Methods of Interpretation


Well-established approaches for determination of tracer-based piston-flow ages are discussed in detail in references listed earlier in this report. These approaches were applied in this effort and are described briefly in this section.


Assigning a CFC- or SF₆-Based Piston-Flow Age


Recharge Altitude, Recharge Temperature, and Excess Air


The application of CFCs and SF₆ to groundwater dating is based, in large part, on relating measured aqueous concentrations of CFCs or SF₆ to atmospheric concentrations inferred to be present at points of recharge at the time of recharge. Relating aqueous concentrations to atmospheric concentrations is based on Henry’s Law. Henry’s Law states that for water at equilibrium with air, the concentration of a gas dissolved in water is proportional (through the Henry’s Law constant, K_H) to the partial pressure of that gas in the air. Values of K_H defining solubility relations for each of the CFCs and for SF₆ are given in International Atomic Energy Agency (2006). Application of Henry’s Law requires estimates of recharge altitude, recharge temperature, and excess air. Excess air is the component of atmospheric air (atmospheric gases), beyond the amount that can be attributed to air-water solubility, that is incorporated into shallow groundwater during or following recharge (Heaton and Vogel, 1981).


Dating with CFCs and SF₆ is relatively insensitive to recharge altitude, and for most of the groundwater sites in this report, the water-table altitude served as a reasonable estimate of the recharge altitude. For sites where recharge might occur at altitudes substantially greater than the water-table altitude (more than several hundred feet above the water-table altitude), a sensitivity analysis was done to help constrain results (appendix G).


Recharge temperature generally has a large effect on the interpretation of tracer-based piston-flow ages derived from concentrations of CFCs and SF₆ in groundwater. The major dissolved gases can be used to infer recharge temperature, or, if major dissolved-gas data are not available, climatological data can be used.


Where climatological data were used to estimate recharge temperature, the approach in this report was to use the mean annual ground temperature at the water table [mean annual air temperature (MAAT) + 1°C (Stute and Schlosser, 2000)]. Nearby climate-station data were adjusted to the estimated recharge altitude at a site using the average environmental lapse rate of 0.00198°C/ft (Driscoll, 1986, p. 49). For sites where recharge might occur at altitudes substantially greater than the water-table altitude and, thus, at lower recharge temperatures, a sensitivity analysis was done (appendix G). In the absence of major dissolved-gas data, an excess-air concentration of 2 cc(STP)/kg was used for groundwater recharge through sandy sediments (Busenberg and Plummer, 1992; Dunkle and others, 1993; Sun and others, 2010); excess-air concentrations in fractured rock and karst aquifers, which can have amounts of excess air larger than those assumed for sandy aquifers, were handled on a case-by-case basis (appendix G).


Where major dissolved-gas data were available, N₂ and Ar data were used in the unfractionated-air (UA) model to infer recharge temperature (Heaton and Vogel, 1981). The UA model rests upon assumptions that gases dissolved in groundwater originate from air-water solubility (Henry’s Law partitioning) and the introduction of additional gas during recharge from processes facilitating air-bubble entrainment (for example, resulting from a fluctuating water table). With the UA model, the additional gas is assumed to be unfractionated; that is, the entire volume of the bubble of entrapped excess air is assumed to have the composition of air and to be dissolved completely. Although some fractionation does occur in many aquifers, the effects on calculated recharge temperatures generally are of minor importance in groundwater with low concentrations of excess air (Cey and others, 2008; Klump and others, 2008).


In applying the UA model, there are two known variables—concentrations of Ar and N₂—and four unknown variables—recharge altitude, recharge temperature, excess air, and excess N₂ (generally, N₂ from denitrification of nitrate in suboxic water). The recharge altitude usually can be assumed to be similar to the water-table altitude, as discussed above, but there still remain three unknown variables with only two known variables. Guidelines for interpretation of recharge temperature and excess air are given in Plummer and others (2003) and discussed below.


In this report, samples from a given network that were oxic and thus likely to have had little or no excess N₂ from denitrification were used for the first step of this analysis. Oxic samples were considered those with concentrations of O₂ ≥ 1 mg/L (Lindsey and others, 2003), Mn ≤ 50 μg/L (Paschke, 2007), Fe ≤ 100 μg/L (Paschke, 2007), and CH₄ ≤ 1 μg/L. In this initial analysis, major dissolved-gas data from these oxic sites were used to estimate recharge temperatures and excess air, under the assumption that N₂ from denitrification was negligible and that the UA model applies. The application of four redox-indicator species (O₂, Mn, Fe, and CH₄ ) in this analysis resulted in a system in which mixing of oxic water (O₂ ≥ 1 mg/L) and suboxic water (identified where water contained Mn >50 μg/L, Fe >100 μg/L, and(or) CH₄ > 1 μg/L) along flow paths or in well bores could be recognized.


