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Multi-Rectangular Diagram Concept in Groundwater
Quality Assessment and Application in Pakistan
Zekai Sen a & Niaz Ahmad b
a Istanbul Technical University , Maslak, Istanbul, Turkey
b Pakistan Institute of Nuclear Science and Technology , P.O. Nilore, Islamabad, Pakistan
Published online: 22 Jan 2009.
To cite this article: Zekai Sen & Niaz Ahmad (2002) Multi-Rectangular Diagram Concept in Groundwater Quality Assessment
and Application in Pakistan, Water International, 27:2, 271-278, DOI: 10.1080/02508060208687001
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International Water Resources Association
Water International, Volume 27, Number 2, Pages 271–278, June 2002
Multi-Rectangular Diagram Concept in Groundwater
Quality Assessment and Application in Pakistan
Zekai Sen, Istanbul Technical University, Maslak, Istanbul, Turkey, and Niaz Ahmad,
Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Islamabad, Pakistan
Abstract: The concept of multi-rectangular diagrams (MRD) is introduced to replace many clas-
sical and triangular coordinates (Piper diagrams) to examine the multi-variate association of chemi-
cal constituents present in groundwater. MRD eliminates the drawbacks of classical trilinear dia-
grams effectively. Comparison between MRD and the classical trilinear diagram is presented. MRD
is used for the assessment of groundwater quality in Chaj Doab area of Pakistan. The differentiated
dominant groundwater types in the study area are sodium bicarbonate, calcium bicarbonate and
sodium sulfate. Sodium bicarbonate is the most abundant type of groundwater in the central part of
the study area.
Keywords: Groundwater, quality, hydrochemistry, multi-rectangular diagram, Pakistan, linear
diagram.
Introduction
applications, and the most commonly used diagram is the
Groundwater quality is equally important as quantity trilinear scatter of groundwater samples on the basis of
in any region for water resources planning, operation, and three cations and three anions.
management. If necessary protections are not taken, ground-
In this paper a new method of multi-rectangular dia-
water quality may deteriorate because of salt-water intru- gram (MRD) is developed for the quantification of ground-
sion, urban development, and waste disposals. water quality in general. This method eliminates the
Measurements of groundwater chemical qualities require drawbacks present in the use of classical trilinear diagrams.
standard methods for reporting combined results of vari- The new methodology is tested in the Chaj Doab area of
ous constituents of water analysis. The kinds and concen- Pakistan for the evaluation of groundwater quality charac-
trations of constituents depend upon the environment, teristics (Ahmad, 1998).
groundwater movement, and the groundwater source. Be-
cause of greater exposure to soluble materials in geologic
Historical Data and Description
strata, higher proportions of dissolved constituents are found
of Chemical Diagrams
in groundwater than surface waters. In Quaternary eolian
sands and alluvial areas, the quality of infiltrating surface
There are a number of chemical variables, which de-
areas may have a significant effect on the groundwater fine together the overall worth of water from the stand-
quality. Regional groundwater quality variations appear de- point of its use. Therefore, the joint presentation of
pending on the hydrologic, geomorphologic, and especially multivariate chemical associations has been a problem for
lithologic (geologic) features over an area. It is, therefore, a long time. Researchers have been trying to represent the
necessary to have groundwater samples at different loca- combined effect of major constituents responsible for
tions within study area for the appreciation of regional varia- groundwater quality on a single diagram. In this pursuit,
tions. This provides an opportunity to obtain regional quality Hill (1940) succeeded for the first time in transforming the
variation maps and efficient sampling of the regional vari- above idea into a practical form by making the use of
abilities. Monitoring of groundwater quality over time at triangular coordinates. Piper (1944) further refined this
different locations gives a dynamic basis for quality opera- work and introduced an explicit form of triangular coordi-
tion and management studies. However, in practice, most nates, which are known as Piper diagrams. Trilinear dia-
often collective assessments of different water samples on grams by Piper (1944) have two separate sets of triangular
an ionic basis serve as guidance for the appreciation of coordinates for anions and cations, respectively. Water
groundwater quality classifications in the area. Such classi- samples are plotted as percentages of total anion or cation
fications have been achieved in the past through bar, pie, concentrations in milliequivalents. The projection of points
and trilinear (Piper) diagrams at various levels of complex- in the two triangulars on a rhomboid area indicates the
ity in addition to statistical, relative-frequency diagrams. type of water classification. This diagram is convenient
Each one of these procedures has limitations in practical for the representation of widely divergent water types.
