Here, we present an improved water quality index (WQI) model for assessment of coastal water quality using Cork Harbour, Ireland, as the case study. The model involves the usual four WQI components - selection of water quality indicators for inclusion, sub-indexing of indicator values, sub-index weighting and sub-index aggregation - with improvements to make the approach more objective and data-driven and less susceptible to eclipsing and ambiguity errors. The model uses the machine learning algorithm, XGBoost, to rank and select water quality indicators for inclusion based on relative importance to overall water quality status. Of the ten indicators for which data were available, transparency, dissolved inorganic nitrogen, ammoniacal nitrogen, BOD₅, chlorophyll, temperature and orthophosphate were selected for summer, while total organic nitrogen, dissolved inorganic nitrogen, pH, transparency and dissolved oxygen were selected for winter. Linear interpolation functions developed using national recommended guideline values for coastal water quality are used for sub-indexing of water quality indicators and the XGBoost rankings are used in combination with the rank order centroid weighting method to determine sub-index weight values. Eight sub-index aggregation functions were tested - five from existing WQI models and three proposed by the authors. The computed indices were compared with those obtained using a multiple linear regression (MLR) approach and R² and RMSE used as indicators of aggregation function performance. The weighted quadratic mean function (R² = 0.91, RMSE = 4.4 for summer; R² = 0.97, RMSE = 3.1 for winter) and the unweighted arithmetic mean function (R² = 0.92, RMSE = 3.2 for summer; R² = 0.97, RMSE = 3.2 for winter) proposed by the authors were identified as the best functions and showed reduced eclipsing and ambiguity problems compared to the others.

Coastal water quality assessment is an essential task to keep "good water quality" status for living organisms in coastal ecosystems. The Water quality index (WQI) is a widely used tool to assess water quality but this technique has received much criticism due to the model's reliability and inconsistence. The present study used a recently developed improved WQI model for calculating coastal WQIs in Cork Harbour. The aim of the research is to determine the most reliable and robust machine learning (ML) algorithm(s) to anticipate WQIs at each monitoring point instead of repeatedly employing SI and weight values in order to reduce model uncertainty. In this study, we compared eight commonly used algorithms, including Random Forest (RF), Decision Tree (DT), K-Nearest Neighbors (KNN), Extreme Gradient Boosting (XGB), Extra Tree (ExT), Support Vector Machine (SVM), Linear Regression (LR), and Gaussian Naïve Bayes (GNB). For the purposes of developing the prediction models, the dataset was divided into two groups: training (70%) and testing (30%), whereas the models were validated using the 10-fold cross-validation method. In order to evaluate the models' performance, the RMSE, MSE, MAE, R², and PREI metrics were used in this study. The tree-based DT (RMSE = 0.0, MSE = 0.0, MAE = 0.0, R² = 1.0 and PERI = 0.0) and the ExT (RMSE = 0.0, MSE = 0.0, MAE = 0.0, R² = 1.0 and PERI = 0.0) and ensemble tree-based XGB (RMSE = 0.0, MSE = 0.0, MAE = 0.0, R² = 1.0 and PERI = +0.16 to -0.17) and RF (RMSE = 2.0, MSE = 3.80, MAE = 1.10, R² = 0.98, PERI = +3.52 to -25.38) models outperformed other models. The results of model performance and PREI indicate that the DT, ExT, and GXB models could be effective, robust and significantly reduce model uncertainty in predicting WQIs. The findings of this study are also useful for reducing model uncertainty and optimizing the WQM-WQI model architecture for predicting WQI values.

With the significant increase in WQI applications worldwide and lack of specific application guidelines, accuracy and reliability of WQI models is a major issue. It has been reported that WQI models produce significant uncertainties during the various stages of their application including: (i) water quality indicator selection, (ii) sub-index (SI) calculation, (iii) water quality indicator weighting and (iv) aggregation of sub-indices to calculate the overall index. This research provides a robust statistically sound methodology for assessment of WQI model uncertainties. Eight WQI models are considered. The Monte Carlo simulation (MCS) technique was applied to estimate model uncertainty, while the Gaussian Process Regression (GPR) algorithm was utilised to predict uncertainties in the WQI models at each sampling site. The sub-index functions were found to contribute to considerable uncertainty and hence affect the model reliability - they contributed 12.86% and 10.27% of uncertainty for summer and winter applications, respectively. Therefore, the selection of sub-index function needs to be made with care. A low uncertainty of less than 1% was produced by the water quality indicator selection and weighting processes. Significant statistical differences were found between various aggregation functions. The weighted quadratic mean (WQM) function was found to provide a plausible assessment of water quality of coastal waters at reduced uncertainty levels. The findings of this study also suggest that the unweighted root means squared (RMS) aggregation function could be potentially also used for assessment of coastal water quality. Findings from this research could inform a range of stakeholders including decision-makers, researchers, and agencies responsible for water quality monitoring, assessment and management.

