Residence times of groundwater along a flow path in the Great Artesian Basin determined by 81Kr, 36Cl and 4He: Implications for palaeo hydrogeology

groundwaters. Towards the end of the transect the in ﬂ uence of ephemeral recharge is less while diffuse recharge and the initial chloride concentration at recharge were higher.


Introduction
The Great Artesian Basin (GAB) is a continental-scale multi-layered aquifer system, one of the largest groundwater basins in the world (Habermehl, 1980).Because of its large size and relatively easy access to free-flowing artesian waters it has been considered an ideal "field laboratory" for the application and assessment of dating old groundwater.Previous investigations have included seminal studies on Chlorine-36 ( 36 Cl) (Bentley et al., 1986a;Torgersen et al., 1991), Helium-4 ( 4 He) (Torgersen and Clarke, 1985) and in more recent times Krypton-81 ( 81 Kr) (Collon et al., 2000;Lehmann et al., 2003).In the latter study accelerator mass spectrometry (AMS) measurements of the 81 Kr abundances were conducted for the first time in a regional study of the same part of the GAB as presented here.Of these three isotopes, 81 Kr is the most suitable for age interpretation of old groundwater, because 36 Cl and 4 He are often not straightforward to untangle as they are complicated by uncertain model assumptions.Along a hydraulic transect from the Finke River recharge zone in the south-western GAB (Fig. 1), we constrained groundwater flow velocities by a set of dating tracers that cover time ranges from decades ( 85 Kr) to over hundreds and thousands of years ( 39 Ar, 14 C), and to hundreds of thousands of years ( 81 Kr, 36 Cl).
The most used tracer for dating very old groundwater is 36 Cl (half-life 301 kyr).The widespread availability of Accelerator Mass Spectrometry (AMS) from the late 1980s meant that 36 Cl could henceforth not only be sampled easily but analysed relatively routinely.This combined with the high solubility of chloride resulted in widespread optimism in the research community that the ultimate methodology for dating old groundwater was within reach.However, this optimism soon faded when it was realised that much more complementary information would be required to interpret 36 Cl, including the spatial and temporal variability of the 36 Cl input as well as information about sources and sinks of chloride.The reader is referred to a number of comprehensive reviews on 36 Cl (Aggarwal et al., 2013;Phillips, 2000).In this paper we demonstrate that with independent knowledge of the groundwater age chronology from 81 Kr measurements, we have the potential to unravel the chlorine isotope systematics and the chloride input into the groundwater system.This procedure provides additional information on the groundwater flow system not possible by other methodologies, and under ideal situations it may provide "proxy" evidence for paleoclimate.
Helium-4 is another isotope commonly used to obtain information on old groundwater (Kipfer et al., 2002).The basic principle of this method is that, as 4 He is produced in the sub surface by the decay of uranium (U) and thorium (Th) its concentration increases with increasing residence time.For quantitative age dating the local accumulation rate of 4 He needs to be determined as well as the He influx to the aquifer from various sources.The production rate can be calculated from U and Th concentrations in the aquifer.However, the He influx from neighbouring strata is far more difficult to quantify.As a result, 4 He is often considered to be a semi-quantitative indicator of groundwater age at best.Many previous studies in the GAB have been devoted to the accumulation of He in groundwater (Torgersen andClarke, 1985, 1987;Torgersen and Ivey, 1985).However, up until the present, it has not been possible for the 4 He clock to be calibrated against a reliable residence time indicator, not only for the GAB, but also for other large aquifers systems around the globe (Torgersen, 2010).
It is only recently that the detection of 81 Kr at natural levels has been developed with a precision sufficient to date groundwater (Gerber et al., 2017;Jiang et al., 2020;Matsumoto et al., 2018;Ram et al., 2021;Sturchio et al., 2014;Yechieli et al., 2019;Yokochi et al., 2019;Yokochi et al., 2021), but it has for a long time been potentially considered to be the most reliable isotope to quantify long groundwater residence times (Lehmann et al., 1993;Lehmann et al., 2003).This is because krypton (Kr), being a noble gas is inert and as a result does not undergo chemical reactions.Furthermore, it has a well-known atmospheric concentration of 1.099 ± 0.009 ppm (Aoki and Makide, 2005).Variations of the 81 Kr/Kr ratio over time are relatively small (Buizert et al., 2013;Zappala et al., 2020).In addition, both subsurface and anthropogenic sources of 81 Kr are considered minimal in most cases (Aggarwal et al., 2015;Purtschert et al., 2013;Purtschert et al., 2021;Sturchio et al., 2004).However the application of this potentially ideal groundwater tracer has been limited in the past because of poor detection efficiency of 81 Kr which has resulted in large volumes of water required for degassing (Purtschert et al., 2013).Nevertheless, recent development of Atom Trap Trace Analysis method (ATTA) has improved the detection efficiency, which has resulted in a much lower volume of water being required for sampling and processing (Lu et al., 2014;Zappala et al., 2020;Zhang et al., 2020).
Our study area is in the south-western GAB.This region may represent an ideal area for testing the application of 81 Kr in groundwater studies because: a) the hydrogeology of the region is relatively well known (Love et al., 2013); b) there have been previous studies on the source and sinks of chloride (Love et al., 2000); c) there have been numerous hydrochemical and environmental tracers studies in the region (Priestley et al., 2017;Radke et al., 2000;and, d) the first successful set of groundwater 81 Kr samples were analysed by AMS in this region (Collon et al., 2000;Lehmann et al., 2003).It is assumed that there has been effectively zero diffuse recharge in the region since the end of the Pleistocene and that modern day recharge only occurs beneath isolated riverbeds referred to as ephemeral river recharge (ERR).
In this paper we show that 81 Kr ages provide a reasonable representation of the groundwater residence time.Our confidence in this comes from the lack of major sources or sinks of Kr in the subsurface and that the input function is known and constant through time.Furthermore, a previous study in this area, provided the first 81 Kr dates from four wells in the region, indicating that this new dating tool was worthy of further consideration (Lehmann et al., 2003).
The aim of this paper is to: • Assess the feasibility of radioactive noble gas tracers ( 85 Kr, 81 Kr and 39 Ar) for the determination of groundwater flow velocities over a large range of flow distances.• Use the calculated 81 Kr ages to calibrate the 36 Cl and 4 He groundwater clocks.• Obtain a better understanding of the palaeo hydrogeology and in particularly the history of recharge from the Finke River over time.

