基于分形理论和信息熵的渭河流域生态环境状况研究
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摘要
渭河是黄河第一大支流，其生态环境的健康状况直接关系到渭河流域社会经济的可持续发展。近年来，渭河流域生态环境状况恶化严重，这将制约和阻碍着区域社会经济的健康发展，因此有必要探讨一种新的方法定量去研究渭河流域生态环境状况的变化，为渭河流域的生态环境治理提出行之有效的措施，以保障渭河的健康生命，促进渭河流社会经济的可持续发展。
运用分形理论研究了渭河流域干流和支流主要水文测站径流序列的波动特征，主要运用多重分形非趋势波动分析方法计算和分析了1日、连续多日以及月径流序列的多重分形波动特征，也探讨了渭河流域南北侧亚流域地貌信息与流域侵蚀产沙以及流域径流过程多重分形波动强度的关系，在此基础上讨论了渭河和泾河流域典型时段日径流过程多重分形波动特征与林地、草地和耕地面积变化的关系，并分析得到了渭河流域径流波动的重要影响因素，主要得到以下几个结论：
（1）所选取的渭河干流林和支流部分水文测站1日、连续多日以及月径流过程均具有明显的多重分形性。因此，用单一分形来描述1日、连续多日以及月径流过程的分形特性是不够的。
（2）通过综合分析，可以认为1日径流序列、连续3日、连续7日、连续15日径流序列更易受到影响因素（降水、蒸发、入渗、森林植被、用水等）的影响，其反映水文现象周期性变化的能力较差，因此波动性大，多重分形性明显，而年径流的变化相对平稳。
（3）通过对渭河流域南北侧亚流域的地貌信息熵和流域面积分析发现，南侧支流流域的地貌发育较北侧成熟，北侧流域地貌大多处于壮年期，水流下切的侵蚀程度大，这与北侧支流流域的产沙较大相吻合。但南侧流域主要支流的流域面积相对北侧较小，影响径流波动的因素较少，因素间的相互作用抵消的也少，因而其径流过程的波动程度较大，与对南北侧支流径流过程的多重分形波动程度的分析结果相一致。
（4）植被覆盖率与河川径流的关系，与流域所处气候区及地形、地质、土壤等环境条件有关。不同的地形地质情况，导致植被覆盖率对径流过程的影响存在差异。
通过建立渭河流域和泾河流域日径流过程多重分形参数与流域生态环境状况的关系，尝试获得评判研究区域生态环境状况的分形学量化指标，研究表明：在渭河流域，森林覆盖率的提高并不导致径流波动的减小；耕地面积的扩大对应径流径流波动增强；而林草植被覆盖率越高，其径流波动越小。
可见，林草植被覆盖率尤其是草地覆盖率可以作为评判渭河流域生态环境优劣的重要指标。即林草植被覆盖率高，生态环境优良，反之生态环境不佳。由此可知，本区实施退耕还林还草，对促使径流过程平稳化效果显著，同时可以明显减少北侧流域的侵蚀产沙对生态环境状况的破坏，保障渭河的健康生命，以促进渭河流域生态环境和社会经济的可持续发展。
Wei River is the largest tributary of the Yellow River.Its ecological environment’s healthstatus is directly related to the sustainable socio-economic development of the Wei RiverBasin. In recent years, the ecological environment of the Wei River was deteriorated seriously,which would restrict and hamper the regional socio-economic’s healthy development. So it isnecessary to explore a new method to quantitatively study the change of eco-environmentalconditions in the Wei River basin and take some effective managemental measures for theeco-environment in the Wei River Basin. They can safeguard the Wei River healthy life, andpromote its sustainable socio-economic development.
In this thesis, fractal theory was used to deal with the fluctuation characteristic of runoffseries in the main hydrological stations which located in the mainstream and tributaries of theWei River. The multi-fractal fluctuation characteristics of the daily, consecutive daily andmonthly runoff series in the Wei River were mainly calculated and analyzed by MF-DFA. Italso discussed that the relationship of morphologic information of north and south sub-basin,sediment yields in a basin and multi-fractal fluctuations in runoff process. On the basis of theprevious calculations and analysis, this thesis discussed that the relationship betweenmulti-fractal fluctuations characteristic in the typical time’s runoff process in the Wei Riverand condition changing,including of woodland area, grassland area and arable land area, andanalyzed the important factors which affect runoff’s fluctuation in the Wei River basin. Thefollowing conclusions can be obtained through the research:
(1) The daily, consecutive daily and monthly runoff processes of partly hydrologicalstation of the main and tributaries of the Wei River had the multi-fractal characteristic.Therefore, it is not enough that using singular fractal to describe the fractal characteristics ofthe daily, consecutive daily and monthly runoff processes.
(2) Through comprehensive analysis, we think that daily, consecutive3daily,consecutive7daily and consecutive15daily runoff were vulnerably affected by impactfactors (precipitation, evaporation, infiltration, forest vegetative ratio, water, etc.).They havepoor ability to reflect the cyclical changes in hydrological phenomena, so its fluctuation is great,the multiple fractal nature is obvious, but changes in annual runoff is relatively stable.
(3) Through analyzing the geomorphic information entropy and the area changing ofnorth and south sub-basin of the Wei river, showed that the degree of landform development of the south bankside is more mature than the north bankside, north side of the basinlandscape is mostly stay in the stage of strong life, degree of down-cut erosion is great, it isconsistent to a larger sediment yields of the north side tributaries. But area of the maintributaries of the south side of the watershed is relatively smaller than the north side, lessfactors can affect runoff fluctuation degree, interactions among factors is less, so thefluctuations of the runoff process is violent, this is consistent with the multi-fractal fluctuationanalysis results of the north and south tributary runoff process.
