Investigation of quantitative and qualitative changes in groundwater of Ardebil plain using ensemble artificial intelligence-based modeling Open Access

Throughout the world, groundwater is a major source of fresh water for many uses like drinking, agricultural and industrial purposes. According to Gintamo et al. (2022), population growth and increased groundwater consumption pose considerable threats to aquifers. Today, the development of communities living in semi-arid areas, where food production is tightly controlled by the amount and distribution of rainfall and groundwater, depends on people's effort to manage limited water resources. Thus, it can be seen that in the near future, the interaction between the growth of urbanization and the application of an efficient management method to conserve water resources will continue. Due to costly and time-consuming solutions to groundwater problems and even in many cases the impossibility of a complete solution, analysis of these valuable resources is vital.

Neural networks have also been applied successfully for studies of quantitative and qualitative changes in groundwater. Groundwater modeling is complicated by the influence of natural and/or human factors such as complexity, nonlinearity, multi-scales, and randomness, all of which affect quantitative and qualitative assumptions (Nourani et al. 2014). These specific models cannot provide explicit equations and physical relationships which are not easily predictable. So in complex phenomena, black-box models are generally used. The efficiency of the model is strongly influenced by the quality and quantity of input and output data. Semi-distributive or conceptual models are the interface between the above two models (Nourani 2017). The use of Black-box AI (Artificial intelligence) approaches has gained popularity in current years because of its good performance, specifically [i.e. Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference Systems (ANFIS), Support Vector Machines (SVM), and, Emotional Artificial Neural Network (EANN)] which are capable of handling complex phenomena have become prominent in water resource issues. The artificial neural network has been used as a different approach to estimating aquifer water quality (Maier & Dandy 1996). Moreover, Derbela & Nouiri (2020), employed ANN models to predict the dynamic changes in piezometric levels in Nebhana aquifers. Correlation analysis demonstrated that the piezometric levels were toughly influenced by monthly rainfall, evapotranspiration, and initial water table level, Also this study revealed that ANN models can be adopted for future groundwater prediction to estimate trends in piezometric levels. Dehghani & Torabi Poudeh (2022) concluded that ANN's performance can be enhanced effectively through combination with other models. During another study analyzing groundwater quality, Shwetank & Chaudhary (2022) used four ANFIS models to identify the best one. The results, however, determined that all four models were dependable. SVM is another AI-based model for reliable estimation of groundwater level and quality. This method tries to minimize the operation risk. Nordin et al. (2021) in a comprehensive study, compared four widely used AI methods [ANN, ANFIS, EA (evolutionary algorithm), and SVM] for modeling and forecasting groundwater quality. As a result of their generalization and faster optimization, EA, and SVM have surpassed ANN and ANFIS in predictive modeling applications. Hydrological studies have been successfully implemented using EANN, a novel version of the classic ANN model. As part of their research in the area of modeling rainfall-runoff in watersheds, Nourani (2017) applied an emotional Artificial Neural network method. He predicted the runoff level by two methods of modeling named EANN and FFNN using the parameters of two catchments with different climate conditions and the results showed that EANN can have 13 and 34% higher efficiency in terms of training and validation, respectively. In addition, in the field of GWL, another study was conducted to assess the efficacy of the EANN model for forecasting one month in the field of GWL.

Today, soft computing tools and artificial intelligence, by accepting that the results can be inaccurate in some parts and by focusing on the human mind and nature, are used to model nonlinear hydraulic and hydrological processes. But using different models to solve a specific issue may lead to distinct results. It is obvious that some models will show higher performance than other models. in other words, no single model is better than another for the analysis and study of hydrological processes (Shamseldin et al. 1997). Using a collection of individual models in combination, the ensemble method can provide results with high predictive accuracy and low errors using the advantages of all models at the same time. Sharghi et al. (2019) used the ensemble method and a 19% increase was gained by using these models. Nadiri et al. (2015) incorporated four models including a feed-forward neural network (FFNN), backpropagation neural network, ANFIS, and, SVM to predict GWL in Meshgin plain. Despite the ability of all models, the results show the superiority of the ensemble method over any of the individual AI models.

