水系结构分形特征的研究进展

doi:10.11867/j.issn.1001-8166.2019.1.0048

地球科学进展 ›› 2019, Vol. 34 ›› Issue (1): 48 -56. doi: 10.11867/j.issn.1001-8166.2019.1.0048

水系结构分形特征的研究进展

孟宪萌 ¹(

),张鹏举 ¹,周宏 ²,刘登峰 ³

1. 中国地质大学（武汉）环境学院，湖北武汉 430074
2. 中国地质大学(武汉)地质调查研究院，湖北武汉 430074
3. 西安理工大学水利水电学院，陕西西安 710048

收稿日期:2018-09-21 修回日期:2018-12-10 出版日期:2019-01-10
基金资助:
中国地质调查局项目“清江水文地质调查”(编号：DD20190327);中国地质大学（武汉）中央高校基本科研业务费专项资金资助项目“越流系统中咸水运移规律的研究”(编号：CUG160205)

Recent Advances in Fractal Characteristics of River Network Structure

Xianmeng Meng ¹( ),Pengju Zhang ¹,Hong Zhou ²,Dengfeng Liu ³

1. School of Environmental Studies, China University of Geosciences, Wuhan 430074, China
2. Geological Survey of China University of Geosciences, Wuhan 430074, China
3. School of Water Resources and Hydropower, Xi’an University of Technology, Xi’an 710048, China

Received:2018-09-21 Revised:2018-12-10 Online:2019-01-10 Published:2019-03-05
About author:Meng Xianmeng (1982-), male, Luoyang City, He'nan Province, Associate professor. Research areas include hydrology and water resources. E-mail: mengxianmeng2000@sina.com
Supported by:
Project supported by the China Geological Survey “Hydrogeological survey in Qingjiang Watershed”(No. DD20190327);The Fundamental Research Funds for National University, China University of Geosciences (Wuhan) “Research on the salt transport in a leaky aquifer”(No. CUG160205)

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水系结构对流域调洪蓄水能力、区域景观格局、洪水径流过程和城市管网水网建设等有着重要的影响，定量描述水系结构特征是认识其结构变化规律的前提和基础。由于水系结构无特征尺度，使得分形理论在定量刻画其结构特征中得到广泛应用。通过归纳整理近年来国内外有关分形理论在水系结构特征方面的研究成果，对分形理论的发展进行了梳理，重点归纳总结有关水系分形结构的主要研究内容：水系分形模型的建立及特征参数的计算、水系分维影响因素的探究、水系分维的应用研究。针对3个主要内容分别进行了评述和探讨，指出分形理论在水系结构研究方面仍有广阔的应用研究价值和拓展空间，建立统一的水系分维数计算标准、开展多标度多影响因素下的水系分维研究,以及揭示水系分维数与相关物理现象中蕴含规律之间的关系将是未来的发展方向。

关键词: 水系, 自相似, 分形, 分维数, 影响因素

The river network structure has a significant influence on the flood regulation and water storage capacity of watershed, landscape pattern in watershed, flood and runoff processes, and the construction of pipeline network for water supply and drainage. Quantitative description methods for the river network structure are the premise and basis for a deep understanding of its changing rules. As there is no characteristic scale in the river network, fractal theory is widely used in the description of the characteristics of river network structure. This paper summarized the current advancement in fractal characteristics of river network structure in three aspects: $①$ Establishment of fractal model for the description of river network structure and calculation of its parameters; $②$ Analysis of factors influencing the fractal dimension of river networks; $③$ Application of the fractal dimension of river networks. Based on the review and discussion from the three aspects, it is pointed out that the fractal approach is a theoretically attractive and potentially very effective framework in quantitative description and analysis of the river network structure. And the future direction is to propose a unified computation method for the fractal dimension, interpret multi-fractal characteristics of the river network structure, analyze the different influencing factors on the fractal dimension and reveal the relationship between the fractal dimension and the complicated regularities contained in physical phenomena.

Key words: River network, Self-similarity, Fractal, Dimension, Influencing factors.

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