{"id":104,"date":"2026-04-10T02:53:05","date_gmt":"2026-04-10T02:53:05","guid":{"rendered":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/ch033-xhtml\/"},"modified":"2026-05-12T01:59:14","modified_gmt":"2026-05-12T01:59:14","slug":"4-5-sensitivity-of-age-to-input-parameters","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/4-5-sensitivity-of-age-to-input-parameters\/","title":{"raw":"4.5 Sensitivity of Age to Input Parameters","rendered":"4.5 Sensitivity of Age to Input Parameters"},"content":{"raw":"
\r\n
\r\n\r\nBased on low solubility and sensitivity to excess air, the behavior of [latex]He[\/latex] is like [latex]Ne[\/latex] as shown in Figure 5<\/span><\/a>. Early [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age\u2011dating studies relied solely on [latex]Ne[\/latex] and [latex]He[\/latex] measurements, and some noble gas labs continue to use this approach. Step\u00a02a in Figure 15<\/span><\/a> refers to the [latex]Ne[\/latex]\u2011only model. It is instructive to carefully review the [latex]Ne[\/latex]\u2011only model formulation shown in Equation\u00a0(21)<\/span> because\r\n\r\n<\/div>\r\n
    \r\n \t
  1. [latex]_{\\ }^{3}{He}_{trit}[\/latex] can be determined manually using just two gas concentrations with simplifying assumptions,<\/li>\r\n \t
  2. therefore, the equation can be used to develop an intuition about the sensitivity of [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] ages of different variables required for calculation of [latex]_{\\ }^{3}{He}_{trit}[\/latex].<\/li>\r\n<\/ol>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]_{\\ }^{3}{He}_{trit} =_{\\ }^{4}{He}_{m}\\left( R_{m} - R_{terr} \\right) -_{\\ }^{4}{He}_{sol}\\left( R_{sol} - R_{terr} \\right) - \\left( \\frac{_{\\ }^{4}{He}}{Ne} \\right)_{EA}\\left( {Ne}_{m} - {Ne}_{sol} \\right)\\left( R_{a} - R_{terr} \\right)[\/latex]<\/th>\r\n<\/span>(21)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
    \r\n\r\nwhere:\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]_{\\ }^{4}{He}_{m}[\/latex]<\/th>\r\n=<\/th>\r\nmeasured concentration of [latex]_{}^{4}{He}[\/latex]<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    [latex]R_{m}[\/latex]<\/td>\r\n=<\/td>\r\nmeasured [latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio; commonly referred to simply as [latex]R[\/latex] as in the notation [latex]\\frac{R}{R_{a}}[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]R_{terr}[\/latex]<\/td>\r\n=<\/td>\r\n[latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio for terrigenic [latex]He[\/latex] (Table\u00a04<\/span><\/a>)<\/td>\r\n<\/tr>\r\n
    [latex]R_{sol}[\/latex]<\/td>\r\n=<\/td>\r\n[latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio for water in solubility equilibrium with air at assumed recharge temperature and elevation; [latex]R_{sol}[\/latex] is equal to [latex]{\\alpha R}_{a}[\/latex], where [latex]\\alpha[\/latex] is the air\u2011water fractionation factor (0.98)<\/td>\r\n<\/tr>\r\n
    [latex]\\left( \\frac{_{\\ }^{4}{He}}{\\ \\ Ne} \\right)_{EA}[\/latex]<\/td>\r\n=<\/td>\r\n[latex]\\frac{_{}^{4}{He}}{Ne}[\/latex] ratio of excess air dissolved in the sample; 0.288 for complete dissolution (unfractionated excess air)<\/td>\r\n<\/tr>\r\n
    [latex]{Ne}_{m}[\/latex]<\/td>\r\n=<\/td>\r\nmeasured [latex]Ne[\/latex] concentration in water<\/td>\r\n<\/tr>\r\n
    [latex]{Ne}_{sol}[\/latex]<\/td>\r\n=<\/td>\r\n[latex]Ne[\/latex] concentration for water in solubility equilibrium with air at assumed recharge temperature and elevation<\/td>\r\n<\/tr>\r\n
    [latex]R_{a}[\/latex]<\/td>\r\n=<\/td>\r\n[latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio of atmospheric air<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
    \r\n\r\nExercise\u00a06<\/u><\/span><\/a>\u2ba7 provides an opportunity to practice calculating estimated groundwater age including the additional calculations needed to determine tritium-helium age such as the [latex]Ne[\/latex]\u2011only formulation.\r\n\r\n<\/div>\r\n
    \r\n\r\nOnly [latex]_{}^{4}{He}[\/latex] and [latex]Ne[\/latex] concentrations explicitly appear on the right\u2011hand side of Equation\u00a0(18)<\/span>, so it is worth noting that [latex]_{}^{4}{He}\\ R_{x} =_{}^{4}{He}\\ (\\frac{_{}^{3}{He}}{_{}^{4}{He)}}_{x}[\/latex] where [latex]x[\/latex] is, for example, a subscript as shown in Equation\u00a0(21)<\/span>. This simplifies to a [latex]_{}^{3}{He}[\/latex] concentration.\r\n\r\n<\/div>\r\n
    \r\n\r\nThe first term in Equation\u00a0(21)<\/span>, i.e. the [latex]_{\\ }^{4}{{He}_{m}\\left( R_{m} - R_{terr} \\right)}[\/latex], is equivalent to the first term in Equation\u00a0(18)<\/span>, i.e. the [latex]_{\\ }^{3}{He}_{m}[\/latex] minus a [latex]_{\\ }^{3}{He}_{terr}[\/latex] component. The second and third terms in Equation\u00a0(21)<\/span>\u2014which represent solubility equilibrium and excess air components at an assumed recharge temperature\u2014are equivalent to the second term in Equation\u00a0(18)<\/span>, i.e. [latex]_{\\ }^{3}{He}_{atm}[\/latex] minus a [latex]_{\\ }^{3}{He}_{terr}[\/latex] component.\r\n\r\n<\/div>\r\n
    \r\n\r\nRelative to other noble gases, [latex]He[\/latex] is least sensitive to recharge temperature (as shown in Figure 3<\/span><\/a> of Section\u00a02) and salinity (as shown in Figure 4<\/span><\/a> of Section\u00a02). Similarly, [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age is mildly sensitive to recharge temperature and elevation, as shown in Figure 17<\/span><\/a>a and Figure 17<\/span><\/a>b, respectively.\r\n\r\n<\/div>\r\n
    \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
    \r\n
    \r\n
    \r\n\r\n<\/span>Figure 17\u00a0\u2011<\/strong>\u00a0Sensitivity of 3<\/sup>H\/3<\/sup>He tracer age for a) recharge temperature and b) elevation. The recharge temperature and elevation sensitivity examples were calculated from a hypothetical base case with 3<\/sup>H = 10 TU, R<\/em>\/Ra<\/sub><\/em> = 1.5, recharge temperature of 10\u00a0\u00b0C, and recharge elevation of 0\u00a0m. Recharge temperature or elevation were then varied over the range shown in the respective plots. While curves shown are non\u2011linear, approximate slopes (red lines) for portions of the curves are annotated for illustration of relative sensitivity.\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
