River water quality index prediction and uncertainty analysis: A comparative study of machine learning models

Highlights

• A new ensemble machine learning model is developed to predict the Water Quality Index (WQI).

• Observed water quality variables in the Lam Tsuen River in Hong-Kong are used to predict the WQI.

• The prediction uncertainty associated with model structure and input variable selection is quantified.

• The three modeled considered, and the ETR model in particular, provide accurate WQI predictions.

Abstract

The Water Quality Index (WQI) is the most common indicator to characterize surface water quality. This study introduces a new ensemble machine learning model called Extra Tree Regression (ETR) for predicting monthly WQI values at the Lam Tsuen River in Hong Kong. The ETR model performance is compared with that of the classic standalone models, Support Vector Regression (SVR) and Decision Tree Regression (DTR). The monthly input water quality data including Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Dissolved Oxygen (DO), Electrical Conductivity (EC), Nitrate-Nitrogen ($\text{NO}3$ -N), Nitrite-Nitrogen ($\text{NO}2$ -N), Phosphate (${PO}_4^{3^{-}}$), potential for Hydrogen (pH), Temperature (T) and Turbidity (TUR) are used for building the prediction models. Various input data combinations are investigated and assessed in terms of prediction performance, using numerical indices and graphical comparisons. The analysis shows that the ETR model generally produces more accurate WQI predictions for both training and testing phases. Although including all the ten input variables achieves the highest prediction performance (${R^2}_{test}=0.98$, ${RMSE}_{test}=2.99$), a combination of input parameters including only BOD, Turbidity and Phosphate concentration provides the second highest prediction accuracy (${R^2}_{test}=0.97$, ${RMSE}_{test}=3.74$). The uncertainty analysis relative to model structure and input parameters highlights a higher sensitivity of the prediction results to the former. In general, the ETR model represents an improvement on previous approaches for WQI prediction, in terms of prediction performance and reduction in the number of input parameters.

Introduction

Surface water in rivers plays a vital role in the environment, social health and economic development [[1], [2], [3]]. Various elements affect water quality in rivers, including natural factors such as rainfall and erosion, and human factors such as urban, agricultural and manufacturing practices [[4], [5], [6]]. Because surface water is the primary source of freshwater worldwide, its degradation can lead to significant consequences on drinking water availability and, more generally, on economic development and future strategies [[7], [8], [9]]. The interaction of rivers with the surrounding environment, with the related exchange of urban, industrial and agricultural contaminants along their path, leads to water pollution [10,6,11,12].

The Water Quality Index (WQI) “as a classification indicator” has been widely utilized to evaluate and categorize the quality of both ground and surface waters and plays a significant role in water resources management [[13], [14], [15]]. This index integrates several physical and chemical factors in a single parameter, to quantify the state of water quality [16,17]. Computing this indicator provides an efficient approach for water quality assessment.

The application of the WQI was first presented by [18,19] and later adopted and modified by numerous practitioners [[20], [21], [22]]. All these applications originated from the general concept of Water Quality Index proposed by the National Sanitation Foundation (NSF) of the United States, and the NSFWQI [18] is the most commonly adopted method worldwide.

In general, WQI formulations include lengthy calculations and thus require considerable time and effort. Also, the conventional methods for computing the WQI need a large number of physical and chemical data, typically at daily intervals. Hence, alternative approaches to calculate WQI in a computationally-efficient and accurate way are required. Such improvement may benefit environmental engineers when monitoring and assessing water quality.

Over the past few decades, Artificial Intelligence (AI), in the form of machine learning models, has been increasingly applied to solve various environmental engineering problems, including river water quality modeling [6,[23], [24], [25], [26]].Machine learning models represent a significant innovation in the research on monitoring and control of several engineering processes [[27], [28], [29]] and their algorithms can be used to carry out accurate predictions without the need for complex programming. Machine learning models are ultimately based on data mining and identification of patterns between data, through the construction of algorithms using a subset of the dataset (training data) and verification of the prediction performance using a separate subset of the dataset (testing set) [[30], [31], [32]].

