Simulation of Drainage Network based on the Concept of Random Walk Models

Abstract

This paper consists of two parts. The first part is to summarize a current of studies on simulation of drainage basin networks by using random walk models and to ascertain the meaning of some studies. Leopold and Langbein (1962) at first introduced the concept of entropy in thermodynamics to discuss the evolution of drainage basin networks and applied random walk models to development of drainage networks. They showed two types of construction of random walks. In the second type random walks are constructed on a rectangular cross-section graph paper by using a table of random numbers As the proceedings was very simple and clear and progress was seen in the techniques of Monte-Carlo or random walk computer simulation which has been applied with considerable success in nuclear and molecular physics, the second type of construction has occupied an important position in the study of random walk computer simulation models since 1962. Schenk (1963) at first, carried out Monte-Carlo or random walk computer simulation basing upon the concept of random walk by Leopold and Langbein. Later, his computer simulation model was taken as a fundamental pattern in the study of drainage basin networks simulated by computer. Smart et al. (1967). Hiramatsu and Shimazu (1970), and Kayane and Shimano (1974) have made contributions to this study. They modified Schenck's random walk computer simulation models in their own ways. Kayane and Shimano simulated drainage basin networks by using biased random walk models. According of their models higher occurrence probability would be given to the down-stream direction taking into account the fact that the consequent stream is liable to develop on an originally inclined land surface. The second part is of the simulation of drainage basin network which is modified in this paper. In this simulation model, some varied probability distributions bounded by some rows are given to the generatron field which has a matrix of 80×160 on a computer and these probability distributions and boundaries are changed several times until the drainage network is completed. By this model, it is found that simulation of drainage network may be performed for various cases assuming that the streams develop on originally complexly-inclined land surfaces and are those effected by crustal movements while networks are developing. Some examples of generated drainage networks are shown in Figs. from 2 to 9. Streams above the third order (by Strahler system) are indicated by thick lines.