    \r\n\r\nIn contrast to recharge temperature, recharge elevation, and salinity, [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age is sensitive to excess air. The sensitivity to excess air is twofold, based on the total amount of excess air (Figure 18<\/span><\/a>a) and the extent of dissolution of air bubbles during the formation of excess air measured in the groundwater sample (Figure 18<\/span><\/a>b). In the context of Equation\u00a0(21)<\/span>, this sensitivity is based on the [latex]\\left( {Ne}_{m} - {Ne}_{sol} \\right)[\/latex] term (where excess [latex]Ne[\/latex] indicates excess air) and the value of the [latex]_{}^{4}{He}[\/latex]\/ [latex]Ne[\/latex] term.\r\n\r\n<\/div>\r\n
    \r\n\r\nIn the case where [latex]R\/R_{a}[\/latex] is small\u2014suggesting relatively little [latex]_{\\ }^{3}{He}_{trit}[\/latex] in the sample\u2014a very modest overestimation of excess air (>\u00a00.6\u00a0ccSTP\/kg) can yield a negative tracer age. The [latex]_{}^{4}{He}[\/latex]\/[latex]Ne[\/latex] term can range from the value for atmospheric air (0.288; using this value assumes complete dissolution of air at the time excess air is formed, i.e., UA) to 0.8 for partial dissolution.\r\n\r\n<\/div>\r\n
    \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
    \r\n
    \r\n
    \r\n\r\n<\/span>Figure 18\u00a0\u2011<\/strong>\u00a0Sensitivity of 3<\/sup>H\/3<\/sup>He tracer age to excess air. Graph a) is based on a hypothetical sample with 3<\/sup>H = 10 TU, recharge temperature of 10 \u00b0C, and recharge elevation of 0 m. For a sample with \u201ctrue\u201d excess air = 0 ccSTPkg-1<\/sup>, adding 4\u00a0ccSTPkg\u20111<\/sup> excess air reduces the tracer age from 12.9\u00a0years to 3.3\u00a0years when R<\/em>\/Ra<\/sub><\/em> = 1.5. In graph b), tracer age was calculated for two samples with moderate excess air (2 or 5\u00a0ccSTP\/kg), but with different 4<\/sup>He\/Ne ratios as shown in Equation\u00a0(21)<\/span> ranging from 0.288 (atmospheric air) to 0.8 (the ratio of air that is fractionated by the ratio of Ne to He solubilities). While curves shown are non\u2011linear, approximate slopes (short red lines) for portions of the curves are annotated to illustrate relative sensitivity.\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
    \r\n\r\nInspection of the [latex]Ne[\/latex]\u2011only formulation in Equation\u00a0(21)<\/span> shows how the [latex]_{}^{4}{He}[\/latex]\/[latex]Ne[\/latex] ratio could impact the determination of [latex]_{\\ }^{3}{He}_{trit}[\/latex] and therefore tracer age. More complex model formulations such as the closed\u2011system equilibration (CE) model and the partial re\u2011equilibration (PR) model (Stute et al., 1995), are also based on different assumptions about fractionation of gases, particularly for excess air. The CE model in its simplest form is equivalent to the UA model, while the PR model yields very different estimates of [latex]He[\/latex] content when compared with other noble gases. While it is advisable to seek the simplest model(s) that reasonably fit the noble gas data (i.e., start first with [latex]Ne[\/latex]-only and\/or UA model as shown in Figure 15<\/span><\/a>, Step\u00a02a), it is also important to consider other noble gas models as warranted by the data and\/or conceptual models of the sampled system. Comprehensive discussion of excess air models can be found in Aeschbach\u2011Hertig & Solomon (2013).\r\n\r\n<\/div>\r\n
    \r\n\r\nThe prevalence of the [latex]R_{terr}[\/latex] variable in Equation\u00a0(21)<\/span> illustrates how [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] ages may be sensitive to assumptions about terrigenic [latex]He[\/latex]. Similarly, other methods for determination of [latex]_{}^{4}{He}_{terr}[\/latex] (Figure 15<\/span><\/a>, Step\u00a03) can be used to evaluate the magnitude of [latex]_{}^{4}{He}_{terr}[\/latex]. If [latex]_{}^{4}{He}_{terr\\ }[\/latex]is <\u00a0109<\/sup>\u00a0ccSTP\/g, then [latex]_{}^{3}{He}_{trit}[\/latex] is not sensitive to the selection of [latex]R_{terr}[\/latex] (Figure 19<\/span><\/a>). [latex]_{}^{3}{He}_{terr}[\/latex] may be present due to production of helium in the Earth\u2019s crust and\/or derived from the Earth\u2019s mantle (Table\u00a04<\/span><\/a>). However, mantle sources are negligible (<\u00a00.2\u00a0TU) in many cases and typically not considered (Schlosser et al., 1989). However, if present, mantle [latex]He[\/latex] may preclude calculation of groundwater age due to the magnitude of [latex]R_{man}[\/latex].\r\n\r\n<\/div>\r\n
    \r\n\r\nLast, the [latex]_{}^{4}{He}_{m}[\/latex] variable in Equation\u00a0(21)<\/span> is key to calculating [latex]_{}^{3}{He}_{trit}[\/latex]. Figure 19<\/span><\/a>b shows how the tracer age is sensitive to the measurement accuracy for [latex]_{}^{4}{He}[\/latex]. For the illustrative example, we observe that the tracer age would be negative if [latex]_{}^{4}{He}[\/latex] were severely underestimated (<\u00a065\u00a0percent of solubility at the assumed recharge temperature and elevation).\r\n\r\n<\/div>\r\n
    \r\n\r\n\"\"\r\n\r\n<\/div>\r\n
    \r\n
    \r\n
    \r\n\r\n<\/span>Figure 19\u00a0\u2011<\/strong>\u00a0Sensitivity of 3<\/sup>H\/3<\/sup>He tracer (apparent) age to variation in a) Rterr<\/sub><\/em> and b) 4<\/sup>He. Simulations were based on a hypothetical sample with 3<\/sup>H = 10 TU, recharge temperature of 10 \u00b0C, and recharge elevation of 0 m. An R\/Ra<\/sub><\/em> of 1.5 was assumed for the Rterr<\/sub><\/em> illustration. While curves shown are non\u2011linear, approximate slopes (short red lines) for portions of the curves are annotated to illustrate relative sensitivity.\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n<\/div>","rendered":"
    \n
    \n

