Journal of Hydrology 519 (2014) 117–130

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Journal of Hydrology

journal homepage: www.elsevier .com/ locate / jhydrol

Carbon-14 in streams as a tracer of discharging groundwater

http://dx.doi.org/10.1016/j.jhydrol.2014.06.0560022-1694/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Current address: University of Saskatchewan, Saskatoon,SK, Canada.

E-mail address: Sarah.Bourke@usask.ca (S.A. Bourke).

Sarah A. Bourke a,b,⇑, Glenn A. Harrington a,c, Peter G. Cook a,d, Vincent E. Post a, Shawan Dogramaci e

a National Centre for Groundwater Research and Training, Flinders University, Bedford Park, SA, Australiab Commonwealth Scientific and Industrial Research Organization (CSIRO), Division of Land and Water, Floreat, WA, Australiac Innovative Groundwater Solutions, Adelaide, SA, Australiad Commonwealth Scientific and Industrial Research Organization (CSIRO), Division of Land and Water, Glen Osmond, SA, Australiae Rio Tinto Iron Ore, 162-168 St Georges Tce, Perth, WA, Australia

a r t i c l e i n f o

Article history:Received 10 March 2014Received in revised form 25 June 2014Accepted 29 June 2014Available online 11 July 2014This manuscript was handled by GeoffSyme, Editor-in-Chief

Keywords:Surface water–groundwater interactionCarbon isotopesGaining streamsGas exchangeIsotope equilibrium

s u m m a r y

Quantification of the volume of groundwater discharge to streams, and the source aquifer of that dis-charge, is required to adequately manage the impacts of groundwater use on stream ecosystems. Thishas been achieved through longitudinal surveys of gaseous tracers, but their effectiveness can be limitedby rapid equilibration between the stream and the atmosphere. Here we develop the use of carbon-14 indissolved inorganic carbon (DIC) in a stream as a tracer of groundwater discharge. A controlled equilibra-tion experiment was conducted, during which groundwater with an initial 14C activity of 5.5 pMC wasallowed to equilibrate with the atmosphere over 72 days. The effective transfer velocity for 14C was mea-sured as 0.013 m d�1. The method was then tested at an artificial groundwater discharge location, wherethe effective transfer velocity was measured as 0.025 m d�1. In these simple systems, the ratio of theeffective 14C transfer velocity to the CO2 gas transfer velocity is a function of pH, and proportional tothe fraction of DIC present as CO2. The method was then applied along a reach of the Daly River, Australia,where groundwater discharge is known to occur. A decrease of 7 pMC was observed across the majorspring discharge zone, with subsequent equilibration with the atmosphere occurring over at least tensof kilometres. This allowed for the effective transfer velocity to be estimated at between 0.09 and0.15 m d�1, and for the 14C activity of groundwater discharge to be estimated at between 60 and66 pMC. The equilibration of 14C in stream DIC is in the order of 10 times slower than for gas tracers,which may allow for the detection of smaller groundwater discharge fluxes than is possible with gas trac-ers. If the total groundwater discharge flux is known, measurements of 14C in stream DIC can also be usedto infer the 14C activity of discharging groundwater. This method may be a useful alternative to directgroundwater sampling, particularly in remote basins with few groundwater wells.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Knowledge of the source of groundwater discharging to streamsis important for understanding the potential risks of stream deple-tion due to groundwater abstraction, or surface water contamina-tion. Often groundwater discharge to streams originates frommultiple aquifers, and has a range of aquifer residence times. Bymeasuring multiple age indicators along a stream, each sensitiveto a different range of groundwater residence times, it is theoreti-cally possibly to identify groundwater contributions of differingages. Previous studies have quantified groundwater discharge tostreams using radon-222 (222Rn), which is sensitive to groundwa-ter discharge with residence times longer than a few days (Cook

et al., 2003, 2006; Gardner et al., 2011). Groundwater dischargewith residence times less than 100 years has been detected usingchlorofluorocarbons (CFCs), SF6, tritium (3H), or the ratio of tritiumto helium-3 (3H/3He) (Cook et al., 2003, 2006; Smerdon et al., 2012;Stolp et al., 2010). The only groundwater age tracer that has beenused to specifically quantify old groundwater discharge is terrigen-ic helium-4 (Gardner et al., 2011; Smerdon et al., 2012). Helium-4((4He))can be used to measure groundwater residence timesgreater than 100 years, but is most sensitive to much longerresidence times (P10,000 years) (Cook and Herczeg, 2000).

A potential limitation of dissolved gases as tracers of groundwa-ter discharge to streams is that they degas rapidly to the atmo-sphere, and so the tracer concentration is most sensitive to thegroundwater discharge flux close to the sampling location. The rateof equilibration with the atmosphere therefore provides a limit onthe sampling resolution required to detect groundwater discharge,with faster equilibration requiring finer sampling resolution (Cook,

118 S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130

2012). For carbon-14 (14C), the process of equilibration is driven byCO2 exchange across the air–water interface, and is effectively buf-fered by the other dissolved inorganic carbon species in solution.The rate of equilibration of 14C is therefore likely to be muchslower than the rate of equilibration of CO2, and other gas tracers.While a number of studies have investigated gas transfer rates forCO2, the rate of 14C equilibration between total dissolved inorganiccarbon (TDIC) and the atmosphere has not previously beenquantified.

If discharge of groundwater induces a detectable change in 14Cactivity of dissolved inorganic carbon (DIC – used interchangeablywith TDIC) along a stream reach, this can be used to quantifygroundwater discharge from a source aquifer with known 14Cactivity. Alternatively, if the quantity of groundwater discharge isknown, changes in stream 14C activity can be used to infer the14C activity of groundwater discharging into the stream. Giventhe relative ease of sampling surface waters, this could provide auseful technique for estimating groundwater 14C activity in theabsence of direct groundwater samples.

While many studies have measured the carbon-13 (13C) signa-tures of stream DIC (Aucour et al., 1999; Doctor et al., 2008;Hagedorn and Cartwright, 2010; Hélie et al., 2002; Mayorgaet al., 2005), and d13C has been used as a tracer of groundwater dis-charge (Meredith and Kuzara, 2012), there are few published stud-ies that have measured the 14C activity of DIC in streams. Thosestudies that have measured 14C in stream DIC were focussed onquantifying carbon fluxes associated with stream ecosystems(Raymond et al., 2004; Raymond and Hopkinson, 2003) and theefflux of CO2 from streams to the atmosphere (Mayorga et al.,2005). As far as we are aware, this is the first study to apply 14Cas a tracer of groundwater discharge to streams. Furthermore, webelieve that this is the first study to measure the rate of equilibra-tion of 14C in TDIC in groundwater exposed to the atmosphere.

The aims of this paper are twofold. Firstly, we test the hypoth-esis that 14C activity of dissolved inorganic carbon in a stream canbe used to detect groundwater discharge to a stream, with a muchlower sampling resolution than is required for other dissolved gastracers. Additionally, we test the hypothesis that changes in stream14C activity across a groundwater discharge zone can be used toinfer the 14C activity of the discharging groundwater.

In order to test these hypotheses, a controlled equilibrationexperiment is presented during which rates of carbon isotopeequilibration between old (approximately 30 ka) groundwaterand the atmosphere were measured. Next, the rate of carbon iso-tope equilibration is measured in a naturally ephemeral creekchannel receiving artificial groundwater discharge. Finally, theapplication of 14C as a tracer of groundwater discharge to streamsis demonstrated in the Daly River in northern Australia. The DalyRiver was chosen as the test site because there are discrete spring(groundwater) discharge zones that have previously been mapped,and because previous studies suggest that the total carbon pool isdominated by dissolved inorganic carbon at the time ofsampling (dry season, baseflow conditions) (Robson et al., 2010;Tickell, 2011).

2. Theory

2.1. Isotopic equilibration mechanisms

Conceptually, we begin with a stream containing dissolvedinorganic carbon that is in chemical and isotopic equilibrium withthe atmosphere. Suppose that groundwater with a different DICconcentration and 14C activity then enters the stream at a discretelocation. We assume that at the location of groundwater discharge,the isotopic composition of the stream is determined by the mixing

fractions of TDIC in groundwater and surface water. Downstreamof the location of groundwater discharge, there are two processesthat can drive carbon isotopic re-equilibration between the streamand atmosphere; chemical exchange and isotopic exchange(Broecker et al., 1980; Broecker and Walton, 1959).

