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络的发生和发展。认识到这一点，本研究的目的是研究细沟形态与土壤径流的关系，并在可能的情况下了解从细沟估算土壤流失量的方法。本研究利用分形几何的新概念--分维，探讨了土壤流失与细沟形态分维的关系。首先，对裸露坡面上发育的细沟网络进行了光影观测，证实了它们具有分维特征。并讨论了由功率谱得到的分维与熵之间的关系。另一方面，在三年多的时间里，也观察到了土壤表面形态和土壤径流的季节性变化。本试验测量了土壤径流的时间变化，讨论了细沟形态的分维与土壤流失的关系，得到了由4种不同土壤组成的就地坡面细沟形态的分维。这些土壤是分解的花岗岩土壤“Masado”、“Kuroboku”、风化凝灰岩和火山粘性土。借助分形几何领域中的随机模式模型，模拟了细沟模式的形成过程。模拟结果表明，模拟结果与现场坡面形成的细沟形态非常相似。

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.