Nonlinear Rational Method: Peak Discharge and Hydrograph Computation Without the Time of Concentration

Lumped hydrological modeling approaches based on the Rational Method (RM) continue to be used in engineering practice despite the advent of various sophisticated hydrological modeling tools in the past decades. While the simplicity, low data requirements, and intuitiveness of the RM explain its longevity, many simplifying assumptions and uncertainties make its successful use difficult. Time of concentration (Tc) estimates, for instance, can vary up to 500% and lead to large discrepancies in rainfall intensity computations. We propose the Nonlinear Rational Method (NRM), which combines the low data requirements of the RM for rainfall abstraction with the Nonlinear Reservoir Algorithm to route overland flows while searching for a critical rainfall duration for the maximum peak discharge of the outflow hydrograph, thereby avoiding the need to compute Tc. The NRM is compared against the Storm Water Management Model (SWMM) and the RM-based Peak Flow Search Approach (PFSA). NRM peak discharges were within 15% of SWMM predictions in a systematic analysis of 12 synthetic subcatchments and within 2% of peak flows in a realistic watershed. The NRM was also compared with experimental datasets, indicating its ability to correctly reproduce peak flows. The ability to represent dissimilar subcatchments and to compute peak discharges without uncertainties from Tc makes the NRM an attractive choice for smaller urban catchment hydrological designs.