Joint inversion of groundwater flow,heat, and solute state variables: a multipurpose approach for characterization and forecast of karst systems

Characterization of karst systems and forecast of their state variables are essential for groundwater management and engineering in karst regions. These objectives can be met by the use of process-based discrete-continuum models (DCMs). However, results of DCMs may suffer from inversion nonuniqueness. It has been demonstrated that the joint inversion of observations regulated by different natural processes can tackle the nonuniqueness issue in groundwater modeling. However, this has not been tested for DCMs thus far. This research proposes a methodology for the joint inversion of hydro-thermo-chemo-graphs, applying to two small-scale sink-to-spring experiments at Freiheit Spring, Minnesota, USA. In order to address conceptual uncertainty, a multimodel approach was implemented, featuring seven mutually exclusive variants. Spring hydro-thermo-chemo-graphs, for all the variants simulated by MODFLOW-CFPv2, were jointly inverted using a weighted least squares algorithm. Subsequently, models were compared in terms of inversion and forecast performances, as well as parameter uncertainties. Results reveal the suitability of the DCM approach for simultaneous inversion and forecast of hydro-physico-chemical behavior of karst systems, even at a scale of meters and seconds. The estimated volume of the tracer conduit passage ranges from approximately 46–51 m³, which is comparable to the estimate from the flood-pulse method. Moreover, it was demonstrated that the thermograph and hydrograph contain more information about aquifer characteristics than the chemograph. However, this finding can be site-specific and should depend on the analysis scale, the considered conceptual models, and the hydrological state, which are potentially affected by minor unaccountable processes and features.