## Abstract

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.

Original language | English |
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Pages (from-to) | 556-568 |

Number of pages | 13 |

Journal | Journal of Hydrology |

Volume | 559 |

Issue number | April 2018 |

DOIs | |

Publication status | Published - Apr 2018 |

## Keywords

- Flow regime
- Kinematic wave
- Sensitivity analysis
- Sheet-flow
- Travel time
- Unit hydrograph