(4)The relationship between vegetational coverage and runoff, related with climate,topography, geology, soils, and other environmental conditions in the watershed. Differenttopographic and geologic conditions,lead to effect of vegetation cover on the runoff processare different.
Through establish the relationship between multifractal parameters of Weihe River dailyrunoff process and the state of ecological environment, this article try to obtain fractalmeasurement method on evaluation of regional ecological environment,result shows: in WeiRiver watershed, higher forest coverage not means smaller runoff fluctuation, and, hightercropfield area means bigger runoff fluctuation and worse state of ecological environment, buthighter forest-grass vegetation coverage related to the smaller runoff fluctuation.
So, forest-grass vegetation coverage could be take as important indicator to judge thestate of the ecological environment in Weihe area.That is, the high the forest-grass vegetationcoverage, the excellent of the eco-environmental, if on the contrary, the ecologicalenvironment is poor. From this, change more cropfield into grassland is the effective way toreduce the erosion degree and sediment yields in north bankside of the basin significantly,andmake the environmental conditions improved, to keep the healthy of the river, and to promotesustainable development of ecological environment and social economy of the Wei River, too.
运用分形理论研究了渭河流域干流和支流主要水文测站径流序列的波动特征，主要运用多重分形非趋势波动分析方法计算和分析了1日、连续多日以及月径流序列的多重分形波动特征，也探讨了渭河流域南北侧亚流域地貌信息与流域侵蚀产沙以及流域径流过程多重分形波动强度的关系，在此基础上讨论了渭河和泾河流域典型时段日径流过程多重分形波动特征与林地、草地和耕地面积变化的关系，并分析得到了渭河流域径流波动的重要影响因素，主要得到以下几个结论：
（1）所选取的渭河干流林和支流部分水文测站1日、连续多日以及月径流过程均具有明显的多重分形性。因此，用单一分形来描述1日、连续多日以及月径流过程的分形特性是不够的。
（2）通过综合分析，可以认为1日径流序列、连续3日、连续7日、连续15日径流序列更易受到影响因素（降水、蒸发、入渗、森林植被、用水等）的影响，其反映水文现象周期性变化的能力较差，因此波动性大，多重分形性明显，而年径流的变化相对平稳。
（3）通过对渭河流域南北侧亚流域的地貌信息熵和流域面积分析发现，南侧支流流域的地貌发育较北侧成熟，北侧流域地貌大多处于壮年期，水流下切的侵蚀程度大，这与北侧支流流域的产沙较大相吻合。但南侧流域主要支流的流域面积相对北侧较小，影响径流波动的因素较少，因素间的相互作用抵消的也少，因而其径流过程的波动程度较大，与对南北侧支流径流过程的多重分形波动程度的分析结果相一致。
（4）植被覆盖率与河川径流的关系，与流域所处气候区及地形、地质、土壤等环境条件有关。不同的地形地质情况，导致植被覆盖率对径流过程的影响存在差异。
通过建立渭河流域和泾河流域日径流过程多重分形参数与流域生态环境状况的关系，尝试获得评判研究区域生态环境状况的分形学量化指标，研究表明：在渭河流域，森林覆盖率的提高并不导致径流波动的减小；耕地面积的扩大对应径流径流波动增强；而林草植被覆盖率越高，其径流波动越小。
可见，林草植被覆盖率尤其是草地覆盖率可以作为评判渭河流域生态环境优劣的重要指标。即林草植被覆盖率高，生态环境优良，反之生态环境不佳。由此可知，本区实施退耕还林还草，对促使径流过程平稳化效果显著，同时可以明显减少北侧流域的侵蚀产沙对生态环境状况的破坏，保障渭河的健康生命，以促进渭河流域生态环境和社会经济的可持续发展。
Wei River is the largest tributary of the Yellow River.Its ecological environment’s healthstatus is directly related to the sustainable socio-economic development of the Wei RiverBasin. In recent years, the ecological environment of the Wei River was deteriorated seriously,which would restrict and hamper the regional socio-economic’s healthy development. So it isnecessary to explore a new method to quantitatively study the change of eco-environmentalconditions in the Wei River basin and take some effective managemental measures for theeco-environment in the Wei River Basin. They can safeguard the Wei River healthy life, andpromote its sustainable socio-economic development.
In this thesis, fractal theory was used to deal with the fluctuation characteristic of runoffseries in the main hydrological stations which located in the mainstream and tributaries of theWei River. The multi-fractal fluctuation characteristics of the daily, consecutive daily andmonthly runoff series in the Wei River were mainly calculated and analyzed by MF-DFA. Italso discussed that the relationship of morphologic information of north and south sub-basin,sediment yields in a basin and multi-fractal fluctuations in runoff process. On the basis of theprevious calculations and analysis, this thesis discussed that the relationship betweenmulti-fractal fluctuations characteristic in the typical time’s runoff process in the Wei Riverand condition changing,including of woodland area, grassland area and arable land area, andanalyzed the important factors which affect runoff’s fluctuation in the Wei River basin. Thefollowing conclusions can be obtained through the research:
(1) The daily, consecutive daily and monthly runoff processes of partly hydrologicalstation of the main and tributaries of the Wei River had the multi-fractal characteristic.Therefore, it is not enough that using singular fractal to describe the fractal characteristics ofthe daily, consecutive daily and monthly runoff processes.
