia-Solsona et al. (2007) and unpublished data.c Unpublished data.


220 channel usually remain constant, the background has to bemonitored. Average measurements of 228Th in different coastalsettings are presented in Table 1. The parent measurement isusually not needed for 223Ra because supported 227Acactivities are negligible in most instances (Hwang et al.,2005; Moore and Krest, 2004). For example, Shaw and Moore(2002) reported 227Ac activities of ~0.005–0.008 dpm100 L−1 in surface oceanic waters. However, relatively highlevels of 227Ac (0.046±0.005 dpm 100 L−1) have beenmeasured in deep sea waters where it is used as a deep seatracer (Geibert et al., 2008-this issue) and in some ground-waters (Charette, personal comm.)

2.3. Efficiencies determination

The calibration of any detector should be carried out using astandard material with certified activities close to thoseexpected in the real samples. Thus, the RaDeCC systemrequires to be calibrated with known 223Ra and 224Ra activitiesadsorbed ontoMn-fiber. In this study, 232Th and 227Ac standardsolutions that are known to have their daughters (228Ra, 228Ac,228Th and 224Ra from 232Th; and 227Th and 223Ra from 227Ac)in radioactive equilibrium have been used. AMn-fiber standard

Table 2Reference solution activities used for the Mn-fiber standard preparation

Reference solution Half-life(year)

Reference date Activity(dpm mL

232Th 1.4·1010 Apr 7 1992 57.12

227Ac 21.8 Jun 21 1990 220

226Ra 1600 May 27 2003 5.95

Calibrated activities adsorbed onto the Mn-fiber and corresponding efficienc

was prepared on July 2004 by adsorbing known activities of232Th and 227Ac reference solutions onto Mn-fiber. In order toobtain a standard with a radium composition close to realsamples, 226Ra was also added (see details in Table 2).

We chose the following 232Th (224Ra), 227Ac (223Ra) and226Ra activities to produce the Mn-fiber standard: 20 dpm 232Th,2.8 dpm 227Ac and 10 dpm 226Ra. About 4 L of radium-freeseawater was used for the preparation of the standard. We passedthe solution through the Mn-fiber several times to ensure aquantitative adsorption of thorium, actinium and radium. In orderto confirm the actual activities (Table 2), the produced standardswere also counted at the laboratory of Dr. M.A. Charette (WoodsHole Oceanographic Institution, Massachusetts, USA), wherethey were measured with an already calibrated RaDeCC system.In order to calculate the efficiencies of our detectors,wemeasuredthe standards and divided the final 219 and final 220 cpm by theactivities of 223Ra and 224Ra on the standard, appropriately decaycorrected (232Th decay is negligible). Detailed description ofthese calculations is given in the Annex (Eqs. (13) and (14)).

Accurate determination of the detector efficiencies is anindispensable requisite for obtaining reliable results. By properpreparation and measurement of the Mn-fiber standards anddetermination of efficiencies, smaller uncertainties will be

−1)Activity on the Mn-fiber standard(dpm) at July 2004

RaDeCCefficiencies (%)

19.2 54±3(224Ra)

2.9 42±3(223Ra)

10.1

ies for the RaDeCC system.


Fig. 4. Detector efficiencies (219, 220 and total) resulted from RaDeCC standard measurements plotted against the water content of the Mn-fiber. Theproper interval to work within is indicated by the vertical dashed lines and covers a range of water-to-fiber ratio from 0.3 to 1.2 (gH2O/gfiber) (similar toresults from Sun and Torgersen (1998)). Average 219, 220 and total efficiencies are indicated with horizontal lines and are 42±3, 54±3 and 131±6%,respectively.


propagated when analyzing samples. Also, malfunctioning ofthe system (drift in detector plateaus, leek in the system) can bedetected by regular measurement of the standards. Anotherimportant aspect is themoisture of theMn-fiber standards. In thisstudy, thewater content of theMn-fiber standards has been foundto be optimal when working at 0.3–1.2 gH2O/gfiber (Fig. 4), theseare similar results to those obtained by Sun and Torgersen(1998). Based on our experience, the Mn-fiber standard looses~4 % of its water content during each measurement which takes3 h, thus requiring rewetting after several measurements. For thecalculations presented in this study, efficiencies obtained fromseveral standard measurements throughout a 5-months periodwill be used. The average efficiencies and their standarddeviations are 42±3 %, 54±3 % and 131±6 % for the 219,220 and total channels respectively (Fig. 5).

