Modeling urban sewers with artificial fractal geometries

Scott Jeffers and Franco Montalto


Sewer models are used to simulate complex urban hydrology.  However, the development of physically based models can be difficult given the limited availability of sewer plans and the time required to incorporate the actual system layout including pipe locations, sizes, inverts, and catchment characteristics.  By contrast, fractal geometries could potentially be used to overcome some of these constraints. In this study, a highly impervious residential urban catchment (54 ha) serviced by a combined sewer in East Boston, Massachusetts is modeled using Storm Water Management Model (SWMM). Two different modeling techniques are compared.  The first is a physically based model developed from the physical characteristic of the network obtained from municipal sewer maps; the second is an artificial model developed based on fractal scaling laws often used to describe natural river basins.  Both models were calibrated to one month of empirical 5-minute interval sewer flow measurements and predicted similar total discharge volumes and peak flows over the course of 10 observed rainfall events (0.5-12.7 mm) with Nash-Sutcliffe model efficiency coefficient (NSE) values of 0.85 over the duration of observed flow.  In a neighboring 24 ha catchment, this process was repeated creating a second comparison between a physically and artificially based model using pipe and catchment model parameters obtained from the previous calibration and evaluated to a second set of observed flow over the same period.  Again, both models predicted similar total discharge volumes and peak flows, although, over the duration of the observed flow, the physically based model was more accurate than the artificial model (NSE of 0.85 and 0.75 respectively).  In both cases, the models were most accurate at simulating storms larger than 5 mm with most deviation in smaller events.  Model resolution was tested by simulating the 54 ha catchment as 1, 10, 24, and 173 subcatchments and showed that accurate simulations could be produced in all of the resolutions however, caution should be taken when employing low resolution aggregated models as suggested from previous academic research

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