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Journal of Hydrology

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Review papers

A review of the use of radiocarbon to estimate groundwater residence timesin semi-arid and arid areas

Ian Cartwrighta,⁎, Matthew J. Currellb, Dioni I. Cendónc, Karina T. Meredithc

a School of Earth, Atmosphere and Environment, Monash University, Clayton, VIC 3800, Australiab School of Engineering, RMIT University, Melbourne, VIC 3000, Australiac Australian Nuclear Science and Technology Organisation, Institute for Environmental Research, Kirrawee DC, NSW 2232, Australia

A R T I C L E I N F O

This manuscript was handled by CorradoCorradini, Editor-in-Chief, with the assistanceof Stephen Worthington, Associate Editor

Keywords:RadiocarbonGroundwaterResidence timesAgesSemi-aridArid

A B S T R A C T

Groundwater is an important resource in arid and semi-arid regions and determining its residence times iscritical for sustainable use. Radiocarbon (14C) is currently the primary geochemical tracer for determining re-sidence times of regional groundwater systems. The analysis of 14C contents of dissolved inorganic carbon (DIC)became more straightforward following the development of accelerator mass spectrometry, which has led to anincrease in the number of studies using 14C. However, the interpretation of 14C data is not always straightfor-ward and many studies consider relatively few of the multiple processes that may affect the 14C contents of DICin groundwater. Commonly, studies have focussed on correcting 14C contents for closed-system dissolution of14C-free calcite, which is a near-ubiquitous process. However, especially in semi-arid and arid areas, un-certainties in the initial 14C contents and δ13C values of recharge due to the presence of low-14C soil CO2 in thedeep unsaturated zone, recharge by rivers, or open-system calcite dissolution pose problems for mass balancecalculations. Additionally, processes such as methanogenesis and mineralisation of organic carbon may be lo-cally important. Most studies also assume a constant atmospheric 14C content and non-dispersive piston flow inaquifers, which results in residence times being underestimated and makes it difficult to compare the ground-water archive to other palaeoclimate or palaeoenvironment records. Additionally, mixing of water withinaquifers, diffusion of 14C between low and high permeability layers, and sampling from multiple units in long-screen wells may limit whether a meaningful residence time can be determined. Overall, while it is relativelystraightforward to estimate broad ranges of residence times or determine general patterns of groundwater flow,the quest to quantify residence times, flow rates, and recharge remains a challenge. The use of multipleradioactive tracers, better characterisation of δ13C values and 14C contents of the potential sources of DIC, andmore critical assessment of flow systems will improve the utilisation of this important tracer.

1. Introduction

Determining the residence time (the time since the aliquots of waterin a sample were recharged) of groundwater is critical for under-standing hydrogeological systems. Groundwater residence times arecommonly calculated to characterise aquifer systems, determine ratesof groundwater flow and recharge, calibrate groundwater flow models,and/or determine whether water recharged during past climates (pa-laeowaters) are present in aquifers (Clark and Fritz, 1997; Kalin, 2000;Edmunds, 2001; Scanlon et al., 2002; Scanlon et al., 2006; Edmunds,2009; Cartwright et al., 2017a). Together, this information is critical formanaging groundwater resources and assessing whether the use ofgroundwater is sustainable. The semi-arid and arid zones (Köppen-Geiger Zones BS, BW and CS: Köppen, 1884; Kottek et al., 2006; Peel

et al., 2007) cover c. 15% of the Earth’s land surface (c. 2.2× 107 km2)and supported 14.4% of the global population in the year 2000 (Safrieland Adeel, 2005). In some of these regions (e.g., northwest China andthe Arabian Peninsula), population growth and development are pla-cing increased demands on water resources (Arnell, 1999; Ragab andPrudhomme, 2002; Edmunds et al., 2006; Currell et al., 2012; Gleesonet al., 2012; Haddeland et al., 2014; Gleeson et al., 2016). Given thatsurface water supplies are often limited and may diminish further be-cause of climate change, groundwater represents a critical resource inthese areas and thus understanding residence times is vital for its sus-tainable use.

This paper reviews the application of radiocarbon to determine re-sidence times of regional groundwater in arid and semi-arid environ-ments. We examine issues relating to the interpretation of radiocarbon

https://doi.org/10.1016/j.jhydrol.2019.124247Received 31 July 2019; Received in revised form 14 October 2019; Accepted 15 October 2019

⁎ Corresponding author.E-mail address: ian.cartwright@monash.edu (I. Cartwright).

Journal of Hydrology 580 (2020) 124247

Available online 17 October 20190022-1694/ © 2019 Elsevier B.V. All rights reserved.

T

and stable carbon isotope data and also assess problems relating toestimating residence times that result from mixing and dispersion.Understanding residence times is vitally important given the worldwidedependence of people in such areas on groundwater, and the depletionof groundwater resources that has occurred disproportionately in aridand semi-arid regions over recent decades (Currell et al., 2012; Gleesonet al., 2012).

With a half-life of 5730 years, 14C is one of the cosmogenic isotopesthat mainly originate from the interaction of cosmic rays with atmo-spheric gases. 14C is produced in the troposphere and stratosphere byneutron activation of 14N and is incorporated into atmospheric gases(e.g. CO2, CO and CH4). Dissolved inorganic carbon (DIC) is ubiquitousin groundwater with DIC concentrations ranging from a few to severalthousand mg/L. The common presence of DIC has led to the widespreaduse of radiocarbon (14C) to estimate residence times of groundwater inregional aquifers (Clark and Fritz, 1997; Kalin, 2000). There is a pro-gression from earlier studies that utilised liquid scintillation countingand BaCO3 precipitation followed by benzene synthesis (Fontes, 1971;Stuiver and Polach, 1977) to a predominance of studies using accel-erator mass spectrometry (AMS) since the late 1990s. The developmentof AMS techniques allow precise (commonly c.± 1%) determinationsof 14C/12C or 14C/13C ratios to be made from a few milligrams of C(Synal, 2013; Kutschera, 2016). This transition also reduced the need tocollect and process large (often in excess of 100 L) volumes of water inthe field that, aside from not always being practical, was prone tocontamination by atmospheric CO2 (Aggarwal et al., 2014). The in-crease in the number of facilities globally together with the ease ofmeasurement has contributed to the increased number of 14C studies ofgroundwater. For example, published studies listed on the Scopus®database increased from less than 20 per year before 1990 to more than50 per year since 2010.