2.1.1. Chemical exchangeCarbon cycling in stream systems is complex, and may involve

reactions between inorganic and organic carbon, dissolution orprecipitation of particulate carbon, and CO2 production or con-sumption (Aucour et al., 1999; Hagedorn and Cartwright, 2010;Hélie et al., 2002; Raymond and Bauer, 2001b). In the currentstudy, in-stream DOC was expected to be small relative to DIC,and so we did not explicitly account for DIC production throughmineralization of dissolved organic carbon (DOC) or particulateorganic carbon (POC). The validity of this is approach is discussedin Section 5. In other stream systems with high DOC concentra-tions, or rapid mineralization rates, this source of DIC may needto be explicitly included in the carbon isotopic mass balance.

In our analysis, we assume that the dominant process drivingcarbon isotopic equilibration downstream of a groundwater dis-charge zone is the exchange of CO2 between the stream and theatmosphere. Groundwater typically has high levels of dissolvedCO2 that will degas to the atmosphere through gas exchange upondischarge to a river. This degassing of CO2 causes an increase in pH,which shifts the distribution of carbonate species in the TDIC pool(Appelo and Postma, 2005). There is a fractionation effect associ-ated with this CO2 exchange because of the different molecularweights of 12CO2

13CO2 and 14CO2. As the CO2 degasses, this frac-tionation causes an enrichment of the carbon isotopic signatureof TDIC in the stream (Choi et al., 1998; Doctor et al., 2008).

The CO2 exchange flux is driven by the degree of disequilibriumfrom the atmosphere, with the rate of change in CO2 concentrationin a volume, V (L3), of water with surface area, A (L2), given by;

@CO2

@t¼ kCO2

AV

CO2eq � CO2� �

ð1Þ

where CO2 is the concentration of dissolved CO2 in solution (M L�3),CO2eq is the concentration of dissolved CO2 in equilibrium with theatmospheric CO2 partial pressure (M L�3), t is time (T), and kCO2 isthe gas transfer velocity (L T�1). This gas transfer velocity is a func-tion of the diffusion coefficient of CO2 and the turbulence in theboundary layer at the air–water interface (Genereux and Hemond,1992; Raymond and Cole, 2001). Equations in the form of Eq. (1)can also be written for each carbon isotopologue of CO2, however,because 12C is much more abundant than 13C or 14C, chemicalexchange will be dominated by 12CO2.

The enrichment caused by fractionation during CO2 degassingcan be simulated as a Rayleigh distillation process (Hendy, 1971),described by;

d ffi eT lnðf Þ þ d0 ð2Þ

where d is the carbon isotopic composition of the remaining solu-tion, d0 is the initial carbon isotopic composition, f is the fractionof dissolved inorganic carbon remaining in solution, and eT is thetotal enrichment factor (Clark and Fritz, 1997). This enrichment fac-tor is expressed relative to HCO3

�, which dominates the dissolvedcarbon species in the pH range of natural waters (6.5–8.5). In thisopen system, where degassed CO2 is continuously removed fromthe system, eT will be the sum of an equilibrium enrichment,eg_HCO3�, due to the different solubilities of each isotopologue ofCO2, and a kinetic enrichment, ek, driven by the different gas trans-fer velocities of each isotopologue (Zhang et al., 1995), such thateT = eg_HCO3�+ek.

S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130 119

2.1.2. Isotopic exchangeThere are two main processes of isotopic exchange in a stream

receiving groundwater discharge: (1) between species within theTDIC pool, and (2) between dissolved CO2 and atmospheric CO2.Within the TDIC pool, isotopic equilibration is driven by isotopicexchange between CO2(aq), HCO3

� and CO32�, and is achieved within

minutes (Mills and Urey, 1940; Zeebe et al., 1999). As a result, iso-topic equilibration of dissolved CO2 and TDIC with the atmospherewill proceed at effectively the same rate.

Isotopic exchange between the atmosphere and the solutionwill occur whenever the isotopic composition of dissolved CO2 isnot in isotopic equilibrium with atmospheric CO2. For 14CO2 thisexchange is described by;

14CO2ðgÞ þ12 CO2ðaqÞ $12 CO2ðgÞ þ14 CO2ðaqÞ ð3Þ

where 14CO2(g) is 14CO2 gas in the atmosphere, 14CO2(aq) is 14CO2 gasdissolved in the water, 12CO2(g) is 12CO2 gas in the atmosphere and12CO2(aq) is 12CO2 gas dissolved in the water.

2.1.3. Achievement of isotopic equilibriumIsotopic equilibration between the stream and the atmosphere

can be driven by either chemical exchange or isotopic exchange,or a combination of the two (Broecker and Walton, 1959; Lynch-Stieglitz, 1995). These two exchange processes are driven by differ-ent gradients (chemical concentration vs. isotopic composition),but they are not entirely independent. This is because CO2

exchange alters the isotopic composition of the water, and hencechanges the isotopic gradient between the water and the atmo-sphere, which drives the isotopic exchange process (Broeckeret al., 1980). This means that, although chemical equilibrium isnot required for isotopic exchange to occur, isotopic equilibriumcannot be achieved while chemical (gas) exchange is ongoing.

2.2. Carbon isotope mass balance

A mass balance approach was used to simulate carbon isotopeequilibration in (1) an evaporating pan of water, and (2) a gainingor losing stream. This allowed an effective transfer velocity to beestimated for each system, which describes the rate of equilibra-tion with the atmosphere.

2.2.1. Mass balance of water exposed to the atmosphereThe water balance of an evaporating pan of water is given by;

@V@t¼ �EA ð4Þ

where V is the volume of water (L3), E is the evaporation rate (L T�1)and A is the surface area of the pan (L2).

For a non-reactive, non-gaseous solute, the change in concen-tration in the pan over time is described by;

V@c@t¼ cEA ð5Þ

where c is the solute concentration in the water (M L�3).For a radioactive gas, the change in concentration in the pan

over time is given by;

V@c@t¼ EAc þ kAðceq � cÞ � kdAc ð6Þ

where k is the gas transfer velocity (L T�1), ceq is the gas concentra-tion of water in equilibrium with the atmosphere (M L�3), k is theradioactive decay constant (T�1), and d is water depth (L). Eq. (6)can be used to simulate changes in concentration for gases suchas radon-222 as well as different CO2 isotopologues.

When considering the carbon isotopic composition of TDIC, theonly portion of TDIC that is available for exchange (chemical or

isotopic) is CO2, with bicarbonate and carbonate remaining in solu-tion (Broecker et al., 1980; Broecker and Walton, 1959). In the car-bon isotope mass balance, we assume that 12CO2 is at equilibriumwith the atmosphere, which implies that chemical exchange isnegligible. The flux of 12CO2 out of the water to balance the influxof 14CO2, as per Eq. (3), will be negligible because of the much lar-ger abundance of 12C relative to 14C. This means that the mass bal-ance of 12CTDIC becomes;

V@

@t

12

CTDIC ¼12 CTDICAE ð7Þ

For 14C, with a half-life of 5730 years (Kalin, 2000), radioactivedecay of 14C is negligible at the timescale of the experiment(72 days), so that;

V@

@t

14

CTDIC ¼14 CTDICAEþ akkCO2 Að14CO2eq �14 CO2Þ ð8Þ

where 14CTDIC is the concentration of 14C in water (M L�3), 14CO2 isthe concentration of 14CO2 in the water (M L�3), 14CO2eq is the 14CO2

concentration of water in the pan when it is at isotopic equilibriumwith the atmosphere (M L�3), kCO2 is the gas transfer velocity of CO2

(L T�1) (as defined in Eq. (1)), and ak is the kinetic fractionationfactor to account for the different gas transfer velocities of 12CO2

and 14CO2. The value of this ak is very close to 1 (0.9992 at 20 �C)(Zhang et al., 1995), and so it is neglected in subsequentcalculations.

