This document analyzes water quality data from three sampling stations along a 25 km section of the Pisuerga River in Spain affected by seasonal and pollution influences. Exploratory data analysis methods, including principal component analysis, ANOVA, and cluster analysis, were used to differentiate spatial and temporal sources of variation and assign them to polluting sources. PCA identified reduced factors related to mineral content, pollution, and temperature. ANOVA showed mineral content was seasonal/climate dependent, while pollution by organic matter and nutrients originated from anthropogenic sources like wastewater. Cluster analysis achieved meaningful water sample classification based on seasonal and spatial criteria.

1. ASSESSMENT OF SEASONAL AND POLLUTING EFFECTS
ON THE QUALITY OF RIVER WATER BY EXPLORATORY
DATA ANALYSIS
MARISOL VEGA*, RAFAEL PARDO*
M
, ENRIQUE BARRADO and LUIS DEBA
 N
Departamento de QuõÂmica AnalõÂtica, Facultad de Ciencias, Universidad de Valladolid, 47005
Valladolid, Spain
(First received December 1996; accepted March 1998)
AbstractÐ22 Physico-chemical variables have been analyzed in water samples collected every three
months for two and a half years from three sampling stations located along a section of 25 km of a
river a€ected by man-made and seasonal in¯uences. Exploratory analysis of experimental data have
been carried out by box plots, ANOVA, display methods (principal component analysis) and unsuper-
vised pattern recognition (cluster analysis) in an attempt to discriminate sources of variation of water
quality. PCA has allowed the identi®cation of a reduced number of ``latent'' factors with a hydrochemi-
cal meaning: mineral contents, man-made pollution and water temperature. Spatial (pollution from
anthropogenic origin) and temporal (seasonal and climatic) sources of variation a€ecting quality and
hydrochemistry of river water have been di€erentiated and assigned to polluting sources. An ANOVA
of the rotated principal components has demonstrated that (i) mineral contents are seasonal and climate
dependent, thus pointing to a natural origin for this polluting form and (ii) pollution by organic matter
and nutrients originates from anthropogenic sources, mainly as municipal wastewater. The application
of PCA and cluster analysis has achieved a meaningful classi®cation of river water samples based on
seasonal and spatial criteria. # 1998 Elsevier Science Ltd. All rights reserved
Key words: water quality, surface water, hydrochemistry, exploratory data analysis, ANOVA, box plot,
principal component analysis, pattern recognition, cluster analysis.
INTRODUCTION
River basins generally constitute areas with a high
population density owing to favourable living con-
ditions such as the availability of fertile lands,
water for irrigation, industrial or drinking purposes,
and ecient means of transportation. Rivers play a
major role in assimilating or carrying o€ industrial
and municipal wastewater, manure discharges and
runo€ from agricultural ®elds, roadways and
streets, which are responsible for river pollution
(Stroomberg et al., 1995; Ward and Elliot, 1995).
Rivers constitute too the main water resources in
inland areas for drinking, irrigation and industrial
purposes; thus, it is a prerequisite for e€ective and
ecient water management to have reliable infor-
mation of water quality.
The discharge of industrial and municipal waste-
water and manure can be considered a constant
polluting source, but not so the surface runo€
which is seasonal and highly a€ected by climate.
Flow in rivers is a function of many factors includ-
ing precipitation, surface runo€, inter¯ow, ground-
water ¯ow and pumped in¯ow and out¯ow.
Seasonal variations of these factors have a strong
e€ect on ¯ow rates and hence on the concentration
of pollutants in the river water.
Long-term surveys and monitoring programs of
water quality are an adequate approach to a better
knowledge of river hydrochemistry and pollution,
but they produce large sets of data which are often
dicult to interpret (Dixon and Chiswell, 1996).
Most discussions on trend detection focus on ana-
lysing a single variable, while routine monitoring
programs ordinarily measure several variables. The
problem of data reduction and interpretation of
multiconstituent chemical and physical measure-
ments can be approached through the application
of multivariate statistical methods and exploratory
data analysis (Massart et al., 1988; Wenning and
Erickson, 1994). The usefulness of multivariate stat-
istical tools in the treatment of analytical and en-
vironmental data is re¯ected by the increasing
number of papers cited in Analytical Chemistry
Reviews (Brown et al., 1994, 1996).
Cluster analysis and principal component analysis
(PCA) have been widely used as they are unbiased
methods which can indicate associations between
samples and/or variables (Wenning and Erickson,
1994). These associations, based on similar magni-
tudes or variations in chemical and physical constitu-
ents, may indicate the presence of seasonal or man-
made in¯uences. Hierarchical agglomerative cluster
Wat. Res. Vol. 32, No. 12, pp. 3581±3592, 1998
# 1998 Elsevier Science Ltd. All rights reserved
Printed in Great Britain
0043-1354/98 $19.00 + 0.00
PII: S0043-1354(98)00138-9
*Author to whom all correspondence should be addressed.
[E-mail: solvega@wamba.cpd.uva.es].
3581

2. analysis indicates groupings of samples by linking
inter-sample similarities and illustrates the overall
similarity of variables in the data set (Massart and
Kaufman, 1983). PCA is used to reduce the dimen-
sionality of the data set by explaining the correlation
among a large set of variables in terms of a small
number of underlying factors or principal com-
ponents without losing much information (Jackson,
1991; Meglen, 1992), and allows to assess associ-
ations between variables, since they indicate partici-
pation of individual chemicals in several in¯uence
factors. Exploratory data analysis has been used to
evaluate the water quality of rivers, and seasonal,
spatial and anthropogenic in¯uences have been evi-
denced (Brown et al., 1980; Bartels et al., 1985;
Grimalt et al., 1990; Librando, 1991; Andrade et al.,
1992; Aruga et al., 1993; Elosegui and Pozo, 1994;
Pardo et al., 1994; Battegazzore and Renoldi, 1995;
Voutsa et al., 1995).
In this work, PCA, analysis of variance
(ANOVA) and agglomerative hierarchical cluster
analysis have been used to investigate the water
quality of the Pisuerga river (Duero basin, Spain),
to assess the in¯uence that pollution and seasonality
have on the quality of river water, and to discrimi-
nate the individual e€ects of climate and human ac-
tivities on the river hydrochemistry.
