水深环境梯度下柽柳种群分布格局的分形分析

利用计盒维数和信息维数两种分形方法分析了黄河三角洲湿地柽柳种群的空间分布特征及其随水深梯度的变化。结果表明,不同水深梯度下柽柳种群分布格局的计盒维数均较大,随着水深的增大而逐渐减小,但变化幅度较小,反映了不同水深梯度下柽柳种群对水平空间的占据程度较大;信息维数总体上随水深的增大而减小,在水深低于-1．55m范围内,信息维数较大,柽柳种群的微观结构较为复杂,格局强度较高,水深高于-1．55m时,信息维数较小,柽柳种群的微观结构较为简单,格局强度较弱。水深-1．55m可能是黄河三角洲湿地柽柳种群分布格局的一个阅值。     

牛肉大理石花纹计盒维和信息维的测定

对牛肉大理石花纹几何特征进行定量描述，是牛肉大理石花纹等级自动判定系统的关键技术。通过对牛肉大理石花纹图像分形特征的分析及分形维数的测定，试图以分形维对牛肉大理石花纹的分布特征进行定量描述。作者以中国及美国牛肉分级系统中的大理石花纹标准图版为研究对象，通过图像预处理，将其转化为二值数字图像，然后根据变粗视化程度的像素点覆盖法，编写出计盒维和信息维的测定程序，计算出上述每一幅图像在不同标尺下的非空盒个数及信息量，再根据标尺与非空盒个数及信息量的关系，分析图像的分形特征；通过回归分析的方法，测定出图像的计盒维数和信息维数。试验结果显示，在一定的标度范围内，牛肉大理石花纹标准图像具有分形性，并且显示出多重分形特征；图像的计盒维数和信息维数均呈现出随着牛肉大理石花纹等级的增加而增大的变化趋势。     

基于DEM的黄土高原沟谷节点分形特征研究

以ASTER GDEM为主要数据源,在黄河中游多沙粗沙区提取22个小流域的沟谷节点(channel junctions,CJs),采用计盒、关联维2种方法对比研究CJs分形特征,并讨论其分形的内涵与影响因素;基于CJs分形特征的聚类分析,探讨样区的侵蚀程度差异。结果表明:(1)黄土高原CJs分形特征明显,不同分形方法度量的几何维数变化相同,盒维数大的样区关联维数也大;(2)CJs分形特征与黄土地貌的发育相关,不同地貌类型呈现出不同的分形维数;但2种分形方法度量出的分维值差异均能与地貌类型保持对应,分形维数排序为:黄土梁峁状丘陵沟壑黄土破碎塬黄土梁状丘陵沟壑黄土塬黄土山地黄土峁梁状丘陵沟壑黄土风蚀沙丘;(3)依据CJs盒维数、关联维数对样区进行聚类分析,结果表明22个样区划分为4种类型,大致对应剧烈侵蚀区、强烈侵蚀区、中度侵蚀区、轻度侵蚀区。研究表明分形方法能较好的刻画黄土高原不同地貌沟谷节点特征,并能在一定程度上反映沟谷侵蚀状况。     

基于图像分析的杂草分形维数计算

介绍了分形维数的理论计算公式和试验公式，分析了计盒维数的计算方法，运用Matlab软件设计了图像的处理和基于图像的计盒维数的计算程序。随机地选择了4种双子叶杂草和两种单子叶杂草共6种杂草作为研究对象，运用自行设计的程序分别计算了杂草叶的RGB三色图像的分形维数并以其平均值作为杂草叶的分形维数。研究结果表明该文给出的分形维数的计算方法可靠；研究结果也验证了杂草叶具有分形特征；研究结果还说明不同种类的杂草 ，其叶的分形维数明显不同，可以用分形维数为特征参数识别杂草。     

