| 水系结构的分形和分维——Horton水系定律的模型重建及其参数分析 |
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| 引用本文： | 陈彦光,刘继生.水系结构的分形和分维——Horton水系定律的模型重建及其参数分析[J].地球科学进展,2001,16(2):178-183. |
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| 作者姓名： | 陈彦光 刘继生 |
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| 作者单位： | 1. 北京大学城市与环境学系,
2. 东北师范大学地理系, |
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| 基金项目： | 国家自然科学基金!资助项目“城市体系空间网络的分形结构及其演化机制”(编号 :40 0 710 35 )中关于“城市环境支持系统”的部分研究内容 |
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| 摘 要： | 基于标准分形水系等级序列的镜象对称性，重建水系构成定律：从Horton第一，第二定律出发，导出关于河流长度与位序关系的三参数Zipf模型，从Horton第二，第三定律出发，导出广义的Hack定律；从Horton第一，第三定律出发，导出关于河流长度一流域面积关系的异速生长方程，根据上述数学变换结果建立了水系分维方程式，澄清了不同空间，不同类型的各种维数之间的数理关系。
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| 关 键 词： | 分形 对称性 Horton定律 Hack定律 水系结构 |
| 文章编号： | 1001-8166(2001)02-0178-06 |
FRACTALS AND FRACTAL DIMENSIONS OF STRUCTURE OF RIVER SYSTEMS：MODELS RECONSTRUCTION AND PARAMETERS INTERPRETATION OF HORTON’S LAWS OF NETWORK COMPOSITION |
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| CHEN Yan guang ,LIU Ji sheng.FRACTALS AND FRACTAL DIMENSIONS OF STRUCTURE OF RIVER SYSTEMS：MODELS RECONSTRUCTION AND PARAMETERS INTERPRETATION OF HORTON’S LAWS OF NETWORK COMPOSITION[J].Advance in Earth Sciences,2001,16(2):178-183. |
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| Authors: | CHEN Yan guang LIU Ji sheng |
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| Institution: | 1.Department of Urban and Environmental Sciences,Peking University,Beijing 100871,China;
2.Department of Geography,Northeast Normal University,Changchun 130024,China |
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| Abstract: | Based on standard fractal stream system model and mirror-im agesymmetry of series of channel classes, the first three models of Horton's la ws of network composition can be ‘reconstructed’ by mirror writing the ordinal numbers of channels,i.e., writing ordinals from the highest level to the grass roots. ① From the first and the second laws, we deduce out a three-p arameter Zipf's model, L(r)=C(r-a)-dz,where r is the rank of a river in a network which is marked in order of size, L(r) is the length o f the rth river, as for parameters C=L1Rb/(Rb-1 )]dz, a=1/(1-Rb),and dz=lnRl/lnRb=1 /D. I n the parameter expressions, Rb and Rl are the bifurcation ratio and length ratio respectively, and D is the fractal dimension of river hierarch ies. ② From the second and the third laws, a generalized Hack's model is derive d out as Lm=μAbm, where Lm is the lengt h of the mth order river, Am is the corresponding catchment area , μ =L1A-b1，b=lnRl/lnRa, and in the parameters, Ra is basin area ratio, L1 is the main stream length, and A1 is the drain age area of the mainstream. It is evident that L1=μAb1 is the classic al Hack model. ③ From the first and the third laws, an allometric relationship is deduced as Nm=ηA-σm,where Nm is the number of mth order rivers, Am is corresponding catchment area, η=N1Aσ1,σ=lnRb/lnRa. As an attempt, the geographical space is divided into three: Space 1, existence space-real space; Space 2, evolution space-phase space; Space 3, correlation s pace-order space. Defining Dr, Dn, and Ds as the fractal di mension of rivel, network, and catchment area in real space, and Dl, D b, and Da as the generalized dimension corresponding to Dr, Dn, and Ds, we can construct a set of fractal dimension equations as fo llows, dz=Dl/Db=lnRl/lnRb≈Dr/Dn, b= Dl/Da=lnRl/lnRa≈Dr/Ds, and σ=Db/Da=lnRb/lnRa≈Dn/Ds. These equations show the physical distinction and mathematical relationships between varied dimensions of a system of rivers. |
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| Keywords: | River network Fractals Symmetry Horton's laws Hack's law |
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