principal component analysis an appropriate tool for water quality.pdf
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Ecological Modelling 178 (2004) 295311
Principal component analysis: an appropriate tool for water qualityevaluation and managementapplication to a tropical lake system
Bernard Parinet a,, Antoine Lhote a,b, Bernard Legube a
a Laboratoire de Chimie de lEau et de lEnvironnement, UMR CNRS 6008, ESIP; 40 Avenue du Recteur Pineau, 86022 Poitiers, Franceb Laboratoire de Chimie de lEau INP-HB, BP 1093 Yamoussoukro, Cote dIvoire
Received 10 April 2003; received in revised form 3 February 2004; accepted 12 March 2004
Abstract
An eutrophic lake system characteristic of IvoryCoast provided us with the opportunity to check that the values of all analytical
variables are linked to both causes and effects of eutrophication (feedback effect). Therefore, none of these values can accurately
describe a trophic state alone. To solve this difficulty we suggest here, that relationships between analytical variables are able to
generate better descriptors than variables themselves. We show that principal component analysis (PCA) using coefficients of
linear regression is, by construction, an appropriate tool for this purpose.
The graphic representations obtained underline that: (i) the first principal component is linked to the trophic potential and
the second one to the trophic level; (ii) the graphical locations of the different lakes studied are consistent with their apparent
features; (iii) allochthonous inputs have a spreading effect on the graphic representation. Extension of this model to other lakes,
located in the same geographical area, was successfully carried out. Furthermore, it has been shown that it is possible to reducethe number of analytical parameters to four (pH, conductivity, UV absorbance at 254 nm and permanganate index for raw water)
without notably impairing the quality of the PCA representation. Moreover, these very simple parameters are easier to quantify
than classical one (nutrients, chlorophyll-a, etc.) and make their use easier for the water resources management.
2004 Elsevier B.V. All rights reserved.
Keywords: Tropical water quality; Lake eutrophication; Macrophyte; Algae; Principal component analysis (PCA)
Abbreviations: T, water temperature; cond, electrical conduc-tivity; EH , redox potential (with standard hydrogen electrode as
reference); DO, dissolved oxygen; SS, suspended solids; PO4-P,
orthophosphate ions; Ptot, total phosphorus; PIRW, permanganate
index in acidic medium on raw water; PIFW, permanganate index
in acidic medium on filtered water; Chl-a, chlorophyll a; UV abs,
UV absorbance at 254 nm; Na, sodium ions; K, potassium ions;
NH4, ammonium ions; NO3-N, nitrate ions; Ca, calcium ions; Mg,
magnesium ions Corresponding author. Tel.: +33-5-49453918;
fax: +33-5-49453768.
E-mail address: [email protected]
(B. Parinet).
1. Introduction
In order to identify and classify the different trophic
states of waters (lakes or rivers), two main types oftrophic indicators have been and are still being used
(Pesson, 1980), belonging to biocenosys (biologi-
cal factors) or biotope (physico-chemical factors).
The aim of the biological approach of eutrophica-
tion is to measure its impact on the environments
biodiversity. Thus, several classification indexes have
been drawn up (Woodiviss, 1964; Vernaux, 1982;
Kelly, 1998; Seele et al., 2000). Working with such
indexes requires quite complex analysis since it is
necessary to identify the local fauna and flora (Dodds
0304-3800/$ see front matter 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2004.03.007
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296 B. Parinet et al. / Ecological Modelling 178 (2004) 295311
et al., 1998; Stambuck-Giljanovic, 1999). For the
physico-chemical approach, the aim is to quantify
the trophic state of an aquatic environment by mea-
suring a number of physico-chemical parameters(Carlson, 1977; Ryding and Rast, 1994). It is obvious
that the two approaches are similar since the biodi-
versity of an aquatic environment is conditioned by
the physico-chemical quality of its water (Gara and
Coimbra, 1998;Thornton, 1987).
As for the physico-chemical approach, the study of
the eutrophication process of superficial waters faces
an important difficulty: the choice of analytical pa-
rameters that are the most appropriate to describe the
phenomenon (Moss, 1998).
Although it is currently admitted that nitrogen,
phosphorus and chlorophyll parameters cannot beignored (OCDE, 1982; Salas and Martino, 1990),
the values of all analytical variables are more or
less linked to both causes and effects of eutrophi-
cation (feedback effect). Therefore, neither their
intrinsic values nor derived index, can satisfactorily
describe the trophic state of the aquatic system by
itself (Hakanson, 2000).
