In this study, we sampled 302 groundwater samples across New Zealand from over 20 aquifers, ranging from highly anoxic to oxic conditions (Fig. 1). Not all age tracers were determined at all 302 sites, as is summarized in Table 1. To prevent sampling of stagnant water, the well was flushed with at least three times its volume or until DO and EC stabilized. Tritium was analysed in 1 L water samples, using electrolytic enrichment and liquid scintillation counting (LSC) detailed in Morgenstern and Taylor (2009). For analysis of the gaseous tracers Halon-1301 and SF6 as well as the CFCs, groundwater was sampled under rigorous exclusion of air to avoid contamination of the samples with modern air (Oster et al., 1996). For determination of CFC-11, CFC-12 and CFC-113, 125 mL glass bottles with aluminium foil cap liners were used. For determination of Halon-1301 and SF6, 1 L brown borosilicate bottles were used. The sampling methods are detailed in van der Raaij and Beyer (2017). The gas samples were subsequently purged and analysed on a gas chromatograph with attached electron capture detector (GC/ECD). Simultaneous analysis of Halon-1301 and SF6 is detailed in Beyer et al. (2014, 2015). The analytical setup for determination of Halon-1301 and SF6 also allowed the simultaneous determination of CFC-12 (Busenberg and Plummer, 2008; Beyer et al., 2014; Bartyzel and Rozanksi, 2016). However, an appropriately concentrated standard gas is needed to establish its calibration curve. CFC-12 concentrations were therefore not determined simultaneously with Halon-1301and SF6 in this study. CFC-12 was analysed separately, together with CFC-11, CFC-113, Ar and N2, as described in van der Raaij and Beyer (2017).

The amount of gaseous tracers in all groundwater samples was determined by establishing a calibration curve (least-squares fit, forced through 0/0) with certified air standard at various pressures. We analysed blank samples (only containing N2), which indicated 0 signal for SF6 and Halon-1301. In addition, the statistical difference between the intercept of the calibration curves for SF6 and Halon-1301 (when not forced through 0/0) were not significant (at 99 % confidence). The intercept of the calibration curve was therefore considered insignificantly different from 0, and hence the calibration curve was forced through 0/0 to simplify the calibration procedure and to ensure 0 signal is interpreted as a concentration of 0 (fmol L-1, for example). This procedure follows the suggestion of Helsel and Hirsch (2002) and Caulcutt and Boddy (1983).

The compositions of the certified air standards for analysis of Halon-1301 and SF6 (supplied by the NOAA in 2014) and for analysis of the CFCs (supplied by the Scripps Institution of Oceanography in 2011) are summarized in Table 2. A calibration curve was established every day before measurement commenced, since the performance of the GC/ECD can change from day to day, due to fluctuations in the environment (e.g. temperature) or aging of the material (e.g. column fill). If applicable, the amount of gaseous tracers in the water sample were corrected for headspace and/or excess air (by dissolved Ar and N2 determination described in Heaton and Vogel ,1981). We note that that method is sensitive to excess N2 produced, for example, by denitrification. We determined the presence of excess N2 (as a product of denitrification) on the basis of anomalously high inferred recharge temperatures determined from N2 / Ar ratios. Specifically, we identified samples for which the inferred recharge temperature were significantly higher than the mean annual air temperature at that location (using climate data from NIWA National Climate Database, 2016). Assessment of the performance of Halon-1301 as a groundwater age tracer at these sites allows for assessment of degassing into excess N2 as a possible cause of reduced Halon-1301 concentrations.

The equivalent atmospheric molar ratio at time of equilibrium (for groundwater samples at recharge) was determined using the solubility relationship or Clarke–Glew–Weiss fit (Warner and Weiss, 1985) given in Eq. (1). The solubility fit parameters for Halon-1301, SF6, CFC-11, CFC-113 and CFC-12 are summarized in Table 3. In contrast to the solubility of the CFCs and SF6, which have been well studied and directly measured (Bullister et al., 2002; Wilhelm et al., 1977), the solubility parameters of Halon-1301 have only been estimated by Deeds (2008), using the solubility estimation methods of Meylan and Howard (1991) and Meylan et al. (1996). Actual solubility measurements of Halon-1301 are not available in the literature (according to our searches and further backed up by D. Deeds, personal communication, 6 March 2015). In our previous study (Beyer et al., 2015), we used modern (equilibrated tap and river) water to estimate solubility and to validate the solubility estimates. In this study, we confirmed our previous estimate by using solubility estimated from four additional modern (river) water samples. lnKx=A+B100T+ClnT100, with Kx as solubility (estimated as either a Henry (KH), Bunsen (KB) or Ostwald (KO) coefficient), T as recharge temperature (in K) and A,B,C as solubility fit parameters, given in Table 2. A salinity term can be added to Eq. (1), but this is negligible for most groundwater applications and so is ignored here.

