In this study, we combine stochastic network models that reproduce the actual width function and the width function based instantaneous unit hydrograph (WFIUH) that directly makes use of a width function and converts it into runoff hydrographs. We evaluated the stochastic network models in terms of reproducing the actual width function and also the robustness of the semi-distributed model (WFIUH) in application to a test watershed in South Korea. The stochastic network model has an advantage that it replicates width functions of actual river networks, whereas the WFIUH has an advantage that the parameter values are physically determined, which can be potentially advantageous in prediction of ungauged basins. This study demonstrates that the combination of the Gibbsian model and the WFIUH is able to reproduce runoff hydrographs not just for the case of uniform rainfall over the test catchment but also for moving storms. Therefore, results of this study indicate that the impact of spatial and temporal rainfall variation on runoff hydrographs can be evaluated by the suggested approach in ungauged basins even without detailed knowledge of river networks. Once the regional similarity in river network configuration is identified, the proposed approach can be potentially utilized to estimate the runoff hydrographs for ungauged basins.