In fact, it seems obvious that eutrophication pro-
cesses modify chemical equilibriums, and act on the
relationships that link each variable to the others
(Strain and Yeats, 1999).The aim of this study is to verify that these relation-
ships make up a set of informations that could pro-
vide a good way of characterising the state of the sys-
tem. Although the relationships linking all variables by
pairs are not always linear, the whole set of coefficients
obtained from linear regression is probably a better
criterion of waters trophic state than the variables
themselves. Moreover, proceeding this way indirectly
takes into account all the physico-chemical, biological,
morphological and hydrological parameters of lakes.
However, it is generally not easy to find a suitableaquatic system that is able to illustrate this. The lakes
studied here present the rare advantage of being sup-
plied by the same streams running across a restricted
geographical zone of geological and climatic simi-
larity. Moreover, the trophic characteristics of these
waters are altered by their passage through different
agricultural and urban zones. So, it become easy to
compare their different behaviours.
Such a system provides us with the opportunity
to verify the precedent assertion. In previous studies
(Lhote, 2000; Parinet et al., 2001) we showed that the
feedback effect was an important feature of the be-
haviour of these lakes. We concluded that the intrin-
sic values of analytical parameters are not sufficient tomake a correct assessment of their nature and trophic
status.
Given the complexity of the process, a multidi-
mensional statistical treatment of collected variables
should be looked for. The well-known method of prin-
cipal components analysis (PCA), using coefficients
of linear correlation offers this possibility (Wenning
and Erickson, 1994; Aruga et al., 1993).Over the last
20 years, this method has been widely used in many
fields dealing with the study of the natural environ-
ment, (Tomassone et al., 1993)including eutrophica-
tion of water (Reisenhofer et al., 1995; Vega et al.,1998; De Ceballos et al., 1998; Perona et al., 1999).
However, as far as we know, and given the way it has
been used, it has not yet provided answers to the ques-
tions this kind of study generally poses. Nevertheless,
the originality of the lake system under study provided
us with the opportunity to test the relevance of this
tool.
2. Materials and methods
2.1. Location of the site under study
The town of Yamoussoukro is located in the centre
of Ivory Coast, 250 km to the north-west of Abidjan,
at about 65 North latitude. A set of lakes was built
there on two connected rivers (Fig. 1).We studied ten
of them, numbered from 1 to 10. The surfaces of the
lakes and of their drainage basins are given inTable 1.
They are usually less than 3 m deep.
2.2. General description of the lakes
The trophic status of the lakes are direct conse-
quence of their own local situation. Thus, lakes 14
located in an area of low urban density are colonised
by phytoplankton.
Lake 5, located in the centre of the town, receives
domestic wastewaters. This lake had been, over a long
period of time, entirely covered with water hyacinths
(Eichhornia crassipes), a very invasive floating macro-
phytes (Bard et al., 1991) and rooted macrophytes like
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B. Parinet et al. / Ecological Modelling 178 (2004) 295311 297
Fig. 1. Yamoussoukros lake system.
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Table 1
Drainage basins and lake areas
Lake number
1 2 3 4 5 6 7 8 9 10
Lake area (km2) 0.15 0.14 0.08 0.09 0.45 0.10 0.08 0.10 0.10 0.11
Drainage basin area (km2) 7.5 1.25 1.00 1.10 3.75 2.05 1.45 1.10 1.00 3.80
lotuses (Nelumbo nucifera). During the study period,
following the manual removal of the macrophytes in
July 1995, the water was strongly colonised by al-
gae, which can be noted from high concentrations of
chlorophyll-a, close to 200g/l.
Lake 6 presents a similar situation; it was almost en-
tirely covered byE. crassipesin the first period of our
study (before July 97) and was then clear by manualremoval. As the elimination of water hyacinths highly
modified the characteristics of this lake, we will anal-
yse the two periods separately. Therefore, numbers 6a
and 6b refer to lake 6 for the first and second period,
respectively.
Lake 7 receives wastewater from a densely popu-
lated area. Although this lake was also part of our
work, the results from this lake will not be shown here
because the water is closer to a wastewater pool rather
than of lake.
Finally, lakes 9 and 10 are almost completelycovered with lotuses (N. nucifera) which are rooted
macrophytes, with few water lettuces (Pistia stra-
tiotes), while lake 8 is periodically colonised by water
lilies (Nymphea lotus) and algae.
Table 2 sums up the state of colonisation of the lakes
by aquatic plants.
