Research On Fractal Box Dimension Of River Network In Loess Plateau Based On DEM

Fractal theory was first put forward by American mathematician Mandelbrot,who used fractal dimension to describe complex figures in nature.With the development of fractal theory,it has been widely used in various fields.Fractal theory plays a very important role in the study of geography.Fractal dimension can describe the development stages of Davies landform erosion cycle theory quantitatively.Previous studies have applied the fractal theory to the morphological analysis of gully landform and the difference of geomorphic pattern,and analyzed the morphological characteristics of gully from the scale of the whole country,different landforms,different watersheds,different scales and different regions.Loess Plateau,as one of the four plateaus in China,has a vast area and serious soil erosion,which is one of the most valuable regions for research.After tens of thousands of years of accumulation and transportation,the loess on the Loess Plateau has gradually formed the present landform of thousands of ditches and ravines under the combined action of wind and water erosion.Based on SRTM1 data of 30 meters,10 complete basins on the Loess Plateau were selected as experimental sample areas to study their fractal characteristics.This paper discusses the spatial differentiation characteristics of box dimension of 22 basins in the middle reaches of the Yellow River basin and both banks of the main river basin.In order to improve work efficiency,this paper develops a software for calculating box dimension in Net.5 environment based on C#language.The software can calculate the box dimension with different box length and calculate the scale-free interval by itself on the premise that the fractal characteristics are better.The main research contents and results show that:(1)The box dimension method was used to extract the digital river networks under 15 thresholds from 10 sample areas,and the fractal dimension analysis was carried out respectively.The results show that the river network has obvious fractal characteristics and the value of box dimension is closely related to the selection of confluence threshold.Under the confluence threshold of 200-3000,the box dimension values of Huangshui Basin,Zuli River Basin,Luohe River Basin,Yanhe River Basin,Wuding River Basin,Sanchuan River Basin,Tuwei River Basin,Kuye River Basin,Huangfuchuan Basin and Hunhe Basin are1.3056-1.0901,1.2837-1.0721,1.3063-1.0905,1.2810-1.0632,1.3279-1.0969,1.2943-1.0765,1.3173-1.0906,1.3064-1.0763,1.2963-1.0737,1.3012-1.0817,respectively.The experimental results show that there is a good quantitative statistical model between confluence threshold and box dimension value.The dimension of the river network box keeps increasing with the decrease of the threshold,and its expression can be summarized asD₁(28)ax ^b,where D₁is the box dimension,x is the confluence threshold,and a and b are the coefficients.The watershed development stage based on box dimension discrimination is also approaching to the prime stage.Therefore,the selection of appropriate confluence threshold is of guiding significance for quantitative description of watershed development stage.(2)There are significant differences in the fractal characteristics of basins under different geomorphic types,and there are also significant differences in the trends between confluence threshold and box dimension.The watershed thresholds of different geomorphic types are different from the inflection points of the box dimension quantitative statistical model.For the loess landform,the loess hills and gully areas of the loess hilllock and loess ridge areas are the most complex,and the basin of this landform type region has the largest box-dimension value,while the box-dimension value of loess plateau and loess plateau is relatively small.Combined with the quantitative statistical model between confluence threshold and box dimension,with the constant increase of coefficient a,the sequence of soil and water loss regionalization on the Loess Plateau is the loess hilly region,the loess rocky mountainous region,and the sandstorm region.(3)To calculate the fractal dimension of water system,it is necessary to appropriately select the scale-free interval of fractal.The experimental results show that in the 10 sample regions selected in this paper,on the premise that all have fractal characteristics,the larger the range of scale-free interval,the larger the value of box dimension.In the case of the same scale-free range,the longer the length of the box side length,the larger the box dimension value.Therefore,the selection of scale-free interval affects the value of box dimension,and thus affects the quantitative description of the development stage of watershed geomorphology.In this paper,manual determination method and correlation coefficient test method are selected,and the scale-free interval of river network fractal features is selected with self-developed software.Under this method,the three scale-free intervals selected in this paper all show good fractal characteristics,indicating that it is not completely reasonable to use a single box dimension to describe the development stage of the whole basin.(4)The river network is composed of the main stream and its tributaries.This paper adopts Strahler classification method to explore the fractal characteristics of river tributaries.The first order tributaries were extracted from the digital river network of 10 complete basins in the experimental area.The experimental results show that the first order tributaries have obvious fractal characteristics.Under the threshold of 200 box dimension calculation level tributaries,Huangshui Basin,Zuli River Basin,Luohe River Basin,Yan River Basin,the Wuding River Basin,Sanchuan River Basin,Tuwei River Basin,Kuye River Basin,Huangfuchuan Basin and Hunhe Basin level tributaries box dimension were 1.0190,1.0330,1.0148,0.9805,1.0178,1.1435,1.1590,1.1569,1.1467,1.1419.The box dimensions of the whole basin were 1.3056,1.2837,1.3063,1.2810,1.3279,1.2943,1.3173,1.3064,1.2963 and1.3012,respectively.The experimental results show that the box dimension of the first tributary is smaller than that of the whole basin.In order to further verify the relationship between the tributaries and the box dimension value,the experiment shows that with the increasing of the number of tributaries,the form of the river network becomes more complex,the density of the river network becomes larger,and the box dimension value also increases.The quantitative statistical model between the confluence threshold value and the box dimension value can be summarized asD₂(28)mx(10)n,where D₂is the box dimension,x is the river network density,and m and n are the coefficients.The formula reveals that the value of box dimension is positively correlated with the density of the river network.With the decrease of the coefficient m,the corresponding order of soil and water loss zones on the Loess Plateau is the loess hilly region,the loess rocky mountainous region,and the sandstorm region.(5)The 22 complete watersheds on the left and right banks of the main stream in the middle reaches of the Yellow River Basin have good fractal characteristics.The box dimension values of the left bank of the main stream show a small large small variation law,and the box dimension distribution of the right bank is relatively stable.In the middle reaches of the Yellow River,the box dimension of the left bank is larger than that of the right bank.The statistical model of confluence threshold box dimension A and the statistical model of river network density box dimension coefficient m have opposite characteristics in spatial trend.