Prediction of groundwater quality indices using machine learning algorithms

Water, being one of the most essential resources for mankind, is used for different purposes like drinking, irrigation, recreation, navigation, domestic, fisheries, industrial and many more. About 75% of the surface area of the earth is covered by water with a total quantity of about 1,386 M km³ (Kaushik et al. 2004). Out of which, 97.5% of the earth's water is in the oceans, which is not appropriate for human utilization or consumption without proper treatments. Only 2.5% is available as a freshwater. Out of this, about 24.4 M km³ is locked in polar ice caps and only 10.6 M km³ is available as fresh water in reservoirs, rivers, lakes, streams, and groundwater. Groundwater is one of the basic sources, which is used for several purposes throughout the world such as for irrigation, drinking and industrial use. The groundwater quality is dependent on environmental conditions and geological features. Groundwater contamination is a major problem, which poses serious threats to human health and environmental quality worldwide (Mohamed et al. 2015). It may be due to various human activities such as industrial, agricultural and other related activities, which lead to leaching of organic matter, pesticides, and nitrates deep into the aquifer (Su et al. 2019). Further groundwater quality is usually determined by the concentration of physical, chemical, and biological parameters (Kumari & Rai 2020). Panghal et al. (2021) reported that approximately 82% of the area of Tosham block, Haryana, had poor and very poor water quality for drinking purposes and 18% of area was unsuitable for drinking. It was also observed by Kumari & Rai (2020) that 45.31% of the area of southern Haryana had poor and very poor water quality for drinking purposes in the month of May, 2014. Hence, it is necessary to know the chemical composition of groundwater in order to determine its suitability for drinking purposes.

Many researchers have evaluated the potability of groundwater based on major parameters; that is, pH, Electrical Conductivity (EC), Total Hardness (TH), Calcium (Ca²⁺), Magnesium (Mg²⁺), Sodium (Na⁺), Potassium (K⁺), Sulphate (SO₄²⁻), Chloride (Cl⁻), Bicarbonate (HCO₃⁻), Nitrate (NO₃²⁻), and Fluoride (F⁻) as mentioned by (Vasanthavigar et al. 2010; Zahedi 2017; Kumari & Rai 2020; Maghrebi et al. 2021). However, measurement of all these parameters in groundwater often poses difficulty as it is a quite expensive and tedious task (Kumar et al. 2016). Hence, reducing the effective cost and the subjectivity for evaluating water quality is a great challenge. Keeping in view the typical issues related to easy determination of water quality, several water quality indices have been derived in the past based on various water quality parameters and are available in the literature. Therefore, the researchers have mentioned index-based methods for evaluating water quality for drinking purposes; that is, water quality index (WQI) by Adimalla et al. (2020b); Tyagi et al. (2020); Wang et al. (2020), Entropy water quality index method (EWQI) by Kumar & Augustine (2021), Canadian WQI by Dao et al. (2020), US National Sanitation Foundation WQI by Lumb et al. (2011) and so on. However, the EWQI is considered an effective method to provide exact and comprehensive information about the overall quality of water for drinking purposes and has been used in recent studies by Adimalla et al. (2020b) and Wang et al. (2020).

Various machine learning approaches have been used extensively to predict groundwater quality for drinking purposes due to their improved performance in comparison to statistical methods over last three decades (Haghiabi et al. 2018; Aldhyani et al. 2020; Lu & Ma 2020; Nayan et al. 2021). Due to easy availability of water quality data from different sources in India, machine learning approaches are being successfully applied. With the advancement of new machine learning tools like Deep Neural Network and XGBoost, these new approaches are being used to analyze and, further, to predict the water quality in comparison to already reported work using other conventional machine learning models. Granata et al. (2017) purposed two models, namely Support Vector Regression (SVR) and Regression Trees (RT), for predicting wastewater quality. Najafzadeh et al. (2019) suggested a model to forecast the water quality index of Karoun River in Iran by pairing gene expression programming (GEP), evolutionary polynomial regression (EPR), and model tree (MT). Another study conducted by Najafzadeh & Ghaemi (2019) predicted biochemical oxygen demand (BOD) and chemical oxygen demand (COD) of Karoun River in Iran using machine learning models. Najafzadeh et al. (2021) have used four different machine learning models such as Polynomial Regression (EPR), M5 Model Tree (MT), Gene-Expression Programming (GEP), and Multivariate Adaptive Regression Spline (MARS). These four models helped in predicting the water quality index of Karoun River in Iran. Najafzadeh & Niazmardi (2021) have attempted to predict the water quality of the Karoun River with eleven water quality indicators using a Support Vector Regression (SVR) model using different kernels.

