MATHEMATICAL MODELLING FOR POLLUTION ASSESSMENT IN AQUATIC ENVIRONMENTS OF MYSORE DISTRICT

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MATHEMATICAL MODELLING FOR POLLUTION ASSESSMENT
IN AQUATIC ENVIRONMENTS OF MYSORE DISTRICT N.S.
VEERESHA KUMAR, SHANKAR P.HOSMANI  Department of
studies in Botany, University of Mysore,
Manasagangotri, Mysore 570 006 India E-mail
veeresh_kanamadugu_at_rediffmail.com
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ABSTRACT.   The importance of PCA as an
appropriate tool for water quality assessment has
been greatly emphasized. This method can be
applied to eutrophication processes and
physico-chemical and biological variables. This
phenomenon modifies the state of equilibrium of
the aquatic medium and therefore a change in
every relation linkage analytical variable
appears. By computation of a principal component
analysis made with correlation coefficient takes
into account these changes and becomes an easy
and appropriate tool for the description of the
lake parameters. A detailed idea of the status of
pollution of any water body is of much importance
because it keeps in proper management of these
waters. The result of the mathematical modelling
for pollution assessment in the two lakes under
study indicates that Chikka Hunsur lake is more
polluted with less diversity and ranges from a
weak eutrophic nature to highly eutrophic nature
occasionally becoming moderately polluted. The
diversity and frequency of plankton often go hand
in hand frequency of diatoms is high while other
groups are less dominant, the dispersion of
organisms is 11 with single groups forming
bloom resulting in pollution. In contrast Santhe
lake is less polluted with more diversity and
ranges from oligotrophic to weak eutrophic
tending to be eutrophic during May when
zooplankton increase in number. The Soyers
frequency index and Bellan Santinis dominance
index are high and the dispersion is only 3
with diatoms dominant. Therefore diversity
indices, which constitute mathematical models,
serve as important tools in pollution assessment
of aquatic environments. Principal component
analysis serves in identifying key toxic
parameters and helps in proper modelling of lake
ecosystems.
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INTRODUCTION   A detailed idea of the status of
pollution of any water body is of much importance
because it intimately keeps in proper management
of these waters. A physico-chemical approach to
monitor water pollution is most common but it
provides a mosaic picture of the environment.
Chemical analysis, although valuable and
necessary, doses not provide all the information
required in pollution assessment. It is not
correlation of contaminants that are concerned
but the effect of these on organisms. In such
processes a key toxic chemical may be over looked
and therefore a precise model applicable to the
water body in study is most essential. In the
present investigation, 2 water bodies have been
selected. Various mathematical models, which are
applicable to the water bodies, have been applied
and the best suitable model is suggested. This
will probably help in understanding the
biodiversity and maintenance of lake ecosystem.
The two water bodies selected for the present
study are Santhe lake and Chikka Hunsur lake.  
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MATERIALS AND METHODS The present study was
carried out in the Santhe lake and Chikka Hunsur
lake of Mysore district located at 12 º - 18 º N.
latitude and 076º - 081º E. longitude. The
physical features and other aspects of the lakes
are described in Table 1. Sampling was done
between January 2004 and December 2004 for 12
months. The samples were taken in 1 litre
plastic bottles. The water samples for plankton
study were preserved by using 10 ml of Lugos
iodine solution and examined under a compound
microscope. The collection, preservation ,
enumeration and identification of plankton were
made as described by Hosmani and Vasanth kumar
(1996). The physico-chemical analysis of the
water was carried out as per the standard
methods APHA (1995) and Trivedy and Goel(1986).
Further PCA was also done. This data provides
brief but precise explanations of the
interrelationship of the various
physico-chemical and biological parameters
analyses. Using PAST statistical software
program, data can be analyzed by multivariate
analysis, PCA biplot obtained.
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RESULTS AND DISCUSSION   The over all
physico-chemical composition of both lakes are
analysed and the major content in Chikka Hunsur
lake is magnesium (38) and chloride (20), where
as magnesium constitutes 60 and chloride is 10
in Santhe lake. Calcium content is same (9) in
both lakes. Nitrate is twice as much in Chikka
Hunsur lake than in Santhe lake. Dissolved oxygen
is 2 and BOD is 1, on the contrary BOD is
negligible and dissloved oxygen is 1.
