Water Quality Index and Regression Models for Predicting Water Quality and Water Quality Parameters for Tumkur Amanikere Lake Watershed, Tumkur, Karnataka, India

By Rajendra D. S. Prasad¹, C. Sadashivaiah², and G. Ranganna³
July 2009

  1. Research Scholar, Department of Civil Engineering, Siddagnaga Institute of Technology (SIT), Tumkur - 572 103, India
  2. Principal, Karavali Institute of Technology, Neeru Marga, Mangalore - 575 029, India
  3. Visiting Professor, UGC-CSA, Department of Mathematics, Central College Campus, Bangalore University, Bangalore - 560 00, India
Water quality indices aim at giving a single value to the water quality of a source on the basis of one or the other system which translates the list of constituents and their concentrations present in a sample into a single value. One can then compare different samples for quality on the basis of the index value of each sample. The present work relates to the development of water quality index for the study area Tumkur amanikere watershed based on the experimental results of physicochemical analysis of water samples of the watershed. The Water Quality Index (WQI) for the study area found to vary from 112.58 to 842.92. The high value of WQI at these sampling locations has been found to be mainly from the higher values of iron, nitrate, Total Dissolved Solids (TDS), hardness, fluorides, bicarbonates, magnesium and manganese in the groundwater. Regression models are also developed to quantify and predict water quality parameters based on the available TDS value.

Key words: Groundwater, Regression model, Water Quality Index (WQI), Water Quality standards, World Health Organization (WHO).


The crucial role of water as the trigger and sustainer of civilizations has been witnessed throughout the human history. But, uptill as late as 1960s, the overriding interest in water has been vis a vis its quantity. Except in manifestly undesirable situations, the available water was automatically deemed utilizable water [8]. Only during the last three decades of the twentieth century the concern for water quality has been exceedingly felt so that, by now, water quality has acquired as much importance as water quantity [1].

According to WHO, about 80% of all the diseases in human beings are caused by water. Once the groundwater is contaminated, its quality cannot be restored by stopping the pollutants from the source. It is therefore imperative to regularly monitor the quality of groundwater and device ways and means to protect it. Water Quality Index (WQI) is one of the most effective tools to communicate information on the quality of water to concerned citizens and policy makers [3-7].

The formulation and use of indices has been strongly advocated by agencies responsible for water supply and control of water pollution. Once the water quality data has been collected through sampling and analysis, a need arises to translate it into a form that is easily understood. Once the WQI are developed and applied, they serve as convenient tools to examine trends, to highlight specific environmental conditions, and to help governmental decision-makers in evaluating the effectiveness of regulatory programmes [7-9].

The following four steps are most often associated with the development of any WQI; depending on the sophistication being aimed at, additional steps may also be taken [10-17]:

Salient features of the Study Area

The proposed area under study i.e. Tumkur Amanikere lake watershed is located 0.5 km away from Tumkur Town on National Highway No.4. Tumkur town is 70 km away from the capital city Bangalore. Figure 1 shows the location map of Tumkur Amanikere lake watershed. The main occupation of Tumkur district population is agriculture and horticulture. It is also one of the major educations, small & medium sized industrial centers in Karnataka. Table 1 presents the snapshot of the Tumkur amanikere lake watershed. Groundwater in the study area occurs under water table conditions in the watershed and fractured granite and Gneisses.

Table 1 · Characteristic of Tumkur Amanikere Lake Watershed
Latitude N: 13° 21’ N
Longitude E: 77° 07’ E
Altitude Apx. 785 meters above sea level
Area 835 acres.
Climate Rainfall Annual rainfall of 965 mm.
Humidity The maximum humidity is in monsoons and early summer is the period of minimum humidity.
Temperature The maximum temperature is 38 °C, while the minimum is 11 °C.
Capacity 7.95MCUM
Population 2,48,000 (2001 census)

Figure 1 · Location of Tumkur Taluk and Tumkur Amanikere Lake Watershed
Fig 1 Fig 1


Groundwater samples were collected from 22 locations from Tumkur amanikere lake watershed (Jan - February 2008). The collected water samples were transferred into precleaned polythene container for analysis of chemical characters. Chemical analyses were carried out for the major ion concentrations of the water samples collected from different locations using the standard procedures recommended by APHA-1994 [6]. The analytical data can be used for the classification of water for utilitarian purposes and for ascertaining various factors on which the chemical characteristics of water depend.

