ANALYZING THE POLLUTION OF NINE POINTS ON THE PARAÍBA DO SUL RIVER USING MULTIVARIATE STATISTICS

Abstract

Objective: The aim of this study is to accurately analyze water quality at strategic monitoring points over a decade through the combined use of statistical methods in the Paraíba do Sul River Basin in the Fluminense region of the state of Rio de Janeiro, Brazil. Theoretical framework: PCA was invented in 1901 by Karl Pearson and today, it is most used as a tool for Exploratory Data Analysis and for making predictive models. PCA can be done by decomposing a covariance matrix into eigenvalues, usually after centering (and normalizing or using Z-scores) the data matrix for each attribute (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000). Method: The data was obtained from the INEA and ANA agencies over a decade at nine points on the Paraíba do Sul River and treated with Multivariate Statistics. Final Considerations: This study showed the adverse effects included the concentration of pollutants, the silting up of the river, the reduction in oxygen and the increase in water temperature, all reflected in sharp drops in the WQI. Implications of the research: The use cases of Multivariate Statistics are multiplying in the scientific literature and are proving to be highly effective in dealing with data where the assumptions of Normality are confirmed. Originality/value: Despite being well-known statistical tools, Factor Maps are widely used and can bring innovations to their application, as in the case of environmental variables.

Alternate abstract:

Objetivo: O objetivo deste estudo é analisar com precisão a qualidade da água em pontos estratégicos de monitoramento ao longo de uma década por meio do uso combinado de métodos estatísticos na Bacia do Rio Paraíba do Sul na região fluminense do estado do Rio de Janeiro, Brasil. Referencial teórico: A PCA foi inventada em 1901 por Karl Pearson e, atualmente, é mais usada como uma ferramenta para análise exploratória de dados e para a criação de modelos preditivos. A PCA pode ser feita decompondo uma matriz de covariância em valores próprios, geralmente após centralizar (e normalizar ou usar escores Z) a matriz de dados para cada atributo (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000). Método: Os dados foram obtidos das agências INEA E ANA durante uma década em nove pontos do Rio Paraíba do Sul e tratados com Estatística Multivariada. Considerações Finais: Esse estudo mostrou os efeitos adversos incluíram a concentração de poluentes, o assoreamento do rio, a redução do oxigênio e o aumento da temperatura da água, todos refletidos em quedas acentuadas no IQA. Implicações da pesquisa: Os casos de utilização de Estística Multivariada se multiplicam pela literatura científica e se mostram altamente eficazes para tratar dados em que os pressupostos de Normalidade se confirmam. Originalidade/valor: Apesar de serem Ferramentas Estatísticas bastante conhecidas, o Mapa Fatorial são muito utilizados e podem trazer inovações na sua aplicação como no caso de variáveis ambientais.

Alternate abstract:

Objetivo: El objetivo de este estudio es analizar con precisión la calidad del agua en puntos de control estratégicos a lo largo de una década mediante el uso combinado de métodos estadísticos en la cuenca del río Paraíba do Sul, en la región fluminense del estado de Río de Janeiro, Brasil. Marco teórico: El ACP fue inventado en 1901 por Karl Pearson y actualmente se utiliza sobre todo como herramienta para el análisis exploratorio de datos y para crear modelos predictivos. El ACP se puede realizar descomponiendo una matriz de covarianza en valores propios, normalmente después de centrar (y normalizar o utilizar puntuaciones Z) la matriz de datos para cada atributo (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000). Método: Los datos se obtuvieron de las agencias INEA y ANA a lo largo de una década en nueve puntos del río Paraíba do Sul y se procesaron mediante Estadística Multivariante. Consideraciones finales: Este estudio demostró que los efectos adversos incluían la concentración de contaminantes, el encenagamiento del río, la reducción del oxígeno y el aumento de la temperatura del agua, todo ello reflejado en fuertes descensos del IQA. Implicaciones de la investigación: Los casos de utilización de la Estadística Multivariante se multiplican en la literatura científica y son muy eficaces para tratar datos en los que se confirman los supuestos de Normalidad. Originalidad/valor: Aunque se trata de herramientas estadísticas muy conocidas, los Mapas de Factores se utilizan ampliamente y pueden aportar innovaciones a su aplicación, como en el caso de las variables medioambientales.

Headnote

ABSTRACT

Objective: The aim of this study is to accurately analyze water quality at strategic monitoring points over a decade through the combined use of statistical methods in the Paraíba do Sul River Basin in the Fluminense region of the state of Rio de Janeiro, Brazil.