Table 2
Colonisation of the studied lakes by aquatic plants
Lake Macrophytes Estimation of the algae density from the Chl-a concentration
1 A few Lotuses upstream +
2 ++
3 +++
4 ++++
5 Lotuses, Pistia, Hyacinths (1020% covered) ++++
6 Hyacinths before July 97 ++++(after July 97)
7 Pistia and others (usually 100% covered) +++++(if no macrophytes)
8 Water lilies, Lotuses, Hyacinths (10% covered) +++
9 Lotuses and Hyacinths (up to 95% covered in June 1995) +
10 Lotuses, Pistia and others (100% covered until July 1998)
2.3. Physico-chemical analyses
To follow up the water quality of the 10 stud-
ied lakes, 21 sampling stations were chosen, usually
at the entrance and exit of each lake. The constant
sampling period for all the lakes was a 2 h one
(from 8 to 10 a.m.). Sampling and analysis of the
18 physico-chemical parameters taken into accountwas carried out between April 1996 and April 1998
(twice a month during the rainy season and once a
month otherwise). At each location, 1 l of water was
sampled, 50 cm below the surface; 250 ml were then
transferred into a brown glass bottle, for later analy-
sis of chlorophyll. After in situ analysis, bottles were
kept in the dark in a cooler.
Analytical methods followed normalised French
standard methods (AFNOR, 1994). The following
parametersT, pH, cond, EH, DO were determined in
situ, and the others (SS, PO4-P, Ptot, NO3-N, NH4,PIRW, PIFW, Chl-a, UV abs, Ca, Mg, Na and K) in
the laboratory within a 3 h delay. The floating macro-
phytes could not be quantified, because no satisfac-
tory method is available. Their surface density on the
lake depending on the orientation and strength of the
wind.
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3. Results and discussion
3.1. Data treatment
As previously mentioned, the measurement of 18
chemical and physical variables were carried out
twice a month during the rainy season and once a
month during otherwise on 21 sampling sites and
on 9 lakes. Eleven thousand analysis was carried
out during 23 months. A detailed statistical study
(ANOVA, Box plots, etc.), tests and more comments
on this large data base can be found through pre-
vious published works (Lhote, 2000; Parinet et al.,
2001).
As PCA is a non parametric method of classifi-
cation, it makes no assumptions about the under-lying statistical distribution of the data (Vega et
al., 1998; Helena et al., 2000; Kalin et al., 2000;
Wunderlin et al., 2001). Nevertheless, in conjunc-
tion with the KolmogorovSmirnov test, it could be
found (Table 3) that most variables were normally
distributed particularly when applied to individual
lake. When applied to the nine lakes, some vari-
ables could differ from normality, especially in the
case of nutrients (P-PO4, Ptot, N-NH4 and N-NO3)
that were the less normally distributed variables.
For these parameters, we obtained approximatelynormal distribution with a Ln (x + a) transfor-
mation.
To examine the suitability of these data for factor
analysis, KaiserMeyerOlkin (KMO) and Bartletts
tests were performed. KMO is a measure of sam-
pling adequacy that indicates the proportion of vari-
ance which is common variance, i.e. which might
be caused by underlying factors. High value (close
to 1) generally indicates that factor analysis may
be useful, which is the case in this study: KMO
= 0.85 (Table 4). If KMO test value is less than
0.5, factor analysis will not be useful. Bartletts test
of sphericity indicates whether correlation matrix is
an identity matrix, which would indicate that vari-
ables are unrelated. The significance level which is
0 (Table 4) in this study (less than 0.05) indicate
that there are significance relationships among vari-
ables.
Finally, PCA was applied to normalized data, and
so the covariance matrix coincides with the correlation
matrix.
3.2. Comments on physico-chemical parameters
evolution
This part presents a synthesis of the measurements.Figs. 2 and 3show the mean values of some studied
parameters for each lake, over the 2 years of the study.
A simplified comment is given here for pH, conduc-
tivity and alkalines (Na) ions, PO4-P, Ptot, and Chl-a.
3.2.1. pH
Significant spatial variation of pH was noted
(Fig. 2a). This could be essentially explained here
by the physico-chemical and biological reactions due
to the presence of aquatic vegetation. Comparison
of lakes 6a and 6b demonstrates that the low pH of
water is a consequence of the macrophytes growth.
On the other hand the relatively higher pH in lakes
2, 3, 4, 5, 6b and 8, compared to lake 1 are probably
due to the presence of phytoplankton.
Such observations underline the fact that the envi-
ronment has a strong feedback effect on the pH.
3.2.2. Conductivity and alkaline ions
Fig. 2c and 2d relative to conductivity and con-
centrations of sodium ions are logically quite similar,
since conductivity depends particularly on alkaline
ions in the studied waters. The important increase ofthese parameters from lake 4 to lake 5 is probably due
to the discharge of domestic wastewater, as demon-
strated by the high value of conductivity of lake 7
(500S/cm) which can be considered as the first col-
lector of Yamoussoukros wastewaters. Therefore, in
this lake system, conductivity will be dependent of
the degree of pollution from urban inputs.
