Abstract This paper presents the effect of the threshold (S) used in the extraction of the stream network on the morphological characteristics, fractal dimensions, and the hydrologic response of arid basins. Four basins with areas vary between 252 and 2726 km2 are considered as a sample in Makkah Al-Mukarramah region, Saudi Arabia (SA). Three different values of the threshold are used for each basin: 0.5 km2, 1.0 km2, and 2.0 km2. The methodology estimated the fractal dimensions of the mainstream and the stream network of the basins based on Horton-Strahler ratios and compared them with measurements from GIS software using the box-counting technique. Two theoretical procedures were used to compute the fractal dimensions. The fractal dimension of the mainstream (d2) is closer to the measured (d) when compared to (d1). Both d1 and d2 overestimated the d values. In contrast, the fractal dimension of the stream network (D1) is closer to the measured (D) values when compared to D2. Both D1 and D2 overestimated D. The values of d range between 1.05 and 1.13 while the D values range between 1.36 and 1.71. Based on the theory of geomorphological instantaneous unit hydrograph (GIUH), it has been shown that the GIUH varies depending on the threshold. The computed GIUH parameters for different thresholds showed that the values of the peak discharge ( q p ) varies between 0.46 and 1.96 (1/hour) and the values of time to peak ( t p ) varies between 0.28 and 1.11 hour. The comparison between observed and estimated storm hydrographs of the gauged Dara basin showed high variability with different thresholds. The relative error (RE) in peak discharge ( Q p ) varies between 0 and 59%. While the RE in runoff volume varies between −7.9% and −58.4%. The RE in lag time ( T l a g ) varies between 6.3% and −275%. The GIUH based on gamma distribution seems not to be a representative model to the hydrographs in arid regions and other models should be investigated. A new approach has to be followed to develop a GIUH that does not depend on the threshold or finding an appropriate threshold that can be used for accurate flood predictions.

中文翻译：

---

河流抽取阈值对干旱盆地形态特征、分形维数和水文响应的影响

摘要 本文介绍了用于提取河流网络的阈值（S）对干旱盆地的形态特征、分形维数和水文响应的影响。面积介于 252 和 2726 平方公里之间的四个盆地被视为沙特阿拉伯 (SA) 麦加穆卡拉玛地区的样本。每个流域使用三个不同的阈值：0.5 平方公里、1.0 平方公里和 2.0 平方公里。该方法基于 Horton-Strahler 比率估计了流域主流和河流网络的分形维数，并将它们与使用盒计数技术的 GIS 软件的测量结果进行了比较。使用两种理论程序来计算分形维数。与 (d1) 相比，主流 (d2) 的分形维数更接近测量值 (d)。d1 和 d2 都高估了 d 值。相比之下，与 D2 相比，河流网络的分形维数 (D1) 更接近测量 (D) 值。D1 和 D2 都高估了 D。d 的值介于 1.05 和 1.13 之间，而 D 值介于 1.36 和 1.71 之间。基于地貌瞬时单位水位线（GIUH）理论，已经表明 GIUH 随阈值而变化。计算出的不同阈值的 GIUH 参数表明，峰值流量 (qp) 的值在 0.46 和 1.96（1/小时）之间变化，达到峰值的时间（tp）值在 0.28 和 1.11 小时之间变化。测得的达拉盆地的观测和估计风暴水位线之间的比较显示出不同阈值的高变异性。峰值放电 (Q p ) 的相对误差 (RE) 在 0 到 59% 之间变化。而径流中的 RE 在 -7.9% 和 -58.4% 之间变化。滞后时间 (T lag ) 中的 RE 在 6.3% 和 -275% 之间变化。基于伽马分布的 GIUH 似乎不是干旱地区水文过程线的代表性模型，应研究其他模型。必须遵循一种新方法来开发不依赖于阈值的 GIUH 或找到可用于准确洪水预测的合适阈值。