Theoretical framework: PCA was invented in 1901 by Karl Pearson and today, it is most used as a tool for Exploratory Data Analysis and for making predictive models. PCA can be done by decomposing a covariance matrix into eigenvalues, usually after centering (and normalizing or using Z-scores) the data matrix for each attribute (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000).

Method: The data was obtained from the INEA and ANA agencies over a decade at nine points on the Paraíba do Sul River and treated with Multivariate Statistics.

Final Considerations: This study showed the adverse effects included the concentration of pollutants, the silting up of the river, the reduction in oxygen and the increase in water temperature, all reflected in sharp drops in the WQI.

Implications of the research: The use cases of Multivariate Statistics are multiplying in the scientific literature and are proving to be highly effective in dealing with data where the assumptions of Normality are confirmed.

Originality/value: Despite being well-known statistical tools, Factor Maps are widely used and can bring innovations to their application, as in the case of environmental variables.

Keywords: Multivariate Statistics, Factor Map, River, Environmental Variables.

RESUMO

Objetivo: O objetivo deste estudo é analisar com precisão a qualidade da água em pontos estratégicos de monitoramento ao longo de uma década por meio do uso combinado de métodos estatísticos na Bacia do Rio Paraíba do Sul na região fluminense do estado do Rio de Janeiro, Brasil.

Referencial teórico: A PCA foi inventada em 1901 por Karl Pearson e, atualmente, é mais usada como uma ferramenta para análise exploratória de dados e para a criação de modelos preditivos. A PCA pode ser feita decompondo uma matriz de covariância em valores próprios, geralmente após centralizar (e normalizar ou usar escores Z) a matriz de dados para cada atributo (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000).

Método: Os dados foram obtidos das agências INEA E ANA durante uma década em nove pontos do Rio Paraíba do Sul e tratados com Estatística Multivariada.

Considerações Finais: Esse estudo mostrou os efeitos adversos incluíram a concentração de poluentes, o assoreamento do rio, a redução do oxigênio e o aumento da temperatura da água, todos refletidos em quedas acentuadas no IQA.

Implicações da pesquisa: Os casos de utilização de Estística Multivariada se multiplicam pela literatura científica e se mostram altamente eficazes para tratar dados em que os pressupostos de Normalidade se confirmam.

Originalidade/valor: Apesar de serem Ferramentas Estatísticas bastante conhecidas, o Mapa Fatorial são muito utilizados e podem trazer inovações na sua aplicação como no caso de variáveis ambientais.

Palavras-chave: Estatística Multivariada, Mapa Fatorial, Rio, Variáveis Ambientais.

RESUMEN

Objetivo: El objetivo de este estudio es analizar con precisión la calidad del agua en puntos de control estratégicos a lo largo de una década mediante el uso combinado de métodos estadísticos en la cuenca del río Paraíba do Sul, en la región fluminense del estado de Río de Janeiro, Brasil.

Marco teórico: El ACP fue inventado en 1901 por Karl Pearson y actualmente se utiliza sobre todo como herramienta para el análisis exploratorio de datos y para crear modelos predictivos. El ACP se puede realizar descomponiendo una matriz de covarianza en valores propios, normalmente después de centrar (y normalizar o utilizar puntuaciones Z) la matriz de datos para cada atributo (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000).

Método: Los datos se obtuvieron de las agencias INEA y ANA a lo largo de una década en nueve puntos del río Paraíba do Sul y se procesaron mediante Estadística Multivariante. Consideraciones finales: Este estudio demostró que los efectos adversos incluían la concentración de contaminantes, el encenagamiento del río, la reducción del oxígeno y el aumento de la temperatura del agua, todo ello reflejado en fuertes descensos del IQA.

Implicaciones de la investigación: Los casos de utilización de la Estadística Multivariante se multiplican en la literatura científica y son muy eficaces para tratar datos en los que se confirman los supuestos de Normalidad.

Originalidad/valor: Aunque se trata de herramientas estadísticas muy conocidas, los Mapas de Factores se utilizan ampliamente y pueden aportar innovaciones a su aplicación, como en el caso de las variables medioambientales.

Palabras clave: Estadística Multivariante, Mapa De Factores, Río, Variables Ambientales.

