Laboratory of Ecohydrology, Environmental Engineering Institute, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
Proc Natl Acad Sci U S A. 2014 Feb 18;111(7):2417-24. doi: 10.1073/pnas.1322700111. Epub 2014 Feb 3.
Moving from the exact result that drainage network configurations minimizing total energy dissipation are stationary solutions of the general equation describing landscape evolution, we review the static properties and the dynamic origins of the scale-invariant structure of optimal river patterns. Optimal channel networks (OCNs) are feasible optimal configurations of a spanning network mimicking landscape evolution and network selection through imperfect searches for dynamically accessible states. OCNs are spanning loopless configurations, however, only under precise physical requirements that arise under the constraints imposed by river dynamics--every spanning tree is exactly a local minimum of total energy dissipation. It is remarkable that dynamically accessible configurations, the local optima, stabilize into diverse metastable forms that are nevertheless characterized by universal statistical features. Such universal features explain very well the statistics of, and the linkages among, the scaling features measured for fluvial landforms across a broad range of scales regardless of geology, exposed lithology, vegetation, or climate, and differ significantly from those of the ground state, known exactly. Results are provided on the emergence of criticality through adaptative evolution and on the yet-unexplored range of applications of the OCN concept.
从排水网络配置最小化总能量耗散的精确结果是描述景观演化的一般方程的稳定解出发，我们回顾了最优河流模式的具有尺度不变结构的静态特性和动态起源。最优河道网络（OCN）是通过对动态可及状态的不完美搜索来模拟景观演化和网络选择的跨越网络的可行最优配置。然而，OCN 是无环的跨越配置，仅在由河流动力学施加的约束所产生的精确物理要求下才是如此——每个跨越树都是总能量耗散的精确局部最小值。值得注意的是，动态可及的配置，即局部最优解，稳定为多种亚稳态形式，尽管它们具有普遍的统计特征。这种普遍特征很好地解释了跨越广泛尺度的河流地貌的测量比例特征之间的联系，无论地质、暴露的岩性、植被或气候如何，与确切知道的基态有很大的不同。还提供了通过自适应进化出现临界性的结果，以及 OCN 概念尚未探索的应用范围。
