Hydraulic modelling of the two-directional interaction between sewer and river systems
Sewer networks and river systems are most often studied in a separate way. The main reason is that different authorities are responsible for the water management in both systems and that system information in seldom shared. Sewer and river systems may, however, interact in two directions. The first direction is straightforward: the effluent of urban drainage systems and combined sewer overflows have an impact on the receiving river. In mathematical modelling applications, this influence can be described by using the output of the sewer model as an input for the river model (i.e. a one-directional linking of the two models). In the opposite direction, a high water level in the river may avoid excess sewer flow to be discharged into the river (in wet weather). In the absence of non-return valves river water even can enter the sewer system. In both cases this will cause an increase of the flood risk along the sewer system. In mathematical modelling applications, this influence can be described by using the river water level as a boundary condition for the sewer model (i.e. a one-directional linking of the two models). When one wants to model both directions of sewer network - river system interaction, multiple iterations have to be made using the one-directionally linked sewer and river models (cf. supra). This can be very time-consuming. A better, less time-consuming solution is to integrate the numerical schemes of both models into one single model (i.e. a two-directional linking of the models).
The SOBEK software of WL | Delft Hydraulics makes it possible to link sewer and river models in a two-directional way and solve each timestep simultaneously the sewer and river equations, including the coupling conditions. This software was used in the study to link existing models for the sewer network of Erpe-Mere (Belgium) and its receiving Molenbeek river. Existing models were available in the HydroWorks / InfoWorks CS software (Wallingford Software, United Kingdom) for the sewer system, and in MIKE11 (DHI Software, Denmark) for the river network. Both models were imported into the SOBEK software for the purpose of the study. Simulation results of the separate models were compared as to investigate the uncertainty in the modelling results due to the differences in the modelling code used. Afterwards, the effect of the two-directional linking of the two systems on the simulation results was investigated. Both historical rain events and synthetic rainfall events were simulated and the effect on the flow conditions was investigated. In order to do this analysis, a comparison was made of the results when (i) the sewer and river models are treated completely separate (i.e. no linking), or (ii) the models are linked in a one-directional way (where the output of the sewer system is used as input in the river model or where the river water levels are used as a downstream boundary condition for the sewer system), or (iii) the models are two-directionally linked (using one single model). It is shown that for the simulation results along the river the two-directional linking generates similar results in comparison with the one-directional linking. However, for the results of the sewer model large differences are found under high flow conditions. Hence, the case study illustrates that two-directional sewer-river interactions can largely influence sewer flood risk estimations and consequently also have an impact on sewer system design.