1 INTRODUCTION

During the last century, statistics revolutionized science by presenting useful models that modernized the research process in the direction of better research parameters, making it possible toguide decision making in a wide variety of areas. Statistical methods were developed as a mixture of science and logic for the solution and investigation of problems in various areas of human knowledge (Abraão et al., 2024; Akdur, 2022; Antonio et al., 2023; Borges et al., 2024; de Araújo et al., 2021; Mazza et al., 2022, 2024; N. A. S. Sampaio, Mazza, Siqueira, et al., 2024; Nilo Antonio de Souza Sampaio et al., 2024; Silva et al., 2023)

The launch of a new product and/or process usually involves working with a large number of variables. Conscientious planning of the experiments that must be used to manipulate these variables and arrive at the desired answers is indispensable if reliable results are to be obtained and if consistent statistical analyses are to be carried out. In this context, it is no longer possible to develop products and processes empirically as was done in the past. The strong competition, the diffusion of technological processes and the responsibility of the scientific community now make such procedures impossible. The optimization of processes and products requires more than ever a robust statistical study (Cardoso et al., 2022; Carvalho, 2023; da Motta Reis et al., 2023; De Almeida et al., 2020; Espuny et al., 2023; F. da S. Gomes et al., 2022; F. M. Gomes et al., 2023; Junior et al., 2023; Roberto Campos Leoni et al., 2017; Reis et al., 2024; Sales et al., 2022; N. A. S. Sampaio, Mazza, Siqueira, et al., 2024; Nilo Antônio de Souza Sampaio, Carvalho, et al., 2025; Vasconcelos et al., 2024).

Multivariate statistical methods and multivariate statistical analysis tools study the behavior of three or more variables simultaneously. They are used mainly to find the least representative variable and eliminate it, simplifying statistical models, where the number of variables becomes a problem to understand the relationship between the various groups of variables (R.C. Leoni et al., 2017)

The aim of this study is to accurately analyze water quality at strategic monitoring points over a decade through the combined use of statistical methods.

2 THEORETICAL BACKGROUND

Various methods of statistical analysis can be used to determine the degree of similarity between related species. One of the most widely applied methods is cluster analysis. Hierarchical cluster analysis, which determines on an input basis the similarity of a particular input with respect to other inputs, seems particularly useful. This statistic has several advantages. First, it allows for the mixing of both qualitative and quantitative data, and therefore all available information about the sample can beused. In addition, each input is treated as an individual entity of equal weight in the analysis, unlike a number of other multivariate techniques that rely on variation across groups of inputs(Antônio, Sampaio, Caraschi, Miranda, Carina, Galli, Bezerra, et al., 2025; Antônio, Sampaio, Caraschi, Miranda, Carina, Galli, Helenita, et al., 2025; Antônio, Sampaio, Sérgio, et al., 2025; Chakraborty et al., 2018; Mazza et al., 2024; Peeters & Martinelli, 1989; N. A. S. Sampaio, Mazza, Sérgio, et al., 2024; Nilo Antonio de Souza Sampaio et al., 2024; Nilo Antônio de Souza Sampaio, Carvalho, et al., 2025; Nilo Antônio de Souza Sampaio, Silva, et al., 2025).

Multivariate statistical analysis was previously applied to evaluate water quality parameters in urban water bodies highlighting how anthropogenic actions, land use, and occupation influence surface water. This study used methods such as principal component analysis (PCA) and hierarchical clustering (HCA) to identify quality patterns and their relationship with pollution sources, highlighting the significant impact of urbanization on the deterioration of water resources (Abraão et al., 2025).

Although the multivariate methods proved efficient in identifying patterns, the model used is limited to retrospective analysis without predicting future water quality. Applied probability curves of water quality parameters as a subsidy forthe legal classification of water bodies (Guimarães et al., 2016) . Their study proposed using probabilistic statistics to estimate the frequency with which quality parameters meetthe standards established by environmental legislation.

Their study proposed using probabilistic statistics to estimate the frequency with which quality parameters meetthe standards established by environmental legislation. Although effective for identifying trends and helping to classify water bodies into specific classes, this approach lacks mechanisms for predicting future changes or the impacts of extreme climatic events, such as droughts or floods (Abraão et al., 2024).

PCA was invented in 1901 by Karl Pearson and today, it is most used as a tool for Exploratory Data Analysis and for making predictive models. PCA can be done by decomposing a covariance matrix into eigenvalues, usually after centering (and normalizing or using Z-scores) the data matrix for each attribute (Derksen et al., 2000; Febriani et al., 2020; Semagn et al., 2000).

