Please wait a minute...
img img
地球科学进展  2003, Vol. 18 Issue (2): 178-184    DOI: 10.11867/j.issn.1001-8166.2003.02.0178
1.北京大学城市与环境学系,北京 100871;2.中国科学院地理科学与资源研究所资源与环境信息系统国家重点实验室,北京 100101
Chen Yanguang1, Li Baolin2
1.Department of Geography, Peking University, Beijing 100871, China;2.State of Key Labortory of Resources & Environment Information System, CAS, Beijing 100101, China
 全文: PDF(109 KB)  

根据对分形水系的新近认识探讨了吉林省水系结构的自相似规律。Horton-Strahler的水系标度定律隐含着水系的位序-规模法则和河流长度-流域面积的异速生长关系,这暗示着α= lnRb/lnRl是一种等级结构的维数,不能将之与空间结构维数混同;Hack模型的标度因子b=lnRl/lnRa是一种广义的空间维数之比,不能据之确定主河道的分维。基于上述思想,对吉林省10个主要水系的等级结构进行考察,发现气候相对湿润的山区水系的α值高于气候相对干燥的平原地区水系的α值,而平原-干燥区水系的b值高于山地-湿润区水系的b值。从河流发育的地质、地貌背景和气候-水文关系等角度对上述现象进行了的初步解释,并根据洮儿河的异常α值修正了LaBabera-Rosso的水系分维定义。

关键词: 水系分维Horton定律Hack定律吉林省河流    

Fractal river networks and the relationship between mainstream length and drainage area of Jilin Province are researched in the paper by means of new theoretical progress in fractal geomorphology. It has been proved that the parameter (α) based on Horton’s law, which is always expressed as α=lnRb/lnRl, is a fractal dimension in hierarchical sense instead of spatial sense, and  the double of the scaling factor(b) based on Hack's model,L=μAb, which can be written as b=lnRl/lnRa, is not fractal dimension of river courses, but a ratio of generalized dimension of mainstream to that of corresponding catchment (the latter is not always equal to 2). A discovery is made that the α values of river networks in mountainous areas or rainy places are greater than those in flatlands or the areas with less rainfall, and the b values to the contrary. The contributing factors of the spatial patterns of α- and b- values of river systems distributing in Jilin's map are directed to the configuration of land surface, property of rocks, and precipitation, etc. One of the definition on fractal dimensions of river networks given by LaBarbera and Rosso,D=min(2,2logRb/logRa), has been revised as D=min[2,max(1,2logRb/logRa)], according to the calculated results from the data of Jilin's rivers.

Key words: River network    Relation of mainstream length to catchment area    Fract.
收稿日期: 2002-01-18 出版日期: 2003-04-01
:  K90  

国家自然科学基金项目“城市体系空间网络的分形结构及其演化机制” (编号:40071035)资助.

通讯作者: 陈彦光     E-mail:
作者简介: 陈彦光(1965-),男,河南罗山人,副教授,主要从事地理分形和地理系统的空间复杂性研究.
E-mail Alert


陈彦光,李宝林. 吉林省水系构成的分形研究[J]. 地球科学进展, 2003, 18(2): 178-184.

Chen Yanguang, Li Baolin. STUDIES OF THE FRACTAL NETWORK COMPOSITION OF RIVERS IN JILIN PROVINCE,CHINA. Advances in Earth Science, 2003, 18(2): 178-184.


[1] Hong Shizhong, Hong Shimin. Studies on fractal dimensions in geoscience [J]. Exploration of Nature, 1988,7(2): 33-40. [洪时中,洪时明. 地学领域中的分维研究:水系、地震及其它[J].大自然探索,1988,72):33-40.]

[2] Kong Fanchen, Ding Guoyu. The relationships between tectonic movement and the analytical results of stream systems and loess valleys in Shanxi and its neighborhood using fractal geometry[J]. Seismic Geology, 1991, 13(3): 221-229. [孔凡臣,丁国瑜. 山西及邻区水系与黄土冲沟的分形几何分析结果与构造活动的关系[J].地震地质,1991,133):221-229.]