Chlorophyll-a content is higher in Chikka Hunsur
lake representing higher planktonic numbers in
it. The feature of interest is that in both
lakes, magnesium, calcium and chloride are the
principal components. Iron and phosphate content
seem to play a lesser role in maintaining the
growth of plankton.   Assessment of water
quality has traditionally relied upon the water
quality parameters and the phytoplankton and
zooplankton. Many other studies have used
multivariate techniques such as PCA and weighted
averages to relate water chemistry to planktonic
organisms. Other simpler methods of representing
lake models based on phytoplankton and
zooplankton composition to elucidate the
community structure are Soyers index for
frequency, Bellan and Santinis quantitative
dominance index, Shannon and Weaver diversity
index, Pielous evenness index, Pearsons
correlation matrix, Boyds index and Nygaards
algal index, correlation matrix, hierarchical
cluster analysis and dendrograms also provide
simple methods of lake modelling where abundant
data are available.
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Standard methods have been adopted for the
analysis of physico-chemical parameters. They
include pH, total dissolved solids, dissolved
oxygen, free carbon dioxide, total alkalinity,
carbonates, bicarbonates, total hardness,
calcium, chloride, nitrate, phosphate,
biochemical oxygen demand, magnesium, total
acidity, sodium, iron and chlorophyll-a.
  Phytoplankton and zooplankton were also
determined using standard methods prescribed and
the collection, preservation, identification and
enumeration has been given in detail. The results
of physico-chemical parameters of both the lakes
are presented in (Table-2 and 3). Various models
of diversity indices (mathematical) have been
analysed and the results subjected to statistical
analysis to provide a brief but precise
explanation of the inter-relationships of the
various physico-chemical and biological
parameters. MATHEMATICAL MODELS (DIVERSITY
INDICES) Shannon and Weaver Index for Chikk
Hunsur lake did not show significant differences,
the evenness index reveals that the distribution
of species throughout the year is regular. The
diversity index and evenness index go hand in
hand upto April but further deviate considerably.
The Soyers frequency index indicated that Chikka
Hunsur lake is dominated by diatoms only, 24 of
the total plankton is dominated by diatoms only
while 72 is occupied by all other groups and
overall comparison of diversity indices are shown
in (Table 4).
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Table 4 Comparison of Diversity Indices
Table 4 Comparison of Diversity Indices
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In Santhe lake the evenness of species is also
similar by the species diversity and species
evenness are low. Dominance values of species
also indicate that diatom species are more.The
species richness and species evenness in both
lakes does not differ significantly. The over all
phytoplankton distribution in Chikka Hunsur lake
showed that Bacillariophyceae (35), Cyanophyceae
and Desmidaceae (18) each, Euglenophyceae (15),
Chlorococcales (14). In Santhe lake
Bacillariophyceae (53), Chlorococcales (16),
Desmids (15), Cyanophyceae (11) and
Euglenophyceae (5). The diversity index of Boyd
in Chikka Hunsur lake and Santhe lake indicates
that both the water bodies are moderately
polluted. The relative abundance of
phytoplanktons is high, while the relative
abundance zooplankton varied from a minimum of
24 to 40 in Santhe lake. In Chikka Hunsur lake
the relative abundance of both plankton was high.
  Nygaards index, which utilized the total count
of various algal groups, indicated that Santhe
lake varied from oligotrophic to weak eutrophic
where as Chikka Hunsur lake was eutrophic
throughout the period of study. The Shannon and
Weaver diversity index and Pielous evenness
index for zooplankton showed a great variation in
both lakes, and were maximum during the months of
October. Further the diversity of zooplankton in
Santhe lake is well marked as compared to Chikka
Hunsur lake. ( Fig 1, 2, 3 and 4).
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Another important mathematical model used is the
Pearsons correlation matrix, which leads to the
classification of important clusters in
hierarchy dendrograms can be obtained to
correctly represent the clusters or groups of
parameters. In Santhe lake Bacillariophyceae and
Desmidaceae constitute an important cluster while
Euglenophyceae and Chlorococcales form another
cluster, while the impact of physio-chemical
parameters is less designated in Chikka Hunsur
lake the physico-chemical parameters had a
greater impact on Euglenophyceae.   PCA was
applied to the data to identify the important
taxa related to physico-chemical analysis.
