Hybrid Nonlinear Reservoir Routing Algorithm (HNRA): A Time of Concentration-Agnostic Approach for the Rational Method Framework

Urban watersheds face increasing water stressors due to intensified extreme rainfall events, inland flooding, and expanded impervious surfaces. Meanwhile, the traditional Rational Method is used worldwide to compute flow peaks in small watersheds due to its simplicity and low data requirements. The simplifying assumptions and hypotheses associated with the use of the Rational Method are widely known and often make the method difficult to use. One key hypothesis is the existence of a time of concentration (Tc), which depends on various watershed characteristics. Over the decades, different formulations for Tc have been proposed, and they can differ significantly in their estimates, leading to significant uncertainty about which peak flows should be used in design. We propose a method to mitigate the impact of Tc uncertainty by modifying the Nonlinear Reservoir Routing algorithm in EPA-SWMM and adopting it within a Rational Method framework. The new HNRA methodology uses the simpler abstraction (i.e., runoff coefficient C) and rainfall (rainfall intensity derived from IDF data), which is often available for Rational Method implementation. Rather than assuming that peak flows occur when rainfall duration matches Tc, a heuristic search is performed to determine the critical rainfall duration with rainfall intensity from IDF that yields the maximum peak flow. The proposed algorithm, applicable to small watersheds, is amenable to implementation in spreadsheet-like tools and in the context of semi-distributed hydrological calculations, yielding not only peak flows but also flow hydrographs. The HNRA was systematically compared to SWMM modeling results using CN-based abstractions, yielding promising results. Future research will extend the comparison for more complex geometries and include ccomparisons with traditional Rational Method implementations.

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