Kernel principal component analysis-based water quality index modelling for coastal aquifers in Saudi Arabia

Abstract

This study developed a novel Water Quality Index (WQI) using Kernel Principal Component Analysis (PCA) to assess groundwater quality (GWQ) in the coastal aquifers of Al-Qatif, Saudi Arabia. A total of 39 groundwater samples were collected from shallow and deep wells and analyzed for key physicochemical parameters. Six kernel types were tested, and the polynomial kernel was found to be most effective in preserving variance and reducing dimensionality. The Kernel PCA-based WQI classified wells into ‘Very Bad,’ ‘Bad,’ and ‘Medium’ categories, with scores such as W3 (WQI = 25.51, “Very Bad”), W31 (WQI = 46.7, “Bad”), and W38 (WQI = 56.75, “Medium”). Salinity and EC presented poor Sub-Index (SI) scores, reflecting the impact of seawater intrusion and over-extraction, while pH consistently showed high SI values (100), indicating natural buffering. By integrating non-linear dimensionality reduction, the proposed framework enhances traditional WQIs and facilitates more targeted and transparent groundwater decision-making. This includes identifying priority wells for remediation and supporting sustainable abstraction policies. The findings offer insight into sustainable water management in arid and semi-arid regions that are confronting groundwater degradation.

Introduction

Groundwater is a vital natural resource, replenished through various natural and artificial recharge processes such as rainfall infiltration, river seepage, lateral subsurface flow, and managed aquifer recharge^1–3. Its availability is especially critical in arid and semi-arid regions, where surface water is scarce and rainfall is intermittent^4,5. It constitutes nearly 99% of the world’s freshwater, excluding snow and ice⁶, and supports critical uses such as domestic supply, agriculture, and industry. Coastal areas, which host a significant share of the global population, depend heavily on groundwater for these purposes^7,8. However, coastal aquifers face increasing environmental pressures—seawater intrusion, salinization, and pollution from agricultural and urban activities—which severely affect groundwater quality (GWQ)^3,9,10.

In Saudi Arabia, where more than 80% of the water supply is sourced from groundwater¹¹. These pressures are especially acute. With annual extraction exceeding 17 billion m³¹², regions such as Al-Qatif experience intense stress from over-abstraction, high evapotranspiration, and rapid urban expansion^13,14. These dynamics contribute to declining water quality, especially in coastal zones where geological and hydrological conditions favor saltwater intrusion. As demands grow, there is an urgent need for advanced tools to monitor and evaluate GWQ¹⁵. A combination of natural processes and anthropogenic activities, including mineral dissolution, seawater intrusion, agricultural runoff, and industrial discharge, influences the GWQ¹⁶. Assessment methods vary widely and include direct comparison to regulatory limits, the use of integrated indicators such as the Water Quality Index (WQI)², geospatial mapping¹⁷, machine learning^18,19, and statistical approaches²⁰.

The WQI is widely used to simplify complex hydrochemical datasets into a single interpretive value, guiding decisions on water usability for drinking, irrigation, and other applications^21–23. While effective, the traditional WQI relies on fixed weighting schemes and linear aggregations, which may overlook non-linear interactions and fail to capture complex trends. To enhance the robustness of WQI construction, statistical methods such as Principal Component Analysis (PCA) have been used to determine data-driven weights and reduce redundancy^24–26.

PCA, however, assumes linearity and cannot effectively account for the complex, non-linear relationships that often characterize groundwater systems, particularly where salinity, ion mobility, and anthropogenic influence intersect²⁷. In such cases, PCA may fail to resolve overlapping or intertwined gradients in water quality parameters, leading to oversimplified or misleading interpretations. This is especially possible for arid coastal environments, such as Al-Qatif, where interacting processes, including seawater intrusion, reverse ion exchange, and variable abstraction rates across aquifer depths, drive hydrochemical variability. These processes produce multi-scale, non-linear behavior in physicochemical parameters—particularly in salinity, chloride, nitrate, bromide, and EC—making traditional linear projections insufficient for accurate representation of water quality patterns. In contrast, Kernel PCA offers a powerful extension. By mapping input data into a higher-dimensional feature space using non-linear kernel functions, Kernel PCA can uncover latent structures that classical PCA cannot detect^28,29. This enables more flexible modeling of GWQ patterns in regions where both natural processes and localized contamination contribute to variability.

Despite its potential, Kernel PCA has rarely been applied in the context of groundwater for WQI development. Studies have not evaluated the comparative performance of different kernel types in preserving data variance or capturing key hydrochemical interactions. This study addresses this gap by developing a Kernel PCA-based WQI for groundwater assessment in the coastal aquifers of Al-Qatif, Saudi Arabia. Six kernel types—linear, polynomial, radial basis function (RBF), sigmoid, cosine, and Laplacian—were evaluated for their ability to retain variance and reduce dimensionality. The proposed approach integrates kernel-based dimensionality reduction with physicochemical analysis to construct a data-driven WQI, offering a novel framework for GWQ assessment under complex, non-linear conditions.