Study area
Our study area is the western margin of the GAB in the Finke River recharge zone and extents hundreds of kilometres towards the interior of the GAB where the aquifer becomes confined (Fig. 1).The study section starts near the Finke River recharge zone and extends about 300 km downstream.At the beginning of the transect the main aquifer of the GAB (referred to as the Cadna-Owie Formation-Algebuckina Sandstone or J aquifer in this section of the GAB) crops out and is unconfined for approximately 40 km until it becomes a confined system overlain by the confining Bulldog Shale.The study area is arid with potential evapotranspiration ranging up to 3000 mm/yr.Average annual rainfall is 200 mm/yr, with approximately 85 % occurring in the months of January to March.In this area of the GAB the only effective recharge occurring today is via ephemeral river recharge (ERR).This recharge to the main J aquifer of the GAB occurs in the outcrop area beneath the Finke River where the main J aquifer outcrops during infrequent times of intense rainfall that originate from monsoons that travel across the continent from the north.Stable isotope data indicate that this typically occurs in the months of January to March (Fulton et al., 2013).Fulton et al. (2013) mapped the potential recharge zone to be 13 km 2 , with a length of 36 km and an average river bed width of 370 m (Fulton et al., 2013).Ephemeral river recharge beneath the Finke River recharge zone was estimated to be 380-850 mm per annum, in contrast to diffuse recharge surrounding the river which is in the order 0.1-0.25 mm/yr (Wohling et al., 2013).Groundwater flows in a southeast direction from the Finke River recharge zone to towards a more central portion of the GAB.Clearly, modern day ERR occurs beneath the Finke River today but how significant this recharge has been in the past remains unresolved.
Previous studies in the arid central Australia have shown that subsurface production of 36 Cl, as well as diffusion of solutes from adjacent aquitards, complicates the interpretation of 36 Cl dating results (Love et al., 2000;Priestley et al., 2017).Furthermore, it has been shown that there are spatial variations in the 36 Cl/Cl input value, and in all cases, the input values are below what could be expected from latitudinal variation of the 36 Cl/Cl input ratio alone.Based on Cl/Br in samples upstream from the Finke River recharge zone halite dissolution has occurred from the Bitter Springs Formation and has been discharged to the river.This effect can account for the lower 36 Cl/Cl input value of 60 × 10 −15 (Fulton et al., 2013;Wohling et al., 2013).While in the region to the south-west of the Finke River recharge zone there is no evidence of young groundwater being influenced by dissolution of evaporates.In this area the 36 Cl/Cl input ratio was determined to be 125 × 10 −15 based on measurements on selected young groundwater samples in the unconfined part of this aquifer where an anthropogenic component can be ruled out (Lehmann et al., 2003;Love et al., 2000).

Field and analytical methods
Groundwater was sampled in November 2009 from unconfined and confined sections (including artesian wells) of the main J aquifer of the GAB (Fig. 1).The sampling sites were selected along a transect in the direction of groundwater flow.The transect begins in the Finke River recharge area and extends past Dalhousie Springs.A total of 19 wells were purged several times until stable field parameters of pH, temperature and salinity were achieved (Table 1).
Samples for 4 He were taken in copper tubes using standard techniques (Aeschbach-Hertig and Solomon, 2013).He isotopes, as well as the main isotopes of Ne and the heavy noble gases were measured at the Institute of Environmental Physics, Heidelberg University, following the methods described by (Beyerle et al., 2000).Radioactive noble gases 85 Kr, 39 Ar and 81 Kr were sampled in the field using a large volume gas extraction system (Purtschert et al., 2013).The vacuum cylinder gas extraction system was optimized for remote fieldwork and achieved an extraction efficiency of 80-90 % at a water flow rate of 20 L/min.Approximately 2000-3000 L of groundwater were degassed in the field and gases were collected in preevacuated steel containers.
The gas obtained by degassing was analysed for major gas composition on a quadrupole mass spectrometer before separating the Ar and Kr gases for further analysis.Krypton was extracted from the bulk gas at the University of Bern by multistep gas chromatography (Loosli and Purtschert, 2005), and the isotope ratios 81 Kr/Kr and 85 Kr/Kr were determined using the ATTA-3 instrument in the Laboratory for Radiokrypton Dating, Argonne National Laboratory (Jiang et al., 2012).Based on the Atom Trap Trace Analysis method (Du et al., 2003), ATTA-3 is a selective and efficient atom counter capable of measuring both 81 Kr/Kr and 85 Kr/Kr ratios of environmental samples in the range of 10 −14 -10 −10 .In the apparatus, atoms of a targeted isotope ( 81 Kr, 85 Kr, or the control isotope 83 Kr) were captured by resonant laser light into an atom trap and counted by observing the fluorescence of the trapped atoms.For 81 Kr dating in the age range of 50 kyr -1500 kyr, the required sample size was at the time of analyses 5-10 micro-L STP of krypton gas, which could be extracted from approximately 100-200 kg of water or 40-80 kg of ice.Both the reliability and reproducibility of the method were examined with an inter-comparison study among different methods and instruments.The 85 Kr/Kr ratios of 12 samples, in the range of 10 −13 to 10 −10 , were measured independently in three laboratories: a low-level counting (LLC) laboratory in Bern, Switzerland, and two ATTA laboratories, one in Argonne and the other in Hefei, China.The results agree at the precision level of 7 % (Du et al., 2003;Jiang et al., 2012).
The detection limit of ATTA-3, defined as the lowest isotope ratio detectable by ATTA-3, is approximately 1 dpm/cc for 85 Kr/Kr.Here we use the conventional units of dpm/cc, which stands for the number of 85 Kr decays per minute per mL-STP of Kr gas.For conversion, 100 dpm/cc corresponds to the 85 Kr/Kr ratio of 3.03 × 10 −11 .This detection limit, caused by the instrument memory effect, was determined with measurements of an 85 Kr-dead sample.Argon was also extracted from the bulk gas by cryogenic distillation. 39Ar activities were measured by low-level gas proportional counting at the Physics Institute, University of Bern (Loosli, 1983;Loosli and Purtschert, 2005).
Radiocarbon ( 14 C) was collected in 1 L bottles in the field and analysed by AMS at the Rafter Radiocarbon Laboratory in New Zealand.An additional aliquot collected for Carbon 13 ( 13 C) was also analysed at the same laboratory. 36Cl samples were filtered with 0.45 μm membrane filters and then the chloride was prepared as AgCl according to the preparation scheme reported in (Tosaki et al., 2011).The 36 Cl/Cl ratios were analysed with the AMS (accelerator mass spectrometry) system at the Tandem Accelerator Complex, University of Tsukuba (Sasa et al., 2010), along with diluted NIST 36 Cl standards ( 36 Cl/Cl = 1.60 × 10 −12 ).

