Width-Function based Instantaneous Unit Hydrograph rainfall runoff model: relationship between Width Function, hillslope flow velocities and concentration times

The Width Function (WF), measuring the number of channel links or the portion of contributing area at the same hydrologic distance (i.e. the distance measured along the downhill flow path) to the outlet, is an important river basin hydrologic parameter. The rescaled WF, obtained by weighting the flow distances with the corresponding flow velocity, characterizes the residency time distribution, that represents the WF Instantaneous Unit Hydrograph (IUH) or WFIUH, a useful tool for the prediction of the hydrologic response in ungauged basins. The rescaled WF is usually obtained by hypothesizing two constant flow velocities, one for the channel part of the basin and one for the hillslope part of the basin, neglecting the heterogeneity of surface flow patterns throughout the basin. This works aims to verify the eventual improvements in the characterization of the flow hydrograph of the WFIUH considering the spatial distribution of hillslope flow velocities as a function of local terrain properties (e.g. slope, land use etc) and river basin lumped parameters (e.g. lag time)