The rate of change of the isotopic ratio 14C/12C in TDIC, referredto as RTDIC, is described by;

@

@tRTDIC ¼

@

@t

14CTDIC12CTDIC

ð9Þ

By applying the quotient rule, and equating 12C to TDIC, thechange in isotopic ratio, R, of the TDIC in the water can bedescribed by (full derivation in Appendix A);

@

@tRTDIC ¼ kCO2

AV

CO2

TDICðRCO2eq � RCO2Þ ð10Þ

where RCO2 is the ratio of 14C/12C in CO2 (which is often expressedrelative to a standard in either pMC or ‰) in the water at time t,and RCO2eq is the ratio of 14C/12C (either in pMC or ‰) of water inthe pan when it is at isotopic equilibrium with the atmosphere. Thisequation can be used to simulate the isotopic equilibration of waterin the pan as a function of time. Equations for the change in ratio of13C/12C in TDIC can also be rewritten, following the form of Eqs. (9)and (10).

From Eq. (10) it can be seen that the difference between the rateof isotopic change of RTDIC relative to the gas transfer velocity ofCO2 is a function of the proportion of TDIC that is present as dis-solved CO2, which is in turn a function of pH (Appelo andPostma, 2005). This effect of speciation is incorporated into alumped parameter, ke (L T�1) that is the effective transfer velocityof 14C in TDIC. The rate of change of isotopic ratio is then describedby;

@

@tRTDIC ¼ ke

AVðRCO2eq � RCO2 Þ ð11Þ

where;

ke

kCO2¼ CO2

TDICð12Þ

2.2.2. Mass balance of gaining or losing streamIn a stream system, the mass is integrated over distance, rather

than time. The water balance of a stream with groundwater dis-charge or recharge is given by;

120 S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130

dQdx¼ qgw � Ew ð13Þ

where Q is stream discharge (L3 T�1), qgw is groundwater flux into(positive values) or out of (negative values) the stream (L2 T�1), Eis the evaporation rate (L T�1), w is stream width (L) and x is the dis-tance along the stream (L).

Streams can be broadly categorized, based on their mode ofinteraction with the underlying/adjacent aquifer, as gaining(groundwater discharges to the stream) or losing (groundwater isrecharged by the stream). The equations for the change inconcentration along a stream are different for gaining and losingstreams. In the case of a gaining stream (qgw > 0), the rate ofchange in concentration of a non-reactive, non-gaseous tracer isgiven by;

Qdcdx¼ Ewc � qgwðcgw � cÞ ð14Þ

where c is the concentration in the stream (M L�3), and cgw is theconcentration in the groundwater (M L�3). This is comparable toEq. (5) for an evaporating pan of water.

For a radioactive gas, the change in concentration along a gain-ing stream is described by (Cook et al., 2003);

Qdcdx¼ Ewc � qgwðc � cgwÞ þ kwðceq � cÞ � kdwc ð15Þ

This is comparable to Eq. (6) for the evaporating pan, and isused in the current study for simulating both radon-222 (seeSection 4.3) and CO2 isotopologues.

The mass balance of 12C in TDIC in a gaining stream that is atchemical equilibrium with the atmosphere such that there is nogas transfer of CO2, is given by;

Q@

@x

12

CTDIC ¼ Ew12CTDIC � qgwð12CTDIC �12 CTDICgwÞ ð16Þ

For 14C, the radioactive decay rate is slow and this term can beneglected, so that the rate of change of 14C in TDIC along a gainingstream is given by;

Qddx

14

CTDIC ¼ Ew14CTDIC � qgwð14CTDIC �14 CTDICgwÞ

þ kCO2wð14CO2eq �14 CO2Þ ð17Þ

where 14CTDICgw is the concentration of 14C in the groundwater(M L�3).

Using R-notation (see Eq. (11)), applying the quotient rule toEqs. (16) and (17), assuming that the 12CO2 in the stream is in equi-librium with the atmosphere, and that the 12C in solution is equalto the TDIC, and again using the effective transfer velocity, ke,which incorporates the effect of speciation, the rate of change ofisotopic ratio along the stream is given by (full derivation inAppendix A.2);

@

@xRTDIC ¼ ke

wQ

RCO2eq � RCO2� �

�qgw

QTDICgw

TDICRTDIC � RTDICgw� �

ð18Þ

which can be used to simulate the carbon isotopic ratio along astream in delta notation (‰) or pMC.

In a losing stream (or losing reach of a stream, qgw < 0), the rateof change in concentration of a conservative ion along a losingstream is described by (Bourke et al., in review WRR);

Qdcdx¼ Ewc ð19Þ

the change in concentration of a radioactive gas tracer is describedby;

Qdcdx¼ Ewc þ kwðceq � cÞ � kdwc ð20Þ

and the change in isotopic ratio is given by:

@

@xRTDIC ¼ ke

wQ

RCO2eq � RCO2� �

ð21Þ

In subsequent sections, the isotopic ratio of 14C/12C in TDIC isreferred to as simply 14C, and the isotopic ratio of 13C/12C in TDICis referred to as 13C, following the standard convention for ground-water studies.

3. Methods

3.1. Controlled equilibration experiment

Groundwater from the Yarragadee aquifer (Water CorporationBalcatta well-field) in the Perth Basin, Australia, was used in a con-trolled experiment during which total dissolved inorganic carbonin the water is allowed to equilibrate with atmospheric CO2. TheYarragadee aquifer was chosen as the source of groundwater forthe experiment because carbon isotopic composition had previ-ously been measured, and it was anticipated that the 14C activityof TDIC would be substantially depleted (Meredith et al., 2012). Acircular pan (1.2 m in diameter, 0.25 m in height) containing0.26 m3 of groundwater was placed outside under cover and shel-tered from direct rainfall input (located in Perth, Australia (31�570S,115�470E), see Fig. 1). The water was kept constantly circulating bypump (Aquagarden, 44W) without turbulence breaking the watersurface. Water level and temperature were monitored continu-ously using a pressure transducer (Insitu level troll 300) correctedfor barometric pressure (Insitu barotroll). Water samples (225 mL)for major ion analysis were collected at intervals of hours toweeks for a period of 72 days between April 4th and June 14th,2012. The pH was measured using a WTW Multi 3420 Set D, andalkalinity was determined by titration using sulphuric acid (HachAlkalinity Digital Titration Kit). Chloride was measured by discreteanalyser, and calcium was measured by ICP-OES (SGS laboratories,Perth).

Water samples were collected for carbon isotope (13C/12C and14C) analysis in 1 L plastic bottles (no preservative) and analysedusing accelerator mass spectrometry (AMS) (Rafter radiocarbonlaboratory, GNS Science, New Zealand). Dissolved inorganic carbonwas converted to CO2 through the addition of phosphoric acid. ThisCO2 is then converted to graphite by reduction with hydrogen overan iron catalyst, and the isotopic composition of this graphite isdetermined by AMS. Carbon isotope data (d13C and d14C) arereported in delta notation, as permil (‰). The d14C is not correctedfor sampling date or fractionation (Stuiver and Polach, 1977). Car-bon-14 data are also reported as percent modern carbon (pMC),which are the units most commonly used for reporting the 14Cactivity of groundwater. This pMC is calculated from;

pMC ¼ ASN

AABSð22Þ

where ASN is the activity of the sample normalized to d13C of �25‰

and AABS is the activity of the oxalic acid standard normalized withrespect to d13C and corrected for radioactive decay since 1950(Stuiver and Polach, 1977).

Determination of the gas transfer velocity for CO2 (kCO2)requires the consideration of the shifting speciation during CO2

evasion. The kCO2 was estimated using a hydrochemical modelingapproach (PHREEQC v2.18, Parkhurst and Appelo (1999)) to simu-late CO2 degassing, with the gas transfer velocity constrained bythe measured pH and alkalinity during the chemical equilibrationphase. PHREEQC solves the mass action equations for each speciesand simulates user-defined kinetic reactions. The kinetics of theCO2 degassing were defined by Eq. (1), with an atmospheric CO2

partial pressure of 10�3.4 atm (400 ppm).

Fig. 1. Locations of study sites in Perth (controlled equilibration experiment), Marrandoo (artificial groundwater discharge) and the Daly River.