Results
For ease of comparison and discussion the sampled wells were split into three groups (Fig. 1): • Group I samples located closest to the Finke River recharge zone (red dots in figures) • Group II represent the intermediate wells (green triangles in figures) • Group III represent the wells furthest along the transect (blue triangles in figures) Table 1 For well locations we refer to Fig. 1.Bore type S (stock), M (monitoring) and T (small town supply Well 19 is an outlier and does not belong to any group.The groundwater there most likely originates from a westerly recharge source (black square in figures).

Radionuclides data consistency and reduction
The purpose of this section is to review the internal consistency of the data set and to apply corrections to the data where required.The activities of the radioactive noble gases 85 Kr, 39 Ar, 81 Kr as well as 14 C activities and 36 Cl/Cl ratios are summarized in Table 2, and tracer-tracer plots are compared with each other in order of increasing half-lives in in Fig. 2. Fig. 2a displays three samples with elevated 85 Kr values in combination with 39 Ar values <20 % of the activity in the modern atmosphere (pmAr).These are possibly the result of contamination of the Kr gas fraction which was purified and shipped to Argonne National Laboratory after the Ar gas fraction was separated at the University of Bern from the crude gas which implies that only the 81 Kr activities need to be corrected (and not 39 Ar).This is the case for samples 9 and 14.The 81 Kr value of the highly  air contaminated sample 7 was neglected.Since it is assumed that the contamination occurred in the northern hemisphere the corresponding atmospheric 85 Kr activity in the northern hemisphere ( 85 Kr atm ) of 75 dmp/cc Kr (Winger et al., 2005) was used to calculate the fraction α of air contamination in the 81 Kr sample (α = 85 Kr m / 85 Kr atm ). 81 Here the indices m and corr refer to the measured and corrected 81 Kr values, respectively. 81Kr activity is given in percent of the modern atmospheric value (pmKr).
The comparison of 39 Ar and 14 C activities reveals a rather consistent pattern (Fig. 2b).The 39 Ar active samples show the highest 14 C activities ranging from 40 to 90 pmC (percent modern carbon).Three samples from Group 1 and all samples from Group 2-3 have 39 Ar activities (given in percent of the modern atmospheric activity concentration pmAr) below the detection limit except for sample 12 which has an elevated 39 Ar value.Since this sample is 85 Kr free, air contamination during sampling can be excluded.The 39 Ar activity was measured twice with reproducible results so we are confident that the value is real.One possibility could be that this sampling location represents modern recharge from vertical flow from the surface.However, this seems very unlikely as this location is a zone of upward hydraulic head which would negate downward flow today.This site also has 320 m of overlying low permeability units.Furthermore, all the other dating tracers indicate old groundwater.Locally elevated underground in-situ production of 39 Ar within in the aquifer at great depth (Lehmann et al., 1993) cannot be excluded but seems to be unlikely because the 39 Ar values of all others samples from Groups 2-3 are below detection limit in agreement with previous findings (Lehmann et al., 2003).However, this site also has elevated 36 Cl/Cl in comparison to the depleted 81 Kr value (Fig. 2d).This may possibly support the existence of a locally elevated neutron flux (Purtschert et al., 2021).We interpret this as a local phenomenon and assume negligible underground production of 39 Ar for all other samples.The 39 Ar values of Group 1 were therefore interpreted in terms of groundwater residence time without corrections for underground production.
Elevated 14 C activities of Group 1 waters coincide with the highest 81 Kr values (Fig. 2c).Samples with 81 Kr values <80 % modern are strongly depleted in 14 C with values between 3 and 10 pmc.However, even the most 81 Kr depleted waters have 14 C concentrations significantly above the detection limit of ∼0.5 pmC.The origin of this offset of ∼4 pmC remains a conundrum but may be an analytical artefact rather than representing the real situation in the aquifer. 14C contamination e.g. during sampling was observed in other studies (Aggarwal et al., 2014;Yokochi et al., 2017) in particular when conventional sampling and counting techniques were applied.Such an effect was however not expected for the radiocarbon AMS technique as applied in our study.The comparison with the 81 Kr data in combination with the improbability of the admixture of young water components in the downstream part of the artesian aquifer allows us to conclude that samples with 14 C activities below 4 pmc are older than the practical upper end of the 14 C dating range of 40 kyrs.
81 Kr activities and 36 Cl/Cl ratios correlate well (Fig. 2d).The largest scatter is observed for Group 1 where 36 Cl/Cl ratios range between 40 and 90 × 10 −15 for a relatively small range of 81 Kr values between 80 and 100%modern.Further downstream (Groups 2-3) the activities of both tracers decrease simultaneously.A more detailed discussion of both tracers in terms of groundwater residence time and flow velocity will follow in Section 5.1.δ 13 C values of DIC (Table 1) are relatively constant along the flow line and range mostly between −10 and −12 ‰.This is comparable to the assumed signature of soil CO 2 (Fulton et al., 2013).This indicates that dissolution of carbonate minerals during recharge beneath the Finke River is minimal.As a result, we present 14 C ages (Table 2) calculated with a constant initial activity of 86 pmC calculated from the mean of 39 Ar active samples under consideration of an offset of 4 pmC (Section 5.1).