Our literature review has evidenced great attention to WQI simulation using AI models [33]. Tripathi and Singal [34] employed the Principal Components Analysis (PCA) method to select the optimal input variable combination and provide an innovating Water Quality Index computation method for the Ganges river in India. Using this method, they could reduce 28 parameters to only nine, including Electrical Conductivity (EC), power of Hydrogen (pH), Dissolved Oxygen (DO), Total Dissolved Solids (TDS), Sulfate (SO4), Magnesium (Mg), Chlorine (Cl), Total Coliform (TC) and Biochemical Oxygen Demand (BOD), which led to a dramatic reduction in computational time. Zali et al. [35] addressed the effects of six major input parameters, namely DO, BOD, Chemical Oxygen Demand (COD), pH, Nitrate ($\text{NO}3$) and Suspended Solids (SS), on the Water Quality Index using Artificial Neural Networks (ANNs). Conducting a sensitivity analysis, they identified the relative importance of each parameter in WQI determination and concluded that DO, SS, and $\text{NO}3$ are the key input parameters. Nigam and SM [36] used a fuzzy-based model to calculate the ground Water Quality Index and compared its prediction performance with other common calculation methods, finding that the fuzzy-based model outperforms them in prediction and water quality classification. Srinivas and Singh [37] developed a novel fuzzy decision-making method to predict WQI in rivers, employing an Interactive Fuzzy model (IFWQI); their findings indicate a significant improvement in WQI prediction performance of their proposed model compared to the classic fuzzy method. Yaseen et al. [38] assessed the WQI prediction performance of hybrid methods based on Adaptive Neuro-Fuzzy Inference System (ANFIS), namely ANFIS-FCM (Fuzzy C-Means data clustering), ANFIS-GP (Grid Partition), and ANFIS-SC (Subtractive Clustering); they observed ANFIS-SC to be the best performing model. Hameed et al. [39] used two ANN models, namely Back-Propagation Neural Network (BPNN) and Radial Basis Function Neural Network (RBFNN), for describing the relationship between WQI and several chemical parameters (i.e. BOD, COD, DO, Nitrate, pH, Suspended Solids) in tropical environments, and obtained better prediction results with the RBFNN model.

While typical AI models based on ANN and ANFIS are widely developed for WQI simulation, environmental scientists have been exploring other robust and reliable AI models [25,26,33]. Tree-based models, such as Decision Trees (DTs), are another popular approach applied successfully for various hydrological and environmental problems, such as rainfall forecasting [40]. The Support Vector Machine (SVM) model is also acknowledged as a powerful machine learning technique for both linear and nonlinear regression problems and has been used in various scientific issues with high prediction accuracy [[41], [42], [43]]. Concerning the application of decision-tree and support vector regression models for water quality parameter prediction, Granata et al. [44] developed a Support Vector Regression (SVR) model and a Regression Tree (RT) model to predict concentrations of Total Suspended Solids (TSS), Total Dissolved Solids (TDS), COD and BOD; they found the SVR model to provide the best predictions. Li et al. [45] proposed a hybrid SVR model with FireFly Algorithm (FFA) to predict WQI using monthly water quality parameter data, showing a significant improvement in prediction performance when compared to the standalone SVR model. Kamyab-Talesh et al. [46] studied the optimization of the SVM model to identify the parameters that mostly affect the WQI and found that Nitrate is the most important parameter for WQI prediction. Wang et al. [47] investigated the performance of three machine learning models, SVR, SVR-GA (Genetic Algorithm) and SVR-PSO (Particle Swarm Optimization), to predict WQI by employing the spectral indicators Difference Index (DI), Normalized DI and Ratio Index (RI) which were obtained from remote sensing, and found the SVR-PSO to be the best performing model.

Although various AI models have been introduced for modeling WQI, several limitations are still observed, such as model hyper parameters tuning, case study stochasticity characteristics, and model flexibility. Ensemble machine learning models offer a way to overcome those limitations and are recently gaining popularity [48]. Several ensemble bagging and boosting models are available, such as MadaBoost, Gradient Boost, AdaBoost and Random Forest, and have proved to be significantly useful tools for prediction [49,50]. More recently developed models, such as Extra Tree or Bagging Regression, are simpler to code and have shown potential to replace other classic AI algorithms [51,52]. The ensemble approaches are a combination of standalone models such as SVM and Decision Trees to construct a better performing prediction model [[53], [54], [55]]. The application of ensemble machine learning models for water quality studies has been limited and is the focus of this investigation. Specifically, this study presents a novel ensemble machine learning model, namely the Extra Tree Regression (ETR) ensemble method, to overcome several drawbacks in the available approaches for WQI prediction, such as the large number of input variables and their uncertainty.

A numerous benchmark models such as ANNs, and ANFIS can be compared with the ETR model in the present study; however, two standalone machine learning models, namely a Decision Tree Regression (DTR) model, which is based on a tree-based algorithm, and a Support Vector Regression (SVR) model, are adopted as benchmark models for the ETR model in the current study. Using the Python programming language in the Anaconda data science platform, the prediction performance of the three models is quantified and compared, and an uncertainty analysis relative to model structure and input parameter selection is carried out too.