Study on the Relationship Between the Fractal Characteristics of Rill Patterns on the Soil Surface and the Rate of Run-off Sediment

可以毫不夸张地说，防止土壤侵蚀的最好方法是控制土壤表面细沟网的发生和发展。意识到这一点，本研究的目的是调查细沟模式与土壤径流之间的关系，并在可能的情况下了解估算细沟土壤流失量的方法。由于细沟网具有不规则和复杂的图案，用经典的几何概念来表达这些图案是很困难的。本文应用分形几何的新概念——分形维数，探讨了土壤流失量与细沟形态分形维数的关系。首先，我们观察了光秃秃山坡上发育的细沟网络，并证实了它们具有分形特性。讨论了从功率谱中得到的分形维数与熵的关系。另一方面，在3年多的时间里，还观察了土壤表面形态和土壤径流量的季节性变化。在坡面进行了人工降雨试验。在此试验中，测量了土壤流失量的时间变化，探讨了细沟形态分形维数与土壤流失量的关系。得到了由四种不同土壤组成的现场斜坡上发育的细沟图案的分形维数。这些土壤是复合花岗岩土“Masado”、“Kuroboku”、风化凝灰岩和火山黏结土。利用分形几何中常用的随机模式模型对细纹的形成过程进行了模拟。模拟的结果表明，模拟的模式与现场斜坡上形成的细沟模式非常相似。

It is not too much to say that the best method to prevent soil erosion is to control the occurrence and the development of rill networks on the soil surface. Realizing this point, the purpose of this study is to investigate the relationship between the rill patterns and soil run-off, and, if possible, to know the method to estimate the soil loss from the rills.As rill networks have a irregular and complex patterns, it is difficult to express the patterns numerically by the classic geometrical concepts. In this study, the relationship between the soil loss and fractal dimensions of rill patterns was discussed by using the new concept of fractal geometrics i. e. fractal dimensions.First, we observed photograhically rill networks that develop on the bare slopes, and confirmed that they have a properties of fractal. And the relation between the fractal dimensions and entropy which can be obtained from power spectrum was discussed. On the other hand, the seasonable change of configuration of soil surface and the soil run-off have been also observed over three years on the test plots.Experiments were carried out by supplying artificial rainfall on the slope. In this experiment, the time variations of soil run-off were measured, and the relationship between the fractal dimensions of rill patterns and soil loss was discussed.The fractal dimensions of rill patterns that develop on-the-spot slopes which was composed of the four different soil were obtained. These soil are decomposite granite soil "Masado", "Kuroboku", weathered tuff and volcanic cohesive soil.The process of formation of rill patterns was simulated with the aid of a random pattern model, which is used in the fields of fractal geometry. As a results of the simulation, the simulated patterns were very similar to the rill patterns that develop on-the-spot slopes.