基于元胞模型的河道纵剖面调整动态模拟

Dynamic modelling on stream profile evolution based on cellular models

纵剖面的调整是河道演化的重要内容,其对于河道整治及水沙灾害机理研究都具有重要意义。利用多年观测资料可以较为精确地分析和推断河道纵剖面的调整过程。但是,这种方法不能从过程机理上对纵剖面的调整进行模拟分析。而自然条件下河道边界条件的复杂性使得对河道纵剖面演化的物理过程模拟有很大困难。元胞自动机是一个时间、空间和状态都离散的动力模型,是研究复杂系统动态演化过程的有力工具。本文以黄河尾闾河道为例,利用一维元胞模型对河道纵剖面的调整进行动态模拟。模拟揭示了河道纵剖面在初始形态、不同水沙组合以及河道延伸等情况下的演化规律与趋势。

Cellular automata （CA） are discrete, dynamical systems that are divided into small cells with each cell taking a certain state. The basic idea of cellular automata or extended cellular automata （cellular models） is to reduce a complex system using complex rules into something simpler. This paper discusses a one-dimensional cellular model for simulating river profile evolution. In the mode, channel is represented by a series of square cells which are linked one by one. The model is started by applying a ＂package＂ of water and sediment to the first cell. Erosion takes place as the water moves from each cell to its neighbors. Sediment is routed downstream according to a transport equation with the transport rate dependent on the elevation difference between two adjacent cells. The eleva- tion of each cell will change depending on the difference between sediment input and output of a cell. When the ＂package＂ has been routed across the last cell, a new ＂package＂ is applied at the first location and the whole process is repeated. Rules used in the model are simple. When these rules are applied at small scales, the resulting profile has large-scale properties. For example, despite of the original form, the stream profile always tends to evolve to an equilibrium profile when keeping the water and sediment entering the first cell constant. It also showed that discharge has much effect on channel evolution. The channel prolongation causes the rise of the riverbed throughout the downstream. This study is a first step towards applying cellular models to complex geographical system modelling.