Spatial distribution of tracer activities
In Fig. 3 the contamination corrected tracer activities are plotted as a function of distance from the recharge area (RA), where the Finke River crosses the J aquifer outcrop.85 Kr values (Table 2, not shown in the graph) below 2.4 dpm/ccKr indicate a lower age limit of 40 years for all waters.This is also supported by the highest 39 Ar activity of 65 ± 7 pmAr which corresponds to a residence time of ∼170 years.With increasing distance from the recharge area, the 39 Ar values decreases rapidly to the below detection limit around 40 km from the Finke River.This is also the location where a sharp decrease of 14 C activities is observed.Within 10-20 km, the 14 C activities decrease from 70 to 17 pmC (Fig. 3c).This rapid decrease in 14 C corresponds to the approximate location where the aquifer transfers from an unconfined to a confined system (Fig. 1).In this section the aquifer thickness increases from 30 m to almost 200 m which may imply a reduction of the flow velocity.
All Group 1 waters show modern or slightly sub-modern 81 Kr activities (Fig. 3d).For Group 2 groundwater wells the 14 C ages increase beyond the dating range of the radiocarbon method.This is consistent with the decreasing 81 Kr activities in this area (Fig. 3d and e).The lowest 81 Kr values of 34 and 36 pmKr are observed for Group 3 groundwaters.This corresponds to an 81 Kr age of ∼350 kyrs.Sample number 13 appears to be closely related to Sample 19 being sourced from the west (Fig. 1).It has a higher 81 Kr value than would be expected if it were along a common flow transect from the north.Fig. 3e shows that the highest 36 Cl/Cl ratios are found close to the recharge area.Most samples of Group 1 cluster at 36 Cl/Cl ratios in the range 50-60 × 10 −15 .Similarly to 81 Kr, the ratios decrease within Group 2 and reach the lowest values in Group 3 wells down gradient.Although there is considerably more scatter in the 36 Cl/Cl values.
Concentrations of dissolved 4 He also show a very pronounced evolution with distance (Fig. 3f).Group 1 water close to the recharge area are low in 4 He with concentrations < 10 −6 cm 3 STP /g w .Within Group 2 an increase is observed after approximately 150 km from the Finke River recharge area.Waters of Group 3 are most enriched in 4 He by three orders of magnitude in relation to air saturated water (ASW).Also here, sample 13 is an outlier with a lower 4 He concentration suggesting a shorter flow path from a westerly source as indicated by the potentiometric surface (Fig. 1, note no 4 He data are available for sample 19).

Stable isotopes
The stable isotope composition of the groundwater varies over a large range between −10.7 ‰ to −6 ‰ for δ 18 O and −74 ‰ to −43 ‰ and for δ 2 H (Table 1 and Fig. 4).The most depleted waters are from Group 1 close to the recharge area.Further downgradient (Group 2 & 3), the stable isotope composition is characterised by more enriched values.The best fit of the data has a slope of is 6.4 ± 0.2, while the deuterium excess (defined by δ 2 H -8×δ 18 O) decreases from +11 ‰ in the recharge area to +3.5 ‰ for the oldest waters.This indicates that groundwater that infiltrated in the past was subject to greater evaporation than the younger waters.This is also supported by the highest Cl concentrations found for Group 2 and Group 3 waters.However, it must be considered that part of the chlorine accumulated in the subsurface.This distinction is made in the discussion, taking into account the 81 Kr ages.

Groundwater residence times and flow velocities
The comprehensive set of dating tracers covering age ranges of decades ( 85 Kr) to centuries ( 39 Ar) to millennia's ( 14 C) and up to hundreds of thousands of years ( 81 Kr, 36 Cl and 4 He) along a groundwater flow path consistently indicate increasing residence time with decreasing piezometric heads and distance from the Finke River recharge area (Table 2).This unique dataset allows for the inter-comparison of the suitability of the different dating tracers, particular in relation to 81 Kr data, and for an understanding of the recharge and flow dynamic of this part of the GAB.The very old apparent residence times imply recharge over different climate periods.
In this paper, the term "tracer age" refers to the decay (or accumulation in the case of 4 He) time of the individual tracer that has been elapsed between groundwater recharge and the sampling location in the aquifer system.The distinct half-lives (and decay constants λ) of 39 Ar, 14 C and 81 Kr cover very different ranges of residence times, t.The 39 Ar, 14 C and 81 Kr percent modern values are converted directly to groundwater ages using the radioactive decay law: where C and C 0 are the measured and initial concentration respectively.For 39 Ar and 81 Kr, initial activities C 0 of 100 pmAr and 100 pmKr were assumed.An initial 14 C concentration of 86 pmC was calculated from the mean of samples with a detectable 39 Ar activity (samples 2, 3 and 8 in Fig. 8).From this initial value and from all measured activities an offset of 4 pmC was subtracted as outlined in Section 4.1.The resulting tracer ages for 39 Ar, 14 C and 81 Kr are listed in Table 2 and are compared in A fit through the decay ages of sampling points reveal the mean flow velocity between those sampling points, which is independent of the initial concentration C 0 (Fig. 6).Thereby it is assumed that the observed gradient of tracer concentrations along a flow line is mainly the result of aging rather than mixing of different water masses (i.e.piston flow).The age gradients are determined individually for 39 Ar, 14 C and 81 Kr (Fig. 6 A, B and C).For 14 C, two different slopes were calculated for the first part of the transect and the further downstream part, respectively.The fitting results are depicted in Fig. 6 and show a clear trend as function of flow distance, time and dating tracer.On short timescales and as calculated from the 39 Ar data a flow velocity of ∼90 m/yr close to the recharge can be derived.Downstream, the 14 C data indicate a further decrease of the flow velocity to ∼10.9 m/ yr up to ∼30 km, while further down gradient (∼ 30-90 km) flow velocities decrease to ∼4 m/yr.A similar pattern for the 81 Kr data can be observed where, on 81 Kr timescales of hundreds of thousands of years an average flow velocity of ∼1 m/yr can be concluded.Further downgradient (∼150-300 km) these decreases to ∼0.3 m/yr (Fig. 6).Fig. 6D, displays the various calculated velocities from the different tracers versus an analytical model of tracer velocity (see Section 5.2).The decrease of flow velocities (or increase of spatial age gradients) as function of flow and tracer timescales may have several reasons: • The assumption of conservative flow within the aquifer is not fulfilled.If significant quantities of water seep through the aquitards (leaky aquitards) the flow velocity within the aquifer would decrease according to the mass conservation law.The observed reduction of flow velocity along the flow line by two orders of magnitude would imply that 99 % of the recharge is lost by upward leaking through the aquitard.• Transient hydrodynamic conditions either due to naturally changing recharge rates and/or the change from pre-exploitation conditions to a situation with heavy groundwater abstraction would modify the age gradient within the system.A new tracer steady state in the whole system is only achieved after a transient phase during which the new hydraulic state propagates through the system (Rousseau-Gueutin et al., 2013;Zuber et al., 2010).However, if the mean groundwater age is large in comparison with the characteristic timescale of the changes in the system, as it is the case here, a hydrologic quasi-steady state can still be assumed.• Also, the progressive admixture of older water along the flow line would cause a faster aging along the flow than anticipated in a piston flow scenario.Towards the centre of the basin the regional flow directions from the western and the north-eastern recharge areas converge (Radke et al., 2000;Torgersen et al., 1991) which could cause an apparent spatial aging.
• Dominant recharge at a point source, as it is postulated in our study area today, into a 3-dimensional aquifer system would also lead to a decreasing flow velocity as function of distance from the source.
We judge the last possibility to be the most likely and this scenario is investigated in more detail in the following section.

