Assessing the impact of travel time formulations on the performance of spatially distributed travel time methods applied to hillslopes

Rainfall–runoff models are valuable tools to simulate the hydrologic response of a watershed. In recent years, Spatially Distributed Travel Time (SDTT) methods have been developed as an alternative to semi-distributed and distributed models. In these methods, the travel times of grid-cells are summed along flow paths and then convoluted to generate the hydrograph at the outlet. Some aspects of these models remain poorly understood, including the implications of different travel time formulations, the extent to which SDTT models take into account the interaction among cells, the effects of grid-cell resolution, and the validity of the kinematic wave (KW) assumptions in this context. In this study, we use an analytical approach as well as a SDTT model to investigate the significance of considering upstream contributions when calculating the travel times of cells and its influence on the computed time of concentration and overall hydrograph shape. We also analyze the effect of terrain resolution on the performance of SDTT models. Lastly, we study the validity of the KW assumptions when SDTT models are applied to a plane. Results show that considering upstream contributions when computing travel times yields much better results, increasing the modified coefficient of efficiency of the simulated hydrographs from 0.24 to 0.81 on the best case scenario. When using a travel time expression that neglects upstream contributions, finer grid cell sizes reduce the accuracy of the time of concentration and the simulated hydrograph, decreasing efficiency from 0.5 to −0.02 in the worst case scenario. Finally, the KW approximation applies to the plane irrespective of the grid-cell resolution when upstream contributions are considered in the SDTT model for a wide range of slopes and roughness coefficients.