METHODS
Sampling stations
The Pisuerga river belongs to the Duero river basin,
which is located in the Castilla y Leo
 n region (Centre-
North of Spain). The inland geographic situation of the
basin, surrounded by mountains, conditions an extremely
continental climate. Precipitations in the area are scarce,
ranging from 313 to 571 mm yrÿ1
, with a mean of
442 mm yrÿ1
. Precipitations are maximum in November
(49.8 mm) and minimum in August (13.2 mm). The annual
mean temperature is 128C, and extreme values of ÿ48C
and 328C are registered in January and July, respectively.
The river ¯ows in direction North±South from the
Northern mountains through a high tableland to run into
the Duero river, and is the main drainage stream in that
direction; in spring, snow melting in the Northern moun-
tains causes a marked increase in river ¯ow. Along its
course, the river pass through limestone, marl, gypsum
and sandstone soils which are the main contributors to the
high levels of minerals in the river water. An important
agricultural activity devoted to irrigated crops takes place
in riverine areas where the use of nitrogenous fertilisers is
a common practice. 12 Km upstream its mouth, the river
crosses the town of Valladolid, major industrial centre of
the region with a population of ca. 400 000. Municipal
wastewater is directly discharged into the river (estimated
volume is ca. 57 millions m3
yrÿ1
) as the wastewater and
sewage treatment plant is still being built. Moreover,
although big industries settled in the area purify their
wastewater, small industries are suspected to discharge
residues into the river. The combination of both a high
population density in the area and an extreme continental
climate causes river hydrology and hence river pollution to
be strongly in¯uenced by seasonality.
The investigated river section is located at 41823'24N
and 04827'00W, and is in average 690 m over the sea level.
It covers a length of 25 km from Cabezo
 n de Pisuerga,
small village located 13 km upstream Valladolid, and the
village of Simancas, in the mouth of the Pisuerga river,
12 km downstream Valladolid. Major industrial activity in
the area is concentrated in the North of the city, upstream
the bridge called Puente Mayor, and municipal discharges
into the river are mainly produced from Puente Mayor to
Simancas.
Selected sampling stations were located in Cabezo
 n de
Pisuerga, Puente Mayor and Simancas, in an attempt to
isolate and identify the polluting sources: in Cabezo
 n de
Pisuerga the river has not received industrial and munici-
pal wastewater yet, and the water quality in this station
can be considered to re¯ect pollution from overland ¯ow
and from agricultural and manure discharges; Puente
Mayor re¯ects the situation in which industrial wastewater
has been discharged, but no municipal residues; in
Simancas the river has received all the polluting dis-
charges.
Selected stations were sampled every three months for
two and a half years. A total of 10 samples were collected
from each station on the following dates: 06/04/90, 03/07/
90, 09/10/90, 09/01/91, 03/04/91, 02/07/91, 10/10/91, 09/
01/92, 10/04/92 and 06/07/92. Samples are identi®ed
throughout by means of a four-character code XYZZ,
where X means the sampling station (C, Cabezo
 n; P,
Puente Mayor and S, Simancas), Y is the month of
sampling (A, April; J, July; O, October and E, January)
and ZZ means the year (90, 91 or 92).
Analytical procedures
Sample containers were 1 l polyethylene bottles provided
with hermetic-locking caps. Bottles and caps were cleaned
by soaking into 50% HCl for three days, rinsed with
desionized water and soaked into 2 M HNO3 for another
three days, ®nally rinsed with desionized water, drained,
wrapped in polyethylene bags and stored until required.
Samples were collected by means of a Go-Flo device
from the middle of the stream at a depth of 15 cm, from
stone bridges existing in each of the sampling stations.
Prior to sample collection, sampling device and containers
were rinsed twice with the water to be sampled.
Temperature, pH, conductivity and dissolved oxygen
measurements were performed in situ. Duplicate samples
were taken out from each sampling station and immedi-
ately ®ltered under nitrogen pressure through cellulose
nitrate ®lters (pore size 0.45 mm) into acid-washed poly-
ethylene bottles. One duplicate was acidi®ed to pH 2 by
addition of 100 ml of 10 M HCl to each 100 ml sample and
used for determination of metals, hardness, nitrogen (as
ammonia, nitrite and nitrate) and phosphorous (as phos-
phate). The second duplicate was kept at its natural pH
and used for determination of the remaining anions (bicar-
bonate, chloride and sulphate), conductivity and organic
matter (as chemical oxygen demand, COD, and biochemi-
cal oxygen demand, BOD). Samples were immediately
transported to the laboratory and stored at 48C until their
analysis, which was accomplished within one week.
22 Physico-chemical parameters have been determined
by following standard and recommended methods of
analysis (APHA-AWWA-WPCF, 1985; AOAC, 1990).
Table 1 displays the variables measured and their units,
the analytical techniques employed, and the abbreviations
used henceforth. A total of 660 analysis were carried out
(22 variables in 30 samples). Two replications of each
analysis were performed and mean values were used for
calculations.
Data treatment
Exploratory data analysis was performed by linear dis-
play methods (principal component analysis) and by unsu-
pervised pattern recognition techniques (hierarchical
cluster analysis) on experimental data normalized to zero
Marisol Vega et al.
3582

3. mean and unit variance in order to avoid misclassi®cations
arising from the di€erent order of magnitude of both nu-
merical value and variance, of the parameters analysed. As
the methods of classi®cation used here are non-parametric,
they make no assumptions about the underlying statistical
distribution of the data and therefore no evaluation of
normal (Gaussian) distribution of the data is necessary
(Sharaf et al., 1986).
Principal component analysis was applied to normalized
data to assess associations between variables, since this
method evidences participation of individual chemicals in
several in¯uence factors, which commonly occurs in
hydrochemistry. Diagonalization of the correlation matrix
transforms the original p correlated variables into p uncor-
related (orthogonal) variables called principal components
(PCs), which are weighed linear combinations of the orig-
inal variables (Mellinger, 1987; Meglen, 1992; Wenning
and Erickson, 1994). The characteristic roots (eigenvalues)
of the PCs are a measure of their associated variances,
and the sum of eigenvalues coincides with the total num-
ber of variables. Correlation of PCs and original variables
is given by loadings, and individual transformed obser-
vations are called scores.