Finke River recharge source
One of the key questions that remains unresolved in understanding ephemeral river recharge (ERR) in this part of the GAB is how long the Finke River has been a source of groundwater recharge.For the following analyses we hypothesize that the Finke River recharge zone is a point source.This seems reasonable considering that the section where the Finke River crossed the outcrops of the J-aquifer is only 36 km long and 350 m in width which is relatively small considering a transect distance of >300 km.Then, if we assume steady state groundwater flow in an aquifer with constant porosity and recharge from a point source with strength S (m 3 /yr) and the law of mass conservation it follows that: where v D (R) is the Darcy velocity and A(R) the cross section where groundwater moves as function of distance R from the point source (Fig. 7).The cross-sectional area A(R) may increase because of radial flow away from the point source (which is strictly not fulfilled) it follows from Eq. ( 3) that the local Darcy velocity, v D (R), decreases inversely proportional with distance R from the point source: v D R ð Þ∼ 1 R .For constant porosity ϕ, this Table 3 36 Cl and Cl parameters used in Eq. ( 8), where R SE = is the 36 Cl/Cl in secular equilibrium with the J sandstone aquifer R EX is the 36 Cl/Cl of the secular equilibrium of the external source R ERR is the 36 Cl/Cl input ratio of the ephemeral river recharge, R D is the 36 Cl/Cl input ratio of diffuse recharge component, and C ERR is the initial Cl concentration of the ephemeral river recharge.relationship is also valid for the water flow velocity v = v D / ϕ.Then, the total flow time T to a certain distance R from the point source is: implying that R(T) ∼ T 0.5 .Consequently, the flow velocity decreases as function of residence time T according to: Fig. 5. Column graph showing the comparison of possible tracer age ranges for 39 Ar, 14 C and 81 Kr for the various well locations (Tables 1 and 2).The length of the column represents the potential limits in the tracer's data as constrained by the measured value, the analytical uncertainty, and the half-life of the tracer.While 39 Ar is the best age constraint for the samples close to the recharge area (group 1), 81 Kr is the tracer of choice for the oldest waters.In the intermediate range (e.g., wells 4, 5) 14 C provides the best age constraint (smallest age bands).with n = 0.5.In a three-dimensional case (where H is also increasing with distance) n would be 0.66.The analytical model above is plotted against the observed tracer velocity data in Fig. 6D.We note that this distribution follows one that we would expect from a point source and conclude that our data are consistent with the presence of the actual Finke River recharge plume (Radke et al., 2000).Whether ERR was also the dominating recharge mechanism in the past or for group 2-3 waters cannot be concluded from the dating tracers alone.For this purpose, methods and tracers that are sensitive to recharge mechanisms are required.

Systematics of 36 Cl and Cl
If we accept that 81 Kr provides the most accurate chronology of old groundwater residence times of up to 400,000 years between the Finke River and Dalhousie Springs, we can then try to evaluate the temporal evolution of 36 Cl (expressed as the 36 Cl/Cl and Cl concentration) as well as the different source of chloride.The chloride mass balance as function of groundwater residence time can generally be expressed as (Bentley et al., 1986b;Phillips, 2000).
where, a: Measured 36 Cl concentration in the sample (atoms/L water) expressed as the product of 36 Cl/Cl ratio R and chloride concentration C.
b: Decay of the initial 36 Cl concentration in recharge water, which is defined by the 36 Cl/Cl ratio at recharge (R i ) and the initial chloride concentration C i .
c: In-growth of a secular subsurface equilibrium 36 Cl concentration within the aquifer, which is given by the equilibrium ratio R SE and the initial concentration C i .
d: 36 Cl accumulation due to the addition of Cl from subsurface sources (C a = C-C i ) with a 36 Cl/Cl ratio from the external source of R Ex.
If Cl behaves physically and chemically conservative (no sources or sinks of Cl within the aquifer) only the term b must be considered.However, even in this simple case, assumptions must be made about the local 36 Cl/Cl initial ratio R i which could vary spatially and temporally.Neutron activation of the dissolved 35 Cl by the reaction 35 Cl(n,γ) 36 Cl would continuously add 36 Cl atoms until a secular production decay equilibrium R se is reached, as described by term c.It is thereby again assumed that the Cl concentration in the water is constant over time.R Se can be estimated based on the elemental composition of the aquifer rocks (Lehmann et al., 1993).However, in the investigated part of the GAB the assumption of constant Cl concentration is not fulfilled (Fig. 9).The Cl concentration increases quasi-linearly with groundwater residence time at an apparent growth rate of ∼3.1 mg/L/kyr (Fig. 9).This increase can either be because of Cl accumulation from subsurface sources (Love et al., 2000) and/or due to changes of the initial chloride concentration C i as a result of varying evaporative enrichment at recharge time.
Without additional information from other tracers, it is impossible to separate both b and c processes (and 36 Cl dating is not possible in this case).However, our 81 Kr data now offer the unique opportunity to better constrain the Cl accumulation history and to deconvolute the relative importance of both processes as a function of groundwater flow time and distance.This information is not only crucial for the characterization of the accumulation processes along the flow path but also for the reconstruction of past recharge conditions which affect the evaporative enrichment of C i .This in turn, provides information about the dominant recharge mechanism as function of time i.e., the importance of ERR versus diffusive recharge.For this purpose, the initial 36 Cl and Cl concentration of the different recharge sources need to be defined.

