2D hydrodynamic approach supporting evaluations of hydrological response in small watersheds: Implications for lag time estimation

The use of integrated flood models represents an approach of growing interest in the literature, being the hydrological and hydrodynamic flood processes described entirely within the two-dimensional (2D) hydrodynamic unsteady flow equations. Due to its ability in simulating complex spatial–temporal dependence of both the hydrodynamic and hydrologic responses of a catchment to rainfall events, this kind of approach paves the way to the development of novel lines of research in catchment hydrology. With particular reference to the lag time estimation, the paper focuses on three interrelated issues: 1) the use of the 2D-SWEs model to provide evidence on the variability of the lag time in small basins, 2) the description of the hydrologic response of small catchments based on characteristic times influencing the hydrodynamic response to rainfall events and 3) the representativeness of hydrodynamic-based rainfall-runoff scenarios in the description of the hydrologic response observed in real events. To that purpose, synthetic rainfall-runoff scenarios for different return periods are firstly generated to analyze the hydrologic response time in three ungauged basins. Then regressive formulas, based on ad hoc variables representing characteristic times, are introduced to interpret the variability shown by the computed lag time. Finally, the physical soundness of the proposed approach is tested against observed rainfall-runoff data in four additional basins. Despite all the simplifications introduced in the proposed approach, the regressive formulas provided a reasonably good agreement with the estimations of the lag time of the observed events, showing errors of the order of 30%. The comparison with the predictions of empirical literature formulas further confirms the potential of the proposed approach. This study represents the basis for future research on basin response to rainfall events through the use of a 2D integrated hydrodynamic-hydrologic modeling