(2) Through comprehensive analysis, we think that daily, consecutive3daily,consecutive7daily and consecutive15daily runoff were vulnerably affected by impactfactors (precipitation, evaporation, infiltration, forest vegetative ratio, water, etc.).They havepoor ability to reflect the cyclical changes in hydrological phenomena, so its fluctuation is great,the multiple fractal nature is obvious, but changes in annual runoff is relatively stable.
(3) Through analyzing the geomorphic information entropy and the area changing ofnorth and south sub-basin of the Wei river, showed that the degree of landform development of the south bankside is more mature than the north bankside, north side of the basinlandscape is mostly stay in the stage of strong life, degree of down-cut erosion is great, it isconsistent to a larger sediment yields of the north side tributaries. But area of the maintributaries of the south side of the watershed is relatively smaller than the north side, lessfactors can affect runoff fluctuation degree, interactions among factors is less, so thefluctuations of the runoff process is violent, this is consistent with the multi-fractal fluctuationanalysis results of the north and south tributary runoff process.
(4)The relationship between vegetational coverage and runoff, related with climate,topography, geology, soils, and other environmental conditions in the watershed. Differenttopographic and geologic conditions,lead to effect of vegetation cover on the runoff processare different.
Through establish the relationship between multifractal parameters of Weihe River dailyrunoff process and the state of ecological environment, this article try to obtain fractalmeasurement method on evaluation of regional ecological environment,result shows: in WeiRiver watershed, higher forest coverage not means smaller runoff fluctuation, and, hightercropfield area means bigger runoff fluctuation and worse state of ecological environment, buthighter forest-grass vegetation coverage related to the smaller runoff fluctuation.
So, forest-grass vegetation coverage could be take as important indicator to judge thestate of the ecological environment in Weihe area.That is, the high the forest-grass vegetationcoverage, the excellent of the eco-environmental, if on the contrary, the ecologicalenvironment is poor. From this, change more cropfield into grassland is the effective way toreduce the erosion degree and sediment yields in north bankside of the basin significantly,andmake the environmental conditions improved, to keep the healthy of the river, and to promotesustainable development of ecological environment and social economy of the Wei River, too.
引文
艾南山,岳天祥.1988.再论流域系统的信息墒.水土保持学报,2(4):1~9
艾南山.1987.侵蚀流域系统的信息嫡.水土保持学报,2(1):1~8
常福宣.2011.分形理论在水文水资源研究中的应用.[博士毕业论文].四川:四川大学
程花花.2011.基于分形理论的安庆气候变化分析.[硕士毕业论文].安徽:安徽大学
陈靖.2009.基于GIS的渭河下游水质模拟及评价研究.[硕士毕业论文].陕西:西北大学
程磊,徐宗学,罗睿,米艳娇.2009.渭河流域1980-2000年LUCC时空变化特征及驱动力分析.水土保持研究,16(5):1~6
陈腊娇,冯利华.2006.马莲河流域日径流过程分维与土壤侵蚀关系初探.西北林学院学报,(5):11~13
陈莹,许有鹏.2008.长江干流日径流序列的多重分形特征研究.地理研究,(4):819~828
陈亚宁,杨思全.1999.天山麦兹巴赫冰川湖突发性洪水分形特征研究.冰川冻土,(3):253~256
丁晶,刘国东.1999.日径流过程分维估计.四川水力发电,18(4):74~76
