| 基于盒维数的水系分维值估算 |
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| 引用本文： | 郑楠炯.基于盒维数的水系分维值估算[J].中国农村水利水电,2020(5):33-38,52. |
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| 作者姓名： | 郑楠炯 |
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| 作者单位： | 广东省水利电力勘测设计研究院 |
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| 基金项目： | 国重点研发计划项目(2016YFC0402605)。 |
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| 摘 要： | 水系分维值反映河网的复杂程度。利用Arcgis平台及其ModelBuilder基于30和90 m精度DEM(Digital Elevation Model,数字高程模型)提取泗合水流域、韩江流域及子流域河网,采用盒维数法计算系列阈值下的可能水系分维值,并与实际河网计算的分维值比较。结果表明:①泗合水流域分维值相关系数R\+2大于0.98,韩江流域R\+2大于0.97,二者分别在无标度区间内统计自相似,表现出较好的分形特征;②DEM分辨率对盒维数法计算水系分维值影响小;③流域水系分维值随汇流阈值的初增而骤减,然后平缓减小至趋于1;④选择合适的汇流阈值使数字河网与实际河网吻合时,数字河网的分维值一定程度上可以代表实际河网的分维值;⑤流域水系发育均匀时,具有较强的统计自相似性,整个流域与各子流域分维值相近,水系分维值与流域面积不相关。
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| 关 键 词： | 分维值 盒维数 DEM 阈值 河网 |
Fractal Analysis of Drainage Networks Based on Box Dimension |
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| ZHENG Nan-jiong.Fractal Analysis of Drainage Networks Based on Box Dimension[J].China Rural Water and Hydropower,2020(5):33-38,52. |
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| Authors: | ZHENG Nan-jiong |
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| Institution: | (Guangdong Hydropower Planning and Design Institute,Guangzhou 510635,China) |
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| Abstract: | Fractal dimension of drainage reflects the complexity of the river.The larger the fractal dimension,the more mature,the more complex and intense the water system is.Drainage networks of Siheshui Basin and the Hanjiang River Basin and Hanjiang's sub-basins are extracted based on 30 m and 90 m precision DEMs(Digital Elevation Models)by Arcgis.In order to avoid repetitive manual operation and improve computational efficiency,Arcgis'ModelBuilder and Microsoft's Excell are used to make the drainage networks extracted and the fractal dimension values analyze quantitative and automated.Potential drainage fractal dimension values in series confluence thresholds are calculated by box-counting method and compared with the fractal values of actual river networks.This paper analyzes the relationship between fractal dimension values with the resolution of DEMs,confluence thresholds,kinds of the river network diagrams and the drainage area.The results show that:①The correlation index(R\+2)of drainage networks in Siheshui Basin are more than 0.98 and that of Hanjiang Basin are more than 0.97,showing that the study basins are homogeneous in scale-free range and have good fractal character respectively.②Resolution of DEMs,such as 30 m and 90 m precision,have little effect on fractal value based on box-counting method without considering the accuracy of river network.③Fractal dimension values vary from the confluence thresholds of the drainage networks extracted from DEMs,and decrease sharply along with the increases in thresholds at the beginning,and then decrease gently to be value 1,but be more than 1.④The actual fractal dimension value of the river is unique and should be calculated based on real drainage networks.In another way,selecting the appropriate confluence threshold to make digital river network and the actual river network matches,the fractal dimension value of the digital river network can represent the actual dimension value of the real river to some extent.⑤When the drainage system is homogeneous,it has strong statistical self-similarity,so that the fractal dimension of the whole basin is similar to that of each sub-basin.Therefore,drainage fractal dimension values are not related to the basin area. |
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| Keywords: | fractal dimension box-counting method DEM threshold drainage network |
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