Having estimated recharge temperatures and excess-air concentrations for the oxic sites in a network, as explained in the preceding paragraph, there remains the task of estimating recharge temperatures and excess-air concentrations at the remaining sites in the network. This was accomplished by using the results from the oxic sites to constrain the analysis of the remaining samples in a given network. Two approaches could be used, with usually similar results. The median excess air from the oxic sites could be used as a constraint for the suboxic sites. With excess air constrained, the major dissolved-gas data would be used to estimate recharge temperature and the amount of excess N₂ from denitrification at the suboxic sites. Alternatively, the median recharge temperature from the oxic sites could be used as a constraint for the suboxic sites. With recharge temperature constrained, the major dissolved-gas data would be used to estimate excess air and the amount of excess N₂ from denitrification at the suboxic sites. In this report, the first of these two approaches was used: excess air was held constant and recharge temperature was allowed to vary. 


For some oxic sites, these calculations yielded negative excess air. This can result from degassing in the aquifer or during sample collection. In these cases, the major dissolved-gas data for the site were not used, and the recharge temperature was selected, as appropriate, from: (1) the median recharge temperature for the oxic sites or (2) MAAT + 1°C. Usually, the excess-air concentration for the oxic sites was used for the site in question.


Unrecognized denitrification can lead to assignment of overly warm recharge temperatures and large amounts of excess air, resulting in tracer-based piston-flow ages that are too young (overly warm recharge temperature) or too old (large amounts of excess air). For a site that was considered oxic, if the recharge temperature estimated by these methods was unusually warm and if the inferred excess air was unusually large compared to other sites in the network, the site was given additional attention. Such unusual samples were evaluated for possible denitrification by comparing inferred recharge temperatures and excess-air concentrations for conditions of (a) no denitrification and (b) denitrification. These types of unusual samples may have been treated as containing a mixture of oxic and suboxic water, thus allowing for denitrification, or such unusual samples may have been treated as outliers, in which case the major dissolved-gas data for that site may have been discarded and the recharge temperature and excess-air concentration determined as described above. Each occurrence was evaluated on a case-by-case basis, using relevant ancillary data, and documented in appendix G.


Where some samples in a network were not analyzed for major dissolved gases, recharge temperatures were assigned, as appropriate, from the median recharge temperature for the oxic sites in the network, or by other methods described above. For excess air, the median excess-air concentration for the oxic sites typically was used.


Finally, there were some sites for which neon (Ne) data in addition to major dissolved-gas data were available. In these cases, Ne data were used to refine estimates for suboxic sites using an approach similar to that used by Plummer and others (2003). Specifically, for the purpose of estimating excess air, the recharge temperature initially was assumed equal to the MAAT + 1°C, and the estimate of recharge temperature and the Ne concentration for a given site were used to estimate excess air (this approach takes advantage of the fact that Ne solubility is relatively insensitive to temperature). Once the excess air was estimated, this estimate along with the major dissolve gas data (that is, N₂ and Ar) were used to estimate recharge temperature and excess N₂ from denitrification.


Determination of a CFC-Based Piston-Flow Age


Atmospheric CFC mixing ratios that would have been present locally at the time of recharge were calculated from measured aqueous CFC concentrations; estimates of recharge altitude, recharge temperature, and excess air; and application of Henry’s Law. These calculated values of atmospheric CFC concentrations were compared to reconstructed records of atmospheric CFC mixing ratios to calculate CFC-based piston-flow ages (Busenberg and Plummer, 1992; International Atomic Energy Agency, 2006). This resulted in the determination of piston-flow ages based on CFC-11, CFC-12, and CFC-113. These CFC-based piston-flow ages then were evaluated on a site-by-site basis: redox chemistry was considered (to minimize impacts of microbial degradation of CFCs) and the relative differences in piston-flow ages based on CFC-11, CFC-12, and CFC-113 were assessed (to identify samples exhibiting evidence of substantial mixing). Datable sites were those that were not likely to have been subject to substantial degradation or mixing. The most appropriate CFC-based piston-flow age for each datable site was then selected to represent the site. CFC-12-based piston-flow ages generally are the most reliable (least affected by sorption and degradation) of the three CFCs (International Atomic Energy Agency, 2006). However, assignment of the most representative CFC-based piston-flow age for a given site requires consideration of site-specific factors as well as network-specific factors, including the degree of consistency among the three CFCs, extent of environmental CFC contamination, and spatial patterns of tracer-based piston-flow ages inferred from the three CFCs. No CFC-based piston-flow ages were assigned to samples having reconstructed CFC mixing ratios that exceeded the atmospheric CFC mixing ratio at the time of sampling. Finally, evaluation of these interpretations was done using hydrologic data (to evaluate age/depth relations), ³H data (where available) to compare reconstructed ³H concentrations (measured ³H concentrations that are back-decayed, on the basis of CFC-based piston-flow ages, to original ³H concentrations inferred to have been present at the time of recharge; see, for example, Dunkle and others [1993]) to historical ³H records, and other available information (appendix G). These additional assessments are intended to provide some (limited) context and evaluation of the interpretations.