On an other hand, value of conductivity in lake
6a (covered with hyacinths) is lower than its value
in lake 6b (after hyacinths removal). The meaning of
this observation is that conductivity is also dependingon the nature eutrophication processes. Such obser-
vation highlights again the feedback effect on con-
ductivity.
3.2.3. Phosphate and total phosphorus
It is generally admitted that phosphorus (Martin,
1987) plays an important role in the development of
aquatic plants, and is, in most cases, considered as
the limiting factor of eutrophication in temperate lakes
(Vollenweider et al., 1980).
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Table 4
Correlation matrix (a) and level of significance (b)
T pH Cond Ptot SS O2 PO4 EH PIRW PIFW NH4 NO3 Chl-a Ca
(a)a
T 1.000
pH 0.540 1.000
Cond 0.089 0.096 1.000
Ptot 0.071 0.244 0.529 1.000SS 0.394 0.724 0.183 0.652 1.000
O2 0.460 0.813 0.193 0.031 0.489 1.000
PO4 0.290 0.378 0.120 0.235 0.154 0.523 1.000
EH 0.421 0.560 0.280 0.203 0.258 0.722 0.681 1.000 .
PIRW 0.328 0.490 0.507 0.671 0.745 0.264 0.082 0.030 1.000
PIFW 0.293 0.221 0.556 0.560 0.463 0.057 0.269 0.154 0.811 1.000
NH4 0.181 0.246 0.512 0.266 0.084 0.332 0.140 0.346 0.327 0.395 1.000
NO3 0.082 0.115 0.186 0.329 0.082 0.210 0.580 0.370 0.324 0.397 0.229 1.000
Chl-a 0.486 0.701 0.434 0.609 0.836 0.520 0.157 0.302 0.780 0.529 0.024 0.077 1.000
Ca 0.218 0.451 0.601 0.122 0.274 0.485 0.141 0.424 0.121 0.002 0.270 0.018 0.125 1.0
K 0.091 0.066 0.917 0.481 0.188 0.178 0.120 0.262 0.498 0.542 0.514 0.164 0.430 0.4
Na 0.225 0.103 0.902 0.634 0.379 0.063 0.170 0.209 0.672 0.707 0.466 0.277 0.589 0.3
Mg 0.223 0.049 0.606 0.160 0.072 0.090 0.178 0.023 0.316 0.398 0.305 0.056 0.245 0.4
Abs 0.186 0.306 0.521 0.478 0.054 0.462 0.794 0.0657 0.417 0.582 0.445 0.664 0.121 0.2
(b)b
T
pH .000
Cond 0.124 0.107
Ptot 0.179 0.001 0.000
SS 0.000 0.000 0.008 0.000
O2 0.000 0.000 0.006 0.345 0.000
PO4 0.000 0.000 0.058 0.001 0.022 0.000
EH 0.000 0.000 0.000 0.004 0.000 0.000 0.000
PIRW 0.000 0.000 0.000 0.000 0.000 0.000 0.142 0.350
PIFW 0.000 0.002 0.000 0.000 0.000 0.228 0.000 0.022 0.000
NH4 0.009 0.001 0.000 0.000 0.138 0.000 0.034 0.000 0.000 0.000
NO3 0.144 0.067 0.008 0.000 0.142 0.003 0.000 0.000 0.000 0.000 0.001
Chl-a 0.000 0.000 0.000 0.000 0.000 0.000 0.020 0.000 0.000 0.000 0.380 0.158
Ca 0.002 0.000 0.000 0.056 0.000 0.000 0.033 0.000 0.057 0.492 0.000 0.406 0.052
K 0.119 0.194 0.000 0.000 0.007 0.010 0.059 0.000 0.000 0.000 0.000 0.016 0.000 0.0
Na 0.002 0.089 0.000 0.000 0.000 0.207 0.013 0.003 0.000 0.000 0.000 0.000 0.000 0.0
Mg 0.002 0.261 0.000 0.018 0.176 0.120 0.010 0.385 0.000 0.000 0.000 0.235 0.001 0.0
Abs 0.008 0.000 0.000 0.000 0.241 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.057 0.0
KMO test: measure of sampling adequacy: if close to 1, PCA may be useful (KMO test of sampling adequacy: 0.850). Significance level of Barletts te
significance relationship among variables (Bartletts test of sphericity: significance level: 000).a Grey boxes: value of pearson correlation >0.6.b Significance values: in the greyed boxes indicate less significance (only 10 values >0.2).
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Fig. 2. Average value and standard deviations for each lake: (a) pH; (b) DO; (c) cond; (d) Na; (e) SS; (f) Chl-a.