To determine analytical uncertainty, the EURACHEM/CITAC Guide CG4 (Ellison and Williams, 2012) was followed. Analytical uncertainty included the following uncertainties related to the following:

the least square regression (calibration curve),

Uncertainty related to solubility is unknown or has never been reported, so it was not considered in this study. Uncertainty of the solubility of Halon-1301 is relatively high, approx. 10 % (Beyer et al., 2015), and therefore would add 10 % to the total analytical uncertainty for the determination of Halon-1301. We believe that Halon-1301's solubility will be determined with sufficient precision and become available in the near future. To enable comparison of Halon-1301's performance as an age tracer compared to other tracers after availability of a sufficiently accurate solubility value, we did not include the currently high uncertainty in its solubility in the following analysis. For the interested reader, the effect of the uncertainty on the age estimate when adding 10 % uncertainty for solubility is shown in Beyer (2015).

To infer the recharge year or residence time of the groundwater, the equivalent concentration of tritium, Halon-1301, SF6 and the CFCs in the atmosphere at the time of recharge (determined as described above) was compared to their historic atmospheric records (illustrated in Fig. 2). For tritium, radioactive decay is also applied, with its half-life of 12.32 years. Southern Hemisphere atmospheric SF6, CFC-12, CFC-113 and CFC-11 records are available at the GMD/NOAA (http://www.esrl.noaa.gov/gmd/; Thompson et al., 2004) and CDIAC websites (Miller et al., 2008); data from 1973–1995 have been reconstructed by Maiss and Brenninkmeijer (1998). Southern Hemisphere (Cape Grim) atmospheric Halon-1301 concentrations have been summarized and smoothed by Newland et al. (2013). Data from 1969 to 1977 have been reconstructed by Butler et al. (1999). Tritium records for New Zealand are available at Kaitoke, New Zealand. Since seasonal variability of groundwater recharge can affect tritium recharge to groundwater, the tritium recharge is often estimated using recharge weighting techniques (Allison and Hughes, 1978; Stewart and Taylor, 1981; Engesgaard et al., 1996; Knott and Olipio, 2001). Morgenstern et al. (2010) showed that this is less of a problem in New Zealand, because infiltration is relatively constant through the seasons and the summer gap in infiltration occurs at average tritium concentration in rain, so there is little bias. We therefore did not weight the tritium input in this study. However, the tritium input function was scaled according to elevation and altitude (Morgenstern et al., 2010; Stewart and Morgenstern, 2016).

To account for mixing of waters of different age in the aquifer or during sampling, LPMs were used (Małoszewski and Zuber, 1982). The use of LPMs allows inference of an age distribution rather than the mean or apparent age of a groundwater sample. The age distribution is increasingly used as an indicator for quality and contamination risks (e.g. the New Zealand drinking water standard (Ministry of Health, 2008) and the European Water Framework Directive EU Legislature, 2000). Since we did not have reliable estimates of the best-fitting LPM, we initially used a range of LPMs to tests the tracers' performance to infer age. Specifically, the exponential piston flow model (EPM), the dispersion model (DM) and the partial exponential model (PEM) were used (Eqs. 2 to 4). However, since the performance of the age tracers was very similar for the different LPMs employed, we only present results with regard to the EPM. EPM:for′>MRT(1-1n),fEPM=nMRT⋅exp⁡(-n⋅t′MRT+n-1);elsefEPM=0, with MRT = the mean residence time and n= the reciprocal of the ratio of exponential in total flow, which we refer to as E / PM = 1/n, the ratio of exponential to total flow in the following (n has been defined as a ratio of total to exponential flow after Małoszewski and Zuber, 1982). At E / PM = 0 pure piston flow is obtained, and at E / PM = 1 pure exponential flow is obtained. The EPM matches tritium time series data well and therefore is the most commonly used LPM in New Zealand (Morgenstern and Daughney, 2012). DM:fDM=1MRT×14πDPt′MRT×e-1-t′MRT24DPt′MRT

