A novel multivariate approach for water quality index prediction irrespective of the geospatial distinction of water sources having varied end uses

Himanchal Bhardwaj 1✉ Emailhimanchal.1@iitj.ac.in

Rajkumar Satankar 2

Deeptha Giridharan 1

Deepika Bhattu 1

Venkata Ravibabu Mandla 3

Anand Krishnan Plappally 1

Indian Institute of Technology Jodhpur Jodhpur Rajasthan India

2 Poornima College of Engineering Jaipur Rajasthan India

3 National Institute of Rural Development & Panchayati Raj Hyderabad India

Himanchal Bhardwaj ^{1*[0000–0003−4554–5285]}, Rajkumar Satankar², Deeptha Giridharan¹, Deepika Bhattu¹, Venkata Ravibabu Mandla³, Anand Krishnan Plappally¹

¹ Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

² Poornima College of Engineering, Jaipur, Rajasthan, India

³ National Institute of Rural Development & Panchayati Raj, Hyderabad, India

*Corresponding Author

¹ himanchal.1@iitj.ac.in, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India

Abstract

Water quality assessment is fundamental to understanding the suitability of water for human consumption, ecological sustainability, and industrial applications. This study presents an empirical multi-parameter approach for estimating the Canadian Council of Ministers of the Environment (CCME)-based Water Quality Index (WQI) in Kota, Rajasthan, India. Eighteen samples from groundwater, surface water, and municipal supplies were analyzed for six parameters—pH, turbidity, total dissolved solids (TDS), hardness, alkalinity, and iron—following BIS IS 10500:2012 standards. Pareto analysis revealed turbidity and TDS as the most influential, independent drivers of WQI. GIS-based mapping captured spatial and seasonal variation, highlighting persistent water quality stress across the city. A quotient response function was developed using normalized parameters, and a predictive regression model was formulated with TDS and turbidity as core variables. The model achieved high accuracy, with R² values of 91.45% for groundwater, 96.05% for surface water, and 94.37% for municipal water. The results establish a scalable, source-independent framework for predicting WQI, offering robust support for urban water resource monitoring and sustainable management.

Keywords:

CCME

water

quality

regression

GIS

Rajasthan

1. Introduction

Water is a fundamental resource that facilitates the transport of oxygen and nutrients within living organisms, making it indispensable for sustaining biological and ecological processes on Earth (Ejiohuo et al., 2025; Jéquier & Constant, 2009). It supports ecosystems, provides habitat for diverse aquatic species, and serves as a key source of freshwater for drinking, household needs, irrigation, livestock, industry, and other economic activities (Lap et al., 2023; Patel et al., 2023). With the growing global population and the rising demand for agriculture and irrigation, pressure on water resources continues to increase, leading to widespread scarcity and depleting its quality (Shams et al., 2023). Water quality is governed by its physical, chemical, and biological characteristics, which are influenced by both natural processes and human activities and predicting water quality is an essential component of smart water management, as it helps monitor pollution and support timely interventions (Akiner et al., 2024; Mahesh et al., 2024).

Water resource structures such as ponds and lakes near Kota city, Rajasthan, which are situated on the banks of the Chambal River, have dwindled over the last half century. It is known that depletion of water resources ensures a cycling frequency increase in water within the hydrologic cycle (Matlock & Morgan, 2011). Kota city has also observed diversions in water resources due to land use shifts during that time (Bhardwaj et al., 2024). Due to these diversions dissolved salts might have risen in these resources depleting their water quality (Reynolds et al., 2007). The water quality directly impacts the organisms that inhabit it as well as human beings who use it for consumption and other livelihood aspects. From time immemorial, there are designated uses for the water from a specific water source which was defined by a specific community at a location (Himanchal et al., 2025; A. Mishra, 2005). Distinct parameters of water in liquid form affect the above-mentioned users or inhabitants.

Diffuse and point sources of pollution are nocuous for the health of a water volume. Eons before India got independent, rules and regulations in terms of the usage of water from a specific water body at a certain location were prescribed by the local community in terms of narratives (Pandey, 1930). The communities propose statements and narratives to define the quality of this location-specific water body. This provides importance to the geospatial information in defining a decentralized thought of a water resource, its quality, purity, value and its use. Kota district in Rajasthan, India, is blessed with Chambal, one of the top 5 cleanest rivers in India (CNBCTV18, n.d.; Economic Times, n.d.). Indices consider several distinct parametric measurements and combine to make water quality an easy-to-understand score. Selection of specific parameters to define indices is the first step. At first, visual observation of the water body and data collection of organisms was a step in the evolution of such indices (Beck, 1954). The plant Saprobia became an indicator for the development of the first water quality index named Saprobic Indices (Canning & Death, 2019; Wallace & Snell, 2010). The next step is that a water quality standard should be followed. This edict should enable the assortment of these parameters, which may have a statistical distribution. For example, the first US water quality standard was enacted in 1914 (Knotts, 1999).

The first development of indices using biological indicator organisms for the streams of Florida was performed in the US (Beck, 1954). Modified Saprobie-Score was a similar index, yet partially mathematically introduced based on the abundance of taxons found in the wetlands (“Phytoplankton in Turbid Environments: Rivers and Shallow Lakes,” 1994). This discussion of biota carries a lot of importance since the Chambal River is a habitat for the endangered Gharial (Gavialis gangeticus) and Gangetic Dolphin (Platanista gangetica) (RSPCB, 2024).

By the 1950s, the development of (use of expert opinion from different knowledgeable people on different distinct parameters to predict) Delphi was introduced into different subject areas, including water quality, by its inventor, the Rand Corporation (Dalkey, 1969).

