A review of single-sample-based models and other approaches for radiocarbon dating of dissolved inorganic carbon in groundwater
Numerous methods have been proposed to estimate the pre-nuclear-detonation 14 C content of dissolved inorganic carbon (DIC) recharged to groundwater that has been corrected/adjusted for geochemical processes in the absence of radioactive decay ( 14 C 0 ) - a quantity that is essential for estimation of radiocarbon age of DIC in groundwater. The models/approaches most commonly used are grouped as follows: (1) single-sample-based models, (2) a statistical approach based on the observed (curved) relationship between 14 C and δ 13 C data for the aquifer, and (3) the geochemical mass-balance approach that constructs adjustment models accounting for all the geochemical reactions known to occur along a groundwater flow path. This review discusses first the geochemical processes behind each of the single-sample-based models, followed by discussions of the statistical approach and the geochemical mass-balance approach. Finally, the applications, advantages and limitations of the three groups of models/approaches are discussed. The single-sample-based models constitute the prevailing use of 14 C data in hydrogeology and hydrological studies. This is in part because the models are applied to an individual water sample to estimate the 14 C age, therefore the measurement data are easily available. These models have been shown to provide realistic radiocarbon ages in many studies. However, they usually are limited to simple carbonate aquifers and selection of model may have significant effects on 14 C 0 often resulting in a wide range of estimates of 14 C ages. Of the single-sample-based models, four are recommended for the estimation of 14 C 0 of DIC in groundwater: Pearson's model, (Ingerson and Pearson, 1964; Pearson and White, 1967), Han & Plummer's model (Han and Plummer, 2013), the IAEA model (Gonfiantini, 1972; Salem et al., 1980), and Oeschger's model (Geyh, 2000). These four models include all processes considered in single-sample-based models, and can be used in different ranges of 13 C values. In contrast to the single-sample-based models, the extended Gonfiantini & Zuppi model (Gonfiantini and Zuppi, 2003; Han et al., 2014) is a statistical approach. This approach can be used to estimate 14 C ages when a curved relationship between the 14 C and 13 C values of the DIC data is observed. In addition to estimation of groundwater ages, the relationship between 14 C and δ 13 C data can be used to interpret hydrogeological characteristics of the aquifer, e.g. estimating apparent rates of geochemical reactions and revealing the complexity of the geochemical environment, and identify samples that are not affected by the same set of reactions/processes as the rest of the dataset. The investigated water samples may have a wide range of ages, and for waters with very low values of 14 C, the model based on statistics may give more reliable age estimates than those obtained from single-sample-based models. In the extended Gonfiantini & Zuppi model, a representative system-wide value of the initial 14 C content is derived from the 14 C and δ 13 C data of DIC and can differ from that used in single-sample-based models. Therefore, the extended Gonfiantini & Zuppi model usually avoids the effect of modern water components which might retain ‘bomb’ pulse signatures. The geochemical mass-balance approach constructs an adjustment model that accounts for all the geochemical reactions known to occur along an aquifer flow path (Plummer et al., 1983; Wigley et al., 1978; Plummer et al., 1994; Plummer and Glynn, 2013), and includes, in addition to DIC, dissolved organic carbon (DOC) and methane (CH 4 ). If sufficient chemical, mineralogical and isotopic data are available, the geochemical mass-balance method can yield the most accurate estimates of the adjusted radiocarbon age. The main limitation of this approach is that complete information is necessary on chemical, mineralogical and isotopic data and these data are often limited. Failure to recognize the limitations and underlying assumptions on which the various models and approaches are based can result in a wide range of estimates of 14 C 0 and limit the usefulness of radiocarbon as a dating tool for groundwater. In each of the three generalized approaches (single-sample-based models, statistical approach, and geochemical mass-balance approach), successful application depends on scrutiny of the isotopic ( 14 C and 13 C) and chemical data to conceptualize the reactions and processes that affect the 14 C content of DIC in aquifers. The recently developed graphical analysis method is shown to aid in determining which approach is most appropriate for the isotopic and chemical data from a groundwater system.