The DM conceptualizes one-dimensional advection–dispersion, with DP as the dispersion parameter (which is defined as DP =Dvx with D as the dispersion coefficient), v as velocity and x as outlet position. When DP = 0, piston flow behaviour is obtained. PEM:fort′>MRTaq⋅ln⁡(m),fPEM=mMRTaq⋅exp⁡-t′MRTaq;elsefEPM=0, where MRTaq=MRTsln⁡m+1, MRTs is the MRT of the sample and m is the reciprocal of the ratio of sampled to total volume (P / EM). This version of the PEM conceptualizes mixing of water in an aquifer that can be described by the exponential model (EM) with only part of the well being screened and/or sampled. At n= 1 (for wells screened across the entire aquifer) the EM is obtained.

To quantify uncertainty in the inferred LPM parameters as a result of uncertainties in the determination of the tracers in groundwater, age modelling was placed into a probabilistic framework, illustrated in Fig. 3. The framework included the generation of tracer concentrations by random sampling of the model inputs from within their uncertainty. LPMs which generated tracer concentrations within ±1 SD of observations were considered as behavioural, i.e. adequately fitting and representative. The remaining LPMs were considered as non-behavioural and were disregarded. Consequently, and in contrast to the commonly inferred single LPM parameter point estimate, age information in this study is determined as behavioural LPM parameter populations (i.e. clouds of MRTs and mixing parameter pairs that produce tracer concentrations within ±1 SD of the observation) illustrated in Fig. 4.

For this study, we considered only uncertainty in the determination of the tracers (i.e. analytical uncertainty, determined as described above). This commonly used approach may underestimate the uncertainty in the age interpretation, but gives a first insight into the performance of Halon-1301 as an age tracer compared to other, better established age tracers. For a more comprehensive analysis, all model uncertainties, such as the uncertainty in the tracer's recharge estimate, as well as assessment of the appropriateness of model components, need to be included in the uncertainty modelling approach, as demonstrated in Beyer et al. (2017), Beyer (2015), Green et al. (2014), Massoudieh et al. (2012, 2014) and Timbe et al. (2014).

Figure 4 illustrates examples of behavioural age interpretations (i.e. population or cloud of LPM parameters that produce tracer concentrations within ±1 SD of the observation) for three sites determined with two tracers. To assess whether Halon-1301 gives comparable age estimates to the ones inferred from SF6, CFC-12, CFC-11 and tritium, we determined whether the inferred LPM parameters populations overlapped (i.e. agreed). No overlap of the inferred LPM parameter clouds implies that the two tracers give differing results which cannot be brought into a 1σ agreement with any parameter combination. If they were non-overlapping, we determined the shortest distance of inferred LPM parameter populations as a measure of difference. As a measure of the shortest distance, we determined the nearest neighbour and minimum Euclidian distance between two data clouds in MATLAB software (Muja and Lowe, 2009). From that, the percentage difference in MRT and the mixing parameter inferred with two tracers (e.g. SF6 and Halon-1301) was determined as follows: Δε%MRT=dmin⁡tracer1,tracer2meanMRTtracer1,MRTtracer2⋅100.

We note that a variety of objective or fitting functions is increasingly used in the hydrological modelling community, suggesting that there is no one criterion that should be applied everywhere (e.g. Beven and Binley, 2014). The general applicability of the approach suggested here (using 1σ and 10 % distance criterion) needs to be assessed further on other datasets.

We decided not use the widely applied one-dimensional comparison of MRTs inferred from different tracers (i.e. MRT(tracer1) versus MRT(tracer 2) plots), since this type of comparison may result in misleading interpretations of the agreement or disagreement between age information inferred from the different tracers. For example, for site C illustrated in Fig. 4, one may conclude that both tracers' inferred MRTs agree. However, when assessing the behavioural MRT and mixing parameter population in Fig. 4, it is evident that both tracers' age interpretations do not agree (i.e. the LPM parameter clouds do not overlap), although the tracers give similar MRT estimates.

