11.application of principal component analysis & multiple regression models in surface water quality assessment

Journal of Environment and Earth Science www.iiste.org
ISSN 2224-3216 (Paper) ISSN 2225-0948 (Online)
Vol 2, No.2, 2012

Application of Principal Component Analysis & Multiple
Regression Models in Surface Water Quality Assessment

Adamu Mustapha1* Ado Abdu2
1. Department of Environmental Science, Faculty of Environmental Studies, Universiti Putra
Malaysia, 43400 UPM Serdang, Selangor, Malaysia.
2. Department of Resources Management & Consumer Studies, Faculty of Human Ecology,
Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.
*E-mail of the corresponding author: amustapha494@gmail.com

Abstract

Principal component analysis (PCA) and multiple linear regressions were applied on the surface water
quality data with the aim of identifying the pollution sources and their contribution toward water quality
variation. Surface water samples were collected from four different sampling points along Jakara River.
Fifteen physico-chemical water quality parameters were selected for analysis: dissolved oxygen (DO),
biochemical oxygen demand (BOD5), chemical oxygen demand (COD), suspended solids (SS), pH,
conductivity, salinity, temperature, nitrogen in the form of ammonia (NH3), turbidity, dissolved solids (DS),
total solids (TS), nitrates (NO3), chloride (Cl) and phosphates (PO43-). PCA was used to investigate the
origin of each water quality parameters and yielded five varimax factors with 83.1% total variance and in
addition PCA identified five latent pollution sources namely: ionic, erosion, domestic, dilution effect and
agricultural run-off. Multiple linear regressions identified the contribution of each variable with significant
value (r 0.970, R2 0.942, p < 0.01).

Keywords: River, Stepwise regression, Varimax factor, Varimax rotation, Water pollution

1. Introduction
With the growth of human populations, commercial and industrial activities, surface water has received
large amount of pollutants from variety of sources (Satheeshkumar, and Anisa, 2011). The quality of surface
water provides significant information about the available resources for supporting life in the ecosystem
(Manikannan et al. 2011). The physical, chemical and biological compositions of surface water is controlled
by many factors such as natural (precipitation, geology of the watershed, climate and topography) and
anthropogenic (domestic, industrial activities and agricultural run-off). Increasing surface water pollution
causes not only deterioration of water quality, but also threatens human health, balance of aquatic
ecosystem, economic development and social prosperity (Milovanovic, 2007). It is imperative to prevent
and control the surface water pollution and to have reliable information on its quality for effective
management (Sing et al. 2005). Characterization of the spatial variation and source apportionment of water

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Vol 2, No.2, 2012
quality parameters can provide an improved understanding of the environmental condition and help policy
makers to establish priorities for sustainable water management (Huang et al. 2010). One of the major
challenges in surface water quality assessment is identifying the sources of pollutants and the contribution
of the parameters/variables in explaining water quality variation. An ever increasing literature on the use of
principal component analysis (PCA) in identifying pollution sources and multiple linear regressions in
estimating the contribution of parameters/variables suggest that the techniques are useful in revealing the
latent pollution sources and it is practical in various types of data (Praveena et al. 2011). PCA provides
information on the most meaningful variables that bring surface water quality variation and allowed the
identification of a reduced number of latent factors/sources of pollution while multiple linear regressions
examine the relationship between single depended variables and a set of independed variables to best
represent relationship in a population.

Several researchers used PCA to identify water quality sources apportionment. For example: Shrestha and
Kazama, (2007); Huang et al. (2010); and Juahir et al. (2011) studied spatial variability of surface water
quality and sources apportionment and classified the studied water bodies into High pollution site (HP),
Moderate pollution site (MP) and Low pollution site (LP). PCA revealed that the pollution levels in the
three zones were mainly influenced by natural sources (temperature and river discharge) and anthropogenic
sources (industrial, municipal and agricultural run-off). Onojake et al. (2011) in their studies, they
discovered that Rivers in Delta State of Nigeria were heavily polluted as a result of industrial discharge and
municipal waste (anthropogenic source of pollution). They used PCA to identify the latent factors that
explain the chemistry of the surface water in which PCA yielded three PC’s with more than 82% variance.
Equally, Hai et al. (2009) studied Taihu lake region in China and discovered that, the surface water in the
region is progressively susceptible to anthropogenic pollution, three PC’s yielded correspond to urban
residential subsistence, livestock farming and farmlands run-off. Similarly, recent study conducted by
Koklu et al. (2010) revealed that, multiple regressions analysis identified important and effective
parameters that contributed to the water quality variation in Melen River system, Turkey.