271

272
Z. Sen and Z. Ahmad
However, some obscured clusters may appear in the case same ion, probability distribution of ions within given con-
of closely related waters. In order to avoid some of the centration bands, assessment of the mean ion concentra-
drawbacks in a trilinear diagram several modifications are tion as an overall representative value of the concentration,
proposed by Hem (1970), Matthess (1973), Schneider and suitability of data for linear regression analyses ac-
(1973), and Sen and Dakheel (1986).
cording to a normal distribution pattern.
The ion ratios procedure developed by Schoeller (1962)
is known as a logarithmic diagram. Here, the ions are iden-
tified by vertical equidistant lines, and the respective con-
centrations are plotted on a logarithmic scale. In
precomputer days, this procedure provided a distinct ad-
Regional Topographic Description
of the Study Area
Pakistan is a country with a multitude of physiographic
vantage. There are also mixing diagrams that are conve- features such as sea, deserts, plains, plateaus, and moun-
nient tools for the investigation of mixing relationships. tains. Physiographically, Pakistan can be divided into North-
However, only constituents that are not prone to ion ex- ern Mountains, Western Mountains, Salt Range, Potwar
change or to reduction-oxidation should be used in this Plateau, and Indus Plains as shown in Figure 1. The North-
procedure. Taussing (1961; 1976) provided a procedure ern mountains have complicated and wonderful orographic
under the name of natural classification of waters that and geologic features distinguished on the surface of the
combines equivalent concentrations of ion pairs in a fixed earth. The highest peaks of the world are found in these
sequence. Only six major groups can be defined in this mountains. They can be further categorized into as
way. This diagram makes it easy to identify significant Siwaliks, Lesser Himalayas, Greater Himalayas, and
changes along the flow path of the water.
Trans-Himalayas. The Siwaliks represent the outer most
The horizontal pattern diagram by Stiff (1951) is use- Himalayas and are recognized as fore-deep furrow de-
ful for the representation of hydrochemical data on maps posits. This feature is found along whole length of the
and in cross section. The frequency concentration dia- Himalayas starting from north west of Pakistan across
grams provide relationships that can be depicted in the the Indus River and ending in Assam (India) covering about
form of ion concentration changing with frequency or rela- 2,600 kilometers in length. The maximum height of these
tive frequency (Sen and Dakheel, 1986). They are useful mountains is 1,000 m. The Lesser Himalayas lie in the
in obtaining information such as different sources for the north and are parallel to Siwaliks. The average height of
Figure 1. Physiographic features of Pakistan.
IWRA, Water International, Volume 27, Number 2, June 2002

Multi-Rectangular Diagram Concept in Groundwater Quality
Assessment and Application in Pakistan
273
these mountains is 3,000 m and the width ranges from 65
Classical Trilinear Diagram
to 80 km. Pir Punjal is the famous mountain range in the
Lesser Himalyas. The Greater Himalayas, which are also
called the Central Himalayas, lie north and parallel to the
Lesser Himalayas and have an average height of 4,500 m.
Nanga Parbat is the highest peak (8,000 m) in these moun-
tains. The upper ranges of these mountains are covered
with snow throughout the year. The Trans-Himalayas lie
to the north of the Greater Himalayas and include the great
mountain ranges of Kara Korum, Aling Kangri, Kailas,
and Ladakh. The average height of these mountains is
6,000 m, and the world’s highest peaks – Mount Everest
(8,717 m) located in Nepal and K2 peak (8,489 m) situ-
ated in Pakistan are also found in these mountains. These
mountains are permanently covered with snow.
Piper diagrams permit a classification of analysis, ac-
cording to twelve geochemical families and a visualization
of physical-chemical evolutions in water from a group of
data. The twelve groups are indicated in Figure 2 as A1,
A2, A , and A for anions; C1, C , C , and C for cations;
and fi3nally as4I, II, III, and IV in2the3combin4ation region.
Piper triangles allow identification of the chemical char-
acterization of the water families from different geographic
origins
Piper diagrams have the benefits of being the first
diagrams available in literature that provide qualitative
multivariable inter-relationships and are universally used
for groundwater quality assessments (Hiscock et al., 1996).