The estimated solubility of Halon-1301 using modern equilibrated water samples in this study was comparable to the solubility estimated previously (Beyer et al., 2015); see Fig. 5. We therefore considered the use of the previously estimated solubility coefficients as reasonable for estimating equivalent atmospheric mixing ratios from concentrations of Halon-1301 in water (procedure described in Sect. 2). To more accurately determine the solubility of Halon-1301 and reduce uncertainty in its determination, further study is needed (also pointed out in Beyer et al., 2015). Accurate measurement of the solubility of Halon-1301 is beyond the scope of this study, as specialized equipment is required due to its extremely low solubility.

In the following, we discuss age interpretations when employing the EPM only. We note that although the EPM is the most commonly employed LPM in New Zealand and other places around the world, we could not with confidence exclude that groundwater mixing at the studied sites is better represented by the DM, PEM or other more complex models, because time series age tracer data are lacking for the vast majority of assessed sites. However, very similar conclusions in terms of the tracer's age interpretation and agreement or disagreement of the inferred age information can be drawn when using the DM and PEM.

Halon-1301 data were limited to one measurement at each site (Halon-1301 has only recently been discovered). Time series SF6, tritium and CFC data, although available for a few sites, were not employed in this study. We decided to use only one observation at each site for each tracer to infer age, allowing an unbiased comparison of the tracers' performance as age tracers. As a result, relatively large uncertainties in inferred age information were obtained, as is subsequently shown. To constrain the uncertainty in inferred age information further and assess the value of time series Halon-1301 data, we are aiming to collect and analyse time series Halon-1301 data in New Zealand groundwater for a direct comparison of time series Halon-1301 and other tracer data.

We emphasize that one should not conclude that the assessed age tracers are not useful because the uncertainties in the age interpretations presented in this study appear large. Instead, this study reiterates what is increasingly recognized in the literature – that there may be issues related to uncertainty in the age estimate and that one needs to apply multiple tracers or time series tracer data to better constrain age information (Cook and Herczeg, 2000; Gooddy et al., 2006). Further, this study does not attempt to discuss which tracer has the lowest uncertainty in its age interpretation, as this is a complex matter. The uncertainty in the tracer's age estimate is dependent on multiple factors; these include the conditions the tracers' input function (this is dependent on the location of the site), groundwater age and mixing (i.e. the age distribution) at the particular site, in addition to sampling conditions and uncertainty in the determination of the tracers in groundwater. This study only compares Halon-1301 ages with other tracer ages.

First we compared inferred CFC ages with those inferred from tritium to identify the CFC that gives the most reliable age estimates. Misleading CFC age estimates are a common problem (Shapiro et al., 1997; Bartyzel and Rozanksi, 2016; Stewart and Morgenstern, 2001), because CFCs are prone to degradation and contamination. Thereafter, we assessed the performance of Halon-1301 as an age tracer relative to tritium, SF6 (assuming that SF6 and tritium give the most reliable age estimates) and the CFC that has been found “most reliable” in this study (CFC-113). We use the term inferred “age” as a synonym for inferred “age interpretation”, referring to the cloud of behavioural EPM parameters (Fig. 4).

Figure 6 illustrates typical LPM parameter populations that were inferred based on the CFCs and tritium (refer to the figures in Appendix A for details). For the majority of assessed groundwater samples, the CFCs gave similar age estimates to tritium. However, 29 and 38 % of the sites were contaminated or degraded in CFC-12 or CFC-11, respectively, which made it impossible to reliably infer age from the CFCs at these sites. CFC-113 performed considerably better than the other CFCs, with only some (5 %) of the sites being contaminated with CFC-113 or (12 %) degraded in CFC-113. CFC-113 is therefore considered the most reliable age tracer of the three CFCs in this study.

Figure 7 confirms that SF6 is more reliable than the CFCs. At 94 % of the sites, where both tritium and SF6 data were available, SF6 and tritium MRTs matched. Only six sites were contaminated with SF6. SF6 concentrations of these samples were at least 15 % higher, but in some cases several hundred percentage points above current-day atmospheric concentrations. For these samples, comparison of SF6 and Halon-1301 inferred MRTs was not possible. At all except one of these sites, matching Halon-1301 and tritium inferred MRTs were found. At that one SF6-contaminated site where the Halon-1301 and tritium inferred MRTs did not match, evaluation of tritium data was inconclusive, as it gave an ambiguous age interpretation (suggesting the water could be either very young,< 2 years, or older, > 50 years). That site was Halon-1301-free (and also free of CFC-11 and CFC-12), suggesting the water is older than ca. 75 years. Further, CFC-113 concentrations at this site were very low, suggesting that the water is older than 50 years, which does align with CFC-12, CFC-11 and Halon-1301 data suggesting this site may not be degraded in Halon-1301, although we cannot exclude that the CFCs may be degraded too (this is an anoxic site).