This study aims at evaluating the surface water pollution sources through PCA and estimating the
contribution of the significant parameters towards water quality variation using multiple linear regressions
model.

2. Materials and Methods

2.1 Study Area
Jakara Basin is located in the northwestern Nigeria and lies in the center of Kano city, the most populous
city in the whole of Nigeria with over five million people. The region has rapid population growth and
industrial development with increase the mass of sewage discharge (Mustapha and Aris, 2011; Mustapha
and Nabegu, 2011). Jakara Basin is located on longitude 8° 31´ E to 8° 45´ and latitude 12°10´ N and 12°
13´ N. The basin is about 30km2 with north-west, south-west orientation sprawling about 0.33°. Jakara

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Vol 2, No.2, 2012
River receives many inputs both anthropogenic and natural in origin that may cause deterioration of the
river water quality. The River runs through Kano city for a length of about 13.5 km. Approximately 27.2
km downstream of Jakara River, a dam has been constructed to supply the rural populace with portable
water, and to aid irrigation agricultural activities. Jakara dam is the fifth largest of the 22 dams in Kano
state, having a total storage capacity of 651,900,000 m3 and a surface area of 16,590,000 m2 (Mustapha and
Aris, 2011)

2.2 Sampling and Analytical Procedures
The sampling network and strategy were designed to cover wide range of determinant at the key sites,
which reasonably represent the surface water quality in the area. Sampling was carried out every day from
31st July to 30th September, 2011 at four different sampling locations along Jakara River. Grab samples
were collected at 30cm below the water level using a water sampler and acid washed container to avoid
unpredicted changes. The samples were immediately transported to the laboratory under low temperature
conditions in ice-boxes and stored in the laboratory at 4° C until analysis.
All samples were analyzed for fifteen physiochemical parameters namely: dissolved oxygen (DO), five-day
biochemical oxygen demand (BOD5), chemical oxygen demand (COD), suspended solids (SS), pH,
conductivity, salinity, temperature, nitrogen in the form of ammonia (NH3), turbidity, dissolved solids (DS),
total solids (TS), nitrates (NO3), chloride (Cl) and phosphates (PO43-). Water temperature, DO, pH,
conductivity, turbidity, TS, DS, SS and NH3 of the water samples were detected using multi-parameters
monitoring instrument (YSI incorporated, Yellow Spring Ohio, USA). BOD5 determination of the water
samples was carried out using the standard method (APHA, 1998). The dissolved oxygen content was
determined before and after the incubation. Sample incubation was for 5 days at 20°C in BOD bottle and
BOD5 was calculated after the incubation period. COD was determined after oxidation of organic matter in
strong tetraoxosulphate VI acid medium by K2Cr2O7 at 148° C with blank titrations. Cl was determined
using 100 mg/l of the water sample which was measured into 250 mg/L conical flask and pH was adjusted
with 1 M NaOH. 1 ml/g of K2Cr2O4 indicator was then added and titrated with AgNO3 solution. A blank
titration was carried out using distilled water. Cl mg/L was then calculated. NO3 and PO43- were determined
using calorimetric method (APHA, 1998).

2.3 Principal Component Analysis (PCA)
PCA is one of the best multivariate statistical techniques for extracting linear relationships among a set of
variables (Simeonov et al. 2003). PCA is a pattern recognition tool that attempt to explain the variance of a
large data set of inter-correlated variables with a smaller set of variables. PCA provides information on the
significant parameters with minimum loss of original information (Singh et al. 2004). The PC’s can be
expressed using the equation below:

Zij = ai1x1 j + ai 2 x 2 j + ..... + aimxmj (1)

Where Z is the component score, a is the component loading, x is the measured value of a variable, i is the
component number, j is the sample number, and m is the total number of variables.

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Vol 2, No.2, 2012
2.4 Multiple Linear Regressions
Multiple linear regressions is a statistical tool for understanding between an outcome variable and several
predictors (independent variables) that best represent the relationship in a population (Koklu et al. 2010).
The technique is used for both predictive and explanatory purposes within experimental and non-
experimental designed. Multiple linear regressions can be expressed using the equation below:

Y = βο + β 1X 1 + β 2 X 2 + ⋅ ⋅ ⋅ ⋅ ⋅ + βmXm + ε (2)

Where Y represent the dependent variable, X 1 ⋅ ⋅ ⋅ ⋅ Xm represent the several independent variables
βο ⋅ ⋅ ⋅ ⋅β m represent the regression coefficient and ε represent the random error.