Figure 2 · Groundwater Sampling Locations
Fig 2

Water Quality Index (WQI) for Tumkur Amanikere Lake Watershed

Water quality affects the quality of drinking water and the capacity of the lake to support wildlife and healthy ecosystems. Water quality can be degraded by many different stressors in the watershed, including poor development practices and sprawl, poor stormwater management, destruction of wetlands, runoff from agricultural areas, and point source pollution. Water quality indices aim at giving a single value to the water quality of a source on the basis of one or the other system which translates the list of constituents and their concentrations present in a sample into a single value. One can then compare different samples for quality on the basis of the index value of each sample.

Brown et al. (1970) developed a water quality index similar in structure to Horton’s index but with much greater rigour in selecting parameters, developing a common scale, and assigning weights for which elaborate Delphic exercises were performed. This effort was supported by the National Sanitation Foundation (NSF). For this reason Brown’s index is also referred as NSFWQI.

Water quality indices have been used in India but not as extensively as the tool deserves. Except for the first reported Indian WQI (Bhargava 1985), other indices have been mostly weighted sum indices apparently inspired by Brown’s WQI.

For developing WQI for Tumkur amanikere lake watershed, the chemical analyses of 22 water samples analyzed during the year 2008 were considered. Each ground water was analysed for 16 parameters such as pH, EC, TDS, total hardness, bi-carbonate, chloride, sulphate, phosphate, nitrate, fluoride, calcium, magnesium, sodium, potassium, iron and manganese using standard procedures recommended by APHA [6]. However, we have chosen 12 important parameters as others having less or no bearing on the rest.

For computing WQI three steps are followed. In the first step, each of the 16 parameters has been assigned a weight (wi) according to its relative importance in the overall quality of water for drinking purposes as shown table 1. The maximum weight of 5 has been assigned to the parameter nitrate due to its importance in water quality assessment. Magnesisum which is given the minimum weight of 1 as magnesium by itself may not be harmful.

In the second step, the relative weight (Wi) is computed from the following equation:


Where, Wi is the relative weight, wi is the weight of each parameter and n is the number of parameters. Calculated relative weight (Wi) values of each parameter are presented in Table 2.

In the third step, a quality rating scale (qi) for each parameter is assigned by dividing its concentration in each water sample by its respective standard limit value according to the guidelines laid down in the Bureau of Indian Standards (BIS) and the result is multiplied by 100. The equation for qi is shown below:

qi = ( Ci / Si ) x 100

where qi is the quality rating, Ci is the concentration of each chemical parameter in each water sample in mg/l, and Si is the Indian drinking water standard limit for each chemical parameter in mg/l according to the BIS 10500:1991 (reaffirmed in September 2003).

For computing the WQI, the Sub-Index (SI) is first determined for each chemical parameter, which is then used to determine the WQI as per the following equations:

SIi = Wi . qi

SIi is the subindex of ith parameter; qi is the rating based on concentration of ith parameter and n is the number of parameters. The computed WQI values are classified into five types, “excellent” to “ unsuitable for drinking”.

Table 2 · Relative Weight of Chemical Parameters
Chemical Parameters Indian Standards Weight (Wi) Relative Weight (Wi)
pH 6.5 - 8.5 4 0.09756
Total Hardness(TH) 300 - 600 2 0.04878
Calcium – Ca 75 - 200 2 0.04878
Magnesium – Mg 30 - 100 2 0.04878
Bicabonate – CaCO3 244 - 732 3 0.07317
Chloride - Cl 250 - 1000 3 0.07317
Total Dissolved Solids(TDS) 500 - 2000 4 0.09756
Fluoride - F 1 - 1.5 4 0.09756
Manganese - Mn 0.1 - 0.3 4 0.09756
Nitrate – NO3 45 - 100 5 0.12195
Iron - Fe 0.3 - 1.0 4 0.09756
Sulphate – SO4 200 - 400 4 0.09756
Total 41 1.00000

The computed WQI values ranges from 112.58 to 842.92 and therefore, can be categorized into five types “excellent” to “unsuitable for drinking”. Table 3 shows the percentage of water samples that falls under different quality. The high value of WQI at these sampling locations has been found to be mainly from the higher values of iron, nitrate, TDS, hardness, fluorides, bicarbonates, magnesium and manganese in the groundwater.