杜延辉.2008.多重分形和小波理论在小电流接地系统单相接地故障选线中的应用研究.[硕士学位论文].陕西:西南交通大学
冯金良,张稳.1999.海滦河流域水系分形.泥沙研究,(1):62~65
冯平,冯焱.1997.河流形态特征的分维计算方法.地理学报,(52)4:324~330
冯书成,张建存.1991.商洛地区国有林采伐方式的探讨.陕西林业科技，1(1)：22-25
冯小庆.2010.渭河流域径流过程的分形特征及其与生态环境的关系研究.[硕士毕业论文].陕西:西北农林科技大学
傅军,丁晶.1995.嘉陵江流域形态及流量过程分维研究.成都科技大学学报,(1):74~79
高旭,徐永安.1996.分形曲线曲面在三维地貌中的应用.河海大学学报,24(6):83~87
巩合德,王开运.2003.森林水文生态效应及在川西亚高山针叶林群落中的研究.世界科技研究与发展,25(5):41~46
郭志贤,张骅,向立,郭玉奇,何建民,权春生.1997.北洛河流域水土保持综合治理考察研究.水土保持通报,17(3):9~15
黄明斌,刘贤.2002.黄土高原森林植被对流域径流的调节作用.应用生态学报,13(9):1057~1060
江田汉,邓莲堂.2004.全球气温变化的多分形谱.热带气象学报,(6):673~678
蒋忠信.1987.滇西北三江河谷纵剖面的发育图式与演化规律.地理学报,42(1):16~29
金德生,陈浩.1997.河道纵剖面分形-非线性形态特征.地理学报,(2):154~161
菊春燕.2006.天山北坡军塘湖流域春季径流的分形特征研究.[硕士毕业论文].新疆:新疆大学
李凡华,刘慈群.1998.分形在油气田开发中的应用.力学进展,28(1):101~110
李后强,艾南山.1992.分形地貌学及地貌发育的分形模型.自然杂志,(7):516~519
李怀恩,秦耀民,胥彦玲,李家科.2011.陕西黑河流域土地利用变化对非点源污染的影响研究.水力发电学报,
李会方.2004.多重分形理论及其在图象处理中应用的研究.[博士学位论文].陕西:西北工业大学
李静,桑广书,刘小艳.2009.黑河流域生态环境演变研究综述.水土保持研究,16(6):210~215
李锰,朱令人.分形在地貌学中应用的几个问题的分析.地震研究,25(2):155~162
李贤彬,丁晶.1999.水文时间序列的子波分析法.水科学进展,(2):144~149
李越.2004.渭河氮素非点源污染与流域人类活动的关系.[硕士毕业论文].陕西:西安理工大学
梁虹,卢娟.1997.喀斯特流域水系分形、熵及其地貌意义.地理科学,(17)4:310~315
刘德平.1998.分形理论在水文过程形态特征分析中的应用.水利学报,(2):20~25
刘兴坡,周玉文.2004.日污水流量序列的分形特征研究.中国给水排水.20(12):53~55
刘远东.2011.基于分形表述的表面功能结构的数字化建模.[硕士毕业论文].广东:华南理工大学
卢方元.2005.中国股市收益率波动性研究.[博士学位论文].陕西:西南交通大学
卢方元.2006.中国股市收益率长程相关性研究.管理工程学报,20(3):116~119
陆中臣,贾绍凤.1991.流域地貌系统.大连:大连出版社
马千里,宁新宝,王俊.2006.描述睡眠脑电多重分形特性的一种新参数.科学通报,(15)
马新中,陆中臣.1993.流域地貌系统的侵蚀演化与耗散结构.地理学报,48(4):367~375
马宗伟,许有鹏.2009.水系分形特征对流域径流特性的影响-以赣江中上游流域为例.长江流域资源与环境,18(2):35~39
毛战坡.1999.黑河流域非点源污染控制规划研究.[硕士学位论文].陕西:西安理工大学
莫莉.2008.基于水文法的北洛河流域水土保持措施减沙水代价分析.[硕士毕业论文].陕西:西北农林科技大学
庞宇磊.2009.分形理论在交通中的应用.[硕士学位论文].北京:北京交通大学
彭成彬,陈藕.1989.地震中的分形结构.中国地震,5(2):19-26
邱国玉,尹婧,熊育久,赵少华,王佩,吴秀琴,曾爽.2008.北方干旱化和土地利用变化对泾河流域径流的影响.自然资源学报，23(2):211~218
陕西省人民政府办公厅关于印发陕西省渭河流域城镇污水处理设施建设规划的通知.2004.陕西政报
孙然好,潘保田,王义祥.2006.祁连山北麓地貌信息熵与山体演化阶段分析.干旱区地理,29(1):88-93
孙霞,吴自勤,黄畇.2006.分形原理及其应用.合肥:中国科技大学出版社
铁永波,唐川.2005.基于信息熵理论的泥石流沟谷危险度评价.灾害学,20(4):43~46
汪富泉.1999.泥沙运动及河床演变的分形特征与自组织规律研究.[四川大学博士论文].四川:四川大学
王国杰,姜彤,陈桂亚.2006.长江干流径流的时序结构与长期记忆.地理学报,61(1):47~56
王礼先,张志强.2001.干旱地区森林对流域径流的影响.自然资源学报,16(5):439~444
王佩,邱国玉,尹婧,熊育久,谢芳.2008.泾河流域温度与器皿蒸发量时空特征及变化趋势.干旱气象，26(1):17~22
王倩,邹欣庆.2002.基于GIS技术的秦淮河流域水系分维研究.水科学进展,13(6):751~756
王文圣,向红莲.2005.基于连续小波变换的径流分维研究.水利学报,36(5):598~601
王武成,崔文艺.2008.北洛河上游暴雨洪水特性分析.延安大学学报(自然科学版),27(3):93~97
王晓朋,潘懋.2007.基于流域系统地貌信息熵的泥石流危险性定量评价.北京大学学报(自然科学版),43(2):211~215
王协康,方铎,姚令侃.1999.非均匀沙床面粗糙度的分形特征.水利学报,(7):70~74
王秀春,吴姗.2004.泾河流域水系分维特征及其生态意义.北京师范大学学报,(40)3:364~368
王战平.2009.灞河流域水文特性分析.水资源与水工程学报,20(5):176-179
吴中如,潘卫平.1996.分形几何理论在岩土边坡稳定性分析中的应.水利学报,(4):79~82
肖克东,曾斌.1995.分形分维.现代物理知识,7(3):26
谢芳,邱国玉,尹婧,熊育久,王佩.2009.泾河流域40年的土地利用/覆盖变化分区对比研究.自然资源学报，24(8):1354~1365
谢佳兴.2011.基于MF-DFA和MF-SSA的心脏病理时间序列分析.[硕士学位论文].湖北:南京邮电大学
谢先红,崔远来.参考作物腾发量时间序列的长程相关性和多重分形分布.水利学报,(12):1326~1333
谢元博.2010.泾河流域非点源污染特性分析与SWAT模型模拟.[硕士毕业论文].陕西:西安理工大学
胥彦玲.2007.基于土地利用/覆被变化的陕西黑河流域非点源污染研究.[博士学位论文].陕西:西安理工大学
徐陈辉.2008.基于分形理论的水轮机振动分析.[硕士学位论文].河北:河北工程大学
徐涛.2009.甘肃葫芦河流域的径流分布式模拟.[硕士毕业论文].甘肃:兰州大学
薛素玲.2006.基于GIS的黑河流域非点源氮磷模拟.[硕士学位论文].陕西:西安理工大学
燕爱玲.2007.河川径流时间序列的分形特征研究.[博士学位论文].陕西:西安理工大学
杨操静.2007.水安全评价及其在渭河中的应用研究.[硕士毕业论文].陕西:长安大学
杨国良,游勇,李海燕.2007.旅游景区(点)系统空间分布的分形发育及演化特征——以四川省为例.自然资源学报,22(6):963~973
