Density-based global sensitivity analysis of sheet-flow travel time: Kinematic wave-based formulations

Despite advancements in developing physics-based formulations to estimate the sheet-flow travel time (t_SHF), the quantification of the relative impacts of influential parameters on t_SHF has not previously been considered. In this study, a brief review of the physics-based formulations to estimate t_SHF including kinematic wave (K-W) theory in combination with Manning's roughness (K-M) and with Darcy-Weisbach friction formula (K-D) over single and multiple planes is provided. Then, the relative significance of input parameters to the developed approaches is quantified by a density-based global sensitivity analysis (GSA). The performance of K-M considering zero-upstream and uniform flow depth (so-called K-M1 and K-M2), and K-D formulae to estimate the t_SHF over single plane surface were assessed using several sets of experimental data collected from the previous studies. The compatibility of the developed models to estimate t_SHF over multiple planes considering temporal rainfall distributions of Natural Resources Conservation Service, NRCS (I, Ia, II, and III) are scrutinized by several real-world examples. The results obtained demonstrated that the main controlling parameters of t_SHF through K-D and K-M formulae are the length of surface plane (mean sensitivity index T̂_i = 0.72) and flow resistance (mean T̂_i = 0.52), respectively. Conversely, the flow temperature and initial abstraction ratio of rainfall have the lowest influence on t_SHF (mean T̂_i is 0.11 and 0.12, respectively). The significant role of the flow regime on the estimation of t_SHF over a single and a cascade of planes are also demonstrated. Results reveal that the K-D formulation provides more precise t_SHF over the single plane surface with an average percentage of error, APE equal to 9.23% (the APE for K-M1 and K-M2 formulae were 13.8%, and 36.33%, respectively). The superiority of Manning-jointed formulae in estimation of t_SHF is due to the incorporation of effects from different flow regimes as flow moves downgradient that is affected by one or more factors including high excess rainfall intensities, low flow resistance, high degrees of imperviousness, long surfaces, steep slope, and domination of rainfall distribution as NRCS Type I, II, or III.