Simulating the discharge of Nahavand karstic springs based on neural intelligent models

Today, water supply is a topic that is increasingly being considered to meet the needs of various sectors such as industrial, agricultural, and drinking uses and requires researchers to accurately predict the flow of water to use it optimally (Gondwe et al. 2011; Adnan et al. 2017). Due to their high water quality and relatively easy extraction, karst water sources are among the most important groundwater sources extracted by many people worldwide (Smith & Hunt 2010).

The unique and complex features of the karstic areas make these features different from other aquifers (Bakalowicz 2005). Karst aquifers are highly heterogeneous and contain conduits, fractures, and pores that may indicate permeability or flow paths (An et al. 2020). Karst aquifers provide approximately 20–25% of drinking water in the world. It can be said that 9% of the world's population relies on freshwater supply of karst aquifers and karst springs (Andreo 2012; Goldscheider & Drew 2014; Stevanović 2019). Karst formations cover 11% of the geological formations in Iran. Despite the vulnerability, karst aquifers are the main source of water supply, especially in the Zagros mountain range of Iran (Nassery 1992; Drew 2017).

Spring discharge is a highly nonlinear and nonstationary natural process. It is affected by various factors, such as hydrology, meteorology, and human activities (Dudley et al. 2018; Gai et al. 2023). Karstic water sources are widely used all over the world and simulating the discharge of karstic springs still seems an important challenge (Rudolph et al. 2023). One of the reasons for the challenging nature of karst water resources modeling is that it possesses highly variable unknown channel networks.

Intelligent neural methods such as fuzzy logic and artificial neural networks (ANNs) are similar to black boxes that are less constrained by physical issues, can do this without the need to model the environmental factors and geometry affecting the surface flow and perform modeling with acceptable accuracy (El-Shafie et al. 2007). The advantage of using black box models and ANNs in the karstic areas is that detailed information about the physics of hydrological processes is not required (El-Shafie et al. 2007; Guo et al. 2011; He et al. 2014). Among the disadvantages of ANNs is that the order and sequence of input data information are omitted (Kratzert et al. 2018).

The results of studies have shown that the neural intelligent models can capture nonlinear relationships between input and output parameters and identify inherent patterns hidden in time series data (Cerqueira et al. 2019). Intelligent models, including ANNs, are considered a powerful tool to create a relationship between the factors influencing the input and output of springs (Rawat et al. 2019; Wunsch et al. 2022). An important limitation of intelligent modeling in karst is access to temporal and spatial data because climatological stations usually do not exist inside or near karst spring basins, or few stations are available in the region (Wunsch et al. 2022). Therefore, in recent years, new intelligent models such as ANNs have been adopted to simulate karst aquifers to solve these problems (Zeydalinejad et al. 2020).

Gai et al. (2023) used a graph neural network (GNN), and then applied this model to simulate and predict Niangziguan spring discharge in China. Three graph structures were used to optimize the GNN model. The performances of the ChebNet and the Graph Convolutional Network (GCN) models were compared and the results showed that the high-order ChebNet was more adaptable to simulate the karst hydrological processes with nonlinear and nonstationary behaviors than that of GCN. In one study, a model was presented to deal with the problems of unknown/illegal wells. The results showed that the Analytic Element Method (AEM) model is more efficient for solving the problems of unknown wells (Gaur et al. 2023). Wunsch et al. (2022) used convolutional neural networks (CNNs) to process gridded meteorological data directly. They used one-dimensional complex neural network to perform simulations based on artificial intelligence to overcome the problems of karst spring discharge modeling. The results showed that the model used for modeling the spring's discharge is very suitable. In the Alpine and Mediterranean regions, Gholami (2022) reconstructed the temporal changes of spring discharge in an alluvial aquifer on the southern shores of the Caspian Sea. The results indicate the high efficiency of the ANN model in the test and train phases. In a recent study of the Colorado River basin in the United States, it was shown that the flow is very sensitive to temperature and precipitation variations. Different types of methods can be used to accurately predict the flow (Towler et al. 2022). The development of a multilayer model of groundwater under transient conditions was carried out in the Bihar region of India. The results of this study showed that groundwater modeling is an important method for understanding the behavior of aquifer systems and detecting the groundwater head under different hydrological stresses (Omar et al. 2021). Di Nunno & Granata (2020) predicted the discharge of nine springs in the Umbria region using the nonlinear autoregressive exogenous (NARX) model. The results proved that this model performs well for all sources and short-term and long-term predictions. The researchers recommended using the NARX network to predict spring discharge in other areas characterized by karst aquifers. An et al. (2020) used time–frequency analysis methods, SSA and EEMD, to extract the frequency and features of the Niangziguan Springs discharge trend. The long short-term memory (LSTM) neural model was also used to simulate each frequency and trend sequence. The results show that SSA-LSTM and EEMD-LSTM are better than LSTM. The EEMD-LSTM model has the best prediction performance. Rawat et al. (2019) used an ANN to simulate two springs of Hill Campus and Fakua from Tehri Garhwal district of Uttarakhand, India. Rainfall, temperature, and relative humidity data from 1999 to 2003 were used as input to simulate spring discharge. The superiority of the intelligent neural model in simulating spring discharge was pointed out. The ability of ANN and Suport Vector Machine (SVM) methods in simulating the monthly flow was investigated. The results of ANN and SVM models were compared to evaluate the performance of the applied models. The results showed that the SVM model can be used with higher accuracy to predict the monthly flow (Adnan et al. 2017). The performance of two Vensim models and neural networks for simulating spring flow and piezometer for karst aquifer was studied by Kong-A-Siou et al. (2014), and the results showed that the ANN model is more effective in combining karst nonlinearity. The daily discharge of two karst springs on the area of Rouva, island of Crete, Greece was simulated using a multilayer perceptron (MLP) back-propagation ANN. Two models were developed for springs. The results showed that in karst environments, hydraulic behavior is influenced by local conditions, even in a few hundred meters (Paleologos et al. 2013). Population and economic growth have led to water shortages worldwide, especially in the developing countries. Due to the excessive exploitation of groundwater resources in arid and semi-arid regions such as Iran, the simulation of spring discharge is of great importance. The planning and management of surface water resources as one of the main water supply sources become more important. The karst springs on the Nahavand area are the most important water supply source in western Iran. Therefore, the present research can significantly contribute to water supply, which is in line with the management of water resources and development. It is very necessary to understand and investigate karst water sources to develop regions. The springs are bearing high discharge rate due to limestone formations and suitable hydrogeological conditions. In mountainous watersheds such as Nahavand Plain with high altitudes, it is also sometimes difficult to predict the spring's discharges due to the unavailability or shortness of hydrological and meteorological data. The present study also tries to use three neural intelligent models, the input data of the simulation was hydrogeological (measured) and hydrology data without using the lag-time of the investigated springs discharge as an input to analyze the behavior of karst springs in the Nahavand region. The detailed analysis of the spring discharge simulation in the region for the first time shows the importance of this study.