3. Uncertainties associated with radium activitiesdetermined by the RaDeCC system

Each input term in Eqs. (1)–(15) of the Annex that isused to calculate the final activity of 223Ra and 224Ra(Section 2.2.1) introduces uncertainties. For everyequation, uncertainty is calculated according to thelaw of uncertainty propagation for uncorrelated vari-ables, that is, by partially deriving the equation for any

of the involved terms (NIST, 1994). A generalexpression for the absolute uncertainty of a givenfunction (f) that depends on n uncorrelated variables (x1,x2,…, xn) and their uncertainties (Δx1, Δx2,…, Δxn), is:

Df ¼ Df x1; x2; :::; xn;Dx1;Dx2; :::;Dxnð Þ

¼Xni¼1

AfAxi

Dxi

� �2 !1=2

ð1Þ

Using this relationship, the uncertainties associatedwith every mathematical operation are calculated(Eqs. (1.1) to (18.1) in Annex). We consider thelaw of uncertainty propagation for uncorrelatedvariables because no linear relationship has beenfound between 219 and 220 cpm neither between 219and total cpm. However, we acknowledge that insome instances there is significant correlation between220 cpm and total cpm, particularly for high activitysamples, that would cause an underestimation of thefinal uncertainties.

Fig. 6a and b show the relative uncertainty associatedwith the calculations performed from 224Ra and 223Racounts of various water samples with different radium

Fig. 5. Efficiencies for a single RaDeCC detector determined from Mn-fiber standard measurements throughout a 5-month period. The average 219,220 and total efficiencies are indicated by horizontal lines and correspond to 42±3, 54±3 and 131±6 %, respectively.


activities and activity ratios. All river and lagoon watersare 20–50 L samples from the northern Venice lagooncollected in 2005 (Garcia-Solsona et al., 2008-thisissue). River samples with salinity 0.3 had less radiumwhile the higher salinity river samples that wereinfluenced by lagoon waters had high radium activities.The brackish spring and sea water samples (samplevolume of 50 L and salinities of 5.5 and 38,respectively) originate from a karstic coastal area(Spanish Mediterranean coast) where groundwaterdischarge occurs in form of visible springs. The relativeuncertainties shown on Fig. 6a and b include: the chancecoincidence corrections, the interference of 216Po decayevents occurring in the 219 channel (2.55%), theprobability of registering two coincident 219Rn decaysoccurring while the 220 window is open, the efficiencyterm and decay correction as defined in the Annex.

These calculations result in a 224Ra uncertaintyaveraging ~7%, although up to a 14% is reached for low224Ra levels (e.g. sea water) and only a 4 % uncertaintyis found in highly radium-enriched samples (e.g.brackish spring groundwater). In general, the chancecoincidence correction (er Y220CC) is the operation thatintroduces most uncertainty in the 224Ra results: thepropagated uncertainties until the Y220CC correctionaverage 4% and they increase up to 12% afterperforming this correction. The chance coincidenceincreases with the square of the total counts per minute,that is, with every alpha particle registered by thecounting cell. Although not shown in Fig. 6a, the first

measurement (224Ra count) usually results in high 223Rauncertainties. This shows that the second measurement(223Ra count) is very important especially for sampleswith low 223Ra activities and high 224Ra/223Ra activityratios. For instance, a river sample with a 223Ra activityof 0.5 dpm 100 L−1 and a 224Ra/223Ra ratio of 35 willresult in up to ~55% uncertainty in the 223Ra activity ifit is determined from the first count.

Uncertainties derived from the second measurementof the same samples resulted in final propagated 223Rauncertainties averaging 12% (Fig. 6b). In this case, thenumber of the registered 219 counts (er 219 cpm) andthe influence of the 220 counts on the 219 channel (ercorr219) are usually the most important terms inintroducing uncertainties. The first term is directlyrelated to the number of 219 counts, which is frequentlya small number (i.e. often b100 counts). Its uncertaintyranges from 5% (for the spring and lagoon waters) andup to 14% (for the sea water sample). The chancecoincidence correction uncertainty represents only 7%but the corresponding uncertainty of the 220 countsinterference in the 219 channel is again higher, in someinstances up to 16%.

4. Implications of sample volume, decay andcounting time on 224Ra and 223Ra final uncertainties

If 223Ra and 224Ra activities with certain accuraciesare desired, sampling and measurement parameters needto be optimized based on the expected radium activities

Fig. 6. a. Uncertainties associated with each mathematical operation (Eqs. 1–15 in the Annex) performed for the 224Ra count of various watersamples. Water 224Ra activities (from 3 to 320 dpm 100 L−1) indicated in the legend illustrate the range of usual concentrations for each type ofsample. Final 224Ra uncertainty (er Ra-224) of all samples averages at 7 % (black horizontal line). Each term is defined in the Annex. Supported 224Rahas already been subtracted by considering a 228Th activity of 0.02±0.01 dpm L−1. b. Uncertainties associated with each operation (Eqs. 1–15)performed for the 223Ra count of different kind of water samples, with activities ranging from 0.5 to 13 dpm 100 L−1 (indicated in the legend). Thefinal 223Ra uncertainty (er Ra-223) of all samples averages 12 % (black horizontal line). Each term is defined in the Annex.


of the sampled water. The main parameters that areusually the easiest to control and modify duringsampling and measurement are discussed here togetherwith the evaluation of their relative importance inintroducing uncertainties to the final results. This

includes the sample volume (Section 4.1), the elapsedtime between sampling and measurements (Section 4.2)and the length of the counting time (Section 4.3).