3. Results and Discussion

3.1 Descriptive Statistics
Table 1 present range, minimum, maximum, mean, standard deviation and variance of the parameters under
study. It is clear that, SS, DS, TS, Cl and conductivity are the dominant parameters with high mean
concentration of 115.90 mg/L, 104.66 mg L, 105.56 mg/L, 566.88 mg/L and 178.71 mg/L respectively. This
showed that, these variables have common source of origin. The mean value of pH ranged from 6.27 to 7.99
mg/L which the average value of 7.99 mg/L which is slightly above neutral level. The concentration of DO,
BOD5, COD ranged from 0.53 to 6.98; 1.00 to 33.00; 20.00 to 154 mg/L which an average value of 2.99,
5.41, and 49.41 mg/L respectively. The order of abundance is COD > BOD5 > DO, showing less
anthropogenic pressure on the surface water.

3.2 Surface water pollution sources apportionment using principal component analysis
The main purpose of PCA is to reduce the contribution of less significant variables to simplify even more of
the data structure coming from PCA. This can be achieved by rotating the axis defined by PCA, according
to well established rules; the new PCs are now called varifactor (VFs). The measure of sampling adequacy
obtained by the Kaiser-Meyer-Olkin method (KMO) was 0.687, indicating that the degree of inter-
correlation among the variables and the appropriateness of PCA analysis was valid. Similarly, the Bartlett
test of sphericity was significant (p < 0.01), confirming that, the variables are not orthogonal, but
correlated. To reduce the overlap of original variables over each PC, a varimax rotation was conducted
(Zhang et al. 2011).
Table 2 summarizes the PCA result after rotation, including the loadings, eigen values, the amount of
variance explained by each VF and the cumulative variance. The results may be complemented by the
examination of the loadings of the five retained components. VF1 explained 37.9% of total variance, had
strong positive loading on salinity, TS, DS, conductivity and Cl and a moderate negative loading on NH3.
This factor group is highly and positively contributed by the variables related to natural factors (erosion)
and refers to as ionic pollution factor group. The existence of lots of ions and their compound led to high
loading of these variables (Zhang et al. 2011). VF2 had strong positive loading of SS and turbidity and
explained 17.5% of total variance. High concentration of suspended solids will increase turbidity level,
besides, the significant positive correlation between SS and turbidity which indicates common source
between the parameters. The association of these variables may have occurred as a result of run-off around

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Vol 2, No.2, 2012
the basin, which may increased the levels of SS and TS.
VF3 had strong loading on BOD5 and COD and explained 12.1% of the total variance. The values of these
parameters were generally higher, since they measure oxygen demand by both biodegradable and non-
biodegradable pollutants. The high value obtained could suggest that a large amount of the product was lost
to the waste stream. VF4 has strong loading on temperature and DO, explaining 8.5% of the total variance.
This factor may be explained by the higher DO value as a result of increase in water volume in the river
(Kamble and Vijay, 2011).
VF5 had strong loading on NO3 and PO43-, and explained 7.1% of the total variance. The higher value of
nutrients in this factor could have been due to surface run-off from the surrounding farmlands that might
have brought ionic substances such as NO3 and PO43- from fertilizer (Boyacioglu and Boyacioglu, 2008).

3.3 Surface water quality prediction using multiple linear regressions model
To find out the best predictor of water quality variation in the Jakara Basin, a stepwise multiple linear
regressions model was used. Before interpreting the result, classical assumptions of linear regressions was
checked: An inspection of normal p-p plot of regression standardized residuals revealed that all the
observed values fall roughly along the straight line indicating that the residuals are from normally
distributed population. Moreover, the scatter plot (standardized predicted values against observed values)
indicated that, the relationship between the dependent variable and the predictors is linear and the residuals
variances are equal or constant.
The water quality variation in the wet season was explained by five predictor variables namely: DO, BOD5,
SS, TS and Cl. The R-square of 0.94.2 revealed that 94.2% of the variation of water quality was explained
by the mentioned five predictors. The estimate of coefficient of the model is presented in table 3. The Beta
coefficient among the parameters calibrated by stepwise regressions analysis, TS makes the strongest
unique contribution in water quality variation (0.668). The Beta value for DO (0.547) was the second
highest, followed by Cl (0.545), BOD5 (-0.491) and the least contributor was SS with -0.292.
The ANOVA table showed that the F-statistics (F = 112.697) was very large and the corresponding p value
is highly significant (p = 0.0001) or lower than the alpha value (0.01). This indicated that, the slope of the
estimated linear regression model is not equal to zero, confirming that, there is linear relationship between
the predictors of the models.

