{"id":95,"date":"2026-04-10T02:53:01","date_gmt":"2026-04-10T02:53:01","guid":{"rendered":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/ch030-xhtml\/"},"modified":"2026-05-12T01:53:33","modified_gmt":"2026-05-12T01:53:33","slug":"4-2-basic-concepts-and-systematics","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/chapter\/4-2-basic-concepts-and-systematics\/","title":{"raw":"4.2 Basic Concepts and Systematics","rendered":"4.2 Basic Concepts and Systematics"},"content":{"raw":"
\r\n
\r\n\r\nTritium decays via beta emission to stable [latex]_{}^{3}{He}[\/latex]. [latex]\\frac{_{}^{3}H}{_{}^{3}{He}}[\/latex] age dating relies on measurement of both parent ([latex]_{}^{3}H[\/latex]) and child ([latex]_{}^{3}{He}[\/latex]) products that occur during groundwater transport. The physical process starts with\r\n\r\n<\/div>\r\n
    \r\n \t
  1. infiltration of water at the land surface,<\/li>\r\n \t
  2. transport through the vadose zone, and finally<\/li>\r\n \t
  3. recharge to the groundwater system.<\/li>\r\n<\/ol>\r\n
    \r\n\r\nDuring processes (1) and (2), the water is exposed to a gas phase. The gas phase is atmospheric air at the land surface and often a close approximation to atmospheric air at the water table. Thus, any [latex]_{}^{3}{He}_{trit}[\/latex] produced during infiltration and vadose zone transport is generally lost as the dissolved gases in water equilibrate with atmospheric air. Once recharge occurs, process (3), the groundwater is no longer in contact with an atmospheric gas phase.\r\n\r\n<\/div>\r\n
    \r\n\r\nAs a result, and assuming the recharge rate is sufficiently high\u2014nominally, >\u00a03\u00a0mm\u00a0yr-1<\/sup>, (Gilmore et al., 2021; Solomon et al., 1993)\u2014the [latex]_{}^{3}{He}_{trit}[\/latex] begins to accumulate in the groundwater. Accumulation of [latex]_{}^{3}{He}_{trit}[\/latex] continues until groundwater is sampled or exposed again to a gas phase such as when the groundwater discharges to a stream or spring or is pumped out of a well.\r\n\r\n<\/div>\r\n
    \r\n\r\nFigure 13<\/span><\/a> illustrates the accumulation of [latex]_{}^{3}{He}_{trit}[\/latex] over time as the initial [latex]_{}^{3}H[\/latex] in groundwater recharge decays. The horizontal axis illustrates the relevant timescale of the [latex]\\frac{_{}^{3}H}{_{}^{3}{He}}[\/latex] age-dating method, where 2.6\u00a0percent of initial [latex]_{}^{3}H[\/latex] remains after 65\u00a0years and 1.4\u00a0percent remains after 75\u00a0years.\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 13\u00a0\u2011<\/strong>\u00a03<\/sup>H remaining and 3<\/sup>Hetrit<\/sub> produced over time due to radioactive decay. A 3<\/sup>H half\u2011life of 12.32\u00a0years was used.\r\n\r\n<\/div><\/blockquote>\r\n<\/div>\r\n
    \r\n\r\nTo determine the groundwater age from [latex]_{}^{3}H[\/latex](t) and [latex]_{}^{3}{He}_{trit}[\/latex](t), the age equation shown in Equation\u00a0(14)<\/span> is used.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]Age = \\frac{\\ln\\left( 1 + \\frac{_{\\ }^{3}{{He}_{trit}(t)}}{_{}^{3}H(t)} \\right)}{\\lambda}[\/latex]<\/th>\r\n\r\n<\/colgroup>\r\n\r\n\r\n
    <\/span>(14)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n<\/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
    Age<\/em><\/th>\r\n=<\/th>\r\nelapsed time since groundwater recharge, i.e., since exposure to atmosphere (T)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    \u03bb<\/em><\/td>\r\n=<\/td>\r\ndecay constant (T-1<\/sup>)<\/td>\r\n<\/tr>\r\n
    t<\/em><\/td>\r\n=<\/td>\r\ntime of sampling<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
    \r\n\r\nConcentration units for both [latex]_{}^{3}{He}_{trit}[\/latex] and [latex]_{}^{3}H[\/latex] in Equation\u00a0(14)<\/span> are in TU. The age equation assumes that groundwater tracer transport can be described as piston flow<\/em> (Maloszewski & Zuber, 1996). Practically speaking, this assumption means that [latex]_{}^{3}H[\/latex] and produced [latex]_{}^{3}{He}_{trit}[\/latex] travel together without mixing across other groundwater flowlines. <\/span>Exercise\u00a05<\/span><\/a>\u2ba7 provides an opportunity to practice calculating estimated groundwater age.\r\n\r\n<\/div>\r\n
    \r\n\r\nThe age equation is based on the decay of tritium to tritiogenic helium shown in Equation\u00a0(15)<\/span>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]_{\\ }^{3}{H_{trit}(t)} = \\ _{\\ }^{3}{H\\left( t_{0} \\right)(1 - e^{- \\lambda t})\\ }[\/latex]<\/th>\r\n<\/span>(15)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
    \r\n\r\nInitial [latex]_{}^{3}H[\/latex] ([latex]_{}^{3}H[\/latex](t0<\/sub><\/em>)) is equal to the [latex]_{}^{3}H[\/latex](t<\/em>) plus [latex]_{}^{3}{He}_{trit}[\/latex] determined from the groundwater sample as shown in Equation\u00a0(16)<\/span>.\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]_{\\ }^{3}{H\\left( t_{0} \\right)} = \\ _{\\ }^{3}{H(t) +_{\\ }^{3}{{He}_{trit}(t)}\\ }[\/latex]<\/th>\r\n<\/span>(16)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n
    \r\n\r\nThe decay constant (\u03bb<\/em>) is calculated as shown in Equation\u00a0(17)<\/span>, based on the half\u2011life of tritium (12.32\u00a0years; Lucas & Unterweger, 2000).\r\n\r\n<\/div>\r\n<\/colgroup>\r\n\r\n\r\n
    <\/th>\r\n[latex]lambda = \\ \\frac{\\ln 2}{12.32\\ years} = [\/latex]0.05626 yr\u20131<\/sup><\/th>\r\n<\/span>(17)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<\/table>\r\n<\/div>","rendered":"
    \n
    \n

