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Linear multivariate statistical methods are widely used for analysing data sets which consist of a large number of variables. These techniques, which include principal component analysis, factor analysis, canonical correlation analysis, redundancy analysis and discriminant analysis, all produce a set of new variables, commonly called 'factors', according to some criterion which differs for different techniques. Among these techniques, principal component analysis is one of the most popular techniques used for reducing the dimensions of the multivariate data set. In many applications, when Principal Component Analysis (PCA) is performed on a large number of variables, the interpretation of the results is not simple. The derived eigenvectors of the sample covariance or correlation matrix are not necessarily in a simple form, with all coefficients either 'large' or 'negligible'. To aid interpretation, it is fairly common practice to rotate the retained set of components, often using orthogonal rotation. The purpose of rotation is to simplify structure, and thus to make it easier to interpret the low-dimensional space represented by the retained set of components. Thus, quantification of simplicity is a two step process. The first set involves the extraction of the feature from the data called components, while the second stage uses a rotation method to simplify the structure. One of the two main purposes of this thesis is to combine into one step these two separate stages of dimension reduction (finding the components) and simplification (rotation). This goal is achieved by combining these two objectives in the form of a single function leading to what we call Simplified Components (SCs). Another objective is to discover which of the many possible criteria suggested in factor analysis can be adopted in the proposed procedure of SCs. Thus, a simplified one-step procedure of SCs is proposed, using four measures of simplicity, namely varimax, quartimax, orthomax and equamax indices.

Although there has been progress in the area of Multivariate Statistical Process Control (MSPC), there are numerous limitations as well as unanswered questions with the current techniques. MSPC charts plotting Hotelling's T2 require the normality assumption for the joint distribution among the process variables, which is not feasible in many industrial settings, hence the motivation to investigate nonparametric techniques for multivariate data in quality control. In this research, the goal will be to create a systematic distribution-free approach by extending current developments and focusing on the dimensionality reduction using Principal Component Analysis. The proposed technique is different from current approaches given that it creates a nonparametric control chart using robust simplicial depth ranks of the first and last set of principal components to improve signal detection in multivariate quality control with no distributional assumptions. The proposed technique has the advantages of ease of use and robustness in MSPC for monitoring variability and correlation shifts. By making the approach simple to use in an industrial setting, the probability of adoption is enhanced. Improved MSPC can result in a cost savings and improved quality.

The Atherton Tablelands basalt aquifer is a major source of groundwater supply for irrigation and other agricultural use. The Tertiary to Quaternary age basaltic aquifer can be regarded as a generally unconfined, layered system, comprising numerous basalt flows separated by palaeo-weathering surfaces and minor alluvial gravels of palaeo-drainage channels. Layers of massive basalt and clay-rich weathered zones act as local aquitards, with some local perched aquifers also present. The aquifer is regarded as a system in which several factors interact to produce the overall characteristics of the hydrogeochemistry of the groundwaters. They include the mineralogical composition of both the basalt aquifer and the thick overlying weathered zone, the porosity and permeability of the basalt aquifer, its thickness, bedrock composition, and climate and topography. The hydrogeochemical processes operating in this aquifer system have been investigated though the analysis of 90 groundwater samples collected from October 1998 to October 1999, groundwater chemistry data provided by the Queensland Department of Natural Resources & Mines for more than 800 groundwater samples, rain water samples collected during 1999 by CSIRO, stream chemistry data provided by CSIRO and James Cook University, and mineralogical and whole rock geochemistry data of drill chip samples. The methods used in this research study include the assessment of groundwater major ion chemistry data and field physico-chemical parameters using hydrochemical facies and statistical approaches, investigation of the mineralogical composition of the aquifer, assessment