The Research Of Nonlinear Characteristics And Fractal In The River-network

The river-network is physically consisted of many large or small rivers which are all curved, and each large bend contains small bend. Therefore, how to describe actual external and macroscopical characteristics of the river such as the dense distribution and flexuosity has been noticed by many scholars. Much research has been taken to testify that the fractal in many nonlinear sciences is one of the most effective methods in the field of river-network. Furthermore, river-network is a far-from-equilibrium and open complex system, and involves many kinetic, geologic and hydrometeorological factors, including the microcosmic and directly measurable innate characteristics of the river, which are affected by physical, chemical and biologic factors and finally form complex and ordered network structure. So the biggest problem at present is how to combine external and macroscopical characteristics and microcosmic innate characteristics of river to build a vivid system. Meanwhile, basic theory and data of river-network needed by scientific research and forecast is quite scarce until now.Firstly, box-dimension is used in calculating riverway dimension of Yellow-River delta ancient route of the past 150 years, it is found that riverway dimension can reflect the characteristics of modern riverway of Yellow-River downstream, and the whole trend and association can basically reflect the degree of upgrowth and dynamic factor in the course of the evolution of Yellow-River ancient route. It comes to a conclusion that river and water system are natural fractal in the range of a certainty scale and hold statistical self-similarity. Therefore, we can use fractal theory in the research of river systems. Fractal dimension is a basic parameter of describing essential features of river and water system, and it includes whole information and the result of fluvial dynamics.The shortage of basic data is the biggest difficulty in the research on the river-network. Besides the calculation of dimension, 150-years annual precipitation of Yellow-River valley and 150-years annual runoff of Lijin hydrologic station in Yellow-River downstream were creatively forecasted via annual runoff of Sanmenxia in Yellow-River valley by BP neural-network. It is found that the predicted data is much reliable and precise and manual neural-network can be regarded as a reliable predictive method of supplementing the absent data.Furthermore, the foremost mission is to develop the basic theory on river systems. Four formulae including point dimension, single-width line dimension, different-width line dimension and area dimension are novelly developed by DLA model in fractal dynamics. Considering the poor distinguishability of the actual valley map at present, the four formulae are validated by the use of drawn specific pictures, and then the essential differences between four formulae and box dimension are identified, which should be introduced to the river dynamics. The result showed that these formulae not only incorporate the computational function of box dimension but also roughly reflect the geometric structures and dynamics of river systems, which provide an important mathematical framework to discuss the non-linear characteristics and dynamics of river, and also implicate a new clue to solve the other similar problems.