Table 3 · Water Quality Classification based on WQI Values
WQI Value Water Quality Nș of Samples Percentage of Water Samples
< 50 Excellent 0 0
50 – 100 Good 0 0
100 – 200 Poor 5 22.72727
200 – 300 Very Poor 5 22.72727
> 300 Unsuitable for Drinking 12 54.54545

Regression Models for Predicting Water Quality Parameters

Regression models are used to predict one variable from one or more other variables. Regression models provide the scientist with a powerful tool, allowing predictions about past, present, or future events to be made with information about past or present events. The scientist employs these models either because it is less expensive in terms of time and/or money to collect the information to make the predictions than to collect the information about the event itself, or, more likely, because the event to be predicted will occur in some future time.

The chemical analyses of the groundwater and the percent compliance with the Indian standards [2] and WHO [3] are summarized in Table 4.

Table 4 · Comparison of Groundwater Quality with Drinking Water Standards, Indian and WHO
Parameters Indian Standard Percent Compliance WHO Percent Compliance
pH 6.5 – 8.5 77 7.0 – 8.0 36.36
Electrical conductivity mmhos/cm - - - -
Total dissolved solids 500 63.63 1000 100
Total hardness as CaCO3, mg/L 300 36.36 100 0
Carbonate, mg/L - - - -
Bicarbonate, mg/L - - - -
Chloride, mg/L 250 95.45 250 95.45
Sulphate, mg/L 200 100 250 100
Phosphate, mg/L - - - -
Nitrate, mg/L 45 72.72 50 77
Fluoride, mg/L 1 100 1 100
Calcium, mg/L 75 63.63 75 63.63
Magnesium, mg/L 30 0 30 0
Sodium, mg/L - - 200 -
Potassium, mg/L - - - -
Iron, mg/L 0.3 77 0.1 18.18
Manganese, mg/L 0.1 77 0.05 0

Normal statistics of water quality parameters of 22 samples are presented in Table 5.

Table 5 · Normal Statistics of Water Quality Parameters of Groundwater Samples
Parameters Minimum Maximum Arithmetic Mean Standard Deviation Coefficient of Variation - CV Median of the Lower Half Median Median of the Upper Half
pH 6.27 8.9 6.9795455 0.6477321 0.0928043 7.05 6.815 6.8
TH mg/l 213 690 381 140.16963 0.3678993 295 340.5 6.8
Ca++ mg/l 14.03 98.6 31.445 20.154812 0.6409544 24.05 26.05 30.06
Mg++ mg/l 36.45 150.7 73.512273 29.690976 0.4038914 57.715 67.555 67.555
HCO3- mg/l 160 436 260.40909 67.025694 0.2573862 222 252 348
Cl- mg/l 62.38 255.9 125.415 58.247656 0.4644393 83.17 101.585 144
EC mmhos/cm 540 1540 880 315.59468 0.3586303 640 720 660
TDS mg/l 280 800 460 166.87606 0.362774 335 375 490
F- mg/l 0.09 0.92 0.5245455 0.2766763 0.5274592 0.47 0.62 0.62
Mn mg/l 0.11 0.83 0.3927273 0.2482353 0.6320807 0.225 0.37 0.43
NO3- mg/l 11.2 65.3 34.054545 18.787121 0.5516774 32.1 30.4 38.6
Fe++ mg/l 0.05 0.52 0.2154545 0.1309208 0.6076494 0.14 0.18 0.21
SO4- mg/l 0 57 25.090909 16.236083 0.6470903 14 22 25
Na+ mg/l 8 48 26.272727 13.547735 0.5156577 20 21 22
K+ mg/l 0.2 4 1.7272727 0.9803701 0.5675827 1.9 1.7 1.7
PO4- mg/l 0.05 5.8 1.2418182 1.668614 1.3436862 1.09 0.475 0.47

The following regression models have been obtained from the results of analysis water samples of Tumkur Amanikere lake watershed. Considering a known value of TDS, the percentage contribution of each ion can be obtained by substituting an average ionic value for the entire study area. The models were developed using MS Excel linear regression charts as shown in figures 2 and 3 below:

Figure 2 · Linear Regression for TDS vs CI
Fig 2

Figure 3 · Linear Regression for TDS vs EC
Fig 3

Table 6 shows the regression equations for parameters and coefficient of determination R² and Correlation coefficient (r).