The parameters that have to be determined with thebest possible accuracy before sample measurement are

Fig. 7. Relationship between 220 cpm and total cpm found in natural coastal waters that allows the estimation of the total cpm for a given sample withknown 220 cpm. The equation is therefore used to estimate the total cpm in all the calculations presented in this study.


the detection efficiencies and the background levels.Useful routine practices also involve: i) checks for anyleaks in the gas circuit; ii) efficient purging betweensamples to lower the background, which will depend onthe activity of the previously measured sample; iii)regular efficiency checks with Mn-fiber standard(Dimova et al., 2008-this issue) with adequate moisturecontent (0.3 to 1 gH2O/gfiber; Sun and Torgersen, 1998)and iv) regular verification of the electronics for shifts indetector plateaus. The efficiencies for 219, 220 and totalchannels for our system have been carefully calculatedand were found to have uncertainties below 6%. A totalbackground count rate of 1.5 cpm has been averaged

Table 3Estimated 219, 220 and total counts for different sample volumes and rameasurement) and from 1 to 25 dpm 100 L−1 of 223Ra (second measuremen

224Ra count

Volume (L) 220 counts 219 counts Total coun

10 25–875 2–80 151–233020 50–1750 5–159 257–397130 75–2625 7–239 352–542640 100–3500 9–318 439–677050 125–4375 11–398 521–803960 150–5250 14–477 600–9250100 250–8750 23–795 888–1370

from 50 measurements and then used in all presentedcalculations.

For the purpose of demonstrating how the abovelisted parameters affect the final uncertainties, we usedaverage 223Ra and 224Ra activities measured in surfacecoastal water samples of three different regions (Table 1)as these types of waters are most commonly observed inSGD studies. The coastal areas comprise of an intertidalmarsh, a karstic area and a small cove. By establishingan initial value for the 220 counts, the counts in the totalchannel have been estimated from a relationship of220 cpm versus total cpm (n=77 and R2 =0.992;Fig. 7). In a similar way, we can establish a relationship

dium activities ranging from 3 to 180 dpm 100 L−1 of 224Ra (firstt)

223Ra count

ts 220 counts 219 counts Total counts

25–875 8–292 208–320650–1750 17–583 354–546675–2625 25–875 484–7467100–3500 33–1167 604–9318125–4375 42–1458 717–11,064150–5250 50–1750 825–12,731

5 250–8750 83–2917 1223–18,862


Fig. 8. a. Water sample volume plotted against relative uncertainties (%) of 224Ra for different radium activities. From the estimated 220 counts, the219 counts are calculated using an average ratio determined in natural waters (220/219=11; n=78, see Table 1) and the total counts derived from therelationship existing between 220 cpm and total cpm (see text for details). The counting time is set at 2 h and the sampling to counting decay period at2 days. b. Sample volume versus relative uncertainties (%) of 223Ra for different radium activities. The samples are measured 10 days after samplingand the counting time is 8 h. From the estimated 220 counts, the 219 counts are calculated using an average ratio determined in natural waters (220/219=3; n=78) and the total counts derived from the relationship between 220 cpm and total cpm.


Fig. 9. a. 224Ra activities plotted against their relative uncertainties (%) considering different decay times in days before the 224Ra count. The countingtime is set at 2 h and the decay correction in the total channel is assumed to be the same as in the 220 channel since 224Ra (T1/2=3.66 days) is the mostabundant isotope that is likely recorded in the total channel. b. 223Ra activities plotted against their relative final uncertainties (%) consideringdifferent decay period in days before the 223Ra count. Counting time is set at 8 h. The half-life derived from the counts registered in the total channel isconsidered to be that of 224Ra since no low 226Ra/224Ra ratios are found in the considered coastal water samples.


between 219 and 220 counts for the 224Ra and 223Rameasurements. This requires a correction for the elapsedtime between the first and second measurements for allsamples and then calculating average ratios from everymeasurement. Following these calculations, we obtain

ratios that are close to the average 220/219 ratio found insurficial waters (Table 1), which equals 11 in the firstmeasurement and 3 in the second measurement. Weused a value of 0.02±0.01 dpm L−1 (n=78) 228Th tocorrect for supported 224Ra. This average value agrees

Table 4Estimated 219, 220 and total counts for different decay periods and activities ranging from 3 to 180 dpm 100 L−1 of 224Ra (first measurement) andfrom 1 to 25 dpm 100 L−1 of 223Ra (second measurement)224Ra count 223Ra count