    Based on low solubility and sensitivity to excess air, the behavior of [latex]He[\/latex] is like [latex]Ne[\/latex] as shown in Figure 5<\/span><\/a>. Early [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age\u2011dating studies relied solely on [latex]Ne[\/latex] and [latex]He[\/latex] measurements, and some noble gas labs continue to use this approach. Step\u00a02a in Figure 15<\/span><\/a> refers to the [latex]Ne[\/latex]\u2011only model. It is instructive to carefully review the [latex]Ne[\/latex]\u2011only model formulation shown in Equation\u00a0(21)<\/span> because<\/p>\n<\/div>\n

      \n
    1. [latex]_{\\ }^{3}{He}_{trit}[\/latex] can be determined manually using just two gas concentrations with simplifying assumptions,<\/li>\n
    2. therefore, the equation can be used to develop an intuition about the sensitivity of [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] ages of different variables required for calculation of [latex]_{\\ }^{3}{He}_{trit}[\/latex].<\/li>\n<\/ol>\n\n\n\n\n<\/colgroup>\n\n\n
      <\/th>\n[latex]_{\\ }^{3}{He}_{trit} =_{\\ }^{4}{He}_{m}\\left( R_{m} - R_{terr} \\right) -_{\\ }^{4}{He}_{sol}\\left( R_{sol} - R_{terr} \\right) - \\left( \\frac{_{\\ }^{4}{He}}{Ne} \\right)_{EA}\\left( {Ne}_{m} - {Ne}_{sol} \\right)\\left( R_{a} - R_{terr} \\right)[\/latex]<\/th>\n<\/span>(21)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
      \n