S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130 121

The simulated TDIC evolution during CO2 degassing was used tocalculate the enrichment associated with fractionation during thisprocess. The fraction of TDIC remaining in solution after the initialdegassing phase was determined from the results of the hydro-chemical model. This fraction remaining was then used to calculatethe enrichment associated with CO2 degassing using a Rayleighdistillation approach (Eq. (2)). Temperature dependent enrichmentfactors were applied, at a temperature of 20 �C, which was theaverage water temperature during the experiment. At this temper-ature, the kinetic enrichment factor for 13C is �0.8‰ and equilib-rium enrichment factor is �8.5‰, giving a total enrichmentfactor of �9.3‰ (Zhang et al., 1995). The enrichment of 14C wasassumed to be twice as large as the 13C enrichment (Craig, 1957),resulting in a kinetic enrichment factor of �1.6‰, equilibriumenrichment factor of �17.0‰ and a total enrichment factor of�18.6‰.

3.2. Field application 1: Artificial groundwater discharge

The use of 14C as a tracer of groundwater discharge was testedat a location of artificial groundwater discharge near Marandoo(Lower Fortescue River, Southern Branch (23�360S, 118�20E)) inthe Pilbara region of north-western Australia. The Pilbara regionhas numerous iron ore mining operations that require dewateringof the mine pit to ensure safe mining conditions. Where dewater-ing volumes are in excess of water requirements for processing,this water is disposed of by discharging it to a nearby ephemeralcreek line (which is normally dry). This water flows along thecreek, until it is lost to evaporation and infiltration into the under-lying alluvial aquifer associated with the creek. This system pro-vides a proxy for groundwater discharge to a stream, with therelatively constant volume of dewatering discharge entering thecreek at a fixed location, simulating a discrete groundwater dis-charge zone. The isotopic equilibration rate between the creekand the atmosphere is determined by measuring the 14C activityin TDIC along the creek. Given that this ephemeral creek hadrecently wetted (within 7 weeks of sampling), in-stream CO2 pro-duction is probably limited to bacterial synthesis and the effect

on isotopic equilibration is likely to be negligible (McIntyre et al.,2009). The dewatering discharge had been abstracted from twoproduction wells at consistent rates (13.9–14.2 ML d�1) for the4 days prior to sampling, minimizing the potential variation inthe carbon-14 activity of the dewatering discharge.

The stream channel was dry above the dewatering dischargeoutlet and the only components of the water balance are stream-flow losses to evaporation and infiltration. Water samples (1.5 L)were collected at six locations between 500 and 1500 m apart,along a 10 km reach downstream of the dewatering discharge loca-tion on August 16th, 2012. Chloride, calcium and isotopic compo-sition were measured using the methods outlined in Section 3.1.Streamflow was measured at each sampling location using anacoustic Doppler velocity meter (Sontec Flowtracker) followingthe methods described in Buchanan and Somers (1969). The datawere fit using a mass balance model based on Eqs. 20–22. Theparameters used in the mass balance model are summarised inTable 1. The value of RCO2eq was assumed to be equal to the 14Cratio in TDIC measured at the end of the controlled equilibrationexperiment, 108 pMC.

3.3. Field application 2: Daly River

The Daly River flows in a north-westerly direction across theOoloo Dolostone aquifer system in tropical northern Australia. An120 km-long reach of the river (beginning at 14�21.80S,131�34.50E) provided an ideal location for testing the applicationof the method, as previous studies have estimated groundwaterdischarge flux of up to 106 m3 d�1 for a 5 km section of this reach(Cook et al., 2003; Smerdon et al., 2012). Stream flow measure-ments (Streamflow ADCP) were taken at three locations alongthe 120 km reach (at river distances of 0, 42 and 67 km) betweenthe 12th and 18th of October 2012. Water samples were collectedbetween the 15th and 18th of October, 2012 at six locations (riverdistances of 0, 3.5 35, 42, 67, and 115 km) based on locations sam-pled in previous studies and site accessibility, which is limited inthis remote part of the country. Water samples were analysed formajor ions using ICP-OES (Waite Laboratory, CSIRO, Adelaide).

Table 1Mass balance model parameters.

Symbol Description Value Units Fitted toa

Controlled equilibration experimentA Surface area 1.13 m2

E Evaporation rate 0.014 m d�1 Water volume, chloridekCO2 CO2 gas transfer velocity 1.1 m d�1

ke Effective transfer velocity 0.013 m d�1 14C, 13C13Ca 13C in equilibrium with atmosphere �2.3 ‰14Ca 14C in equilibrium with atmosphere 108 pMC

Artificial groundwater dischargeQ0 Initial stream flow 0.08 m3 s�1

w Stream width 5 md Stream depth 0.3 mE Evaporation rate 0.01 m d�1 Streamflow, chlorideqgw Infiltration flux �0.6 m3 d�1 m�1 Streamflow, chlorideke

14C effective transfer velocity 0.025 m d�1 14C14ca Atmospheric 14C activity 108 pMC

Daly RiverQ0 Initial stream flow 12.3 m3 s�1

d Stream depth 1.5 mw Stream width 50 mqgw Groundwater discharge flux 10–200 m3 d�1 m�1 Streamflow, radonE Evaporation rate 0.007 m d�1

ke14C effective transfer velocity 0.13 m d�1 14C

kRn Radon gas transfer velocity 1 m d�1

kRn Radon decay rate 0.181 d�1

cRn Groundwater radon concentration 7 Bq L�1

14ca Atmospheric 14C activity 108 pMC14cgw Groundwater 14C activity 63 pMC 14CTDICgw/TDIC Ratio of TDIC in groundwater:stream 1 –

a All other parameters fixed.

6

7

8

9

pH

Measured pH

Simulated pH

(a)

-946

-944

-942

-940

-16

-15

-14

0 0.5 1 1.5

δ14C

(‰)

δ13C

(‰)

Time (days)

Simulated δ13C

Measured δ13C

Simulated δ14C

Measured δ14C

(b)

kCO2 = 1.1 m d-1

Fig. 2. Controlled equilibration experiment degassing phase: (a) simulated pHincrease and (b) associated isotopic enrichment of 13C and 14C in TDIC.

122 S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130

Radon-222 activities were determined by liquid scintillation usinga LKB Wallace Quantulus counter with a detection limit of3 mBq L�1 (Leaney and Herczeg, 2006). Water samples were ana-lysed for carbon isotopic composition by AMS as described inSection 3.1.

The data were analysed using a mass balance model(Section 2.2) and the parameters summarised in Table 1. Streamgeometry, evaporation rate and radon gas transfer velocity weretaken from previously published mass balance models of the DalyRiver (Cook et al., 2003; Smerdon et al., 2012). Measured streamflow and radon data were used to constrain groundwater dischargeusing manual calibration based on visual comparison of simulatedand observed data. The measured 14C data were used to constrainthe effective transfer velocity and 14C activity of the discharginggroundwater. The 14C activity of discharging groundwater wasassumed to be constant along the stream reach, which is reason-able based on the distribution of aquifers across the study site(Tickell, 2011).

Previous studies in the Daly River basin conducted at the sametime of year as this study (October) measured the alkalinity of thegroundwater in the Ooloo dolostone to be 410 ± 75 mg L�1 as HCO3

�

(±stdev, n = 28), alkalinity of spring discharges to be 417 ± 7 mg L�1

as HCO3� (n = 2) (Tickell, 2011). The alkalinity in the river during

this was 374 ± 17 mg L�1 as HCO3� (n = 6). Based on these data,

we assume that TDIC of the groundwater discharge is similar tothe TDIC in the Daly River and use a TDICgw/TDIC ratio of 1 inEq. (18).

4. Results

4.1. Controlled equilibration experiment

The volume of water in the pan decreased through evaporationfrom 0.26 to 0.15 m3 over the 72 days of the experiment, implying

an average evaporation rate of 0.0014 m d�1. The concentrations ofchloride, alkalinity and calcium all increased throughout theexperiment, consistent with this reduction in water volume. Tem-perature ranged from 10.5 to 26.4 �C with a mean of 19.0 �C, anddiel variation of ±2.5 �C. Evasion of CO2(g) during the first 1.5 daysincreased the pH from 6.9 to 8.3 (Fig. 2a). The gas transfer velocityof CO2(g) during the controlled equilibration experiment was deter-mined in a hydrochemical model (Section 3.1), giving a kCO2 of1.1 m d�1.