The current study develops an enhanced version of WQI that integrates with Kernel PCA to overcome the various limitations presented by the conventional and custom models of WQI. The objectives of the study are:

• i.To develop a Kernel PCA-WQI that provides a robust and reliable framework for evaluating GWQ under extreme variability and complex conditions.
• ii.To determine the overall water quality of groundwater from each well and classify it into predefined WQI categories (Very bad, bad, medium, good, and excellent) based on PCA-derived WQI scores.

Study area and description

Description of the study area

The study area is located in the Eastern Province of Saudi Arabia, along the western coastline of the Arabian Gulf. It includes the Al-Qatif governorate, comprising the Al-Qatif region and Tarout Island. This area is characterized by an arid climate with low annual rainfall and high evaporation, contributing to elevated groundwater salinity¹⁴. Evaporative concentration and seawater intrusion are key drivers of salinization in the region’s coastal aquifers³⁰. Groundwater is the principal water source for domestic, agricultural, and industrial use. The subsurface lithology of the Al-Qatif region comprises several distinct formations that control groundwater occurrence and quality. The dominant geologic units include the Dammam Formation, composed mainly of dolomitized limestone and marl; the Hadrukh Formation, characterized by interbedded shales and sandstone; and the Dam Formation, which contains marine clays and marls^3,31. These formations serve as host strata for three major aquifers: the shallow Neogene aquifer and the deeper Alat and Al-Khobar aquifers. The Al-Khobar aquifer, developed in karstified limestone of the Dammam Formation, is especially productive. Overlying Quaternary deposits, such as sabkha and eolian sand, also influence recharge and salinity through land–sea interactions and evapotranspiration.

The hydrochemical characteristics and water quality of shallow and deep aquifers in the study area reveal distinct patterns driven by depth-dependent recharge and salinization processes. The shallow aquifers—primarily hosted within unconsolidated sediments and sabkha zones—exhibited elevated levels of salinity, EC, Na⁺, and Cl⁻, which are indicative of seawater intrusion and increased vulnerability to surface contamination³². In contrast, deep aquifers associated with the Dammam and Hadrukh formations showed comparatively lower concentrations of these ions and greater buffering capacity due to lithological confinement and reduced direct interaction with surface activities³. Similar trends have been reported that salinization and ionic enrichment were more pronounced in shallow wells, particularly those located near the coastline and in faulted zones with high transmissivity³¹. The terrain consists of a flat coastal plain, underlain by both shallow and deep aquifers. The shallow Neogene aquifer reaches depths of up to 12 m, while the deeper Alat and Al-Khobar aquifers extend to approximately 130 m. Groundwater exploitation is more intensive in the deeper aquifers due to salinity issues in the upper layers. Water levels range from less than 1 m to 11 m, with lower levels near the coast. The central part of Al-Qatif shows relatively higher groundwater levels, attributed to a reduction in abstraction and partial recharge through treated wastewater³³.

Data collection

A systematic collection of water samples from both shallow and deep aquifers in Al-Qatif was conducted to facilitate a comprehensive laboratory analysis of physicochemical properties. Groundwater sampling was conducted between March and April 2022, following standard procedures recommended by the United States Environmental Protection Agency (EPA). The samples were obtained using submersible pumps after approximately 15 min of pumping to ensure that stale water was adequately removed³⁴. To ensure the groundwater data’s representativeness and accuracy, in-situ measurements of key physicochemical parameters, including pH, turbidity, and electrical conductivity (EC), were performed using a multimeter. At the laboratory, samples were filtered using a 0.45 μm membrane to remove suspended particles and then stored at a constant temperature of 4 °C until the beginning of the analysis. Each well was analyzed for different physical and chemical parameters, including pH, electrical conductivity (EC), calcium carbonate (CaCO₃), turbidity, and concentrations of sodium (Na⁺), potassium (K⁺), magnesium (Mg²⁺), calcium (Ca²⁺), fluorine (F⁻), chlorine (Cl⁻), bromine (Br⁻), nitrate (NO₃⁻), sulfate (SO₄²⁻), and salinity, with the measurements reported in mg/L, while pH is unitless and EC is expressed in µS/cm. Figure 1 illustrates the study area of the Al-Qatif region and the locations of the wells, while Table 1 provides a statistical overview of the GWQ parameters. The observed high standard deviations in several hydrochemical parameters, salinity, EC, Na⁺, and Br⁻, reflect the strong spatial heterogeneity across the study area. This variation arises from localized seawater intrusion and site-specific anthropogenic influences.