The quite low values of PO4-P (Fig. 3e) as well asits
important variability with the allochthonous input led
to high standard deviations. The analysis of this figure
shows that phosphate concentration is not linked to
chlorophyll-a (compareFigs. 2f and 3efor lakes 3 and5). Lake 5, with chlorophyll-a concentration twice that
of lake 3 has the same phosphate concentration. A low
value of phosphate concentration can be measured in
a mesotrophic lake (little phosphorus inputs) as well
as in an hypereutrophic one (available phosphate is
consumed by biomass).
Nonetheless, PO4-P concentration seems to depend
on the nature of the biomass. Indeed, the highest
PO4-P concentrations were those of lakes colonised
by macrophytes (lakes 6a and 10): lake 6a was cov-
ered with water hyacinths and lake 10 was partly
covered by P. stratiotes associated to lotuses rooted
in the sediments.
This result has to be linked to EH value in these
lakes, which was about 150 mV compared to 350 mVin other lakes (Table 3). Indeed, a reducing environ-
ment (EH < 200 mV) leads to a release of mineral
phosphate accumulated in sediments (Ryding and
Rast, 1994).
As for lakes with a high phytoplanktonic biomass,
they are characterised by a generally lower level of
phosphate.
Measurements of total phosphorus (Fig. 3f), car-
ried out on the raw water after mineralization, include
the quantity of phosphorus contained in phytoplank-
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B. Parinet et al. / Ecological Modelling 178 (2004) 295311 303
Fig. 3. Average value and standard deviation for each lake: (a) PIRW; (b) UV abs; (c) NO3-N; (d) NH4; (e) PO4-P; (f) Ptot.
ton and other aquatic organisms. For that reason, they
give an apparently better representation of the trophic
state of the environment in the case of colonisation by
phytoplankton.
Fig. 3fis quite similar to that showing the evolution
of chlorophyll (Fig. 2f)for the first five lakes, whichconfirms the link between total phosphorus and phy-
toplankton (both linked to external load).
However, in the case of colonisation by macro-
phytes, another interpretation of total phosphorus
should be made. This parameter is one of those
used in the trophic classification (OCDE, 1982).
Applied to our system, the values of total phospho-
rus and chlorophyll-a mainly correspond to hyper-
eutrophic lakes. However, this classification does
not take into account the great differences exist-
ing among the states of the lakes, as seen pre-
viously.
3.2.4. Chlorophyll-a
Chlorophyll-a concentration is considered as a good
indicator of the phytoplanktonic biomass (Forsgergand Ryding, 1980; Cloot and Ros, 1996). The high
increase of this parameter between lake 1 (located in
a rural area) and lake 5 (urbanised area) can be ex-
plained by urban wastewaters. It must be reminded
that the first four lakes are fed by the same stream,
then their differences in composition is mainly due to
the nature of their inputs. For the first four lakes, we
can note an opposite evolution of DO concentration
(Fig. 2b) and Chlorophyll-a (Fig. 2f). We could con-
sider this, as surprising result, but it has to be noticed
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that measurements were carried out in the morning
when oxygen production by phytoplankton has not yet
compensated its nocturnal consumption.
Lakes 1 and 6a cannot be labelled using the sametrophic state, even if they are both very poor in
chlorophyll-a lake 6a is colonised by macrophytes
that prevent light from penetrating into the water.
Photosynthesis is thus blocked and phytoplankton
cannot develop. Furthermore, as Nakai et al. (1996)
mention, macrophytes may release algaecide con-
stituents. On the other hand, lake 6b results, show that
once hyacinths have been removed, the concentration
in chlorophyll-a rapidly increases, until it reaches that
of lake 5.
These results clearly show that trophic states are
multiform and that those with macrophytes growthmust be separated from those with algae growth.
3.3. Interpretation with the use of principal
component analysis (PCA)
Because of the feedback effect, which depends on
the particular characteristics of each lake, the above
comments pointed out that the intrinsic values of ana-
lytical data are not sufficient to make a correct assess-
ment of the trophic status of these lakes.
The trophic levels should therefore be evaluatedfrom other criteria, which will indirectly take into ac-
count relations between analytical parameters.
In this section, we examine how application of
principal component analysis, using correlation coef-
ficients, can describe the various trophic states of this
aquatic system.
3.3.1. Analysis of the 18 variables from the 10 lakes
The study of the main variables presented above
with the examination of the correlation matrix
(Table 4) shows, for all lakes, a good consistencebetween the results. For instance we can observe a
good correlation between some couple of variables
Chl-a and PIRW, SS and pH, cond and Na or K,
DO and pH. The correlation between SS and pH
which could, at first, appear surprising, is easily ex-
plained by the fact that, in most lakes, SS are made
up of algae biomass which affects the pH (photo-
synthesis). Concerning the correlation between pH
and Chl-a (Table 5), it can be noted that the value
of this correlation coefficient depends strictly on the
Table 5
R-value of pH/Chl-a correlation
Lake R value of pH/Chl-a correlation
1 0.1452 0.354
3 0.171
4 0.625
5 0.624
6a 0.254
6b 0.821
8 0.748
9 0.07
10 0.77
considered lake. In fact, its the same for all others
couples.