Initial parameters
The initial 36 Cl/Cl at recharge must be estimated based on recent samples which infiltrated prior to 1950 to exclude the contribution of bomb derived 36 Cl to estimate groundwater residence times of old groundwater.Previous estimates (Love et al., 2000) concluded an average initial R i in precipitation and groundwater of 125 ± 10 × 10 −15 -600 km to the south-west of our study area.In this area, the dominant recharge mechanism is diffuse.
The best candidates in our study area are 85 Kr free samples (thus free of 36 Cl from the nuclear tests in the 1960's) with detectable 39 Ar and 14 C activities (therefore containing fresh recharge on the 36 Cl timescale).Almost all samples of Group 1 fulfil these criteria (Fig. 8).The highest 36 Cl/Cl ratio was measured at site 3 with a value of 91 ± 5 × 10 −15 .However, most samples with young 39 Ar and 14 C signatures have a much lower 36 Cl/Cl Fig. 7. Diagrammatic representation of the analytical model of a decrease of flow velocity of groundwater originating from a point source (Eq.( 5)).a) for constant aquifer thickness H (n = 0.5 in Eq. ( 5)) b) with linearly increasing H (n = 0.66 in Eq. ( 5)).ratio around 55-60 × 10 −15 (Figs. 3 and 8).Considering the half-lives of 36 Cl (310 kyr), 39 Ar (269 yr) and 14 C (5730 yr), 36 Cl decay can be excluded as the reason for the 36 Cl/Cl depletion of those samples compared to sample 3 or samples found elsewhere in this part of the GAB (Love et al., 2000 and Fig. 7).The admixture of old groundwater is also unlikely because Group 1 water are located close to the outcrop and presumed recharge area of the J aquifer and because the quasi modern 81 Kr activities do not indicate the presence of a substantial old water component (Fig. 3 and Fig. 6).
The only reasonable explanation is that the source of recharge is not direct precipitation, but water with a low 36 Cl/Cl due to the addition of chloride with a depleted 36 Cl signature .Indeed, water sampled along the Finke River (New Crown Station and Old Crown Town) showed 36 Cl/Cl of 60 × 10 −15 and 64 × 10 −15 , respectively (Fulton et al., 2013).The depleted 36 Cl/Cl ratio of the Finke River, compared to local precipitation, originates from halide dissolution e.g. from the Bitter Springs Formation which crops out along the Finke River further upstream (Fulton et al., 2013).That way ERR from the Finke River is tagged with an initial ratio R ERR = (60 × 10 −15 ) and a relatively low Cl concentration of ∼100 mg/L (C i ) Table 3. Significantly higher initial concentrations are likely due to a different recharge process, with initial ratio 36 Cl/Cl ratio (R D ) and chloride concentration (C D ).Confirming the finding of the previous dating section, this indicates that ERR dominates under present climate conditions with an initial 36 Cl/Cl ratio R i of 60 × 10 −15 as indicated by the mean of Group 1 samples (Fig. 2 and Fig. 8).The average Cl concentration of Group 1 is ∼100-200 mg/L which most likely represents the initial concentration C i for ERR (C ERR in Eq. ( 8)).Since ERR is a relatively rapid recharge mechanism, it is unlikely that the higher Cl concentrations found further down the groundwater flow path are caused by changes of C ERR in the past.The Cl increase of Group 2 and Group 3 samples further downstream may have two reasons: (i) temporal variations of environmental conditions triggering a different recharge mechanism that leads to higher Cl concentrations at recharge, or (ii) accumulation of Cl originating from subsurface sources.
In case of a more humid climate in the past, diffusive recharge over large surface areas would dominate and the initial R i would have been closer to the typical value of local precipitation (120-130 × 10 −15 ).This would also imply higher Cl concentrations at recharge C i .The potential 36 Cl evolutionary pathways are depicted in Fig. 10 where the 36 Cl/Cl ratios are plotted as function of the 36 Cl concentration.Also shown are the 36 Cl/Cl signatures of ERR, precipitation and data from other studies in the area (Love et al., 2000).Those data indicate diffuse recharge with a high initial ratio R i first followed by evaporative enrichment and then followed by a combination of Cl accumulation in the subsurface and radioactive decay (indicated by arrows in Fig. 10).The exact pathways to the data points are ambiguous without additional data (i.e., the solid and dashed paths in Fig. 10 are both possible).However, since evaporative enrichment for ERR is limited (crossed out arrow in the figure), it is clear, that data of group 2-3 must partly originate from diffuse recharge which is characterised be high a 36 Cl/Cl ratio of 120 × 10 −15 and elevated Cl concentration (and thus high N 36Cl ).With that, a new 36 Cl budget can be formulated in which the 36 Cl contributions from ERR and diffuse recharge are separated: The second term describes the ingrowth to secular production-decay equilibrium R se in the aquifer which also depends on the timing of the increase of Cl along the flow path which is a priori unknown.The factor of two assumes an 36 Cl in-situ production rate corresponding to a time averaged Cl concentration of C/2.Eq. ( 7) can be solved for the concentration C D contributed from diffusive recharge: Fig. 9 shows the resulting C D (t) and C a (t) = C-C ERR -C D (t) as function of the 81 Kr ages.Cl accumulation in the subsurface contributes about 2/3 to the observed Cl increase along the flow path.The chloride accumulation rate of ∼1.8 ± 1 mg/L kyr is consistent with values found in other studies in the western GAB (Lehmann et al., 2003;Love et al., 2000).Up to 400 mg/L Cl are attributed to changes of the initial Cl concentration at recharge C D , which first increases with groundwater age but levels off for the oldest waters as indicated in the figure.The groundwaters sampled towards the centre of the basin (group 2-3) are partly originating from areas with diffuse recharge under varying climatic conditions.This is strongly supported by the stable isotope data shown in Fig. 4a where a strong correlation between δ 18 O values and C D can be observed.Group 1 samples fall along the LMWL and are isotopically depleted.Moving away from the Finke River recharge plume, the isotope signature becomes more enriched along a line with slope 6.4.This correlation might be partly caused by evaporation but is rather a mixing line than an evaporation line as demonstrated in Fig. 4b.The shift in the stable isotope signature parallels an increase of the initial Cl concentration C D .Also shown are calculated evaporation and transpiration trends.Transpiration will increase the chloride concentration without affecting the δ 18 O but unrealistic large fractions of water need to be transpired to explain the observed scatter (Sultan et al., 2000).The slope of the evaporation line is too small to explain the observed variation in Cl concentration.This suggests that mixing of water that recharged at different conditions is going on and/or the additions of salt come from dust solutes dissolved during the recharge process (Sultan et al., 2000).Sample 19, for example, which has one of the highest Cl concentrations and a higher Cl accumulation rate is geographically separated from the main transect towards the south.According to the recent piezometric head distribution (Fig. 1) the water originates from a recharge area further south where there is no evidence for any ERR source water (Love et al., 2000) and Fig. 10.

