Analytical solutions for the advection-dispersion model for radon-222 production and transport in shallow porewater profiles

Quantifying the water flux between surface water (SW) and groundwater (GW) bodies is important for determining water balances and understanding controls on surface water quality and sustainable allocation of water resources. Methods that quantify water exchange at point scales are highly desirable due to the heterogeneous nature of SW-GW connectivity. Porewater radon-222 (²²²Rn) profiles can be easily collected and variations of ²²²Rn activity within the sediments below SW bodies can be used to infer water flow and residence times. The current models used to interpret these profiles assume downward flows, limiting their use in gaining, or dynamic environments. We investigate the use of a new analytical solution based on a finite solution of the advection dispersion equation to predict bi-directional water fluxes using ²²²Rn profiles in riverbed sediments. We apply this solution to profiles collected from the Swan Estuary in Western Australia. The estimated fluxes of water from the estuary to groundwater were up to 2.07 m/day, and fluxes from the groundwater to the estuary were up to 1.79 m/day at various times. Estimates made with a previously applied piston-flow model were broadly consistent when predicting fluxes from the estuary to the groundwater; however, the method was unable to predict fluxes from the groundwater to the estuary, as degassing in the surface water meant that all profiles indicated ageing with depth and hence downward flow. The reversal of fluxes was predicted for a period of seasonally high groundwater levels. Our results highlight that not accounting correctly for upward flows can impact predictions of groundwater exchange with surface water bodies such as estuaries. This may lead to errors in water and chemical balances in stream, lake and estuarine environments and sustainable allocation of freshwater resources between ecosystems and human demands.