Fig. 1.

Study area with sample locations. The boundary map data was derived from DIVA-GIS (https://www.diva-gis.org/), and the map was prepared in QGIS software (https://www.https://qgis.org/).

Table 1.

Descriptive statistics of GWQ quality parameters.

Parameter	Mean	Standard deviation	Skewness	Variation coefficient
pH	7.1213	0.4568	0.7567	6.4149
EC	7802	7284	3.5717	93.3506
CaCO3	252	168.9107	1.3195	67.0220
Turbidity	6.6621	11	2.9523	169.6646
Na+	601	722	4.1144	120.0879
K+	31	38	3.6023	120.4794
Mg2+	144	201	4.7064	138.9529
Ca2+	280	167	1.3139	59.4527
F⁻	1.2457	0.9370	1.1984	75.2194
Cl⁻	1607	1712	3.7099	106.5261
Br⁻	6.8015	6.6940	3.2529	98.4195
NO3⁻	8.2285	5.5813	−0.6282	67.8281
SO42⁻	876	861	3.4149	98.2895
Salinity	5446	5667	3.6366	104.0679

Methodology

Kernel principal component analysis (Kernel PCA)

Kernel Principal Component Analysis (Kernel PCA) identifies principal components (PCs) from high-dimensional data and converts it into a lower-dimensional representation that simplifies the model^35,36. Kernel PCA uses a kernel trick to map the original dataset into a high-dimensional feature space where linear separability can be achieved³⁷. Projected PCs can be mapped back to the original space for dimensionality reduction while preserving data structure. Unlike classical PCA, which is based on a linear approach, Kernel PCA uses kernel functions to capture nonlinear relationships in data. Kernel PCA is effective in situations where data lie on nonlinear manifolds due to its unique characteristics. Therefore, it is an essential approach in multivariate statistical analysis and finds a broad range of applications in several scientific and engineering fields^38,39.

Outlier assessment was performed using box-and-whisker plots to visualize the spread and skewness of each parameter (see Fig. 4, presented later). Although several values appeared extreme, they were not removed to preserve the natural variability in the dataset. Instead, min-max normalization was applied to scale all features to the range [0, 1], ensuring uniform contribution to Kernel PCA without discarding relevant hydrochemical signatures. The procedure for conducting the Kernel PCA is summarized in three main steps as follows:

Fig. 4.

Box-and-whisker plot for the normalized dataset.

Step 1 Min-max normalization.

Min-max normalization scales data to a specific range, typically [0, 1], ensuring uniformity across variables for analysis (Eq. 1)⁴⁰.

1

where is the original value, and are the minimum and maximum values of the feature and is the normalized value.

Step 2 Testing suitability for Kernel PCA.

Before applying Kernel PCA, the dataset’s suitability must be verified to ensure meaningful results. This involves two key statistical tests:

• i.Kaiser-Meyer-Olkin (KMO) Test.

The KMO measure evaluates the adequacy of the dataset for PCA by assessing the proportion of variance among variables that can be attributed to common factors⁴¹. A KMO value closer to 1 indicates high suitability, while a value less than 0.5 represents an inappropriate choice for PCA analysis. The overall KMO statistic is computed using Eq. 2 (42).

2

where and are the squared correlation coefficient and the squared partial correlation coefficient, respectively.

• ii.Bartlett’s Test of Sphericity (BTS).

This test indicates whether the dataset’s correlation matrix is significantly different from an identity matrix, which means sufficient interrelationships among variables for PCA^43,44. The null hypothesis assumes that the correlation matrix is an identity matrix. A significant value (< 0.05) rejects , confirming suitability for PCA. Bartlett’s test statistics are calculated using Eq. 3⁴⁵.

3

Where is the sample size, represents the number of variables and is the correlation matrix.

Step 3 Applying Kernel PCA.

Kernel PCA was applied to the normalized dataset to identify key patterns and reduce dimensionality. PCs were derived, with the number of retained components determined by the cumulative variance they explained (at least 90%)⁴⁶. Table 2 shows the comparison of Kernel types and their properties. The kernel that shows higher cumulative variance with fewer components is the best one.

Table 2.

Overview of kernel types, formulae, and their functions^47–49.

Kernel Type	Mathematical Formula	Characteristics	Hyperparameters
Linear		Preserves the original data structure and is equivalent to standard PCA.	None
Polynomial		Maps data into a higher-degree polynomial space and captures feature interactions.	(coefficient),(degree)
RBF		Transforms data into an infinite-dimensional space, effectively capturing complex, nonlinear structures.	(spread of Gaussian)
Sigmoid		Inspired by neural networks and models similarity in a smooth way.	(scale),(shift)
Cosine		Measures the angle between vectors	None
Laplacian		Similar to RBF but uses the L1 norm to capture local structures.	(scale factor)

*is the kernel function for vectors (and) andrepresents the transpose operator.

