Dodds P S, Rothman D H
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt A):4865-77. doi: 10.1103/physreve.59.4865.
Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.
描述河网结构的标度律被证明源自三个简单假设。这些假设为：（1）河网在结构上是自相似的；（2）单一河道是自仿射的；（3）坡面水流汇入河道发生在一个特征距离上（排水密度是均匀的）。我们得到了一组完整的标度关系，将这些标度律的指数联系起来，并发现这些指数中只有两个是独立的。我们进一步证明，在排水密度均匀的地貌情况下，两种主要的河网结构描述（德永定律和霍顿定律）是等价的。用来自真实地貌和一类特殊随机网络的数据对结果进行了检验。