Water dissolves a large number of materials that interact with it due to its high dielectric constant (K. K. Mishra, 2000). Therefore, chemical water indices also gained importance. Almost after a decade Horton (1965) devised the very first chemical water quality index (WQI), which relied on several physico-chemical parameters, their weightings and rating scales (Horton, 1965). Just in the year prior, the presence of macroinvertebrates and larvae of specific organisms in Trent River water in the UK helped to assess water quality through the Trent River Board Biotic Index formulation (Woodiwiss, 1964). This study again underscores the importance of a specific geo-spatial character of parametric variation of the water body. Further adaptation of Saprobic indices brought in chemical and physiological aspects into the indices development (Liebmann, 1966). Lothians River Purification Board Index and the Score-System in the UK were also other running water indices based on Saprobic aspects (Chandler, 1970; Graham, 1965). This also helps to understand the next aspect of the importance of the weight of distinct parameters while defining an index, as well as still and running water. There will always be a hierarchy in terms of the influence of parameters on the prediction of WQI (Brown et al., 1970).

Here, the physico-chemical as well as biological parameters involved in the prediction of the index gain importance over its own probability distribution (Abolli et al., 2022). This thought is basically formed after a Delphi process, which factors in opinions of experts in this field of study for the prediction of the (National Sanitation Foundation-based) water quality indices. Development of fish and wildlife index for a surface water body was performed by O'Connor. Further development of an index for a water source to be used as a public water supply was also proposed by O'Connor in 1971 (O’connor, 1972). After looking into the measurements at a certain geographical region, the factors that may define water quality index (WQI) derivation will emerge along with their importance (Brown et al., 1972).

The physico-chemical formulations of indices can be classified as general water quality indices (WQI), pollution indices, water use-related indices and indices for planning, respectively. During 1970–1980, eight WQIs other than those detailed above were promulgated. Table 1 provides the details of timelines along with the authors.

Table 1

WQIs developed during 1970–1980.
Year	1972	1974	1975	1975	1976	1978	1979	1979
Author	Dinius (Dinius, 1987)	Walski(Walski & Parker, 1974)	Inhaber (Inhaber, 1975)	Janardan and Schaffer (Schaeffer & Janardan, 1979)	Scottish Development Department (SDD) (SRDD, 1976)	Bolton (Bolton et al., 1978)	Bascaron (Bascaron, 1979)	Dunnette(Dunnette, 1979)
Mathematical or Statistical Basis	Arithmetic means of variables	Geometric	Root Mean Square	Non-Parametric Classification	Multiplicative	Weighted Aggregated index	Parameter Normalization	Mathematically derived formula using Delphi weights

From the decadal development in Table 1, it is clear that the indices provide a single value cumulative expression for quantifying the water quality of a point source or a water resource for the common man living by its side. The single value delineates the character of water and its utilization suitability levels. In 1975, the National Academy of Sciences said that measurement techniques of environmental variables were unsatisfactory (NAS, 1975). Recently, the Irish Water Quality Index (IEWQI) was used for assessing and disseminating water quality near the coastal regions in Europe (Uddin et al., 2023). River quality indices such as Basic Water Quality India and Overall Water Quality Index from Vietnam and MDOE-WQI by Malaysia are other such examples which also have sub-indices for individual contaminants (Suratman et al., 2015; Thi Minh Hanh et al., 2011). A recreational WQI was also adopted on water quality of the Potrero de los Funes River flowing through San Luis, Argentina, using physical, microbial and chemical constituent levels (Almeida et al., 2012). Evaluating water quality based on end-use always receives criticism due to its bias towards that use (Dinius, 1987).

WQI were thus categorized under three distinct paradigms. First, a value that translates the relationship between the quantity of each element and to quality of water. Second, a value that can indicate the quantity of a contaminant based on a water standard of a location (Landwehr, 1979). Third, a value that depicts the statistical aspects of the variability of solvents in water. WQI should communicate the quality of water to the dilettante public in an assimilative format without loss of vital water quality information. WQI values of distinct water sources are very important to ensure that all people have distinct options for the varied end-use (Siriwardhana et al., 2023). Rocchini and Swain 1995 announced a new WQI good enough to describe the state of a water source, which can be used to depict water quality of water for use by humans, or for aquatic life, or wildlife (Rocchini & Swain, 1995). The geographical representation of the locations of the natural environment also plays a crucial role in defining the state of water quality of a source. Classical geospatial problems of natural environment, such as water sources, can be vagueness, measurement uncertainties, as well as dynamism, which may be easily noted through temporal studies (Mount, 2009). The need for resolving these problems requires temporal data assessment using a universal multivariate regressive approach (Şener et al., 2021).

Rocchini and Swain 1995 based the development of this WQI on three aspects. The scope, which defines the number of water characteristics which is far away from a specific standard. The second is the frequency with which the different samples don’t adhere to the standard. The amplitude is the third, which states the difference between the measured and the standard. All three in the true sense may add up to 100. This WQI was adopted and practiced in British Columbia, Canada (Rocchini & Swain, 1995).

After understanding the imperatives of this development, the Canadian Council of Ministers of the Environment (CCME) Water Quality Guidelines Task Group, in 1997, planned to modify this WQI to be used in all locations across Canada, thus incorporating universality of application (Neary et al., 2001; Wang et al., 2022).