杨国良.2007.基于分形理论的水下图像分割与识别算法研究.[硕士学位论文].湖北:华中科技大学
杨海军,孙立达,余新晓.1993.晋西黄土区水土保持林水量平衡的研究.北京林业大学学报,15(3):42~50
杨立彬.2007.基于河流健康的渭河流域水资源合理配置研究.[硕士毕业论文].陕西:西安理工大学
姚建,丁晶,艾南山.2004.岷江上游日径流过程分维分析及其生态脆弱性表征.长江流域资源与环境,13(4):380~383
姚令侃,方铎.1997.非均匀沙自组织临界性及其应用研究.水利学报,(3):26~32
姚胜利.2008.渭河流域水文一体化管理初探. http://10000067898.8.sunbo.net/show_=LPUIL41&dname=VGV2051&xpos=165[2008-12-31]
余姝萍,刘国东,吴媛.2005.岷江上游日径流过程分维分析及其生态脆弱性表征.西南民族大学学报,31(1):79-~84
苑莹,庄新田.2007.国际汇率的多重分形消除趋势波动分析.管理科学,(4):80~85
苑莹,庄新田.2008.中国股票市场的长记忆性与市场发展状态.数理统计与管理,27(1):156~163
张明明.2007.黑河干流中游平原区水资源系统分析及其优化调配研究.[硕士毕业论文].陕西:西北大学
张强.2010.长江与沱江交汇河段通航水位研究.[硕士学位论文].重庆:重庆交通大学
张之湘.2005.卵石推移质输移随机性研究.[博士学位论文].四川:四川大学
张志强，王礼先，余新晓，Klaghofer.2001.森林植被影响径流形成机制研究进展.自然资源学报,16(1):79~84
赵辉.2008.南方花岗岩地区红壤侵蚀与径流输沙规律研究.[博士学位论文].北京:北京林业大学
郑祚芳,张秀丽,曹鸿兴.2007.用去趋势涨落分析研究北京气候的长程变化特征.地球物理学报,(02)
周杜辉.2011.渭河流域经济空间分异及其优化对策研究.[硕士毕业论文].陕西:西北大学
周胜明,唐德善.2005.黑河治理项目中游节水研究.水利科技与经济,11(9):548~549
周毅,汤国安.2009.基于DEM的黄土流域地貌发育新量化新指标.南京师范大学虚拟地理环境教育部重点实验室
周宇.2000.洞庭湖变迁的分形研究.水文与水资源,21(2):37~38
朱永清.2006.黄土高原典型流域地貌分形特征与空间尺度转换研究.[博士学文论文].陕西:西安理工大学
庄新田,黄小原.2003.资本市场的分形结构与复杂性.东北大学出版社
Barbera L and Rosso R.1989. On fractal geometry of river networks. Water Resour. Res.,25(4):735~741
Davis W M.1899. The geographical cycle. Geogr.J.,14:481~501
Dietler D and Zhang Y.1992. Fractal aspects of the swiss landscape. Physica A,191:213~219
Feder J.1988. Fractals. New York and London
GuPta V K and Waymire E.1990. Multiscaling properties of spatial rainfall and river flow Distributions.Geophys. Res,95(3):1999~2009
GuPta V K.1989. Statistical self-similarity in river networks parameterized by elevation. Water ResourcesBulletin,25(3)
Hosking J R M.1984. Modeling persistence in hydrologic time series using fractional Difference. WaterResour. Res.,20(12):1898~1908
Kantelhardta J W, Zschiegner S A.2002. Multi-fractal de-trended fluctuation analysis of nonstationarytime series.Physica A,316:87~114
Koscielny-Bunde E, Kantelhardt J W, Braun P, Bunde A, Havlin S.2006. Multi-fractal of River RunoffRecords:De-trended Fluctuation Studies. Journal of Hydrology,322(1-4):120~137
Liu H H and Molz F J.1997. Multi-fractal analyses of hydraulic conductivity distributions. Water Resour.Res.,33(11):2483~2488
Lovejoy S, Schertzer D, Tsonis A A.1987. Functional box-counting and multiple elliptical dimensions inrain. Science,235:1036~1038
Mandelbrot B B.1977. Fractals: Form, Chance and Dimension. San Francisco: Freeman
Mandelbrot B B.1982. The Fractal Geometry of Nature. New York: Freeman
Mekerhar A I, Ibbitt R P, Brown S L R, Dunean M J.1998. Data for Ashley river to test Channel networkand river basin heterogeneity concepts. Water Resour. Res.,34(1):139~142
Montanari A, Rosso R and Taqqu.1997. Fractionally differenced ARIMA models applied to hydrologictime series: identification estimation, and simulation. Water Resour. Res.,33(5):1035~1044
Nikora V L, Sapozhnikov V B, Noever D A.1993. Fractal geometry of individual river-channels and itscomputer simulation. WaterResour.Res,29(10):3561~3568
Nikora V L.1991. Fractal structures of river plan forms. Water Resour.Res,27(6):1327~1333
Peng C K, Buldyrev S V.1994. Mosaic organization of DNA nucleotides. Phys Rev E,49:1685~1689.
