Revision of Fontes & Garnier's model for the initial ¹⁴C content of dissolved inorganic carbon used in groundwater dating

The widely applied model for groundwater dating using ¹⁴C proposed by Fontes and Garnier (F&G) (Fontes and Garnier, 1979) estimates the initial ¹⁴C content in waters from carbonate-rock aquifers affected by isotopic exchange. Usually, the model of F&G is applied in one of two ways: (1) using a single ¹³C fractionation factor of gaseous CO₂ with respect to a solid carbonate mineral, εg/ₛ, regardless of whether the carbon isotopic exchange is controlled by soil CO₂ in the unsaturated zone, or by solid carbonate mineral in the saturated zone; or (2) using different fractionation factors if the exchange process is dominated by soil CO₂ gas as opposed to solid carbonate mineral (typically calcite). An analysis of the F&G model shows an inadequate conceptualization, resulting in underestimation of the initial ¹⁴C values (¹⁴C₀) for groundwater systems that have undergone isotopic exchange. The degree to which the ¹⁴C₀ is underestimated increases with the extent of isotopic exchange. Examples show that in extreme cases, the error in calculated adjusted initial ¹⁴C values can be more than 20% modern carbon (pmc). A model is derived that revises the mass balance method of F&G by using a modified model conceptualization. The derivation yields a “global” model both for carbon isotopic exchange dominated by gaseous CO₂ in the unsaturated zone, and for carbon isotopic exchange dominated by solid carbonate mineral in the saturated zone. However, the revised model requires different parameters for exchange dominated by gaseous CO₂ as opposed to exchange dominated by solid carbonate minerals. The revised model for exchange dominated by gaseous CO₂ is shown to be identical to the model of Mook (Mook, 1976). For groundwater systems where exchange occurs both in the unsaturated zone and saturated zone, the revised model can still be used; however, ¹⁴C₀ will be slightly underestimated. Finally, in carbonate systems undergoing complex geochemical reactions, such as oxidation of organic carbon, radiocarbon ages are best estimated by inverse geochemical modeling techniques.