基于归一化植被指数的流域植被覆盖分形维数研究

量化和表征植被覆盖空间分布的复杂性是研究植被与地表物质迁移关系的重要问题。为研究植被覆盖分形维数的表征特点及其在不同尺度上的变化特征,该文基于地理信息系统平台,利用分形布朗运动理论,结合像元归一化植被指数(normalized difference vegetation index,NDVI)的空间分布,提出并计算了植被覆盖分形布朗运动(fractional brownian motion,FBM)分形维数。结果显示,流域植被覆盖的空间分布具有统计自相似性,可用分形维数表征,其值在2.5~3之间,越接近2.5,表示植被覆盖空间分布越复杂。植被覆盖FBM分形维数与流域内均值化NDVI值和NDVI值的变异系数无直接关系,与单位面积不同NDVI值的像元数呈极显著负相关(R=0.66,P0.01)。植被覆盖FBM分形维数具有尺度效应,随流域面积增大而增大,到一定尺度后趋于平稳。流域植被覆盖FBM分形维数能够克服NDVI像元点奇异值等对植被空间分布量化表征计算的干扰,相对传统表征植被覆盖的指数,其在水文、土壤侵蚀等模型中具有更广泛的应用意义。     

基于GIS的流域土地利用/土地覆被分形特征

该文以西安市沪灞河流域为例,结合遥感数据成图与GIS空间分析建模,开发了流域土地利用/土地覆被斑块形状分维数、空间结构盒维数、空间分布信息维数与区域形态半径维数的计算脚本,并对各种分形维数的特征与意义进行了研究.结果表明:土地利用/土地覆被斑块形状分维数、空间结构盒维数、空间分布信息维数与区域形态半径维数是几种性质不同功能各异的分形维数,四者能够表征土地利用/土地覆被在斑块水平、斑块类型水平以及景观水平3个层次的分形特征;斑块形状分维数体现了不同地类斑块形状的复杂程度及其所受人类活动干扰的强度;空间结构盒维数反映了不同地类空间结构的复杂程度和不规则程度;空间分布信息维数反映了不同地类斑块空间分布的均衡程度;形态半径维数反映了不同地类区域形态针对某一中心点的聚散特征.     

基于GIS的流域地貌形态分形盒维数测定方法研究

流域地貌形态分形维数测定是目前地貌分形研究的薄弱环节,对于流域水土流失预报模型中地貌因子量化具有重要科学意义。依据分形盒维数测定原理,结合流域地貌的复杂三维立体特性,提出了以地形等高线为基本数据源,以GIS技术作为主要实现手段的流域地貌形态分形盒维数测定方法,编制出了相关测算程序,并以岔巴沟流域为例进行了实证研究。结果表明,该方法快速、准确、数据可靠,可实现不同尺度流域地貌形态分形盒维数的测定。     

陕北黄土丘陵沟壑区土壤粒径分布分形特征

将激光衍射技术和分形分析结合,多重分形分析应用多重分形参数Rényi维数谱,研究土壤粒径分布(PSD)分形特征。结果表明:土壤PSD分形维数D在2.28～2.47之间,D与土壤黏粒含量线性相关。计算黏粒、粉粒和砂粒分形维数D黏粒、D粉粒和D砂粒,三者之间存在D黏粒D粉粒D砂粒的关系,分别用D黏粒、D粉粒和D砂粒计算分裂概率,发现小团粒具有较小的分裂概率。因此,分裂概率具有尺度依赖性,并随着土壤粒径的减小而降低。多重分形分析表明,由PSD获取的Rényi维数谱为反S型递减函数,与理论的多重分形Rényi维数谱相似,说明土壤PSD具有多重分形特征。     

土壤样本分形几何特征的图像分析方法

土壤水分的持留与水分和溶质的运移,在很大程度取决于土壤孔隙的几何性质,而用数字图像处理方法能够较准确地加以识别。本文采用面积法和周长法分别计算了土壤样本图像的孔隙分形维数和多重孔隙轮廓线分形维数,并分析了它们同土壤质地之间的关系。结果表明,土壤孔隙空间在一定尺度范围内才存在明显的分形特征,土壤质地越细(粘粒含量越高)分形维数越大。与周长法相比较,用面积法计算的孔隙分形维数对土壤质地更为敏感。     