Conventions for the reporting of 14C data are discussed by Stuiverand Polach (1977), Kalin (2000), Plummer and Glynn (2013). For AMS,the international standard is the National Bureau of Standards (NBS)oxalic acid. Normalisation of 14C/12C or 14C/13C ratios to 14C activities(A14C) in percent modern carbon (pMC) is common. This normalisationcommonly assumes that the δ13C values of DIC are −25‰, which isgenerally appropriate for archaeology and tree-ring studies. By con-trast, the range of geochemical processes that occur in the unsaturatedzone and below the water table commonly results in groundwater DIChaving a range of δ13C values. Because these processes may affect the14C contents and δ13C values differently (Clark and Fritz, 1997; Hanet al., 2012; Plummer and Glynn, 2013; Meredith et al., 2016), severalauthors (e.g., Kalin, 2000; Plummer and Glynn, 2013; Han andPlummer, 2016) recommend that 14C values not be normalised (un-normalised 14C ratios are denoted as a14C in pmc). However, this re-commendation is not commonly adhered to with many publicationsreporting normalised values received from the analytical facilities ornot reporting whether normalisation has been carried out. Additionally,pmc, pmC, and pMC (and other variations such as %MC) notations areused interchangeably (Supplement Table 1). The errors in calculatedresidence times introduced by incorrect normalisation are small relativeto the other uncertainties in radiocarbon dating. However, more com-plete reporting is desirable, especially for subsequent comparison orcompilation of data. Here we use the generic term “14C contents”(Meredith et al., 2016) for the 14C of DIC in groundwater.

While 14C contents of groundwater may be used as a qualitativeindicator of residence time or mixing of older and younger water inaquifers (Dassi et al., 2005a; Hamed et al., 2008; Iverach et al., 2017;Miller et al., 2017; Priestley et al., 2017), many studies use this tracer toestimate residence times (Supplement Table 1). The detection limit of14C contents determined by AMS are<1 pmc and precision is typically1–2% (Plummer and Glynn, 2013). Thus, under ideal circumstanceswhere the flow system is simple with little large-scale mixing, the initial14C content of recharge is known, and the sources of DIC in thegroundwater are well understood, 14C could be used to determine

residence times as old as 40 ka with an uncertainty of less than a fewthousand years. However, potential contamination with atmosphericCO2 during sampling and uncertainties in quantifying the sources ofDIC in groundwater result in large uncertainties in waters with low 14Ccontents (Plummer and Glynn, 2013; Han and Plummer, 2016). Anupper limit of 25 to 30 ka is probably more realistic (Kalin, 2000; Clark,2015), which still encompasses the residence times of groundwater inmany regional aquifers. Due to the magnitude of the half-life and theelevated atmospheric 14C contents of up to 200 pMC produced by at-mospheric nuclear tests in the 1950s and 1960s (the “bomb-pulse”), it isdifficult to use 14C to estimate residence times of regional groundwaterwhere these are less than one or two thousand years (Clark and Fritz,1997; Kalin, 2000; Clark, 2015). However, estimating the residencetimes of post-bomb-pulse recharge using 14C in combination with othertracers such as 3H or the chlorofluorocarbons (CFCs) is sometimespossible (Le Gal La Salle et al., 2001; Cartwright et al., 2007).

Following recharge, the groundwater is isolated from the atmo-sphere and 14C decays to the common isotope of nitrogen (14N). Asgroundwater commonly contains significant non-radiogenic 14N, theuse of 14C to determine residence times relies on determining the loss ofthe parent isotope rather than the accumulation of the daughter. Inmost studies of regional groundwater (Supplement Table 1), residencetimes (t) are calculated assuming that atmospheric 14C contents havebeen constant over time. This yields conventional radiocarbon ages inyears Before Present (BP) where 1950 CE=0 years BP. The assumptionof constant atmospheric 14C contents allows residence times to be cal-culated from the measured 14C of DIC (14Ct) using the decay equation:

⎜ ⎟= − ⎛⎝

⎞⎠

t ln CC q

8267 1414 .

t

i (1)

Clark and Fritz (1997), where q is the proportion of DIC introducedvia recharge and 14Ci is the initial 14C of DIC in the recharging water.Some authors (Vengosh et al., 2007; Burg et al., 2013; Huang et al.,2017) combine the 14Ci and q terms into a single term (often denoted asA0) that accounts for processes such as carbonate dissolution that affect14C contents post recharge; however, because both 14Ci and q can vary,it is useful to separate them.

1.1. The terrestrial carbon cycle and carbon isotope ratios

The use of 14C contents to determine residence times relies on un-derstanding the changes to carbon isotope ratios in the terrestrialcarbon cycle (Fig. 1). A major challenge in using 14C to estimate re-sidence times results from estimating the proportion of DIC that origi-nates as recharge (q in Eq. (1)) rather than being derived from withinthe aquifers. Most groundwater originates as direct recharge by rainfallthat infiltrates through the soils and regolith to the water table, al-though in arid and semi-arid regions recharge from ephemeral riversmay also be important (Scanlon et al., 2002, 2006; Healy, 2010). DIC inthe recharging groundwater is derived from a combination of atmo-spheric CO2, DIC in surface waters, dissolution of CO2 from the soilzone, and weathering of carbonate minerals in the unsaturated zone(Clark and Fritz, 1997).Fig. 2.

The fractionations of 13C/12C and 14C/12C ratios in the terrestrialcarbon cycle are described below. Prior to the significant combustion offossil fuels, the atmosphere had a pCO2 of 10−3.5 atm and the δ13Cvalue of atmospheric CO2 was c. −6.5‰ (Clark and Fritz, 1997: Fig. 1).The concentration of CO2 in the soil zone is considerably higher (pCO2

commonly 10–3 to 10–1 atm) than the atmosphere; hence, soil zone CO2

is generally more important as a source of DIC in the recharginggroundwater. The uptake of CO2 by plants via photosynthesis frac-tionates the 13C/12C ratios, with the degree of fractionation varyingwith the photosynthetic pathway (O'Leary, 1981; Farquhar et al., 1982;O'Leary, 1988; Farquhar et al., 1989). Around 80% of plant species usethe C3 photosynthetic pathway (Still et al., 2003) and the resultant

I. Cartwright, et al. Journal of Hydrology 580 (2020) 124247

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plant material typically has δ13C values between −37 and −20‰ witha modal value of c. −27‰ (Kohn, 2010) (Fig. 1). C4 plants, whichaccount for approximately 15% of species and include common cropssuch as maize and sugar cane as well as many grasses, have δ13C valuesthat are generally between −16 and −10‰. Approximately 6% of

plant species, mainly in desert environments, use CAM photosynthesis,which involves both C3 (daytime) and C4 (night) pathways (Smith andWinter, 1996). The resultant biomass δ13C values are intermediatebetween those of C3 and C4 plants.

