INTERNATIONAL JOURNAL OF GEOMATICS AND GEOSCIENCES
Volume 2, No 3, 2012
© Copyright 2010 All rights reserved Integrated Publishing services
Research article ISSN 0976 – 4380
Submitted on December 2011 published on February 2012 868
Groundwater quality assessment with two multi-criteria decision making
methods LI Peiyue, WU Jianhua, QIAN Hui
School of Environmental Science and Engineering, Chang’an University
No. 126 Yanta Road, Xi’an, 710054, China [email protected]
ABSTRACT
Groundwater quality is basic for groundwater pollution control and remediation. The study
presented a quality assessment of phreatic water. Twenty samples were collected from the
Yinchuan Plain and ten indices were selected for the comprehensive water quality
assessment. TOPSIS method and osculating value method were applied. The study shows that
the phreatic groundwater in the Yinchuan Plain has been polluted with F-, TH, TDS, SO4
2-
and NO2-. The water should be properly treated before used for drinking. The two methods
are applicable in water quality assessment. The OVM is stricter than the TOPSIS method in
water quality assessment.
Keywords: TOPSIS, entropy weight, osculating value, water quality assessment.
1. Introduction
Groundwater, as an important natural resource, is vital to all lives on earth, especially, to
human beings. As the global population are increasing and the groundwater is becoming
more and more precious. However, with the development of society and economy,
groundwater is under the pressure of being polluted. The groundwater pollution has become
an international issue which attracts international attention. On the 24 August 2011, the
Chinese government has passed the National Groundwater Pollution Control Programs for
the period from 2011to 2020, which has brought a new era for groundwater resources
protection in China.
Groundwater quality assessment is the basis for groundwater pollution control and
remediation. Many scholars around the globe have paid their attention to this field. For
example, Baba and Tayfur (2011) identified the groundwater pollution in Turkey and the
effects of polluted groundwater on human health. Choi and Lee (2011) discussed the natural
attenuation capacity of a petroleum contaminated groundwater at a military facility in Korea.
Hamzaoui-Azaza et al. (2011) conducted a hydrochemical and statistical investigation,
discussed the sources of dissolved ions and assessed the chemical quality of the groundwater
in Zeuss–Koutine aquifer, southeastern Tunisia. Wu et al. (2010) and Li et al. (2010a) carried
out water quality assessments in Jingyuan and Pengyang County, China, respectively. Their
studies showed that the water quality in the two counties was in general good except for some
areas. The water quality in the two regions was influenced by hydrogeological conditions and
anthropogenic activities.
The aims of the present work are 1) to assess the water quality in the Yinchuan Plain with
two different multi-criteria decision making methods and 2) to compare the two multi-criteria
decision making methods. This study is essential for the groundwater pollution identification,
groundwater pollution control and groundwater protection.
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 869
2. Materials and Methods
2.1 Study area
The study area is part of the Yinchuan Plain which is a fault formed basin during the
Quaternary. The Yinchuan Plain is a traditional agricultural region where the second largest
river of China, the Yellow River, runs through the plain along the east border. The Yellow
River water is mainly diverted for irrigation, but domestic water is predominately dependent
on groundwater. It is said that there would have no the plain if there were no water, and this
is true. Water plays an important role in promoting the regional economy and keeping the
society stability. The selected study area is located in the north of the plain (Figure 1).
Figure 1: Location of the study area
2.2 Data collection
Twenty groundwater samples were collected from the phreatic aquifer of the Yinchuan Plain
which is a traditional agricultural farming area. To guarantee the consistency and reliability
of the sample analysis, the standard procedures for sample collection, preservation, and lab
examination recommended by the Standard Examination Methods for Drinking Water were
followed. These samples were analyzed in the laboratory of the Ningxia Institute of Land and
Resources Investigation and Monitoring. For each sample, eighteen indices including
carbonate, bicarbonate, chloride, sulphate, calcium, magnesium, sodium, potassium, pH,
chemical oxygen demand (COD), total dissolved solid (TDS), total hardness (TH), nitrate,
nitrite, ammonia nitrogen (NH4+), fluoride (F
-) and total iron (Tfe) were analyzed and among
them ten major indices (TDS, TH, Cl-, SO4
2-, NO3
-, NO2
-, NH4
+, Tfe, F
- and CODMn) were
selected for the comprehensive water quality assessment.
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 870
2.3 TOPSIS method
TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method is one of
the most popular multiple criteria decision making methods and has been incorporated with
fuzzy theory and many other theories and widely used in various fields. It was first
introduced by Hwang and Yoon (1981). The procedures of TOPSIS in water quality have
been introduced in detail by Li et al. (2011a, b) and they are summarized as follows:
1. Procedure 1: Constructing the initial decision matrix according to the observed water
quality data
2. Procedure 2: Normalizing the initial decision matrix to eliminate the effects of complex
relations
3. Procedure 3: Determining the weight of each index
4. Procedure 4: Determining the positive and negative ideal reference points
5. Procedure 5: Calculating the distances to the positive and negative ideal reference points
using Euclidean distance
6. Procedure 6: Calculating the closeness coefficient (CC) of each sample and performing
the water quality assessment
2.4 Osculating value method
Osculating value method (OVM) is another multiple objective decision making optimization
method which determines the water quality by the osculating values ordering of different
water samples and the quality standards of different ranks. The water quality is determined by
the ordering of the Euclidean distance (E). Li et al. (2010b) have discussed its application to
water quality assessment and the steps are generally similar to the TOPSIS. The steps are
shown in Figure 2.
