Accuracy of Kinematic Wave Approximation for Flood Routing. II. Unsteady Analysis

The applicability of the kinematic wave (KW) approximation was investigated for unsteady flow in prismatic channels. Each of the 16 cases analyzed under steady flow conditions by Moramarco et al. (2008) was now perturbed such that synthetic discharge hydrographs varying around the steady value $Q_0$ and characterized by different values of the wave period $T$ and steady wave travel times, $T_0^{\prime }$ , were obtained. Therefore, based on the kinematic wave number $K$ and steady Froude number ${\mathsf{F}}_0$ , a set of 224 experimental tests were carried out and the KW accuracy was investigated by routing synthetic discharge hydrographs. In this case, the dynamic wave solution DYW was also considered as a benchmark and adopting the critical-flow depth at the downstream end. The performance of KW was assessed using different accuracy measures: (a) errors in dimensionless maximum flow depth along the channel ${\epsilon }_{\max }$ ; (b) explained variance ${\mathrm{NS}}_Q$ on discharge hydrographs at the outlet section; and (c) errors in peak discharge ${\epsilon }_{Q_p}$ and water level ${\epsilon }_{h_p}$ at the downstream channel end, and errors in time to peak discharge ${\epsilon }_{t_{Q_p}}$ and water level ${\epsilon }_{t_{h_p}}$ always at the downstream end. Based on these KW accuracy measures, different scenarios for the KW applicability were found as a function of the quantities $K{\mathsf{F}}_0^2$ and $T∕T_0^{\prime }$ . It was found that the KW applicability depended on the accuracy measure of interest and different criteria were accordingly defined. Moreover, the comparison between the proposed KW applicability criteria and the existing ones shows that these latter tend to limit the KW application and, hence, they have to be used with caution. This insight was also inferred from an analysis of flood events that occurred along an equipped branch of the upper Tiber River in central Italy. Therefore, also based on the real case study, it was shown that there is not a single rule for the KW applicability but different criteria can be defined, taking care, however, that their application strictly depends on the selected accuracy measure.