Traditional groundwater quality modelling approaches use either time series analysis or statistical methods. These approaches work by assuming some relationship between the dependent and independent variables as well. Mostly they require data to satisfy some statistical characteristics (e.g. normal distribution etc.), hence, are found to achieve inferior results during prediction. On the other hand, Artificial Intelligence (AI) based models do not require any assumptions about data as well as the relationship between dependent and independent variables. Exhaustive literature review suggests that AI-based predictive models are also found to perform better than the statistical methods. Meyers et al. (2017) have proposed three different models such as ANN, SVM, and RF for evaluating water quality in the United Kingdom (UK). Nayan et al. (2021) have used the GBM model to predict the water quality of a Bangladesh river for irrigation purposes for the time period of 2013–2019. El Bilali et al. (2020) determined the groundwater quality for drinking purposes by using ANN models. Di et al. (2019) applied machine learning models to predict water quality in the Yangtze River in China. These studies suggest that ANN, SVM, and GBM work well in predicting water quality and hence can effectively be used for water quality modelling with the available datasets. Recently, new machine learning models like Extreme gradient boosting (XGBoost) and Deep Neural Network (DNN) have been applied in water engineering applications (Najah Ahmed et al. 2019; El Bilali et al. 2021; Ibrahem Ahmed Osman et al. 2021). DNN has emerged as a powerful tool for various applications in civil engineering as studied by (Wu et al. 2018; Dick et al. 2019; Kumar & Abraham 2019; Pal 2019). It seems from literature review that limited numbers of studies are available on the use of DNN, XGBoost and GBM algorithms in water resource engineering, especially predicting water quality for drinking purposes using two indices, EWQI and WQI, over Haryana state in India. This study is aimed at comparing the performance of these three machine learning models on the basis of performance parameters such as Correlation Coefficient (CC), Root Mean Square Error (RMSE), Nash–Sutcliffe efficiency (NSE) and Index of agreement (d) on 392 data sets from Haryana state for 12 hydrochemical parameters. Two indices, EWQI and WQI, were manually calculated for the data set and compared with the predicted values obtained by applying DNN, XGBoost and GBM algorithms. Further most significant parameters affecting the groundwater quality were also determined from the same data set by using three algorithms. At the end uncertainty and reliability analyses were also carried out. The outcomes of the article are expected to provide scientific information about quality of the groundwater that will be further useful in management and sustainable development of the groundwater resource in Haryana state.

The importance of each feature is calculated based on their prediction performance. Each feature is replaced by the noise and prediction takes place for the particular instance. The higher the value of prediction indicates greater score of each feature. Thus, it assesses all features by the individual scores which become important during training and the feature with higher score plays the major role in making the key decision with boosted trees.

The processing node is basic component of a back-propagation neural network (BPNN). Each processing node of BPNN performs two functions and behaves as a biological neuron. Initially it sums up the input values and this sum of input is then passed through the activation function to create the output. The activation function f can be used as any differential function. In BPNN, all processing nodes are arranged into layers, which are fully interconnected to the next layer. There is no connection of nodes of the same layer. A BPNN, typically, consists of an input layer that serves as a distribution structure of data that is inputted into the network and is not used for any form of processing. After this layer, one or more processing layers are known as hidden layers. The output layer is the final processing layer. A neural network having two or more hidden layers with a huge number of nodes and using mathematical modeling is mostly known as a DNN (Pal 2019).

Initializing BPNN weights is an important factor that affects the functioning of the neural network. The initial weights should be selected before the start of network training and should be in a reasonable range. Random weight initialization is normally used with a standard BPNN to find an optimal set of weights using a stochastic gradient descent approach. Xavier weight initialization was proposed as the weight initialization technique for DNN because of the poor performance of random weight initialization with a standard gradient descent-based optimization approach. This approach assigns the weights from a Gaussian distribution with zero mean and some finite variance, thus allowing the variance of the outputs of a layer to be equal to the variance of its inputs.