Decay days 220 counts 219 counts Total counts Decay days 220 counts 219 counts Total counts

0.5 133–4650 10–349 583–89951 121–4230 10–338 530–8182 8 146–5112 38–1318 882–13,6092 100–3500 9–318 439–6770 10 100–3500 33–1167 604–93183 83–2896 9–299 363–5602 12 68–2396 30–1033 414–63804 68–2396 8–282 300–4636 14 47–1641 26–915 283–43695 57–1983 8–265 249–3836 16 32–1124 23–810 194–29916 47–1641 7–249 206–3174


with literature values, as activities of 228Th are quiteconstant in a coastal areas (due to the rock source andthorium affinity to particles), they usually range from0.01 to 0.02 dpm L−1 (Moore, 2003, 2006; Moore andArnold, 1996). The 223Ra and 224Ra activity rangesconsidered in the following sections are 1–26 dpm100 L−1 and 3–180 dpm 100 L−1, respectively. Theseintervals cover a variety of radium activities found innatural waters (Charette et al., 2003; Charette andBuesseler, 2004; Hwang et al., 2005; Kelly and Moran,2002; Moore, 2006).

4.1. Selecting appropriate water sample volumes

Typical counting times for the 224Ra measurementare up to 3 h, or less depending on the activity of thesample (see Section 4.3). The 3-hour limit prevents thegeneration of too many 224Ra and 226Ra decay productsin the counting chamber, which increase the total countsand therefore, the chance coincidence correction.

In order to evaluate the implication of the samplingparameters on the uncertainty propagation, the first variableconsidered is the sampled volume, which can be adjusted inthe field. For the purpose of the calculations presented in thissection we predetermine the counting time to be 2 h. Thetime elapsed between sampling and measurement willdepend on how soon one can transport the samples from thefield to the lab, the number of counters available and the

Table 5Estimated 219, 220 and total counts for different counting times and activitiefrom 1 to 25 dpm 100 L−1 of 223Ra (second measurement)

Countingtime (h)

224Ra count

220 counts 219 counts Total counts

0.5 25–875 2–80 110–16931.0 50–1750 5–159 219–33852.0 100–3500 9–318 439–67702.5 125–4375 11–398 549–84633.0 150–5250 14–477 658–10156

amount of samples that need to be analyzed. In order toevaluate the influence of sampling different volumes on thefinal propagated uncertainty, the decay time has been set at2 days.

The volumes considered in these calculations varyfrom 10 L to 100 L and the estimated 220 countscorrespond to 224Ra activities varying from 3 to180 dpm 100 L−1. The lower region of this intervalrepresents activities typical for coastal ocean, seawaterand river water samples. The highest radium valuesrepresent groundwater, estuarine, or other enrichedsamples. The corresponding estimated 219 and totalcounts are specified in Table 3.

Fig. 8a shows a plot of sample volume versus relativeuncertainties in 224Ra activity for different radiumenrichments. For high activity water samples (N110 dpm100 L−1) a volume of 25 L is enough to achieve a 7%uncertainty, and 40 L for 5%. When typical coastal watersare sampled (~20 dpm 100 L−1), 40 L of water is requiredto reach 7% of relative uncertainty. The exponentiallydecreasing trends also show that even with very large(impractical) sample volumes it is impossible to achievebetter than ca. 4% uncertainty. This limit is due to thepropagation of uncertainties from other parameters likeefficiency, background and others.

The second measurement (223Ra count) is moresensitive to the optimization of the sample volumebecause of the lower abundance of the 235U decay series

s ranging from 3 to 140 dpm 100 L−1 of 224Ra (first measurement) and

Countingtime (h)

223Ra count

220 counts 219 counts Total counts

4 50–1750 17–583 302–46596 75–2625 25–875 453–69898 100–3500 33–1167 604–931810 125–4375 42–1458 755–11,64812 150–5250 50–1750 906–13,977

Fig. 10. a. The 220 counts (solid symbols) and the respective 224Ra activities (open symbols) are plotted against the relative uncertainty (%) of 224Rafor different counting times (224Ra decay throughout the counting period has been neglected). Radium activities range from 3 to 140 dpm 100 L−1 andthe elapsed time between sampling and measurement has been set at 2 days. b. 219 counts (solid symbols) and 223Ra activities (open symbols) plottedagainst the relative uncertainty (%) of 223Ra for different counting times (the 223Ra decay throughout the counting period has been neglected). Theelapsed time between sampling and measurement has been set at 10 days.