of concentrations and activities of the ions in solution, the degree of saturation with respect to both primary and secondary minerals, and hydrogeochemical modelling to determine the likely controls on the chemical evolution of these groundwaters. The basaltic groundwaters are mostly Mg-Ca-Na, HCO3 type waters, with electrical conductivities generally less than 250 μS/cm and pH values from 6.5 to 8.5. Dissolved silica (H4SiO4) comprises a large proportion of the total dissolved load, with average concentrations of around 140 mg/L. Concentrations of potassium, chloride and sulphate are low, that is, generally less than 3 mg/L, 15 mg/L and 10 mg/L, respectively. Despite the very low salinity of the Atherton Tablelands basalt groundwaters, the relative concentrations of the major ions are comparable to groundwaters from other basaltic regions, and are consistent with expected waterrock interactions. A variety of multivariate statistical techniques may be used to aid in the analysis of hydrochemical data, including for example, principal component analysis, factor analysis and cluster analysis. Principal component factor analyses undertaken using the hydrochemical data for the Atherton groundwaters has enabled the differentiation of groundwaters from various lithological formations, the underlying geochemical processes controlling groundwater composition in the basalt aquifer to be inferred, relative groundwater residence and flow directions to be inferred and mapping of the estimated thickness of the basalt aquifer. The limitations of multivariate statistical methods have been examined, with emphasis on the issues pertinent to hydrochemical data, that is, data that are compositional and typically, non-normally distributed. The need to validate, normalize and standardize hydrochemical data prior to the application of multivariate statistical methods is demonstrated. Assessment of the saturation states of the Atherton basalt groundwaters with respect to some of the primary minerals present indicate that the groundwaters are mostly at equilibrium or saturated with respect to K-feldspar, and approach equilibrium with respect to the plagioclase feldspars (albite and anorthite) with increasing pH. These groundwaters are at equilibrium or saturated with respect to the major secondary minerals, kaolinite, smectite (Ca-montmorillonite) and gibbsite. They also tend to be saturated with respect to the oxidation products, goethite and hematite, common accessory minerals in the Atherton Tablelands basalt sequence. Silicate mineral weathering processes are the predominant influence on the composition of these basalt groundwaters. These weathering processes include the weathering of pyroxenes, feldspars and other primary minerals to clays, aluminium and iron oxides, amorphous or crystalline silica, carbonates and zeolites, releasing ions to solution. The contribution of substantial organic carbon dioxide to the groundwater is an important factor in the extent to which silicate mineral weathering occurs in this aquifer system. Evaporative enrichment of recharging waters, oxidation and ion-exchange reactions and the uptake of ions from, and decomposition of, organic matter, are processes that have a minor influence on the composition of the basalt groundwaters. The relationships observed between mineralogical compositions, basalt character and groundwater occurrence in the Atherton Tablelands region improved the understanding how groundwater is stored and transmitted in this basalt aquifer system. Groundwater is mostly stored in vesicular basalt that may be fresh to highly weathered, and movement of this water is facilitated by pathways through both vesicular and fractured basalt. Related work undertaken as part of this research project showed that the groundwater flow patterns defined by the hydrogeochemical interpretations correspond well with the spatial trends in water level fluctuations, and response to recharge events in particular. Groundwater baseflow to streams and discharge to topographic lows in the Atherton Tablelands region is indicated by the relationships between the major cations and anions in the stream waters. Fracture zones are likely to be preferred pathways of groundwater movement. Recharge estimates, based on a chloride mass balance, range from 310 mm/yr in the north-western part of the study area (north of Atherton) to 600 mm/yr in the wetter southern and eastern parts of the study area. These recharge estimates should be treated with caution however, due to the low groundwater chloride concentrations and the high variability in rainfall chloride concentrations. The findings of this research project have improved the understanding of the hydrogeochemical processes controlling the composition of the low salinity basalt groundwaters in the Atherton Tablelands region, and are applicable to other basalt groundwater systems, particularly those in high rainfall environments.

