Investigating the age distribution of fracture discharge using multiple environmental tracers, Bedrichov Tunnel, Czech Republic

Abstract

The transit time distribution (TTD) of discharge collected from fractures in the Bedrichov Tunnel, Czech Republic, is investigated using lumped parameter models and multiple environmental tracers. We utilize time series of $\delta ^{18}O$, $\delta ^{2}$H and $^3$H along with CFC measurements from individual fractures in the Bedrichov Tunnel of the Czech Republic to investigate the TTD, and the uncertainty in estimated mean travel time in several fracture networks of varying length and discharge. We compare several TTDs, including the dispersion distribution, the exponential distribution, and a developed TTD which includes the effects of matrix diffusion. The effect of seasonal recharge is explored by comparing several seasonal weighting functions to derive the historical recharge concentration. We identify best fit mean ages for each TTD by minimizing the error-weighted, multi-tracer $\chi ^{2}$ residual for each seasonal weighting function. We use this methodology to test the ability of each TTD and seasonal input function to fit the observed tracer concentrations, and the effect of choosing different TTD and seasonal recharge functions on the mean age estimation. We find that the estimated mean transit time is a function of both the assumed TTD and seasonal weighting function. Best fits as measured by the $\chi ^2$ value were achieved for the dispersion model using the seasonal input function developed here for two of the three modeled sites, while at the third site, equally good fits were achieved with the exponential model and the dispersion model and our seasonal input function. The average mean transit time for all TTDs and seasonal input functions converged to similar values at each location. The sensitivity of the estimated mean transit time to the seasonal weighting function was equal to that of the TTD. These results indicated that understanding seasonality of recharge is at least as important as the uncertainty in the flow path distribution in fracture networks and that unique identification of the TTD and mean transit time is difficult given the uncertainty in the recharge function. However, the mean transit time appears to be relatively robust to the structural model uncertainty. The results presented here should be applicable to other studies using environmental tracers to constrain flow and transport properties in fractured rock systems.