The principal component analysis showed that the
eigenvalues of the two first principal components rep-
resent up to 62% of the total variance (PC135.3%; PC227.2%) of the observations. This percentage rises up
to 75.5% when taking into account three components.
However, considering the large number of variables
studied (18), we decided for greater clarity, to plot
factor loadings on a PC1PC2axes plane (Fig. 4a). To
correctly interpret this graph, the factor loadings for
each variable on the unrotated components must be
taken into account, as shown in Table 6. The twelveparameters shown in the greyed boxes of this table
are well represented on the plane under consideration,
either by the first component (cond, Na, K, PIFW,
PIRW, Ptot, UV abs) or by the second (pH, DO, EH,
SS, Chl-a).
A close look at Fig. 4ashows that well correlated
variables with mineral character (Na, K and cond),
contribute to the construction of component 1, as well
as PIFW which is rather characteristic of organic mat-
ter. The observation of data shows that these variables
are linked to allochthonous inputs due to urban pol-lution in lakes 5, 6 and 8. Therefore, the first compo-
nent favours the characterisation of allochthonous in-
puts. The positive values on component 1 correspond
to important inputs, and the negative values to low
inputs.
DO, pH, EH and, to a lesser degree, T, contribute
to the construction of component 2. The positive val-
ues of this component will characterise a colonisation
of phytoplanktonic type. Indeed, in an aquatic envi-
ronment, photosynthesis brings a simultaneous rise in
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Fig. 4. Loadings of the 18 experimental variables (a) and scores of the lakes on the plane defined by principal components 1 and 2
obtained by the 18 experimental variables (b).
pH, DO and EH in the epilimnion, in the conditions
of this study (Fig. 2a and 2b). The negative values
of this component rather characterise a reducing and
acid medium, resulting from macrophytes colonisa-
tion (Fig. 2a), the vegetal cover lowering the water
temperature. Thus, this component characterises thenature of the plants, which colonise the water, and the
intensity of their development.
SS and Chl-a, located next to diagonal XX sepa-
rating the positive values of components 1 and 2, are
characteristic of external inputs with phytoplanktonic
development (simultaneous influence of components
1 and 2 in their positive values). UV abs, PO4-P and
NH4, next to diagonal YY, are characteristic of al-
Table 6
Loadings of the principal components 1 and 2
Variable Component 1 Component 2 Variable Component 1 Component 2
Na 0.918 0.114 NO3-N 0.429 0.289
Cond 0.856 0.165 pH 0.135 0.901
K 0.836 0.145 O2 0.077 0.886
PIFW 0.825 0.132 EH 0.300 0.786
PIRW 0.812 0.407 SS 0.492 0.696
Ptot 0.759 0.139 Chl-a 0.635 0.678
UW abs 0.695 0.518 T 0.189 0.638
NH4 0.522 0.371 PO4-P 0.296 0.611
Mg 0.519 0.495 Ca 0.323 0.530
lochthonous inputs with growth of macrophytes (re-
ducing environment leading to a release of phosphates
and a reduction of nitrate into ammonia). The pres-
ence of macrophytes means a rise in UV abs (Fig. 3b)
and a low temperature value.
3.3.2. Analysis of the lakes with 18 variables
With the same approach as onFig. 4a (build with
18 variables), Fig. 4bshows the scores of each lake
during the period of the study.
In relation to component 1 (characteristic of al-
lochthonous inputs), the position of all lakes is com-
pletely in agreement with observations drawn in the
commented results: low allochthonous inputs for lakes
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306 B. Parinet et al. / Ecological Modelling 178 (2004) 295311
1, 2, 3 and 9 and important for lakes 8, 5 and 6 (lakes
4 and 10 being intermediate).
In relation to component 2 (characteristic of nature
and development of biomass), lakes 6a, 9 and 10, cov-ered with macrophytes, were to be found in the neg-
ative part of this component while lakes 2, 3, 4, 8, 5
and 6b are in the positive part, subject to greater phy-
toplanktonic growth.
The positions of lakes 6a and 6b in relation to com-
ponent 2 confirm the choice of this component for a
characterisation of the nature of the biomass present
in the water. In fact, lake 6a was covered by hyacinths
while lake 6b had been undergoing phytoplanktonic
development after they were removed. The similar po-
sition of lake 6 in relation to component 1 in its two
configurations (6a and 6b) logically justifies that al-lochthonous inputs have changed little between the
periods of study. The type of biomass seems then to
be independent of allochthonous inputs.