The enrichment associated with fractionation during CO2

degassing was calculated using a Rayleigh distillation approach(Eq. (2) and Section 3.1), giving an enrichment of 1.5‰ in d13Cand 3.0‰ in d14C (Fig. 2b), which equates to an increase of less than

Fig. 3. Controlled equilibration experiment: measured d13C (a), and (b) pMC.Simulated d13C, and pMC using an effective transfer velocity of 0.013 m d�1 (solidline) and ±40% of this value (dashed lines).

Fig. 4. Artificial groundwater discharge: (a) stream discharge, (b) chloride and (c)pMC. Measured (open circles) and simulated with an effective transfer velocity (ke)of 0.025 m d�1 (solid line) and ±20% of this value (dashed lines).

S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130 123

1 pMC. This simulated enrichment correlates well with theobserved enrichment in 13C during the first 1.5 days of the experi-ment, but is much smaller than the observed enrichment in 14C,

which was �835‰ after 1.5 days (an increase of 109‰). This sug-gests that isotopic exchange dominated the equilibration processfor 14C even while chemical exchange (i.e., CO2 degassing) wasongoing. This is because the isotopic signature of 14C was furtherfrom equilibrium with the atmosphere than 13C and so the isotopicexchange flux for 14CO2 was larger than for 13CO2. Although satura-tion indices for calcite were greater than 1 during the experiment,the evolution of Ca2+ could be fully explained by evapo-concentra-tion. This suggests that calcite was not precipitating and so frac-tionation effects associated with this process could be neglected.

Over the 72 days of the experiment d13C increased from �15.6to �2.3‰, d14C increased from �943.6 to 77.2‰ and percent mod-ern carbon increased from 5.5 to 107.7 pMC. The effective transfervelocity (ke) of both 13C and 14C was determined using a mass bal-ance approach (Table 1, Eq. (11)). The best fit to d 13C, d 14C andpMC was achieved with an effective transfer velocity of0.013 m d�1 (Fig. 3). The sensitivity of the model to this effectivetransfer velocity is shown by plotting ±40% values on each plot.

The extent to which dissolved carbon speciation (which is afunction of pH), determines the rate of equilibration in this systemis assessed by comparing; (1) the ratio of the effective transfervelocity of 14C to the gas transfer velocity of CO2, and (2) the ratioof CO2 to TDIC (see Eq. (12)). If these ratios are equal, this impliesthat carbon speciation was the major determinant of the rate of 14Cequilibration in TDIC in solution. The best-fit ke (0.013 m d�1) is1.2% of the kCO2 (1.1 m d�1). This correlates well with the expectedproportion of TDIC that is CO2 (0.7–1.1%), given the pH range mea-sured during the experiment (8.3–8.5) (Table 2). The close agree-

ment between these two ratios kekCO2

vs: CO2TDIC

� �suggests that carbon

speciation was the limiting factor for isotopic equilibration in thiscontrolled equilibration experiment, and equilibration was domi-nated by isotopic exchange.

Table 2Relationships between pH, kCO2 and ke.

Setting pH CO2/DIC (%)

Isotope exchange experiment 8.3 1Artificial groundwater discharge 8.0 2Daly River 7.8 4

4.2. Field application 1: Artificial groundwater discharge

Streamflow decreased from 0.08 to 0.01 m3 s�1 along the 10 kmreach of the creek, driven by losses to evaporation and infiltration(Fig. 4). Chloride increased from 110 to 116 mg L�1 due to evapora-tion along the 10 km reach. Carbon isotopic composition becamemore enriched with distance along the 10 km, with d14C increasingfrom �890 to �603‰ and percent modern carbon increasing from11 to 31 pMC.

These data were analysed using a mass balance approachdescribed by Eqs. 20–22, with an evaporation rate of 0.004 m d�1

and an infiltration flux of 0.6 m2 d�1. The effective transfer velocitywas calibrated to measured 14C activity along the upstream 6 km.The best fit to the measured data (by visual comparison) wasachieved with an effective transfer velocity, ke, of 0.025 m d�1

(Fig. 4). Given the stream geometry (stream width of 5 m, a streamdepth of 0.3 m) and flow rate, this 6 km distance equates to a per-iod of 1.7 days of exposure to the atmosphere. The measured 14Cactivity at a distance of 10 km was not able to be fit with the sameeffective transfer velocity, which may reflect a different initial 14Cactivity in the dewatering discharge.

The CO2 gas transfer velocity was not measured in this system,but kRn for a nearby stream (also ephemeral and receiving dewater-ing discharge) was measured at 1.8 m d�1 (Bourke et al. accepted J.Hydrol). Based on the difference in the diffusion coefficients ofradon and CO2, this implies a kCO2 of around 2.0 m d�1 (Genereuxand Hemond, 1992). If we assume that the kCO2 for the Pilbaradewatering discharge is between 1.6 and 2.4 m d�1 (±20% of2.0 m d�1), the estimated ke is between 1.0% and 1.6% of the

kCO2 (m d�1) ke (m d�1) ke/kCO2 (%)

1.1 0.013 1.41.4–2.2 0.025 1.4–2.51.2 0.09–0.15 7.5–12.5

70

75

80

85

90

14C

(pM

C)

(c)

0

20

40

Stre

am fl

ow

(m3

s-1 )

(a)

0

2

4

Rad

on

(Bq

L-1)

(b)

0

100

200

0 50 100

GW

dis

char

ge(m

3d-

1m

-1)

Distance downstream (km)

This study

Smerdon et al. (2012)

Cook et al. (2003)

(d)

Simulated

This study

Nov 2009

Oct 2001

Sep 2000

Simulated

This study

Nov 2009

Oct 2001

Sep 2000

Fig. 5. Daly River mass balance model: (a) stream flow, (b) radon, (c) pMC and (d)groundwater (GW) discharge.

70

80

90

14C

(p

MC

) Measuredke = 0.09ke = 0.13ke = 0.17

70

80

90

14C

(pM

C) Measured

60 pMC

63 pMC

66 pMC

70

80

90

0 50 100

14C

(pM

C)

Distance (km)

Measured

TDIC 0.8

TDIC 1.0

TDIC 1.2

(a)

(b)

(c)

Fig. 6. Daly River mass balance model: sensitivity to (a) effective transfer velocity(ke), (b) groundwater pMC and (c) TDIC ratio (gw:sw).

124 S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130

kCO2. The pH of dewatering discharge was 8 in August 2012, whichcorresponds to CO2(aq) being 2% of TDIC. This value correlates rea-sonably well with the ratio of ke to kCO2, suggesting that the simpleconceptual model outlined in Section 2 adequately describes theevolution of 14C in TDIC in the streamflow generated by artificialgroundwater discharge at Marandoo.

4.3. Field application 2: Daly River

Measured 14C in stream TDIC along the Daly River, varied from76 to 86 pMC (d14C from �230 to �161‰), while d13C varied from�10.6 to �11.6‰. Across the major groundwater discharge zone,stream flow increased from 12.3 to 25.5 m3 s�1, radon-222increased from 0.6 to 2.9 Bq L�1, and 14C decreased from 82.8 to76.0 pMC, (Fig. 5). Based on measured stream discharge and radondata from this and previous studies (Cook et al., 2003; Smerdonet al., 2012), the maximum estimated groundwater dischargewas at a distance of 27–33 km, correlating well with the previouslymapped location of the spring system. The estimated magnitude ofthe major groundwater discharge in this study is within 10% ofpublished estimates (Cook et al., 2003; Smerdon et al., 2012).

The mass balance simulation of stream 14C is most sensitive tothe groundwater discharge flux, the 14C activity (pMC) of thegroundwater discharge and the effective transfer velocity (Fig. 6).The groundwater discharge flux is well constrained by the mea-sured variation in streamflow and radon activity. The measuredvariation in 14C along the river was used to constrain the effectivetransfer velocity and the 14C activity of the groundwater discharge.In the absence of a measured value immediately upstream of thegroundwater discharge zone these two parameters cannot be fitindependently, or uniquely. A similar fit to the data can beachieved using a range of gas transfer velocities and 14C activitiesof groundwater discharge. Fig. 5 presents a ke, of 0.13 m d�1, 63pMC, but other combinations are also possible. A larger ke requiresa correspondingly lower pMC, with possible values of ke varyingfrom 0.09 to 0.15 and groundwater 14C activity varying from 61to 66 pMC. This corresponds to the lower range of values for 14Cactivity in the Ooloo Dolsotone aquifer based on direct groundwa-ter sampling, which ranged from 60 to 108 pMC (Tickell, 2011).