As far as individual anions and cations are concerned, it
gives significant information about their dominance and
non-dominance, but it has drawbacks when the cations
and anions are transferred to rhombohydral rectangle to
evaluate their combined effects. Some of these shortcom-
ings are already pointed out by Sen and Al-Dakheel (1986),
and are mentioned here:
The Western Mountains include the Hindu Kush, Safed
Koh, Sulaiman, and Kirthar ranges. In the northwest, Hindu
Kush separates the boundary of Pakistan and Afghani-
stan. These mountains are covered with snow during win-
ter only. Safed Koh lies in the south of Hindu Kush and
merges with Sulaiman Range. The Kirthar range is found
to the south of the Sulaiman range.
The Salt Range Mountains are conspicuous features
in the northwestern part of Himalayas. These are flat-
topped mountains having elevations up to 660 m on aver-
age. These are abruptly rising from the Punjab plains and
start from Jhelum with a continuous stretch towards west.
The Salt Range bends to the south after crossing the Indus
River and extends to the districts of Bannu and Dera Ismail
Khan.
• Only three cations and anions can be represented by
Piper diagram and the remaining ones are reduced by
joining them to the nearest chemical partner, such as
Na and K are taken together as one variable. Among
anions, CO3 is lumped with HCO3, and F and NO3
with Cl. Therefore, the individual effect of the cations
and anions is depressed.
• Water samples showing different water chemistry in
the base triangles may plot as a single point when pro-
jected to rhombic rectangle. For example in Figure 2,
Points 1 and 2 shown in the diagram possess obviously
different water chemistry but in the rhombic rectangle
they overlap each other, and it is not possible to distin-
guish them as representing different groundwater quali-
ties.
The Potwar Plateau, where the capital of Pakistan,
Islamabad, is located, is a highly eroded and dissected land
area. It is located north of Salt Range and south of
Rawalpindi hills. It has a length of about 240 km and width
of 100 km with an average elevation of 500 m.
The Indus Plains constitute the area stretching from
south of the Himalayas and Salt Range to the Arabian
Sea. These plains cover an area of 20,000 km2 which is a
fertile land supporting the agriculture existence of the coun-
try. They have north-south length about 1,100 km with
variable width from 200 to 80 km.
The study area is sandwiched between the rivers
Jhelum and Chenab in the northeastern part of Pakistan,
and is locally called Chaj Doab. The word “Chaj” is de-
rived from the very names of the rivers of the area and
“Doab” means area between two waters. The Chaj Doab
area is a part of the Punjab plains and lies between longi-
tudes 74°30’E and 72°10’E and latitudes 31°N and 33°N.
The present study concentrates particularly on a part of
the Chaj Doab area that is bounded between the rivers
Jhelum and Chenab and the Upper Jhelum and Lower
Jhelum canals, which is administratively a part of the Gujrat
district. Generally, all of the Chaj Doab is the target of the
present study.
Figure 2. Well locations in Chaj Doab study area.
IWRA, Water International, Volume 27, Number 2, June 2002

274
Z. Sen and Z. Ahmad
Besides these drawbacks, another significant point that
must be taken into consideration in the trilinear diagram
interpretation in the projection area is that only the lower
portion marked as I, corresponding to the NaHCO type
of water, shows water quality without any confusion.3How-
ever, all of the other points may have a mixture of ground-
water quality. Another limitation of Piper diagrams observed
during the course of the present study is that if the data
points are large enough, the utility of trilinear diagrams
becomes rather vague because differentiation between dif-
ferent category waters is not very efficient, as most of the
points in cation and anion triangles and the rhombohydral
field occupy the same places. Therefore, their individual
effects are masked.
Chemical analyses of groundwater from about 800
well locations as shown in Figure 3 are plotted on Piper
diagram in Figure 4. The anion triangle shows that the
Figure 4. Chaj Doab Piper diagram scatter.
waters of most of the wells fall in the HCO3 dominant IV in the rhombic part of Piper diagram do not give clear
region, only a few of them are dominant in SO , and oth- classification as these zones hold the combined effect of
ers occur in the mixed region of the triangle.4Thus, the both mixed and dominant regions from the cation and an-
waters of the area are dominant in bicarbonates as far as ion base triangles. However, there are also a large num-
anions are concerned.
ber of points lying in this ambiguous part of the rhombic
In the cation triangle, the waters of the area are domi- rectangle. Therefore, Piper diagrams reveal partial infor-
nant in Na content, only a few of the wells are dominant in mation about the water qualities of the study area, and we
Ca content, and a substantial number of the wells lie in are left with difficulties in differentiating among prevalent
mixed zone. An important point to note here is that the water qualities in the area.
