The present study attempts to identify universal relationships between the geographical characteristics of a basin and the streamflow within a basin by using the parameter regionalization method of a water balance model, with the aim of gaining hydrological knowledge that might enable predictions of streamflow in ungauged basins. To this end, we first revisited existing regional relationships between the parameters of a Tank model and the geographical characteristics in Japanese mountainous basins, and translated the regional relationships between the geographical characteristics of a basin and streamflow. Second, we used a physically distributed rainfall-runoff model to perform a sensitivity analysis on the effect of the geographical characteristics of a hypothetical basin on its streamflow, with the aim of obtaining physically explainable relationships between these factors. Finally, we selected regional relationships that were also explained in the sensitivity analysis as potentially representing universal hydrological knowledge that might help to predict streamflow in ungauged basins. As a result, we obtained the following potentially universal hydrological knowledge: (1) the fraction of surface flow is less in large basins than in small basins; (2) the infiltration at the ground surface is higher if a basin is covered by soil with a high vertical permeability; (3) the fraction of prompt interflow is higher if a basin is covered by soil with a high horizontal permeability; (4) the fraction of delayed interflow is lower in large basins than in small basins and (5) the storage capacity at the ground surface is high if the ground surface is very rough.