In this article Bureau of Indian Standards (IS 10500: 2012) governs the limits of water contamination for the region under study while adopting the CCME WQI. For calculating WQI using the CCME procedure, F1 (or Scope) defines the percentage of quality parameters that do not meet their objectives at least once during the time period under consideration (“failed variables”), relative to the total number of parameters studied. F2 (or Frequency) defines the percentage of each of the parametric tests that do not meet standards in IS 10500: 2012. F3 is the amplitude by which parameters did not meet the values quoted by IS 105000: 2012 (Dhanush et al., 2024; Hurley et al., n.d.; Xiang et al., 2021). The CCME WQI (Y) can be calculated from the measured parametric values using the following formulae,

$\:{Y}_{i}=CCME\:WQI=100-\left[\sqrt{\frac{\left(\left({F1}^{2}\right)+\left({F2}^{2}\right)+\left({F3}^{2}\right)\right)}{1.732}}\:\:\right]\:$

Eq. 1

In 2022-23, almost 48 water sources in different locations across the municipal city limits of Kota, Rajasthan, India were studied and are as illustrated in Fig. 1 (RSPCB, 2024).

The requirements of high-water quality standards are mandated in the creation of the proposed Smart City in Kota. Further loss of traditional water bodies due to unplanned development and pressure of the present water infrastructure of Kota mandated such a study. The work was able to tabulate all elemental content levels in the water samples from about 46 stations and their adherence to the Indian standard IS 10500: 2012 (drinking water specification). Shifts in the manufacturing and industrial sectors during the 80s-90s to the present-day education industry also caused changes in land and water use patterns in Kota (Bhardwaj et al., 2024). Traditional water bodies were forcefully shut down to pave the way for building construction, making the region flood prone. Further, a decrease in NDWI values from 1980 onwards with an increase in population has been a subject of concern for the city officials (RSPCB, 2024). From 1980, Kota lost 56.6% of its surface water bodies. This means that those locations of the city which lost their wetlands or watershed are prone to flash floods even with a small precipitation. This study derives data from more than two scores of locations at Kota city, which were visited, and water was collected for testing. Therefore, this investigation becomes mandatory for assessing the capacity of the water resources of this city through which the Chambal River flows.

Fig. 1

The municipal land use map of Kota in Rajasthan state of India, for 2019, showing built-up land where this water source quality measurement experiment at more than 40 locations was envisaged.

2. Methodology

2.1 Study Area

As depicted in Fig. 2, Kota district is located in the south-eastern section of Rajasthan State, between N 24 25' and N 25 51' latitude and E77 26' and E76 38' longitude. It is flanked on the north by the districts of Sawai Madhopur and Tonk, on the south by the district of Jhalawar, on the east by the district of Baran, and on the west by the districts of Bundi and Chittorgarh (Bhardwaj et al., 2024). Municipal land in the north and north-west part of the district, as shown in Fig. 2, is the study area under consideration. From the locations depicted in Fig. 1, eighteen random locations were mapped in Fig. 2. These locations have 6 hand pump locations, 6 surface water bodies, as well as 6 piped municipal water points.

Fig. 2

The eighteen distinct locations across Kota City from where water samples were collected and tested.

2.2 Testing and Data Collection

The water sources are far apart, as can be inferred from Fig. 2. A total of 18 samples are collected from different places in Kota. Sample collection is performed for all three seasons namely rainy, summer and winter of 2022-23. The bottles made from high-density polyethylene (HDPE) were carefully rinsed twice with water in the field prior to sampling (Reimann et al., 2007). Sampling methods enumerated by Munro Mortimer (2007)were followed for surface water samples (Munro Mortimer, 2007). These were then tested for their physicochemical properties at the spot using two portable electronic water quality measurement systems (Labwan, LW-7PAR-L-66741, India, Water Quality Meter, Deluxe Water and Soil Analysis Kit, Manti Lab Solutions, India). These tests were also performed at all three seasons in 2022-23. The procedures outlined in the manuals of these devices were followed while electronically measuring the parameters of the samples from all 18 locations, as shown in Fig. 2. Table 2 focuses on the water quality standards from Bureau of Indian Standards (BIS) (IS 10500:2012) guidelines alongside World Health Organization (WHO) guidelines. Specific laboratory tests for other parameters were performed by the state-run laboratory at Tabela House in Kota, Rajasthan, India.

Table 2

Water Quality Standards derived from WHO and BIS(IS 10500:2012) guidelines
S No.	Characteristic Parameter	WHO Guidelines	BIS (IS 10500:2012)
S No.	Characteristic Parameter	WHO Guidelines	Desirable Limit	Permissible Limit
1	pH	6.5–8.5	6.5–8.5	No relaxation
2	Turbidity (NTU)	< 1 NTU (ideal) / ≤ 5 NTU (max)	≤ 1 NTU	≤ 5 NTU
3	TDS (mg/L)	< 600 mg/L (palatable); avoid > 1 000 mg/L	≤ 500 mg/L	≤ 2000 mg/L
4	Hardness (as CaCO₃)	Usually < 200 mg/L to avoid scaling; up to ~ 500 accepted	≤ 300 mg/L	≤ 600 mg/L
5	Alkalinity (as CaCO₃)	No explicit guideline; depends on buffering needs	≤ 200 mg/L	≤ 600 mg/L
6	Iron (mg/L)	< 0.3 mg/L (to prevent taste/staining)	≤ 0.3 mg/L	≤ 1.0 mg/L

For the CCME WQI (Y) predictions, those parameters whichever is complete in all aspects were used (Thi Minh Hanh et al., 2011). These were pH, Turbidity (NTU), Total Dissolved Solids TDS (mg/L), Total Hardness (mg/L as CaCO3), Total Alkalinity (mg/L as CaCO3), and Iron content (mg/L as Fe), apart from other measured parameters such as Chloride, Fl, As, NO₃, total coliforms, dissolved oxygen, conductivity, biological oxygen demand, resistivity and chemical oxygen demand, respectively. For understanding the importance of each variable towards a single value index, a principal component analysis was performed on the different constituent concentrations in the water samples (Chen et al., 2021; Leardi, 2007).