It is a mathematical procedure that uses an orthogonal transformation (orthogonalization of vectors) to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. The number of principal components is always less than or equal to the number of original variables. Principal components are independent only if the data are normally (jointly) distributed. PCA is sensitive to the relative scale of the original variables. Depending on the application area, PCA is also known as the discrete Karhunen-Loève transform (KLT), the Hotelling transform or the proper orthogonal decomposition (POD) (Mazza et al., 2022; Mo et al., 2017). PCA describes, in geometric terms of principal components, the covariance of variables (in this case, the RGB channels) using the smallest number of eigenvectors The new subsystem then consists of the axes of the principal components, and the coordinates of the samples on these new axes are called scores. Since each principal component is a linear combination of the original variables, the coefficients of these variables (i.e. the eigenvectors) are called loadings (Godinho et al., 2008).

Principal component analysis (PCA) is one of the most common methods used in information analysis and is used for its ability to understand data due to the existence of correlation among several measured variables (Coelho de Oliveira et al., 2017).

3 MATERIALS AND METHODS

This work can be classified as applied research, as it aims to provide improvements in the current literature, with normative empirical objectives, aiming at the development of policies and strategies that improve the current situation (Bertrand & Fransoo, 2002; de Araújo et al., 2021). The approach to the problem is quantitative, as is the modeling and simulation research method. The research stages were carried out following the sequence shown in Figure 1

The Middle Paraíba do Sul is a region located in the state of Rio de Janeiro, Brazil, and is crossed by the Paraíba do Sul River, as mentioned above. Throughout this region, there are several water collection points, which are essential for supplying the cities, the industrial sector, agriculture and other activities that depend on this vital resource (Pessoa et al., 2020).

Figure 1 shows INEA's water quality monitoring stations in hydrographic region III of the Paraíba do Sul River. The 9 points cover the municipalities of Resende, Porto Real, Barra Mansa, Volta Redonda, Barra do Piraí, and Três Rios (Instituto Estadual do Ambiente, 2024). These municipalities are located in an area marked by significant industrial and agricultural activities, which contribute to both point and diffuse pollution. The data are essential for assessing long-term trends in water quality and informing environmental management strategies in the region.

The NSF (National Sanitation Foundation) Water Quality Index (WQI) is a methodology used to calculate water quality based on different analysis parameters. This index is widely used to assess and compare water quality in bodies of water such as rivers, lakes and reservoirs.

Calculating the NSF WQI involves measuring various water quality parameters, such as organic oxygen, pH, turbidity, suspended solids, fecal coliforms, among others. Each parameter is given a specific weight according to its importance in overall water quality.

The weights assigned to each parameter may vary according to the specific version of the NSF WQI (Table 1). Generally, however, there are three variables that have the greatest weight in the calculation of the WQI:

4 RESULTS AND DISCUSSION

Considering that the climate of the region studied is classified as tropical humid, with two distinct seasons: a dry season (from May to September) and a rainy season (from October to April), the WQI Temporal Analysis was divided into dry and rainy seasons (Njuguna et al., 2019).

In Figure 2, the graph shows the water quality indicators in the dry and rainy seasons over ten years, from 2012 to 2022, for the Paraíba do Sul River, considering the average annual values for the nine sampling points.

Data collection was interrupted by the COVID-19 pandemic in 2020, resulting in only three recorded sampling campaigns, all during the rainy season. This justifies the absence of the Boxplot for the dry season in this year's graph. These gaps in data collection have an essential impact on the analysis, mainly due to the lack of complete seasonal information. The unavailability of dry season data this year prevents a proper assessment of the variations between seasons, which is crucial to understanding how climatic factors affect water quality. Without this data, the interpretation of seasonal and inter-annual trends is hampered, which can lead to partial or less reliable conclusions about pollution patterns, discharge regimes or process efficiency.

In addition, the gaps make it more difficult to validate predictive models or simulations since a database is incomplete and cannot represent behavior in different environmental conditions. Limitations can also arise when comparing with other years, compromising analyses that rely on continuous historical series. These restrictions are particularly relevant for longterm monitoring studies and for decision-making in environmental management policies.

The 2014/2015 drought was an extreme weather event that caused significant impacts on the Paraíba do Sul river basin. The temporal graph shows that the WQI in the dry season of that year was much higher than in the rainy season, which is a significant difference that indicates that the river's water quality was noticeably impaired by the lack of rainfall predicted for the rainy season or by the lack of adequate flow control in the existing dams in the area (Vieira, 2008). This reduction in water flow affected water quality since the concentration of pollutants increased in the river. This resulted from less dilution of the same load of pollutants in the water (Massone & dos Santos, A. A., Ferreira, P. G., & Carreira, 2023).

