Definition of new equivalent indices of Horton-Strahler ratios for the derivation of the Geomorphological Instantaneous Unit Hydrograph

qThe Horton-Strahler concept has been important in river basin geomorphology; it describes scaling properties and identifies GIUH but has also attracted criticisms, because it depends on the threshold area S, which is used to extract the channel network from digital elevation models (DEM), on the position of the outlet and on the few number of ratios used to identify the scaling laws. To overcome these limitations, this paper proposes new indices independently of S and which have similar properties than the Horton-Strahler ratios. Applications were conducted on seven French basins. The methodology consists on analyzing the morphometric properties, such as the drained area, the number of sources, and the length of the channel network as a function of S. The results show that Horton-Strahler ratios vary considerably with S. Particularly, while the Omega-order length L-Omega is a staircase function of S, results show that the channel network is articulated around two main nodes independent of S, which are descriptors of L-Omega. Then, we compared the properties of Horton-Strahler laws to those obtained from self-similarity analysis, which enables to define new indices independent of S. These indices are calculated automatically from DEM, have similar properties as the Horton-Strahler ratios, and are used to calculate the GIUH independently of S. The four new descriptors R-Be, R-Le, R-Ae, and L-e, which have similar properties as R-B, R-L, R-A, and L-Omega respectively, are equivalent to those of Horton-Strahler's laws and can be used as indicators of hydrological similarity for catchment comparison and regionalization.