基于分形地质统计学的草地土壤空间变异
摘要
空间变异与格局及其尺度效应问题是当前科学发展的前沿热点。地质统计学(GS)被公认为揭示空间变量变异性的先进科学。然而,研究者在肯定GS优势的同时,也认识到其某些不足。如虽然可表征随机变量的结构。但多从数理统计角度进行,不是严格物理或自然意义上变化规律和结构的揭示;克里格法(kriging)求解会产生“平滑效应”,得不到两点间的局部变化特征。对多数自然变量,相邻两信息点间通常并非是线性变化或光滑过渡的,存在局部、非线性变化特征,传统的地质统计学不能很好的处理这种非线性问题,分形地质统计学(FS)则善于解决这一问题。
FS借助分形的自相似性和克里格法的无偏最优插值,从分形的角度定量刻画变量空间分布的特征,揭示变量的局部非线性变化并实现预测模拟。目前,FS尚未形成系统理论,本文总结了其发展历程,提出其理论体系框架,并以干旱区草地土壤、植被为研究对象,应用FS对土壤(含水量、盐分、有机质、全氮)、植被地上生物量的空间结构和变异性进行研究,并与传统GS进行比较,认为:
(1)FS是传统GS的发展,分形维数能够表征变量分布的复杂性。方位-分维估值与多维分形克里格均以克里格法为基础,能够较好的模拟区域变量的空间分布。方位-分维估值法与克里格插值结果相近,实质是一种角度变换的分形插值,其约束条件少,计算简单,但估计标准方差大于克里格法。多维分形克里格在反映变量总体分布趋势的同时,得到变量更多的局部变化,减少了克里格法的“平滑效应”,实质是滑动加权平均基础上加入了奇异性校正的结果。
(2)草地土壤、植被在空间上存在明显的空间变异特征并具有多级变异结构,只有在同一级结构中较大尺度的变化性才包含较小尺度的变化性,即使是同一级的结构,随着采样尺度的增加,插值的精度也会降低,因此,采样尺度的增加和减小与所研究问题的性质密切相关,不能盲目改变。
(3)土壤颗粒含量的分形维数与沙粒含量呈显著的线性负相关关系,与粘粉粒含量呈显著的线性正相关关系,并与土壤N、有机质、盐分含量正相关。分形维数可表征土壤颗粒物质损失状况和化学元素含量,作为土壤特性的综合性定量指标并反映土壤沙质荒漠化程度。
本研究进一步发展了FS理论体系,有助于GS的非线性发展,从分形的角度对土壤、植被特性空间分布进行分析与模拟,有可能创造学科新的增长点。
Pattern of spatial variability and the problem of scale effect is a hot point in the forefront of the scientific development. Geostatistics (GS) is recognized as an advanced science which can reveal the variability of the space variables. However, when many researchers definite the advantages of the GS, they also discovered some of the disadvantages. For example, it can characterize the structure of the random variables. But from the view of mathematical statistics, it can not revealed strictly which from the physical or the regulation and the structure of nature. Kriging method will have a "smooth effect”, while it can not get the characteristics of partial changes between two points. Typically, for the most natural variables, it is not linear or smooth transition between two adjacent points, it exists a partial, non-linear, changes of characteristics. For traditional geostatistics, it can not be well deal with the nonlinear problems, but Fractal Geostatistics (FS) can solve this problem well.
From the perspective of the fractal spatial to describe the distribution of characteristically variables, FS reveals partial non-linear changes in variables and realizes the forecast and simulation with the help of self-similar fractal and Unbiased Kriging optimal interpolation. At present, FS has not yet formed theories; this article summarized the development of its history and established a theoretical frame. FS takes soil and vegetation to study and it does research on soil (moisture, salt, organic matter, total nitrogen), the spatial structure and variability of vegetation biomass above ground, and compared with the traditional GS, the conclusions are:
(1) FS is the development of traditional GS; the fractal dimension can characterize the complexity of the variable distribution. The valuation of fractal dimension orientation and multi-dimensional fractal are based on Kriging, they can simulate the distribution of the spatial variables better. The result of the valuation of Fractal dimension orientation and the Kriging interpolation are similarly, essentially, it is a Perspective transformation of fractal interpolation, it has less restrictive conditions and a simple calculation, but its estimated variance is bigger than Kriging variance. multi-dimensional fractal Kriging reflect the overall distribution of the trend variables, meanwhile, it can get more variable changes and high-frequency information, and reduce the "smooth effect" of Kriging, essentially ,it is based on the slide which weighted average by adding a correct result of singular.
(2) There is an obvious spatial variability and variability with multi-level structure in space of the soil and vegetation of grassland, only with the primary structure , the changes of large-scale can contain the small-scale, even if the structure is at the same level, with the increasing of Random sampling scale, the accuracy of the interpolation will reduce, therefore, we can not be blind to change, the increasing and reducing of the sampling scale which is closely related to the problem that we do.
(3) The fractal dimension of particle content and sand content in soil showed a significant linear negative correlation, viscosity content was showed a significant positive correlation, at the same time; it is relevant to the soil nitrogen, organic matter, and salt content. Fractal dimension can characterize the loss of situation of soil particulate matter and chemical element content, as comprehensive and quantitative indicators, it reflects the degree of soil desertification.