Table 1 shows the results of the Paired T-Test for the difference in the WQI averages for all the years of the decade. Where the PValue was more significant than 0.05 (5%), the null hypothesis is accepted, i.e., no difference between the dry and wet seasons exists. Where the PValue was less than 0.05 (5%), the null hypothesis is rejected, so there is a difference between the dry and wet seasons. Most of the years observed showed a significant difference between the dry and wet seasons. In particular, the year 2014 was atypical in that the difference between the averages was huge due to the severe drought that occurred that year, as explained above (Tokuda et al., 2023).

Principal Component Analysis (PCA) is a data analysis technique that reduces the dimensionality of a data set. This is done by identifying the main components of the data set, which are the variables that explain most of the variance in the data.

The arrows on a PCA graph represent the projections of the original observations onto the new main axes. Nearby arrows indicate that the observations are similar in terms of the variables that explain most of the variance in the data. Opposite arrows indicate that the observations are different in terms of these variables.

The relationship between the arrows and the principal components is that the arrows point in the direction of the principal components. The magnitude of the arrow indicates the importance of the principal component for the observation.

Figure 2 shows the PCAs of each point studied so far, and the relationship between the arrows that represent the components that make up the IQA will be explained point by point.

pH and Dissolved Solids: There is no correlation between these two parameters, as they are affected by different factors. pH is a measure of the acidity of the solution, while dissolved solids are affected by factors such as geology, vegetation, climate and human activities.

Turbidity and Phosphorus: There is a correlation between turbidity and phosphorus as shown at all the Collection Points, as turbidity can increase the concentration of phosphorus in the water. This can occur due to the blocking of sunlight, hindering the photosynthesis of aquatic plants, and the difficulty of water treatment filters in removing phosphorus. 25.

Water and Air Temperature and Dissolved Oxygen: The temperature of water and air are correlated, affecting the solubility of oxygen in water. The warmer the water, the lower the solubility of oxygen. Therefore, as water temperature increases, dissolved oxygen decreases.

Nitrate (NO3-) and Biochemical Oxygen Demand (BOD): Nitrate and BOD are correlated due to the influence of organic matter in the water. BOD is a measure of the oxygen consumed by the decomposition of organic matter, while nitrate can be produced as a result of this process.

Dissolved Oxygen and Nitrate (NO3-): There is no correlation between these two parameters, as they are affected by different factors. Dissolved oxygen is influenced by water temperature, salinity, turbidity and the presence of pollutants, while nitrate is affected by water temperature, the presence of organic matter and the presence of nitrifying bacteria.

Contribution to the Water Quality Index (IQA): Some parameters, such as turbidity, phosphorus, BOD and water and air temperature, have a greater contribution to the WQI through the weights of the calculations, thus significantly influencing the quality of water for human consumption and aquatic life.

PS418 e PS419:

Both have a correlation between water temperature, air temperature, turbidity and total phosphorus due to the influence of similar factors, such as heat exchange and the presence of organic matter in the water and the industrialization of the site 26.

PS415 e PS430:

Both PS415 and PS430 point out that dissolved oxygen (DO) is not correlated with other parameters, as it is affected by factors other than those affecting turbidity, total phosphorus, water and air temperature, as well as nitrate (NO3-), which also does not correlate with DO.

PS419 e PS425:

Both PS419 and PS425 have a correlation between turbidity and total phosphorus due to the presence of organic matter in the water, cities with more agricultural activities.

PS421 e PS423:

Both PS421 and PS423 highlight the correlation between turbidity, total phosphorus and biochemical oxygen demand (BOD), as well as the importance of these parameters for the Water Quality Index (IQA). They also mention the correlation between water temperature, air temperature and these parameters, due to their influence on water quality.

5 FINAL CONSIDERATIONS

The temporal analysis of the dry and rainy seasons of the Paraíba do Sul River, together with the assessment of the Water Quality Index (WQI) at the nine points studied, offers deep insights into the dynamics and challenges faced by the river basin. The study highlighted the significant influence of extreme weather events, such as the 2014/2015 drought, which left deep marks on water quality, directly impacting the Paraíba do Sul River. The adverse effects included the concentration of pollutants, siltation of the river, a reduction in oxygen and an increase in water temperature, all reflected in sharp drops in theWQI.

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