      where:<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n\n
      [latex]_{\\ }^{4}{He}_{m}[\/latex]<\/th>\n=<\/th>\nmeasured concentration of [latex]_{}^{4}{He}[\/latex]<\/th>\n<\/tr>\n<\/thead>\n
      [latex]R_{m}[\/latex]<\/td>\n=<\/td>\nmeasured [latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio; commonly referred to simply as [latex]R[\/latex] as in the notation [latex]\\frac{R}{R_{a}}[\/latex]<\/td>\n<\/tr>\n
      [latex]R_{terr}[\/latex]<\/td>\n=<\/td>\n[latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio for terrigenic [latex]He[\/latex] (Table\u00a04<\/span><\/a>)<\/td>\n<\/tr>\n
      [latex]R_{sol}[\/latex]<\/td>\n=<\/td>\n[latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio for water in solubility equilibrium with air at assumed recharge temperature and elevation; [latex]R_{sol}[\/latex] is equal to [latex]{\\alpha R}_{a}[\/latex], where [latex]\\alpha[\/latex] is the air\u2011water fractionation factor (0.98)<\/td>\n<\/tr>\n
      [latex]\\left( \\frac{_{\\ }^{4}{He}}{\\ \\ Ne} \\right)_{EA}[\/latex]<\/td>\n=<\/td>\n[latex]\\frac{_{}^{4}{He}}{Ne}[\/latex] ratio of excess air dissolved in the sample; 0.288 for complete dissolution (unfractionated excess air)<\/td>\n<\/tr>\n
      [latex]{Ne}_{m}[\/latex]<\/td>\n=<\/td>\nmeasured [latex]Ne[\/latex] concentration in water<\/td>\n<\/tr>\n
      [latex]{Ne}_{sol}[\/latex]<\/td>\n=<\/td>\n[latex]Ne[\/latex] concentration for water in solubility equilibrium with air at assumed recharge temperature and elevation<\/td>\n<\/tr>\n
      [latex]R_{a}[\/latex]<\/td>\n=<\/td>\n[latex]_{}^{3}{He}[\/latex]\/[latex]_{}^{4}{He}[\/latex] ratio of atmospheric air<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n