Origin and rate of accumulated helium
The isotope signature of accumulated helium indicates two distinct endmembers: atmospheric helium with a 3 He/ 4 He ratio of air saturated water (ASW) (1.36 × 10 −6 ) plus a radiogenic component (Fig. 11a).A linear fit in the 3 He/ 4 He vs. Ne/ 4 He plot reveals a ratio of 1.5 × 10 −8 for the radiogenic components which is typical for crustal production (Stute et al., 1992).No mantle helium contribution is indicated by the data.
Using the Ne excess (ΔNe) from excess air (Table 2) and assuming a recharge temperature and elevation of 20 °C and 400 m respectively, the fraction of radiogenic 4 He rad can be calculated (Kipfer et al., 2002) which is plotted in Fig. 11b as a function of 81 Kr derived tracer ages.There is a systematic increase of 4 He rad with increasing 81 Kr age which highly supports the chronology of 81 Kr ages and is indicative for a relatively homogeneous groundwater flow path.The 4 He in-situ accumulation rate (A He ) can be calculated based on the [U] and [Th] concentrations of the aquifer rocks of 0.8 ppm and 6 ppm respectively (Andrews and Lee, 1979;Lehmann et al., 2003), an aquifer density of ρ = 2.6 g/cm 3 , a porosity of ϕ = 0.2, and a helium release factor of 1 into the water filled pore space (Mazor and Bosch, 1992).
The resulting helium in situ accumulation rate A He of 4 × 10 −12 cm 3 STP / g w /yr, is depicted in Fig. 11b.
It is obvious that in-situ production is not sufficient to explain the observed 4 He increase rate, a situation found in other aquifers (Aggarwal et al., 2015;Torgersen, 2010;Torgersen and Clarke, 1985).In particular for the samples further away from the recharge area (group 2-3 waters), the helium accumulation rate exceeds the expected value from in-situ production by almost two orders of magnitude, which is in line with observations made in other parts of the GAB.Torgersen and Ivey, (1985) proposed a model in which an external 4 He flux of 3 × 10 −6 cm 3 STP / cm 2 /yr originating from the underlying strata enters the aquifer from below.Their model assumes a transversal dispersion coefficient of 0.1 m 2 /yr and 4 He no-flow upper boundary (Torgersen and Ivey, 1985).This leads to a nonlinear 4 He accumulation rate with age and flow distance with a transition from an in-situ accumulation rate to an accumulation rate determined by the basal 4 He flux strength.The point in time (and flow distance) where the transition occurs is determined by the depth of the screened borehole interval in relation to the total depth of the aquifer.A borehole that intersects only the upper part of the aquifer "sees" the basal 4 He flux later than a well completed deeper in the formation.The corresponding model line for an aquifer thickness H = 400 m and a well tapping to the top layer of the aquifer is shown in Fig. 11b.There is a reasonable agreement between the Torgersen and Ivy model and the data, also the transition point to the higher accumulation rate between groups 1 and 2 waters is well represented.Thus, our 81 Kr data support the general concept of a (crustal) He influx as developed in the past at other parts of the GAB (Torgersen and Clarke, 1985;Torgersen and Ivey, 1985).Other scenarios where e.g. the source of 4 He (and chloride) occurs in the overlying Bulldog Shale (Lehmann et al., 2003;Love et al., 2000) or in impermeable layers within the aquifer which pre-accumulated 4 He in the past cannot be completely excluded but are less supported by the data.The good correlation between the concentration of radiogenic helium 4 He rad and the reconstructed chloride accumulation (C a ) points to a common source and transport process of helium and chloride (Fig. 11c) (Lehmann et al., 2003;Zhang et al., 2007).