Kernel parameter tuning was conducted via grid search. For the polynomial kernel, combinations of degree = [2, 3, 4, 5] and gamma = [0.01, 0.1, 1] were tested. The optimal configuration (degree = 3, gamma = 0.1) was selected based on the few PCs needed to exceed 95% cumulative variance. Similar parameter tuning was applied to RBF and sigmoid kernels, while linear and cosine kernels required no tuning.

All analyses were performed using Python (version 3.13). The scikit-learn library was used for Kernel PCA and data normalization, including the implementation of six kernel types. Scipy.stats was used to conduct Bartlett’s test of sphericity, and the factor_analyzer module was used for calculating the Kaiser-Meyer-Olkin (KMO) statistic. Visualization and plotting were performed using the matplotlib and seaborn libraries. The pseudocode in Algorithm 1 outlines the key computational steps for implementing Kernel PCA, including normalization, kernel matrix computation, centering, eigen-decomposition, and projection into PC space. This method enables the transformation of original groundwater parameters into a lower-dimensional feature space for the development of the WQI.

Algorithm 1

Pseudocode for Kernel PCA used in groundwater data transformation.

Water quality index (WQI)

The development of WQI has evolved significantly over time, with foundational contributions from⁵⁰. They developed the most widely accepted method, which involves computing the quality rating scale for each water quality parameter and multiplying it by the weight of each parameter. These weights are inversely proportional to recommended standards. In this work, the WQI is prepared with weights from Kernel PCA based on standards and practices concerning GWQ. Figure 2 illustrates the overall research methodology for developing Kernel PCA-Based WQI. PCA has also been implemented to further develop and interpret the dataset. Finally, the final model of the WQI provides a numerical index ranging from 0 to 100, categorizing water quality based on the classification scheme. Table 3 presents the scores and classification based on the proposed ranking criteria.

Fig. 2.

Research methodology flowchart for the development of Kernel PCA-Based WQI.

Table 3.

WQI ranking criteria ⁵¹.

WQI	Category
0–25	Very bad
26–50	Bad
51–70	Medium
71–90	Good
91–100	Excellent

The permissible limit refers to the maximum concentration that is considered safe for use or consumption. Table 4 provides the standard permissible limits for GWQ parameters. The permissible levels were compiled from the World Health Organization (WHO) and the Ministry of Environment, Water and Agriculture (MEWA)^52,53. The procedure for the WQI is categorized into five steps after performing the PCA. The steps are as follows:

Table 4.

Permissible limits of groundwater parameters ^52,53.

Parameter	Standard
pH	7
EC	1000 µS/cm
CaCO₃	500 mg/L
Turbidity	5 NTU
Na+	200 mg/L
K+	12 mg/L
Mg2+	50 mg/L
Ca2+	75 mg/L
F⁻	1.5 mg/L
Cl⁻	200 mg/L
Br⁻	2 mg/L
NO₃⁻	50 mg/L
SO₄²⁻	250 mg/L
Salinity	1000 mg/L

Step 1 Sub-index (

).

The sub-index () is calculated using either Eq. 4 or 5 depending on the observed values of the parameters.

4

where is the observed value, denotes the ideal value, and is the permissible limit.

Purpose Eq. 4 is used when the observed value is within the permissible range (i.e., ).

Behavior:

• It linearly scales the deviation of between and .

• If approaches , the score approaches 0.

• If ​ is closer to , the score approaches 100.

• The use of max(0, …) ensures that the sub-index cannot drop below 0.

If exceeds ​, a log transformation is applied:

5

Purpose This Eq. 5 is used when the observed value 

exceeds the permissible limit .

Behavior:

• A logarithmic transformation is applied to dampen the penalty for values of that exceed ​.

• This prevents extreme deviations from having disproportionately large penalties compared to a linear scale.

• The inclusion of as a scaling factor ensures the score decreases more gradually.

• Unlike Eq. 4, there is no explicit floor of , meaning can technically drop below zero for very high .

Step 2 Weight of a parameter ().

The initial weight is determined based on the PCA loading () of parameter on the selected PCs as shown in Eq. 6⁵⁴:

6

where is the number of retained PCs, represents the eigenvalue (explained variance) of the PC, and ​ is the loading of the parameter on the PC.

Step 4 Normalized weight 

.

 The weights are normalized to ensure their sum equals 1 (Eq. 7)⁵⁵:

7

If weights are negative, absolute values are applied to adjust relative contributions.

Step 5 Final score.