Table 6Optimal sampling and measurement parameters to attain uncertaintiesof 7% and 12% for 224Ra and 223Ra, respectively

Activity(dpm100 L−1)

223Ra 0–2 3 4–5 5–6 7–20 N20224Ra 0–15 15–20 20–40 40–60 60–150 N150

Volume (L) ≥100 ≥40 ≥35 ≥25 ≥20 ≥15Decay days(days)

223Ra ≤12 ≤16 ≤16 ≤16 ≤16224Ra 0.5 ≤4 ≤6 6 6

Countingtime (h)

223Ra N8 ≥6 ≥4 ≥4 4224Ra 3 1–2 0.5–1 ≥0.5 ≥0.5


and its isotopes in natural waters. The counting time forthe calculations in this measurement is set at 8 h whereasthe elapsed time period between sampling and themeasurement is fixed at 10 decay days, which allows theinitial 220/219 ratio to decrease from 11 to 3.

The relative uncertainty in 223Ra depending on thesample volume for different radium activities isrepresented in Fig. 8b. For coastal waters of 3 dpm100 L−1, a 12% uncertainty is attained when sampling40 L. The volume of water required to achieve the sameuncertainty significantly rises when considering lessenriched waters; for example, with 2 dpm 100 L−1 of223Ra, around 75 L of sample is required. If samplesrelatively enriched in 223Ra are measured (i.e. 7 dpm100 L−1), 20 L are enough to obtain a relativeuncertainty of 12% which decreases to 10% if on isable to sample 40 L. The figure also shows that there'san asymptotic limit of 7% for the 223Ra uncertainty andthat lower uncertainties are very difficult to reach, evenwhen large amounts of water are collected (N100 L).

It is important to point out that when measuring highradium activities, the coincidence corrections defined byEqs. (1)(5) (in the Annex) may not work properlybecause they were developed for relatively low levels ofradium activities (~20 cpm in the 220 channel).Therefore, when expecting high activity samples, onlysmall sample volumes should be passed through the Mn-fiber or the sample should not be analyzed beforesignificant 224Ra decay has occurred.

4.2. The influence of 223Ra and 224Ra decay betweensampling and measurement on final uncertainties

Radium decay during the time elapsed betweensampling and measurement will depend on how soonafter collection the samples can be analyzed. Althoughassuming the shorter this time period is, the more countswe will register keeping the same counting time, it isworth checking how much we gain by rushing thesamples to for measurement. Moreover, if too manysamples are collected simultaneously, the counting timehas to be optimized because if limited by the number ofcounters available not all samples will be accuratelyanalyzed before radium decay becomes too restrictive.

224Ra activities plotted against relative uncertaintiesconsidering different decay periods before the samplemeasurement are depicted in Fig. 9a. The sample volumeis set at 40 L, the counting time is 2 h, and the 224Raactivities represent a range from 3 to 170 dpm 100 L−1.The decay needs to be considered in the recorded countsof the three channels. The 219 and 220 registered countsare decay corrected based on the elapsed time and the

respective half-lives of the radium isotopes (223Ra and224Ra) (Table 4). The counts registered in the total channelare mostly alpha particles coming from the 224Ra–220Rnpair so that the total counts are decay corrected accordingto the 224Ra half-live (T1/2=3.66 days) (Table 4). Since nohigh 226Ra/224Ra ratios were found in the consideredsamples, the 222Rn (226Ra daughter) decays will notsignificantly affect the recorded counts in the totalchannel, validating this assumption.

For coastal 224Ra activities of 25–30 dpm 100 L−1, adecay period of 4–6 days between sampling andmeasurement results in a 7% uncertainty which onlydecreases to 6% when measuring concentrations of45 dpm 100 L−1 within 4 days of sampling. It has alsobeen observed (Fig. 9a) that under the above mentionedmeasurement and sampling conditions 224Ra activitieslower than 20 dpm 100 L−1 cannot be determined withbetter than 7% uncertainty even by measuring themimmediately after collection (e.g. 0.5 days). Thesesamples require larger sample volumes in order tofurther reduce the uncertainties.

The longer-lived 223Ra is usually measured within 8–16 days after sampling. Fig. 9b represents 223Raactivities plotted against their relative uncertaintiesconsidering different decay time before measurement.In the calculations included in this figure, the samplevolume has been fixed at 40 L, the counting time is keptconstant at 8 h, and the 223Ra activities vary from 0.7 to26 dpm 100 L−1. For 223Ra activities of at least 3 dpm100 L−1, as much as 16 days can elapse until thecounting in order to measure the activity with a 12%uncertainty. Uncertainties of no better than 7% can bereached for very high 223Ra levels, such as 25 dpm100 L−1. For low activities (i.e. ≤2 dpm 100 L−1), thecounting time or the sample volume should be increased.

4.3. The influence of the counting time

Usually, sample counting times have to be optimizedto allow large sample throughput through the RaDeCC


systems. On the other hand, the longer the counting is,the larger number of counts is recorded, and thecounting statistics improves. Table 5 shows the resultsof calculations of linear variation of 220 counts with theduration of the counting and the corresponding 219 andtotal counts. We neglected the radium decay correctionsduring the period over which the sample was counted.

