流域水系地貌定律的适应性与异质性研究  

Study on adaptability and heterogeneity of water system geomorphic laws in watersheds

作　　者：李发文[1] 刘慧婉 仇昊雨 彭诗涵 LI Fawen;LIU Huiwan;QIU Haoyu;PENG Shihan(State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学水利工程智能建设与运维全国重点实验室,天津300072

出　　处：《水资源保护》2025年第2期19-29,共11页Water Resources Protection

基　　金：国家重点研发计划项目(2023YFC3006601);国家自然科学基金项目(52239004)。

摘　　要：利用ArcGIS提取不同空间尺度的水系资料,对Horton定律和Hack定律在黄河、淮河、海河和长江流域的适应性和异质性进行了研究并提出了7类地貌单元的分支比和长度比参数的推荐值。结果表明:Horton定律的对数回归拟合相关系数普遍在0.9以上,Hack定律的双对数回归拟合相关系数也在0.6以上,两大定律在不同地貌具有良好的适应性;除大通河、沁丹河和信江等个别流域外,流域分支比均为3~5,长度比均为1.5~3.0,且不同地貌发育阶段的霍顿比呈显著梯度递减趋势,不同地貌单元的霍顿比也呈一定梯度分布,不同地貌单元的霍顿比分布相似度高,各流域水系具有很大自相似性;两大定律在水系地貌方面具有显著的空间异质性,霍顿比在空间上呈现随机正态分布,其空间自相关性不明显;高原区、高山区、高原-中低山过渡区、中低山老年期区、中低山壮年期区、丘陵区、平原区等7类地貌单元的分支比推荐值分别为4.58、4.02、4.34、4.50、4.02、4.25、4.20,长度比推荐值分别为2.66、2.28、2.22、2.28、2.23、2.26、2.12。Using ArcGIS to extract water system data at different spatial scales,the adaptability and heterogeneity of Horton’s law and Hack’s law in the Yellow River,Huaihe River,Haihe River,and Yangtze River basins was investigated,and recommended values for branch ratio and length ratio parameters for seven types of geomorphic units were proposed.The results show that the logarithmic regression fitting correlation coefficient of Horton’s law is generally above 0.9,and the double logarithmic regression fitting correlation coefficient of Hack’s law is also above 0.6,indicating that the two laws have good adaptability in different landforms.Except for a few watersheds such as Datong River,Qindan River,and Xinjiang River,the branch ratio of each watershed is 3 to 5,and the length ratio is 1.5 to 3.0.Moreover,the Horton ratio of different geomorphic development stages shows a significant gradient decreasing trend,and the Horton ratio of different geomorphic units also exhibits a certain gradient distribution.The distribution similarity of Horton ratio of different geomorphic units is high,and the water systems in each watershed have great self-similarity.The two laws have significant spatial heterogeneity in water system geomorphy,with the Horton ratio exhibiting a random normal distribution in space and no obvious spatial autocorrelation.The reference values for branch ratios in seven geomorphic regions,including plateau area,high mountain area,plateau middle low mountain transition area,middle low mountain elderly area,middle low mountain middle-aged area,hilly area,and plain area,are 4.58,4.02,4.34,4.50,4.02,4.25,and 4.20,respectively,and the reference values for length ratios are 2.66,2.28,2.22,2.28,2.23,2.26,and 2.12,respectively.

关 键 词：DEM 河网提取 Horton定律 Hack定律 地统计 聚类分析 流域水文响应 水系地貌 

分 类 号：TV213.4[水利工程—水文学及水资源]