The final is calculated by multiplying the normalized weights () with the ​ as shown in Eq. 8 :

8

where is the adjusted relative weight of the parameter .

Combining all steps, the general equation becomes (Eq. 9):

9

Results and discussion

Kaiser–Meyer–Olkin (KMO) and bartlett’s tests of sphericity (BTS)

The appropriateness of the dataset for Kernel PCA was evaluated through the KMO test and BTS. The KMO test measures sampling adequacy by quantifying the proportion of variance accounted for by underlying PCs. A KMO value nearing 1 indicates a dataset suitable for PCA, while a KMO value below 0.5 indicates that the dataset is unsuitable for PCA. In this current study, the observed KMO value is 0.79, indicating adequate sampling. Conversely, Bartlett’s test of sphericity assesses whether the correlation matrix resembles an identity matrix. This imply that the variables are uncorrelated and thus not conducive to PCA⁴⁶. In this analysis, a p-value of 0.000 (below the 0.05 threshold) justifies rejecting the null hypothesis, confirming the existence of significant relationships among the variables. Both tests confirmed that the dataset is suitable for the PCA.

Figure 3 presents the results of PCA suitability and the correlation heatmap illustrating the relationships between the parameters. The correlation matrix highlights essential trends in GWQ parameters, revealing strong positive correlations between EC, salinity, Na⁺, and Cl⁻, which significantly contribute to the ionic strength of groundwater. K⁺, Mg²⁺, and Ca²⁺ also highly correlate with EC, further emphasizing their influence on water chemistry. In contrast, pH exhibits negative correlations with CaCO₃ and SO₄²⁻, suggesting that lower pH levels enhance processes like carbonate dissolution. Turbidity shows moderate correlations with both EC and SO₄²⁻, suggesting partial influences on ionic variations. On the other hand, nitrate generally exhibits a weak correlation with most parameters, indicating localized human activities, such as agricultural runoff.

Fig. 3.

Correlation matrix heatmap and PCA suitability tests.

Kernel PCA-based WQI

Normalization of raw data represents the first step in developing the Kernel PCA-based WQI. It is one of the essential steps that makes the range of the data uniform, providing all variables with an opportunity to contribute to the analysis⁵⁶. Figure 4 shows a box-and-whisker plot that visually summarizes the distribution, variability, and outliers of each physicochemical parameter. NO₃⁻ and pH exhibit high variability, as evidenced by their more extensive interquartile ranges (IQR) and multiple outliers. In contrast, EC, CaCO₃, turbidity, and salinity display relatively minor IQRs, indicating more consistent values across the dataset. The outliers observed in Cl⁻, F⁻, and Ca²⁺ parameters suggest localized anomalies or unique physicochemical characteristics in specific wells.

The comparison of CV across five types of Kernels PCA—linear, polynomial, radial basis function (RBF), sigmoid, cosine, and Laplacian—reveals significant differences in their ability to retain data variability, as shown in Table 5. The polynomial kernel performed exceptionally well, capturing 98.33% of the variance in the first PC. By PC5, it captures 99.77% of the variance, and by PC7, it nearly achieves complete variability at 99.98%. The strong performance of the polynomial kernel PCA can be attributed to its ability to preserve maximum variability while capturing essential feature directions and efficiently reducing dimensionality⁵⁷. The polynomial kernel helps reduce intrinsic dimensionality while preserving the dataset’s statistics⁵⁸. The cosine kernel performs well, capturing 96.13% of the variance with PC5 and 99.99% cumulatively with PC9. Both polynomial and cosine kernels are effective at reducing dimensionality while preserving significant variability, making them suitable for non-linear data applications.

Table 5.

Comparison of CV for kernel types.

PC	Linear (CV)	Polynomial (CV)	RBF (CV)	Sigmoid (CV)	Cosine (CV)	Laplacian (CV)
PC1	0.73341	0.98329	0.34067	0.75024	0.59494	0.33498
PC2	0.88383	0.99344	0.57161	0.90435	0.86133	0.51469
PC3	0.93498	0.99543	0.66110	0.93824	0.91480	0.61207
PC4	0.95852	0.99673	0.72179	0.96203	0.94356	0.67532
PC5	0.97478	0.99772	0.77394	0.97729	0.96128	0.73530
PC6	0.98502	0.99831	0.81349	0.98795	0.97709	0.78262
PC7	0.99222	0.99874	0.85003	0.99226	0.99029	0.82351
PC8	0.99688	0.99914	0.88323	0.99559	0.99557	0.85417
PC9	0.99934	0.99941	0.91533	0.99874	0.99904	0.88390
PC10	0.99969	0.99962	0.94184	0.99939	0.99950	0.91060
PC11	0.99987	0.99978	0.96049	0.99985	0.99979	0.93535
PC12	0.99993	0.99989	0.97702	0.99996	0.99990	0.95873
PC13	0.99997	0.99996	0.99203	0.99999	0.99995	0.98017
PC14	1.00000	1.00000	1.00000	1.00000	1.00000	1.00000