Bacteriologically mediated aerobic decay of plant matter in soilsconverts the biomass C back to CO2. Due to outgassing, this processfractionates the 13C/12C ratios by c. 4‰ (Cerling et al., 1991). Hence,the δ13C of CO2 produced from the decay of typical C3 vegetation(δ13C=−27‰) is c. −23‰ and the δ13C of soil CO2 produced fromthe decay of C4 vegetation (δ13C=−12.5‰) is c. −8.5‰. However,although these values are often quoted, the range of possible δ13C va-lues within the C3 and C4 plant classes are several per mil (Kohn,2010). The dissolved CO2 dissociates into HCO3

− and CO32− with the

relative proportion of each C species varying proportional to pH (Vogelet al., 1970; Deines et al., 1974; Mook et al., 1974). In low pH waters,aqueous CO2 dominates, HCO3

− is dominant at circumneutral pH, andCO3

2− at high pH. As each species has a different fractionation factor,the δ13C of the DIC varies with pH and temperature. At pH=6.5 and20 °C, the DIC in equilibrium with CO2 gas with a δ13C=−23‰ has aδ13C of c. −19‰ (Fig. 1). Carbonate minerals (especially calcite) mayprecipitate from the DIC due to evapotranspiration in the soil and theformation of pedogenic carbonates (as either nodules or calcrete layers)is particularly common in semi-arid and arid areas (Quade et al., 1995;Breecker et al., 2009; Takeuchi et al., 2010). Pedogenic calcite formedin equilibrium with soil CO2 that has a δ13C of −23‰, at 20 °C has aδ13C of c. 12‰ (Bottinga, 1968).

The internationally accepted radiocarbon dating reference of 100pMC is 95% of the 1950 CE content of 14C in the NBS oxalic acidnormalised to δ13C=−19.3‰. The factor of 0.95 adjusts the 14Ccontent of the oxalic acid to that of ‘pre-industrial’ (1840 to 1860) woodfrom C3 vegetation. Due to the higher mass difference, processes in thecarbon cycle fractionate 14C/12C ratios by c. 2.3 times the 13C/12Cfractionations (Saliege and Fontes, 1984; Cerling et al., 1991). Thus, the14C content of atmospheric CO2 in equilibrium with that vegetation is c.104 pMC. The aerobic decay of pre-industrial C3 vegetation results insoil zone CO2 having a 14C content of 100.5 pMC; the corresponding 14Ccontent of DIC at pH=6.5 and 20 °C is c. 101.4 pMC. As with the stablecarbon isotopes, differences in vegetation type and pH or temperaturesin the soil zone result in differences in the 14C content of the DIC.However, these differences are minor compared with some of un-certainties that are inherent in using 14C (discussed below).

1.2. Carbon-14 as a residence time tracer

An ideal groundwater residence time tracer would be non-reactive,be derived only from recharging water, have well-defined input func-tions, and be easily (and cheaply) measured. The utility of 14C to de-termine groundwater residence times largely stems from its convenienthalf-life, ubiquitous presence of DIC, and relative ease of measurementrather than it being an ideal tracer. Issues affecting the use of 14C in-clude the several potential sources of 14C-free carbon contained inaquifers that may be difficult to estimate and processes that affect the14C contents of DIC in the recharging water. Relatively little attentionhas also been paid to the long-term variability of 14C contents of at-mospheric CO2 and adopting more realistic conceptualisations of flowin aquifers. Thus, despite its wide use, deriving groundwater residencetimes from 14C is not always straightforward and is prone to over-simplification. Supplement Table 1 summarises a range of 14C residencetime studies in arid and semi-arid groundwater illustrating the wide useof 14C in these environments. Where possible, we have indicated themethods used in the studies for analysis of 14C, reporting of the carbonisotope ratios, and correction for the input of 14C-free DIC in ground-water for residence time calculations.

Fig. 1. Schematic diagram showing changes to δ13C values and 14C contents ina pre-industrial region dominated by C3 vegetation. Red text denotes processesimportant in semi-arid regions but not commonly assessed. Abbreviations:uz=unsaturated zone, WT=water table. Adapted from (Clark and Fritz,1997). (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)

Fig. 2. Summary of 14C contents of CO2 from the unsaturated zone (lines showdata trends) and the shallowest groundwater (circles) at Ti Tree (Wood et al.,2015), Saskatoon (Bacon and Keller, 1998), North Dakota (Haas et al., 2016),and Nevada (Walvoord et al., 2005). BGS= below ground surface.

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2. Concentrations and isotopic ratios of DIC in arid and semi-aridregions

This section summarises key issues that affect the use of 14C to es-timate the residence times of groundwater. Some of these are commonto groundwater from all environments; however, several are more im-portant in semi-arid and arid regions. There are several potentialsources of 14C-free DIC in aquifers, which result in values of q in Eq. (1)being< 1. If unaccounted for, the addition of 14C-free DIC results in theoverestimation of groundwater residence times. Understanding theinput of 14C-free DIC is a major challenge in interpreting radiocarbondata in groundwater from all environments (Fontes, 1992; Aravenaet al., 1995; Clark and Fritz, 1997; Kalin, 2000; Coetsiers andWalraevens, 2009; Cartwright, 2010b; Han et al., 2012; Plummer andGlynn, 2013; Han and Plummer, 2016).

Closed-system dissolution of carbonates in the aquifer matrix is alikely source of 14C-free carbon, and is the process most commonlyconsidered in determining groundwater residence times. Values of qmay be calculated from major ion geochemistry or the δ13C values ofDIC in groundwater via mass balance, geochemical modelling usingprograms such as PHREEQC or NETPATH, or graphical techniques(Pearson and Hanshaw, 1970; Vogel, 1970; Tamers, 1975; Fontes andGarnier, 1979; Clark and Fritz, 1997; Geyh, 2000; Coetsiers andWalraevens, 2009; Clark, 2015; Salmon et al., 2015; Han and Plummer,2016). The simplest form of the isotope mass balance equation

= −−

q δ C δ Cδ C δ C

DIC calcite

recharge calcite

13 13

13 13 (2)

estimates q from the measured δ13C values of groundwater DIC(δ13CDIC), calcite in the aquifers (δ13Ccalcite), and the DIC of ground-water recharge (δ13Crecharge). This mass balance approach assumes thatthe δ13C values of the components are well known and that closed-system calcite dissolution is the major process affecting 14C contents ofgroundwater DIC. While some studies discuss these assumptions, andthey are well explained in reference texts such as Fontes (1992), Clarkand Fritz (1997), and Kalin (2000), it is not uncommon for isotope massbalances to be carried out with little discussion. While the δ13C of DIC isroutinely measured, many studies assume values of the δ13C of calcite(commonly using a typical marine value of 0‰) and very few directlyconstrain the δ13C of the recharging water.

