Joint inversion of radiogenic Helium-4 and hydraulic head observations with a neural network surrogate: Application for the Neogene aquifer, Belgium

Environmental tracers are naturally occurring widespread substances in a hydrogeological system that can be used to identify flow pathways, travel times, groundwater age, and recharge rates. However, these are not typically included during the numerical model inversion process. Recent work has broadened their use in a quantitative way by incorporating them in formal solutions of the inverse problem to estimate hydraulic properties and groundwater fluxes. This is commonly done with numerical codes that at least enable one-way coupling of the different processes, i.e., groundwater flow and solute-transport. Helium-4, carbon-14 and temperature-depth profile measurements represent a valuable source of information which can be exploited to support performance assessment studies. For the Neogene aquifer in Flanders, groundwater flow and solute transport models have been developed in the framework of safety and feasibility studies for the underlying Boom Clay Formation as potential host for geological disposal of radioactive waste. However, the simulated fluxes by these models are still subject to large uncertainties, as they are typically constrained by hydraulic heads only. While the evaluation of candidate host formations continues, the use of age tracers (e.g. ⁴He) as additional (unconventional) state variable for inverse conditioning is being explored. Current methodological developments to integrate such additional unconventional observations will allow i) to test our current understanding and corresponding models of the system, and ii) to potentially decrease the uncertainties associated with model outcomes by a joint inversion approach. From previous campaigns, a total of 18 ⁴He_rad observations have been collected at selected sites across the Nete catchment. Furthermore, the accumulation of ⁴He_rad by in situ production and crustal flux is included in the inversion of the ⁴He-transport model, where the uncertainty of groundwater flow and transport model parameters is evaluated. Additionally, a Latin hypercube sampling (LHS) design is done with parameters drawn from prior distributions. The corresponding simulation results are used to construct a neural network surrogate model  to be used for uncertainty quantification using Bayesian inference. Here, we will present the first results and interpretations of Helium-4 as potential additional state variable for inverse conditioning, and constraining groundwater flow and solute transport models at the catchment scale.