The development of a Bayesian modeling approach for estimation of the age distribution of groundwater using radioactive isotopes and anthropogenic chemicals is described. The model considers the uncertainties associated with the measured tracer concentrations as well as the parameters affecting the concentration of tracers in the groundwater, and it provides the posterior probability densities of the parameters defining the groundwater age distribution using a Markov chain Monte Carlo method. The model also incorporates the effect of dissolution of aquifer minerals on diluting the 14C signature and the uncertainties associated with this process on the inferred age distribution parameters. Two demonstration modeling cases have been performed. First, the method was applied to simulated tracer concentrations at a discharge point of a hypothetical 2‐D vertical aquifer with two recharge zones, leading to a mixed groundwater age distribution under different presumed uncertainties. When the error variance of the observed tracer concentrations is considered unknown, the method can estimate the parameters of the fitted exponential‐lognormal distribution with a relatively narrow credible interval when five hypothetical samples are assumed to be collected at the discharge point. However, when a single sample is assumed, the credible intervals become wider, and credible estimations of the parameters are not obtained. Second, the method was applied to the data collected at La Selva Biological Station in Costa Rica. In this demonstration application, nine different forms of presumed groundwater age distributions have been considered, including four single forms and five mixed forms, assuming the groundwater consists of distinct young and old fractions. For the medium geometrical standard deviationδc,i = 1.41, the model estimates a young groundwater age of between 0 and 350 years, with the largest odds being given to a mean age of approximately 100 years, and a fraction of young groundwater of between 15% to roughly 60%, with the largest odds for 30%. However, the method cannot definitively rule out larger fractions of young groundwater. The model provides a much more uncertain estimation of the age of old groundwater, with a credible interval of between 20,000 to 200,000 years.

In this paper, a methodology is proposed for identifying the best equations for estimating the time of concentration (ToC) of watersheds located in a specific geographic region. The methodology primarily works on the basis of modifying available equations to minimize their bias for any particular region of interest. In the methodology, for each watershed, the ToC considered as "reference" is determined using the Natural Resource Conservation Service (NRCS) velocity method employed in the TR-55 model and geographic information systems data. Moreover, a ranking-based selection strategy is developed for evaluating and selecting the best performing methods. In a case study, the proposed methodology is applied to 72 watersheds and subwatersheds in Khorasan Razavi province, Iran. According to the study, the California equation (with a correction factor of 1.715), the Kirpich (Tennessee) equation (with a correction factor of 1.721), and the Arizona DOT equation (with a correction factor of 1.126) have the best performance for the selected watersheds.

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