    Tritium decays via beta emission to stable [latex]_{}^{3}{He}[\/latex]. [latex]\\frac{_{}^{3}H}{_{}^{3}{He}}[\/latex] age dating relies on measurement of both parent ([latex]_{}^{3}H[\/latex]) and child ([latex]_{}^{3}{He}[\/latex]) products that occur during groundwater transport. The physical process starts with<\/p>\n<\/div>\n

      \n
    1. infiltration of water at the land surface,<\/li>\n
    2. transport through the vadose zone, and finally<\/li>\n
    3. recharge to the groundwater system.<\/li>\n<\/ol>\n
      \n

      During processes (1) and (2), the water is exposed to a gas phase. The gas phase is atmospheric air at the land surface and often a close approximation to atmospheric air at the water table. Thus, any [latex]_{}^{3}{He}_{trit}[\/latex] produced during infiltration and vadose zone transport is generally lost as the dissolved gases in water equilibrate with atmospheric air. Once recharge occurs, process (3), the groundwater is no longer in contact with an atmospheric gas phase.<\/p>\n<\/div>\n

      \n

      As a result, and assuming the recharge rate is sufficiently high\u2014nominally, >\u00a03\u00a0mm\u00a0yr-1<\/sup>, (Gilmore et al., 2021; Solomon et al., 1993)\u2014the [latex]_{}^{3}{He}_{trit}[\/latex] begins to accumulate in the groundwater. Accumulation of [latex]_{}^{3}{He}_{trit}[\/latex] continues until groundwater is sampled or exposed again to a gas phase such as when the groundwater discharges to a stream or spring or is pumped out of a well.<\/p>\n<\/div>\n

      \n

      Figure 13<\/span><\/a> illustrates the accumulation of [latex]_{}^{3}{He}_{trit}[\/latex] over time as the initial [latex]_{}^{3}H[\/latex] in groundwater recharge decays. The horizontal axis illustrates the relevant timescale of the [latex]\\frac{_{}^{3}H}{_{}^{3}{He}}[\/latex] age-dating method, where 2.6\u00a0percent of initial [latex]_{}^{3}H[\/latex] remains after 65\u00a0years and 1.4\u00a0percent remains after 75\u00a0years.<\/p>\n<\/div>\n