Cluster analysis is an unsupervised pattern recognition
technique that uncovers intrinsic structure or underlying
behaviour of a data set without making a priori assump-
tions about the data, in order to classify the objects of the
system into categories or clusters based on their nearness
or similarity. In hierarchical cluster analysis the distance
between samples is used as a measure of similarity.
Hierarchical agglomerative cluster analysis was carried out
on the normalised data by means of the complete linkage
(furthest neighbour), average linkage (between and within
groups) and Ward's methods, using squared Euclidean dis-
tances as a measure of similarity (Massart and Kaufman,
1983; Willet, 1987).
RESULTS AND DISCUSSION
Table 2 summarises brie¯y the mean value and
standard deviation of the 22 measured variables in
the river water samples from the three stations. It
must be noticed the high dispersion of most vari-
ables (high standard deviations), which indicates
variability in chemical composition between
samples, thus pointing to the presence of temporal
variations caused likely by polluting sources and/or
climatic factors.
Recommended guide levels of these variables and
maximum levels allowed by the European Directive
80/778/EEC concerning the quality of water intended
for human consumption are included in Table 2. It
must be emphasised that average concentrations of
some variables such as chloride, COD, iron, manga-
nese, sodium, ammonia, nitrite, phosphate and sul-
phate are higher than those recommended by the
European legislation, therefore this water resource is
not adequate for human consumption or industrial
purposes and needs to be puri®ed.
High levels of phosphate may originate from mu-
nicipal wastewater discharges since it is an important
component of detergents. The presence of nitrate in
the river section sampled is suspected to originate
from overland runo€ from riverine agricultural ®elds
where irrigated horticultural crops are grown and the
use of inorganic fertilisers (usually as ammonium
nitrate) is rather frequent. This practice could also
explain the high levels of ammonia, but this pollutant
may also originate from decomposition of nitrogen-
containing organic compounds such as proteins and
urea occurring in municipal wastewater discharges.
In the presence of high levels of organic matter,
nitrate can be reduced in some extent to nitrite, what
could explain the high concentration of this pollutant
in some samples. The high sulphate contents found
in waters of the Pisuerga river are probably a conse-
quence of the morphology of soils irrigated by the
river, which are formed mainly by limestone, marl
and gypsum.
Exploratory data analysis using box plots
Normal probability plots of the variables in con-
junction with the Anderson±Darling normality test
Table 1. Physico-chemical parameters determined and analytical techniques used
Variable Abbreviation Analytical technique Units
Biochemical oxygen demand BOD potentiometry/O2 probe mg O2 lÿ1
Calcium Ca ¯ame AAS mg lÿ1
Chloride Cl ion chromatography mg lÿ1
Chemical oxygen demand COD redox titrometry (KMnO4) mg O2 lÿ1
Conductivity COND conductometry mmho cmÿ1
Dissolved solids DS drying at 1808C/weighing mg lÿ1
Iron Fe ¯ame AAS mg lÿ1
Flow rate FLOW (*) m3
sÿ1
Hardness HARD EDTA titrometry mg CaCO3 lÿ1
Bicarbonate HCO3 acid±base titrometry mg lÿ1
Potassium K ¯ame AES mg lÿ1
Magnesium Mg ¯ame AAS mg lÿ1
Manganese Mn ¯ame AAS mg lÿ1
Sodium Na ¯ame AES mg lÿ1
Ammonium NH4 spectrophotometry mg lÿ1
Nitrite NO2 spectrophotometry mg lÿ1
Nitrate NO3 spectrophotometry mg lÿ1
Dissolved oxygen OXYG potentiometry/O2 probe mg lÿ1
pH pH potentiometry/pH probe pH units
Phosphate PO4 ion chromatography mg lÿ1
Sulphate SO4 ion chromatography mg lÿ1
Temperature TEMP temperature probe 8C
(*) Data supplied by Confederacio
 n Hidrogra
 ®ca del Duero.
Water quality analysis using exploratory data 3583

4. demonstrated that most variables were not normally
distributed. However, these normality tests applied
to individual sampling stations resulted in normal
distributions for most variables, thus pointing to
the existence of di€erences in water composition
among stations.
Box plots (also called box-and-whisker plots) of
individual variables in the three sampling stations
were examined. Figure 1 shows an example of
box plots for some meaningful variables related to
the quality of river water, such as conductivity
(mineralization), COD, dissolved oxygen or am-
monium. The line across the box represents the
median, whereas the bottom and top of the box
show the locations of the ®rst and third quartiles
(Q1 and Q3). The whiskers are the lines that
extend from the bottom and top of the box to
the lowest and highest observations inside the
region de®ned by Q1ÿ1.5(Q3ÿQ1) and
Q3+1.5(Q3ÿQ1). Individual points with values
outside these limits (outliers) are plotted with
asterisks.
Table 2. Statistical descriptives for the 30 samples analysed
Cabezo
 n Puente Mayor Simancas
Variable Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. Min. Max. Guide level* Max.*
BOD 2.8 0.8 3.2 0.7 3.7 1.2 1.5 6.5
Ca 77.0 9.6 77.1 7.4 76.5 8.9 58.8 91.2 100
Cl 23.3 7.7 24.3 8.0 28.3 9.9 12.2 46.1 25 200
COD 3.1 1.2 3.6 0.8 5.0 2.0 0.7 10 2 5
COND 589 123 599 98 629 115 402 773 400
DS 398 81 410 67 427 69 273 524 1500
Fe 0.10 0.05 0.12 0.04 0.11 0.05 0.01 0.19 0.05 0.2
FLOW 45.0 42.6 37.0 20.9 37.5 21.2 14.8 129.2
HARD 250.1 43.6 253.1 32.6 254.4 35.1 179.1 302.9
HCO3 150.4 17.8 142.8 20.9 156.1 23.4 96.1 176.8
K 4.8 1.9 5.2 1.8 6.2 2.2 2.8 10.4 10 12
Mg 14.0 5.3 14.8 4.8 15.4 4.5 6.2 23.8 30 50
Mn 0.03 0.02 0.03 0.02 0.04 0.02 0.01 0.08 0.02 0.05
Na 19.4 9.5 20.2 7.7 25.6 10.0 7.1 40.5 20 150
NH4 0.63 0.62 0.51 0.23 1.66 0.92 0.05 3.61 0.05 0.5
NO2 0.32 0.32 0.13 0.09 0.35 0.30 0.03 1.08 Absence 0.1
NO3 11.2 7.3 11.9 7.0 10.4 8.4 0.3 29.9 25 50
OXYG 8.1 1.8 8.4 1.8 4.9 3.3 0.7 11.4
pH 8.0 0.2 8.1 0.5 7.6 0.3 7.2 8.8 6.5±8.5 9.5
PO4 0.84 0.32 0.86 0.30 1.61 0.63 0.35 2.50 0.3 3.3
SO4 105.4 34.9 108.9 28.7 112.7 28.1 50 150 25 250
TEMP 13.6 5.9 14.5 7.7 14.3 7.3 2.2 24.9 12 25
(*) Recommended guide levels and maximum concentrations allowed by the European Directive 80/778/EEC concerning the quality of
water intended for human consumption.
