Spatial control of groundwater contamination,using principal component analysis

A study on the geochemistry of groundwater was carried out in a river basin of Andhra Pradesh to probe into the spatial controlling processes of groundwater contamination, using principal component analysis (PCA). The PCA transforms the chemical variables, pH, EC, Ca²⁺, Mg²⁺, Na⁺, K⁺, HCO \(_3^- \) , Cl^?, SO \(_4^{2-} \) , NO \(_3^-\) and F^?, into two orthogonal principal components (PC1 and PC2), accounting for 75% of the total variance of the data matrix. PC1 has high positive loadings of EC, Na⁺, Cl^?, SO \(_4^{2-} \) , Mg²⁺ and Ca²⁺, representing a salinity controlled process of geogenic (mineral dissolution, ion exchange, and evaporation), anthropogenic (agricultural activities and domestic wastewaters), and marine (marine clay) origin. The PC2 loadings are highly positive for HCO \(_3^- \) , F^?, pH and NO \(_3^- \) , attributing to the alkalinity and pollution controlled processes of geogenic and anthropogenic origins. The PC scores reflect the change of groundwater quality of geogenic origin from upstream to downstream area with an increase in concentration of chemical variables, which is due to anthropogenic and marine origins with varying topography, soil type, depth of water levels, and water usage. Thus, the groundwater quality shows a variation of chemical facies from Na⁺ > Ca²⁺ > Mg²⁺ > K⁺: HCO \(_3^- \) > Cl^? > SO \(_4^{2-}>\) NO \(_3^- \) > F^?at high topography to Na⁺ > Mg²⁺ > Ca²⁺ > K⁺: Cl^? > HCO \(_3^- \) > SO \(_4^{2-}>\) NO \(_3^- \) > F^? at low topography. With PCA, an effective tool for the spatial controlling processes of groundwater contamination, a subset of explored wells is indexed for continuous monitoring to optimize the expensive effort.     

Multiple group principal component analysis

Common Principal Component Analysis is a generalization of standard principal components to several groups under the rigid mathematical assumption of equality of all latent vectors across groups (i.e., principal component directions), whereas the latent roots are allowed to vary between groups (differing inflations of dispersion ellipsoids). In practice, data that fulfill these strict requirements are relatively rare. Examples from palaeontology are used to illustrate the principles. Compositional data can be made to fit the Common Principal Component (CPC) model by the appropriate logratio covariance matrix.     

Quantitative Zn speciation in a contaminated dredged sediment by μ-PIXE, μ-SXRF, EXAFS spectroscopy and principal component analysis

Dredging and disposal of sediments onto agricultural soils is a common practice in industrial and urban areas that can be hazardous to the environment when the sediments contain heavy metals. This chemical hazard can be assessed by evaluating the mobility and speciation of metals after sediment deposition. In this study, the speciation of Zn in the coarse (500 to 2000 μm) and fine (<2 μm) fractions of a contaminated sediment dredged from a ship canal in northern France and deposited on an agricultural soil was determined by physical analytical techniques on raw and chemically treated samples. Zn partitioning between coexisting mineral phases and its chemical associations were first determined by micro-particle-induced X-ray emission and micro-synchrotron-based X-ray radiation fluorescence. Zn-containing mineral species were then identified by X-ray diffraction and powder and polarized extended X-ray absorption fine structure spectroscopy (EXAFS). The number, nature, and proportion of Zn species were obtained by a coupled principal component analysis (PCA) and least squares fitting (LSF) procedure, applied herein for the first time to qualitatively (number and nature of species) and quantitatively (relative proportion of species) speciate a metal in a natural system.The coarse fraction consists of slag grains originating from nearby Zn smelters. In this fraction, Zn is primarily present as sphalerite (ZnS) and to a lesser extent as willemite (Zn₂SiO₄), Zn-containing ferric (oxyhydr)oxides, and zincite (ZnO). In the fine fraction, ZnS and Zn-containing Fe (oxyhydr)oxides are the major forms, and Zn-containing phyllosilicate is the minor species. Weathering of ZnS, Zn₂SiO₄, and ZnO under oxidizing conditions after the sediment disposal accounts for the uptake of Zn by Fe (oxyhydr)oxides and phyllosilicates. Two geochemical processes can explain the retention of Zn by secondary minerals: uptake on preexisting minerals and precipitation with dissolved Fe and Si. The second process likely occurs because dissolved Zn and Si are supersaturated with respect to Zn phyllosilicate. EXAFS spectroscopy, in combination with PCA and LSF, is shown to be a meaningful approach to quantitatively determining the speciation of trace elements in sediments and soils.     