[3] Li Houqiang, Ai Nanshan. Fractal geomorphology and fractal models of landform evolution [J]. Journal of Nature, 1992,15(7): 516-519. [ 李后强,艾南山. 分形地貌学及地貌发育的分形模型[J] 自然杂志,1992,157):516-519.]

[4] He Longhua, Zhao Hong. The fractal dimension of river networks and its interpretation [J]. Scientia Geographica Sinica, 1996,16(2): 124-128. [何隆华,赵宏. 水系的分形维数及其含义[J].地理科学,1996,162):124-128.]

[5] Feng Ping, Feng Yan. Calculation on fractal dimension of river morphology [J]. Acta Geographica Sinica, 1997, 52(4): 324-330. [冯平,冯焱. 河流形态特征的分维计算方法[J].地理学报,1997,154):324-330.]

[6] Luo Wenfeng, Li Houqiang, Ding Jing, et al. Horton law and fractal nature of branching networks [J]. Advances in Water Science, 1998, 9(2): 118-123. [罗文锋,李后强,丁晶,等.Horton定律及分枝网络结构的分形描述[J].水科学进展,1998,92):118-123.]

[7] Veitzer S A, Gupta V K. Random self-similar river networks and derivations of generalized Horton laws in terms of statistical simple scaling [J]. Water Resources Research, 2000, 36 (4): 1 033-1 048

[8] Troutman B M, Over T M. River flow mass exponents with fractal channel networks and rainfall [J]. Advances in Water Resources, 2001, 24 (9/10): 967-989.

[9] Schuller D J, Rao A R, Jeong G D. Fractal characteristics of dense stream networks [J]. Journal of Hydrology, 2001, 243 (1/2): 1-16.

[10] Schuller D J, Rao A R, Jeong G D. Fractal characteristics of dense stream networks [J]. Journal of Hydrology, 2002,243 (1/2): 1-16.

[11] Da Costa F P, Grinfeld M, Wattis J A D. A hierarchical cluster system based on Horton-Strahler rules for river networks [J]. Studies in Applied Mathematicas, 2002,109 (3): 163-204.

[12] Vicsek T. Fractal Growth Phenomena [M]. Singapore: World Scientific Company, 1989.

[13] Horton R E. Erosional development of streams and their drainage basins: Hydrophysical approach to quantitative morphology [J]. Bulletin of Geophysical Society of America, 1945, 56:275-370.

[14] Strahler A N. Hypsometric (area-altitude) analysis of erosional topography[J]. Bulletin of Geological Society of America, 1952, 63: 1 116-1 142.

[15] Chen Yanguang, Liu Jisheng. Fractals and fractal dimensions of structure of river systems: Models reconstruction and parameters interpretation of Horton's laws of network composition [J]. Advances in Earth Sciences, 2001,16(2):178-183. [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地球科学进展,2001,162):179-183.]

[16] Hack J T. Studies of longitudinal streams profiles in Virginia and Maryland [J]. U.S. Geological Survey Professional Papers, 1957, 294B: 45-97

[17] LaBarbera P, Rosso R. On the fractal dimension of stream networks [J]. Water Resources Research, 1989,25(4): 735-741

[18] Rosso R, Bacchi B, LaBarbera P. Fractal relation of mainstream length to catchment area in river networks [J]. Water Resources Research, 1991, 27(3): 381-387

[19] Tarboton DG, Bras RL, Rodriguez-Iturbe. Comment on "On the fractal dimension of stream networks" by P. LaBarbera and R.Rosso[J]. Water Resources Research, 1990,26(9): 2 243-22 444

[20] Feder J. Fractals [M]. New York: Plenum Press, 1988.

[21] Mandelbrot B B. The Fractal Geometry of Nature [M]. New York: W.H.Freeman, 1983.

[22] Marani A, Rigon R, Rinaldo A. A note on fractal channel network [J]. Water Resources Research, 1991, 27(12): 3 041-3 049.

[23] Gray D M. Interrelationships of water shed characteristics [J]. Journal of Geophysical Research, 1961, 66(4): 1 215-1 223.

[24] Longley P A, Batty M. Fractal measurement and line generalization [J]. Computer Geosciences, 1989, 15(2): 167-183.