Fig. 1. Box plots for conductivity, COD, dissolved oxygen and ammonium in Cabezo
 n (C), Puente
Mayor (P) and Simancas (S).
Marisol Vega et al.
3584

5. Box plots provide a visual impression of the lo-
cation and shape of the underlying distributions.
For example, box plots with long whiskers at the
top of the box (such as that for ammonium at
Simancas) indicate the underlying distribution is
skewed toward high concentration. Box plots with
large spread indicate seasonal variations of the
water composition (see conductivity box plot). By
inspecting these plots it was also possible to per-
ceive di€erences among the three stations. For
example, dissolved oxygen in Simancas is lower and
has a greater spread compared with that in
Cabezo
 n and Puente Mayor. At the same time,
COD and ammonium are higher in Simancas, thus
pointing to a deterioration of the water quality
downstream likely caused by the discharge of mu-
nicipal wastewater.
Analysis of variance (ANOVA) examines the
di€erent e€ects (usually called sources of variation)
operating simultaneously on a response to decide
which e€ects are statistically signi®cant and to esti-
mate their contribution to the variability of the re-
sponse (Sche€e, 1959; Ross, 1988). Two-way
ANOVA of independent variables showed the exist-
ence of seasonal and/or spatial di€erences. For
example, seasonal signi®cant di€erences were found
for conductivity, temperature or ¯ow, whereas for
ammonium, phosphate or pH the di€erences were
mainly due to the sampling station. For COD and
BOD both sources of variation were signi®cant.
Box plots and ANOVA showed similar trends for
each variable; however, these are univariate tech-
niques inadequate for the investigation of our mul-
tivariate data table as the variables are correlated.
Principal component analysis
The covariance matrix of the 22 analysed vari-
ables was calculated from data normalised as
described in Section 2.3 and, therefore, coincides
with the correlation matrix (Table 3). Because the
three sampling stations were combined to calculate
the correlation matrix, the correlation coecients
should be interpreted with caution as they are
a€ected simultaneously by spatial and temporal
variations. Nevertheless, some clear hydrochemical
relationships can be readily inferred: High and posi-
tive correlation (underlined values) can be observed
between bicarbonate, sulphate, chloride, calcium,
magnesium, potassium, sodium, dissolved solids,
conductivity and hardness (r = 0.572 to 0.977),
which are responsible for water mineralization.
Flow rate is negatively correlated to most variables,
since an increase in ¯ow rate causes dilution of con-
taminants. This anti-correlation is highly signi®cant
for ``mineral'' components (conductivity, hardness,
dissolved solids, magnesium and sulphate). BOD
and COD are strongly correlated (r = 0.893) and
also with ammonia, phosphate (closely related to
contamination for organic mater) and potassium.
As expected, dissolved oxygen is negatively corre-
Table
3.
Correlation
matrix
of
the
22
physico-chemical
parameters
determined
BOD
Ca
Cl
COD
COND
DS
Fe
FLOW
HARD
HCO
3
K
Mg
Mn
Na
NH
4
NO
2
NO
3
OXYG
pH
PO
4
SO
4
TEMP
BOD
1.000
Ca
ÿ0.117
1.000
Cl
0.413
0.758
1.000
COD
0.893
ÿ0.036
0.516
1.000
COND
0.260
0.887
0.916
0.321
1.000
DS
0.316
0.825
0.881
0.334
0.974
1.000
Fe
0.177
ÿ0.270
ÿ0.137
0.065
ÿ0.154
ÿ0.102
1.000
FLOW
ÿ0.164
ÿ0.497
ÿ0.394
ÿ0.108
ÿ0.592
ÿ0.571
ÿ0.048
1.000
HARD
0.229
0.898
0.860
0.240
0.977
0.951
ÿ0.151
ÿ0.659
1.000
HCO
3
0.270
0.648
0.712
0.347
0.774
0.762
ÿ0.251
ÿ0.484
0.770
1.000
K
0.679
0.442
0.748
0.649
0.701
0.713
ÿ0.100
ÿ0.356
0.656
0.644
1.000
Mg
0.552
0.579
0.772
0.484
0.849
0.868
0.016
ÿ0.683
0.879
0.725
0.736
1.000
Mn
0.492
0.109
0.434
0.437
0.333
0.311
0.464
ÿ0.431
0.346
0.285
0.423
0.521
1.000
Na
0.238
0.809
0.914
0.350
0.929
0.902
ÿ0.118
ÿ0.419
0.841
0.705
0.697
0.683
0.280
1.000
NH
4
0.709
0.110
0.483
0.773
0.378
0.384
0.094
ÿ0.170
0.291
0.485
0.663
0.419
0.359
0.468
1.000
NO
2
0.324
0.062
0.190
0.258
0.195
0.233
ÿ0.110
ÿ0.198
0.222
0.381
0.381
0.341
0.329
0.118
0.327
1.000
NO
3
ÿ0.010
ÿ0.021
ÿ0.172
ÿ0.114
ÿ0.018
0.072
0.208
0.187
ÿ0.019
ÿ0.211
ÿ0.047
ÿ0.014
ÿ0.314
ÿ0.074
0.021
ÿ0.109
1.000
OXYG
ÿ0.531
ÿ0.009
ÿ0.375
ÿ0.634
ÿ0.282
ÿ0.246
ÿ0.016
0.389
ÿ0.247
ÿ0.435
ÿ0.476
ÿ0.444
ÿ0.613
ÿ0.286
ÿ0.559
ÿ0.555
0.453
1.000
pH
ÿ0.541
0.402
ÿ0.031
ÿ0.544
0.112
0.030
ÿ0.337
ÿ0.132
0.159
ÿ0.048
ÿ0.112
ÿ0.144
ÿ0.292
0.076
ÿ0.477
ÿ0.365
ÿ0.173
0.442
1.000
PO
4
0.434
0.209
0.506
0.601
0.409
0.378
0.026
ÿ0.395
0.342
0.532
0.503
0.406
0.590
0.451
0.613
0.453
ÿ0.376
ÿ0.847
ÿ0.374
1.000
SO
4
0.130
0.902
0.873
0.209
0.971
0.944
ÿ0.097
ÿ0.594
0.949
0.682
0.572
0.781
0.297
0.900
0.224
0.112
0.014
ÿ0.182
0.160
0.338
1.000
TEMP
0.290
ÿ0.080
0.122
0.278
0.092
0.041
0.022
ÿ0.481
0.150
0.142
0.198
0.359
0.568
ÿ0.025
ÿ0.031
0.359
ÿ0.501
ÿ0.712
ÿ0.070
0.463