2.3 Multi-parameter Regression Modeling Approach

The multivariate analysis and its methodology are referred to from (Plappally, 2010). Here, CCME WQI (Y) prediction is carried out using different water quality indicator variables (X_i for i = 1, 2…n) (Dhanush et al., 2024). Further, it is necessary to convert all the correlated predictor random variables X_i’s to completely non-correlated predictor variables referred to as NCX_i’ s, where i = 1, 2, …, n. If the required response variable is Y, we therefore have,

$\:Y={f}_{1}\left({X}_{1},\:\:\:{X}_{2},\:\dots\:\dots\:,\:{X}_{n}\right)=\:{f}_{2}\left(NC{X}_{1},\:\:\:NC{X}_{2},\:\dots\:\dots\:,\:{NCX}_{Kn}\right)$

Eq. 2

For transforming the correlated electro-kinetic parameters to NCX_i’s, the following matrix transformation may be performed. In order to transform the correlated X_i variables to non-correlated independent variables NCX_i for i = 1, 2, ….k; the follows process may be implemented as,

In other words, left hand side of the above equation is a normal data set after the above processing in Eq. 3. [T] is the n x n transformation matrix. The new uncorrelated independent NCX_i is N(0,

) for i = 1, 2, ……... n and

= Eigen value or variance of NCX_i, for i = 1, 2, …….n. Further elaboration of the background calculations is presented in Appendix 1. A quotient response modeling approach is also adopted since one of the variables may be the most powerful influencer of water quality index (WQI) as per the principal component analysis. Therefore, the modeling approach will provide a new type of response function R, expressed in the form

$\:R=\:\raisebox{1ex}{${X}_{i}$}\!\left/\:\!\raisebox{-1ex}{$Y$}\right.$

for i = 1, 2…., n (Plappally, 2010).

2.4 Spatial Distribution Maps

The spatial analysis of these parametric tests performed is interpolated to the whole area of Kota city. ArcGIS (v 10.8, IIT Jodhpur) software’s Geospatial Wizard Toolbox carried out the interpolation for all six parameters- pH, Turbidity (NTU), Total Dissolved Solids TDS (mg/L), Total Hardness (mg/L as CaCO₃), Total Alkalinity (mg/L as CaCO₃), and Iron content (mg/L as Fe). The distribution of these parameters in a geospatial manner is valuable for assessing the water quality indices limits in Kota city. From Table 3, RBF was chosen for generating contours for the water contaminant as well as the WQI variable discussed in this article. RBF interpolation is an effective method for filling spatial gaps. Its flexibility and precision make it highly suitable for modelling environmental variables where data sparsity and irregularity are common (Das, 2025; He et al., 2019).

Table 3

Review of the available Interpolation Techniques while plotting in ARC-GIS
No.	Technique	Description	Use Cases
1	Inverse Distance Weighting (IDW)	Weighs nearby points more heavily for estimating values at unsampled locations.	Simple terrains, environmental data (e.g., air quality, temperature) (Setianto & Triandini, 2013)
2	Ordinary Kriging	A geostatistical method using spatial autocorrelation assumes a constant mean.	Soil nutrients, rainfall, pollutants (Cressie, 1988)
3	Universal Kriging	Like ordinary Kriging, but accounts for spatial trends.	Groundwater studies, terrain modelling (Gundogdu & Guney, 2007)
4	Regression Kriging	Combines regression models with Kriging of residuals.	Land use, remote sensing data interpolation (Pham et al., 2019)
5	Spline Interpolation (Thin Plate/Regularized)	It fits a smooth surface through known points.	Elevation models, hydrology mapping (Hutchinson, 1995)
6	Radial Basis Functions (RBF)	Like splines but uses radial symmetry.	Continuous environmental surfaces (He et al., 2019)
7	Nearest Neighbor (Thiessen Polygons)	Assigns the value of the nearest sample point.	Quick estimates in sparse data contexts (Teegavarapu, 2014)

3. Results and Discussion

3.1 Characterization of Water Quality Parameters

The pH value of water samples is assessed by measuring the electromotive force of a cell (Labwan, LW-7PAR-L-66741, India, Water Quality Meter, Deluxe Water and Soil Analysis Kit, Manti Lab Solutions, India), which should be done within 2 hours of sample collection. Pure water is normally neutral in nature (River Chambal is considered one of the purest surface water bodies in India), as opposed to rainwater, which has a pH of around 5.6 and is somewhat acidic (Gupta et al., 2022). Figure 3 depicts the pH variations of water samples for various seasons and various sources from Kota city.

Fig. 3

pH variations of water samples from September 2022 (Rainy), February 2023(Winter), and May 2023(Summer).

The Chambal River can be classified as oligo-saprobic and suitable for public water supply, irrigation and aquatic wildlife, including endangered species (Saksena et al., 2008). The locations 1, 2 and 3 fall under different categories, yet still they have the same neutral values for pH. This is because of the anthropogenic factors shown in Fig. 4. Samples numbered 1, 2 and 3 are about the canal coming from the Chambal River. Thus, Chambal River water influences the pH values of these 3 samples. Figure 4 serves as a saliency map that supports findings from the water quality tests. Most interestingly, 1, 7, 9, and 11 geospatially can be seen very apart from each other in Fig. 4, and their pH overlaps with each other almost all year long. A constructed canal can be seen running very close to these points in Fig. 4.

