Nonparametric estimation of groundwater residence time distributions: What can environmental tracer data tell us about groundwater residence time?

Residence time distributions (RTDs) have been used extensively for quantifying flow and transport in subsurface hydrology. In geochemical approaches, environmental tracer concentrations are used in conjunction with simple lumped parameter models (LPMs). Conversely, numerical simulation techniques require large amounts of parameterization and estimated RTDs are certainly limited by associated uncertainties. In this study, we apply a nonparametric deconvolution approach to estimate RTDs using environmental tracer concentrations. The model is based only on the assumption that flow is steady enough that the observed concentrations are well approximated by linear superposition of the input concentrations with the RTD; that is, the convolution integral holds. Even with large amounts of environmental tracer concentration data, the entire shape of an RTD remains highly nonunique. However, accurate estimates of mean ages and in some cases prediction of young portions of the RTD may be possible. The most useful type of data was found to be the use of a time series of tritium. This was due to the sharp variations in atmospheric concentrations and a short half-life. Conversely, the use of CFC compounds with smoothly varying atmospheric concentrations was more prone to nonuniqueness. This work highlights the benefits and limitations of using environmental tracer data to estimate whole RTDs with either LPMs or through numerical simulation. However, the ability of the nonparametric approach developed here to correct for mixing biases in mean ages appears promising.