Lake Water Monitoring Data Assessment by Multivariate Statistics ()
1. Introduction
The careful monitoring of natural water systems like river streams, lakes, wells, and underground sources is a very responsible task. Usually, a set of chemical and physicochemical parameters reflecting the surface or underground water quality are carefully analysed and the results obtained are compared to certain threshold values in order to decide if the water quality meets the quality desired. The choice of quality parameters is normally standardized and described in various instructions and directives for individual countries or unions like EU [1-4]. Recently, a very specific attention requires a different type of water quality parameter called “toxicity” (“ecotoxicity”) [5-7]. It is also important to note that lake waters are important element of the aquatic ecosystems. They constitute ecological niches (especially in combination with the lake bottom sediments) supporting not only fish but also benthic organisms, i.e. animals and plants living on the bottom of bodies of water, and are a source of nutrients for aquatic organisms such as small invertebrates and protozoans. An assessment of the effect of pollution on life in lake water bodies requires also monitoring of bottom sediment samples both for chemical, physicochemical, and toxicity parameters. They are very useful material for various environmental studies because they act as sorption column and provide a clear image of all events taking place in the overlying water layer.
Very often, however, the monitoring data are considered in a “univariate” way—each parameter separately. In the reality the state of an ecosystem is depending simultaneously on many factors and parameters. Therefore, these systems are multivariate in nature. That is why the classification, modeling and interpretation of the monitoring data sets have to be performed by the use of the chemometrics and environmetrics [8-14], where the references given are only a tiny part of many environmetric studies. The specific point in the studies of lake waters is that there is lack of intelligent data analysis of the monitoring sets comprising of different water quality parameters simultaneously interpreted.
The aim of the present chapter is to demonstrate the role of environmetric classification, modeling, and interpretation of monitoring data from the lake systems of Pirin Mountain, Bulgaria.
2. Chemometric Methods
The modern chemometrics is a branch of chemistry (very often related to analytical chemistry) which deals with the application of mathematical and statistical methods in order to evaluate, classify, model, and interpret chemical and analytical data, to optimize and model chemical and analytical processes and experiments and to extract a maximum of chemical and analytical information from experimental data. When the methods of chemometrics are applied to data sets obtained by monitoring of various environmental compartments (surface water, atmosphere, soil, sediments, biota etc) the term environmetrics is used to stress the information ability of the methods to gain specific information from samples of the total environment.
Very important methods of multivariate statistics employed in environmetrics are cluster analysis, principal components analysis and self-organizing maps of Kohonen which will be briefly presented and applied.
Cluster analysis (CA) is an exploratory data analysis tool for solving classification problems [15]. CA enables objects stepwise aggregation according to the similarity of their features. As a result hierarchically or non-hierarchically ordered clusters are formed. Primary standardization of features becomes necessary to avoid effects of dimensionality on the classification results. There are a variety of different measures of inter-cases distances and inter-cluster similarities and distances to use as criteria when merging nearest clusters into broader groups or when considering the relation of an object to a cluster. The most applied is the Euclidean distance (after the standardization of the raw data).
In case of CA one task is related with determination of similarity between measured objects as well as similarities between the features describing the objects. As in case of distance measure various algorithms (linkage techniques) are available to decide on the number of clusters. Very popular linkage algorithm in hierarchical clustering problems is Ward’s method [15].
In hierarchical agglomerative clustering the graphical output of the analysis is usually a dendrogram—a tree-like graphics, which indicates the linkage between the clustered objects with respect to their similarity (distance measure). For practical reasons the Sneath index of cluster significance is widely used. It represents this significance on two levels of distance measure D/Dmax relation: 1/3Dmax and 2/3Dmax. Only clusters remaining compact after breaking the linkage at these two distances are considered significant and are object of interpretation.
Principal Component Analysis (PCA) seems to be the most widespread multivariate chemometric technique and is a typical display method (also known as eigenvector analysis, eigenvector decomposition or Karhunen-Loéve expansion). It enables revealing the “hidden” structure of the data set and helps to explain the influence of latent factors on the data distribution [16,17]. PCA transforms the original data matrix into a product of two matrices, one of which contains the information about the objects and the other about the features. The matrix characterizing objects contains the scores (understood as projection) of objects on principal components (PCs). The other one, characterizing features is a square matrix and contains the set of eigenvectors (understood as weights, in PCA terminology called “loadings”) of the original features in each PC.
Some important features of PCA could be summarized as follows. The principal components axes (the axes of the hidden variables) are orthogonal to each other. Most of the variance of the data is contained in the first principal component. In the second component there is more information than in the third one etc. For interpretation of the projected data both the score and the loading vectors are plotted. In the score plots, the grouping of objects can be recognized. A loading plot reveals the importance of the individual variables with respect to the principal component model.
A very important task in PCA is the estimating the number of principal components necessary for a particular PC model. Several criteria exist in determining the number of components in the PCA model: percentage of explained variance, eigenvalue—one criterion, Scree— test, cross validation [16,17].
Interpretation of the results of PCA is usually carried out by visualization of the component scores and loadings.
Self Organizing Map (SOM) algorithm has been proposed by Kohonen in 1980 [18]. It is a neural-network based model which shares, with the conventional ordination methods, the basic idea of displaying a high-dimensional signal manifold onto a much lower dimensional network in an orderly fashion (usually 2D space). The most common shape of the Kohonen map is a rectangular grid with the number of hexagonal nodes.
