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.     

Assessment of regional drought vulnerability and risk using principal component analysis and a Gaussian mixture model

Due to the complex characteristics of drought, drought risk needs to be quantified by combining drought vulnerability and drought hazard. Recently, the major focus in drought vulnerability has been on how to calculate the weights of indicators to comprehensively quantify drought risk. In this study, principal component analysis (PCA), a Gaussian mixture model (GMM), and the equal-weighting method (EWM) were applied to objectively determine the weights for drought vulnerability assessment in Chungcheong Province, located in the west-central part of South Korea. The PCA provided larger weights for agricultural and industrial factors, whereas the GMM computed larger weights for agricultural factors than did the EWM. The drought risk was assessed by combining the drought vulnerability index (DVI) and the drought hazard index (DHI). Based on the DVI, the most vulnerable region was CCN9 in the northwestern part of the province, whereas the most drought-prone region based on the DHI was CCN12 in the southwest. Considering both DVI and DHI, the regions with the highest risk were CCN12 and CCN10 in the southern part of the province. Using the proposed PCA and GMM, we validated drought vulnerability using objective weighting methods and assessed comprehensive drought risk considering both meteorological hazard and socioeconomic vulnerability.

     

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.     

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.     

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.     

基于灰色关联度分析法和主成分分析法对泥页岩储层评价方法的探讨

泥页岩储层的影响因素众多,明确各因素间的内部联系才能更好地评价储层。为对比灰色关联法和主成分分析法在储层评价中的适用性,本文选取鄂尔多斯盆地东缘上古生界Y88井丰富的储层数据进行分析。通过对比两种多元统计方法的原理、算法和结果,认为主成分分析法把各项因子视为离散变量,通过降维后用三个综合评价指标来反映储层的优劣,是对各项指标的概括性分析;灰色关联法将参数分为参考数据列和比较数据列,参考数据列的有机碳含量高低与储层的优劣成正相关,参考数据列对评价对象具有可测性。因此,若是对评价对象的概括性分析,用主成分分析法比较合适;若是对评价对象的可测性分析,如有机碳含量的高低决定能不能形成泥页岩储层,则用灰色关联法评价更合理。     

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。     

Assessment of groundwater water quality in central and southern Gulf Coast aquifer,TX using principal component analysis

Principal component analysis has been applied for source identification and to assess factors affecting concentration variations. In particular, this study utilizes principal component analysis (PCA) to understand groundwater geochemical characteristics in the central and southern portions of the Gulf Coast aquifer in Texas. PCA, along with exploratory data analysis and correlation analysis is applied to a spatially extensive multivariate dataset in an exploratory mode to conceptualize the geochemical evolution of groundwater. A general trend was observed in all formations of the target aquifers with over 75 % of the observed variance explained by the first four factors identified by the PCA. The first factor consisted of older water subjected to weathering reactions and was named the ionic strength index. The second factor, named the alkalinity index explained greater variance in the younger formations rather than in the older formations. The third group represented younger waters entering the aquifers from the land surface and was labeled the recharge index. The fourth group which varied between aquifers was either the hardness index or the acidity index depending on whether it represented the influences of carbonate minerals or parameters affecting the dissolution of fluoride minerals, respectively. The PCA approach was also extended to the well scale to determine and identify the geographic influences on geochemical evolution. It was found that wells located in outcrop areas and near rivers and streams had a larger influence on the factors suggesting the importance of surface water–groundwater interactions.     

基于主成分分析和最近邻算法的断层识别研究

断层是影响煤矿安全的致灾地质因素,查明断层特征是煤矿三维地震勘探的主要目的之一。常规断层解释中采用的人机交互解释方法,其可靠性在一定程度上取决于解释者的经验。为提高断层解释精度,提出一种基于主成分分析和最近邻算法来检测沿目标层断层分布的方法。首先,选择峰峰矿区羊东煤矿作为研究区域,从矿区高精度处理后获得的三维地震数据中提取10个地震属性;然后,采用主成分分析法(PCA)将上述10个地震属性整合为6个综合属性;同时,将属性信息与从矿区15口井和3条巷道确定的139个点的断层信息相结合,构建已知数据信息;在该数据信息的基础上,分别组建出数据集1和数据集2两种数据集,2种数据集的训练集与测试集的比分别为9∶1和3∶7。利用这些数据集以及十折交叉验证的方法,开展基于最近邻算法(kNN)的断层识别准确率测试,数据集1的测试准确率为87.75%,数据集2的测试准确率为71.63%;这表明训练数据量越大,断层识别准确率越高,从而也说明高密度三维地震在该方法的应用中存在一定优势。在对kNN模型的分类性能进行测试时,使用通过PCA进行降维处理的数据作为输入,计算出的分类准确率分别为89.23%和73.79%;这是因为PCA降低了原始输入特征的维数,从而减少了所需的计算量并提高了这些特征的表征能力。综合结果表明,结合PCA和kNN方法可以有效地识别断层分布,减少主观人为因素的影响,提高断层解释的效率。      

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.     

Analysis of factors controlling soil N2O emission by principal component and path analysis method

Nitrous oxide (N₂O) is a potent greenhouse gas. Mitigating N₂O emission is critical for combating global climate change and improving the ecological environment. Many studies have focused on factors affecting N₂O emission from agricultural soils, but rarely on the relationship among these factors. In the present study, continuous measurement on N₂O emission was conducted in a maize system in Griffith, Australia and the relationships between N₂O emission, soil properties and weather conditions were examined. Principal component analysis and path analysis were used to analyze these data in correlation coefficient and the direct and indirect effects to N₂O emission. Results indicated that (1) the major factors affecting N₂O emission were WFPS, mineralized nitrogen (Mineral N), daily mean temperature (T _mean) and CO₂ concentration. The factors of direct influence N₂O emission were following Mineral N, CO₂, WFPS, and T _mean. The indirect influence N₂O emission was following T _mean, WFPS, Mineral N, and CO₂ concentration. (2) The standard multiple regression describing the relationship between N₂O emission and its major factors were Y = ?37.162 + 0.5267 X ₁ + 0.4331 X ₂ + 0.3014 X ₃ + 0.2392 X ₄ (r = 0.924, p < 0.01, n = 151), where Y is N₂O emission, X ₁ is Mineral N, X ₂ is CO₂, X ₃ is WFPS and X ₄ is T _mean. (3) N₂O emission from agricultural soils can be monitored and mitigated through improved management practices such as irrigation, straw retention and fertilizer application.     

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).     

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。     

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.     

主成分分析与Bayes判别法在突水水源判别中的应用

准确有效地判别突水水源是解决矿井水害的前提条件。基于淮北袁店二矿各含水层共59个水样水质化验资料,利用主成分分析法,计算各水样的因子得分,并进行系统聚类,剔除错误样本。利用剩余水样作为学习样本,检验Bayes判别函数的判定准确性,得出准确率为92.5%,并进行交叉验证。利用该判别函数对某工作面底板下一富水区水样进行判别,结果与实际情况吻合。结果指示基于主成分分析与Bayes判别法较单一Bayes判别法更加准确,能够消除样本变量之间的相互影响,实现对突水水源的快速有效判别。