[1] Mandelbrot B B. How long is the coast of Britain-statistical self-similarity and fractionaldimension[J]. Science, 1967,156(3775):636-638.
[2] Mandelbrot B. Fractal Form, Chance and Dimension[M]. San Francisco:Freeman, 1977.
[3] 李斌斌,李占斌,宇涛,等.基于归一化植被指数的流域植被覆盖分形维数研究[J].农业工程学报,2014,30(15):239-247.
[4] 周兴林,肖神清,肖旺新,等.粗集料表面纹理粗糙度的多重分形评价[J].华中科技大学学报:自然科学版,2017,45(2):29-33.
[5] 杜修力,张佩,金浏,等.基于分形理论的北京地区砂砾石地层细观建模[J].岩石力学与工程学报,2017,36(2):437-445.
[6] Goodchild M F. Fractals and accuracy of geographical measures[J]. Math. Geol., 1980,12(2):85-98.
[7] Mark D M, Aronson P B. Scale-dependent fractal dimension of topographic surface[J]. Math. Geol.,1984,16(7):671-684.
[8] Andrle R, Abrahams A D. Fractal techniques and the surface roughness of talus slopes[J]. Earth Surf. Proc. Landform,1989,14(4):197-209.
[9] Matsushita M, Ouchi S. On the self-affinity of various curves[J]. Physica D,1989,38(1/4):246-251.
[10] Andrle R. Estimating fractal dimension with the divide method in geomorphology[J]. Geomorphology,1992.5(1):131-141.
[11] 高鹏.流域水系的多标度分形研究及应用[J].中国地质灾害与防治学报,1995,6(2):31-38.
[12] 曹汉强,朱光喜,李旭涛,等.多重分形及其在地形特征分析中的应用[J].北京航空航天大学学报,2004,30(12):1182-1185.
[13] 李锰,朱令人,龙海英.不同类型地貌的各向异性分形与多重分形特征研究[J].地球学报,2003,24(3):237-242.
[14] 鲁克新,王民,李占斌,等.岔巴沟流域三维地貌多重分形特征量化[J].农业工程学报,2012,28(18):248-254.
[15] 王民.基于GIS的流域地貌多重分形特征与侵蚀产沙关系研究[D].西安:西安理工大学,2009.
[16] 王民,崔灵周,胡彩虹,等.基于投影覆盖法的小流域模型地貌分形特征[J].水电能源科学,2012,30(6):74-77.
[17] ChhabraA, Jensen R V, Direct determination of the f(alpha)singularity spectrum[J]. Physical Review Letters, 1989,62(12),1327-1330.
[18] Chhabra A, Jensen R V. Direct determination of the f(a) singularity spectrum[J]. Phys Review Letters,1989,62(2):1327-1330.
[1]梁春玲,梁海清,张祖陆.祖厉河流域水系分维与地貌发育阶段浅析[J].水土保持研究,2006,13(03):187.
LIANG Chun-ling,LIANG Hai-qing,ZHANG Zu-lu.Fractal Dimension of the River Networks and Developing Stage of Drainage Geomorphic of Zuli River Basin[J].Research of Soil and Water Conservation,2006,13(05):187.
[2]倪化勇.泥石流流域地貌形态的统计分形[J].水土保持研究,2006,13(06):92.
NI Hua-yong.Statistical Morphological Fractal Research on Debris Flow Drainage[J].Research of Soil and Water Conservation,2006,13(05):92.
[3]冉大川,张志萍,罗全华,等.大理河流域1970-2002年水保措施减洪减沙效益深化分析[J].水土保持研究,2011,18(01):17.
RAN Da-chuan,ZHANG Zhi-ping,LUO Quan-hua,et al.More Comprehensive Analysis on Benefits of Flood & Sediment Reduction of Soil and Water Conservation Measures During 1970-2002 in Dali River Basin[J].Research of Soil and Water Conservation,2011,18(05):17.
[4]倪化勇.海螺沟景区典型泥石流流域地貌特征及灾害防治[J].水土保持研究,2010,17(01):154.
NI Hua-yong.Geomorphologic Characteristics of Typical Debris-flow Basins in Hailuogou Scenic Spot and Disaster Prevention[J].Research of Soil and Water Conservation,2010,17(05):154.
[5]杨殊桐,时鹏,李占斌,等.大理河流域退耕还林工程对生态系统服务功能的影响[J].水土保持研究,2018,25(06):251.
YANG Shutong,SHI Peng,LI Zhanbin,et al.Effect of Grain for Green Project on Ecosystem Service in Dali River Basin[J].Research of Soil and Water Conservation,2018,25(05):251.
收稿日期:2017-01-18;改回日期:2017-03-28。
基金项目:国家重点研发计划项目(2016YFC0402404);国家自然科学基金项目(51479180)
作者简介:王民(1973-),男,河南省唐河县人,博士,高级工程师,主要从事水土资源与生态环境方面研究。E-mail:thwmg@126.com
通讯作者:崔灵周(1971-),男,陕西省蓝田县人,博士后,主要从事流域地貌分形特征量化模型等方面研究工作。E-mail:clingzhou@126.com