Figure 2: Flow chart of OVM in water quality assessment
2.5 Determination of Weight
In the present study, information entropy theory was used to determine the weight of each
index. It is calculated as follows (Li et al. 2010b, 2011b):
For a given set of water quality data, the eigenvalue matrix X can be constructed as follows:
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 871
11 12 1
21 22 2
1 2
n
n
m m mn
x x x
x x xX
x x x
=
L
L
M M O M
L
(1)
Where, m is the total numbers of samples, (i=1, 2,…, m). Each sample has n evaluated
parameters (j=1, 2,…, n).
For the efficiency type, the construction function of normalization is:
min
max min
( )
( ) ( )
ij ij
ij
ij ij
x xy
x x
−=
−
(2)
While for the cost type, the construction function of normalization is:
max
max min
( )
( ) ( )
ij ij
ij
ij ij
x xy
x x
−
=
−
(3)
After transform, the standard-grade matrix Y can be obtained and shown below:
11 12 1
21 22 2
1 2
n
n
m m mn
y y y
y y yY
y y y
=
L
L
M M O M
L
(4)
Then the ratio of index value of the j index and in i sample is:
∑=
=
m
i
ijijij yyP1
/ (5)
Because the Pij calculated by formula (5) may get a zero which will be nonsense in the
following calculation. Therefore, a revised form of formula (5) proposed by Zhang and Ren
(2011) was used in the study. They have proved the effectiveness of the modification.
1
( 0.0001) / ( 0.0001)m
ij ij ij
i
P y y=
= + +∑ (6)
The information entropy is expressed by the formula below:
1
1ln
ln
m
j ij ij
i
e P Pm
=
= − ∑ (7)
The smaller the value of ej is, the bigger the effect of j index. Then the entropy weight can be
calculated with the below formula:
1
1
(1 )
j
j n
j
j
e
e
ω
=
−
=
−∑ (8)
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 872
In the formula, ωj is defined as the entropy weight of jth parameter.
3. Results and Discussion
3.1 Hydrochemical characteristics
The statistical analysis results of physiochemical indices are shown in Table 1.
Table 1: Physiochemical Analysis Results of Samples
Items TH TDS Na+ K
+ Mg
2+ Ca
2+ Cl
- SO4
2-
N 20 20 20 20 20 20 20 20
Min 106.1 420 83 1.23 10 26.1 70 55.8
Max 1201.1 3162 618 20.7 194.4 160.3 573.4 1661.4
Mean 584.75 1239.85 205.95 4.52 84.72 96.77 171.63 517.18
SD 85336.02 414215.29 23066.26 22.86 2907.96 1312.08 14862.05 127952.94
SL 450 1000 — — — — 250 250
n 16 11 3 15
Items HCO3- CO3
2- NO3
- NO2
- NH4
+ Tfe F
- CODMn
N 20 20 20 20 20 20 20 20
Min 32.2 9 1 0 0 0.01 0.44 0.45
Max 384.4 64 24.6 0.65 17.8 0.39 25.2 19.1
Mean 267.66 26.2 6.65 0.1 1.06 0.07 3.36 2.42
SD 6537.35 190.69 51.06 0.03 15.81 0.01 28.73 17.19
SL — — 20 0.02 0.2 0.3 1 3
n 2 10 4 1 19 3
Note: N is the total numbers of samples, Min denotes the minimum value of an index, Max
represents the maximum value of an index, Mean is the mean value of an index, SD is the
standard deviation, SL is the maximum acceptable limit of a index in the national standard, n
is the numbers of samples exceeding the acceptable limit of the standard and — denotes there
is no such limit in the standard
The groundwater in the study area is partially polluted. Of the 20 water samples, 19 samples
are with F- exceeding the acceptable limit of the national standard, 16 samples are with
unacceptable TH and 15 with SO42-
. The TDS and NO2- are also beyond the standard limits
significantly. Pollution can also be observed in other indices. The highest concentration of
TH is 1201.1 mg/L and the lowest is 106.1 mg/L. The distributions of TH, TDS, F-, SO4
2- and
NO2- are illustrated in Figures 3 to 7, respectively. It can be seen form the Figure 3 that the
TH increases from south to north. The acceptable concentration of TH in drinking water is
450 mg/L and the figure shows that approximately 2/3 of the study area is polluted with
regard to TH. The Table 1 shows that the maximum of TDS is 3162 mg/L and the minimum
is 420 mg/L with the average of 1239.85 mg/L. The statistical analysis shows that the
groundwater is seriously polluted with respect to TDS. It can also be observed from the
Figure 4 that over half of the study area is high with TDS. The TDS shows a decrease trend
from northeast and southeast to the middle.