During the training phase of BPNN, network weights are continuously updated and adjusted using the learning rate as one of the user-defined parameters. The value of the learning rate is generally selected randomly, based on the experiences and the earlier reported works. Gradient descent algorithms were generally used to update the network weights with the help of a learning rate in a BPNN. The introduction of adaptive learning rate methods allowed adjusting the learning rate adaptively throughout the training process of a DNN. In order to update the weights of a DNN, an adaptive moment estimation based optimization algorithm was proposed (Kingma & Ba 2015) and found to perform well. Use of Adam requires several user-defined parameters during training but studies suggest that the default values as suggested by (Kingma & Ba 2015) work well with most of the datasets.

Similar to BPNN, optimal values of several user-defined parameters need to be obtained during training of a deep neural network. These parameters include the activation function, optimization algorithm, number and type of hidden layers, number of nodes in the hidden layer, hidden and dropout layers, updaters (i.e., learning rate optimization algorithm), weight initialization method, batch size (i.e., number of training samples used in one iteration) and the number of epochs. One epoch is defined as when an entire training dataset has passed once through the neural network both in forward and backward directions.

Haryana state is a landlocked state in the north-west part of India as shown in Figure 1. The latitude of Haryana state extends between 27°39′ and 30°35′N and longitudes between 74°27′ and 77°36′E. The total geographical area of Haryana state is 44,212 Km². The normal average annual rainfall is about 617 mm, which is received primarily through the southwestern monsoon. The climate of the state is arid to semi-arid with a very hot summer temperature of approximately 45 °C.

The dataset used in this study was downloaded from India Water Resources Information System (IWRIS; https://indiawris.gov.in). A dataset collected from national groundwater monitoring stations distributed Figure 1(b) over 20 districts of Haryana state during the year 2016, which was used to predict the groundwater quality for drinking purposes given in Table 1. A total of 392 samples were collected and analyzed for 12 important hydrochemical parameters so as to access the groundwater quality. This dataset was randomly divided in such a way that 294 (75%) samples are used for the training, whereas the remaining 98 (25%) were used for testing the models. To calculate the groundwater quality, two different water quality indices, Entropy water quality index (EWQI) and Water quality index (WQI) were calculated using 12 parameters. In order to reduce the effect of large variation in input and output values, normalization of different input and output parameters was also performed.

EWQI has been frequently used to estimate the water quality for domestic/drinking, agricultural purpose etc. in the past and have been applied to determined water quality by (Shannon 1948). The steps involved in the calculation EWQI are as under follow.

The results of EWQI obtained from above equation are listed in Table 2 (Aouiti et al. 2021). Out of 392 groundwater samples, only 14.80% of groundwater samples are unsuitable for drinking, while 32.40% of samples have good quality and only 17.60% samples exhibited excellent quality of groundwater for drinking purposes.

The WQI method has been commonly used to access the drinking water quality in various geological topographies (Aly et al. 2015; Chung et al. 2015; Adimalla & Qian 2019; Adimalla et al. 2020a; Gaikwad et al. 2020). The following steps are includes for calculation of WQI according to Horton (1965):

• 1.
  In the first instance, ‘assigning weight’: twelve parameters are weighted according to its relative importance. The weight 5 is assigned to the most significant parameters and 1 is for the least significant. The relative weight (⁠⁠) is obtained from Equation (15) and has been shown in Table 3.

  

  (15)

  where, is the weight of each parameter and n is the number of parameters.
• 2.
  In second instance, ‘quality rating (⁠⁠) scale calculation’ firstly, the water sample concentration is multiplied by 100 and then the results are divided by its limits given by the BIS (2015) in Equation (16):

  

  (16)

  where, is the concentration of chemicals in the water sample in (mg/l), and is the drinking water standard for each chemical parameter BIS (2015).
• 3.
  In the third instance, ‘calculation of water quality index (WQI)’, firstly (water quality index of the parameter) value is calculated by Equation (17) and WQI equals the sum of all the values of of each parameter as by Equation (18):

  

  (17)

  

  (18)

Wang et al. (2017) described the WQI into five categories as listed in Table 4. It can be noted from Table 4 that 16.58% of samples exhibited excellent water quality, 29.34% good water quality and 13.26% of water samples fell under unsuitable for drinking purposes.

The values of EWQI and WQI obtained for predicting the groundwater quality are shown in Tables 2 and 4. The perusal of Tables 2 and 4 shows that 50% of the samples fall under 0–100 for EWQI, while 45.92% of the samples fall under 0–100 in WQI. The comparison of EWQI and WQI shows that most of the samples of EWQI are more effective than WQI. As compared with past studies undertaken by Kumari & Rai (2020) and Panghal et al. (2021), the results obtained in this study are superior thereby, suggesting the importance of successful application of the three machine learning models.