河网区灌溉水利用系数的尺度转换

大尺度灌区灌溉水利用系数的测定条件难以保障,而小尺度灌区的灌溉水利用系数可以通过试验测定,如何通过小尺度灌区的灌溉水利用系数来预测大尺度灌区的灌溉水利用系数,就有必要对灌溉水利用系数的尺度转换问题进行研究。河网灌区的特点是没有统一的水源引水口,通常是由若干个小灌区合并成一个大灌区,是一个典型的自相似系统。论文以地处里下河水网地区的盐城市水稻灌区作为研究对象,于2012-2013年对9个县区不同规模的样点灌区进行了灌溉水利用系数的试验观测,利用分形理论研究了河网灌区的分形特征,运用盒维数法计算了盐城市河网灌区和不同尺度灌区的盒维数,其盒维数介于1.703~1.996之间,并随着面积尺度的增加而增大。基于灌溉水利用系数与灌区面积、盒维数的相关性,建立了河网灌区灌溉水利用系数尺度转换模型,并通过验证,表明该尺度转换模型能够较好地预测河网灌区灌溉水利用系数,同时也能够很好地实现灌溉水利用系数的尺度转换,为分析河网灌区灌溉水利用系数及其尺度效应提供了新途径。     

Fractal features of soil particle redistribution along sloping landscapes with hedge berms in the Three Gorges Reservoir Region of China

Most studies have evaluated the effects of soil redistribution under water erosion or tillage erosion within hill slope landscapes, yet few studies have demonstrated soil particle redistribution from the sloping lands with a hedge berm. In this study, soil particle redistribution and fractal dimension from sloping lands with or without a hedge berm were investigated. The main radius of soil particles being redistributed from the sloping lands ranged between 0.002 and 0.02 mm, whether or not a hedge berm existed. However, there were significant differences between sloping land with a hedge berm and without a hedge berm (P < 0.05). The values of the bias coefficient ranged from ?0.893 to ?0.817, and the values of peak convex coefficient ranged from ?1.619 to ?1.371. And the order of values of the fractal dimension for land with a hedge berm of 10 cm height was as follows: upper slope > middle slope > lower slope, and the sequence of the values of fractal dimension from sloping land without a hedge berm was upper slope >middle slope > lower slope. There was also a significant difference between the upper (US) and middle slope (MS) position (P < 0.05), and results also showed highly significant correlations (R²=0.9088 without hedge berm, R² = 0.9048 with hedge berm, respectively). A regression analysis was performed to establish the logarithmic relationship between peak convex coefficient and soil depth (R² = 0.9461 without hedge berm, R² = 0.9780 with hedge berm, respectively). The correlation between fractal dimension and bias coefficient was significant (P = < 0.05). Our results suggest that fractal dimension, bias coefficient and peak convex coefficient were sensitive indices to evaluate the soil particle redistribution and the farming activities, such as building a hedge berm, could better describe the characters of soil structure and soil particle redistribution from sloping cultivated land.     

兴国县红壤颗粒分形及其与环境因子的关系

以土壤颗粒组成数据为基础，运用分形模型，分析了红壤丘陵山区林地土壤颗粒的分形维数。结果表明：84个耕层土壤颗粒的分形维数D为2．568～2．828，其中紫色土2．722，红壤2．700，棕红壤2．693，黄红壤2．670，黄壤2．713。D随土壤质地的变细而增大。从空间分布上看，研究区域的西部和东南部D值较大，而西南部和北部D值较小，D在2．7～2．8的面积最大，为1171km^2，占总面积的47．0％，D在2．8以上的面积最小，为48km。，占总面积的1．9％。土壤分维数和坡向、海拔之间呈显著正相关关系，而与坡度、平面曲率、剖面曲率之间无明显的相关关系。     