Application of principal component analysis to understand variability of rainfall

The usefulness of principal component analysis for understanding the temporal variability of monsoon rainfall is studied. Monthly rainfall data of Karnataka, spread on 50 stations for a period of 82 years have been analysed for interseasonal and interannual variabilities. A subset of the above data comprising 10 stations from the coherent west zone of Karnataka has also been investigated to bring out statistically significant interannual signals in the southwest monsoon rainfall. Conditional probabilities are proposed for a few above normal/below normal transitions. A sample prediction exercise for June–July using such a transition probability has been found to be successful.     

Environmental factors of road slope stability in mountain area using principal component analysis and hierarchy cluster

Nine environmental factors of 147 roadside soil samples were administered in Sichuan Basin of China and principal component analysis was conducted using the Pearson correlation matrix. The results show that the first four principal components whose eigenvalue is over 1.00 can be extracted. The first principal component which is consisted of rock type, soil type, weathering degree, and soil depth is the most important factor of all. The geographical position which is consisted of altitude, longitude, and latitude is included in the second and the third principal components. The fourth principal component shows that the terrain factor influences the rock slope stability. The hierarchy cluster shows that rock type and soil type play the maximum positive correlation, while the slope and the aspect present the maximum negative correlation.     

Water quality of the Chhoti Gandak River using principal component analysis,Ganga Plain,India

Chhoti Gandak is a meandering river which originates in the terai area of the Ganga Plain and serves as a lifeline for the people of Deoria district, Uttar Pradesh. It travels a distance of about 250 km and drains into Ghaghara near Gothani, Siwan district of Bihar. It has been observed that people of this region suffer from water-borne health problems; therefore water samples were collected to analyse its quality along the entire length of Chhoti Gandak River.     

Thoughts on use of principal component analysis in petrogenetic problems

The use of principal component analysis in studying chemical trends in volcanic rock suites is described. It is suggested that eigenvectors generated from a correlation matrix, rather than a covariance matrix, could be used in this context. In the latter situation many elements are swamped by silicon's numerical size and range. In the former situation the alkalies and titanium begin to show their true importance.     

Statistical inverse analysis based on genetic algorithm and principal component analysis: Method and developments using synthetic data

This study concerns the identification of parameters of soil constitutive models from geotechnical measurements by inverse analysis. To deal with the non‐uniqueness of the solution, the inverse analysis is based on a genetic algorithm (GA) optimization process. For a given uncertainty on the measurements, the GA identifies a set of solutions. A statistical method based on a principal component analysis (PCA) is, then, proposed to evaluate the representativeness of this set. It is shown that this representativeness is controlled by the GA population size for which an optimal value can be defined. The PCA also gives a first‐order approximation of the solution set of the inverse problem as an ellipsoid. These developments are first made on a synthetic excavation problem and on a pressuremeter test. Some experimental applications are, then, studied in a companion paper, to show the reliability of the method. Copyright © 2009 John Wiley & Sons, Ltd.     

主成分分析法在页岩气有利区优选中的应用

在多因素叠合法优选页岩气发育有利区的基础上,构建了涵盖地质背景、页岩生烃、储集、保存、资源和开采条件6个方面17项指标的页岩气发育有利区综合评价原始指标体系,并运用主成分分析法对湘鄂西地区下寒武统牛蹄塘组页岩气发育有利区进行了实例分析。结果表明,主要影响湘鄂西地区牛蹄塘组页岩气发育有利区分布的因子为页岩品质的优劣、资源规模的大小和保存条件的好坏,通过定量评价,综合得分排在前3位的有利区分别为中央复背斜有利区、桑植—石门复向斜南有利区和宜都—鹤峰复背斜有利区。     