The use of algorithms XGBoost, DNN and GBM needs setting of several user-defined parameters. For all three algorithms used in the present study, H2o Auto-ML software (H2O.ai. 2020) was applied. To obtain the optimal value of various hyper parameters of different algorithms, Auto-ML uses 5 -fold cross validation and grid search method. During training phase, the DNN produces a ranked list of different input variables using Geodon's method (Gedeon 1997) whereas GBM and XGBoost use a gain value to rank various input attributes as discussed in (Xu et al. 2014; Chen & Guestrin 2016). The optimal values of various parameters obtained in predicting EQWI and WQI are provided in Table 5.

To obtain the value, first relative average error is determined from Equation (25) and next, if the value of RAE ≤ Δ then = 1, otherwise = 0.

Where, Δ is the threshold value of the water quality parameter and as per Chinese standards the optimum value of Δ is 0.2, or 20%. is determined as the number of times the value of RAE≤Δ. The same equations have been applied in determining the water quality of a data set for estimating EWQI and WQI.

Table 6 provides results obtained in terms of CC, RMSE, NSE and d values with both training and test datasets for predicting the groundwater quality using EQWI and WQI. A comparison of these values suggests the slightly improved performance of EWQI by optimized DNN (CC = 0.989, RMSE = 0.037, NSE = 0.995 and d = 0.999) in comparison to XGBoost (CC = 0.976, RMSE = 0.056, NSE = 0.994 and d = 0.999) and GBM (CC = 0.959, RMSE = 0.074, NSE = 0.992 and d = 0.998). However, the performance of WQI using DNN (CC = 0.975, RMSE = 0.055, NSE = 0.991 and d = 0.998) in comparison to XGBoost (CC = 0.944, RMSE = 0.082, NSE = 0.986 and d = 0.998) and GBM (CC = 0.968, RMSE = 0.062, NSE = 0.980 and d = 0.998). The overall results also suggest slightly improved performance by GBM in comparison to XGBoost while using WQI as a groundwater quality index whereas XGBoost achieves better results with EWQI.

Table 7 shows the performance results obtained in terms of uncertainty (U₉₅) and reliability analysis for predicting the groundwater quality using EWQI and WQI in both training and testing stages. From this table, it is evident that the performance of EWQI using DNN achieved the lowest value of U₉₅ (21.60) when compared with XGBoost (U₉₅ = 22.31) and GBM (U₉₅ = 22.17) in the training stage. While in the testing stage, the value of U₉₅ of EWQI optimized by DNN is more accurate (U₉₅ = 19.78) in comparison to XGBoost (U₉₅ = 20.91) and GBM (U₉₅ = 20.22). Additionally, prediction of EWQI using DNN is more reliable (98.59) in comparison to XGBoost (96.46) and GBM (97.17) in the training stage. While in the testing stage, the performance of EWQI using DNN has a higher level of reliability (98.16) when compared with XGBoost (97.08) and GBM (97.16). To conclude, in terms of uncertainty (U₉₅) and reliability, DNN performs better than the other two models for training as well as testing. The same trend has been observed for estimation of WQI in terms of uncertainty and reliability under the training and testing category. However, when two indices, EWQI and WQI, are compared, the prediction of EWQI is superior to WQI in the three algorithms used in this article.

Further, Figures 2 and 3 provide plots between predicted and actual values of EWQI and WQI using DNN, XGBoost, and GBM respectively. It can be observed from Figure 2 that generally, most of the predicted values for EWQI as the groundwater quality index fall near the line of perfect agreement (i.e. a line at 45°). Four more lines in the range of ±25% and ±10% error between the actual and predicted values of EWQI and WQI are also plotted in the graphs. Figure 2(a) shows that most of the value predicted by DNN of EWQI were well ±10% error line from the line of perfect agreement. It can be inferred from Figure 2(b) that some predicted values by XGBoost of EWQI are also lying away from the ±25% error line. Figure 2(c) shows that some predicted values by GBM are lying away from ±10% error line and ±25% error line. Figure 3(a) demonstrates that most of the value predicted for WQI by DNN were well ±10% error line from the line of perfect agreement. Comparison of Figures 2(a)–2(c) and 3(a)–3(c) also suggests that the predicted EWQI and WQI values by DNN are in good agreement with the actual EWQI and WQI respectively, suggesting its improved performance in comparison to both XGBoost and GBM in the present study.

