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 Fréchet 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 km2 and 0.002% of the basin area for basins large than 2700 km2.The comparison between the measured and the equivalent hydrographs of Nash and Fréchet models for each event shows that there are obvious discrepancies in terms of peak discharge, time to peak, time 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 ranges between 12.5% for Nash to 61% for Fréchet, RE of is −53.8% for both Nash and Fréchet, while RE of is 0.0% for both Nash and Fréchet and RE of runoff volume ranges between −37.5% for Nash to −34.5% for Fréchet. The study recommends investigating other GIUH models to improve the RE in arid regions.

中文翻译：

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使用等效 Horton-Strahler 比率开发地貌瞬时单位水文图 (GIUH) 以预测干旱地区的山洪暴发

摘要 Horton-Strahler 比率对于描述河流网络和使用 GIUH 概念识别流域的水文响应很重要。这些比率通常对用于从数字高程模型 (DEM) 中提取河流网络的选定阈值区域敏感。研究正在寻求找到合适的阈值，但没有成功。河流网络属性的自相似性方法可以使用与阈值区域无关的参数来估计等效的 Horton-Strahler 比率。这种方法应用于沙特阿拉伯的四个干旱盆地。等效的 Horton-Strahler 比率用于根据 Nash 和 Fréchet 水文过程图模型推导出 GIUH。结果表明，Horton-Strahler 比率和最高阶流的长度强烈依赖于阈值，因此 GIUH 特性显示出由于阈值的差异。本研究建议对于小于 280 平方公里的流域使用等于流域面积的 0.02% 的阈值面积，对于大于 2700 平方公里的流域使用等于流域面积的 0.002% 的阈值面积。 Nash 和 Fréchet 的实测和等效水位线的比较每个事件的模型显示，在高峰流量、高峰时间、时间滞后和径流量方面存在明显差异。Nash 模型的结果相对较好地代表了实测的水文过程线。一些事件的最小相对误差 (RE) 是：RE 范围在 Nash 的 12.5% 到 Fréchet 的 61% 之间，Nash 和 Fréchet 的 RE 均为 -53.8%，而 Nash 和 Fréchet 的 RE of 均为 0.0%，径流体积的 RE 介于 Nash 的 -37.5% 至 Fréchet 的 -34.5% 之间。该研究建议调查其他 GIUH 模型以改善干旱地区的可再生能源。