mixed zone of cation triangle carries significantly higher
number of chemical analyses as compared to that of anion
Modern Multi-rectangular Diagrams
In order to overcome the difficulties of classical dia-
triangle. This means that the same dominant anion is shared
by more than one non-dominant cations to maintain chemi-
cal equilibrium. Having a look at the rhombic rectangle grams in the interpretation of groundwater quality data,
where the points from the base triangles have been trans- another scheme is developed and proposed here which
ferred, the NaHCO3 type waters can be quickly picked not only presents the information about the cations and
up as shown by subzone I in the rhombohydral rectangle. anions separately, but also gives very clear hydrochemical
Therefore, the NaHCO type of groundwater is identified facies classifications. Hydrogeochemical processes active
as the dominant one in3the study area. Zones II, III, and in shaping the chemistry of groundwater can also be de-
termined from this new methodology. The procedure is
very simple in comparison to Piper diagrams. The new
diagram is called a Multi-Rectangular Diagram (MRD)
and is shown in Figure 5. All the major cations (Ca, Mg,
Na, K) are plotted on horizontal axis, and the major anions
(HCO , CO , SO4, Cl) are drawn on vertical axis. Each of
the ax3es is 3further divided into three adjacent and non-
III
overlapping minor axes, and each one of these minor axes
represents the respective cation and anion pairs completely.
II
IV
Although in accordance with the classical trilinear diagram
three – cations or anions are considered on the corre-
sponding axes – there is no restriction for increasing the
minor axis number in MRD. In fact, the number of minor
axes may be thought of as equal to the number of relevant
and significant anions or cations or any groundwater qual-
ity variable such as pH, TDS, EC, etc. Again in this scheme,
milliequivalent per liter percentages of total cations and
anions are each considered as 100 percent as they are in
the Piper diagram. From each chemical analysis of a
groundwater sample, the highest cation and anion are
I
A3
C3
C1
2
1
A1
1
C2
A4
2
C4
A2
Ca
Cl
Figure 3. Piper trilinear diagram.
IWRA, Water International, Volume 27, Number 2, June 2002

Multi-Rectangular Diagram Concept in Groundwater Quality
Assessment and Application in Pakistan
275
picked up and then plotted as a point in the respective ters, hydrochemical facies maps can be prepared which
field. This newly developed MRD procedure eliminates show prevalent types of waters in the study area.
the shortcomings of the Piper trilinear diagrams. The loss Hydrogeochemical processes shaping the chemistry of
of information occurs when cation and anion pairs from groundwater during its flow can also be inferred from the
the base triangles as proposed by Piper are projected to present diagram to some extent.
rectangular field. In both of these presentations, one can-
It is also possible to say something about the history
not easily distinguish the projected rectangle between domi- of groundwater from the present diagram. For example,
nant and non-dominant types of groundwater quality waters falling in Square A (see Figure 5) are indicative of
because the same area in the rectangle is occupied by the freshwaters in recharge areas where considerable move-
mixed and dominant cations and anions. However, in the ment of water has not taken place. The Sub-area A2 shows
newly proposed diagram, initially plotted points are not that ion exchange has occurred in which Ca in the water
further projected to any new field. The diagram is divided has been replaced most probably by Na from the sedi-
into nine major square fields and each major field is fur- ments/rocks through which water has moved. Sub-area
ther divided into four sub-areas in order to decide about A3 gives the indication of calcite dissolution. Occurrence
dominance or nondominance of cations and anions (see of waters in Sub-area A is not common but may be pos-
Figure 5). On the whole, the diagram carries 36 sub-areas sible in coastal areas whe4 re more saline seawater intrudes
and each sub-area delivers complete information about the fresh aquifers and a reverse ion exchange process takes
the respective cation and anion pair which falls in that place in which Ca in the solution increases at the cost of
area. Twelve sub-areas are available for each cation and Na. If the chemical ionic pair falls in square D, the dissolu-
anion, respectively. For further explanation, let us describe tion of dolomite minerals is expected. Again the four sub-
one major rectangle in our diagram. The first sub-area in areas in D show the extent to which dolomite minerals
each major rectangle shows that both the cation and anion have been dissolved. Square G is very important because
are the non-dominant type as shown in Figure 5. If the in the sedimentary areas of the world, the waters are of
point lies in the second sub-area, then anion is the domi- NaHCO3 type. Na enters the groundwater system by ion
nant one, but cation is non-dominant. The third sub-area exchange process with Ca and dissolution of halite mineral
shows the dominance of both cation and anion, while the (NaCl) (Freeze and Cherry, 1979; Mandel and Shiftan,
fourth sub-area is indicative of the dominance of cation, 1981). If the waters lie in this square (G) then there is a
and the non-dominance of anion. Therefore, the first, sec- strong indication of ion exchange and dissolution geochemi-
ond, and fourth sub-areas give a mixed type of water, and cal processes. Squares H and I favor dissolution of gyp-
the third sub-area in each major square shows the domi- sum and halite as the water gets older along its flow path.