The RBF kernel demonstrates the weakest performance in retaining CV. At PC1, it accounts for only 34.07% of the variance (CV = 0.340674), and by PC5, it captures just 77.39% of the CV, which is lower than that of other kernels. Although the RBF kernel eventually reaches 96.05% variance at PC11, its slower accumulation suggests inefficiency in capturing variability in the earlier components. While the RBF kernel is known for its effectiveness with non-linear data, it lacks a systematic approach for selecting and integrating optimal parameters to enhance performance⁵⁹. The poor performance of the RBF kernel makes it unsuitable for this analysis, as it risks losing critical data variability essential for clustering and interpreting physicochemical patterns. The Laplacian kernel has the weakest performance compared to the other kernels. At PC1, it captures only 33.49% of the variance (CV = 0.33498), which is even lower than that of the RBF kernel. By PC5, it retains 73.53%, trailing behind all the other kernels. Even at PC12, where most kernels approach full variance retention, the Laplacian kernel still falls short, achieving only 95.87% CV at PC13. In contrast, the linear and sigmoid kernels demonstrate intermediate performance, retaining 95.85% and 96.20% variance by PC4, respectively, and reaching near-total variability by PC8.

Figure 5 shows the CV results of different kernels in Kernel PCA with a 95% threshold. The polynomial kernel quickly achieves this threshold in the first PC, effectively capturing most of the data’s variability early. However, the linear and sigmoid kernels require three PCs to reach the 95% threshold, whereas the cosine kernel achieves this within four PCs. The RBF kernel lags, crossing the 95% mark only after the tenth PC. The Laplacian kernel performs the weakest. Testing various kernels in PCA offers valuable insights into their suitability for specific datasets. The polynomial kernel is selected for this study due to its ability to retain the highest CV with fewer components.

Fig. 5.

Comparison of cumulative variance of kernels with a 95% threshold.

Table 6 presents the SI and WQI scores for groundwater parameters, offering a detailed assessment of water conditions in the coastal aquifers of the study area. The WQI, derived as a weighted sum of using adjusted relative weights to categorize GWQ across wells into classes based on the WQI ranking criteria by⁵¹ as shown in Table 1, earlier. Notably, W2, W3, and W4, with WQI values of 31.27, 30.26, and 28.82, respectively, fall into the “Bad” category, while W11 exhibits the worst water quality, with a WQI of 10.64, classified as “Very Bad.” Conversely, wells such as W16, W18, and W19, with WQI values of 63.94, 61.84, and 64.63, are classified as “Medium,” indicating moderate GWQ in certain parts of the coastal aquifer.

Table 6.

Results of the SI and WQI scores for the water quality parameters.