Fig. 4

The eighteen sampling sites overlaid on satellite imagery for Kota city.

From Fig. 5, locations 7, 9, and 16 were found to have turbid groundwater during the winter season. Surface water samples collected from Kishore Sagar Lake (48) and Kala Talab (8) during summer 2023 were found to be highly turbid beyond 15 NTU. This water clarity diminishes due to an increase in the density of contaminants in surface water bodies, due to evaporative losses in the summer, as can be observed from Fig. 6.

Fig. 5

Turbidity variations of water samples from September 2022 (Rainy), February 2023(Winter), and May 2023(Summer).

Fig. 6

Turbidity interpolated map for the locations.

Fig. 7

TDS variations of water samples from September 2022 (Rainy), February 2023(Winter), and May 2023(Summer).

In rainy and winter seasons, the total dissolved solids are found to have a similar distribution at different locations in Kota City, irrespective of the source from which water was collected. In Fig. 7, the hand pumps at 9 and 14 were found to carry a lot of dissolved salts. This supports the fact that with rains coming in, ground water pumped through hand pumps in the northern parts tends to remain brackish as shown in Fig. 8. This phenomenon was due to the leaching of salt into the groundwater during the precipitative events during that period.

Fig. 8

Interpolated map for the TDS parameter of Rainy Season.

Fig. 9

Total Hardness variations of water samples from September 2022 (Rainy), February 2023(Winter), and May 2023(Summer).

Ions such as Fe ²⁺ ions may contribute to the very high hardness of water in location 14, as observed from Fig. 9 in all the seasons consistently (IITK, 2024). This may also indicate the presence of mines related to iron ore or iron-bearing soils in the nearby locations.

Fig. 10

Total Alkalinity variations of water samples from September 2022 (Rainy), February 2023(Winter), and May 2023(Summer).

In rainy and winter seasons, the total alkalinity values are found to have a similar distribution at different locations in Kota City, irrespective of the source. From Fig. 10, it is observed that Alkalinity was the lowest at the Abheda Talab (17) and was at par with the best supply of piped water close to the governing railway headquarters of the city at location 13. It is imperative to note that the city railway headquarters was provided with the best water possible at all seasons by the municipality from Fig. 3 to Fig. 11. This also impresses upon the safety of water provisioned by the Kota municipality for the long-distance commuters using the train as a mode of transportation. Iron contamination is a major problem found in location 14. It appears as an anomaly in Fig. 11 during the rainy season, therefore, it may be attributed to leaching Fe from a point source. Fe-bearing soil or a corroded iron pipe may be the primary reason for such an anomaly at the location (MNDH, 2023). This may be the reason for the high levels of water which is noted in Fig. 9 for the same location.

Fig. 11

Iron variations of water samples from September 2022 (Rainy), February 2023(Winter), and May 2023(Summer).

The results in Fig. 11 are supported by the loading plot of the rainy season in Fig. 12, which showcases a very small angle between the loading lines of iron (mg/l Fe) and total hardness (mg/L). Here, the pairs of vectors of Fe and total hardness as well as TDS and alkalinity aver strong positive correlation. The locations 20, 28, 33 and 38 lie on the rocky land as per Fig. 1 and have a modicum variation in hardness, alkalinity, as well as iron content in their water samples collected during the rains.

Fig. 12

The loading plot of components in the rainy season.

It is to be observed that the data plot distributions in Fig. 7 and Fig. 10 were almost mirroring and support the small angles between the loading of TDS and alkalinity observed in Fig. 12 and Fig. 13 for Kota city.

Fig. 13

Component loadings for the winter season.

The smallest angle between Fe and turbidity in Fig. 13 confirms a highly positive correlation and Fe can be considered as a contaminant that can be reason for the water to be turbid. In both rainy and winter seasons, TDS and alkalinity vector loadings in Fig. 12 and Fig. 13 respectively have a small angle affirming high correlation. With winter coming in, parts towards the north along the downstream of Chambal tend to have comparatively higher TDS than the rest of the region. This salinity in groundwater (GW) and municipal water (MW) can be due to river flow, as illustrated in Fig. 14.

Fig. 14

TDS map of winter season

From Fig. 3 and Fig. 7, the small angle formed between the loading of pH and TDS in Fig. 12 can be confirmed to be true in the case of location 11. Therefore, groundwater pumped from the hand pump in location 11 will showcase high alkalinity in summer. Turbidity and alkalinity vectors have an acute angle between them during summer and are correlated to second component.

Fig. 15

The component loadings for the Summer season.

In support of this observation in Fig. 15, with summers coming in, groundwater pumped through hand pumps in the northern parts tends to become brackish.

The spatial as well as climatic variability during the experiment makes it difficult to present ground, surface, and municipal water quality variations with distinct parameters such as pH, TDS, turbidity, hardness, alkalinity, or iron content values that are available for each of the 18 stations. Therefore, WQI values are calculated following CCME guidelines and using the Indian standard for drinking water quality for defining the limits. Table 4 provides the F1, F2, and F3 calculations (Lumb et al., 2006).