      Exercise\u00a06<\/u><\/span><\/a>\u2ba7 provides an opportunity to practice calculating estimated groundwater age including the additional calculations needed to determine tritium-helium age such as the [latex]Ne[\/latex]\u2011only formulation.<\/p>\n<\/div>\n

      \n

      Only [latex]_{}^{4}{He}[\/latex] and [latex]Ne[\/latex] concentrations explicitly appear on the right\u2011hand side of Equation\u00a0(18)<\/span>, so it is worth noting that [latex]_{}^{4}{He}\\ R_{x} =_{}^{4}{He}\\ (\\frac{_{}^{3}{He}}{_{}^{4}{He)}}_{x}[\/latex] where [latex]x[\/latex] is, for example, a subscript as shown in Equation\u00a0(21)<\/span>. This simplifies to a [latex]_{}^{3}{He}[\/latex] concentration.<\/p>\n<\/div>\n

      \n

      The first term in Equation\u00a0(21)<\/span>, i.e. the [latex]_{\\ }^{4}{{He}_{m}\\left( R_{m} - R_{terr} \\right)}[\/latex], is equivalent to the first term in Equation\u00a0(18)<\/span>, i.e. the [latex]_{\\ }^{3}{He}_{m}[\/latex] minus a [latex]_{\\ }^{3}{He}_{terr}[\/latex] component. The second and third terms in Equation\u00a0(21)<\/span>\u2014which represent solubility equilibrium and excess air components at an assumed recharge temperature\u2014are equivalent to the second term in Equation\u00a0(18)<\/span>, i.e. [latex]_{\\ }^{3}{He}_{atm}[\/latex] minus a [latex]_{\\ }^{3}{He}_{terr}[\/latex] component.<\/p>\n<\/div>\n