The range of effective gas transfer velocities in the Daly River isbetween four and seven times larger than the effective transfervelocity in the artificial groundwater discharge study (Field applica-tion 1 at Marandoo), and an order of magnitude larger than the gastransfer velocity of the controlled equilibration experiment. Basedon the in-situ pH of 7 measured in the Daly River, CO2 would bearound 4% of the total TDIC pool. The kRn in the Daly River has beenpreviously estimated as 1 m d�1 (Cook et al., 2003), which, based ondiffusion coefficients, implies a kCO2 of 1.2 m d�1. This value is notinconsistent with estimates of kCO2 in other Australian rivers, whichreport a multi-year average value of 2.3 m d�1 (Hagedorn andCartwright, 2010). If the kCO2 in the Daly River is 1.2 m d�1, thenthe effective transfer velocity is between 7.5% and 12.5% of thekCO2. The elevated ke/kCO2 ratio, relative to the CO2/TDIC ratio,inconsistent with the theory outlined in Section 2. This suggeststhat other processes beyond those which were included in thedevelopment of Eq. (18) have had a significant effect on the 14Cactivity of TDIC along the study reach. These processes, whichmay include either fractionation effects or in-stream CO2 produc-tion, are increasing the rate of isotopic equilibration in the DalyRiver, above what would be expected based on TDIC speciation.

5. Discussion

5.1. Process understanding

This study has provided a number of insights into the processesdriving carbon isotope equilibration in groundwater exposed to theatmosphere. During the controlled equilibration experiment, theprocess of isotopic equilibration was (1) driven by isotopicexchange, (2) not dependent on chemical equilibrium to progress,and (3) resulted in a flux of 14CO2 in the opposite direction to theCO2 degassing flux. Previous authors have suggested that carbonisotope composition of stream water DIC would be determined

S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130 125

by fractionation associated with CO2 degassing, suggesting theeffects of isotopic exchange would be negligible while there waschemical disequilibrium between the stream and the atmosphere(Doctor et al., 2008). This is in contrast with oceanographic studiesthat have highlighted the possibility of isotopic equilibration pro-gressing in the opposite direction to chemical equilibration(Lynch-Stieglitz, 1995). During the first 1.5 days of the controlledequilibration experiment the CO2 gradient was driving CO2 eva-sion, which would have enriched the 14C activity of the residualwater by 3‰, or less than 1 pMC through fractionation effects(see Section 4.1, Fig. 2). This is consistent with Doctor et al.(2008), who observed an enrichment of between 3 and 5‰ associ-ated with fractionation during CO2 degassing from a stream. In theequilibration experiment in this study, the 14C enrichmentobserved during this period of chemical equilibration was morethan ten times larger than any predicted fractionation effect, withan increase of 109‰, or 11 pMC. In this simple system we canexclude fractionation effects associated with the chemicalexchange process, and conclude this enrichment must have beendriven by isotopic exchange of 14CO2 in the opposite direction tothe CO2 evasion flux.

The equation for the 14C mass balance in a gaining stream,which was applied to the Daly River (Eq. (18)), assumes that thestream is in chemical equilibrium with the atmosphere, such thatthere was no net exchange of CO2 across the air–water interface.However, the assumption of chemical equilibrium between thestream and atmosphere is unlikely be valid in natural stream sys-tems. Even in the absence of groundwater discharge, streams aregenerally supersaturated with respect to CO2 which drives a netCO2 evasion from the stream to the atmosphere (Butman andRaymond, 2011; Raymond et al., 1997; Richey et al., 2002). ThisCO2 excess is produced by plant respiration and other reactionsthat convert dissolved organic carbon (DOC) or particulate organiccarbon (POC) to dissolved inorganic carbon (DIC) (Cole et al., 2007).

5.2. In-stream DIC production

The magnitude of the effect of chemical exchange processes notexplicitly accounted for in the 14CTDIC mass balance (Section 2.2)can be assessed by comparing the ke/kCO2 ratio to the CO2/TDICratio. If the ke/kCO2 ratio is much larger than CO2/TDIC, then the rateof equilibration of carbon isotopes is greater than can be explainedby isotopic exchange and speciation effects, and is likely to beenhanced by chemical exchange. In the controlled equilibrationexperiment and at the artificial discharge site (Marandoo) the ratioof ke/kCO2 was similar to the proportion of CO2 in TDIC. However, inDaly River, the ratio of ke/kCO2 was up to three times larger than theproportion of CO2 in TDIC. This suggests a significant enhancementof the rate of isotopic equilibration along the stream by chemicalexchange processes and associated fractionation effects.

The effect of in-stream CO2 production on the rate of carbon iso-topic equilibration depends on the carbon source. If respired CO2 isin isotopic equilibrium with the atmosphere it will increase therate of equilibration downstream of a groundwater discharge zone.In addition, diurnal temperature variation within the stream willdrive a cycle of CO2 efflux and influx, with kinetic and equilibriumfractionation effects similar to those described in Section 2.1,which could further enhance the isotopic equilibration rate(Inoue and Sugimura, 1985).

The influence of DIC produced from mineralized DOC or POC isless predictable. Many studies have measured predominantly mod-ern 14C activities in stream DOC, (Hedges et al., 1986; Mayorgaet al., 2005; Palmer et al., 2001; Raymond and Hopkinson, 2003),in which case conversion of DOC into DIC would increase the rateof 14C equilibration downstream of the groundwater dischargezone. However, depleted 14C activities have been measured in

stream DOC in some systems (Caraco et al., 2010; Raymond andBauer, 2001a; Raymond et al., 2004), in which case conversion ofDOC into DIC would reduce the rate of 14C equilibration down-stream of the groundwater discharge zone.

The influence of mineralization of DOC into DIC in the DalyRiver can be quantified using measurements of d13C in DIC(Aucour et al., 1999; Cameron et al., 1995; Hélie et al., 2002;Telmer and Veizer, 1999). The d13C signature of plant-derivedorganic carbon is depends on which photosynthetic pathway theyemploy; the C3 (Calvin cycle) or C4 (Hatch and Slack cycle) (Clarkand Fritz, 1997; Hélie et al., 2002). The most common pathway isC3, which results in organic carbon with a d13C of around �27‰

(Clark and Fritz, 1997). Significant mineralization of DOC into DICwould be expected to shift the d13C signature of stream DIC closerto this values (Aucour et al., 1999; Hagedorn and Cartwright, 2010;Telmer and Veizer, 1999). In the Daly River, the d13C values mea-sured in this study did not vary substantially along the stream(�10.6‰ to �11.6‰), suggesting that the influence of DOC conver-sion into DIC is negligible in this river system. This is perhaps notsurprising given that previous studies have found that the concen-tration of DOC is 610% of the concentration of TDIC in the DalyRiver during low flow conditions (Robson et al., 2010; Tickell,2011). However, the influence of DOC and POC is may be more sig-nificant in other streams where DIC does not dominate the totalcarbon pool. Therefore, the influence of DOC/POC mineralizationon the 14C activity of stream TDIC should be assessed for individualstudy sites.

Precipitation or dissolution of carbonate minerals (particulateinorganic carbon, PIC) could also alter the carbon isotopic of in-stream TDIC. Precipitation of carbonate minerals would act tolower the stream 14C activity and d13C signature (Keppel et al.,2012), while the effect of dissolution would be to shift the streamTDIC closer to the isotopic composition of the minerals being dis-solved (for marine carbonates d13C is usually between 5‰ and�5‰) (Clark and Fritz, 1997). Saturation indices were calculatedfor the Daly River samples, with values between 0 and 1 for calciteand between 1 and 2 for dolomite. This suggests that carbonateminerals are more likely to be precipitating than dissolving inthe Daly River. However, the minimal (�1‰) variation in d13C sug-gests that carbonate mineral precipitation did not have a signifi-cant effect on the carbon isotopic composition of TDIC in theDaly River. Further studies are required to quantify the effects ofdegassing fractionation, diffusion, diurnal temperature variation,calcite precipitation and in-stream production of CO2 in naturalstream systems.