Table 4

CCME F1, F2, and F3 scores along with calculated WQI.
Sample No.	Source of Water	Category	Latitude	Longitude	F1	F2	F3	WQI (CCME)
1	Handpump	Ground water	25.16165	75.873456	33.33	11.11	1.153	79.7
7	Handpump	Ground water	25.205226	75.890442	83.33	55.55	49.32	35.54
9	Handpump	Ground water	25.226222	75.885965	100	66.66	67.36	20.45
11	Handpump	Ground water	25.246898	75.901792	66.66	55.55	22.78	48.19
14	Handpump	Ground water	25.202736	75.856571	83.33	66.66	42.21	33.73
16	Handpump	Ground water	25.193964	75.819039	83.33	55.55	46.31	36.29
2	Canal	Surface Water	25.142141	75.892902	33.33	11.11	23.79	75.49
3	Flowing Water	Surface Water	25.113779	75.920407	33.33	11.11	0.55	79.71
8	Kala Talab	Surface Water	25.210302	75.894912	83.33	55.55	58.83	32.93
17	Abhera Talab	Surface Water	25.202741	75.792006	33.33	16.66	37.97	69.27
19	Kota Lake	Surface Water	25.182998	75.806336	66.66	38.88	23.38	53.43
48	Kishor Sagar Lake	Surface Water	25.184182	75.852821	50	38.88	57.9	50.44
13	Municipal pipeline	Municipal water	25.218341	75.870811	66.66	33.33	11.61	56.44
15	Municipal pipeline	Municipal water	25.201477	75.837495	33.33	22.22	5.91	76.61
20	Municipal pipeline	Municipal water	25.144425	75.830471	50	22.22	5.44	68.25
28	Municipal pipeline	Municipal water	25.139694	75.811309	66.66	27.77	28.79	55.109
33	Municipal pipeline	Municipal water	25.130996	75.843625	16.66	16.66	0.93	86.38
38	Municipal pipeline	Municipal water	25.134043	75.846481	50	27.77	25.32	63.88

Interpretations from Fig. 16 illustrates that southern locations of Kota city are found to have comparatively good quality (CCME WQI Value 80–94) water available, even though water is sourced from a lake, hand pump or municipal supply. Large regions in the study area come under water with marginal CCME water quality indices of 45–64 (Iqbal et al., 2024). Northwest parts of the location have the worst quality water sources, with CCME WQI values ranging from 0 to 44. But it is to be understood that these WQI calculations were arrived at from those basic variables of pH, TDS, Turbidity, Hardness, Alkalinity or iron content (Hu et al., 2022). Therefore, there will be some major variables that may influence WQI values.

Fig. 16

Using Eq. 1, the CCME WQI variability in different water sources is geospatially depicted using RBF interpolation.

3.2 Statistical Modeling

A Pareto analysis is performed between the various variables that were used to calculate the F1, F2 and F3 calculations and also the WQI measurements shown in Table 4. In Fig. 17, the bars that represent factors C, B, which are TDS (mg/L) and Turbidity (NTU) cross the reference line for statistical significance, that is, at 2.012. TDS (mg/L) and Turbidity (NTU) are statistically significant at the 0.05 level of confidence for the current CCME WQI (Y) values.

Fig. 17

Pareto chart illustrating TDS (mg/L) as the most influential parameter for defining WQI.

Thus, from the Pareto chart, it is evident that TDS (mg/L) content in water samples is a major parameter that influences water quality. From Plappally et al, 2010, the Y_i (WQI CCME) can be written as a function of X1 (TDS mg/l). Therefore, Y_i can be modelled using a lognormal quotient response ln Q = ln

$\:\frac{\frac{{X}_{1}}{{X}_{1max}}}{\frac{{Y}_{i}}{{Y}_{imax}}}$

(Plappally, 2010).

$\:ln\frac{\frac{{X}_{1}}{{X}_{1max}}}{\frac{{Y}_{i}}{{Y}_{imax}}}=a+bln\frac{{X}_{1}}{{X}_{1max}}$

Eq. 4

It is well known that turbidity is the water clarity parameter defining the quality of any water source in a visual manner. Further Fig. 17 also makes it a significant parameter influencing the CCME WQI (Y). Therefore, turbidity NTU is considered as another variable X₂, then ln Q = ln

$\:\frac{\frac{{X}_{1}}{{X}_{1max}}}{\frac{{Y}_{i}}{{Y}_{imax}}}$

predicted in Eq. 4 is again expressed as

$\:ln\frac{\frac{{X}_{1}}{{X}_{1max}}}{\frac{{Y}_{i}}{{Y}_{imax}}}=a+bln\frac{{X}_{1}}{{X}_{1max}}+cln\frac{{X}_{2}}{{X}_{2max}}$

Eq. 5

Eq. 5 provides a new model to predict WQI CCME with minimum predictor variables, namely total dissolved solids and Turbidity. Eq. 5 can be used to predict Y_i for any season for any water source in any region across the world.

Eq. 4 and Eq. 5 are applied to all eighteen stations in this study, one after the other, to understand the influence of TDS individually and separately, along with turbidity taken together, respectively.

