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A null‐space Monte‐Carlo (NSMC) approach was applied to account for uncertainty in the calibration of the hydraulic conductivity (K) field for a three‐dimensional groundwater flow model of a major water supply system in Switzerland. The approach generates different parameter realizations of the K field using the pilot point methodology. Subsequently, particle tracking (PT) was applied to each calibrated model, and the resulting particles are interpreted as the spatial pathline density distribution of multiple sources. The adopted approach offers advantages over classical PT which does not provide a means for treating uncertainty originating from the incomplete description of subsurface heterogeneity. Uncertainty in the K field is shown to strongly influence the spatial pathline distribution. Pathline spreading is particularly evident in locations where the information content of the head observations does not sufficiently constrain the estimated parameters. Despite the predictive uncertainty, the pumped drinking water at the study site is most likely dominated by artificially‐infiltrated groundwater originating from the local infiltration canals. The model suggests that within the well field, the central pumping wells could be extracting regional groundwater, although the probability is relatively low. Nevertheless, a rigorous uncertainty assessment is still required since only a few realizations resulted in flow paths that support the field observations. Model results should therefore not be based on only one model realization; rather, an uncertainty analysis should be carried out to provide a sufficiently large suite of equally probable simulations that include all potential sources and pathways. Article impact statement: An inverse stochastic modeling approach with particle tracking provides probability information beyond classical deterministic approaches. [ABSTRACT FROM AUTHOR]

• We propose a new inversion method based on a 3D discrete fracture network modeling. • The method permits to infer the connectivity and fracture hydraulic properties. • The method has been successfully applied to hydraulic tomography data set. • The identified fracture connectivity structure agrees well with independent data. In sparse fracture systems flow and transport patterns are often dominated by main flowpaths and characterized by a strong complexity induced by the fractures' surface roughness, hierarchical arrangement in networks, and from the interaction of the fractures with the surrounding rocks. The accurate characterization of the hydraulic properties and connectivity of major fracture zones is essential to model flow, solute and heat transport and fluid pressure propagation in fractured media. In this study, we present a novel deterministic inverse modeling method for imaging the connectivity and spatial variability of transmissivity and storativity of a network of fractures. The method is based on a numerical model that simulates fluid flow in a simple three-dimensional (3-D) discrete fracture network (DFN) with a fixed fracture network structure. The forward model is coupled to an inverse algorithm to match observed pressure transients obtained from sequential hydraulic cross-hole tests. This method has been successfully tested for constant rate injection tests carried out at the Grimsel Test Site (GTS) in Switzerland. Cross-hole injection tests were conducted in a tomographic configuration, with hydraulic responses monitored at four observation intervals at various depths in two different boreholes. A discrete fracture network approach with a simple parametrization is developed to estimate log-transformed transmissivity (T) and storativity (S) values of hydraulically active fractures between boreholes by inverting the pressure transients, under the hypothesis that T and S are independent variables. We identified several permeable fractures and their connectivity without attempting to represent explicitly the true fracture network geometrical properties (length, orientation, dip), focusing instead on the calibration of a simple model capturing the observed pressure main behavior. The identified inter-borehole connectivity structure agrees well with independent information, including additional data from a cross-borehole step rate injection and hydrogeophysical data. Hence, the proposed tomography approach appears to be a promising approach for characterizing the connectivity structure and hydraulic properties of the main flowpaths in sparsely fractured rock. [ABSTRACT FROM AUTHOR]