To collect groundwater samples for this study, 47 different locations were selected in a way to incorporate all blocks in the Rohtak district. The groundwater samples collected in this study are primarily from the government hand pumps and domestic tube wells (Fig. 2) during the Pre monsoon and Post monsoon periods (2022) as per the standard procedures of the American Public Health Association (APHA, 2012). Before collecting the water samples for testing, hand pump and tube wells were allowed to run for 4–5 minutes to discard any water in the pipes. Each sample was collected in 1000 mL clean high-density polypropylene bottles. The latitude and longitude of all the sampling sites and the source were geocoded using a portable global positioning system (GPS). The pH, total dissolved solids (TDS), and electrical conductivity (EC) were measured on-site using portable equipment.
2.3 Laboratory analysis of samples
The samples were carefully transported to the laboratory in an icebox after collection to preserve their integrity and stop any degradation. As soon as they arrived, they were immediately stored at 4°C to ensure their preservation and readiness for further analysis. The major cations like Ca2+ and Mg2+ were determined by the Volumetric titration method using EDTA, and other Na+ and K+ were determined by the flame photometer method (APHA, 2012). The major anions NO3−, SO42−, and F− were determined using a spectrophotometer as described in APHA (2012). The other anions, like Cl−, CO32−and HCO3− were determined by using titration method. With the help of Eq. (1), the Ionic balance error (IBE) between the cations and anions was determined to verify the accuracy of a thorough hydrochemical analysis of each groundwater sample.
$$IBE=\frac{\sum Cations-\sum Anions}{\sum Cations+\sum Anions}\times 100\%$$
1
All the above concentrations of cations (Mg2+, Ca2+, Na+, K+) and anions (Cl−, SO42−, NO3−, CO32−, HCO3−, F−) are in mg/L. The IBE was observed for groundwater samples to fall within the acceptable limit of ± 5%.
2.4 Entropy Water Quality Index (EWQI)
Entropy water quality index (EWQI) helps in representing all hydrochemical information by one value that accurately depicts the water quality for drinking purposes (Adimalla, 2021; Amiri et al., 2014; Raheja et al., 2022b). The calculation of EWQI involves several steps, as described below
Step 1. The most significant parameter is an entropy weight, often connected with "\(m\)" groundwater samples, each with "\(n\)" hydrochemical parameters. The estimation of the eigenvalue matrix "\(X\)" which is linked to all hydrochemical parameters and calculated by the following equation:
$$X=\left[\begin{array}{ccc}{x}_{11}& {x}_{12}& {..x}_{1n}\\ {x}_{21}& {x}_{22}& {..x}_{2n}\\ {x}_{m1}& {x}_{m2}& ..{x}_{mn}\end{array}\right]$$
2
Where \("m"\) (\(i=\text{1,2},3,\dots ..,m\)) is the number of groundwater samples collected during the study, and \("n"\) (\(j=\text{1,2},3,\dots ..,n\)) is the number of hydrochemical parameter for each sample.
Step 2. Now standard evaluation matrix \("Y"\) and \("{y}_{ij}"\) is calculated by using equations (3) and (4).
$$Y=\left[\begin{array}{ccc}{y}_{11}& {y}_{12}& {..y}_{1n}\\ {y}_{21}& {y}_{22}& {..y}_{2n}\\ {y}_{m1}& {y}_{m2}& ..{y}_{mn}\end{array}\right]$$
3
$${y}_{ij}=\frac{{x}_{ij}-{\left({x}_{ij}\right)}_{min}}{{\left({x}_{ij}\right)}_{max}-{\left({x}_{ij}\right)}_{min}}$$
4
Where, \({x}_{ij}\) is the \({j}^{th}\) evaluation index of the \({i}^{th}\) groundwater sample, \({\left({x}_{ij}\right)}_{max}\) is the maximum value of hydrochemical parameter, and \({\left({x}_{ij}\right)}_{min}\) is the minimum value of a hydrochemical parameter.
Step 3. After calculating standardized value, a ratio of index value, and information entropy \({"e}_{j}"\) are calculated by following equations (5) and (6).
$${P}_{ij}=\frac{{y}_{ij}}{\sum _{i=1}^{m}{y}_{ij}}$$
5
$${e}_{j}=-\frac{1}{\text{ln}m}\sum _{i=1}^{m}{P}_{ij}\text{ln}{P}_{ij}$$
6
Step 4. Entropy weight \("{w}_{j}"\) and quality rating scale \("{q}_{j}"\) are computed by equations (7) & (8).
$${w}_{j}=\frac{1-{e}_{j}}{\sum _{j=1}^{n}(1-{e}_{j})}$$
7
$${q}_{j}=\frac{{c}_{j}}{{s}_{j}}\times 100$$
8
In which the term \("{c}_{j}"\) is the concentration of the hydrochemical parameter as in mg/L, and \({s}_{j}\) is the drinking water standard for each parameter (WHO, 2017).
Step 5. Finally, \(EWQI\) is calculated by the following Eq. (9).
$$EWQI=\sum _{j=1}^{n}{w}_{j }{q}_{j}$$
9
The EWQI is rated as excellent if it is below 25, good between 26 and 50, medium between 51 and 75, poor between 76 and 100, and extremely poor if it is beyond 100. Additionally, Table 1 shows the classification and rankings for the EWQI and groundwater quality (Adimalla, 2021; Dashora et al., 2022).
Table 1
Classification of groundwater quality as per EWQI
EWQI scale | Rank | Groundwater quality |
< 25 | I | Excellent quality |
26–50 | II | Good quality |
51–75 | III | Medium quality |
76–100 | IV | Poor quality |
> 100 | V | Extremely Poor quality |
2.6 Spatial interpolation method
The Geostatistical Analyst tool in ArcMap offers various interpolation methods to analyze and interpolate spatial data using Inverse Distance Weighting (IDW), Kriging, Natural Neighbor, Spline, Radial Basis Functions, and Local Polynomial Interpolation. In this study, IDW technique was used to draw spatial distribution diagrams. IDW is a deterministic interpolation method used to evaluate values at unmeasured locations based on the values of surrounding measured locations. The method calculates the weighted average of the measured values, where the weights decrease as the distance from the predicted location increases and represented by Eq. (10).
$${Z}_{p}=\frac{\sum _{i=1}^{n}{w}_{i}\times {Z}_{i}}{\sum _{i=1}^{n}{w}_{i} }$$
10
Where,\({Z}_{p}\) is the estimated value, \({w}_{i}\) is assigned weight, \(n\) is the number of measured values. Furthermore, to determine the hydrochemistry and functional sources of ions, various analyses such as major ions correlation, US salinity diagram, and Gibbs diagram were also plotted for the water samples.