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 873
Figure 3: Distribution of TH in the area
Figure 4: Contours of TDS in the study area
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 874
Figure 5: Spatial distribution of F-
Figure 6: Distribution of SO42-
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 875
Figrue 7: Spatial variation of NO2-
High fluoride concentration water is particularly disastrous to human. The acceptable limit of
F- in drinking water is 1.0 mg/L in the national drinking water standard. The statistical
analysis shows that the highest concentration of F- is 25.2 mg/L and the lowest is 0.44 mg/L,
and 19 of the 20 samples exceeded the permissible limit for F−. The F
- concentration (Figure
5) shows an increase trend from the east to the west and over 80% of the whole study area
has been polluted by F-. The SO4
2- and NO2
- pollution are also serious in the study area. It can
be seen from the Figures 6 and 7 that the SO42-
concentration increases from south and north
and from west to east, and the NO2- concentration increases gradually from the surrounding
areas to the middle.
It can be concluded from above analysis that the groundwater in the study area has been
polluted. The groundwater is already not fit for direct human consumption. If the
groundwater is used for drinking, some necessary measures should be taken before water
supply. However, the suitability for irrigation use was not assessed in the paper. Therefore,
further assessment for irrigation purpose is required.
3.2 Water quality assessment
The water quality was assessed with the methods introduced above and the results are shown
in Table 2.
Of the 20 samples, only one sample is good quality water, and most of the water samples are
fair quality which is generally fit for drinking, but before consumption, some necessary
measures should be taken to ensure the indices are all within the acceptable limits. Otherwise,
some human health problems may be caused by the water. Some samples are poor quality and
some are even polluted. These samples are not fit for human drinking. Generally speaking,
Fair quality water is fit for drinking with proper pretreatment, poor quality water can be used
for irrigation and polluted water must be treated before used.
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 876
Table 2: Water Quality Assessment Results
Sample
No. E
Water quality
of OVM
Quality
description CC
Water quality
of TOPSIS
Quality
description
W01 4.64 III Fair 0.86 III Fair
W02 8.95 IV Poor 0.76 IV Poor
W03 7.37 IV Poor 0.79 IV Poor
W04 2.54 III Fair 0.91 III Fair
W05 2.41 III Fair 0.91 III Fair
W06 2.61 III Fair 0.90 III Fair
W07 6.61 IV Poor 0.81 III Fair
W08 6.44 IV Poor 0.81 III Fair
W09 5.89 III Fair 0.82 III Fair
W10 3.30 III Fair 0.88 III Fair
W11 4.04 III Fair 0.86 III Fair
W12 11.91 IV Poor 0.70 IV Poor
W13 3.25 III Fair 0.89 III Fair
W14 18.88 V Polluted 0.57 IV Poor
W15 17.04 IV Poor 0.59 IV Poor
W16 2.88 III Fair 0.89 III Fair
W17 0.67 II Good 0.95 II Good
W18 8.56 IV Fair 0.77 III Fair
W19 6.13 III Fair 0.81 III Fair
W20 11.92 IV Fair 0.70 III Fair
The assessment results by the two methods are a little different. For example, sample W07
and W08 are poor quality waters based on OVM, but are fair quality waters by TOPSIS
method. Sample W14 is polluted water according to OVM, but poor quality water by TOPSIS.
Theses differences show that the OVM is stricter than the TOPSIS method in water quality
assessment. The stricter assessment will ensure the human health but will reduce the total
available volumes of groundwater. Most of the assessment results by the two methods are the
same, which shows that the two methods can both be applied to water quality assessment.
4. Conclusions
OVM and TOPSIS were used for the comprehensive water quality assessment. The following
conclusions are reached.
1. The phreatic groundwater in the Yinchuan Plain has been seriously polluted with
respect to F-, TH, TDS, SO4
2- and NO2
-. Other indices are also high in content. The
comprehensive assessment shows most of the samples are fair quality waters and can
be used for drinking with proper treatment. Other poor quality water can be used for
irrigation and polluted water should be treated before used.
Groundwater quality assessment with two multi-criteria decision making methods
LI Peiyue, WU Jianhua and QIAN Hui
International Journal of Geomatics and Geosciences
Volume 2 Issue 3, 2012 877
2. The two methods (OVM and TOPSIS) are both applicable in water quality
assessment, although their assessment results are a little different. The OVM is
stricter than the TOPSIS method in water quality assessment.
Acknowledgements
The research was supported by the Doctor Postgraduate Technical Project of Chang’an
University (CHD2011ZY025 and CHD2011ZY022), the Special Fund for Basic Scientific
Research of Central Colleges (CHD2011ZY020) and the National Natural Science
Foundation of China (40772160 and 41172212). The anonymous reviewers and the editor are
greatly acknowledged for their useful comments on the paper.
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4. Wu JH, Li PY and Qian H., (2011), Groundwater Quality in Jingyuan County, a
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