Robert A, Roy A G.1990. On the fractal interpretation of the main-stream length-drainage arearelationship.Water Resour.Res.,26(9):839~842
Rodriguez-Iturbe I, Ijjasz-Vasquez E and Bras, Tarboton D G.1992. Power law distribution of dischargeand energy in river basins. Water Resour. Res.,28(4):1089~1093
Rodriguez-Iturbe I, Marani M, Rigon R and Rinaldo A.1994. Self-organized river basin landscapes: fractaland multifractal characteristics. Water Resour. Res.,30(12):3531~3539
Rodriguez-Iturbe I, Rinaldo A.1997. Fractal river basins-Change and self-organization.CambridgeUniversity Press
Sapozhnikov V B and Foumula-Georgou E.1996. Self-affinity in braided rivers, Water Resour.Res,32(5):1429~1439
Svensson C, Olsson J and Berndtsson R.1996. Multifractal properties of daily rainfall in two differentclimates.Water Resour.Res.,32(8):2463~2472
Tarboton D G, Bras R L, Rodriguez-Iturbe I.1989. The fractal nature of river networks.Water Resour.Res.,24(8):1317~1322
Tchiguirinskai I, Lu S, Molz F J, Williams T M, Lavallee T.2000. Mult-fractal versus monofractal analysisof wetland topography. Stochastic Environmental Research and Risk Assessment,14(l):8~32
艾南山.1987.侵蚀流域系统的信息嫡.水土保持学报,2(1):1~8
常福宣.2011.分形理论在水文水资源研究中的应用.[博士毕业论文].四川:四川大学
程花花.2011.基于分形理论的安庆气候变化分析.[硕士毕业论文].安徽:安徽大学
陈靖.2009.基于GIS的渭河下游水质模拟及评价研究.[硕士毕业论文].陕西:西北大学
程磊,徐宗学,罗睿,米艳娇.2009.渭河流域1980-2000年LUCC时空变化特征及驱动力分析.水土保持研究,16(5):1~6
陈腊娇,冯利华.2006.马莲河流域日径流过程分维与土壤侵蚀关系初探.西北林学院学报,(5):11~13
陈莹,许有鹏.2008.长江干流日径流序列的多重分形特征研究.地理研究,(4):819~828
陈亚宁,杨思全.1999.天山麦兹巴赫冰川湖突发性洪水分形特征研究.冰川冻土,(3):253~256
丁晶,刘国东.1999.日径流过程分维估计.四川水力发电,18(4):74~76
杜延辉.2008.多重分形和小波理论在小电流接地系统单相接地故障选线中的应用研究.[硕士学位论文].陕西:西南交通大学
冯金良,张稳.1999.海滦河流域水系分形.泥沙研究,(1):62~65
冯平,冯焱.1997.河流形态特征的分维计算方法.地理学报,(52)4:324~330
冯书成,张建存.1991.商洛地区国有林采伐方式的探讨.陕西林业科技，1(1)：22-25
冯小庆.2010.渭河流域径流过程的分形特征及其与生态环境的关系研究.[硕士毕业论文].陕西:西北农林科技大学
傅军,丁晶.1995.嘉陵江流域形态及流量过程分维研究.成都科技大学学报,(1):74~79
高旭,徐永安.1996.分形曲线曲面在三维地貌中的应用.河海大学学报,24(6):83~87
巩合德,王开运.2003.森林水文生态效应及在川西亚高山针叶林群落中的研究.世界科技研究与发展,25(5):41~46
郭志贤,张骅,向立,郭玉奇,何建民,权春生.1997.北洛河流域水土保持综合治理考察研究.水土保持通报,17(3):9~15
黄明斌,刘贤.2002.黄土高原森林植被对流域径流的调节作用.应用生态学报,13(9):1057~1060
江田汉,邓莲堂.2004.全球气温变化的多分形谱.热带气象学报,(6):673~678
蒋忠信.1987.滇西北三江河谷纵剖面的发育图式与演化规律.地理学报,42(1):16~29
金德生,陈浩.1997.河道纵剖面分形-非线性形态特征.地理学报,(2):154~161
菊春燕.2006.天山北坡军塘湖流域春季径流的分形特征研究.[硕士毕业论文].新疆:新疆大学
李凡华,刘慈群.1998.分形在油气田开发中的应用.力学进展,28(1):101~110
李后强,艾南山.1992.分形地貌学及地貌发育的分形模型.自然杂志,(7):516~519
李怀恩,秦耀民,胥彦玲,李家科.2011.陕西黑河流域土地利用变化对非点源污染的影响研究.水力发电学报,
李会方.2004.多重分形理论及其在图象处理中应用的研究.[博士学位论文].陕西:西北工业大学
李静,桑广书,刘小艳.2009.黑河流域生态环境演变研究综述.水土保持研究,16(6):210~215
李锰,朱令人.分形在地貌学中应用的几个问题的分析.地震研究,25(2):155~162
李贤彬,丁晶.1999.水文时间序列的子波分析法.水科学进展,(2):144~149
李越.2004.渭河氮素非点源污染与流域人类活动的关系.[硕士毕业论文].陕西:西安理工大学
梁虹,卢娟.1997.喀斯特流域水系分形、熵及其地貌意义.地理科学,(17)4:310~315
刘德平.1998.分形理论在水文过程形态特征分析中的应用.水利学报,(2):20~25
刘兴坡,周玉文.2004.日污水流量序列的分形特征研究.中国给水排水.20(12):53~55
刘远东.2011.基于分形表述的表面功能结构的数字化建模.[硕士毕业论文].广东:华南理工大学
卢方元.2005.中国股市收益率波动性研究.[博士学位论文].陕西:西南交通大学
卢方元.2006.中国股市收益率长程相关性研究.管理工程学报,20(3):116~119
陆中臣,贾绍凤.1991.流域地貌系统.大连:大连出版社
马千里,宁新宝,王俊.2006.描述睡眠脑电多重分形特性的一种新参数.科学通报,(15)
马新中,陆中臣.1993.流域地貌系统的侵蚀演化与耗散结构.地理学报,48(4):367~375