Accordingly, again Bacillriophycae were the most
dominant form in both the lakes. The dendrograms
used as a mathematical model suggests that in
Chikka Hunsur lake there are five important
groups with the linkage between air temperature
and Chlorococcales being the prominent factor,
while in Santhe lake there are 4 groups of which
chloride, bicarbonate and Cyanophyceae are the
prominent factors. And Cyanophyceae and
Chlorococcales are the most prominent groups in
both lakes. Among all the models discussed so far
the CCA/PCA (Canonical Correspondence Analysis)
or Principal Component Analysis) biplot is the
best model. It is possible to interpret the first
important factor and the second factor in turn
relate to biological activity of the lakes. For
interpretation of the biplot the factor loadings
for each variable on the unrotated component are
taken into account. The length of the
environmental line indicates the strength of the
correlation with the ordination axis and its
proximity to the axis indicates the degree of
correlation. The biplot produced is a two
dimensional entity where two components are taken
into account. More than two component plotting
appear over lapping in hyperspace and is
difficult to analyze. (Fig. 4 and 5)
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The overall consideration of the biplot in Chikka
Hunsur lake, taking into account the length of
the variables and their proximity to X and Y
axis, total alkalinity, chlorophyll-a, and carbon
dioxide control the growth of Chlorococcales and
Euglenaceae to a greater extent and lower
quantities of dissolved oxygen, chloride, sodium
and BOD have an impact on Desmids and
Bacillariophyceae considering the monthly values
Bacillariophyceae and Euglenophyceae were
dominant and zooplankton formed a close
coordination with phytoplankton.In Santhe lake
the strength of the co-ordination was high among
carbonates, BOD, chlorophyll-a, towards
Cyanophyceae and Bacillariophyceae phytoplankton
and zooplankton also had a close co-ordination in
Santhe lake also. And PCA biplot of both the
lakes are shown in (Fig. 4 and 5). Among all the
mathematical models studied in this
investigation, the PCA model analysis serves as
an appropriate tool for water quality evaluation.
Other indices or models also support this model
and all the data put together can be useful in
monitoring pollution levels in these waters.
Conclusion Biological indices represent
mathematical models of community changes. Changes
in water quality will affect resident biota, and
indices that reflect these changes in a
particular community are useful indication of
water quality. The importance of PCA as an
appropriate tool for water quality assessment has
been greatly emphasized. This method can be
applied to eutrophication processes and
physico-chemical and biological variables. This
phenomenon modifies the state of equilibrium of
the aquatic medium and therefore a change in
every relation linkage analytical variable
appears. By continuation of a PCA made with
correlation coefficient takes into account these
changes and becomes an easy and appropriate tool
for the description of the lakes.
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The method applied for the present study to the
two lakes (Chikka Hunsur and Santhe lake) shows
that a precise description could be made from a
huge data of variables. It also shows that it is
possible to simplify the description, without
impairing its quality, by using a few important
parameters, out of the 26 variables and a large
list of phytoplankton and zooplankton that
appeared in the lakes. In addition it is also
possible to identify the allo-cathomous or
auto-cathomous origin of variables. The model
enables us to reduce the number of variables in
determining the relation between physico-chemical
and biological parameters in lake ecosystems.
Interpretation of the data although principal
component analysis using reduced number of
variables, choosing global once like pH,
dissolved oxygen, carbon dioxide, phosphate and
nitrate explains that the significance of the
components remains the same and the absence of
one or two variables dose not act as the
model. The result of the mathematical modelling
for pollution assessment in the two lakes under
study indicates that Chikka Hunsur lake is more
polluted with less diversity and ranges from a
weak eutrophic nature to highly eutrophic nature
occasionally becoming moderately polluted. The
diversity and frequency of plankton often go hand
in hand frequency of diatoms is high while other
groups are less dominant, the dispersion of
organisms is 11 with single groups forming bloom
resulting is pollution. In contrast Santhe lake
is less polluted with more diversity and ranges
from oligotrophic to weak eutrophic tending to be
eutrophic during May when zooplankton increase in
number. The frequency index and dominance index
are high and the dispersion is only 3 with
diatoms dominant. Therefore diversity indices,
which constitute mathematical models, serve as
important tools in pollution assessment of
aquatic environments.
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Thanking you