In Taiwan, more than 20% of the major rivers are mildly to heavily pollute by domestic, industrial, and agricultural wastewaters due to the low hook-up rate of public underground sewerage systems in rural areas. Thus, constructed or engineered wetlands have been adopted as the major alternatives to cleanup polluted rivers. Constructed wetlands are also applied as the tertiary wastewater treatment systems to polish the secondary wastewater effluents to meet water reuse standards with lower operational costs. The studied Kaoping River Rail Bridge Constructed Wetland (KRRBCW) is the largest constructed wetland in Taiwan. It is a multi-function wetland and is used for polluted creek water purification and secondary wastewater polishment before they discharge into the Kaoping River. Although constructed wetlands are feasible for contaminated water treatment, wetland sediments are usually the sinks of organics and metals. In this study, water, sediment and macrophytes samples were collected from the major wetland basins in KRRBCW. The quarterly investigation (from 2007 to 2009) results show that more than 97% of total coliforms (TC), 55% of biochemical oxygen demand (BOD), and 30% of nutrients [e.g., total nitrogen (TN), total phosphorus (TP)] were removed via the constructed wetland system. However, results from the sediment analyses show that wetland sediments contained high concentrations of metals (e.g., Cu, Fe, Zn, Cr, and Mn), organic contents (sediment oxygen demand = 1.7 to 7.6 g O2/m2-d), and nutrients (up to 18.7 g/kg of TN and 1.22 g/kg of TP). Thus, sediments should be excavated periodically to prevent the release the pollutants into the wetland system and causing the deterioration of wetland water quality. Results of polymerase chain reaction (PCR), denaturing gradient gel electrophoresis (DGGE), and nucleotide sequence analysis reveal that an increase in microbial diversities in the wetland systems was observed. Results from the DGGE analysis indicate that all sediment samples contained significant amounts of microbial ribospecies, which might contribute to the carbon degradation and nitrogen removal. Gradually disappearing of E. coli was also observed along the flow courses through the natural attenuation mechanisms. The factor analysis of SPSS 12.0 shows that 17 water-quality items of the study site could obtain four to six principal components, including nitrate factor, phosphorus factor, eutrophication factor, organic factor, and environmental background factor, the major influencing components are nutrition factor and eutrophication factor. The ponds of the study site were classified into two or three clusters depend on in-and-out flow location. This study attempted to establish a forecasting model of wetland pollutants concentration through the time series (ARIMA), results show that the outcome of the B7 pond was better than others. Results indicate that the ARIMA model can be used to simulate the trend of treatment efficiency using the wetland system. Experience and results obtained from this study would provide solutions for water quality control. Thus, the wetland system has a significant effect on water quality improvement and is capable of removing most of the pollutants from the local drainage system before they are discharged into the downgradient water body. Other accomplishments of this constructed wetland system include the following: providing more green areas along the riversides, offering more water assessable eco-ponds and eco-gardens for public, and rORPabilitating the natural ecosystem. The Kaoping River Rail Bridge Constructed Wetland has become one of the most successful multi-function constructed wetlands in Taiwan. The experience obtained from this study will be helpful in designing similar natural treatment systems for river water quality improvement and wastewater treatment.

To determine the relationship between vegetation and environmental parameters in the middle and upper watershed of Nan-Tze-Shian stream, the first comprehensive multivariate statistical analysis of the woody vegetation data obtained from field survey, is presented. According to physiognomy and plant composition, 70 homogenous stands were sampled in the area. Each plot is composed of twenty 5 ¡Ñ 5 m2 quadrates. Five environmental factors including plot location, altitude, slope, aspect and microtopography were recorded. All woody plants in each plot species with dbh ≥ 1cm present in the quadrates were identified, and their dbh were measured. In addition, ground layer species were identified and evaluated by their coverage. The vascular plants inventory recorded a total of 118 families, 321 genera and 563 species. Among the 203 woody plants, the families are rich in species including Lauraceae, Fagaceae, Theaceae, Symploaceae and Moraceae. Detrended correspondence analysis (DCA) was applied to the ordination analysis, to clarify the spatial variation of the 70 plots and search for relationship of the variation with 5 environmental variables. Classification of the vegetation types was conducted by the cluster analysis (CA), two-way indicator species analysis (TWINSPAN) and tabular comparison method. The results obtained from the analysis are that the distribution of vegetation types and flora are obvious and sensitive to the elevation and whole light sky space (WLS) and the floristic classification distinguished 9 forest types: Neolitsea acuminatissima - Cyclobalanopsis morii, Vaccinium randaiense - Castanopsis cuspidata, Pasania kawakamii - Cyclobalanopsis stenophylloides, Beilschmiedia erythrophloia, Engelhardtia roxburghiana - Cyclobalanopsis longinux, Helicia formosana - Machilus konishii kusanoi, Castanopsis formosana, Machilus zuihoensis - Schefflera octophylla and Ficus irisana - Machilus kusanoi associations. The associations were re-arranged by tabular comparison method for developing a hierachy of forest vegetation system. This hierachical system consists of Three alliances, characterized by Cyclobalanopsis stenophylloides, Beilschmiedia erythrophloia and Machilus kusanoi, respectively. Finally, I ascribed the vertical vegetation spectrum along with altitude gradient. The altitudinal boundaries between upper Quercus, lower Quercus and Machilus-Castanopsis zones are ca. 1800 m and 1200 m, respectively. The results might help us to understand the habitat diversity and plant diversity in the area, and those are expected to apply to vegetation mapping and environment monitoring.

