河网演化过程与地貌特征、水流侵蚀等因素密切相关。结合水流侵蚀作用和原始地貌特征,本文提出了一种河网演化模型。模型将代表侵蚀点的规则点阵分布于高度无规起伏的“坡面”之上,由连接点阵的“四方格子”边作为可供选择的流路,从而对地表网格化。当网格中侵蚀点上的所有“湖点”消失时,河网演化过程达到稳态。稳态河网形态的统计结果显示了与自然河网相一致的诸多标度规律,如流域面积及河流长度的累积概率符合幂律分布,河网某级别支流的平均长度与该级别之间符合指数标度等。从模型的主要思想看,这些标度规律的动力学根源在于河网演化过程中同时存在的确定性(侵蚀)和随机性(地表起伏)。

Usually, river patterns are greatly related to the natural factors, such as water erosion, landform, etc. Based on water erosion mechanism and original landform, a lattice model for river networks is proposed in order to simulate the growth process and to understand the selection of the nature, namely, fractal structure and scaling behaviors. The lattice is located at an inclined plane with fluctuant surface. The edges of the lattice are the possible water route. The selection of water route is dominated by the order of nature, that is, water flows downwards. A lattice point might be a "lake point", since its altitude is less than that of all the nearest neighbors. A steady river network might be set up as soon as all of the lake points disappear. Meanwhile, the scaling relationships dominating the fractal structure might be established. The statistical results on the landscape of the surface and the network connected by the water routes which actually mimic the river channels follow the Horton's laws. The laws suggest that the ratio of the average stream lengths of rank ω+1 to those of rank ω has a fixed value that is independent of ω. The same statements also hold for the ratios of average stream numbers and basin areas. The results show that the cumulative probabilities for the both stream lengths and basin areas conform to the power law distributions. These are in accord with those observed in the real river networks. These power laws indicate that there is no any characteristic scale in a river network. The spirit of the model shows that the dynamical origin of the scaling behavior might lie in both determinacy (erosion) and chance (fluctuations on the surface of the earth).