In the following, we further discuss the performance of Halon-1301 as an age tracer in comparison to SF6, tritium and CFC-113. Of particular interest was the magnitude of occurrence of reduced Halon-1301 concentrations and their possible cause. In our previous study, we concluded that the most likely reasons for reduced Halon-1301 concentrations are degradation and sorption of Halon-1301 to aquifer material (Beyer et al., 2015). To further assess the reasons for Halon-1301 reduction in groundwater in this study, we studied the groundwater environment (i.e. redox state and excess N2) and compared the performance of Halon-1301 with that of the CFCs more closely in samples that indicated presence of reduced concentrations of Halon-1301 compared to tritium and SF6.

Figure 8 illustrates typical LPM parameter populations that were inferred from SF6, Halon-1301, CFC-113 and tritium data in this study (figures for all sites are presented in Appendix A). As mentioned previously, we found that the inferred LPM parameter populations were relatively large for most sites, and most tracers, particularly the mixing parameter (E / PM), was difficult to constrain. This is mostly due to the use of only one tracer observation to infer age at each site, which cannot sufficiently constrain the uncertainties in the LPM parameters. To reduce the uncertainty in the inferred LPM parameters further, time series tracer data are needed and/or multiple tracers need to be applied complementarily.

Overall, none of the samples indicated significantly elevated Halon-1301 concentrations (i.e. > 10 % reduced Halon-1301 inferred ages, or concentrations above 10 % of modern-day air). This finding is in line with our previous finding, suggesting the absence of local sources of Halon-1301 that could lead to contamination of Halon-1301 in groundwater. Considering that these sites cover a large fraction of New Zealand's groundwater systems, Halon appears to not be impacted by geologic or anthropogenic local sources in general.

Figure 9 illustrates that 99 % of the sites where both tritium and Halon-1301 have been determined showed matching tritium and Halon-1301 inferred ages (±10 %). Since tritium is seen as one of the most reliable age tracers in New Zealand (mentioned previously), this finding is really positive, suggesting Halon-1301 is equally as reliable as tritium at 230 sites, although at 90 sites significant difference in E / PM (> 10 %) were found (Fig. 9), which can be related to both tracers' input functions. Specifically, as tritium input is a pulse function, it is easier to constrain the mixing model (mixing parameter). Halon-1301, however, has an S-shaped input, making it more difficult to constrain the mixing model (mixing parameter). We note that with SF6, with its near-linear input from 1985 onwards, we expect that constraining of the mixing parameter is even poorer than with Halon-1301, which is assessed subsequently.

At 79 % of the sites where comparison between Halon-1301 and SF6 inferred ages was possible (i.e. where both SF6 and Halon-1301 were determined and SF6 was not contaminated), inferred Halon-1301 MRTs agreed within ±10 % of the SF6 inferred MRTs (Fig. 10). E / PMs inferred from Halon-1301 also agreed with the ones inferred from SF6 at the majority of sites. Further, Fig. 8 (and Appendix A) suggest that in most cases Halon-1301 can constrain the mixing parameter and the MRT better than SF6, as indicated by the generally “narrower” LPM parameter ranges inferred with Halon-1301, although the difference was not statistically significant. We note that in any case, time series tracer data are necessary to better constrain the mixing parameter and allow a more conclusive comparison of the tracers' performance as age tracers.

For the remaining 21 % of the samples (where comparison of both SF6 and Halon-1301 was possible), Halon-1301-inferred ages were elevated compared to the ages inferred from SF6. In the following, we assess whether Halon-1301 is likely to be reduced at these sites (summary shown in Table 4).