Determination of SF₆-Based Piston-Flow Age


Atmospheric SF₆ mixing ratios that would have been present locally at the time of recharge were calculated from measured aqueous SF₆ concentrations; estimates of recharge altitude, recharge temperature, and excess air; and application of Henry’s Law. Following Busenberg and Plummer (2000), these atmospheric SF₆ mixing ratios were compared to reconstructed records of atmospheric SF₆ mixing ratios to calculate SF₆-based piston-flow ages. SF₆ does not seem to degrade (Busenberg and Plummer, 2000), so screening SF₆ interpretations on the basis of redox conditions was not necessary. No SF₆-based piston-flow ages were assigned to samples having reconstructed SF₆ mixing ratios that exceeded the atmospheric SF₆ mixing ratio at the time of sampling. Finally, evaluation of these interpretations was done by analyzing age/depth relations, reconstructed ³H relations, and other available information (appendix G). 


Assigning ³H/³He-Based Piston-Flow Age


Dating with ³H/³He is based on measuring ³H and its decay product ³He. Recharge temperatures and recharge altitudes, needed for calculating ³He from air-water solubility, were estimated by methods used for estimating recharge temperatures and recharge altitudes for CFC and SF₆ dating. Measured ³He/⁴He ratios and helium (He) concentrations were used to resolve various ³He sources: ³He from air-water solubility (constrained by recharge temperature and recharge altitude), from excess air (constrained by Ne concentrations), from terrigenic sources (assuming a terrigenic ³He/⁴He ratio of 2 × 10^-8 cc/g at STP; Mamyrin and Tolstikhin, 1984; Schlosser and others, 1989), and from ³H decay (assuming a ³H half-life of 12.32 years; Lucas and Unterweger, 2000). Samples generally were not dated if : (1) they contained low concentrations of ³H (less than about 1 TU) in combination with elevated terrigenic helium (20 percent or more of the total helium), (2) they contained high concentrations of ⁴He (Δ⁴He greater than about 200 percent, where Δ⁴He is the amount of ⁴He in the water sample that is in excess to that attributed to solubility equilibrium with air, expressed as a percentage of the ⁴He in water at solubility equilibrium), and (3) they had gases that had been fractionated (for example, samples in which Δ⁴He was less than ΔNe, where ΔNe is the amount of Ne in the water sample that is in excess to that attributed to solubility equilibrium with air, expressed as a percentage of the Ne in water at solubility equilibrium). The interpretations were evaluated using age-depth relations, reconstructed ³H relations, and other available information (appendix G). 


Ancillary Chemistry, Water Level, Well Construction, and Tritium Concentration Data


Ancillary chemistry, water level, well construction, and ³H concentration data for individual sites were obtained from the NAWQA Data Warehouse (DWH): http://infotrek.er.usgs.gov/traverse/f?p=NAWQA:HOME:0:


Estimates of spatial and temporal variations in ³H in precipitation were used for reconstructed ³H analysis. Reconstructed ³H analysis is based on back-decaying measured ³H concentrations in groundwater, using tracer-based piston-flow ages to estimate the time-dependent amount of ³H decay, and comparing these undecayed or original ³H concentrations to historical ³H inputs (for example, Dunkle and others, 1993; Ekwurzel and others, 1994). This analysis can provide a valuable check on tracer-based piston-flow ages in aquifers where recharge is dominated by precipitation.


Estimates of ³H in precipitation were based on International Atomic Energy Agency data from 10 long-term stations in the conterminous United States. Missing temporal records were replaced with values based on correlation using long-term data sets from Ottawa, Canada (August 1953–December 1987), and Vienna, Austria (January 1988–December 2001); and ³H concentrations were interpolated in space. Concentrations prior to August 1953 were estimated using graphical prebomb distributions (Thatcher, 1962).


First posted January 27, 2011