5.3. Effective transfer velocity of 14C

In spite of in-stream CO2 production, and potential fractionationeffects associated with chemical exchange, depleted 14C signaturesassociated with groundwater discharge into the Daly River per-sisted for tens of kilometres downstream of the mapped spring dis-charge location (0.5–3 days travel time). While the equilibration of14C with the atmosphere is driven by CO2(g) exchange, it is bufferedby the other carbonate species in solution and so the effectivetransfer velocity of 14C in DIC is much slower than the gas transfervelocity of CO2. The effective transfer velocities of 14C measured inthis study are between 0.16% and 14% of the reported range of val-ues of kCO2, which vary between 1 and 8 m d�1 (Butman andRaymond, 2011; Hagedorn and Cartwright, 2010; Raymond andCole, 2001; Richey et al., 2002).

When compared to other gas tracers that have previously beenapplied as tracers of groundwater discharge, the equilibration rateof 14C is in the order of 10 times slower, with reported gas transfervelocities of 4He, CFCs, SF6 and Rn ranging from 1.0 to 2.5 m d�1

(Cook et al., 2003, 2006; Gardner et al., 2011; Smerdon et al.,

126 S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130

2012). It may therefore be advantageous to use 14C as a tracer toquantify groundwater discharge to systems when there are smallgroundwater discharge volumes, or low concentrations of othergas tracers in the discharging groundwater. However, this persis-tence of the groundwater discharge signal over longer distancescould also limit the usefulness of 14C to detect specific locationsof discrete groundwater discharge in previously un-mapped sys-tems. Preliminary streamflow measurements and sampling forradon-222, amongst other tracers, along the stream reach wouldallow for these discrete zones of discharge to be detected, andcould then be used to inform a secondary sampling campaign formeasuring 14C along the stream at larger spatial samplingintervals.

To compare the spatial sampling resolution required to detectgroundwater discharge using 14C, 222Rn and 4He, we calculate thescale length, defined by Cook (2012) as Q

kwþdwk. Using the Daly Riverinput parameters (Table 1) and the simulated stream flow (12.3–33.0 m3 s�1) as an example, the scale length for 222Rn ranges from17 to 45 km. Similarly, the scale length for 4He ranges from 8 to23 km. In stark contrast, the scale length for 14C, using an effectivetransfer velocity of 0.13 m d�1, ranges from 151 to 407 km.

5.4. Advantages of 14C over 13C

While this study is the first to apply 14C in stream TDIC as a tra-cer of groundwater discharge to streams, 13C has previously been

Fig. 7. Nomogram showing the relationships between parameters in the groundwate

used in this context (Doctor et al., 2008; Meredith and Kuzara,2012). Data from this and previous studies show that the variationin d 14C in natural waters can be an order of magnitude larger thanthe variation in d 13C (Cole and Caraco, 2001; Mayorga et al., 2005;Raymond et al., 2004). For the Daly River samples, the measure-ment error for d13C was 0.2‰ (20% of the measured variation ind13C), while for d14C the measurement error was 1.5‰ (0.1% ofmaximum possible disequilibrium). Given the larger variationbetween end members relative to the measurement error in theDaly River, 14C was more sensitive as a tracer of groundwater dis-charge to streams than 13C, and has the added benefit of providinginformation on the aquifer residence time of the groundwater dis-charge. However, this may not be the case in other streams wherethe carbon isotopic signature of TDIC is significantly influenced bythe organic carbon pool (Hagedorn and Cartwright, 2010; Hélieet al., 2002).

Another advantage of 14C over 13C is that it can potentially beused to quantify the 14C activity of discharging groundwater, andthereby identify the source of groundwater discharge. If the totalgroundwater discharge to the stream is constrained, as done in thisstudy using stream gauging and 222Rn, then the 14C activity of thegroundwater discharge can also be constrained through measure-ments of stream 14C. The 14C activity of groundwater inferred fromchanges in stream 14C activity will be the volume-weighted aver-age for all groundwater discharging to the stream. Given that flowlines converge at locations of groundwater discharge (Freeze andWitherspoon, 1967; Winter, 1999) the 14C activity inferred from

r term of the equation for change in carbon isotope ratio along a gaining stream.

Fig. 8. Nomogram showing the relationships between parameters in the gas transfer term of the equation for change in carbon isotope ratio along a gaining stream.

S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130 127

the stream may be more representative of the ‘‘average’’ 14C activ-ity of groundwater discharge than that inferred from direct sam-pling of groundwater wells. In practice, if stream 14C activity (inTDIC) is being used to attribute groundwater discharge to a partic-ular groundwater source, some a priori knowledge of the range ofgroundwater 14C activities in potential source aquifers would berequired.

5.5. Future application of the method

In this study we did not explicitly quantify the rates of chemicalexchange within the stream, or between the stream and the atmo-sphere. Future application of 14C in streams as a tracer of ground-water discharge should include in-situ measurement of stream pHand alkalinity, direct measurement of kCO2, and estimates of thealkalinity of potential groundwater sources where possible. Thiswould allow for better constraints on the chemical exchangemechanisms influencing the 14C activity of stream TDIC.

The application of 14C as a tracer of groundwater discharge tostreams, and the use of stream 14C to constrain the source of dis-charging groundwater, will be most successful when the groundwa-ter discharge induces a significant depletion in stream 14C activityrelative to that which would be expected for the stream in equilib-rium with atmosphere. The magnitude of the 14C decrease in thestream is related to the 14C activity of the groundwater relative tothe stream 14C activity, and to the TDIC of the groundwater relative

to the stream TDIC (see Eq. (19)). Therefore, the sensitivity of thismethod will be greatest in systems with large gradients in 14C activ-ity between groundwater and the stream. However, a smaller gradi-ent in 14C activity between groundwater discharge and the streamcan be offset by a strong gradient in TDIC, and vice versa.

In an effort to assist future studies in determining if this methodwill be useful, we have constructed nomograms to illustrate the rela-tionships between parameters in the groundwater discharge andgas transfer terms of Eq. (18) (Figs. 7 and 8 respectively). If three ofthe parameters represented in the nomogram are known, the fourthcan be estimated by joining a line through the known parameter val-ues to the pivot line. The example lines shown in each figure repre-sent the major groundwater discharge zone in the Daly River. Thechange in isotopic ratio with distance (@R

@x) is 20 times larger forgroundwater discharge (0.004, Fig. 7) compared to the value forthe gas transfer term (0.0002, Fig. 8). Therefore the decrease in 14Cacross the groundwater discharge zone was measurable and couldbe used to infer the 14C activity of the discharging groundwater.

6. Conclusion

This paper demonstrates that 14C in streams can be used as atracer of groundwater discharge. In contrast to other gas tracersthe 14C activity of the stream TDIC is a function of the entire TDICpool, of which only CO2 exchanges with the atmosphere. As aresult, the effective transfer velocity of 14C in TDIC is much slower

128 S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130

than the CO2 gas transfer velocity, and the signal of groundwaterdischarge can persist for hundreds of kilometres downstream.The effective transfer velocity of 14C in TDIC is related to the gastransfer velocity of CO2 through the stream pH, which determinesthe proportion of TDIC that is dissolved CO2.

Because of this slower equilibration rate relative to other gastracers, the signal of groundwater discharge in stream 14C will per-sist further downstream than other gas tracers. This allows for alarger spatial sampling interval, and may provide for the detectionof smaller groundwater discharge volumes, than is possible usingother gas tracers. The collection of surface water samples is mucheasier and cheaper than installing groundwater wells to directlymeasure the 14C activity of groundwater. The inference of ground-water 14C activity from the 14C activity of streams receivinggroundwater discharge could therefore be a valuable alternativeto direct groundwater sampling, particularly in remote or deepbasins with few groundwater wells.

Acknowledgements

This work was undertaken as part of a collaborative projectbetween the National Centre for Groundwater Research and Train-ing (NCGRT) and Rio Tinto Iron Ore. The National Centre forGroundwater Research and Training is an Australian Governmentinitiative supported by the Australian Research Council and theNational Water Commission and CSIRO Water for a Healthy Coun-try. The authors would like to thank the Water Corporation for pro-viding groundwater from the Yaragadee aquifer for the controlledequilibration experiment, Sam Pettett for providing water samplesfrom Marandoo, and Allan Russ for providing water samples fromthe Daly River.

