Legacy pollutants in fractured aquifers: Analytical approximations for back diffusion to predict atrazine concentrations under uncertainty.

We present novel analytical approximations for the estimation of travel distance and relative height of solute concentration peaks within a single fracture system for pollutants that have been temporarily applied at a constant rate in the past. These approximations are used to investigate the spatiotemporal evolution of the concentration of atrazine, as an example for many other so-called legacy compounds that are still found in the groundwater of fractured rock aquifers even decades after their application has stopped. This is done in a stochastic framework to account for the uncertainty in relevant parameters, focusing on probabilities of exceeding the given legal concentration limit and the expected length of the recovery period. We specifically consider the properties of the Muschelkalk limestone aquifer in the Ammer river catchment in SW Germany, and the three major types of carbonate rock facies: Shoal, Tempestite, and Basinal limestones. Atrazine sorption parameters have been determined in laboratory experiments. The simulations confirm that diffusion-limited sorption and desorption may cause considerable atrazine levels long after application stop. For the properties of the considered rock facies types, and corresponding parameter ranges, atrazine concentration above the legal limit is supposed to be limited to locations referring to only a few years of travel time. If the concentration exceeds the legal limit by the year 2022, it will take decades to centuries until recovery.