At 39 of these 62 sites where Halon-1301 inferred MRTs were elevated compared to SF6, tritium inferred ages agreed with the Halon-1301 inferred ages (±10 %). This suggests that concentrations of Halon-1301 in these samples were not reduced, despite elevated Halon-1301 inferred MRTs compared to those inferred using SF6. For only one of the remaining sites, the Halon-1301 inferred MRT was also elevated compared to the MRT inferred from tritium, suggesting reduced concentrations of Halon-1301 were present in this sample.

The remaining 22 sites at which Halon-1301 inferred MRTs were higher than those inferred using SF6 did not have tritium information. CFC-113 and CFC-12 inferred MRTs at only two of these sites agreed with Halon-1301 inferred MRTs, suggesting that at these sites Halon-1301 reliably infers groundwater age. At 10 of the remaining 21 sites, CFC-113 data were unavailable. At 5 of these 10 sites, Halon-1301 inferred MRTs agreed with those inferred with CFC-12 (and at one site also with CFC-11). Although two of these five samples were anoxic and CFCs are also known to degrade under anoxic conditions, the fact that age interpretations inferred from Halon-1301 or CFC-12 data match at these sites suggests that these sites are not likely degraded in Halon-1301 (or CFC-12), but further data are needed to confirm this exclusively.

At the remaining five of the seven sites, both CFC-12 and CFC-11 data were unavailable (in addition to unavailable tritium and CFC-113 data). As we do not have further data, we cannot exclude that Halon-1301 concentrations are reduced in these samples. Anoxic conditions in two of these samples could suggest that degradation of Halon-1301 occurred at these sites, but further data are needed to confirm this supposition.

In summary, this leaves 10 sites with likely reduced concentrations of Halon-1301 (as per comparison to tritium and CFC-113), of which 7 are anoxic, 2 have an unknown redox state, and 1 is oxic. At the one oxic site, it is unlikely that reduced concentrations of Halon-1301 were caused by degradation, suggesting that degradation may not (at least solely) be causing a reduction in Halon-1301 concentrations. Sorption in the aquifer remains a possible reason, also suggested by the relatively high MRT (12 years for Halon-1301 and 25 years for SF6). However, mixing of anoxic and oxic water at this site may have occurred, or the redox state may have been otherwise wrongly evaluated. Another possible cause of reduced concentrations at this one oxic site is uncertainties in the solubility of Halon-1301 and uncertainties in the input of Halon-1301 (due to its relatively flat atmospheric concentration over the last 5 years). At the remaining anoxic sites (10 sites or 3 % of the assessed sites), the lack of oxygen strongly suggests degradation of Halon-1301 that can only occur under anoxic conditions.

Discrepancies in recharge temperature to mean recharge temperature of the region suggesting excess N2 were found in 29 sites. Of these, 25 showed matching SF6, Halon-1301, CFC-12, CFC-113 and tritium inferred ages, suggesting that degassing into headspace created by denitrification did not affect any of the gaseous tracers at these sites. At the remaining four sites, Halon-1301 inferred MRTs were significantly different to CFC-113 and SF6 inferred MRTs. However, at these four sites Halon-1301 inferred MRTs matched those inferred from CFC-12 (tritium was unavailable at two of these sites: one of which had Halon-1301 inferred MRT and was different to that inferred with tritium, and the other in which Halon-1301 inferred MRT matched that inferred from tritium). This suggests that degassing did effect the gaseous tracers, the most the least soluble ones (SF6 and CFC-113). Halon-1301 (and similarly CFC-12) appear to be less affected by degassing into headspace created by de-nitrification, production of methane or when groundwater is brought to the ground surface, making it a more reliable age tracer than SF6 and CFC-113 in these environments.

In summary, our findings suggest that Halon-1301 performed well as an age tracer at the majority of groundwater sites. Although reduced Halon-1301 concentrations were found in a few samples, resulting in misleading Halon-1301 inferred age estimates, overall Halon-1301 performed significantly better than the CFCs, which are prone to degradation and contamination (shown in this and our previous study). Figure 11 summarizes the performance of the tracers used in this study, highlighting that Halon-1301 performs almost as well as SF6 and tritium, and with a much higher success rate than the CFCs in this study. In particular, Halon-1301 is significantly more reliable than the CFCs (which were either degraded or contaminated at as many as 30 % of the sites) and in some cases SF6 (for six contaminated SF6 samples, Halon-1301 still matched age estimates from tritium).