Undoubtedly, the best way to understand the behavior of an aquifer system is through long-term research for each region. Therefore, with data mining and clustering tools, indicators can be obtained with acceptable accuracy, based on which necessary decisions can be made regarding aquifer management (Al-adamat et al. 2003). Classifying different objects has always been one of the most important human activities and this is part of the learning process that explains why cluster analysis in many cases is considered a branch of cognitive pattern and artificial intelligence. One of the problems in studying an aquifer through AI methods is the number of observation wells in the aquifer, the analysis of each one is time-consuming alone. One of the statistical methods for presenting the distribution map and quantitative and qualitative distribution of several parameters in groundwater aquifers is the use of cluster analysis. The idea of clustering is to collect objects that are similar with the least possible difference between them in a set of specific groups (Kim et al. 2020). Clustering is a way of categorizing multidimensional inputs into homogenous groups, which can be extracted from unlabeled inputs to form clusters with the greatest degree of similarity within groups and the greatest degree of dissimilarity between groups (Nourani & Kalantari 2010). There are several clustering methods commonly used, e.g. k-means (Hsu et al. 2002) and C-means (Ayvaz et al. 2007) which are typically based on the number of clusters (Nourani et al. 2013). Recent works on unsupervised clustering using self-organizing (SOM) maps have been able to find many applications in hydrology (e.g., Hsu et al. 2002; Kalteh et al. 2008; Toth 2009; Nourani & Parhizkar 2013; Nourani et al. 2013). SOM-based Growing Neural Gas Network (GNG) algorithms allow for the learning of complex relationships without knowing any prior knowledge. A topology is created by GNG using the competitive Hebbian tutorial. There is a limit to how many data points can be clustered using most existing techniques, but SOM and GNG provide a solution by quantifying the data, and despite the similarities between the two methods, GNG has been proven to be the best option thus far (Ventocilla & Riverio 2020; Ventocilla et al. 2021). This framework has been used in a variety of fields as a tool for multipurpose analysis specifically because of its high level of flexibility for recognizing complex patterns (Shi et al. 2014; Viejo et al. 2014; Santos & Nascimento 2016; Abdi et al. 2017). Considering the research background and the ability of the GNG method in clustering and pattern recognition also, being aware of no groundwater investigations done with this method at this time, in this article, the mentioned method has been hired for clustering groundwater piezometers. Due to the successes achieved in hydrological studies using black-box models, the focus of this research is on investigating the efficiency of AI methods to predict and investigate changes in groundwater parameters. On the other hand, the vacancy of a deep and comprehensive study that can evaluate the ability of mentioned and especially ensemble methods, on the groundwater of Ardabil plain is felt. Groundwater studies have not previously employed the GNG clustering method. Also, this report is the first to combine four AAN, ANFIS, SVM, and EANN techniques in the field of groundwater.

In this study, the GNG clustering method was used to investigate fluctuations in groundwater level and quality parameters such as TDS and TH to reduce the volume of inputs and classify piezometric stations. A primary objective of the study is to examine how the ANN, ANFIS, SVM, and, EANN techniques perform in groundwater studies. In this regard, four single AI-based models, which are the feed-forward neural network (FFNN), adaptive neuro-fuzzy inference system (ANFIS), support vector machine (SVM), and emotional artificial neural network (EANN) were used for groundwater parameters modeling. Thereafter, the results of individual models were combined using three different ensemble methods named Simple Average Ensemble (SAE), Weighted Average Ensemble (WAE), and Neural Network ensemble (NNE) to improve the predictive performance. In general, the effectiveness of combined models was compared to individual models.

The GNG algorithm can be considered as one of the most powerful ways to train unsupervised and incremental neural networks as it can build and update the network's structure without depending on size and shape information. This method determines the structure of the data by creating a topological map. The formation of the algorithm begins with the creation of a diagram consisting of two nodes, each node is created using a random instance. During this process, the position of the nodes evolves so that the node position vectors are updated to model the data topology, and then large structures are subdivided into smaller structures, each of which forms a cluster shows (Subba Rao 2012). This network is primarily for adding new nodes to a small primary network (Cirrincione et al. 2012). The GNG neurons compete for alignment with the input data set to choose the most similar ones (Morell et al. 2014).

Part of the inspiration for this network comes from the way the biological neural system processes data and information, to learn and generate knowledge. One of the outstanding features of the artificial neural network is its ability to be used in any case that requires learning linear and nonlinear mapping. ANN must first know what it does not know, that is being taught first, and then expect to be able to solve the problem in this way. Generally, artificial neural networks are comprised of three layers, the input, the middle and, the output layers. Several processing elements are found in each layer known as neurons. As each neuron receives an input signal, it converts it into an activated value by using an activation function called a sigmoid. The observational data are given to the input layer and then the input data are processed in the middle layer, and finally, the values predicted by the neural network are obtained from the output layer (Nourani et al. 2011). In comparison with all other methods, feed-forward and back-forward propagation neural networks trained using Levenberg–Marquardt (FFNN-LMB) are the most practical and useful. In terms of predicting groundwater levels, these two approaches were more effective and, successful (Daliakopoulos et al. 2005; Sujatha & Kumar 2010; Chitsazan et al. 2013).

With a neural ensemble model, the outputs from individual models are imported into another FFNN for training as inputs and then a nonlinear ensemble is produced. A trial-and-error process was then employed for determining the ideal number of epochs and hidden layers.

S_(i) is the silhouette value of member i. Higher values of S_(i) indicate more similarity of members in the same cluster. The quality of clustering can be determined by measuring the average width of the silhouette across the entire data set. Distances between clusters are measured as Euclidian distances by using the mean dissimilarity of the clusters a(i). b(i), which expresses the least average dissimilarities between member i and the members of other clusters.

