The physics behind groundwater recession and hydrologically passive
mixing volumes.
Abstract
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.