Well	SI (pH)	SI (EC)	SI (CaCO3)	SI (Turbidity)	SI (Na+)	SI (K+)	SI (Mg2+)	SI (Ca2+)	SI (F⁻)	SI (Cl⁻)	SI (Br⁻)	SI (NO3⁻)	SI (SO42⁻)	SI (Salinity)	WQI	Class
W1	100	0	90.05	76.19	18.02	0	64.81	37.77	53.84	0	0	100	0	0	34.92	Bad
W2	100	0	8.37	51.89	35.01	0	8.39	66.34	75.65	0	0	90.23	12.47	0	31.27	Bad
W3	100	0	77.34	37.11	0	0	41.57	19.2	35.76	0	0	100	0	0	25.51	Very bad
W4	100	0	94.59	31.75	0	0	46.18	28.28	74.4	0	0	100	0	0	30.26	Bad
W5	100	0	98.37	63.68	30.5	0	89.04	60.48	82.38	0	0	100	10.3	0	42.31	Bad
W6	100	0	89.02	57.01	20.85	0	76.79	47.77	48.5	0	0	100	0	0	35.14	Bad
W7	100	0	27.06	45.91	55.26	7.78	13.76	66.4	100	0	0	100	20.72	0	37.53	Bad
W8	100	0	32.32	0	29.18	0	83.23	35.31	88.74	0	0	100	0	0	31.6	Bad
W9	100	0	32.46	8.77	43.62	0	0.5	62.04	61.7	0	0	100	12.59	0	28.82	Bad
W10	100	0	29.64	34.92	37.55	0	99.78	60.59	68.04	0	0	100	9.07	0	37.06	Bad
W11	100	0	73.21	26.41	15.82	0	75.23	40.59	42.21	0	0	100	0	0	30.64	Bad
W12	100	0	49.7	0	0	0	0	16.44	37.61	0	0	100	0	0	18.63	Very bad
W13	100	5.64	100	8.75	76.56	66.65	88.33	26.63	100	23.76	0	93.67	58.62	26.26	52.5	Medium
W14	100	9.4	100	96.25	80.64	73.99	89.92	31.24	100	27.45	0	92.47	60.84	28.01	60.59	Medium
W15	100	8.56	100	86.75	79.17	68.03	86.52	27.29	90.25	26.37	0	93.31	56.85	26.61	57.51	Medium
W16	100	11.49	100	60.5	84.36	75.82	86.12	31.91	100	32.36	0	93.47	53.29	28.13	58.4	Medium
W17	100	24.35	100	79.75	97.87	45.1	95.44	46.46	100	43.63	0	91.05	63.57	43.27	63.94	Medium
W18	100	28.91	100	89	4.46	100	98.71	56.23	100	47.22	0	94.3	68.13	46.59	64.55	Medium
W19	100	17.71	100	84.75	90.96	93.25	91.43	39.54	100	37.38	0	92.84	59.91	36.23	64.83	Medium
W20	99.33	15.74	100	83.25	88.55	97.85	91.94	37.87	100	34.82	0	95.14	61.09	34.99	64.59	Medium
W21	100	11.49	100	94	84.56	86.98	89.76	33.1	98	30.68	0	95.46	59.86	30.06	62.41	Medium
W22	100	8.06	100	91	79.75	72.23	87.4	29.59	100	26.55	0	95.22	58.66	29.09	59.66	Medium
W23	100	12.38	100	92	84.38	82.89	88.04	31.65	100	30.93	0	94.9	57.46	31.19	61.8	Medium
W24	100	2.73	100	96.75	72.47	56.25	86.19	22.17	93	19.71	0	98.01	59.6	21.26	55.77	Medium
W25	100	21.89	100	100	95.07	12.1	93.48	44.38	100	41.41	0	92.51	61.5	38.23	61.53	Medium
W26	100	13.47	100	91.75	85.96	76.06	89.14	32.7	100	32.55	0	94.39	57.91	31.57	61.78	Medium
W27	100	11.13	100	73.5	78.99	50.19	78.5	24.57	87.37	29.71	0	99.13	41.88	28.48	54.09	Medium
W28	50.67	0	100	95	56.37	47.67	70.16	95.79	73.62	1.43	0	100	51.71	4.28	52.94	Medium
W29	52	0	100	98	42.36	25.98	55.7	84.9	93.25	0	0	100	45.45	0	49.16	Bad
W30	52.67	0	100	97.75	41.11	24.04	54.31	83.95	67.62	0	0	100	45.45	0	46.7	Bad
W31	52.67	0	100	98.25	38.44	18.46	49.84	82.14	58.13	0	0	100	42.76	0	44.67	Bad
W32	50.67	0	100	96.25	36.15	16.32	44.37	79.24	94.25	0	0	100	37.76	0	45.97	Bad
W33	56	0	100	98.25	3.49	0	77.89	33.41	93.12	0	0	90.1	0	0	36.96	Bad
W34	50.67	0	100	98.75	31.73	5.38	38.23	75.76	34.75	0	0	100	35.24	0	39.29	Bad
W35	31.33	0	100	97	63.3	41.61	81.64	17.46	46	11.1	0	96.58	54.85	13.71	44.87	Bad
W36	38	1.12	100	97.75	73.57	68.04	84.66	25.48	92.12	36.33	0	88.01	58.01	20.32	54.6	Medium
W37	68	0	100	96.75	65.2	48.72	80.96	13.27	100	12.95	0	93.8	55.67	14.29	50.89	Bad
W38	43.33	17.5	100	97.5	90.73	25.35	90.12	38.5	100	20.3	0	91.14	57.33	39.54	56.75	Medium
W39	38	17.71	100	100	67.22	54.02	82.5	16.42	100	14.43	0	94.84	57.51	39.79	54.42	Medium

The SI calculations reveal that salinity is one of the significant parameters affecting GWQ in the study area. All wells recorded SI values ranging from 0 to 50, reflecting highly saline water. Salinity indicates intense salinization caused by over-extraction of groundwater, which decreases hydraulic pressure and allows seawater intrusion into the aquifers⁶⁰. Similarly, very low SI values were recorded in all wells where extreme levels of EC were above the permissible limits. Salinity strongly influences the EC, which is considered one of the essential indicators showing the TDS in water to reflect the intensity of ionic concentration and the possible seawater intrusion and contamination of groundwater^61,62. Thus, poor scores for salinity and EC in SI continuously indicate that over-extraction has increased the intensity of seawater intrusion in the study area. Br⁻ and Cl⁻ also exhibit extremely low SI values, maintaining zero SI values in all wells. Br⁻ is representative of contamination from anthropogenic activities. It is further increased in the coastal aquifers due to the mixing of seawater⁶³.