nant type of water. After this clear classification of wa- The interpretation of the processes in the remaining rect-
angles is left for future user of these diagrams because in
the present study area waters fall only in the aforemen-
100
tioned squares, namely, A, D, G, and H, only. Chemical
analyses from the study area are plotted on MRD as shown
F3
C2
C3
I3
F2
I2
in Figure 6.
50
100
50
F
The squares in which points fall in MRD are A, D, G,
C
I
and H, which represent Ca (HCO3)2, Mg (HCO )2,
NaHCO3, and Na SO4 water types, respectively. Out3 of
800 samples, the 2percentage falling in squares A, D, G,
and H is 19, 9, 68, and 4, respectively. In each square
mentioned above the behavior of each cation and anion
can be depicted explicitly. Square A holds the water
samples dominant in Ca (HCO )2. The HCO3 content in
Square A lies completely in the 3dominant area while only
a few of the samples are dominant in Ca cation. On the
whole, in Square A, a minor proportion of samples show
Ca (HCO3) dominant types of water. Area A2 of Square
A gives the2information that HCO is also combining with
some other cations present in th3e water in the form of
chemical compounds. HCO3 in Square A increases rap-
idly then attains a constant value with the increase of Ca.
This shows that Ca is not only entering the groundwater
system by the dissolution of calcite but also from some
other source, most probably dissolution of gypsum. Square
D is representative of Mg (HCO3)2 type of waters and
C1
B2
C4
B3
I1
F1
F4
I4
E3
E2
H3
H2
H
B
E
B4
B1
H1
H4
G3
E1
E4
100
50
D3
A2
G2
A3
D2
G
D
A
A4
D4
D1
A1
G4
G1
0
0
50
100
0
50
100
0
50
Mg ( meq / l % )
100
Na ( meq / l % )
Ca ( meq / l % )
Figure 5. Innovative multi-rectangular diagram.
IWRA, Water International, Volume 27, Number 2, June 2002

276
Z. Sen and Z. Ahmad
100
in the study area. The points in Square D show dissolution
F3
C2
C3
I3
of dolomite minerals as the water moves away from re-
charge areas. The wells having their chemistry in square
G lie towards the center of the study area away from the
recharge areas. As the water gets older along its flow
path, the Na gets dominance over Ca by ion-exchange
process. In square G, the decrease in HCO3 with increase
of Na shows that HCO3 is disappearing from the ground-
water system in the form of calcite precipitation where
the equilibrium conditions favor this process. The possibil-
ity of calcite precipitation is confirmed as CaCO nodules
(locally called kankers) of secondary origin associ3ated with
clay horizons are found in the study area as stated by
Kidwai (1963). The points in Square H are indicative that
the dissolution of gypsum has taken place and Na has come
by ion-exchange with Ca. Finally, one reaches the conclu-
sion with the help of MRD that three major hydro-
geochemical processes that are active in the study area
are dissolution, ion-exchange, and precipitation.
F2
I2
50
100
50
F
C
I
C1
B2
C4
B3
I1
F1
F4
I4
E3
E2
H3
H2
B
H
G
E
B4
B1
H1
H4
G3
E1
E4
100
50
D3
A2
G2
A3
D2
D
A
A4
D4
D1
A1
G4
G1
0
0
50
100
0
50
100
0
Among other benefits, MRD can be effectively used
for the construction of hydrochemical facies maps which
otherwise are difficult with classical trilinear diagrams.