      \n

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

      \n
      \n
      \n

      <\/span>Figure 13\u00a0\u2011<\/strong>\u00a03<\/sup>H remaining and 3<\/sup>Hetrit<\/sub> produced over time due to radioactive decay. A 3<\/sup>H half\u2011life of 12.32\u00a0years was used.<\/p>\n<\/div>\n<\/blockquote>\n<\/div>\n

      \n

      To determine the groundwater age from [latex]_{}^{3}H[\/latex](t) and [latex]_{}^{3}{He}_{trit}[\/latex](t), the age equation shown in Equation\u00a0(14)<\/span> is used.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
      <\/th>\n[latex]Age = \\frac{\\ln\\left( 1 + \\frac{_{\\ }^{3}{{He}_{trit}(t)}}{_{}^{3}H(t)} \\right)}{\\lambda}[\/latex]<\/th>\n\n\n\n<\/colgroup>\n\n\n
      <\/span>(14)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n<\/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
      Age<\/em><\/th>\n=<\/th>\nelapsed time since groundwater recharge, i.e., since exposure to atmosphere (T)<\/th>\n<\/tr>\n<\/thead>\n
      \u03bb<\/em><\/td>\n=<\/td>\ndecay constant (T-1<\/sup>)<\/td>\n<\/tr>\n
      t<\/em><\/td>\n=<\/td>\ntime of sampling<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n

      Concentration units for both [latex]_{}^{3}{He}_{trit}[\/latex] and [latex]_{}^{3}H[\/latex] in Equation\u00a0(14)<\/span> are in TU. The age equation assumes that groundwater tracer transport can be described as piston flow<\/em> (Maloszewski & Zuber, 1996). Practically speaking, this assumption means that [latex]_{}^{3}H[\/latex] and produced [latex]_{}^{3}{He}_{trit}[\/latex] travel together without mixing across other groundwater flowlines. <\/span>Exercise\u00a05<\/span><\/a>\u2ba7 provides an opportunity to practice calculating estimated groundwater age.<\/p>\n<\/div>\n

      \n

      The age equation is based on the decay of tritium to tritiogenic helium shown in Equation\u00a0(15)<\/span>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
      <\/th>\n[latex]_{\\ }^{3}{H_{trit}(t)} = \\ _{\\ }^{3}{H\\left( t_{0} \\right)(1 - e^{- \\lambda t})\\ }[\/latex]<\/th>\n<\/span>(15)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
      \n

      Initial [latex]_{}^{3}H[\/latex] ([latex]_{}^{3}H[\/latex](t0<\/sub><\/em>)) is equal to the [latex]_{}^{3}H[\/latex](t<\/em>) plus [latex]_{}^{3}{He}_{trit}[\/latex] determined from the groundwater sample as shown in Equation\u00a0(16)<\/span>.<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
      <\/th>\n[latex]_{\\ }^{3}{H\\left( t_{0} \\right)} = \\ _{\\ }^{3}{H(t) +_{\\ }^{3}{{He}_{trit}(t)}\\ }[\/latex]<\/th>\n<\/span>(16)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n
      \n

      The decay constant (\u03bb<\/em>) is calculated as shown in Equation\u00a0(17)<\/span>, based on the half\u2011life of tritium (12.32\u00a0years; Lucas & Unterweger, 2000).<\/p>\n<\/div>\n\n\n\n\n<\/colgroup>\n\n\n
      <\/th>\n[latex]lambda = \\ \\frac{\\ln 2}{12.32\\ years} =[\/latex]0.05626 yr\u20131<\/sup><\/th>\n<\/span>(17)<\/th>\n<\/tr>\n<\/thead>\n<\/table>\n<\/div>\n","protected":false},"author":7,"menu_order":16,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-95","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\/95","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\/95\/revisions"}],"predecessor-version":[{"id":434,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapters\/95\/revisions\/434"}],"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\/95\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/media?parent=95"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/pressbooks\/v2\/chapter-type?post=95"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/contributor?post=95"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/age-dating-young-groundwater\/wp-json\/wp\/v2\/license?post=95"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}