0.074
1.000
Water quality analysis using exploratory data 3585

6. lated with temperature because the solubility of
oxygen in water decreases with increasing tempera-
ture; BOD, COD and nitrogen and phosphorous
compounds are also anti-correlated with dissolved
oxygen as organic matter is partially oxidized by
oxygen, whilst nutrients are responsible for eutro-
phication of freshwater, thus causing a further
increase in organic matter concentration and,
hence, in oxygen demand. Iron, nitrate and pH
showed no signi®cant correlation with any other
variables.
By applying the Bartlett's sphericity test, a value
of 1006.6 for the Bartlett chi-square statistic was
found (critical value is 234 for 231 degrees of free-
dom at the 95% signi®cance level), con®rming that
variables are not orthogonal but correlated, there-
fore allowing to explain the data variability with a
lesser number of variables (called principal com-
ponents).
Principal components were extracted by the R-
mode principal component method which math-
ematically transforms the original data with no
assumptions about the form of the covariance
matrix. This analysis allows a clustering of variables
on the basis of mutual correlations, and a grouping
of objects based on their similarities. For this analy-
sis, the covariance matrix was diagonalised and the
characteristic roots (eigenvalues) were obtained.
The transformed variables or principal components
(PCs) were obtained as weighted linear combi-
nations of the original variables.
The Scree plot (see Fig. 2) was used to identify
the number of PCs to be retained in order to com-
prehend the underlying data structure (Jackson,
1991). The Scree plot shows a pronounced change
of slope after the third eigenvalue; Cattell and
Jaspers (1967) suggested using all the PCs up to
and including the ®rst one after the brake, so that
four PCs were retained, which have eigenvalues
greater than unity and explain 81.5% of the var-
iance or information contained in the original data
set. Projections of the original variables on the sub-
space of the PCs are called loadings and coincide
with the correlation coecients between PCs and
variables. Loadings of the four retained PCs are
presented in Table 4. PC1 explains 46.1% of the
variance and is highly contributed by most vari-
ables: chloride, bicarbonate, sulphate, conductivity,
dissolved solids, hardness, calcium, potassium, mag-
nesium, sodium and, in a less extent, by BOD,
COD, manganese, ammonia, and phosphate. These
variables were demonstrated to be correlated (see
correlation matrix, Table 3). Flow rate and dis-
solved oxygen have a negative participation in PC1.
PC2 explains 19.0% of the variance and includes
calcium, dissolved oxygen, pH (positive loading),
BOD, COD, nitrite, phosphate and manganese
(negative participation). PC3 (9.8% of the variance)
is positively contributed by nitrate and negatively
by temperature. Finally, PC4 explains 6.6% of the
total variability of the original data and is highly
participated by iron.
As can be seen in Table 4, PC1 is highly partici-
pated by most variables, thus hindering its hydro-
chemical interpretation. In the same way, variables
related to anthropogenic pollution like BOD, COD,
phosphorous or nitrogen compounds have a high
participation on both PC1 and PC2, and therefore
PC2 cannot be explained only in terms of organic
pollution. A rotation of principal components can
achieve a simpler and more meaningful represen-
tation of the underlying factors by decreasing the
contribution to PCs of variables with minor signi®-
cance and increasing the more signi®cant ones.
Rotation produces a new set of factors, each one
involving primarily a subset of the original variables
with as little overlap as possible, so that the original
variables are divided into groups somewhat inde-
Fig. 2. Scree plot of the characteristic roots (eigenvalues)
of principal components (r) and varifactors (q).
Table 4. Loadings of 22 experimental variables on four signi®cant
principal components for 30 river water samples
Variable PC1 PC2 PC3 PC4
BOD 0.523 ÿ0.635 0.353 0.022
Ca 0.702 0.656 ÿ0.073 ÿ0.027
Cl 0.914 0.164 0.101 ÿ0.073
COD 0.574 ÿ0.618 0.322 ÿ0.154
COND 0.925 0.365 0.046 0.036
DS 0.909 0.335 0.139 0.076
Fe ÿ0.074 ÿ0.328 0.195 0.826
FLOW ÿ0.628 ÿ0.095 0.424 ÿ0.347
HARD 0.897 0.394 ÿ0.037 0.101
HCO3 0.821 0.116 ÿ0.050 ÿ0.242
K 0.828 ÿ0.139 0.215 ÿ0.147
Mg 0.901 0.020 0.013 0.216
Mn 0.547 ÿ0.479 ÿ0.253 0.459
Na 0.864 0.317 0.140 ÿ0.067
NH4 0.590 ÿ0.468 0.446 ÿ0.199
NO2 0.388 ÿ0.400 ÿ0.152 ÿ0.218
NO3 ÿ0.160 0.223 0.710 0.303
OXYG ÿ0.576 0.669 0.329 0.136
pH ÿ0.120 0.712 ÿ0.401 ÿ0.082
PO4 0.650 ÿ0.495 ÿ0.205 ÿ0.151
SO4 0.851 0.458 0.003 0.140
TEMP 0.306 ÿ0.469 ÿ0.708 0.143
Eigenvalue 10.148 4.181 2.154 1.459
% Variance explained 46.1 19.0 9.8 6.6
% Cum. variance 46.1 65.1 74.9 81.5
Marisol Vega et al.