Dominant types of water quality can be quickly picked up
50
Mg ( meq / l % )
100
Na ( meq / l % )
Ca ( meq / l % )
Figure 6. Chaj Doab area multi-rectangular diagram.
carries approximately all the samples in Sub-area D2 show- from MRD. Here, dominant type means cations and an-
ing the dominance of HCO3 ion and non-dominance of ions both at more than 50 percent value. With this rule, the
Mg cation with an overall increasing trend. This increas- three dominant water qualities of a Ca (HCO3)2, NaHCO ,
ing trend shows that Mg is entering the groundwater by and Na2SO4 can be distinguished using MRD in the stud3y
the dissolution of dolomite minerals. Square G is carrying area. Others are considered as mixed quality waters.
the majority of water samples and indicates that the wa-
ters of the study area are abundant in NaHCO type. Major
part of these samples in square G lies in sub-a3rea G3 show-
Hydrochemical Facies
ing the abundance of these samples in Na and HCO ions.
The term facies is widely used in geology where it
There is a decreasing trend of HCO3 with the incre3ase of represents slight differences in the character of rocks
Na ion in square G. Only 4 percent of the samples are within a formation. These differences originate due to a
plotted in Square H which shows that these waters are of multitude of depositional environments under which geo-
Na SO4 type. Out of these four percent samples, only few logic formations evolve. Hydrochemical facies is used to
rea2ch the dominant zone H3 while others are either domi- denote the differences in groundwater spatial quality. Gen-
nant in Na or SO ions only. The presence of these points erally, the hydrochemical processes do not occur within
in rectangle H s4hows that gypsum minerals have been sharp boundaries rather they owe inherent transition char-
dissolved by flowing groundwater in the study area.
acter within a particular area. For example, groundwater
The hydrogeochemical history of groundwater in the moves from areas of higher to lower hydraulic gradients.
study area can be assessed with a certain degree of accu- Normally, these are the recharge areas. During
racy with the help of MRD. The wells, which have their groundewater movement, different processes such as so-
chemical analyses lying in Squares A and D of MRD are lution, precipitation, ion exchange, adsorption etc., occur
those from recharge areas. These wells fall in the vicinity according to availability of minerals and equilibrium condi-
of the Jhelum and Chenab Rivers from which recharge tions. Therefore, along the way, groundwater chemistry
takes place. In square A, the initial increase of HCO and does not change abruptly until and unless it meets rocks
constancy in Ca ion show the occurrence of calcite d3isso- with entirely different character. On the other hand, one
lution, and Ca is disappearing by ion-exchange with Na can say groundwater facies are susceptible to geologic
such that HCO3 is shared with both Ca and Na cations. It facies to some extent. The geologic unit in the present
can also be noticed that points reaching sub-area A show study area is mainly composed of alluvium deposited by
an increase in Ca but a constant value of HCO . It 3can be ancient rivers. The chemical content of the sediments is
inferred that Ca is also entering the groundwa3ter system disseminated, although in a heterogeneous way, but it also
other than dissolution of calcite, most probably by the dis- maintains overall symmetry in the area. Therefore, transi-
solution of gypsum minerals, and the presence of points in tion characters in hydrochemical facies are expected to
Square H is the confirmation of gypsum mineral presence occur.
IWRA, Water International, Volume 27, Number 2, June 2002

Multi-Rectangular Diagram Concept in Groundwater Quality
Assessment and Application in Pakistan
277
In the modern age, human activities such as irrigation
The area dominated by Mg (HCO3) is sandwiched
and industrial waste disposal practices have given great between areas abundant in Ca and Na bica2rbonate ground-
impetus to concomitant changes in natural hydrochemical water types. Groundwater identified as Na2 SO4 covers an
facies. In the study area, agriculture has been the main area adjacent to the Upper Jhelum canal. Among other
human activity since ancient times. In the present century, methods used for the differentiation of hydrochemical fa-
the setup of canal networks for irrigation supplies and the cies, MRD is found the most flexible and appropriate. This
frequent use of fertilizers to increase the agriculture prod- diagram sorts out very clearly the status of each and ev-
ucts are the major human reasons affecting the ground- ery cation and anion in the form of its dominance or non-
water chemical facies in Chaj Doab area.