2.1. Other sources of 14C-free DIC

In anoxic groundwater from all environments, bacteria may usecarbon as an electron acceptor and produce CH4 and/or CO2 (Aravenaet al., 1995; Valentine et al., 2004; Leybourne et al., 2006; Coetsiers andWalraevens, 2009; Cartwright, 2010b). Abiogenic methanogenesis isalso recorded, but is probably more common at higher temperaturesthan that recorded in most groundwater (Sherwood-Lollar et al., 2006;Currell et al., 2017). SO4

2− is a more efficient electron acceptor thanCO2, and in the presence of SO4

2− anaerobic bacteria will oxidise or-ganic carbon (represented as CH2O) via reactions of the form:2CH2O+ SO4

2−=H2S+2HCO3−. Because the organic carbon has

low δ13C values, this pathway of methanogenesis produces DIC withlow δ13C values and, due to the 34S/32S fractionations between SO4

2−

and H2S, the residual SO42− has elevated δ34S values. In the absence of

SO42− and NO3

−, bacteria may produce methane from organic carbonvia acetate fermentation (2CH2O+2H2O=CH4+CO2). Due to thefractionation of 13C between CH4 and CO2, (50–80‰: Valentine et al.,2004; Leybourne et al., 2006), the CO2 produced by this reaction hashigh δ13C values. Direct reduction of DIC (Whiticar et al., 1986) alsoresults in the residual DIC having high δ13C values. While methano-genesis resulting from the direct reduction of DIC does not appreciablychange the 14C contents (Clark and Fritz, 1997; Cartwright, 2010b),methanogenesis resulting from the breakdown of old organic material

that is part of the aquifer matrix results in the dilution of 14C (Aravenaet al., 1995; Mayo et al., 2007; Coetsiers and Walraevens, 2009). Thediffusion of exogenic CH4 from deep organic rich formations can beaccompanied by aerobic or anaerobic methanotrophic oxidation(Currell et al., 2017; Iverach et al., 2017). This process can also result indilution of 14C in the receiving aquifers. The occurrence and pathway ofmethanogenesis may be inferred from groundwater geochemistry (e.g.,lack of dissolved oxygen, low nitrate and/or sulphate concentrations,high δ34S and/or δ13C values, and the presence of dissolved methane)(Leybourne et al., 2006; Cheung et al., 2009; Currell et al., 2017).

Locally, geogenic CO2 derived from volcanic outgassing or deepcrustal sources, such as metamorphic devolatilisation, may also be asource of 14C-free DIC (Cartwright et al., 2002; Caliro et al., 2005;Genereux et al., 2009; Koh et al., 2017). CO2 derived from the mantleand many igneous rocks has a δ13C of c.−6‰ (Javoy et al., 1986; Clarkand Fritz, 1997), which contrasts with those of marine limestones andthe DIC derived from the soil zone during recharge. Correction formethanotropic reactions, methanogenesis, or geogenic CO2 input mayagain be made via a sequence of mass balance equations, reactivetransport models, graphical techniques and/or geochemical models.However, in the case of methanogenesis, the pathways vary with thegeochemistry of the waters and the types of bacteria present, whichresults in the geochemical changes being difficult to predict in detail.

2.2. 14C content of unsaturated zone CO2

Commonly, the interpretation of groundwater 14C data implicitlyassumes that the CO2 in the unsaturated zone has 14C contents that aresimilar to those of the atmosphere. This may be appropriate for tem-perate zones with high recharge rates and relatively shallow un-saturated zones. However, the 14C content of CO2 from the deep un-saturated zone in semi-arid or arid regions may be significantly lowerthan that of the atmosphere (Bacon and Keller, 1998; Thorstenson et al.,1998; Wood et al., 2015; Haas et al., 2016; Thorstenson et al., 2016).The 14C contents of unsaturated zone CO2 commonly systematicallydecrease from near atmospheric values at the surface to lower valuesnear the water table. For example, the 14C content of CO2 at Ti Tree(central Australia) decreases from>100 pMC at shallower than 10mbelow ground surface to as low as 50 pMC at the base of the unsaturatedzone (generally between 20 and 35m in this area) (Wood et al., 2015).The 14C content of CO2 from 7m depth in the unsaturated zone atSaskatoon (Canada) is as low as 20 pMC (Bacon and Keller, 1998) andas low as 50 pMC at 8.5 m in the unsaturated zone in North Dakota(USA) (Haas et al., 2016). CO2 at the base of the thick unsaturated zone(c. 110m) in Nevada (USA) has a 14C content of < 20 pMC (Walvoordet al., 2005).

The high 14C contents of the CO2 in the shallow unsaturated zoneprobably results from plant root respiration and/or the decay of recentorganic matter, although the latter is likely only within the root zone(which may be up to a few metres thick in the case of deep-rootedtrees). The low 14C contents of the deeper CO2 most likely result fromthe oxidation of old organic matter below the root zone where there isno contribution of CO2 from root respiration. A decrease of pO2 withdepth (Thorstenson et al., 1998) is also consistent with the oxidation oforganic matter. Changes to the relative importance of root zone re-spiration vs. organic matter oxidation, increasing ages of organic ma-terial with depth, and diffusion within the unsaturated zone producethe observed gradients in 14C contents of CO2. While the 14C contents ofunsaturated zone CO2 are rarely measured, the few studies that havemeasured it in semi-arid to arid regions illustrate that automaticallyascribing low 14C contents of DIC largely to decay in groundwater maysignificantly overestimate groundwater residence times (Wood et al.,2014; Wood et al., 2015).