$\:Ln\:Q=Ln\:\left(\frac{\frac{{X}_{1}}{{X}_{1max}}}{\frac{{Y}_{i}}{{Y}_{imax}}}\right)=a+b\:ln\frac{{X}_{1}}{{X}_{1max}}+c\:ln\frac{{X}_{2}}{{X}_{2max}}$

Eq. 6

Table 5

The non-linear quotient response model for ground water samples for all seasons based on Eq. 3 for the prediction of Yi with the coefficient of determination and Error of the model S
No. of Variables	Coefficients	a	b	c	R² (%)	S, Error of Model
1	Ln X₁/X₁max	1.062	1.484		90.25	0.3085
2	Ln X₂/X₂max	1.173	1.487	0.0646	91.45	0.2983

An analysis of variance, as elaborated by Soboyejo 1968 is performed to assess the efficacy of the model elaborated in Table 5. The analysis uses Var (Q) = 0.9187, Var (X₁) = 0.3766 and Var (X₂) = 2.646, which are variances or errors expected in the quotient response Q, individual predictor variables X₁ and X_2, respectively, using descriptive statistics in Minitab Statistical Software (License- Anand Plappally, IITJ) (Soboyejo, 1968). The analysis of variance for the model defined by Table 5 is written as

$\:Var\left(Q\right)\simeq\:\:{b}_{2}^{2}Var\left({X}_{1}\right)+\:{c}_{2}^{2}Var\left({X}_{2}\right)$

Eq. 7

$\:\:0.9187\simeq\:\:{\left(1.487\right)}^{2}{0.3766+\:\left(0.646\right)}^{2}2.646$

$\:\simeq\:0.8437$

This assessment concludes that the model elaborated in Eq. 6 was good enough in providing a good prediction of Q. However, it is known that regression is performed with independent variables. Here, the correlation between variables X₁ and X_2, as from Table 5 for groundwater samples, is -0.020 at a confidence level of 0.05. Therefore, multivariate analysis is performed to remove the correlations, and new independent variables NCX₁ and NCX₂ corresponding to X₁ and X₂ are found and a new Eq. 8 is written ,

$\:Q=\:{a}^{{\prime\:}}+{{b}_{1}^{{\prime\:}}NCX}_{1}+\:{b}_{2}^{{\prime\:}}{NCX}_{2}$

Eq. 8

$\:=0.0121-0.5711{NCX}_{1}-0.7197{NCX}_{2}$

Where

$\:{a}^{{\prime\:}}$

$\:{b}_{1}^{{\prime\:}}$

and

$\:{b}_{2}^{{\prime\:}}$

are intercept of the model and coefficients of the independent variables in Eq. 8. From this analysis, it is known that the new quotient response variable Q is negatively impacted by TDS and Turbidity.

Table 6

Prediction of Yi with the coefficient of determination and Error of the model S for the Eq. 6 of surface water samples for all seasons.
No. of Variables	Coefficients	a	b	c	R² (%)	S, Error of Model
1	Ln X₁/X₁max	0.563	1.2602		92.85	0.2573
2	Ln X₂/X₂max	0.770	1.2614	0.1108	96.05	0.1975

Again, analysis of variance is performed to assess the efficacy of the model elaborated in Table 6. The analysis uses Var (Q) = 0.8714, Var (X₁) = 0.5094 and Var (X₂) = 2.2719, which are variances or errors expected in the quotient response Q, individual predictor variables X₁ and X,₂ respectively, using descriptive statistics in Minitab Statistical Software (License- Anand Plappally, IITJ). The analysis of variance for the model defined by Table 6 is written as per Eq. 7,

$\:0.8714\:\simeq\:\:{\left(1.2614\right)}^{2}0.5094+\:{\left(0.1108\right)}^{2}2.2719$

$\:\simeq\:0.8385$

This assessment concludes that the model in Table 6 provides a good prediction of Q. But, it is known that regression is performed with independent variables. Here, the correlation between variables X₁ and X_2, as from Table 6 for surface water samples, is -0.005 at a confidence level of 0.05. Therefore, multivariate analysis is performed to remove the correlations and new non correlated NCX_1a and NCX_2a corresponding to X₁ and X₂ are written in Eq. 9 as

$\:Q=\:{a}^{{\prime\:}{\prime\:}}+{{b}_{1}^{{\prime\:}{\prime\:}}NCX}_{1a}+\:{b}_{2}^{{\prime\:}{\prime\:}}{NCX}_{2a}$

Eq. 9

$\:=\:-\:0.6012-0.5186{NCX}_{1a}-0.7548{NCX}_{2a}\:$

Where

$\:{a}^{{\prime\:}{\prime\:}}$

$\:{b}_{1}^{{\prime\:}{\prime\:}}$

and

$\:{b}_{2}^{{\prime\:}{\prime\:}}$

are intercept of the model and coefficients of the independent variables NCX_1a and NCX_2a in Eq. 9. Again, from the analysis of surface water, it is known that the new quotient response variable Q is again negatively impacted by TDS and Turbidity.

Table 7

Prediction of Yi with the coefficient of determination and Error of the model S for the Eq. 6 of municipal water samples for all seasons.
No. of Variables	Coefficients	a	b	c	R² (%)	S, Error of Model
1	Ln X₁/X₁max	0.324	1.082		93.10	0.1628
2	Ln X₂/X₂max	0.446	1.094	0.0456	94.37	0.1520

Further analysis of variance is performed to assess the efficacy of the model elaborated in Table 7. The analysis uses Var (Q) = 0.3621, Var (X₁) = 0.2875 and Var (X₂) = 2.2227, which are variances or errors expected in the quotient response Q, individual predictor variables X₁ and X_2, respectively, using descriptive statistics in Minitab Statistical Software (License- Anand Plappally, IITJ). The analysis of variance for the model defined by Table 7 is written as per Eq. 7,

$\:0.3621\:\simeq\:{\left(1.094\right)}^{2}\:0.2875+\:{\left(0.0456\right)}^{2}2.2227$