Recently, there has been a significant advancement in the water quality index (WQI) models utilizing data-driven approaches, especially those integrating machine learning and artificial intelligence (ML/AI) technology. Although, several recent studies have revealed that the data-driven model has produced inconsistent results due to the data outliers, which significantly impact model reliability and accuracy. The present study was carried out to assess the impact of data outliers on a recently developed Irish Water Quality Index (IEWQI) model, which relies on data-driven techniques. To the author's best knowledge, there has been no systematic framework for evaluating the influence of data outliers on such models. For the purposes of assessing the outlier impact of the data outliers on the water quality (WQ) model, this was the first initiative in research to introduce a comprehensive approach that combines machine learning with advanced statistical techniques. The proposed framework was implemented in Cork Harbour, Ireland, to evaluate the IEWQI model's sensitivity to outliers in input indicators to assess the water quality. In order to detect the data outlier, the study utilized two widely used ML techniques, including Isolation Forest (IF) and Kernel Density Estimation (KDE) within the dataset, for predicting WQ with and without these outliers. For validating the ML results, the study used five commonly used statistical measures. The performance metric (R²) indicates that the model performance improved slightly (R² increased from 0.92 to 0.95) in predicting WQ after removing the data outlier from the input. But the IEWQI scores revealed that there were no statistically significant differences among the actual values, predictions with outliers, and predictions without outliers, with a 95 % confidence interval at p < 0.05. The results of model uncertainty also revealed that the model contributed <1 % uncertainty to the final assessment results for using both datasets (with and without outliers). In addition, all statistical measures indicated that the ML techniques provided reliable results that can be utilized for detecting outliers and their impacts on the IEWQI model. The findings of the research reveal that although the data outliers had no significant impact on the IEWQI model architecture, they had moderate impacts on the rating schemes' of the model. This finding indicated that detecting the data outliers could improve the accuracy of the IEWQI model in rating WQ as well as be helpful in mitigating the model eclipsing problem. In addition, the results of the research provide evidence of how the data outliers influenced the data-driven model in predicting WQ and reliability, particularly since the study confirmed that the IEWQI model's could be effective for accurately rating WQ despite the presence of the data outliers in the input. It could occur due to the spatio-temporal variability inherent in WQ indicators. However, the research assesses the influence of data input outliers on the IEWQI model and underscores important areas for future investigation. These areas include expanding temporal analysis using multi-year data, examining spatial outlier patterns, and evaluating detection methods. Moreover, it is essential to explore the real-world impacts of revised rating categories, involve stakeholders in outlier management, and fine-tune model parameters. Analysing model performance across varying temporal and spatial resolutions and incorporating additional environmental data can significantly enhance the accuracy of WQ assessment. Consequently, this study offers valuable insights to strengthen the IEWQI model's robustness and provides avenues for enhancing its utility in broader WQ assessment applications. Moreover, the study successfully adopted the framework for evaluating how data input outliers affect the data-driven model, such as the IEWQI model. The current study has been carried out in Cork Harbour for only a single year of WQ data. The framework should be tested across various domains for evaluating the response of the IEWQI model's in terms of the spatio-temporal resolution of the domain. Nevertheless, the study recommended that future research should be conducted to adjust or revise the IEWQI model's rating schemes and investigate the practical effects of data outliers on updated rating categories. However, the study provides potential recommendations for enhancing the IEWQI model's adaptability and reveals its effectiveness in expanding its applicability in more general WQ assessment scenarios.

Here, we present the Irish Water Quality Index (IEWQI) model for assessing transitional and coastal water quality in an effort to improve the method and develop a tool that can be used by environmental regulators to abate water pollution in Ireland. The developed model has been associated with the adoption of water quality standards formulated for coastal and transitional waterbodies according to the water framework directive legislation by the environmental regulator of Irish water. The model consists of five identical components, including (i) indicator selection technique is to select the crucial water quality indicator; (ii) sub-index (SI) function for rescaling various water quality indicators' information into a uniform scale; (iii) indicators' weight method for estimating the weight values based on the relative significance of real-time information on water quality; (iii) aggregation function for computing the water quality index (WQI) score; and (v) score interpretation scheme for assessing the state of water quality. The IEWQI model was developed based on Cork Harbour, Ireland. The developed IEWQI model was applied to four coastal waterbodies in Ireland, for assessing water quality using 2021 water quality data for the summer and winter seasons in order to evaluate model sensitivity in terms of spatio-temporal resolution of various waterbodies. The model efficiency and uncertainty were also analysed in this research. In terms of different spatio-temporal magnitudes of various domains, the model shows higher sensitivity in four application domains during the summer and winter. In addition, the results of uncertainty reveal that the IEWQI model architecture may be effective for reducing model uncertainty in order to avoid model eclipsing and ambiguity problems. The findings of this study reveal that the IEWQI model could be an efficient and reliable technique for the assessment of transitional and coastal water quality more accurately in any geospatial domain.