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2.3. Sources of recharge

Recharge of aquifers in high-rainfall areas is dominantly by thedirect infiltration of rainfall (Scanlon et al., 2002; Healy, 2010). Bycontrast, especially in low-relief areas, substantial recharge in arid andsemi-arid regions may occur through flooding of ephemeral rivers(Allison et al., 1985; Scanlon et al., 2002; Scanlon et al., 2006; Morinet al., 2009; Cendón et al., 2010; Meredith et al., 2016). The DIC con-centrations in river water are generally substantially higher than thosein rainfall. Since arid zone soils commonly have low organic carbonconcentrations that result in low pCO2, much of the DIC in groundwatermay originate from river recharge (Cendón et al., 2010; Meredith et al.,2016). The δ13C values of DIC in rivers are governed by in-river pro-cesses, such as mineralisation of dissolved organic carbon, dissolutionof particulate inorganic carbon, in-river respiration and photosynthesis,and exchange with the atmosphere (Quay et al., 1992; Aucour et al.,1999; Telmer and Veizer, 1999; Raymond and Bauer, 2001; Strieglet al., 2007; Cartwright, 2010a). The balance of these processes resultsin variable δ13C values. For example, δ13C values of DIC in the Murray-Darling River system in semi-arid southeast Australia are −10 to −5‰(Cartwright, 2010a; Meredith et al., 2016). DIC in other major riversystems from a variety of environments are similarly variable. For ex-ample, the Ottawa River in Canada has δ13C values of between −16and −8‰ (Telmer and Veizer, 1999), δ13C values in the OkavangoDelta range from −8 to −2‰ at low water levels to −12 to −6‰ athigher flows (Akoko et al. 2013), while Aucour et al. (1999) reportedthat DIC in the Rhone River (western Europe) had δ13C values of be-tween −11 and −5‰. The δ13C values of DIC in river-recharge aregenerally significantly higher than those in equilibrium with soil CO2

and are likely to vary between recharge events as the relative im-portance of the individual in-river processes will also vary. Identifyingthe initial δ13C value of DIC for the mass balance corrections of the typein Eq. (2) may be difficult. Likewise, where recharge is episodic fol-lowing major rainfall events, the δ13C values of DIC in the infiltratingwater may be variable (Meredith et al., 2018). Where samples with arange of 14C contents are present, trends in δ13C values, 14C con-centrations, and DIC concentrations may help constrain the composi-tion of the end-members. Generalised graphical techniques to de-termine the contribution of DIC from different sources were discussedby Han et al. (2012) and Han and Plummer (2016). These techniquesare likely to yield most information where there is a dominant source ofDIC and where the end-members have well-constrained and restrictedgeochemistry (e.g. Meredith et al., 2016).

2.4. Evapotranspiration and open system carbonate dissolution

Semi-arid and arid areas commonly have high potential evapo-transpiration rates relative to rainfall totals (Supplement Table 1).Consequently, the salinity of water in the soils and regolith can be highand calcite precipitation may occur in the soils or on the surface(Herczeg et al., 2001; Hacini et al., 2008; Gocke et al., 2012). Ephem-eral water bodies such as small lakes or pools on the floodplain com-monly have salt crusts that contain calcite together with gypsum andlocally halite. Episodic recharge water may subsequently dissolve thesenear-surface carbonates and, consequently, they may be the source ofsignificant volumes of DIC in the groundwater. As the water table iscommonly relatively deep in arid or semi-arid areas, much of this cal-cite dissolution may occur under open-system conditions.

In an ideal case, the δ13C values of the biomass and the temperatureof evaporation will govern the δ13C values of pedogenic carbonate.However, as discussed above, DIC in surface water may have a widerange of δ13C values resulting from the relative rates of mineralisationof organic matter, exchange with the atmosphere, and photosynthesisby aquatic plants or algae. Consequently, calcite formed by evapo-transpiration of that DIC will also have variable δ13C values. Calciteprecipitated from small volumes of surface or soil water may occurunder conditions approximating Rayleigh crystallisation, which willresult in the progressive decrease of calcite δ13C values as evapo-transpiration proceeds. Not suprisngly, the δ13C values of soil andsurface carbonates are variable (Quade et al., 1989; Quade et al., 1995;Landi et al., 2003; Breecker et al., 2009; Cartwright, 2010a; Cartwrightet al., 2013; Meredith et al., 2016). The δ13C values of pedogenic calcitemay also be temporally variable. δ13C values of calcite deposited byevaporating flood waters from the Darling River (central Australia)were c. 1‰ lower than the calcite present prior to the floods (Meredithet al., 2016).

Where calcite is present in the unsaturated zone, open-system cal-cite dissolution may take place during recharge. If the calcite δ13C va-lues are known, the changes to DIC concentrations, δ13C values, and 14Ccontents caused by open-system calcite dissolution may be predicted(Clark and Fritz, 1997; Gillon et al., 2009; Cartwright et al., 2013). Thedissolution of calcite increases the pH of the water in the unsaturatedzone. If the reservoir of C in the soil CO2 is large compared to that of Cin the DIC, the exchange of C between the DIC and CO2 increases bothδ13C values and 14C contents as pH increases. This reflects the change inproportion of the aqueous CO2, HCO3

− and CO32− species in DIC and

the 13C/12C fractionation factors between those species and CO2. Fig. 3a

Fig. 3. Variation in dissolved inorganic carbon (DIC) concentrations with pH (3a) and 14C contents and δ13C values (3b) during open- and closed-system calcitedissolution for pCO2=10−1 and 10−2.5. From Gillon et al. (2009) and Cartwright et al. (2013).

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shows the changes to pH and DIC concentrations in water that initiallyhas a pH of 5.5 and which contains C as its only dissolved component.The calculations assumed T=20 °C and pCO2 values of 10−2.5 or 10−1.Fig. 3b shows the corresponding changes in the δ13C values and 14Ccontents of DIC assuming that the calcite had a δ13C value of 0‰ andthe 14C content of soil zone CO2 was 100 pmc. 13C fractionations maybe calculated from Vogel et al. (1970) and Mook et al. (1974), and14C/12C fractionations were assumed to be 2.3 times the 13C/12C frac-tionations (Saliege and Fontes, 1984). For an initial pCO2 of 10−2.5,calcite saturation is achieved at pH c. 7.5 resulting in a δ13C of −15‰and a 14C content of c. 104 pmc. For an initial pCO2 of 10-1.0, calcitesaturation is achieved at pH c. 6.7 resulting in a δ13C of −18‰ and a14C content of c. 102 pmc. Most groundwater studies utilise wells thatare screened below the water table and relatively few studies have alsodirectly studied processes in the unsaturated zone by sampling the in-filtrating water. Nevertheless, open-system calcite dissolution may beevident from the presence of high 14C groundwater that also has rela-tively high δ13C values (Carmi et al., 2009; Gillon et al., 2009;Cartwright et al., 2013).