Lake 9 is partially covered with lotuses. Its position
on this graph is effectively that of a lake with a low
colonisation by macrophytes.
As for lake 1 with little allochthonous inputs and
little aquatic plant colonisation, it is found at an ex-
pected position on the graph.
To sum up, the lakes that evolve from area 1 to area
2 (arrow 1 onFig. 4b) will be increasingly colonised
Fig. 5. Month by month scores of the lakes 1, 5 and 10.
by phytoplankton as long as allochthonous inputs in-
crease. The lakes evolving from area 3 to area 4 (ar-
row 2 on Fig. 4b) will be increasingly colonised by
floating macrophytes. Rooted macrophytes are foundmainly in the shallow lakes of area 3 for which al-
lochthonous inputs are low, the nutrients being in the
sediments. As for an evolution from area 4 to area 2
(observed for lake 6) and from area 3 to area 1 (not
observed), it depends on the outcome of the competi-
tion between the plants.
For this kind of water, it seems acceptable to say
that the trophic potential increases along component
1. However, it is necessary to make a distinction based
on the kind and the quantity of biomass produced.
Component 2 seems to be a good representation of the
trophic level.
3.3.3. Time patterns analysis
Fig. 5shows the scores of lakes 1, 5 and 10 (month
by month) between October 1996 and April 1998 on
the plane defined by the components 1 and 2.
It is interesting to note that scores for each month
are distributed in particular zones of the plane,
which depend both on the water quality of the lake
and its seasonal evolution. This remark could be
taken into account for good management of water
bodies.
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B. Parinet et al. / Ecological Modelling 178 (2004) 295311 307
For example, the points corresponding to July 1997
and April 1998 appear quite characteristic for each
lake.
Lake 1 for example, is represented by points whichare located in a small area, which means that the qual-
ity of its water depends little on the season, whereas
the points representing lake 5 (which is in an urban
zone), cover a larger area. This indicates that its wa-
ter quality depends on the season and consequently on
the allochthonous inputs.
The points representing lake 10 (covered with lo-
tuses and P. stratiotes) also spread into a larger area
in the zone corresponding to macrophytes.
The months of July 1997 and April 1998 are shown
on the outer extremities of component 1, characteristic
of allochthonous inputs. These results can be easilyinterpreted by taking into account the rainfall shown
onFig. 6.
The month of July 1997 had a low rainfall (29 mm).
It comes at the end of the rainy season, and followed
June, which had a particularly high rainfall (263 mm).
Lake water was diluted by the rainfall of the previ-
ous months, and the soil was too washed for the al-
lochthonous input to be high.
Fig. 6. Rainfall.
The points representing July 1997 for the three lakes
under consideration are located on the lower values
of component 1 (allochthonous inputs component),
which further confirms the preceding hypotheses.On the other hand, for the month of April 1998,
the situation is reversed. This month is at the begin-
ning of the rainy season, and the rainfall brings to the
lakes the organic and mineral matter accumulated dur-
ing the three previous months. In that case, the points
representing the three lakes are on the side of the high
values of component 1.
In fact, this observation applies to all the lakes of
this system, which shows that the allochthonous inputs
essentially linked to rainfall runoff plays a major role
on the lakes behaviour.
To sum up, the allochthonous inputs have a spread-ing effect on the graphic representation while waters
that receive few of these inputs have a condensed rep-
resentation.
This observation could be used to establish a crite-
rion in order to make a seasonal follow up of the qual-
ity of waters. Moreover, the evolution of the shapes of
these graphical surfaces could provide information on
the kind of problems the water under study encoun-
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308 B. Parinet et al. / Ecological Modelling 178 (2004) 295311
Fig. 7. Variance of factor scores for PC1 and PC2 components for the 10 studied lakes.
ters. For example, plotting of the variance of com-
ponents 1 and 2 scores versus lake number (Fig. 7)
could provide a representation of water quality evolu-
tion for each lake during the studied period. Variance
of factor score 1 gives information about the seasonalvariation of allochthonous inputs, while variance of
factor score 2 gives information about biological or
physico-chemical evolution of the lakes. The annual
evolution of the sum of these two values can be use
as a water quality index.
3.3.4. Interpretation through the PCA using a
reduced number of variables
We may observe that some variables are well corre-
lated. Consequently, it seems possible to simplify this
model. Therefore, we propose here to study how therepresentations of variables and lakes evolve when a
more restricted number of variables are taken into ac-
count.
Among the set of variables that strongly con-
tribute to the construction of the two first compo-
nents, we chose to consider the global ones, because
they are more representatives of the whole system.