Table 6 · Regression Equations, Coefficient of Determination R² and Correlation Coefficient (r) for various Parameters
Parameters Regression Equations Correlation r
Ca 0.072 TDS - 1.679 0.3556 0.596211544
Mg 0.1407 TDS + 8.7836 0.6072 0.779230258
HCO3 0.3357 TDS + 105.99 0.6985 0.835771911
Cl 0.3388 TDS - 30.416 0.9419 0.97053773
Na 0.031 TDS + 12.004 0.146 0.382082598
TH 0.7505 TDS + 32.067 0.8155 0.903075991
EC 1.8906 TDS + 10.342 0.9993 0.999666253
TDS 0.5286 EC - 5.1597 0.9993 0.999666253

The degree of a linear association between any two of the water quality parameters as measured by the simple correlation coefficient(r) is presented in the Table 7. Magnesium and chloride are highly interrelated with total hardness. Bicarbonate, chloride and total hardness are highly interrelated with TDS. This interrelationship indicates that the hardness of the water is permanent in nature.

Table 7 · Correlation Coefficient (r) Matrix of Water Quality Parameters of Tumkur Amanikere Lake Watershed (Year 2008)
Parameters pH TH Ca Mg HCO3 Cl TDS F Mn NO3 Fe
pH 1.000
TH -0.303 1.000
Ca -0.134 0.483 1.000
Mg -0.288 0.935 0.140 1.000
HCO3 -0.116 0.875 0.489 0.792 1.000
Cl -0.135 0.885 0.685 0.722 0.787 1.000
TDS -0.125 0.903 0.596 0.779 0.836 0.971 1.000
Fl -0.125 0.220 0.260 0.143 0.042 0.353 0.389 1.000
Mn -0.215 0.731 0.197 0.747 0.628 0.590 0.593 0.073 1.000
NO3 -0.332 0.793 0.469 0.707 0.688 0.716 0.757 0.454 0.600 1.000
Fe -0.238 0.187 0.049 0.191 0.247 -0.028 0.082 0.302 0.140 0.324 1.000
SO4 -0.410 0.714 0.030 0.795 0.502 0.471 0.528 0.372 0.613 0.574 0.280


During the year 2008, based on the comparisons of chemical constituents with WHO (1994) standards, it is found that, for 22 samples, 14 samples have total hardness value above maximum permissible limit 300 mg/l.

Electrical conductivity of water is a direct function of its total dissolved salts. Hence it is an index to represent the total concentration of soluble salts in water. In this study area, the electrical conductivity of the groundwater samples varied between 540- 1540 mmhos/cm.

The permissible total dissolved salts for drinking water is 500 mg/l. In the absence of potable water source the permissible limit is upto 2000 mg/l. It is found from the analysis, all the well water samples TDS is within the maximum limit of 2000 mg/l. The range of TDS levels in the study area is 280-800 mg/l. 8 samples have TDS values beyond the desirable limit of 500 mg/l. The highest concentration of total dissolved solids was found to be 800mg/l for the sample No.8, due to dense residential area and due to intensive irrigation in that area. High values of TDS in groundwater are generally not harmful to human beings but high concentration of these may affect persons, who are suffering from kidney and heart diseases. Water containing high solids may cause laxative or constipation effects.

Chloride is widely distributed element in all types of rocks in one or the other form. Its affinity towards sodium is high. Therefore, its concentration is high in groundwaters, where the temperature is high and rainfall is less. Soil porosity and permeability also have a key role in building up the chlorides concentrations. The chloride content in the majority of samples (95.45%) of the study area was found to be well within the permissible levels. The chloride content ranges from 22.38 to 255.9 mg/l.

Magnesium exceeds in all the samples. It ranges from 36.45 to 150.7 mg/l. There are no known cases of magnesium poisoning. At large oral doses magnesium may cause vomiting and diarrhoea. High doses of magnesium in medicine and food supplements may cause muscle slackening, nerve problems, depressions and personality changes.

WQI for 22 samples ranges from 112.58 to 842.92. All the samples exceed 100, the upper limit for drinking water. The high value of WQI at these stations has been found to be mainly from higher values iron, nitrate, TDS, TH, fluoridres,, bicarbonates, magnesium and manganese in the groundwater. About 22.72% of water samples are poor in quality. In this part, the groundwater quality may improve due to inflow of freshwater of good quality during rainy season.

Magnesium and chloride are highly interrelated with total hardness. Bicarbonate, chloride and total hardness are highly interrelated with TDS. This interrelationship indicates that the hardness of the water is permanent in nature.

The analysis reveals that the groundwater of the area needs some degree of treatment before consumption and it also needs to be protected from the perils of contamination.


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