Estimating groundwater mean transit time from SF₆ in stream water: field example and planning metrics for a reach mass-balance approach

Stream reach mass-balance can be used to estimate groundwater age at scales larger than individual wells. Atmospherically derived SF₆ was used as an age-dating tracer in reach mass-balance analysis of six stream reaches in Nebraska, USA. The goal was to estimate the flow-weighted mean SF₆ concentration in the groundwater discharge to each reach (C_gw) and the groundwater mean transit time (MTT) based on C_gw. The C_gw in one reach (1.48 fmol/kg) was consistent with a MTT of 27 years. High uncertainty in C_gw prevented plausible MTT estimates in the other reaches. Monte Carlo analyses indicated that low rates of groundwater inflow to the stream reaches (Q_gw) led to high uncertainty in C_gw. This issue can affect the success of any reach mass-balance analysis, for age dating tracers or other solutes. To improve the likelihood of success in future applications of reach mass-balance, two new planning metrics are proposed for use, separately or together: the ratio of groundwater recharge rate (R) to stream density (D) within a watershed, and the long-term average Q_gw/Q_d in a stream reach (where Q_d is stream discharge at the downstream end of the reach). In comparison to the Nebraska study site (R/D = 107 m²/year), more accurate estimation of C_gw was achieved in a previous SF₆ study in North Carolina (USA) with greater R/D (231 m²/year). Larger Q_gw/Q_d is associated with more accurate outcomes in reach mass-balance, and long-term average Q_gw/Q_d in stream reaches may be estimated by GIS analysis of watershed areas and/or stream lengths.