3586

7. pendent of each other (Sharaf et al., 1986; Massart
et al., 1988). Although rotation does not a€ect the
goodness of ®tting of the principal component sol-
ution, the variance explained by each factor is
modi®ed.
A varimax rotation of the principal components
led to 22 rotated PCs (called henceforth varifactors)
whose eigenvalues are plotted in Fig. 2. The Scree
plot shows a pronounced change of slope after the
third eigenvalue, therefore four varifactors explain-
ing 67.8% of the variance were retained (Cattell
and Jaspers, 1967). Eigenvalues and loadings of
these varifactors are displayed in Table 5. It must
be noted that rotation has resulted in an increase of
the number of factors necessary to explain the same
amount of variance of the original data set, so that
the ®rst two varifactors used for graphical represen-
tation explains a lesser amount of variance.
However, smaller groups of variables can be now
associated to individual rotated factors with a
clearer hydrochemical meaning.
Varifactor 1 explains 37.2% of the total variance
and is highly participated by calcium, chloride, con-
ductivity, dissolved solids, hardness, bicarbonate,
magnesium, sodium and sulphate, and can be thus
interpreted as a mineral component of the river
water. This clustering of variables points to a com-
mon origin for these minerals, likely from dissol-
ution of limestone, marl and gypsum soils. Flow
rate contributes negatively to this factor, which can
be explained considering that dilution processes of
dissolved minerals increase with ¯ow. Varifactor 2
contains 16.7% of the variance and includes BOD,
COD and ammonia, whereas pH and oxygen have
a negative contribution to this varifactor. This vari-
factor can be explained taking into account that
high levels of dissolved organic matter consume
large amounts of oxygen; organic matter in urban
wastewater consists mainly of carbohydrates, pro-
teins and lipids which, as the amount of available
dissolved oxygen decreases, undergo anaerobic fer-
mentation processes leading to ammonia and or-
ganic acids. Hydrolysis of these acidic materials
causes a decrease of water pH values. Potassium
contributes in the same extent to varifactor 1 and 2.
Varifactor 3 (8.0% of variance) has a high and
positive load of temperature and negative of dis-
Table 5. Loadings of 22 experimental variables on the ®rst four
rotated PCs for 30 river water samples
Variable
Varifactor
1
Varifactor
2
Varifactor
3
Varifactor
4
BOD 0.116 0.934 0.163 0.111
Ca 0.920 ÿ0.179 ÿ0.093 ÿ0.119
Cl 0.893 0.326 0.048 ÿ0.034
COD 0.180 0.912 0.159 0.011
COND 0.973 0.148 0.049 ÿ0.038
DS 0.950 0.183 ÿ0.001 0.001
Fe ÿ0.131 0.072 0.012 0.970
FLOW ÿ0.496 ÿ0.005 ÿ0.323 ÿ0.094
HARD 0.952 0.089 0.106 ÿ0.033
HCO3 0.697 0.184 0.024 ÿ0.139
K 0.584 0.614 0.089 ÿ0.043
Mg 0.766 0.359 0.289 0.071
Mn 0.248 0.290 0.387 0.472
Na 0.918 0.180 ÿ0.070 0.003
NH4 0.225 0.761 ÿ0.190 0.065
NO2 0.105 0.170 0.182 ÿ0.061
NO3 0.014 ÿ0.003 ÿ0.260 0.104
OXYG ÿ0.132 ÿ0.418 ÿ0.540 ÿ0.016
pH 0.169 ÿ0.434 ÿ0.018 ÿ0.201
PO4 0.276 0.350 0.244 0.045
SO4 0.981 0.008 0.059 0.022
TEMP ÿ0.003 0.114 0.919 0.031
Eigenvalue 8.175 3.677 1.763 1.292
% Variance explained 37.2 16.7 8.0 5.9
% Cum. variance 37.2 53.9 61.9 67.8
Fig. 3. Scores of river water samples on the bidimensional plane de®ned by the ®rst two varifactors.
Space reduction from 22 to 2 dimensions (53.9% of the total variance). Samples collected at Cabezo
 n
de Pisuerga (.), Puente Mayor (Q) and Simancas (R) in January (E), April (A), July (J) and October
(O) from 1990 to 1992.
Water quality analysis using exploratory data 3587

8. solved oxygen, since solubility of gases in water
decreases with increasing temperature. Flow rate
should be expected to have a high and negative
load on varifactor 3, as high temperatures corre-
spond to dry and hot seasons like summer, when
¯ow rate is lower; however, its load is negative but
small (ÿ0.323) because during 1990 a persistent
drought caused low ¯ow rates even in winter sea-
son. Finally, varifactor 4 (5.9% of variance) is par-
ticipated by iron and manganese, which are
hydrochemically related.
Figure 3 displays a plot of sample scores on the
bidimensional plane de®ned by varifactors 1 (min-
eral contents) and varifactor 2 (anthropogenic con-
tamination, namely organic matter). High and
positive scores on varifactors 1 or 2 indicate high
mineral contents or high organic pollution, respect-
ively, whereas those samples with high and negative
scores on varifactors 1 or 2 will correspond to
higher ¯ow rate or dissolved oxygen, thus indicating
a better water quality. From Fig. 3 it can be con-
cluded that sample SJ90 (collected in Simancas in
July 1990) shows the worst quality, with high levels
of both minerals and organics. Samples collected in
January and April 1991 are projected onto negative
varifactor 1 and therefore show the lowest mineral
contents. As pointed above, winter of 1990 was
extremely dry and that fact is re¯ected by the high
scores on varifactor 2 of samples collected in April
and July 1990.