This study developed the FS theoretical system more perfectly. It contribute to the non-linear development of GS, from the view of fractal, soil and vegetation characteristics of the spatial distribution analysis and simulation, it is possible to create a new point of growth disciplines.
FS借助分形的自相似性和克里格法的无偏最优插值,从分形的角度定量刻画变量空间分布的特征,揭示变量的局部非线性变化并实现预测模拟。目前,FS尚未形成系统理论,本文总结了其发展历程,提出其理论体系框架,并以干旱区草地土壤、植被为研究对象,应用FS对土壤(含水量、盐分、有机质、全氮)、植被地上生物量的空间结构和变异性进行研究,并与传统GS进行比较,认为:
(1)FS是传统GS的发展,分形维数能够表征变量分布的复杂性。方位-分维估值与多维分形克里格均以克里格法为基础,能够较好的模拟区域变量的空间分布。方位-分维估值法与克里格插值结果相近,实质是一种角度变换的分形插值,其约束条件少,计算简单,但估计标准方差大于克里格法。多维分形克里格在反映变量总体分布趋势的同时,得到变量更多的局部变化,减少了克里格法的“平滑效应”,实质是滑动加权平均基础上加入了奇异性校正的结果。
(2)草地土壤、植被在空间上存在明显的空间变异特征并具有多级变异结构,只有在同一级结构中较大尺度的变化性才包含较小尺度的变化性,即使是同一级的结构,随着采样尺度的增加,插值的精度也会降低,因此,采样尺度的增加和减小与所研究问题的性质密切相关,不能盲目改变。
(3)土壤颗粒含量的分形维数与沙粒含量呈显著的线性负相关关系,与粘粉粒含量呈显著的线性正相关关系,并与土壤N、有机质、盐分含量正相关。分形维数可表征土壤颗粒物质损失状况和化学元素含量,作为土壤特性的综合性定量指标并反映土壤沙质荒漠化程度。
本研究进一步发展了FS理论体系,有助于GS的非线性发展,从分形的角度对土壤、植被特性空间分布进行分析与模拟,有可能创造学科新的增长点。
Pattern of spatial variability and the problem of scale effect is a hot point in the forefront of the scientific development. Geostatistics (GS) is recognized as an advanced science which can reveal the variability of the space variables. However, when many researchers definite the advantages of the GS, they also discovered some of the disadvantages. For example, it can characterize the structure of the random variables. But from the view of mathematical statistics, it can not revealed strictly which from the physical or the regulation and the structure of nature. Kriging method will have a "smooth effect”, while it can not get the characteristics of partial changes between two points. Typically, for the most natural variables, it is not linear or smooth transition between two adjacent points, it exists a partial, non-linear, changes of characteristics. For traditional geostatistics, it can not be well deal with the nonlinear problems, but Fractal Geostatistics (FS) can solve this problem well.
From the perspective of the fractal spatial to describe the distribution of characteristically variables, FS reveals partial non-linear changes in variables and realizes the forecast and simulation with the help of self-similar fractal and Unbiased Kriging optimal interpolation. At present, FS has not yet formed theories; this article summarized the development of its history and established a theoretical frame. FS takes soil and vegetation to study and it does research on soil (moisture, salt, organic matter, total nitrogen), the spatial structure and variability of vegetation biomass above ground, and compared with the traditional GS, the conclusions are:
(1) FS is the development of traditional GS; the fractal dimension can characterize the complexity of the variable distribution. The valuation of fractal dimension orientation and multi-dimensional fractal are based on Kriging, they can simulate the distribution of the spatial variables better. The result of the valuation of Fractal dimension orientation and the Kriging interpolation are similarly, essentially, it is a Perspective transformation of fractal interpolation, it has less restrictive conditions and a simple calculation, but its estimated variance is bigger than Kriging variance. multi-dimensional fractal Kriging reflect the overall distribution of the trend variables, meanwhile, it can get more variable changes and high-frequency information, and reduce the "smooth effect" of Kriging, essentially ,it is based on the slide which weighted average by adding a correct result of singular.
(2) There is an obvious spatial variability and variability with multi-level structure in space of the soil and vegetation of grassland, only with the primary structure , the changes of large-scale can contain the small-scale, even if the structure is at the same level, with the increasing of Random sampling scale, the accuracy of the interpolation will reduce, therefore, we can not be blind to change, the increasing and reducing of the sampling scale which is closely related to the problem that we do.
(3) The fractal dimension of particle content and sand content in soil showed a significant linear negative correlation, viscosity content was showed a significant positive correlation, at the same time; it is relevant to the soil nitrogen, organic matter, and salt content. Fractal dimension can characterize the loss of situation of soil particulate matter and chemical element content, as comprehensive and quantitative indicators, it reflects the degree of soil desertification.
This study developed the FS theoretical system more perfectly. It contribute to the non-linear development of GS, from the view of fractal, soil and vegetation characteristics of the spatial distribution analysis and simulation, it is possible to create a new point of growth disciplines.
引文
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