$\:\simeq\:0.3487$

This variance analysis of the model presented in Table 7 concludes that the model elaborated is significant enough in providing a good prediction of Q. But it is known that regression is performed with independent variables. Here, the correlation between variables X₁ and X_2, as from Table 7 for municipal water samples, is -0.089 at a confidence level of 0.05. Therefore, multivariate analysis is performed to remove the correlations, and new independent variables NCX_1b and NCX_2b corresponding to X₁ and X₂ are found and a new Eq. 10 is written

$\:Q=\:{a}^{{\prime\:}{\prime\:}{\prime\:}}+{{b}_{1}^{{\prime\:}{\prime\:}{\prime\:}}NCX}_{1b}+\:{b}_{2}^{{\prime\:}{\prime\:}{\prime\:}}{NCX}_{2b}$

Eq. 10

$\:=-0.5759-0.3668{NCX}_{1b}-0.4629{NCX}_{2b}$

Where

$\:{a}^{{\prime\:}{\prime\:}{\prime\:}}$

$\:{b}_{1}^{{\prime\:}{\prime\:}{\prime\:}}$

and

$\:{b}_{2}^{{\prime\:}{\prime\:}{\prime\:}}$

are intercept of the model and coefficients of the uncorrelated variables NCX_1b and NCX_2b in Eq. 10. Again, from the analysis of surface water, it is known that the new quotient response variable Q is again negatively impacted by TDS and Turbidity. Eq. 8, Eq. 9 and Eq. 10 have provided the proof of repeatable applicability of Eq. 6 as the new CCME-based-water-quality index prediction model for distinct water sources from a region. Consistently, a coefficient of determination R² of more than 90% has been showcased for all predictions using Eq. 6 for the individual water sources.

The multivariate analysis confirms the natural tendency that excessive amounts of TDS and turbidity in water are deleterious to water and may have a negative influence on water quality indices. Finally, the said prediction model (Predicted WQI) in Eq. 6 is plotted in Fig. 18 and is found to almost overlap the calculated WQI (Eq. 1) provided in Table 4.

Fig. 18

Graph depicting the Predicted WQI and the Calculated WQI.

6. Conclusion

Water samples collected from eighteen locations in Kota, Rajasthan—covering groundwater, municipal supply, and surface water—were analysed using IS 10500:2012 standards and evaluated through the CCME Water Quality Index (WQI). Six key physico-chemical parameters (pH, turbidity, TDS, total hardness, total alkalinity, and iron) were monitored across three seasons during 2022–23, revealing clear seasonal and spatial variations in water quality. Municipal pipeline sources exhibited the highest WQI (86.38), while groundwater from handpumps showed the lowest (20.45), indicating significant variability in drinking water suitability based on source and location. Pareto analysis identified TDS and turbidity as the dominant contributors to WQI degradation, and spatial contour mapping confirmed that water quality was better in the southwest region of the study area and poorest in the northwest. To accelerate water quality assessment, a novel non-linear regression model was developed using TDS and turbidity to predict WQI. After multivariate analysis removed interdependence between the variables, the logarithmic quotient response (Ln Q) showed a negative relationship with both parameters. The model produced consistent WQI predictions across all seasons, and its accuracy and repeatability were confirmed through analysis of variance (ANOVA). Overall, the study demonstrates that water quality in Kota is strongly influenced by seasonal dynamics and source type, and that TDS and turbidity can be used as reliable predictors for rapid, cost-effective WQI estimation—supporting smarter water monitoring and better resource management.

Electronic Supplementary Material

Below is the link to the electronic supplementary material

Supplementary Material 1

Additional Files

Additional file 1

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Declarations

Acknowledgement

The authors would like to thank the Rajasthan State Pollution Control Board (RSPCB), Kota (S/RSPCB/DPB/20210102) for supporting Dr Deepika Bhattu for this

Research.

Funding

Yes, Rajasthan State Pollution Control Board (RSPCB), Kota (S/RSPCB/DPB/20210102) to Dr. Deepika Bhattu

Author contribution

Himanchal Bhardwaj: conceptualization, data curation, formal analysis, investigation, methodology, writing original draft; Rajkumar Satankar: model development, validation, visualization; Deeptha Giridharan: model development, validation, visualization. Deepika Bhattu: writing-review and editing, supervision. Venkata Ravibabu Mandla: methodology, writing-review and editing, supervision; Anand K Plappally: writing original draft, Editing & Review, supervision.

Ethics approval

Not applicable (results of studies do not involve any human or animal).

Consent to participate

Informed consent was obtained from all participants in the study.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Data Availability Statement

All data used in this article may be shared on request.

Yes

Abstract

Water quality assessment is fundamental to understanding the suitability of water for human consumption, ecological sustainability, and industrial applications. This study presents an empirical multi-parameter approach for estimating the Canadian Council of Ministers of the Environment (CCME)-based Water Quality Index (WQI) in Kota, Rajasthan, India. Eighteen samples from groundwater, surface water, and municipal supplies were analyzed for six parameters—pH, turbidity, total dissolved solids (TDS), hardness, alkalinity, and iron—following BIS IS 10500:2012 standards. Pareto analysis revealed turbidity and TDS as the most influential, independent drivers of WQI. GIS-based mapping captured spatial and seasonal variation, highlighting persistent water quality stress across the city. A quotient response function was developed using normalized parameters, and a predictive regression model was formulated with TDS and turbidity as core variables. The model achieved high accuracy, with R2 values of 91.45% for groundwater, 96.05% for surface water, and 94.37% for municipal water. The results establish a scalable, source-independent framework for predicting WQI, offering robust support for urban water resource monitoring and sustainable management.