Characterization of karst systems, especially the assessment of structure and geometry of conduits along with forecast of state-variables, are essential for groundwater quality/quantity management and implementation/rehabilitation of large-scale engineering projects in karst regions. These objectives can be fully met by utilizing process-based discrete-continuum models, such as MODFLOW-2005 CFPv2, as employed here. However, such tools should be used with the caveat of the potential non-uniqueness of results. This research focuses on the joint-inversion of discharge, water temperature, and solute concentration signatures of Freiheit Spring in Minnesota, USA, in response to a spatiotemporally small-scale hydraulic and transport experiment. Adopting the multi-model concept to address conceptual uncertainty, seven distinctive model variants were considered. Spring hydro-chemo-thermo-graphs for all variants were simultaneously simulated, employing joint-inversion by PEST. Subsequently, calibrated models were compared in terms of calibration performance, parameter uncertainties and reasonableness, as well as forecast capability. Overall, results reveal the reliability of the discrete-continuum flow and transport modeling, even at a spatiotemporally small-scale, on the order of meters and seconds. All conceptualized variants suggest almost identical conduit tracer passage sizes which are close to the flood-pulse method estimates. In addition, the significance of immobile conduit-associated-drainable storages in karst hydrodynamic modeling, which is uniquely provided in our model code, was highlighted. Moreover, it was demonstrated that the spring thermograph and hydrograph carry more information about the aquifer characteristics than the chemograph. However, this last result can be site-specific and depends on the scale of the experiment and the conceptualized variants of the respective hydrological state.

Unsaturated fractured aquifer systems offer a domain for complex gravity-driven flow dynamics leading to the development of preferential flow along fracture networks that often strongly contributes to rapid mass fluxes. This behaviour is difficult to recover by volume-effective modeling approaches (e.g. Richards equation) due to the non-linear nature of free-surface flows and mass partitioning processes at unsaturated fracture intersections. The application of well-controlled laboratory experiments enables to isolate single aspects of the mass redistribution process that ultimately affects travel time distributions across scales. We use custom-made acrylic cubes (20 cm x 20 cm x 20 cm) in analogue percolation experiments to create simple fracture networks with single or multiple horizontal fractures. A high precision multichannel dispenser produces gravity-driven free surface flow (droplets; rivulets) at flow rates ranging from 1 ml/min to 5 ml/min. Hereby, total inflow rates are kept constant while the fluid is injected via 15 (droplet flow) or 3 inlets (rivulet flow) to reduce the impact of erratic flow dynamics. Normalized fracture inflow rates (Q_f/Q_0) are calculated and compared for aperture widths d_f of 1 mm and 2.5 mm. A higher efficiency in filling an unsaturated fracture by rivulet flow observed in former studies can be confirmed. The onset of a capillary driven Washburn-type flow is determined and recovered by an analytical solution. In order to upscale the dynamics and enable the prediction of mass partitioning for arbitrary-sized fracture cascades a Gaussian transfer function is derived that reproduces the repetitive filling of fractures, where rivulet flow is the prevailing regime. Results show good agreement with experimental data for all tested aperture widths.