Sample measurements for the 224Ra isotope usuallytake 1 to 3 h. Fig. 10a shows the relative uncertainty of224Ra depending on the 220 counts for different countingtimes and activities ranging from 3 to 140 dpm 100 L−1.As many as 350 counts in the 220 channel are required toobtain a 7% uncertainty in the final 224Ra concentration.For coastal waters with 15 dpm 100 L−1 of 224Ra, thefirst measurement would need to last for about 3 h, giventhe detector efficiencies, to reach a 7% uncertainty; a 1-hour counting time would be enough to achieve the sameuncertainty in samples with 35 dpm 100 L−1 of 224Ra(Fig. 11a). By recording 1500 counts in the 220 channel(~35 dpm 100 L−1 of 224Ra) within three counting hours,the associated 224Ra uncertainty would decrease down to5.5%. Under the described conditions, the lowest 224Rauncertainty that one could achieve would be 4.5 %.

The measured 219 counts and the respective 223Raactivities are plotted against the calculated relativeuncertainties on Fig. 10b for different counting timesduring the second measurement (223Ra count). Around140 counts in the 219 channel collected over 8 h ofcounting result in an overall uncertainty of 12%,corresponding to a 223Ra concentration of 2.8 dpm100 L−1 for a 40 L sample. For 223Ra activities higherthan 4.5 dpm 100 L−1, 6 h of counting time is enough toreduce the associated final uncertainty to 11%.

5. Conclusions

We performed a detailed analysis of the uncertaintiesassociated with 223Ra and 224Ra measurements via aRadium Delayed Coincidence Counting system. Inparticular, we focused on the influence of the samplevolume, counting time, and the time elapsed betweensampling and measurement on the final 223Ra and 224Rauncertainties. By optimizing these factors for 223Ra and224Ra measurements and considering uncertainties of12% and 7 % (at 1σ confidence interval), respectively asacceptable, we produced an optimal set of sampling andmeasurement parameters listed in Table 6. Asymptoticuncertainty levels are attained at ca. 7% for 223Ra and4% for 224Ra, which could be obtained for typicallyradium-enriched groundwater samples. On the otherhand, because of their low radium content, higher un-certainties would be acceptable for sea water samples.

These results should serve as guidance for watersampling and radium measurements. For example, weshowed that for the above listed uncertainties for waterswith 223Ra ranging between 4 and 5 dpm 100 L−1 and224Ra from 20 to 40 dpm 100 L−1, a minimum volumeof 35 L would be required, the 224Ra could be countedas late as 4 days after collection and the measurementsshould be longer than an hour. For the same sample, thesecond count for 223Ra should be performed no laterthan 16 days from sampling and the counting should lastfor at least 6 h. Other typical combinations of radiumactivities and parameters can be found in Table 6. Theresults presented here were derived on the basis ofefficiencies and backgrounds measured on our RaDeCCsystems, thereby they may vary for other users. Also, theefficiencies may change over time as the system agesand the background levels will depend on the previouslycounted samples and the period for which the systemshave been purged. Therefore it is important that the223Ra and 224Ra uncertainty propagation is carried outfor every RaDeCC system and all measurements.

The importance of precise determination of radiumuncertainties becomesmuch clearer when these tracers areapplied for environmental studies. These short-livedradium isotopes have already been used in many differentapplications, including the estimation of submarinegroundwater discharge (Charette et al., 2001; Charetteand Buesseler, 2004; Hwang et al., 2005; Moore, 2006;Rama and Moore, 1996), estuarine and coastal residencetimes (Kelly and Moran, 2002; Moore et al., 2006) andmixing processes occurring in coastal areas (Kadko andMuench, 2005; Kraemer, 2005). It is obvious that theknowledge of “how good the radium number is” helps tounderstand trends, decipher natural variations, rejectoutliers, and distinguish end-members with differentradium activities in such studies.

Acknowledgements

We acknowledge our colleagues at the Environ-mental Radioactivity Laboratory (Universitat Autòn-oma de Barcelona) for their constructive comments andcollaboration in the field and laboratory work. Wespecially thank Billy Moore and Matt Charette for theirhelp with the introduction of the Radium DelayedCoincidence Counting system into our laboratory. Thiswork was partially supported by the Ministerio deEducación y Ciencia of Spain (grant CGL2006-09274/HID) and a PhD fellowship to EGS. We wish to thankthe editor and the anonymous reviewers whoseconstructive criticism enabled us to improve a previousversion of this paper.