[25] Tayayusa H. Fractals [M]. translated by ShenBuming,Chang Ziwen. Beijing: Earthquake Press, 1992. [高安秀树著,沈步明,常子文译. 分数维[M].北京:地震出版社,1989.]

[26] Melton M A. A derivation of Strahler's channel-ordering system [J]. Journal of Geology, 1959, 67: 345-346

[27] Niu Wenyuan. Theoretical Geography [M]. Beijing: Commercial Press, 1992.[牛文元. 理论地理学[M].北京:商务印书馆,1992.]

[28] Chen Fahu, Ai Nanshan. A quantitative approach to morphology of small loess valleys [A]. In: Papers on Exploring Development of Northwest China [C]. Chengdu: Sichuan Science and Technology Press, 1986: 49-56. [ 陈发虎,艾南山. 黄土小流域形态计量探讨[A].见:西北开发探索论文集[C].成都:四川科学技术出版社,1986,49-56.]

[29] Turcotto D L. Fractals and Chaos in Geology and Geophysics2nd Edition[M]. Cambridge, UK: Cambridge University Press, 1997

[30] Ai Nanshan, Yue Tianxiang. Information entropy and its computational methods of morphological systems [A]. In: The Science and Technology Association of XinJiang Uygur Autonomous Region. Entropy and Inter-sciences [C]. BeJing: Meteorology Press, 1988,118-122. [艾南山,岳天祥. 地貌系统的信息熵及其计算方法[A].见:新疆维吾尔自治区科学技术协会编[C].熵与交叉科学. 北京:气象出版社,1988,118-122.]

[1] 赵春红, 李强, 梁永平, 许亮, 王维泰, 卢海平, 唐春雷. 北京西山黑龙关泉域岩溶水系统边界与水文地质性质[J]. 地球科学进展, 2014, 29(3): 412-419.
[2] 姚旭, 周瑶琪, 李素, 李斗. 硅质岩与二叠纪硅质沉积事件研究现状及进展[J]. 地球科学进展, 2013, 28(11): 1189-1200.
[3] 刘春茹,尹功明,Rainer Grün. 石英ESR测年信号衰退特征研究进展[J]. 地球科学进展, 2013, 28(1): 24-30.
[4] 刘巧, 刘时银. 冰川冰内及冰下水系研究综述[J]. 地球科学进展, 2012, 27(6): 660-669.
[5] 范代读,王扬扬,吴伊婧. 长江沉积物源示踪研究进展[J]. 地球科学进展, 2012, 27(5): 515-528.
[6] 唐学远,孙波,李院生,崔祥斌,李鑫. 南极冰盖研究最新进展[J]. 地球科学进展, 2009, 24(11): 1210-1218.
[7] 邓英尔,贾疏源,黄润秋,李扬红. 岩溶缝洞系统地下水系研究[J]. 地球科学进展, 2008, 23(5): 489-494.
[8] 陈翠华,倪师军,何彬彬,张成江. 基于GIS技术的江西德兴地区水系沉积物重金属污染的潜在生态危害研究[J]. 地球科学进展, 2008, 23(3): 312-322.
[9] 朱晓华,蔡运龙. 中国断层系分维及其灰色预测研究[J]. 地球科学进展, 2006, 21(5): 496-503.
[10] 付伟;周永章;杨志军;张澄博;杨小强;何俊国;杨海生;罗春科. 现代海底热水活动的系统性研究及其科学意义[J]. 地球科学进展, 2005, 20(1): 81-088.
[11] 薛传东,刘星,杨浩,李保珠,谈树成. 昆明市地热田越流含水系统中地下热水的数值模拟[J]. 地球科学进展, 2003, 18(6): 899-905.
[12] 刘春学,秦德先,党玉涛,谈树成. 个旧锡矿高松矿田综合信息矿产预测[J]. 地球科学进展, 2003, 18(6): 921-927.
[13] 朱晓华,蔡运龙,王建. 中国旱涝灾害的分形结构[J]. 地球科学进展, 2003, 18(4): 509-514.
[14] 龚家栋,程国栋,张小由,肖洪浪,李小雁. 黑河下游额济纳地区的环境演变[J]. 地球科学进展, 2002, 17(4): 491-496.
[15] 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.