In the above formulas, y_i is the data related to the model calculation, x_i is the observational data, n is the number of data points and and are the average of the mentioned data.

This section discusses the results obtained from each part separately.

The central piezometers are given in the fifth column of Table 1. Among the central piezometers, the third cluster with the highest coefficient values is the best clustering, and also among the qualitative piezometers, the second cluster is the best cluster for the TDS and TH parameters. This paper revealed, the GNG method scores best in comparison with the others. Thus, due to the obtained results, the GNG can be considered as a reliable method for groundwater level and its chemical parameters clustering.

In the second stage, the best results of each model have been presented in the following sections, which use only one AI method to train and verify. In this case, the current time step is determined by its previous time steps until lag 6. The time steps h(t − 1), h(t − 2), …, h(t − 6) were thus fed into four different methods (ANN, ANFIS, SOM, and EANN) for estimating GWL value h(t) at the current time step.

The value of the SO₄, Ca, Mg, Cl parameters, and GWL, which were more proportional to TDS and TH based on MI processing, was fed as input into the mentioned individual methods for the qualitative process. It was essential to determine the number of middle neurons and calibrate the network at the right number of iterations in order to prevent overfitting in the FFNN model. It is important in order to avoid too small neurons, which may capture inconsistent information, and too many neurons, which may cause overfitting.

To select the most efficient model, training iterations of 2–100 were conducted using the Levenberg–Marquardt algorithm and log-sigmoid function. Here, 2–15 middle neurons were also tested to select the optimal network. Table 2 presents the optimal results of FFNN for both qualitative and quantitative studies.

Another AI-based model is ANFIS, which is characterized for its ability to be used for handling nonlinear processes with uncertainly by employing a fuzzy concept. The Sugeno operation was utilized for the calibration of membership function (MF) parameters. Additionally, MFs of triangular, Gaussian, and trapezoidal shapes showed a good ability for predicting and analyzing groundwater as well as a consistent MF in the output layer. The best model was determined by comparing two and three MFs and the number of 5–500 iterations using a trial-and-error method. The outcomes of optimum ANFIS method are tabulated in Table 2.

The third AI-based method exploited in this investigation was SVR. To model SVR, the radial basis function (RBF) kernel can produce more accurate results because of its smoothness assumption, even though it includes fewer tuning parameters than a model using other kernels (Noori et al. 2011). The results of optimal SVM models are tabulated in Table 2.

The last AI applied in this study was EANN. This method can model through hormonal glands and gives accurate outcomes in learning application (Lotfi et al. 2014). The EANN was designed utilizing the Sigmoid activation function and 1–10 hormone parameters, 1–10 neurons, and 1–2 training iterations were used to select the network with high productivity. Table 2 indicates the ideal results of EANN models.

The third step in the modeling process involved combining the results from four independent artificial intelligence models to enhance prediction efficiency. The linear SAE model outperformed developed AI single models in some piezometers and clusters. It is a fact that the linear averaging of the data set often yields a value lower than the highest and a value higher than the lowest (Nourani et al. 2020). It is possible that WAE is slightly better than SAE as a second ensemble model. This might be the case due to the weighting assigned to the parameters based on their importance. As with FFNN, NNE was also trained using the Levenberg–Marquardt algorithm. In addition, both the output and hidden layers were activated by the sigmoid activation function.

In a trial and error process, the number of middle neurons and the number of iterations for training varied between 2 and 25, and between 5 and 300, respectively. As a combination technique in hydrological modeling, non-linear neural networks have been successfully used (Elkiran et al. 2018; Sharghi et al. 2018; Nourani et al. 2021). The obtained results of ensemble models are presented in Table 3. As shown in this table, all ensemble methods can be used to enhance the performance of single models in GW modeling.

In this study, changes in groundwater levels and their quality were studied and predicted using artificial intelligence networks. In this regard, the GNG clustering technique was used to divide the whole study area into several groups. Furthermore, the piezometers in the quantitative and qualitative wells were modeled. In the next step, to increase the efficiency and accuracy of modeling, the model combination method was performed using simple linear averaging, linear-weighted averaging, and nonlinear neural ensemble procedures. In the end, the obtained results were compared. Based on the outputs, the ensemble model could result in a promising improvement in groundwater parameters modeling, conversely, the efficiency of simple linear averaging and linear-weighted averaging is directly related to individual models, therefore the poor results of each model affect these ensemble models. Among the three different methods of ensemble modeling, the nonlinear neural technique is more efficient. Comparing the results of the third ensemble method with the best result obtained from individual ones, TDS₂ showed the highest improvement of 12%, while P₃₇ indicated the lowest progress of 2%. Considering that in this study only static averaging of the results of individual methods was used, it is suggested that in future studies, by a dynamic and comparative selection of the results of individual methods in terms of minimizing estimation error, the efficiency of the model combination method will be improved. In this study, an ensemble unit is developed using only black-box models. Thus, physical-based models should be included in GW studies, alongside AI models, to investigate and combine their performances.

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

The authors declare there is no conflict.