When a plenty of features is considered it is difficult to compare all maps for all features and thus becomes necessary to find similarity between them, and simultaneously, in the cases’ space and classify them into clusters. Input features’ planes (e.g. variables) could be visualized on a summary SOM map (called also as unified distance matrix or U-matrix) to show the contribution of each feature in the self-organization of the map. U-matrix visualizes distances between neighboring map units, and helps to identify cluster structure of the map. The U-matrix joined with features’ planes can be effectively applied for assessment of inter-features and inter-cases relations. Finally, the best classification with the lowest Davies-Bouldwin index should be chosen (it is a function of the ratio of the sum of within-cluster scatter and between-cluster separation).
Main advantages of SOM algorithm application are: Semi-quantitative information about the distribution of a given feature in the space of the cases; visualization of similarity between positive as well as negative correlated features; visualization and classification of “outliers” i.e. those features or cases which do not belong to a wellorganized, homogeneous populations; SOM is noise tolerant (this property is highly desirable when site-measured data are used).
3. Results and Discussion
The application of the multivariate statistical methods described above as one of the most important tool in assessment of lake water quality can be illustrated by specific case studies. Thus, the classification, data projection, modeling and interpretation of lake water monitoring data sets becomes understandable and turns to be a pattern to follow in lake pollution research.
The data was collected during expeditions in 2001 and 2002 for big number of lakes located in Pirin Mountain, which is one of the highest mountains in Bulgaria. The sampling sites and their heights are indicated in Table 1. The sampling period was between May and October. The sampling itself was performed on the lake surface approximately 2 m from the costal line. The water samples (about 100 mL) were placed in polyethylene flasks. The chemical analysis was carried out within 4 days after sampling at Faculty of Chemistry, University of Sofia. Altogether eleven chemical parameters (major cations and anions like sodium, potassium, calcium, magnesium, chloride, sulfate, nitrate, hydrogen carbonate) were analysed by electrothermal atomic absorption spectrometry and ion chromatography as well as pH (potentiometrically), conductivity (conductometrically), water temperature, and dissolved matter (by summing up of chemical concentrations). Due to the rapid changes of some parameters like pH, temperature, conductivity their determination was done directly at the sampling site by the use of portable instruments. The number of lakes involved in this study was over forty. It is worth to mention that water samples were taken not only from the lakes but also from rivers and springs in the vicinity of the lakes in order to obtain a more realistic estimation of the water quality and of the various natural and anthropogenic impacts.
The data sets from the lakes from the two mountains were classified, modeled and interpreted by the use of cluster analysis, principal components analysis and self-organizing maps of Kohonen. The goal of the environmetric interpretation was to identify groups of similarity between the lakes, to find relationship between the chemical parameters for the lake water quality, to detect hidden factors responsible for the data structure as well as to reveal discriminating chemical parameters, which
Table 1. Short description of the lakes in Pirin subject to assessment.
determine the separation of the lakes in different groups of similarity (or dissimilarity).
The initial data set for the samples from Pirin lakes includes 74 objects (sampling locations and sampling periods). No normal distribution of data (for each of the variables) is found, which means that the input data were subject of standardization before applying multivariate statistics (Table 2).
The first step in the classification of the monitoring data was clustering of the sampling sites (Ward’s method of linkage, squared Euclidean distance as similarity measure, z-transformation of data and check of the cluster significance by the Sneath index). The hierarchical dendrogram is shown in Figure 1.
It is readily seen that a good homogeneity of the water quality for all lakes is found. There is a tiny group of outliers (for the more strict Sneath’s criterion of 2/3Dmax) mostly from the region of Lake Sinanitsa and Sinanitsa River characterized by quite specific lithoral composition.
In Figure 2 the hierarchical dendrogram for linkage of water quality parameters is presented. Four clusters are formed as follows: (nitrate, chloride, sulfate), (potassium, sodium), (calcium, magnesium, conductivity), (hydrogen carbonate, dissolved matter) and pH as an outlier. It could be concluded from the cluster analysis results that factors like water hardness, water acidity, salt content and turbidity are responsible for the relative separation of the sampling events. However, this information is not convincing enough to make final decisions on the lake water quality.
Table 2. Basic statistics for all Pirin lakes.
Figure 1. Hierarchical dendrogram for sampling locations.
In order to gain additional information from the data set PCA was performed on the normalized input data. Firstly, the factor scores plot will be considered (Figure 3).
The homogeneity of the data (very close levels of most of the chemical parameters characterizing the lake water quality) is indicated again by the big cloud of similar objects. The outliers marked are from the specific dolomite circus where the lakes Sinanitsa, Suhodolsko and Gorno Kremensko are located. Again, the separation is due to a geographical (natural) rather than anthropogenic impact.
Figure 4 (PC1 vs. PC2) for the factor loadings (normalized data, Varimax rotation mode) indicates the grouping of the chemical variables with respect to the identified latent factors. It is seen that high correlation along PC1 axis is found for chloride, sulfate and hydrogen carbonate and along PC2 axis—for calcium, magnesium, conductivity and dissolved matter. These results slightly contradict those found by the classification with cluster analysis and that is why a more careful inspection of the PCA results is needed.