A rigorous analytical hydrological model for Ensemble Rainfall-Runoff Analysis (ERRA) of catchments. The paper gives the concepts, mathematical details and several proof-of-concepts. ERRA was designed as a tool for iterative and exploration of hydrological data, through trial and error with analyses of varying degrees of complexity. The broad geosciences community could benefit from this statistical approach. The discussion cites some good examples of applications possible in hydrology, but potential also in other related fields as well.