Properties of the closed-system equilibration model for dissolved noble gases in groundwater
Among a variety of models to describe dissolved noble gas concentrations in groundwater in dependence of recharge temperature (T), excess or entrapped air (A), and other parameters, the closed-system equilibration (CE) model proved to be able to provide good fits to measured concentrations and physically reasonable parameter estimates in a variety of studies. Sometimes, however, it yields unrealistically high values for the parameters A and T in combination with large parameter error estimates. We analyze the origin of this behavior and investigate ways to evaluate samples affected by it. Analyses of the structure of the chi2 space led to the insight that the chi2 surface of well-behaved samples shows two local minima, one at realistic parameter values and another one at unphysical values. Problematic samples, however, show only a single minimum at unrealistic values, where large correlations between the CE model parameters occur, leading to large uncertainties of the parameter estimates. Monte Carlo simulations of problematic samples showed a split-up of the estimated parameters A and T in two clusters, one with realistic, one with unrealistic parameter values. This split-up also occurs to a lesser extent for normal samples as well as synthetic samples with relatively large parameter values. This behavior was found to be the cause for a bias of the CE model as recharge temperature estimator, if the mean T of the entire Monte Carlo ensembles is used as best estimate. We found that the unrealistic cluster corresponds to Monte Carlo realizations with increased Ar in combination with decreased Xe concentrations. By applying such concentration changes to synthetic samples, the problematic fitting behavior of some real samples could be reproduced. We propose a new method for dealing with the observed problems, which involves Monte Carlo analyses and a restriction of the statistical analysis to the cluster with physically realistic solutions. This method is able to retrieve the original parameter values from modified synthetic samples and yields realistic results for problematic physical samples.