•Set-up of a monitoring network in an extreme environment.•Relating geometry of karst conduits to level and temperature hydrographs.•Hydraulic modelling of flood response of a conduit system.•Inverse modelling and parameter optimisation.•Interpretation of hydraulic data obtained in karst caves. The nature of epiphreatic flow remains an important research challenge in karst hydrology. This study focuses on the flood propagation along the epiphreatic system of Reka-Timavo system (Kras/Carso Plateau, Slovenia/Italy). It is based on long-term monitoring of basic physical parameters (pressure/level, temperature, specific electric conductivity) of ground water in six active caves belonging to the flow system. The system vigorously responds to flood events, with stage rising >100 m in some of the caves. Besides presenting the response of the system to flood events of different scales, the work focuses on the interpretation of recorded hydrographs in view of the known distribution and size of conduits and basic hydraulic relations. Furthermore, the hydrographs were used to infer the unknown geometry between the observation points. This way, the main flow restrictors, overflow passages and large epiphreatic storages were identified. The assumptions were tested with a hydraulic model, where the inversion procedure was used for an additional parameter optimisation. Time series of temperature and specific electric conductivity were used to assess the apparent velocities of flow between consecutive points.