On the other Hand, pH maintains a consistently high SI value of 100 in most of the wells. This suggests that the pH remains stable within the acceptable range, usually buffered through the intrinsic buffering capacity of the aquifer⁶⁴. Other parameters, Ca²⁺ and SO₄²⁻, show moderate SI scores, with variability attributed to geological sources and human activities. Alfarrah et al.⁶⁵ investigated high sulfate concentrations in a coastal aquifer in Libya and related them to seawater intrusion, gypsum dissolution, and deep saline waters. Similarly, Awaleh et al.⁶⁶ examined sulfate pollution in aquifers in Djibouti and found that anthropogenic inputs, such as fertilizers and animal manure, contribute significantly to high sulfate levels. Further, Cheng et al.⁶⁷ attributed the contribution of industrial sources to sulfate contamination in coal mining areas as stemming from sulfide mineral oxidation and discharge of sewage waters.

These findings offer critical implications for GWQ management in the Al-Qatif region. The consistent classification of several wells (e.g., W11, W12) as “Very Bad” suggests zones of acute salinization requiring targeted remediation. Salinity, EC, and Br⁻ emerge as Dominant stressors, pointing to the ongoing impact of seawater intrusion exacerbated by over-extraction. Conversely, stable pH values across wells indicate natural buffering potential that may support managed aquifer recharge strategies. The WQI classifications developed here offer a practical framework for prioritizing well rehabilitation, informing pumping restrictions, and guiding the integration of treated wastewater for irrigation, in Alignment with Saudi Vision 2030 objectives for sustainable water use.

Conclusion and recommendation

This research was motivated by the need to enhance GWQ analysis in arid and semi-arid coastal regions where water scarcity, seawater intrusion, and anthropogenic contamination present growing challenges. It proposed a novel WQI based on Kernel PCA, representing methodological advancement in GWQ assessment. By using Kernel PCA for parameter weighting and dimensionality reduction, the framework mitigated the subjectivity inherent in traditional WQI models. Among the kernel types evaluated, the polynomial kernel demonstrated the strongest performance, capturing over 98% of the variance in the first principal component. The associated SI framework enabled a nuanced assessment of deviations from permissible limits, offering a more precise classification of water quality conditions.

The findings revealed substantial spatial and qualitative variability across the 39 sampled wells. Sixteen wells were classified as “Medium,” while another 16 were identified as “Bad,” and seven wells, including W11 (WQI = 10.64), fell into the “Very Bad” category. Salinity, electrical conductivity (EC), and bromide (Br⁻) were identified as the Dominant stressors, whereas pH remained consistently within acceptable limits, reflecting the buffering capacity of the aquifer system. This emphasizes the suitability of the Kernel PCA-based WQI for capturing both extreme and stable groundwater characteristics. The approach Aligns with Saudi Vision 2030 and SDG targets by offering a scalable and reproducible tool for water quality assessment.

The study is subjected to several limitations. The analysis was based on a relatively small sample size and reflects only a single-season event, limiting temporal generalizability. Spatial gaps in monitoring coverage may also obscure transitions between freshwater and saline zones. Future studies can incorporate seasonal monitoring campaigns and higher-resolution spatial sampling to more accurately capture variability. In terms of actionable recommendations, prioritizing wells with “Very Bad” classifications for targeted remediation, particularly those with critical salinity and EC levels. The developed WQI framework can also support the design of decision-support tools for groundwater abstraction regulation, recharge zone identification, and integration of treated wastewater in non-potable applications. Finally, incorporating satellite-derived environmental data or machine learning extensions may further enhance predictive capacity and regional scalability of the approach.

Author contributions

A.A.: Funding Acquisition, Conceptualization, Methodology, Resource, Software, Writing- Reviewing and Editing. A.M.J.: Data Curation, Software, Visualization, Investigation, Validation, Writing- Original draft. S.D.: Supervision, Software, Validation, Formal Analysis, Resource. M.A.: Supervision, Validation, Software, Formal Analysis, Writing- Reviewing and Editing. S.I.A.: Data Curation, Supervision, Validation, Formal analysis, Writing- Reviewing and Editing. Z.M.Y.: Supervision, Validation, Software, Formal Analysis, Writing- Reviewing and Editing.

Funding

This research was supported via funding from Prince Sattam bin Abdulaziz University under project number (PSAU/2025/R/1446).

Data availability

The data is available upon request from the corresponding author (A.M. Jibrin, abdulhayatjm@gmail.com).

Declarations

Competing interests

The authors declare no competing interests.