Our understanding of the subglacial drainage system has improved markedly over the last decades due to field observations and numerical modelling. However, integrating data into increasingly complex numerical models remain challenging. Here we infer two-dimensional subglacial channel networks and hydraulic parameters for Gorner Glacier, Switzerland, based on available field data at five specific times (snapshots) across the melt season of 2005. The field dataset is one of the most complete available, including borehole water pressure, tracer experiments and meteorological variables. Yet, these observations are still too sparse to fully characterize the drainage system and thus, a unique solution is neither expected nor desirable. We use a geostatistical generator and a steady-state water flow model to produce a set of subglacial channel networks that are consistent with measured water pressure and tracer-transit times. Field data are used to infer hydraulic and morphological parameters of the channels under the assumption that the location of channels persists during the melt season. Results indicate that it is possible to identify locations where subglacial channels are more likely. In addition, we show that different network structures can equally satisfy the field data, which support the use of a stochastic approach to infer unobserved subglacial features.