Abstract
The Horton-Strahler ratios are important to describe the stream network and to identify the hydrologic response of a basin using the GIUH concept. These ratios are often sensitive to the selected threshold area for the extraction of the stream network form digital elevation models (DEM). Researches are seeking to find out the appropriate threshold with no success. Self-similarity approach of the properties of the stream network can provide an estimation of equivalent Horton-Strahler ratios using parameters independent of the threshold area. This approach is applied on four arid basins in Saudi Arabia. The equivalent Horton-Strahler ratios are used to derive GIUH based on Nash and Frechet hydrograph models. The results indicate that the Horton-Strahler ratios and the length of the highest order stream depend strongly on the threshold and consequently, the GIUH characteristics show discrepancies due to the threshold. This study recommends to use threshold area that is equal to 0.02% of the basin area for basins less than 280 km(2)and 0.002% of the basin area for basins large than 2700 km(2).The comparison between the measured and the equivalent hydrographs of Nash and Frechet models for each event shows that there are obvious discrepancies in terms of peak discharge, Q(p), time to peak,T-p, time lag,T-lag,and the runoff volume. The results of Nash model are relatively better to represent the measured hydrographs. The minimum relative error (RE) of some events are: RE of Q(p) ranges between 12.5% for Nash to 61% for Frechet, RE of T-p is -53.8% for both Nash and Frechet, while RE ofTlagis 0.0% for both Nash and Frechet and RE of runoff volume ranges between -37.5% for Nash to -34.5% for Frechet. The study recommends investigating other GIUH models to improve the RE in arid regions.