3. Carbon-14 input and flow path geometry

As noted above, the decay equation (Eq. (1)) yields residence timesin radiocarbon years. However, to compare the groundwater residencetimes with other datasets such as palaeoclimate records (Weninger andJöris, 2008), conversion to calendar years is desirable. Calculation ofresidence times in calendar years requires that the variation in atmo-spheric 14C contents over time to be considered. Aside from the ele-vated 14C contents resulting from the atmospheric nuclear tests, therehave been long-term variations in the rate of production of 14C due tovariations in cosmic ray activity (Reimer et al., 2009). Comparisonswith tree-ring chronologies and U-Th ages of corals indicate that the 14Ccontent of atmospheric CO2 was as high as 170 pMC between 28,000and 30,000 years ago.

The use of Eq. (1) also implicitly assumes one-dimensional, non-dispersive flow (piston flow) such that all the groundwater collected atthe well was recharged at the same time (i.e., that it has a definite age).This is obviously an oversimplification as groundwater flows alongpaths of varying lengths and undergoes hydrodynamic dispersion anddiffusion, which affects the solutes such as DIC. Thus, a groundwatersample contains aliquots of water that have a range of residence timesrather than being of a specific and definable age (Maloszewski andZuber, 1982; Cook and Bohlke, 2000; Maloszewski, 2000; Suckow,2014).

In the absence of preferential flow and large-scale mixing, meanresidence times may be estimated using lumped parameter models(Maloszewski and Zuber, 1982; Maloszewski and Zuber, 1992; Cook

and Bohlke, 2000; Maloszewski, 2000; McGuire and McDonnell, 2006;Jurgens et al., 2012). Lumped parameter models allow the variability ofthe 14C input, more realistic flow path geometries, and the effects ofdispersion may be taken into account. The 14C content of groundwaterat time 14Ct is related to the 14C content of DIC in the recharging waterover time (14Ci) via the convolution integral:

= ∫ −∞

−C C q t τ g τ e dτ14 (14 )( ) ( )t iλτ

0 (3)

where τ is the mean residence time, t- τ is the time when the waterrecharged, λ is the decay constant, and g(τ) is the response function thatdescribes the distribution of flow paths and residence times in theaquifer. There are several lumped parameter models that may be ap-plied to different aquifer geometries (Maloszewski and Zuber, 1982;Maloszewski and Zuber, 1992; Amin and Campana, 1996; Cook andBohlke, 2000; Maloszewski, 2000; Jurgens et al., 2012).

The dispersion model, which is derived from the one-dimensionaladvection-dispersion transport equation, is applicable to regionalgroundwater flow systems with layer-parallel flow and is used here toillustrate the effects on calculated mean residence times; similar resultswould be apparent from the other lumped parameter models (Atkinsonet al., 2014; Howcroft et al., 2017). Calculations were made using theTracerLPM program (Jurgens et al., 2012). The input function is the 14Crecord for atmospheric CO2 (Reimer et al., 2009) adjusted for thefractionation between atmospheric CO2 and soil zone CO2 (Fig. 1). Forthis illustration, all DIC was assumed to originate from recharge (i.e.q= 1). The dispersion model requires the dispersion parameter that isthe inverse of the more commonly reported Peclet number and whichdescribes the relative importance of dispersion relative to advection tobe specified. In regional-scale groundwater systems, the dispersionparameter is likely to be between 0.05 and 0.1 (Maloszewski, 2000).Equation (3) may also be applied to piston flow, in which case it ac-counts for the temporal variations in the 14C content of the rechargingwater (Howcroft et al., 2017).

Even where piston flow is assumed, longer mean residence times areestimated using the 14C record in Fig. 4 as the input function than usingthe decay equation with a constant initial 14C content of 100 pMC(Fig. 5). For example, groundwater with a 14C content of 30 pmc yieldsmean residence times of 10.9 vs 9.4 ka from Eq. (1). This is due to thegenerally higher 14C content of atmospheric CO2 over the last 30 kathan the present day values. The mean residence times calculated fromthe dispersion lumped parameter model increase as dispersivity in-creases (i.e., as the dispersion parameter increases). Again, for a 14Ccontent of 30 pmc, the mean residence times are between 11.8 (dis-persion parameter of 0.05) and 12.4 ka (dispersion parameter of 0.01).For a more highly dispersive system (dispersion parameter of 0.5), a 14Ccontent of 30 pmc yields a mean residence time of 17.7 ka. The width of

Fig. 4. Variation of 14C contents of atmospheric CO2 over the past 30,000 years (prior to 1950) based on the IntCal13 and Marine13 14C calibration curves of Reimeret al. (2009).

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the residence time distribution (i.e., the frequency distribution of theages of the individual aliquots of water in the sample) also increaseswith increasing dispersivity (Fig. 6). Since the decay of 14C is ex-ponential, the presence of a significant fraction of water with shorterresidence times than the mean results in higher 14C contents at anygiven mean residence time. While the lumped parameter models aresimplified representations of groundwater systems, they illustrate thatassuming piston flow and certainly ignoring the long-term variation inatmospheric 14C contents will most likely underestimate mean re-sidence times. Additionally, because it is difficult to ascertain the geo-metry of the groundwater flow paths or the degree of dispersion, thedifference in estimated mean residence times between plausible lumpedparameter models represents an additional uncertainty on the

calculated residence times. In the example above, the uncertainty re-sulting from varying the dispersion parameter is 5.3 ka for a residencetime of 14.5 ka (calculated as midway between the highest and lowestestimates). This translates to a relative uncertainty of± 20%, which islarger than the total uncertainty in 14C residence times reported inmany studies. Adopting a wider range of lumped parameter models willincrease this uncertainty.