马宗伟,许有鹏.2009.水系分形特征对流域径流特性的影响-以赣江中上游流域为例.长江流域资源与环境,18(2):35~39
毛战坡.1999.黑河流域非点源污染控制规划研究.[硕士学位论文].陕西:西安理工大学
莫莉.2008.基于水文法的北洛河流域水土保持措施减沙水代价分析.[硕士毕业论文].陕西:西北农林科技大学
庞宇磊.2009.分形理论在交通中的应用.[硕士学位论文].北京:北京交通大学
彭成彬,陈藕.1989.地震中的分形结构.中国地震,5(2):19-26
邱国玉,尹婧,熊育久,赵少华,王佩,吴秀琴,曾爽.2008.北方干旱化和土地利用变化对泾河流域径流的影响.自然资源学报，23(2):211~218
陕西省人民政府办公厅关于印发陕西省渭河流域城镇污水处理设施建设规划的通知.2004.陕西政报
孙然好,潘保田,王义祥.2006.祁连山北麓地貌信息熵与山体演化阶段分析.干旱区地理,29(1):88-93
孙霞,吴自勤,黄畇.2006.分形原理及其应用.合肥:中国科技大学出版社
铁永波,唐川.2005.基于信息熵理论的泥石流沟谷危险度评价.灾害学,20(4):43~46
汪富泉.1999.泥沙运动及河床演变的分形特征与自组织规律研究.[四川大学博士论文].四川:四川大学
王国杰,姜彤,陈桂亚.2006.长江干流径流的时序结构与长期记忆.地理学报,61(1):47~56
王礼先,张志强.2001.干旱地区森林对流域径流的影响.自然资源学报,16(5):439~444
王佩,邱国玉,尹婧,熊育久,谢芳.2008.泾河流域温度与器皿蒸发量时空特征及变化趋势.干旱气象，26(1):17~22
王倩,邹欣庆.2002.基于GIS技术的秦淮河流域水系分维研究.水科学进展,13(6):751~756
王文圣,向红莲.2005.基于连续小波变换的径流分维研究.水利学报,36(5):598~601
王武成,崔文艺.2008.北洛河上游暴雨洪水特性分析.延安大学学报(自然科学版),27(3):93~97
王晓朋,潘懋.2007.基于流域系统地貌信息熵的泥石流危险性定量评价.北京大学学报(自然科学版),43(2):211~215
王协康,方铎,姚令侃.1999.非均匀沙床面粗糙度的分形特征.水利学报,(7):70~74
王秀春,吴姗.2004.泾河流域水系分维特征及其生态意义.北京师范大学学报,(40)3:364~368
王战平.2009.灞河流域水文特性分析.水资源与水工程学报,20(5):176-179
吴中如,潘卫平.1996.分形几何理论在岩土边坡稳定性分析中的应.水利学报,(4):79~82
肖克东,曾斌.1995.分形分维.现代物理知识,7(3):26
谢芳,邱国玉,尹婧,熊育久,王佩.2009.泾河流域40年的土地利用/覆盖变化分区对比研究.自然资源学报，24(8):1354~1365
谢佳兴.2011.基于MF-DFA和MF-SSA的心脏病理时间序列分析.[硕士学位论文].湖北:南京邮电大学
谢先红,崔远来.参考作物腾发量时间序列的长程相关性和多重分形分布.水利学报,(12):1326~1333
谢元博.2010.泾河流域非点源污染特性分析与SWAT模型模拟.[硕士毕业论文].陕西:西安理工大学
胥彦玲.2007.基于土地利用/覆被变化的陕西黑河流域非点源污染研究.[博士学位论文].陕西:西安理工大学
徐陈辉.2008.基于分形理论的水轮机振动分析.[硕士学位论文].河北:河北工程大学
徐涛.2009.甘肃葫芦河流域的径流分布式模拟.[硕士毕业论文].甘肃:兰州大学
薛素玲.2006.基于GIS的黑河流域非点源氮磷模拟.[硕士学位论文].陕西:西安理工大学
燕爱玲.2007.河川径流时间序列的分形特征研究.[博士学位论文].陕西:西安理工大学
杨操静.2007.水安全评价及其在渭河中的应用研究.[硕士毕业论文].陕西:长安大学
杨国良,游勇,李海燕.2007.旅游景区(点)系统空间分布的分形发育及演化特征——以四川省为例.自然资源学报,22(6):963~973
杨国良.2007.基于分形理论的水下图像分割与识别算法研究.[硕士学位论文].湖北:华中科技大学
杨海军,孙立达,余新晓.1993.晋西黄土区水土保持林水量平衡的研究.北京林业大学学报,15(3):42~50
杨立彬.2007.基于河流健康的渭河流域水资源合理配置研究.[硕士毕业论文].陕西:西安理工大学
姚建,丁晶,艾南山.2004.岷江上游日径流过程分维分析及其生态脆弱性表征.长江流域资源与环境,13(4):380~383
姚令侃,方铎.1997.非均匀沙自组织临界性及其应用研究.水利学报,(3):26~32
姚胜利.2008.渭河流域水文一体化管理初探. http://10000067898.8.sunbo.net/show_=LPUIL41&dname=VGV2051&xpos=165[2008-12-31]
余姝萍,刘国东,吴媛.2005.岷江上游日径流过程分维分析及其生态脆弱性表征.西南民族大学学报,31(1):79-~84
苑莹,庄新田.2007.国际汇率的多重分形消除趋势波动分析.管理科学,(4):80~85
苑莹,庄新田.2008.中国股票市场的长记忆性与市场发展状态.数理统计与管理,27(1):156~163
张明明.2007.黑河干流中游平原区水资源系统分析及其优化调配研究.[硕士毕业论文].陕西:西北大学
张强.2010.长江与沱江交汇河段通航水位研究.[硕士学位论文].重庆:重庆交通大学
张之湘.2005.卵石推移质输移随机性研究.[博士学位论文].四川:四川大学
张志强，王礼先，余新晓，Klaghofer.2001.森林植被影响径流形成机制研究进展.自然资源学报,16(1):79~84
赵辉.2008.南方花岗岩地区红壤侵蚀与径流输沙规律研究.[博士学位论文].北京:北京林业大学
郑祚芳,张秀丽,曹鸿兴.2007.用去趋势涨落分析研究北京气候的长程变化特征.地球物理学报,(02)
周杜辉.2011.渭河流域经济空间分异及其优化对策研究.[硕士毕业论文].陕西:西北大学
周胜明,唐德善.2005.黑河治理项目中游节水研究.水利科技与经济,11(9):548~549
周毅,汤国安.2009.基于DEM的黄土流域地貌发育新量化新指标.南京师范大学虚拟地理环境教育部重点实验室
周宇.2000.洞庭湖变迁的分形研究.水文与水资源,21(2):37~38
朱永清.2006.黄土高原典型流域地貌分形特征与空间尺度转换研究.[博士学文论文].陕西:西安理工大学
庄新田,黄小原.2003.资本市场的分形结构与复杂性.东北大学出版社
Barbera L and Rosso R.1989. On fractal geometry of river networks. Water Resour. Res.,25(4):735~741
Davis W M.1899. The geographical cycle. Geogr.J.,14:481~501
Dietler D and Zhang Y.1992. Fractal aspects of the swiss landscape. Physica A,191:213~219