Some properties of principal component scores

Commonly used methods for calculating component scores are reviewed. Means, variances, and the covariance structures of the resulting sets of scores are examined both by calculations based on a large set of electron microprobe analyses of melilite (supplied by D. Velde)and by a survey of recent geological applications of principal component analysis. Most of the procedures used to project raw data into the new vector space yield uncorrelated scores. In exceptions so far encountered, correlations between scores seem to have been occasioned by the use of unstandardized variables with components calculated from a correlation matrix. In a number of cases substantive interpretations of such correlations have been proposed. A different set of correlations results for the same data if scores are computed from standardized variables and components based on the covariance matrix. If unscaled components are rotated by the varimax procedure, the result is a return to the original space. In the work reported here, nevertheless, scores calculated from varimax-rotated scaled vectors are uncorrelated.     

Assessing hydrochemical evolution of groundwater in limestone terrain via principal component analysis

This paper describes the use of multivariate statistical analysis to trace hydrochemical evolution in a limestone terrain at Zagros region, Iran. The study area includes a deep confined aquifer, overlaid by an unconfined aquifer. The method involves the use of principal component analysis (PCA) to assess and evaluate the hydrochemical evolution based on chemical and isotope variables of 12 piezometers drilled in both the unconfined and confined aquifers. First PCA on all variables shows that water–rock interaction under different conditions with respect to the atmospheric CO₂ is the main process responsible for chemical constituents. As a result, combinations of several ratios such as Ca/TDS, SO₄/TDS and Mg/TDS with physico-chemical and isotope variables reveal different hydrochemical evolution trend in the aquifers. Second PCA on the selective samples and variables reveals that displacement of the unconfined samples from dry to wet season follows a refreshing trend towards river samples that is characterized by reducing electrical conductivity and increasing sulphate and tritium contents. However, the refreshing trend cannot be traced in the confined aquifer samples suggesting no recharge from river to the confined aquifer. Third PCA reveals that, chemical composition of water samples in the unconfined aquifer tends to have considerable difference from each other in the end of recharge period. In contrast, the confined aquifer samples have a tendency to show similar chemical composition during recharge period in comparison to end of dry period. This difference is caused by different mechanism of recharge in the unconfined aquifer (through the whole aquifer surface) and the confined aquifer (through the limited recharge area).     

Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data

The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner product-moment of the transformed data matrix are taken directly as the Q-mode scores or scaled by the square roots of their associated eigenvalues and called the R-mode loadings. If the eigenvectors are extracted from the product-moment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the p-largest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing pcomponents will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed—even whether it is Ror Q-mode—the goodness-of-fit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored.     

基于主成分和半参数的大坝变形监测回归模型

主成分分析在一定程度上可以解决大坝变形监测回归模型因子间的复共线性,然而当提取的主成分信息不充分时,主成分回归用于大坝安全预测可能失效。提出以主成分分析提取的主成分作为半参数回归的参数分量,剩余成分和模型误差作为未知的非参数分量对主成分回归进行补偿,建立一种基于主成分和半参数的大坝变形监测混合回归模型。利用某大坝实测资料进行建模分析,结果表明该混合模型能克服回归因子间的复共线性,避免半参数回归补偿最小二乘估计中法矩阵的病态性,比传统的主成分回归和逐步回归模型具有更好的拟合和预报精度。     

用主成分分析和灰色关联度分析评价草原土壤质量

在吉林西部草原生态环境调查的基础上,对草原土壤进行了理化性质、营养成分等系统测试,选择其中的有机质、金氮、全磷、全钾、水解性氮、速效磷、速效钾、碱化度、pH值等项目作为评价指标,应用主成分分析法,对吉林西部17种草地进行综合评价,将吉林西部草原土壤分为五个等级,并用灰色关联度分析方法进行了对比。结果表明,两种评价方法得出的结论基本一致。     