Appendix A

A.1. Derivation of equation for rate of change in 14C/12C in anevaporating pan of water

In an evaporating pan of water that is in chemical equilibriumwith the atmosphere, the mass balance of 12C in TDIC is given by;

V@

@t

12

CTDIC ¼12 CTDICAE ð1:1Þ

where V is the volume of water (L3), A is the surface area of the pan(L2), E is the evaporation rate (L T�1).

If the water in the pan is not in isotopic equilibrium with theatmosphere, the mass balance of 14C in TDIC is given by;

V@

@t

14

CTDIC ¼14 CTDICAEþ akkCO2 Að14CO2eq �14 CO2Þ ð1:2Þ

where 14CO2 is the concentration of 14CO2 in the water at time t(M L�3), and 14CO2eq is the 14CO2 concentration of water in thepan when it is at isotopic equilibrium with the atmosphere(M L�3) ak is the kinetic fractionation factor associated with thevarying gas transfer velocities of 12CO2 and 14CO2, and kCO2 is thegas transfer velocity of 12CO2. The value of this ak is very close to1 (0.9992 at 20 �C), and is neglected in subsequent analysis.

The rate of change of the isotopic ratio 14C/12C in TDIC, referredto as RTDIC, is described by;

@

@tRTDIC ¼

@

@t

14CTDIC12CTDIC

ð1:3Þ

Given the quotient rule;

@

@t

14CTDIC12CTDIC

¼12CTDIC

@@t

14 CTDIC �14 CTDIC@@t

12 CTDIC

ð12CTDICÞ2 ð1:4Þ

Rearranging and substituting 1.1, 1.2 and 1.3 into Eq. (1.4) gives;

@

@tRTDIC ¼

12CTDIC14CTDIC

AEV þkCO2

AV

14CO2eq�14 CO2� �� �

�14 CTDIC12CTDIC

AEV

� �ð12CTDICÞ

2

ð1:5Þ

Cancelling 12CTDIC terms gives;

@

@tRTDIC ¼

14CTDICAEV þ kCO2

AV ð

14CO2eq �14 CO2Þ �14 CTDICAEV

12CTDICð1:6Þ

Which rearranges to give;

@

@tRTDIC ¼

14CTDIC12CTDIC

AEVþ kCO2

AV

112CTDIC

ð14CO2eq �14 CO2Þ

�14CTDIC12CTDIC

AEV

ð1:7Þ

The first and third terms cancel, giving;

@

@tRTDIC ¼ kCO2

AV

112CTDIC

ð14CO2eq �14 CO2Þ ð1:8Þ

This is mathematically equivalent to;

@

@tRTDIC ¼ kCO2

AV

12CO212CTDIC

14CO2eq12CO2

�14CO212CO2

� �ð1:9Þ

If the water in the pan is at chemical equilibrium with theatmosphere, then 12CO2 is equal to 12CO2eq, and this equation canbe written as;

@

@tRTDIC ¼ kCO2

AV

12CO212CTDIC

14CO2eq12CO2eq

�14CO212CO2

� �ð1:10Þ

Using the R notation for isotopic ratios, this simplifies to;

@

@tRTDIC ¼ kCO2

AV

12CO212CTDIC

ðRCO2eq � RCO2Þ ð1:11Þ

Because 99% of total C is 12C, we can assume that 12CO2 equalsthe total CO2 and similarly, that 12CTDIC equals the total TDIC, whichleads to;

@

@tRTDIC ¼ kCO2

AV

CO2

TDICðRCO2eq � RCO2Þ ð1:12Þ

which can be used to simulate the isotopic equilibration ofwater in the pan, either in units of permil or pMC.

A.2. Derivation of equation for rate of change in 14C/12C in a stream inchemical equilibrium with the atmosphere

The mass balance of 12C in TDIC in a stream at chemical equilib-rium with the atmosphere is given by;

Q@

@x

12

CTDIC ¼ Ew12CTDIC � qgwð12CTDIC �12 CTDICgwÞ ð2:1Þ

where Q is the stream discharge rate of water (L3 T�1), w is streamwidth (L), E is the evaporation rate (L T�1).

If the water in the stream is not in isotopic equilibrium with theatmosphere, the mass balance of 14C in TDIC is given by;

Q@

@x

14

CTDIC ¼ Ew14CTDIC � qgwð14CTDIC �14 CTDICgwÞ

þ kwð14CO2eq �14 CO2Þ ð2:2Þ

where 14CO2 is the concentration of 14CO2 in the stream at time t(M L�3), and 14CO2eq is the 14CO2 concentration of the stream whenit is at isotopic equilibrium with the atmosphere (M L�3).

The rate of change of the isotopic ratio 14C/12C in TDIC in thestream, referred to as RTDIC, is described by;

S.A. Bourke et al. / Journal of Hydrology 519 (2014) 117–130 129

@

@xRTDIC ¼

@

@x

14CTDIC12CTDIC

ð2:3Þ

Given the quotient rule;

@

@x

14CTDIC12CTDIC

¼12CTDIC

@@t

14 CTDIC �14 CTDIC@@t

12 CTDIC

ð12CTDICÞ2 ð2:4Þ

Rearranging and substituting 2.1, 2.2 and 2.3 into Eq. (2.4)gives;

@

@xRTDIC ¼

12CTDIC14CTDIC

wEQ �

qgw

Q14CTDIC �14 CTDICgw� �

þ k wQ

14CO2eq �14 CO2� �� �

�14 CTDIC12CTDIC

wEQ �

qgw

Q12CTDIC �12 CTDICgw� �� �

ð12CTDICÞ2 ð2:5Þ

Similar to the evaporating pan of water, the evaporation termscancel, and the equation reduces to;

@

@xRTDIC ¼

12CTDIC k wQ

14CO2eq �14 CO2� �

� qgw

Q14CTDIC �14 CTDICgw� �� �

�14 CTDIC �qgw

Q12CTDIC �12 CTDICgw� �� �

ð12CTDICÞ2 ð2:6Þ

Which, if the stream is at chemical equilibrium with the atmo-sphere, can be rearranged to give the familiar gas transfer term andtwo groundwater discharge terms.

@

@xRTDIC ¼ kCO2

wQ

12CO212CTDIC

14CO2eq12CO2eq

�14CO212CO2

� �

� 112CTDIC

qgw

Q14CTDIC �14 CTDICgw� �� �

þ14CTDIC

12C2TDIC

qgw

Q12CTDIC �12 CTDICgw� �� �

ð2:7Þ

Focussing now on the groundwater terms, which are;

14CTDIC

12C2TDIC

ðqgw

Q12CTDIC �12 CTDICgw� �

� 112CTDIC

ðqgw

Q14CTDIC �14 CTDICgw� �

ð2:8Þ

Expanding and collecting like terms gives;

qgw

Q

14CTDIC12CTDIC

�14CTDIC12CTDIC

12CTDICgw12CTDIC

þ14CTDICgw

12CTDIC�

14CTDIC12CTDIC

� �ð2:9Þ

The second and fourth terms cancel, giving;

qgw

Q

14CTDICgw12CTDIC

�14CTDIC12CTDIC

12CTDICgw12CTDIC

� �ð2:10Þ

Which is equivalent to;

�qgw

Q

12CTDICgw12CTDIC

14CTDICgw12CTDICgw

�14CTDIC12CTDIC

� �ð2:11Þ

Substituting Eq. (2.11) into Eq. (2.7) and using R notation, thechange in isotopic ratio along the stream is given by;

@

@xRTDIC ¼ kCO2

wQ

12CO212CTDIC

ðRCO2eq � RCO2Þ �qgw

Q

12CTDICgw12CTDIC

�ðRTDIC � RTDICgwÞ ð2:12Þ

If we assume that 12C is equal to the total TDIC, this equationbecomes;

@

@xRTDIC ¼ kCO2

wQ

CO2

TDICðRCO2eq � RCO2Þ �

qgw

QTDICgw

TDICðRTDIC

� RTDICgwÞ ð2:13Þ

which can be used to simulate the change in isotopic ratio of thestream, either in permil, or pMC.

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