Feder J.1988. Fractals. New York and London
GuPta V K and Waymire E.1990. Multiscaling properties of spatial rainfall and river flow Distributions.Geophys. Res,95(3):1999~2009
GuPta V K.1989. Statistical self-similarity in river networks parameterized by elevation. Water ResourcesBulletin,25(3)
Hosking J R M.1984. Modeling persistence in hydrologic time series using fractional Difference. WaterResour. Res.,20(12):1898~1908
Kantelhardta J W, Zschiegner S A.2002. Multi-fractal de-trended fluctuation analysis of nonstationarytime series.Physica A,316:87~114
Koscielny-Bunde E, Kantelhardt J W, Braun P, Bunde A, Havlin S.2006. Multi-fractal of River RunoffRecords:De-trended Fluctuation Studies. Journal of Hydrology,322(1-4):120~137
Liu H H and Molz F J.1997. Multi-fractal analyses of hydraulic conductivity distributions. Water Resour.Res.,33(11):2483~2488
Lovejoy S, Schertzer D, Tsonis A A.1987. Functional box-counting and multiple elliptical dimensions inrain. Science,235:1036~1038
Mandelbrot B B.1977. Fractals: Form, Chance and Dimension. San Francisco: Freeman
Mandelbrot B B.1982. The Fractal Geometry of Nature. New York: Freeman
Mekerhar A I, Ibbitt R P, Brown S L R, Dunean M J.1998. Data for Ashley river to test Channel networkand river basin heterogeneity concepts. Water Resour. Res.,34(1):139~142
Montanari A, Rosso R and Taqqu.1997. Fractionally differenced ARIMA models applied to hydrologictime series: identification estimation, and simulation. Water Resour. Res.,33(5):1035~1044
Nikora V L, Sapozhnikov V B, Noever D A.1993. Fractal geometry of individual river-channels and itscomputer simulation. WaterResour.Res,29(10):3561~3568
Nikora V L.1991. Fractal structures of river plan forms. Water Resour.Res,27(6):1327~1333
Peng C K, Buldyrev S V.1994. Mosaic organization of DNA nucleotides. Phys Rev E,49:1685~1689.
Robert A, Roy A G.1990. On the fractal interpretation of the main-stream length-drainage arearelationship.Water Resour.Res.,26(9):839~842
Rodriguez-Iturbe I, Ijjasz-Vasquez E and Bras, Tarboton D G.1992. Power law distribution of dischargeand energy in river basins. Water Resour. Res.,28(4):1089~1093
Rodriguez-Iturbe I, Marani M, Rigon R and Rinaldo A.1994. Self-organized river basin landscapes: fractaland multifractal characteristics. Water Resour. Res.,30(12):3531~3539
Rodriguez-Iturbe I, Rinaldo A.1997. Fractal river basins-Change and self-organization.CambridgeUniversity Press
Sapozhnikov V B and Foumula-Georgou E.1996. Self-affinity in braided rivers, Water Resour.Res,32(5):1429~1439
Svensson C, Olsson J and Berndtsson R.1996. Multifractal properties of daily rainfall in two differentclimates.Water Resour.Res.,32(8):2463~2472
Tarboton D G, Bras R L, Rodriguez-Iturbe I.1989. The fractal nature of river networks.Water Resour.Res.,24(8):1317~1322
Tchiguirinskai I, Lu S, Molz F J, Williams T M, Lavallee T.2000. Mult-fractal versus monofractal analysisof wetland topography. Stochastic Environmental Research and Risk Assessment,14(l):8~32