基于主成分分析法的Q2黄土湿陷特性研究

Q2黄土由于埋藏深,结构相对致密,其湿陷性问题常常被忽视。湿陷系数作为评价黄土湿陷程度的定量指标,其影响因素众多,包括土的含水率、干密度、孔隙比等。由于各因素之间存在一定相关性,所建立的湿陷系数与物理指标之间相关关系往往准确度较低。为降低黄土湿陷指标多重相关性对数据回归分析结果的影响,提高预测精度,以彬州渭化乙二醇项目场地Q2黄土为研究对象,在统计分析场地地层物性指标及湿陷系数与物性单一指标之间相关性的基础上,筛选了7个与湿陷系数相关性较好的指标。采用主成分分析法,通过多元线性回归分析,建立了以累积方差贡献率为基础的Q2黄土湿陷系数计算模型。模型计算值与实测值对比结果表明,该方法有效较低了湿陷系数影响因子之间的多重相关性和相互影响问题,证实了所建立的Q2黄土湿陷系数与独立影响因子之间相关关系的合理性和准确性。     

主成分分析在航空瞬变电磁去噪中的应用

由于航空瞬变电磁二次场数据是一种宽频带信号且幅度较小,因此常常受到随机噪声、天电噪声以及人文噪声的影响。研究针对上述噪声的去噪方法,可以提高处理和解释的精度。这里给出了基于主成分分析的航空瞬变电磁去噪方法,首先应用主成分分析方法对叠加抽道后的单测点衰减曲线进行分解,然后应用曲线趋势对比法和L曲线法对分解后的成分进行分析,确定出有效信号成分,最后使用这些有效信号成分进行重构,从而达到抑制噪声的目的。模拟信号分析以及实测数据的实验结果表明,应用主成分分析法处理航空瞬变电磁数据,在保持反映地下介质分布的有效信号幅度基本不变的条件下,能有效抑制天电噪声和人文噪声,为保幅处理和解释奠定了良好的基础。     

基于主成分分析的重力侵蚀区域提取方法研究

历史重力侵蚀是研究区域重力侵蚀危险性的一个重要数据,通过多期航片、卫星影像结合野外调查是快速确定重力侵蚀发生区域的主要方法.以马来西亚金马仑高原作为研究区,选取不同时相的SPOT5数据,运用主成分分析方法,提取发生重力侵蚀的区域.研究表明,通过多时相主成分分析得到的第二主成分主要反映了地表植被的变化信息,运用阈值法可快速提取可能发生重力侵蚀的区域.     

基于主成分分析的反射光谱在岩石学中的应用——以哈密地区为例

本文首先总结并分析了岩矿常见光谱特征的波长位置及其产生原因。然后基于主成分分析技术对哈密42条岩石实验室光谱进行了定量分析。前两个主成分共包含了96．7％的信息量，代表了原始信息。第一主成分反映了岩石总体反射率大小，称为反照率因子；第二主成分反映了光谱曲线斜率变化，称为形状因子。使用这两个主成分可以区分该区主要岩类，达到了数据压缩和分类的目的。第三和第四主成分尽管所占信息很少，但反映了岩石蚀变信息。为了突出蚀变岩石光谱吸收特征，进而又对经过连续统去除后的光谱进行主成分分析，结果发现，在新生成的第三和第四主成分图上，4种矿石被清晰区分开来。     

Identification of temporal and spatial variations of water quality in Sanya Bay,China by three-way principal component analysis

A large data set obtained by a 1-year monthly determination of water quality from Sanya Bay, South China Sea, was treated by three-way principal component analysis aimed at exploring the spatial and temporal patterns of water quality in Sanya Bay. Tucker3 model of optimum complexity (2, 2, 1) explaining 33.18% of the data variance, allowed interpretation of the data information in three modes. The model explained spatial and temporal variation trends in terms of water quality variables during the study period. Water quality in sampling station (S2) Sanya River was mainly influenced by Sanya River, and water quality in other stations (S1, S3–S10) were mainly influenced by the waters in South China Sea. The results delineated the mouth of Sanya River as critical from pollution point of view. The dry season from October to the next April and rainy season from May to September have different influences on water quality in Sanya Bay. The information extracted by the three-way models would be very useful to regional agencies in developing a strategy to carry out scientific plans for resource use based on marine system functions.