4. Macroscopic mixing, diffusion, and heterogenous flow

Lumped parameter models are valuable in exploring the range ofresidence times that may correspond to measured 14C activities (whichis important for attempts to understand the behaviour of groundwaterin the context of other palaeoclimate archives). While this is probablyan improvement on calculating groundwater ages in radiocarbon years,lumped parameter models still make several major simplifying as-sumptions, namely uniform aquifer thickness, steady state flow, andhomogenous aquifer properties (Maloszewski and Zuber, 1992; Cookand Bohlke, 2000; Jurgens et al., 2012). Additionally, most lumpedparameter models use analytical solutions that assume a smooth dis-tribution of residence times in the groundwater samples, which is verydifficult to validate. In many aquifers, these conditions may not berealised. Hydraulic conductivities of most aquifers are heterogeneouson scales ranging from millimetres to hundreds of metres (Sudicky,1986; Rehfeldt et al., 1992; Bohling et al., 2012). Flow through het-erogeneous aquifers may mix waters with different mean residencetimes. Macroscopic mixing (or “aggregation”) may result in ground-water samples having irregular and unpredictable residence time dis-tributions (Kirchner, 2016; Stewart et al., 2017). Especially wheremixing of waters with significantly different residence times occurs, thesimple calculation of mean residence times from radioisotopes may beimpracticable (McCallum et al., 2014; Suckow, 2014; McCallum et al.,2015; Jasechko, 2016; Iverach et al. 2017; Stewart et al., 2017). Theimpacts of mixing of multiple aliquots of water with a range of re-sidence times may, however, produce groundwater samples with re-sidence time distributions similar to those predicted by the lumpedparameter models (Cartwright and Morgenstern, 2016). Due to theavailability of infrastructure, many studies of regional groundwatersystems have utilised samples from long-screened production wells. Ifthese wells extract water from several discrete higher-permeabilitylayers this may also cause the mixing of water of different residencetimes during sampling that hampers the determination of residencetimes.

Additional complications in estimating residence times arise in dual-porosity and fractured media (e.g., Neretnieks, 1981; Maloszewski andZuber, 1985). Groundwater located in isolated pores in fractured rocksmay have a long residence time and consquently low 14C contents(Fig. 7). Diffusion of DIC between the isolated pores the fractures mayresult in residence times estimated from 14C being far longer than theresidence time of the water flowing through the fractures with thediscrpency increasing as the fracture spacing decreases (Neretnieks,1981). Similarly, diffusion of old DIC from low-permeability clays mayreduce the 14C content of the groundwater in adjacent high perme-ability lithologies, which also increases the apparent mean residencetimes of the groundwater extracted from those units (Davidson andAirey, 1982; Sanford, 1997; Bethke and Johnson, 2008). Adsorption ofsolute tracers such as DIC onto minerals in the aquifer matrix may alsooccur in low-porosity media, which may cause decoupling of 14C and Oand H isotopes, which are part of the water molecule (Maloszewski andZuber, 1985).

In many instances it may be more realistic to consider that thegroundwater is comprised of multiple fractions of waters of differentbroad “ages”. Estimating the fraction of water younger than a thresholdresidence time at which the impacts of aggregation do not significantlyimpact the shape of the residence time distribution may be possible(e.g., Kirchner, 2016). Alternatively, the presence of short-timescale

Fig. 5. 14C contents of DIC vs estimates of mean residence time assuming all 14Cis from recharge. Conv= residence time from Eq. (1) assuming Ci= 100 pmc;PF= piston flow model with Ci from Fig. 4; DM=dispersion lumped para-meter model with dispersion parameters of 0.05, 0.1, and 0.5 and Ci from Fig. 4.For a 14C content of 30 pmc, estimated mean residence times are between 9.4and 17.7 ka. Calculated using TracerLPM (Jurgens et al., 2012).

Fig. 6. Age distribution from the dispersion model for water with a mean re-sidence time of 10,000 years with dispersion parameters of 0.05, 0.1, and 0.5.Note the modal age is younger than the mean residence time and decreases asthe dispersion parameter decreases. Calculated using TracerLPM (Jurgens et al.,2012).

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tracers, such as 3H or the CFCs in groundwater with relatively low 14Ccontents may be used to identify and estimate the fractions of youngerand older water (Jasechko, 2016; Jasechko et al., 2017). However,while these issues are broadly recognised, the desire to estimate re-sidence times will probably continue as they are perceived as beinguseful for assessing practical issues such as sustainability of ground-water extraction or recharge rates. At the very least, the potential ef-fects of mixing and dispersion on groundwater residence times need tobe acknowledged. Employing multiple radioactive tracers or other re-lative residence time indicators (such as stable isotopes or noble gases)may highlight that mixing has occurred (Maloszewski and Zuber, 1985;Le Gal La Salle et al., 2001; Cartwright et al., 2007; McCallum et al.,2014, 2015; Jasechko, 2016; Jasechko et al., 2017).

5. Implications for estimating groundwater residence times

The processes discussed above have implications for whether andhow realistic residence times may be estimated in groundwater fromarid and semi-arid regions. Where 14C contents have been used to es-timate residence times (e.g., Supplement Table 1), most studies haveused the δ13C values of DIC to assess processes that may affect the 14Ccontents either via isotope mass balance calculations or as part of abroader geochemical analysis via programs such as NETPATH. While itis generally recognised that assessment of the 14C contents is needed toderive groundwater residence times, several assumptions are commonlymade. Firstly, few studies consider processes other than closed-systemcalcite dissolution. While some degree of closed-system calcite dis-solution is probably ubiquitous in groundwater systems, open-systemcalcite dissolution and methanogenesis may also be locally important.Relatively few studies have measured the δ13C values of calcite in theaquifer matrix. In some cases, there may be measurements of calciteδ13C values from similar sediments to those that form the aquifers;however, many studies assume that δ13C values of the calcite are closeto 0‰. While a δ13C value of 0% for marine sediments is defensible, theglobal average δ13C of marine carbonates over the last 600Ma hasvaried from approximately −2 to +6‰ (Veizer et al., 1999). Ad-ditionally, individual sediment sequences may have a range of δ13Cvalues due to secular variations in ocean δ13C values, metabolic and/orkinetic processes in the ocean biosphere, diagenesis, or post-deposi-tional alteration (Carpenter and Lohmann, 1997). For example, authi-genic calcite in Late Permian coal measures of the Bowen Basin (QLD,Australia) have δ13C values between −19 and +10.9‰ (Uysal et al.,

2000). Sediments in semi-arid and arid areas also commonly containcalcite veins and cements formed by the circulation of evaporatedgroundwater that is close to saturation with calcite. As outlined above,this calcite is likely to have variable δ13C values. Thus, if it forms asignificant part of the calcite in the aquifer matrix, the extent of closed-system calcite dissolution will be difficult to predict from the δ13C va-lues of DIC unless aquifer carbonate δ13C values are also analysed.Unlike marine calcite that formed during sedimentation, this calcitemay contain above-background 14C contents (i.e. if it was formed in thelast 40 ka). If that is the case, the impacts of dissolution on the 14Ccontents of groundwater are more difficult to predict.