Box plots of varifactors 1, 2 and 3 in the three
sampling stations are shown in Fig. 4. Some im-
portant conclusions are derived from these plots:
varifactor 1 (mineral contents) and varifactor 3
(temperature) show large spread around the me-
dian, thus pointing to an important contribution of
sampling time to the variance of these varifactors.
On the other hand, varifactor 2 (anthropogenic pol-
lution) exhibits small spread, but the median
increases slightly from Cabezo
 n to Simancas, there-
fore indicating that sampling station is the most im-
portant source of variation in explaining the
variance of this varifactor, which is scarcely a€ected
by sampling times.
Two-way ANOVA on the three more relevant
varifactors was carried out and results of the F-test
are displayed in Table 6. Normal probability plots
of varifactors applied to individual sampling
Fig. 4. Box plots for three more signi®cant varifactors in
Cabezo
 n (C), Puente Mayor (P) and Simancas (S).
Table 6. Two-way ANOVA and F-test of the three more relevant rotated PCs
Source of variation
Sum of
squares
Degrees
of freedom
Variance
of squares F
Pooled sum
of squares % Contribution
Varifactor 1
Sampling time 18.399 9 2.044 3.521 13.629 47.0
Sampling station 0.150 2 0.075 0.129
Residual 10.451 18 0.581 15.371 53.0
Total 29.000 29 29.000 100.0
Varifactor 2
Sampling time 11.809 9 1.312 1.941
Sampling station 5.026 2 2.513 3.718 3.250 11.2
Residual 12.165 18 0.676 25.750 88.8
Total 29.000 29 29.000 100.0
Varifactor 3
Sampling time 25.306 9 2.812 15.428 23.643 81.5
Sampling station 0.414 2 0.207 1.135
Residual 3.281 18 0.182 5.357 18.5
Total 29.000 29 29.000 100.0
F calculated as variance of the e€ect/variance of the residual.
Fcrit is 2.456 for 9 and 18 degrees of freedom and 3.555 for 2 and 18 d.f (p = 0.05).
Marisol Vega et al.
3588

9. stations showed that varifactors were normally dis-
tributed, except varifactor 2 at Simancas. However,
the F-test as applied in ANOVA is not too sensitive
to departures from normality of distribution (Miller
and Miller, 1984) and was therefore used to inter-
pret the sources of variation.
Sources of variation that can a€ect sample pro-
jections on varifactors are sampling time (seasonal
e€ect) and sampling station (geographical or pollut-
ing e€ect). A comparison of the estimates of var-
iance by means of the Fisher ratio (F) indicates
that, at the 95% con®dence level, there is a signi®-
cant contribution to the total variance of varifactor
1 due to variation between sampling times
(F>Fcrit(9,18,p = 0.05), but the variation between
sampling stations does not contribute signi®cantly
(F < Fcrit(2,18,p = 0.05). Since varifactor 1 can be
interpreted as water inorganic (mineral) contents,
which increase with decreasing ¯ow rate, it can be
concluded that levels of minerals in the river water
investigated are seasonal and climate dependent,
and are una€ected by sampling location, thus point-
ing to a natural (non-anthropogenic) origin for this
polluting form. For varifactor 2 (organic matter,
nitrogen and phosphorous), only signi®cant contri-
bution to the variance due to di€erences between
sampling stations was found. This indicates that or-
ganic pollution of river water originates from
anthropogenic sources, mainly as municipal waste-
water which is disposed into the river between
Puente Mayor and Simancas. Sampling stations
were demonstrated not to contribute to the variance
of varifactor 3 (temperature), whereas highly signi®-
cant di€erences were found between sampling times,
thus showing that only climate and seasonality are
responsible for variations in water temperature, and
that there is no thermal pollution in the river sec-
tion investigated.
Those sources of variation that were demon-
strated not to contribute signi®cantly to the var-
iance of varifactors (F < Fcritical) were combined
with the residual variance (Ross, 1988) and from
the recalculated sum of squares the contribution of
the e€ect to the variability of the varifactor was
estimated as
%Contribution ˆ
SS0
SST
100,
where SS' is the pooled sum of squares and SST the
total sum of squares. It can be seen in Table 6 that
seasonality contributes by 47.0% and 81.5% to the
variability of varifactors 1 (mineral composition)
and 3 (temperature), respectively, thus evidencing
the strong e€ect that climate has on the variables
explained by these varifactors. Besides, sampling lo-
cation has a negligible contribution to varifactors 1
and 3, but contributes by 11.2% to the variability
of varifactor 2 (anthropogenic pollution); this con-
tribution is smaller than that of the residual
(88.8%), thus indicating the possible existence of an
interaction between both sources of variation:
although the e€ect of sampling time (season) is not
signi®cant, it cannot be completely discarded
(F Fcritical but 1) since climate has also a small
contribution to varifactor 2 due to seasonal vari-
ations of ¯ow rate which cause dilution of pollu-
tants of anthropogenic origin.
Spatio-temporal variations of water quality can
be readily visualised in Fig. 5, where varifactors 1,
2 and 3 have been plotted vs sampling times for the
Fig. 5. Spatio-temporal ¯uctuations of varifactors 1, 2 and
3 and their relationship with river ¯ow rate (ÐÐÐ).
Sampling stations: Cabezo
 n de Pisuerga (), Puente
Mayor (q) and Simancas (r).
