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Title: Flow Time estimation in ungauged basins
Authors: Grimaldi, Salvatore
Petroselli, Andrea 
Alonso, Gustavo
Santini, Monia
Nardi, Fernando
Issue Date: 2009
Publisher: 8th IAHS Scientific Assembly & 37th IAH Congress, 6-12 September 2009, Hyderabad, India
Source: Grimaldi, S. et al. 2009. Flow Time estimation in ungauged basins. 8th IAHS Scientific Assembly & 37th IAH Congress (Hyderabad, India, 6-12 September 2009)
The aim of this work is to focalize the attention on the design flood estimation on small ungauged river basin of limited extension (<150 Km2).
In this contest we refer to the Width Function Based Instantaneous Unit Hydrograph (WFIUH) model, which optimizes, through the DEM, the distributed morphological basin information. The Width Function (WF) is defined as the distance-area function or the probability measure obtained by dividing the number of cells at given hydrologic distance from the outlet by the total number of basin cells (the distance is measured along the flow path and normalized by the maximum distance from the divide to the outlet). WF is easily obtained using common flow direction algorithms on elevation data, but in order to obtain the basin travel time distribution (IUH, or FT, Flow Time) two parameters have to be assigned: the channel and hillslope velocities (Vc, Vh).
Indeed these two values, rescaling the WF expressed in terms of length, provide the travel time of each cell of the basin.
The WFIUH model is not largely applied since these two velocity values have to be calibrated while this IUH approach should be adopted on small and almost ungauged basin. Further improvements can be obtained considering the spatial variability of hillslope velocities with the aim to reduce the number of parameter and to better determine the basin IUH. Overland flow
velocities are recognized to vary with slope length, flow depth, land use and other geomorphic hillslope characteristics. Several approaches for the variability velocity field estimation applied
for FT definition can be found in literature, for instance starting from classic Manning’s law and making assumptions on the hydraulic ratio, or linking hillslope velocity with power laws or local geomorphic properties such as slope or contributing area.
Although several studies have already focused on the relationships between WF, channel flow velocity and hillslope flow velocity, in literature it was not deeply investigated the spatial variability of overland flow velocity and how this variability affects the basin hydrologic response. So, after a brief review of the main methods, aim of this work will be:
A) to highlight if it is useful and what are differences in using a fully spatial distributed hillslope flow velocity field to rescale the FL, as respect to the standard approach which considers constant hillslope and river network velocity values.
B) to evaluate approaches useful for the flow velocity estimation in term of the capability to reproduce appropriate values and in term of the number and type of parameter introduced.
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