Still fewer studies have direct constraints on the δ13C values of CO2

in the unsaturated zone. Some studies report δ13C values of organicmatter in the soil (Pessenda et al., 1998; Cartwright et al., 2010;Hagedorn and Bushner, 2015) or pedogenic carbonates (Cendón et al.,2014), but few report δ13C values of soil CO2 or the DIC in soil water.Many studies assume δ13C values of soil CO2 of c. −23‰ and assign aδ13C value of c. −19 to −18‰ to DIC formed in the soil zone based onthe expected 13C/12C fractionations in the carbon cycle (Fig. 1). Evenwhere the soil carbon pool is derived only from C3 vegetation, thepotential range of δ13C values is still several per mil (Kohn, 2010).Additionally, open system calcite dissolution or recharge by flood wa-ters may result in the δ13C values of the recharging water being variableand difficult to predict. Chemical mass balance based on the major iongeochemistry is potentially an alternative method of determining closedsystem calcite dissolution that does not depend on interpreting δ13Cvalues. However, especially in environments where evapotranspirationrates are high, precipitation of calcite or other Ca-bearing minerals suchas gypsum may make such calculations difficult.

Determining the δ13C values of more of the carbon sources (e.g.,organic matter, DIC in soil water and surface water, and calcite from thesoils or aquifers), and ensuring that groundwater with a range of 14Ccontents from throughout the flow system has been sampled, may allowthe dominant processes impacting DIC contents to be determined (e.g.,via the graphical techniques discussed by Han et al., 2012; and Han andPlummer, 2016). This approach is likely to yield most informationwhere the potential sources of DIC have a restricted range of δ13C va-lues and where there is a small number of geochemical processes im-pacting DIC concentrations and isotopic ratios.

Not accounting for variations in the 14C content of the atmosphere(Fig. 4) makes a significant, yet largely unremarked upon, difference tothe calculated mean residence times. For water recharged greater than

Fig. 7. Schematic illustration of the impacts ofdiffusion on 14C contents of groundwater indual porosity media. Isolation of water in dead-end pathways or isolated pores results in a poolof low 14C DIC that can exchange with higher14C DIC in the fracture/high permeabilitychannel. The diffusive exchange becomes moreimportant as the width of the high-permeabilitychannels decreases.

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15,000 years ago the 14C content of the atmosphere was likely> 120pmc, which results in calculated mean residence times being c. 20%longer regardless of which method is used. This difference is a similarmagnitude to the uncertainties often quoted from uncertainties in thedegree of closed-system calcite dissolution. It is more difficult to assesswhether macroscopic mixing and diffusion are sufficiently significantthat defining a residence time is unreasonable. However, this is ob-viously a critical issue as it dictates whether the results of residencetime calculations are fundamentally valid. The effects of diffusion andmixing may be identified by using 14C in conjunction with other re-sidence time indicators (e.g., Kronfeld et al., 1993; Plummer et al.,2004; Dassi et al., 2005b; Cartwright et al., 2007, 2010, 2017a;Kulongoski et al., 2008; Jasechko, 2016; Jasechko et al., 2017; Iverachet al., 2017; Priestley et al., 2017). Discordant concentrations ofradioisotopes with widely different half-lives (e.g. 3H, 14C, 4He, and36Cl) may indicate diffusive input from low porosity lithologies, theleaking of young water into older regional groundwater, or othercomplexities in the flow systems (Cartwright et al., 2007, 2010; Bethkeand Johnson, 2008; Kulongoski et al., 2008; Eberts et al., 2012;Jasechko, 2016; Jasechko et al., 2017; Iverach et al., 2017; Howcroftet al., 2017). Even where the flow system is reasonably simple, un-certainties in its geometry or the degree of dispersion can result insubstantial uncertainties in mean transit times (Atkinson et al., 2014;Howcroft et al., 2017).

Concentrations of multiple radioactive tracers can potentially beused in models that employ particle tracking and/or direct simulationof ages (Suckow, 2014). Such analysis can help to constrain flow andmixing and provide greater constraints on possible residence times al-though the use of multiple tracer concentration data may result in non-unique solutions. Determining an increasing number of age-tracerconcentrations in a given sample will also amplify the impact of un-certainties embedded in each method. For example, 36Cl has un-certainties relating to the input function that is poorly known over time,the degree of in-situ 36Cl production, and the possibility that Cl is re-cycled through salt lakes and playas in enclosed semi-arid basins(Phillips, 2000; Cartwright et al., 2017b). Dissolved noble gas radio-isotopes will likely have different diffusivities and adsorption coeffi-cients to DIC (e.g., Maloszewski and Zuber, 1985).

6. Conclusions

This review has highlighted the important role that estimatinggroundwater residence time using 14C plays in understanding the hy-drogeology of semi-arid and arid regions. Perhaps because of the im-provements in analytical techniques, such studies are becoming morecommonplace, which is improving our understanding of these criticalenvironments. The application of 14C is not always straightforward,however, and many studies (including several of the authors’) have notconsidered many of the possible problems in its application. Commonly,studies have focussed on estimating residence times and have generallyconsidered the closed-system dissolution of 14C calcite. However, thisneglects other processes that impact the 14C content of DIC (and thetreatment of calcite dissolution is sometimes formulaic). In many casesit may not be possible to estimate a meaningful mean residence time,and even where it is, uncertainties in the geometry of the flow path ordegree of dispersion introduce considerable uncertainties in the meanresidence times that are rarely considered. Estimating broad ranges ofresidence times or fractions of “younger” and “older” water using 14C inconjunction with other tracers will generally be robust (and perhaps isthe only realistic outcome in many situations). While attempts to cal-culate residence times and the parameters that stem from these such asrecharge rates, groundwater fluxes, or sustainable groundwater use,may be desirable, the limitations need to be recognised and the as-sumptions tested. A more critical appraisal of radiocarbon will increaseconfidence in the results and improve our understanding of regionalaquifer systems.

Declaration of Competing Interest

The authors declare that they have no known competing financialinterests or personal relationships that could have appeared to influ-ence the work reported in this paper.

Acknowledgements

We would like to thank the numerous colleagues with whom wehave discussed groundwater residence times, geochemistry, and hy-drogeology over many years. Four anonymous reviewers and editorSteve Worthington are thanked for their helpful comments.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jhydrol.2019.124247.

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