Appendix A. ANNEX

Quantification of 223Ra and 224Ra measured through the RaDeCC

The expressions to calculate the fraction of chance coincidence events which are expected to occur in the 219 and220 channels (Y 219 CC and Y 220 CC) are the following (Giffin et al., 1963; Moore and Arnold, 1996).

Y 220CC ¼cpm total� cpm 220� cpm 219ð Þ2�0:01

h i1� cpm total� cpm 220� cpm 219ð Þ � 0:01½ �f g ð1Þ

Y219CC ¼cpm total� corr 220� cpm 219ð Þ2�0:000093

h i1� cpm total� corr 220� cpm 219ð Þ � 0:000093½ �f g : ð2Þ

Moore and Arnold (1996) used cpm 220 instead of corr 220 in Eq. (2). However, a posterior revision of theequations led Moore to consider corr 220 as the most appropriate term to calculate Y 219 CC (Moore, pers. comm.).

The chance coincidence contribution is then subtracted from the cpm 220 and the cpm 219 to obtain the correctedvalues (in cpm):

corr 220 ¼ cpm220� Y220CC ð3Þ

corr 219 ¼ cpm219� Y219CC: ð4Þ

The final adjustment to the 220 data, which accounts for the 219Rn decays that occur while the 220 window is open,is expressed as:

final 220 ¼ corr 220�1:6� corr 219ð Þ2 � 0:01

h i1þ 1:6 � corr 219ð Þ � 0:01ð Þ½ � ð5Þ

It is here estimated that the detector efficiency for 219Rn and 215Po is 0.8; this value is multiplied by 2 because twoalpha particles are produced for each 219Rn atom decay (Moore and Arnold, 1996; Moore, 2008-this issue). EachRaDeCC system will have its own value for this correction and it must be determined by running standards (Dimova etal., 2008-this issue) to establish the efficiency to use in this calculation. Still, since this is a second order correction,small differences in efficiency are not substantially important.

On the other hand, the time constant of the 219 gate is long enough for 2.55% of the 220Rn–216Po decays to occur inthis window. Then, the final 219 (cpm) are calculated as:

final 219¼corr 219� corr 220� 0:0255ð Þ ð6Þ

In order to convert the final 219 and 220 cpm to activity (dpm), the calculated efficiencies for each channel are applied:

dpm 219 ¼ final 219E 219

ð7Þ

dpm 220 ¼ final 220E 220

ð8Þ

dpm 220 tot ¼ total cpm� total bkg cpmð ÞE total

� dpm 219 ð9Þ




Finally, the 223Ra and 224Ra decay occurred since the sample collected (t1) is considered:

dec� dpm 219 ¼ dpm 219e�k223t1

ð10Þ

dec� dpm 220 ¼ dpm 220e�k224t1

ð11Þ

dec� dpm 220 tot ¼ total cpm� total bkg cpmð ÞE total� e�k224t1

� dec� dpm 219 ð12Þ

In order to calculate the efficiencies for every channel of the detector (E 219, E 220 and E total), we measurerepetitively the Mn-fiber standard, which has known activities of 223Ra in equilibrium with 227Ac (227Acstand decaycorrected to the preparation date of the reference solution) and 224Ra in equilibrium with 232Th (232Thstand) adsorbedonto its surface.

E 219 ¼ final 219stand ðcpmÞ227Acstand ðdpmÞe�k227t2

ð13Þ

E220 ¼ final 220stand ðcpmÞ232Thstand ðdpmÞ ð14Þ

where t2 is the elapsed time between the preparation of the Mn-fiber standard and the counting dates of the standard.The total efficiency is derived from:

E total ¼ total cpm� tot bkg cpm� 2� 219 cpm232Thstand ðdpmÞ ð15Þ

Lastly, by dividing the calculated dec-dpm 219 (Eq. (10)), dec-dpm 220 (Eq. (11)) and dec-dpm 220 tot (Eq. (12)) bythe sampled volume, the activities of the short-lived radium isotopes, 223Ra and 224Ra, are worked out.

223Ra ðdpmL�1Þ ¼ dec� dpm 219volume

ð16Þ

224Ra ðdpmL�1Þ ¼ dec� dpm 220volume

; or ð17Þ1

224Ra ðdpm L�1Þ ¼ dec� dpm 220 totvolume

ð18Þ

1 These two different ways to calculate 224Ra activities are discussed in the text (Section 2.2.1).


Propagation of uncertainties

The absolute uncertainties (Δ1, Δ2, Δ3,… Δ18) associated with the RaDeCC calculations (Eqs. (1)–(18)) in anoperation by operation basis and following the law of uncertainty propagation for uncorrelated variables are expressed as:

DY220CC ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcpmtot2 þ Dcpm2202 þ Dcpm 2192

q

�2� 0:01� cpmtot� cpm220� cpm219ð Þð Þ � 0:01� cpmtot� cpm 220� cpm 219ð Þð Þ2

h i1� 0:01� cpmtot� cpm 220� cpm 219ð Þð Þ2

24

35

ðΔ1Þ

DY219CC ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcpmtot2 þ Dcorr 2202 þ Dcpm 2192

q

�2� 0:000093� cpmtot� corr 220� cpm 219ð Þð Þ� 0:000093� cpmtot� corr 220� cpm 219ð Þð Þ2

h i1� 0:000093� cpmtot� corr 220� cpm 219ð Þð Þ2

24

35

ðΔ2Þ

Dcorr 220 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcpm 2202 þ DY220CC2

qðΔ3Þ

Dcorr 219 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcpm 2192 þ DY219CC2

qðΔ4Þ

Dfinal 220 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcorr 2202 þ ½ 2� 1:6ð Þ2�0:01� corr 219� 1:63 � 0:012 � corr 2192Þ� �

1� 1:6� 0:01� corr 219ð Þ½ �2 � Dcorr 219

" #2vuutðΔ5Þ

Dfinal 219 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDcorr 2192 þ 0:0255� Dcorr 220ð Þ2

qðΔ6Þ

Ddpm219 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDfinal 219E 219

� �2

þ final 219� DE 219

E 2192

� �2s

ðΔ7Þ

Ddpm220 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDfinal 220E 220

� �2

þ final 220� DE 220

E 2202

� �2s

ðΔ8Þ


Ddpm220 tot ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDtotal cpm2 þ Dtotal cpmbkg2

E total2

� �þ total cpm� total cpm bkgÞ � DE total

E total2

� �2

þDdpm2192

s

ðΔ9Þ

Ddec� dpm219 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDfinal 219

e�kRa�223t � E219

� �2

þ final 219� e�kRa�223tDE 219

E 219� e�kRa�223tð Þ2 !2

vuut ðΔ10Þ

Ddec� dpm220 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDfinal 220

e�kRa�224t � E220

� �2

þ final 220� e�kRa�224tDE 220

E 220� e�kRa�224tð Þ2 !2

vuut ðΔ11Þ

Ddec� dpm220 tot ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDtotcpm2 þ Dtotal cpm bkg2

e�kRa�224t � E totalð Þ2 !2

þ total cpm � total cpm bkgð Þ � e�kRa�224tDE total

E total� e�kRa�224tð Þ2 !2

þDdec� dpm2192

vuutðΔ12Þ

DE 219; DE 220 and DE total¼ Standard deviation of 219; 220 and total efficiencies calculated from the Mn� fiber standard measurements performed

ðΔ13; Δ14 and Δ15Þ

D223Ra dpmL�1� � ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDdec� dpm219

volume

� �2

þ dec� dpm219

volume2

� �2s

ðΔ16Þ

2

D224Ra dpmL�1� � ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDdec� dpm220

volume

� �2

þ dec� dpm220

volume2

� �2s

ðΔ17Þ2

D224Ra tot dpmL�1� � ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDdec� dpm220 tot

volume

� �2

þ dec� dpm220 tot

volume2

� �2

:

sðΔ18Þ

2

Acronyms

The definition of the terms that appear in the text from the registered counts to the final quantification of 223Ra and224Ra activities, are listed below. For each term, the relative uncertainty is denoted as “er Term” in the text:

E 219: efficiency of the 219 channelE 220: efficiency of the 220 channelE tot: efficiency of the total channel219 cpm: counts per minute registered in the 219 channel220 cpm: counts per minute registered in the 220 channel

2 The error associated with the sampled volume is estimated to be ±1 L owing to the volumetric calibration of the water drums. This equationaccounts for a typical volumetric error associated to big containers (50 to 100 L) of ±1 L.


tot cpm: counts per minute registered in the total channeltot cpm bkg: counts per minute of the background measurement in the total channelY 220 CC: chance coincidence counts per minute in the 220 channelcorr 220: corrected 220 counts per minute for the chance coincidenceY 219 CC: chance coincidence counts per minute in the 219 channelcorr 219: corrected 219 counts per minute for the chance coincidence and for the 220 interference on the 219channelfinal 220: corrected 220 counts per minute for the interference of the 219 on the 220 channelE-dpm219: 219 activity at counting time (dpm)E-dpm220: 220 activity at counting time (dpm)E-TOT dpm220: 220 activity (calculated via total counts) at counting time (dpm)E-DEC 219: 219 activity at sampling timeE-DEC CORR 220: 220 activity at sampling time (dpm)E-DEC 220 TOT: 220 activity (calculated via total counts) at sampling timeRa-223 dpm/100 L: 223Ra activityRa-224 dpm/100 L: 224Ra activity

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http://dx.doi.org/10.1029/2005JC003041

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uncertainties associated with 223ra and 224ra measurements in water via a delayed coincidence...

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