The physics behind groundwater recession and hydrologically passive mixing volumes.

To estimate groundwater flow and transport, lumped conceptual models are widely used due to their simplicity and parsimony - but these models are calibration reliant as their parameters are unquantifiable through measurements. To eliminate this inconvenience, we tried to express these conceptual parameters in terms of hydrodynamic aquifer properties to give lumped models a forward modelling potential. The most generic form of a lumped model representing groundwater is a unit consisting of a linear reservoir connected to a dead storage aiding extra dilution, or a combination of several such units mixing in calibrated fractions. We used one such standard two-store model as our test model, which was previously nicely calibrated on the groundwater flow and transport behaviour of a French agricultural catchment. Then using a standard finite element code, we generated synthetic Dupuit-Forchheimer box aquifers and calibrated their hydrodynamic parameters to exactly match the test model’s behaviour (concentration, age etc). The optimized aquifer parameters were then compared with conceptual parameters to find clear physical equivalence and mathematical correlation - we observed that the recession behaviour depends on the conductivity, fillable porosity, and length of the catchment whereas the mixing behaviour depends on the total porosity and mean aquifer thickness. We also noticed that for a two-store lumped model, faster and slower store represents differences only in porosities making it rather a dual porosity system. We ended with outlining a clear technique on using lumped models to run forward simulations in ungauged catchments where valid measurements of hydrodynamic parameters are available.