      \n

      Relative to other noble gases, [latex]He[\/latex] is least sensitive to recharge temperature (as shown in Figure 3<\/span><\/a> of Section\u00a02) and salinity (as shown in Figure 4<\/span><\/a> of Section\u00a02). Similarly, [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age is mildly sensitive to recharge temperature and elevation, as shown in Figure 17<\/span><\/a>a and Figure 17<\/span><\/a>b, respectively.<\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n<\/div>\n

      \n
      \n
      \n

      <\/span>Figure 17\u00a0\u2011<\/strong>\u00a0Sensitivity of 3<\/sup>H\/3<\/sup>He tracer age for a) recharge temperature and b) elevation. The recharge temperature and elevation sensitivity examples were calculated from a hypothetical base case with 3<\/sup>H = 10 TU, R<\/em>\/Ra<\/sub><\/em> = 1.5, recharge temperature of 10\u00a0\u00b0C, and recharge elevation of 0\u00a0m. Recharge temperature or elevation were then varied over the range shown in the respective plots. While curves shown are non\u2011linear, approximate slopes (red lines) for portions of the curves are annotated for illustration of relative sensitivity.<\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

      \n

      In contrast to recharge temperature, recharge elevation, and salinity, [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] age is sensitive to excess air. The sensitivity to excess air is twofold, based on the total amount of excess air (Figure 18<\/span><\/a>a) and the extent of dissolution of air bubbles during the formation of excess air measured in the groundwater sample (Figure 18<\/span><\/a>b). In the context of Equation\u00a0(21)<\/span>, this sensitivity is based on the [latex]\\left( {Ne}_{m} - {Ne}_{sol} \\right)[\/latex] term (where excess [latex]Ne[\/latex] indicates excess air) and the value of the [latex]_{}^{4}{He}[\/latex]\/ [latex]Ne[\/latex] term.<\/p>\n<\/div>\n

      \n

      In the case where [latex]R\/R_{a}[\/latex] is small\u2014suggesting relatively little [latex]_{\\ }^{3}{He}_{trit}[\/latex] in the sample\u2014a very modest overestimation of excess air (>\u00a00.6\u00a0ccSTP\/kg) can yield a negative tracer age. The [latex]_{}^{4}{He}[\/latex]\/[latex]Ne[\/latex] term can range from the value for atmospheric air (0.288; using this value assumes complete dissolution of air at the time excess air is formed, i.e., UA) to 0.8 for partial dissolution.<\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n<\/div>\n

      \n
      \n
      \n

      <\/span>Figure 18\u00a0\u2011<\/strong>\u00a0Sensitivity of 3<\/sup>H\/3<\/sup>He tracer age to excess air. Graph a) is based on a hypothetical sample with 3<\/sup>H = 10 TU, recharge temperature of 10 \u00b0C, and recharge elevation of 0 m. For a sample with \u201ctrue\u201d excess air = 0 ccSTPkg-1<\/sup>, adding 4\u00a0ccSTPkg\u20111<\/sup> excess air reduces the tracer age from 12.9\u00a0years to 3.3\u00a0years when R<\/em>\/Ra<\/sub><\/em> = 1.5. In graph b), tracer age was calculated for two samples with moderate excess air (2 or 5\u00a0ccSTP\/kg), but with different 4<\/sup>He\/Ne ratios as shown in Equation\u00a0(21)<\/span> ranging from 0.288 (atmospheric air) to 0.8 (the ratio of air that is fractionated by the ratio of Ne to He solubilities). While curves shown are non\u2011linear, approximate slopes (short red lines) for portions of the curves are annotated to illustrate relative sensitivity.<\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