Conclusions
The quantification and reconstruction of amount and mechanism of groundwater recharge in arid areas is fundamental for the life and economies in those areas.Such aquifers typically include a very large range of groundwater residence times and different climatic zones in the recharge regimes over time.However, the characterization of the age structure of groundwater over extended spatial and temporal scales is a very difficult task.Various tracers need to be combined which cover different dating ranges, but which are also affected by different process that may affect the interpretation in terms of groundwater residence times.One of these is changing recharge conditions which can only be deconvoluted if multiple tracers covering the same time scales are applied.In this study a complete tracer set in incrementally increasing half-lives and dating ranges from decades to millions of years was applied to a large aquifer along a presumed groundwater flow path.In order of increasing dating range this includes the measurements of 85 Kr, 39 Ar, 14 C, 81 Kr, 36 Cl and 4 He rad .This unique combination with partly overlapping and complementing dating ranges allows for a deeper understanding of the hydrogeology of the studied area, and also for the first time, for a comprehensive comparison and assessment of the age information obtained by different applied dating methods.
Generally, the data indicate a consistent age chronology with distance from the Finke River recharge area.The continued increase of groundwater residence times with distance from the Finke River implies the existence of a connected flow system in contrast to the possibility of having partly isolated subsystems.Flow velocities determined by the spatial gradients of the concentrations of 39 Ar, 14 C and 81 Kr decrease with increasing halflife of the used tracer and thus with increasing distance from recharge area.Despite the inherent uncertainties of the individual dating methods this is attributed to a diverging mass flow from a localized recharge point.In the investigated western part of the GAB ERR was the dominant recharge mechanism over long timescales.In the down gradient part of the system where groundwater residence times exceed 100,000 years as indicated by the 81 Kr data the influence and contribution of ERR becomes less important due to the admixture of water originating from other recharge areas.At such timescales transient recharge conditions, water rock interaction, hydrodynamic dispersion and diffusive exchange with the aquitards become increasingly important.As already pointed out in other studies (Phillips, 2000;Phillips et al., 1986) the application of 36 Cl for old groundwater dating is highly complicated in this part of the GAB because the initial parameters R i and C i are not well defined and variable due the multitude of processes and recharge mechanisms which may affect those parameters.
The 81 Kr dating methods allowed deconvoluting the complicated 36 Cl/ Cl systematics in this part of the GAB.The 36 Cl data underpin the decreasing influence of ERR towards the centre of the basin, where groundwater originating from diffuse recharge becomes more important.Varying recharge conditions and related recharge mechanisms are also reflected in variations of the stable isotope signature of the water molecule and the chloride concentration at recharge.However, >50 % of the observed chloride increase along the flow line is caused by subsurface processes.This Cl accumulation rate is accompanied by increasing 4 He rad concentrations.The rate as well as the temporal and spatial pattern of the 4 He concentrations is in good agreement with the assumption of a previously postulated crustal helium flux entering the system from underlying strata.Diffusive exchange with those layers may also affect the 81 Kr ages, but was neglected in this study (Purtschert et al., 2013).This work also demonstrates the potential of very old groundwater as an archive of paleoclimate conditions over long timescales.The 81 Kr dating method not only provides a reliable age chronology but also increases the potential for meaningful climate proxies such as the Cl and stable isotope concentration at time of recharge.

Fig. 1 .
Fig. 1.Map of the study area showing the different groundwater groups.The dashed line represents the potentiometric contours (Rousseau-Gueutin et al., 2013) where the generalised direction of groundwater flow is at right angles to these contour lines.A-B represents the hydrogeological cross section.The boundary between confinedunconfined conditions is also shown.

Fig. 2 .
Fig. 2. Tracer -Tracer plots showing the comparison of tracers with sequential half-lives.Red circles represent Group 1 close to the recharge zone, the green triangles represent the intermediate wells of Group 2 while the blue triangles represent the most distal wells of Group 3. The black square represents a well most likely from a more westerly recharge zone.

Fig. 5
with age bands considering the analytical uncertainties.The Figure demonstrates consistent tracer ages for most wells without consideration of mixing, but it becomes also obvious how the application of tracers with suitable half-life reduces the age uncertainties for the individual age ranges.

Fig. 3 .
Fig. 3. Tracer concentrations versus distance from the Finke River Recharge area (RA).The top left-hand panel shows the location of the wells as a reference.Note all the tracers show an increase in age with distance travelled along the transect.

Fig
Fig. 4. a) Plot of stable isotopic composition of the water molecule in δ 2 H-δ 18 O space.The dashed-dotted line is the global meteoric water line (GMWL) δ 2 H = 8δ 18 O + 10, the dashed line represents the local meteoric water line (LMWL) δ 2 H = 6.9 δ 18 O + 4.5 (Harrington et al., 2013), while the solid red line represents the best fit through the data.b) Displays the relationship between the δ 18 O and the Cl concentration at recharge.The evaporation line was calculated for an equilibrium liquid-water fraction factor ε = 1 % and an initial composition of C D,0 = 5 mg/L and − 10.5 ‰ respectively.

Fig. 6 .
Fig. 6.Groundwater flow velocities as function of groundwater residence times and corresponding dating tracer.Flow velocities were determined from the age gradient of the various tracers, (A) 39 Ar gradient close to the recharge area, (B) 14 C shows the two different velocities close to the recharge area (< 30 km and at 30-90 km).(C) the 81 Kr data displays two different groundwater velocities.As can be observed all flow velocities decrease with increasing distance along the groundwater flow path.(D) compares the calculated flow velocity of the different tracers (blue column) versus the analytical model of a point source in an aquifer of constant (n: 0.5, red columns) or linearly increasing (n: 0.66, green columns) thickness.See Fig. 6 and text for details of the model.A decent agreement between the data and the model can be observed.

Fig. 8 .
Fig. 8.Comparison of 39 Ar (solid symbols) and 14 C activities (open symbols) versus the 36 Cl/Cl ratio.Colours indicate the different well groups as defined in Fig. 1.The dashed line represents the 36 Cl/Cl input function.

Fig. 9 .
Fig. 9. (a) Measured chloride concentration as function of 81 Kr ages, (b) Calculated Cl (C a ) accumulated in the subsurface and (c) Calculated Cl that was already present at recharge (C i ) as a function of 81 Kr ages.The dashed lines in a) and b) represent different Cl accumulation rates as a function of 81 Kr ages.

Fig. 10 .
Fig. 10. 36Cl/Cl ratios vs 36 Cl concentrations (N 36Cl ) in the study area.Also shown are data from Love et al., 2000.The northern transect wells were sampled 500 km to the southwest of the Finke River recharge zone while the southern transect wells were approximately 700 km to the southwest of the recharge zone.Red dots represent wells close to the recharge zone, green intermediate and blue distal samples from the recharge zone.Arrows indicate potential shifts due to different processes.Evaporative enrichment in water components originating from diffuse recharge is the only process that can significantly increase the 36 Cl concentration.Accumulation of Cl from subsurface sources mainly shifts the 36 Cl/Cl ratio to lower ratios but leaves the 36 Cl concentration unchanged.The 36 Cl/Cl signatures of group 3 waters (blue triangles) likely originate from diffuse recharge.Group 2 waters represent a mixture of ERR and diffuse recharge.

Fig. 11 .
Fig. 11.a) 3 He/ 4 He ratio versus Ne/ 4 He, ASW = air saturated water b) 4 He accumulation with time.The solid line shows the calculated evolutions for in-situ production only (blue) and the black dashed line represents the best fit for the model of Torgersen and Ivey (1985) (for model assumptions see text), c).Radiogenic 4 He rad versus in the subsurface accumulated chloride C a .

Table 2
Dating tracers, Helium data and decay tracer residence times.* 85 Kr activities interpreted as contamination and used for 81 Kr correction.