Géosciences Montpellier, Université de Montpellier and CNRS UMR 5243, Montpellier, 34095, France.
Nat Commun. 2018 Sep 17;9(1):3791. doi: 10.1038/s41467-018-06210-4.
Since the 1950s river networks have been intensely researched in geosciences and hydrology. This led to the definition of scaling laws that described the organisation of landscapes under fluvial incision and were later explored by statistical physics and fractal mathematics. The emblematic Hack's Law proposes a power-law relationship between watershed area and main stream length. Though extensively documented, a wide range of values is still reported for Hack's parameters. Some authors associate this dispersion to local geologic and climatic conditions. Here based on the analysis of large sets of river basins in various climatic and geological settings, we confirm the geometric similarity of river networks. We demonstrate that basin shape is mostly related to Hack's coefficient and not to the exponent, independently of external forcing such as lithology and pluviometry.
自 20 世纪 50 年代以来，地球科学和水文学领域一直对河流网络进行深入研究。这导致了定标律的定义，这些定律描述了河流侵蚀下的景观组织，后来被统计物理学和分形数学所探索。标志性的哈克定律提出了流域面积与干流长度之间的幂律关系。尽管已经广泛记录，但哈克参数的报道范围仍然很广。一些作者将这种分散归因于局部地质和气候条件。在这里，我们基于对各种气候和地质背景下的大量河流流域的分析，证实了河流网络的几何相似性。我们证明，流域形状主要与哈克系数有关，而与指数无关，而指数与外部强迫如岩性和降雨无关。