dominance. Here, dominant cation or anion means with
Delineation of hydrochemical facies in groundwater concentration (meq/l) more than 50 percent. Therefore,
quality studies is the major task that provides guidelines in with the help of MRD dominant anions and cations are
future planing and management of groundwater resources. singled out and their maps are constructed as shown in
Different methods such as categorical regional variation, Figures 6 and 7, respectively. According to these figures,
trilinear diagrams, and MRD diagrams are used to differ- HCO3 and SO4 are the two anions that are found at more
entiate the prevalent groundwater chemical facies. First than 50 percent in the groundwater of the area. Bicarbon-
of all, simple facies are evaluated by selecting the highest ate approximately covers the whole study area except in a
value cation and anion among respective cations and an- very small area in the vicinity of the Upper Jhelum canal
ions in each chemical analysis. For example, in a chemical where SO maintains its dominance. Among cations, Na
analysis of groundwater sample if HCO and Ca have the and Ca ar4e the dominant cations found in the area and
highest concentration values, this sampl3e is referred to as some regions devoid of any dominant type.
Ca (HCO3) type. All the analyses are sorted out in the
Na occupies the central part, which is more than half
similar way2, and finally a map is prepared that displays the of the total study area, while Ca remains dominant in SSW
simple hydrochemical facies as given in Figure 7. This in a strip adjacent to the Chenab River. In the remaining
figure identifies four different quality waters which are area, one finds mixed groundwater in cations having con-
NaHCO , Mg (HCO3) , Ca (HCO3)2, and Na SO . Among centration less than 50 percent. From this interpretation, it
these, N3aHCO3 is the2abundant water type 2that2occupies is not necessary that groundwater dominant in a particular
the central part of the area. Ca (HCO3)2 occurs in the anion will also be dominant in some cation, the above fig-
area adjoining rivers Chenab and Jhelum, but it covers a ures display some regions where anions are found domi-
larger area near the Chenab River in comparison to the nant without any cation dominance. This shows that cations
Jhelum River.
are more susceptible to any kind of changes, and their
concentrations are highly variable as compared to anions.
Figure 7. Hydrochemical facies of the study area.
IWRA, Water International, Volume 27, Number 2, June 2002

278
Z. Sen and Z. Ahmad
Conclusions
Mutual interpretation of a number of interactive chemi-
He has written a book published in 1995 by CRC Lewis
Publishers which entitled “Applied Hydrogeology for Sci-
entists and Engineers.”
cal species present in groundwater has been a difficult
task. The earlier workers to achieve this purpose used a
combination of triangular coordinates. In this paper, the
concept of triangular coordinates is modified to multi-rect-
angular diagram (MRD). It is developed to evaluate the
multivariate association of chemical constituents analyzed
in groundwater quality studies. Shortcomings of classical
Piper diagrams are remedied by MRD. This newly devel-
oped diagram is applied for hydrochemical studies of a
part of Chaj Doab area in Pakistan. HCO and SO are
the two anions that are found at more than350 perce4nt in
the groundwater of the area.
Niaz Ahmad is with the Pakistan Institute of Nuclear
Science and Technology, P.O. Nilore, Islamabad, Pakistan.
Discussions open until December 1, 2002.
References
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Among the four different quality waters, NaHCO is
the most abundant water type that occupies central mid3dle
part of the area. Ca (HCO3) occurs in the area adjoining
the Chenab and Jhelum Riv2ers but it covers a larger area
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About the Authors
Dr. Zekai Sen is with the faculty of Civil Engineer-
ing, Hydraulics and Water Power Department at the
Istanbul Technical University in Maslak, Istanbul, Turkey.
Email: zsen@itu.edu.tr. He obtained a B.Sc. and M.Sc.
degrees from the Technical University of Istanbul, Civil
Engineering Faculty, Department of Reinforced Concrete
in 1972. Further postgraduate studies were carried out at
the University of London, Imperial College of Science and
Technology, and Dr. Sen was granted a Diploma of Impe-
rial College (DIC) in 1992, M.Sc. in Engineering Hydrol-
ogy in 1972 and Ph.D in stochastic hydrology in 1974.
Dr. Sen has worked in several different countries and in
different faculties such as the faculty of Earth Sciences,
Hydrogeology Department; Faculty of Astronautics and
Aeronautics, Meteorology Department. His main inter-
ests are hydrology, water resources, hydrogeology, hydrom-
eteorology, hydraulics, science philosophy and history. He
has published about 200 scientific papers in almost 35 dif-
ferent international journals. Also about 300 publications
in international conferences, symposiums and congresses.
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IWRA, Water International, Volume 27, Number 2, June 2002