Water quality analysis using exploratory data 3589

10. stations investigated: Cabezo
 n, Puente Mayor and
Simancas. The average ¯ow rate for the three
stations has been simultaneously plotted to show
the relationship between water quality and ¯ow
rate. Again, the inverse relationship between ¯ow
rate and rotated factors 1 and 3 (mineral com-
ponents in water and temperature, respectively) can
be observed, whilst for varifactor 2 (organic pol-
lution and nutrients) this negative correlation exists
not so markedly. The interaction between sampling
location and sampling time is illustrated in Fig. 5:
maximum variability of varifactor 2 along the river
section sampled occurs in dry seasons (July and
October) when river ¯ow rate decreases. This can
be interpreted taking into account that municipal
wastewater discharges into the Pisuerga river are
the main and nearly constant source of organic
matter, so that an increase in river ¯ow rate causes
dilution of pollutants and hence di€erences between
sampling stations are made less evident. Figure 5
shows also that sample scores on varifactor 2 are
always higher for those samples collected in
Simancas whilst Cabezo
 n and Puente Mayor scores
are similar, thus assessing that the main discharges
of organic mater and nutrients are located between
Puente Mayor and Simancas, which con®rms mu-
nicipal wastewater as the principal source of or-
ganic pollutants for the Pisuerga river. These
conclusions are in good agreement with the spatio-
temporal pro®le exhibited by the complexing ca-
pacity of the Pisuerga river water (Pardo et al.,
1994). Furthermore, di€erences in sample scores
between Simancas and the other two sampling
stations were higher in dry seasons (July and
October) thus con®rming the spatial-temporal inter-
action on varifactor 2.
Temporal variation of some independent vari-
ables associated to contamination of river water is
depicted in Fig. 6. It can be observed that conduc-
tivity behaves in the same way as varifactor 1 (see
Fig. 5 for comparison), since this variable is closely
related to mineral composition of river water, and
therefore to varifactor 1. COD and ammonia are
associated to organic pollution and therefore their
pro®les are similar to that of varifactor 2. As can
be seen in Fig. 6, the highest variation of these con-
taminants occurs in Simancas, as important
amounts of municipal wastewater are discharged
Fig. 6. Temporal variations of some original variables associated to river water pollution and their re-
lation with ¯ow rate (ÐÐÐ). Sampling stations: Cabezo
 n de Pisuerga (), Puente Mayor (q) and
Simancas (r).
Marisol Vega et al.
3590

11. upstream this station. Dissolved oxygen also shows
a periodic pro®le habit related to seasonality with
strong decreases at Simancas, caused by the high
levels of oxygen-consuming organic matter.
Cluster analysis
Cluster analysis allows the grouping of river
water samples on the basis of their similarities in
chemical composition. Unlike PCA that normally
uses only two or three PCs for display purposes,
cluster analysis uses all the variance or information
contained in the original data set. Hierarchical
agglomerative clustering by the Ward's method was
selected for sample classi®cation because it pos-
sesses an small space distorting e€ect, uses more in-
formation on cluster contents that other methods,
and has been proved to be an extremely powerful
grouping mechanism (Willet, 1987); besides, Ward's
method yielded the most meaningful clusters. The
method was applied to normalised data using
squared Euclidean distances as a measure of simi-
larity (Massart and Kaufman, 1983). A similar
classi®cation pattern was obtained by the average
linkage method (between groups).
The dendrogram of samples obtained by the
Ward's method is shown in Fig. 7. Two well di€er-
entiated clusters can be seen, each formed by two
subgroups, with river water quality decreasing from
top to bottom. The ®rst group from the top is
assorted with samples collected in January and
April 1991, and one sample collected in Cabezo
 n in
April 1992; in the PCA method of classi®cation
these samples scored high and negative on varifac-
tor 1 and close to 0 on varifactor 2 (see Fig. 3) thus
indicating the lowest levels of both minerals and or-
ganic matter as these samples were collected in
January and April 1991, when the river ¯ow rate is
at is maximum due to snow melting at the river
sources. This cluster is linked at a rescaled distance
of about 7 to other small but tight group that
includes samples taken out in July 1991 and July
1992 (except that from Simancas) and the sample
PO91. In the PCA analysis these samples were also
grouped on intermediate and negative values on the
varifactor 1 axis. The second main cluster is formed
for two subgroups that are linked at a rescaled dis-
tance of 10: the ®rst of them includes very similar
samples collected in January and April 1992, and
samples CO90 and CO91 and corresponds to
samples scoring high and positive varifactor 1 and
negative varifactor 2 in the PCA analysis (see Fig. 3)
thus pointing to their high levels of minerals and
low of anthropogenic pollutants. The second sub-
group includes samples collected in 1990 (April,
July and October) and samples collected from
Simancas in July and October 1991. These samples
correspond to dry seasons and to the most contami-
Fig. 7. Dendrogram based on agglomerative hierarchical clustering (Ward's method) for 30 river water
samples collected at Cabezo
 n de Pisuerga (C), Puente Mayor (P) and Simancas (S) in January (E),
April (A), July (J) and October (O) from 1990 to 1992.
Water quality analysis using exploratory data 3591

12. nated station (Simancas) and show the worst water
quality in both minerals and organic matter.
CONCLUSIONS
Environmental analytical chemistry generates
multidimensional data that need of multivariate
statistics to analyse and interpret the underlying in-
formation. Water quality data of a river have been
analysed by unsupervised pattern recognition (hier-
archical cluster analysis) and display methods (prin-
cipal component analysis) to extract correlations
and similarities between variables and to classify
river water samples in groups of similar quality.
PCA has found a reduced number of ``latent'' vari-
ables (principal components) that explain most of
the variance of the experimental data set. A vari-
max rotation of these PCs led to a reduced number
of varifactors, each of them related to a small
group of experimental variables with a hydrochemi-
cal meaning: mineral contents for varifactor 1,
anthropogenic pollutants for varifactor 2 or water
temperature for varifactor 3.
PCA in combination with ANOVA has allowed
the identi®cation and assessment of spatial (pol-
lution from anthropogenic origin) and temporal
(seasonal and climatic) sources of variation a€ecting
quality and hydrochemistry of river water. Man-
made pollution was demonstrated to originate from
municipal wastewater discharged into the river
between the sampling stations of Puente Mayor and
Simancas; temporal e€ects were associated to seaso-
nal variations of river ¯ow rate which cause di-
lution of pollutants and hence variations in water
quality. The application of PCA and cluster analy-
sis has achieved meaningful classi®cation of hydro-
chemical variables and of river water samples based
on seasonal and spatial criteria. Both multivariate
techniques led to very similar classi®cation patterns.
AcknowledgementÐThe authors wish to thank the
Confederacio
 n Hidrogra
 ®ca del Duero (Valladolid, Spain)
for providing data of river ¯ow rates.
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