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Orientador: Paulina Setti Riedel / Banca: Paulo Milton Barbosa Landim / Banca: Diana Sarita Hamburger / Resumo: As imagens de satélite, por serem um registro de alvos com diferentes comportamentos espectrais e diferentes arranjos espaciais, respondem com variações tonais de cinza e variações texturais. Esta variação textural é analisada normalmente através de interpretação visual, que é uma sistematização de várias técnicas, as quais convergem para um único objetivo, a compartimentação da imagem. Em geral, a textura apresenta-se como sendo uma arma valiosa na interpretação de formas de relevo, drenagem e de padrões da cobertura vegetal e de uso da terra. Acredita-se que, a partir da utilização das técnicas de processamento digital de imagens e técnicas estatísticas multivariadas, como subsidiária na redução do caráter subjetivo da análise textural e da correspondência entre zonas homólogas, será possível favorecer a discriminação de elementos imageados, e encontrar um modelo que possibilite explicar mais satisfatoriamente a compartimentação e a relação de equivalência entre zonas que constituem texturas semelhantes. Desta forma, o objetivo geral do trabalho, é avaliar diversas metodologias, com intuito de realizar uma compartimentação fisiográfica, explorando o aspecto textural da imagem além da similaridade existentes entre as áreas após compartimentada. A área de estudo abrange os municípios de Itanhaém e Peruíbe localizados no litoral sul do Estado de São Paulo. A partir dos resultados obtidos, verificou-se que o método convencional de fotointerpretação juntamente com a aplicação da análise estatística multivariada, mostrou-se viável de ser aplicado apresentando resultados satisfatórios e inovadores. Já no processamento de alguns algoritmos de textura a redução de informações foi bastante grande, devido à redução dos valores de níveis de cinza e à homogeneização dos alvos; mostrando que o resultados não foram positivos...(Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Satellite images record surface features based on their different spectral behaviors and spatial arrangements. As such, these features are discernable from different shades of gray and textural variations seen in the images. These textural variations represent a systematic utilization of various techniques, which converge for a single objective: compartmentalization of the image. In general, texture is used as an important tool in the interpretation of relief forms, drainage patterns and vegetative cover and land-use patterns. Through the application of digital processing techniques and multivariable statistical analyses, it is possible to reduce the subjective character of textural analysis and correspondence between homologous zones, hence enhance the discrimination of different elements in an image. These methods can help find a model that allows for a better explanation of the compartmentalization and equivalence between zones that consist of similar textures. In this form, the general objective of the study is to evaluate diverse methodologies with the objective of determining the physiographic compartmentalization, exploiting the textural aspect of the image in addition to the existing similarities between areas following compartmentalization. The study area is within the municipalities of Itanhaém e Peruíbe, located along the south coastal region of São Paulo State. Based on the results obtained, it is confirmed that the conventional method of photo-interpretation, together with the application of multivariate statistical analysis, shows that it is a viable combination, yielding both satisfactory and innovative results. Already, in the processing of some textural algorithms, the reduction of information was significant, owing to the reduction of the values in the shades of gray and to the homogenization of targets, showing that the results were not positive...(Complete abstract click electronic access below) / Mestre

This thesis is intent on the introduction to problems of statistical approach to research tasks. It focuses on research assignments, position of research worker and statistician while analyzing, ways of gathering data files and problems connected with them, main types of multivariate statistical methods and possible views of their classification. Moreover, this work includes overview of examples of research assignments, possibilities of their solutions and related data files. First chapter describes statistical approach to the research assignments, and the second one shows concrete examples of these assignments. The enclosed CD includes data files to most of the statistical examples.