Their two-by-two correlation include necessarily
the correlation of other variables, which depend on
them.
Four parameters easy to measure were selected: pH
(as an indicator of nature of biomass), conductivity
(as an indicator of external inputs), UV abs and PIRW
(as indicators of dissolved and particular organic mat-
ter). We can notice that total organic carbon (TOC)could be probably used instead of PIRW. Conductiv-
ity and pH contribute respectively to the construction
of component 1 and component 2, UV abs and PIRW
contribute to the construction of both components and
are located in two different half planes of the graph
(Fig. 8a).Although phosphorus and nitrogen are usu-
ally considered as important parameters for this kind
of study, we did not consider them in this small-scale
model of variables. We will explain this choice latter.
Moreover, it has to be noted that the chosen variables
(except to some extend for conductivity) are more de-
pendent on the effects of eutrophication than on the
causes.Fig. 8ashows the position of the four selected
variables loadings on the principal components 1 and
2. It can be noted that the four variables loadings re-
main in unchanged positions compared to the eighteen
initial ones. Therefore, the signification of the compo-
nents remains the same than in the previous case. The
results obtained with four variables (Fig. 8b) show that
the absence of the other variables does not alter the
model (for the studied case).
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B. Parinet et al. / Ecological Modelling 178 (2004) 295311 309
Fig. 8. Loadings of the four selected experimental variables (a) and scores of the 10 lakes on the plane PC1PC2 obtained by the four
selected variables (b).
3.3.5. Extension of the model to other lakes in the
Yamoussoukro area
Five other lakes were studied in the Yamous-
soukro area in order to test the upgradeability of the
model. For lakes in the whole, one (and two for some
lakes) analytical campaigns were conducted (Lhote,
2000).
The Kossou lake (40 km from Yamoussoukro)is a reservoir of very pure water, with no macro-
phytes and very few chlorophyll-a. The Yabra lake
(20 km from Yamoussoukro) is entirely covered withPistia. The Basilique lake (in Yamoussoukro City)
is entirely covered with Echornia crassipes. The
C.F.P. lake (in Yamoussoukro City) is characterised
by an intermediate urban environment with low
chlorophyll-a concentrations (inferior to lakes 3 and
4), but high conductivity and no macrophytes. The
I.N.S.E.T. lake (7 km from Yamoussoukro) was built
on springs and receives wastewater. It contains many
algae.
For this model, the estimated scores (Fig. 9)of the
five additional lakes were computed by multiplying
the mean values of their five normalised variables by
factor score coefficients. As it could be shown, the
five lakes are totally in accordance with the findings
and the summary description made. It can be noted
that Yabra lake and Basilique lake are indeed in a
macrophyte zone and that the I.N.S.E.T. lake, contain-
ing many algae is in an expected position. Although
these 5 lakes are not supplied by the same waters as
the 10 reference lakes, their PCA representation is in
good agreement with their physico-chemical and bi-
ological features. Consequently, the extension of this
methodology to other tropical water seems possible. In
the same way, it is now possible to envisage building
larger PCA models taking into account a great number
of different tropical lakes.
Fig. 9. Extension of the PCA model (with four variables) to other
lakes in the Yamoussoukro area.
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310 B. Parinet et al. / Ecological Modelling 178 (2004) 295311
4. Conclusion
From the study of the behaviour of these lakes,
it is obvious that the feedback effect can be ap-plied to eutrophication processes, but also to other
physico-chemical and biological ones. This feed-
back effect could be extended to every lake in
tropical but also in temperate climates whatever the
kind of biomass that colonises them. When such a
phenomenon appears, the state of equilibrium of the
aquatic medium is modified. Therefore, we observe a
change in every relation linking analytical variables.
By construction, PCA made with correlation coeffi-
cients, takes into account these changes, and become
an easy and appropriate tool for such a description.
Based on an ideal lacustrian tropical system, this
study tried to show that a precise description could be
made. It also showed that it was possible to simplify
the description (without impairing its quality) by the
use of only four simple parameters: conductivity,
pH, permanganate index (in acidic medium) and UV
absorbance (at 254 nm).
It seemed a priori iconoclastic to describe such a
lake system without considering nutrients (nitrogen
and phosphorus) or morphology contributions. Al-
though, values of analytical variables are linked to
both causes and effects of eutrophication, nutrientsare mostly linked to causes and become unpredictable
variables (because of their allochthonous character).
Consequently, it is better to consider only variables
that are mostly linked to effects.
Acknowledgements
The authors thank the UNDP/GEF project IWC/94/
G31 Aquatic weed control in water bodies for im-
proving/restoring biodiversity, for financial support.
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