Discussion

The suggested Impulse Response Function (IRF) method was directly compared with the conventional RTK method. The RTK method displayed a better model efficiency than the IRF method. However, the RTK method being a simple curve fitting method caused the solutions to be variable each time. This might give a modeler a decent representation of the overall RDII, but each RTK parameter might not provide any physical meanings as they are not unique. The combinations of the nine RTK parameters can be vastly different depending on the level of experience that a model has for the model basin. In contrast, the IRF method presented consistent results.
The IRF method is a physics-based RDII estimation method that is combined with a synthetic hydrograph approach. The RTK method uses a simple curve fitting approach of three triangular hydrographs that represent fast, medium, and slow I&I sources. Because of its flexibility and ability to manipulate any hydrographs, the model tends to provide a decent calibration result. However, the RTK method has many local optimal solutions as nine calibratable coefficients are not independent of each other. While the RTK method displayed better model fitness than the IRF method, The IRF result showed improved model efficiency in the validation period than the calibration period, which might imply the robustness of the modeling approach of using physics-based models.
Moreover, predefining IRFs for each modeling unit can speed up the modeling process, which could help to develop a real-time RDII forecast model in the future. Running the entire physics-based model from scratch for every storm event might not be a feasible option. Thus the IRF approach might be desirable for decision making in urban drainage management.
Another benefit of using the three IRF approach is being able to identify relative contributions of different RDII sources when the model is calibrated. Weighting factors of each modeling unit may provide insights on which RDII source is most problematic in the test sewershed. In turn, this study can shed light on defining RDII based on its sources, which helps decision-makers to better understand their unique local RDII issues and facilitate more effective management of the sewer system.
The results of this study need to be interpreted with caution as it presents only one realization of the method in a selected sewershed. Each sewershed has unique characteristics, e.g., age and material of the sewer system, typical house configuration, drainage practices. Every system deals with different RDII challenges, and some do not even have RDII issues, especially in a newly constructed area. The value of this study is to demonstrate the possibility of modeling RDII using physics-based models that take into account hydrological processes.