4. Conclusion
In this study, principal component analysis (PCA) and multiple regression models were used to evaluate
Jakara River water quality data sets. PCA yielded five PCs with 83.1% total variance correspond to five
pollution sources namely: ionic, erosion run-off, domestic, dilution and agricultural run-off sources.
Multiple linear regression supported PCA result and identified the contribution of each variable with
significant values r =0.970, R2 0.942. These statistical tools provide more objective interpretation of surface
water quality variables. From the analysis, it is clear that DO, BOD5, SS, TS, DS, Cl, salinity and
conductivity were found to be the most abundance parameters responsible for water pollution in Jakara
River. Therefore, there is need to properly manage wastes in the city and monitor human activities, in order
to ensure minimal negative effects on the rivers.

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Vol 2, No.2, 2012
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Table 1. Descriptive statistics of the parameters under study
Parameters Range Min Max Mean SD Variance
DO 6.45 0.53 6.98 2.99 1.59 2.54
BOD 32.00 1.00 33.00 5.41 6.30 39.70
COD 134.00 20.00 154.00 49.41 24.09 580.35
SS 974.00 7.00 981.00 115.90 198.03 392.64
pH 1.72 6.27 7.99 7.14 0.34 0.12
NH3 9.74 0.15 9.89 3.53 2.02 4.07
Temperature 5.17 27.21 32.38 29.53 1.07 1.14
Conductivity 408.00 309.00 412.00 178.71 115.66 134.00
Salinity 25.33 0.14 25.47 10.27 6.87 47.22
Tur. 842.20 7.80 850.00 108.65 192.11 369.72
DS 242.00 169.00 244.00 104.66 674.80 455.00
TS 241.00 348.00 244.00 105.56 672.86 452.00
NO3 11.00 10.00 21.00 14.73 2.83 8.00
Cl 155.00 40.00 156.00 566.88 366.10 134.00
PO43- 24.00 15.00 39.00 28.32 5.52 30.47

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Vol 2, No.2, 2012

Table 2. Rotated component matrix
Parameters VF1 VF2 VF3 VF4 VF5
Salinity 0.970 -0.036 -0.111 0.141 -0.058
TS 0.968 -0.055 -0.135 0.157 -0.031
DS 0.966 -0.083 -0.133 0.161 -0.029
Conductivity 0.962 -0.032 -0.111 0.176 -0.071
Cl 0.951 -0.114 -0.098 0.095 0.001
NH3 -0.533 -0.368 0.351 0.291 -0.042
SS -0.064 0.971 -0.028 -0.125 -0.086
Turbidity -0.128 0.966 -0.029 -0.135 -0.004
COD -0.189 0.015 0.909 -0.004 -0.028
BOD5 -0.21 -0.086 0.871 0.056 -0.079
Temperature 0.219 -0.017 0.309 0.801 -0.016
DO 0.288 -0.136 0.075 0.637 -0.005
pH 0.001 -0.146 -0.249 0.630 -0.054
NO3 -0.075 -0.060 -0.037 0.079 0.884
PO43- -0.020 -0.013 -0.058 -0.188 0.846
Eigen Value 5.7 2.6 1.8 1.3 1.1
Variance (%) 37.9 17.5 12.1 8.5 7.1
*CV (%) 37.9 55.4 67.5 76 83.1
*CV = Cumulative variance
Table 3. Estimates of coefficients of the multiple linear model
Beta Beta
Unstandardized Std. Error standardized
Coeffient coefficient t-value p-value
(Constant) 40.689 7.211 5.642 0.000
DO 23.952 2.058 0.547 11.639 0.000
BOD5 -17.866 1.654 -0.491 -10.805 0.000
SS -5.825 0.953 -0.292 -6.11 0.000
TS 16.979 5.225 0.668 3.25 0.003
Cl -10.995 4.078 -0.545 -2.696 0.011
2 2
Note: R = 0.970; R = 0.942; Adj. R = 0.933

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