In this study the relative importance of each hydrochemical parameter has been compared with each algorithm, so that the variability in the dependent variable can be explained by the independent variables. Figure 4(a)–4(f) depicts the relative importance of different independent chemical variables calculated by using DNN, XGBoost and GBM algorithms. Figure 4(a)–4(c) represents the relative importance of variables for modeling EWQI and Figure 4(d)–4(f) represents the relative importance of variables for modeling WQI. From Figure 4(a)–4(f), it can be observed that the EC is the most significant variable having the highest relative importance to predict the EWQI and the WQI by using the three algorithms DNN, XGBoost and GBM. The pH has the lowest relative importance in prediction of EWQI (DNN = 0.2212, XGBoost = 0.0013 and GBM = 0.0008) and WQI (DNN = 0.1476, XGBOOST = 0.04781 and GBM = 0.0016). The most interesting fact is that Mg attains moderate relative importance for the prediction of EWQI (DNN = 0.4239 and GBM = 0.0033) and WQI (DNN = 0.3645 and GBM = 0.0314) but XGBoost shows a higher relative importance in WQI (0.5545) and lower relative importance in EWQI (0.0021) of this variable. Similarly, TH has moderate relative importance for the prediction of EWQI (DNN = 0.4145 and GBM = 0.0032) and WQI (DNN = 0.3534 and GBM = 0.0213) but XGBoost shows a higher relative importance in WQI (0.873) and lower relative importance in EWQI (0.0481) of this variable. However, the perusal of Figure 4(a)–4(f) shows that there is no definite trend of variable importance of hydrochemical parameters in estimating EWQI and WQI using the three algorithms; that is, DNN, XGBoost and GBM, on this data set.

In the present work, a study has been taken up to assess the performance of DNN, XGBoost, and GBM algorithms for predicting the groundwater quality based on two indices; that is, EWQI and WQI. The comparison of three techniques has been made on the basis of four goodness-of-fit indices, namely: CC, RMSE, NSE and d. The conclusions drawn from this work are as given below:

• 1.

  Three different machine learning models were used to predict EWQI; that is, DNN, XGBoost, and GBM. Out of the three algorithms it is observed that the DNN algorithm performs best in terms of the training as well as testing dataset. For the testing dataset, performance indices have the following values: (CC = 0.989, RMSE = 0.037, NSE = 0.995 and d = 0.999) and for training (CC = 0.998, RMSE = 0.012, NSE = 0.989 and d = 0.997).

• 2.

  Also, in terms of predictions of WQI, DNN performed best in terms of the training and testing dataset. For the testing dataset, performance indices have the following values: (CC = 0.975, RMSE = 0.055, NSE = 0.991 and d = 0.998) and for training (CC = 0.999, RMSE = 0.018, NSE = 0.965 and d = 0.990).

• 3.

  After comparison of all the three algorithms, it was found that DNN based modeling performs slightly better than XGBoost and GBM in estimating both EWQI and WQI in the training as well as testing data set.

• 4.

  After observing the values of various relative importance of variables as given by the three models, the variable ‘EC’ was given the most significance in predicting the dependent variable. However, the parameter ‘pH’ has been considered as the least significant parameter in prediction using the three machine learning models in the present study.

• 5.

  The uncertainty (U₉₅) and reliability analysis of the data set also revealed that the DNN performs better than the other two algorithms (XGBoost and GBM) for training as well as testing in prediction of EWQI and WQI.

• 6.

  The promising results observed in the study suggest that DNN can be used to predict various other bio-chemical and physio-chemical properties of groundwater consumed for drinking purposes.

• 7.

  The findings of this study can be extended further by examining the performance of the DNN model as compared to other machine learning models, considering different possible hydrochemical input parameters.

• 8.

  Furthermore, this study aims to be a mere suggestion to the research community about the application of machine learning models in prediction of ground water quality indices, as it is much needed for economically weaker regions, where not much equipment and resources are available.

First author (Hemant Raheja) is grateful to MHRD, GOI for financially supporting the present work for a Ph.D. scholarship grant (2K19/NITK/PHD/61900011) and to the site (https://indiawris.gov.in) for the data used in this study.

Authors claim there exists no conflict of interest in any form concerning the work done within the present manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.