松嫩平原西部典型盐生景观土壤分形维数及盐碱化特征

为探究松嫩平原西部典型盐生景观土壤颗粒粒度组成及分形特征与土壤盐碱化之间的关系,采用体积分形维数模型计算了6种典型盐生景观土壤表层0—30 cm颗粒组成及分形维数,结合相关分析法分析了土壤分形维数与质地、盐碱特征之间的相关性。结果表明:(1)6种典型盐生景观中农田土壤分形维数值最小(2.35),碱蓬群落土壤最大(2.61),分形维数均值为2.48,分形维数随盐生景观土壤碱化程度增加而增大。(2)土壤质地越粗,砂粒含量越高,分形维数值越小;土壤质地越细,黏粒和粉粒含量越高,分形维数越大。(3)分形维数与盐分含量呈显著正相关(r=0.87,P0.05),尤其与盐分组成中HCO_3~-含量呈极显著正相关(r=0.89,P0.01),与养分中总磷含量呈极显著正相关(r=0.90,P0.01)。(4)土壤颗粒组成中砂粒、粉粒和黏粒与盐分、HCO_3~-及总磷含量也存在极显著相关性。不同盐生景观土壤分形维数与土壤颗粒组成和土壤盐分之间存在显著的相关性,因此可以用分形维数来反映土壤质地和指示土壤盐碱化特征。     

Spatial heterogeneity of loess contour tilled microtopographic slope in rainfall erosion

Loess tilled surface is the geographical unit for the quantitative study of the soil erosion process. Contour tillage has been proved to be the most effictive measure for soil and water conservation in the Chinese Loess Plateau. Studies on the spatial heterogeneity of loess tilled surfaces will contribute to the understanding of the mechanism of erosion evolution. For this, a laboratory experiment was performed on contour tilled sloping surfaces where the hydrological-erosive processes were simulated. At different erosion stages, point cloud measurements were made using a terrestrial laser scanning system (TLS); then the heterogeneity depending on detrending and directionality were analysed by both the semivariogram method and the rescaled range analysis method. Results showed that: (1) the fractal dimensions D_S and D_R were equivalent when determined from either the semivariogram method or the rescaled range analysis method, although the semivariogram method appears to be more reliable in identifying the specific stage of the erosion evolution process; (2) the contour tilled microtopographies had an anisotropy behavior depending on direction; (3) the fractal dimension (either D_S or D_R) in different erosion stages was less than 1.5, which indicates that the microtopography of the sloping surface exhibits characteristics of persistent fractional Brownian motion and positive spatial autocorrelation. Irrespective of tillage measure and slope percentage, the sloping surface can be regarded as having random roughness. The results reveals a quantitative relationship between microtopography and sloping erosion. Also, it may provide guidance for further studies regarding the spatial variability and heterogeneity of various tilled slopes on the microtopographic scale.     

闽南山地3种典型植被类型土壤分形与养分特征

[目的]探索闽南山地不同植被类型土壤分形特征及其与表层土壤颗粒组成、养分含量的相关关系,为评价闽南山地典型植被类型土壤质量,开展土地利用结构调整、土壤侵蚀防治及生态修复等提供参考。[方法]选取土壤颗粒体积分形维数模型对3种典型植被类型林地土壤的分形维数D值进行计算,并与土壤颗粒组成及土壤养分进行相关性分析。[结果]土壤颗粒体积分形维数D值从大到小依次为次生林马尾松林柑橘林;分形维数D值与土壤黏粒和粉粒体积百分数存在显著正相关关系,与砂粒体积百分含量呈显著负相关(p0.05);土壤pH值、全氮、全磷、全钾、水解性氮、有效磷、速效钾和有机碳含量从大到小均为:次生林马尾松林柑橘林;土壤容重为柑橘林马尾松林次生林;分形维数D值与柑橘林的土壤水解性氮含量呈显著正相关,与马尾松林的水解性氮含量、土壤全磷、全钾含量呈显著正相关,与次生林的土壤全磷含量、水解性氮含量呈显著正相关,与有机碳含量均呈显著负相关。[结论]闽南山地不同植被类型会显著影响表层土壤体积分形维数及养分含量,利用土壤体积分形维数可一定程度上反映不同植被类型的土壤颗粒组成及其养分含量。     

Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry

Fractal geometry was deployed to analyse water retention curves (WRC). The three models used to estimate the curves were the general pore‐solid fractal (PSF) model and two specific cases of the PSF model: the Tyler & Wheatcraft (TW) and the Rieu & Sposito (RS) models. The study was conducted on 30 undisturbed, sandy loam soil samples taken from a field and subjected to laboratory analysis. The fractal dimension, a non‐variable scale factor characterizing each water retention model proposed, was estimated by direct scaling. The method for determining the fractal dimension proposed here entails limiting the analysis to the interval between an upper and lower pressure head cut‐off on a log‐log plot, and defining the dimension itself as the straight regression line that interpolates the points in the interval with the largest coefficient of determination, R². The scale relative to the cut‐off interval used to determine the fractal behaviour in each model used is presented. Furthermore, a second range of pressure head values was analysed to approximate the fractal dimension of the pore surface. The PSF model exhibited greater spatial variation than the TW or RS models for the parameter values typical of a sandy loam soil. An indication of the variability of the fractal dimension across the entire area studied is also provided.     

陕北黄土丘陵沟壑区土壤粒径分形特征

应用MS2000激光粒度仪,获取陕北黄土高原米脂县境内10种不同土地利用类型土壤剖面4个层次40个土壤样品的粒径分布（PsD）,利用分形几何学方法分析土壤颗粒体积分形特征。结果表明：由于各土壤样品质地相同,分形维数D变化不大,在2．230～2．521之间;〈0．002mm的土壤粒径体积百分含量与D显著相关,而其余各粒径含量均通过与〈0．002mm的相关性对D产生间接影响,表明PSD的D可以充分代表土壤细化的程度与比例。土壤累积体积分数具有非线性特征,1个D值无法表征整个粒径测量范围内的土壤PSD,因此,以15脚为界,确定了2个分形域,分别计算D1和D2,存在D1〉D2的关系,且用D1和D2计算的分裂概率具有尺度依赖性。     

土壤水分特征曲线的分形模拟

Many empirical models have been developed to describe the soil water retention curve （SWRC）. In this study, a fractal model for SWRC was derived with a specially constructed Menger sponge to describe the fractal scaling behavior of soil; relationships were established among the fractal dimension of SWRC, the fractal dimension of soil mass, and soil texture; and the model was used to estimate SWRC with the estimated results being compared to experimental data for verification. The derived fractal model was in a power-law form, similar to the Brooks-Corey and Campbell empirical functions. Experimental data of particle size distribution （PSD）, texture, and soil water retention for 10 soils collected at different places in China were used to estimate the fractal dimension of SWRC and the mass fractal dimension. The fractal dimension of SWRC and the mass fractal dimension were linearly related. Also, both of the fractal dimensions were dependent on soil texture, i.e., clay and sand contents. Expressions were proposed to quantify the relationships. Based on the relationships, four methods were used to determine the fractal dimension of SWRC and the model was applied to estimate soil water content at a wide range of tension values. The estimated results compared well with the measured data having relative errors less than 10% for over 60% of the measurements. Thus, this model, estimating the fractal dimension using soil textural data, offered an alternative for predicting SWRC.     

新疆三工河流域土壤类型复杂性研究

运用分形理论,选取斑块形状指数,在对三工河流域土壤斑块的标度-频度分形关系进行定量分析的基础上,结合土壤斑块面积-周长分维数,讨论了流域内土壤斑块空间分布的复杂性。结果表明:三工河流域内土壤斑块标度-频度分形关系及土壤类型斑块面积-周长分形关系客观存在;流域内土壤类型分维值具有一定差异,其中潮土的分维数最大,硫酸盐草甸盐土最小。复杂性指数与分维数和形状指数之间具有很好的相关性,能较客观地反映土壤类型斑块在空间分布上的复杂性;流域内高山寒漠土的复杂性指数最大,空间分布最复杂(K=2.403),半固定风沙土的复杂性指数最小,空间分布最简单(K=1.259)。