      \n

      Inspection of the [latex]Ne[\/latex]\u2011only formulation in Equation\u00a0(21)<\/span> shows how the [latex]_{}^{4}{He}[\/latex]\/[latex]Ne[\/latex] ratio could impact the determination of [latex]_{\\ }^{3}{He}_{trit}[\/latex] and therefore tracer age. More complex model formulations such as the closed\u2011system equilibration (CE) model and the partial re\u2011equilibration (PR) model (Stute et al., 1995), are also based on different assumptions about fractionation of gases, particularly for excess air. The CE model in its simplest form is equivalent to the UA model, while the PR model yields very different estimates of [latex]He[\/latex] content when compared with other noble gases. While it is advisable to seek the simplest model(s) that reasonably fit the noble gas data (i.e., start first with [latex]Ne[\/latex]-only and\/or UA model as shown in Figure 15<\/span><\/a>, Step\u00a02a), it is also important to consider other noble gas models as warranted by the data and\/or conceptual models of the sampled system. Comprehensive discussion of excess air models can be found in Aeschbach\u2011Hertig & Solomon (2013).<\/p>\n<\/div>\n

      \n

      The prevalence of the [latex]R_{terr}[\/latex] variable in Equation\u00a0(21)<\/span> illustrates how [latex]_{}^{3}H[\/latex]\/[latex]_{}^{3}{He}[\/latex] ages may be sensitive to assumptions about terrigenic [latex]He[\/latex]. Similarly, other methods for determination of [latex]_{}^{4}{He}_{terr}[\/latex] (Figure 15<\/span><\/a>, Step\u00a03) can be used to evaluate the magnitude of [latex]_{}^{4}{He}_{terr}[\/latex]. If [latex]_{}^{4}{He}_{terr\\ }[\/latex]is <\u00a0109<\/sup>\u00a0ccSTP\/g, then [latex]_{}^{3}{He}_{trit}[\/latex] is not sensitive to the selection of [latex]R_{terr}[\/latex] (Figure 19<\/span><\/a>). [latex]_{}^{3}{He}_{terr}[\/latex] may be present due to production of helium in the Earth\u2019s crust and\/or derived from the Earth\u2019s mantle (Table\u00a04<\/span><\/a>). However, mantle sources are negligible (<\u00a00.2\u00a0TU) in many cases and typically not considered (Schlosser et al., 1989). However, if present, mantle [latex]He[\/latex] may preclude calculation of groundwater age due to the magnitude of [latex]R_{man}[\/latex].<\/p>\n<\/div>\n

      \n

      Last, the [latex]_{}^{4}{He}_{m}[\/latex] variable in Equation\u00a0(21)<\/span> is key to calculating [latex]_{}^{3}{He}_{trit}[\/latex]. Figure 19<\/span><\/a>b shows how the tracer age is sensitive to the measurement accuracy for [latex]_{}^{4}{He}[\/latex]. For the illustrative example, we observe that the tracer age would be negative if [latex]_{}^{4}{He}[\/latex] were severely underestimated (<\u00a065\u00a0percent of solubility at the assumed recharge temperature and elevation).<\/p>\n<\/div>\n

      \n

      \"\"<\/p>\n<\/div>\n

      \n
      \n
      \n

      <\/span>Figure 19\u00a0\u2011<\/strong>\u00a0Sensitivity of 3<\/sup>H\/3<\/sup>He tracer (apparent) age to variation in a) Rterr<\/sub><\/em> and b) 4<\/sup>He. Simulations were based on a hypothetical sample with 3<\/sup>H = 10 TU, recharge temperature of 10 \u00b0C, and recharge elevation of 0 m. An R\/Ra<\/sub><\/em> of 1.5 was assumed for the Rterr<\/sub><\/em> illustration. While curves shown are non\u2011linear, approximate slopes (short red lines) for portions of the curves are annotated to illustrate relative sensitivity.<\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n<\/div>\n","protected":false},"author":7,"menu_order":19,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-104","chapter","type-chapter","status-publish","hentry"],"part":30,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/users\/7"}],"version-history":[{"count":6,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/104\/revisions"}],"predecessor-version":[{"id":440,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/104\/revisions\/440"}],"part":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/parts\/30"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/104\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/media?parent=104"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapter-type?post=104"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/contributor?post=104"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/license?post=104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}