Nahavand region is located in the cold semi-arid climate (BSK) based on Koppen's climate classification (Mané 1975; Fasihi et al. 2024). Summers are fairly mild and winters are relatively cold (Kiyani et al. 2021).

Climate, high altitude, and time are among the most effective external factors in creating karst's geological terrain. Because of tectonic movements in the region, the development of fracture patterns has appeared in the region. The expansion of dissolvable rocks has caused the formation of various types of karstic formations of hydrogeomorphological features importance. The development of karst aquifers with an average discharge of 4 m³/s can be seen in the region, and the most important of these faulted springs is Giyan spring (Sp4), its formation related to the faults in the region (Ghobadi et al. 2012).

ANN has been developed based on the neural structure and function of the human brain (Agatonovic-Kustrin & Beresford 2000; Lingireddy & Brion 2005). A common ANN architecture used in this study is MLP, the simplest and most widely used ANN architecture (Tabari et al. 2015). A neural network can be trained to perform a specific function by adjusting the connection weight values between elements. As a brief description, MLP is a feedforward network consisting of an input, hidden layer(s), and an output layer (Demuth & Beale 1992; Onyari & Ilunga 2013).

The input layer receives the external data, and the output layer produces the final result. Hidden layers are neural nodes between the input and output layers that provide nonlinearity. More complex problems can be solved by increasing the number of neurons or using hidden layers (Rumelhart et al. 1986; Onyari & Ilunga 2013). In this study, the optimal number of neurons is considered from 1 to 20 by trial and error. The selection of the minimum number of nodes is based on the research attempted and is usually considered based on the number of inputs (Sheela & Deepa 2013). This simulation used the Tangent hyperbolic (Tan) and Sigmoid activation function (Sig), Levenberg–Marquardt (LM), and Conjugate Gradient learning rules (Conj).

Principal component analysis (PCA) is a method for statistical analysis and simplification of data sets. PCA mathematically uses an orthogonal transformation to linearly transform the observations of a series of potentially related variables, representing a series of uncorrelated linear variables. These unrelated variables are principal components (Barnett & Preisendorfer 1987; Jang 2017; Hsu et al. 2021). PCA is a powerful tool that attempts to explain the variance of a large data set of correlated variables with a smaller set of independent variables, as well as an MLP implemented to determine the nonlinear ordering of these components. PCA provides information about the most meaningful parameters, which describe the entire data set while allowing training data with minimal loss of original information (Ilaboya & Kayode 2018). The steps of PCA are followed as normalization, correlation coefficient matrix, computation of eigenvalues and eigenvectors, calculation of participation rate, calculation of cumulative participation rate, and calculation of principal component loading (Wu et al. 2021). From the Hebbian principle, there are two choices, Oja's and Sanger's, to implement the model (Bayatvarkeshi et al. 2020). In this research, the learning principle was implemented with two main components: activation functions and second learning rules similar to the neural method.

The co-active neuro-fuzzy inference system (CANFIS) network proposed by Jang et al. (1997) integrates a modular neural network (MNN) and adaptive fuzzy inputs to increase the accuracy of the modeling process. It can be said that the neural network increases the performance of the network by integrating CANFIS and fuzzy inference systems (FIS). The high performance of CANFIS has been demonstrated in modeling many hydrological parameters (Vernieuwe et al. 2005; Zhang et al. 2009). The CANFIS network uses a fuzzy neuron that applies membership functions (MFs). Two main MFs, Bell and Gaussian, are used in the CANFIS network. The number of modular networks will equal the number of outputs; the CANFIS network also uses a hybrid axon to process MF outputs in MNN outputs (Tabari et al. 2012). In general, in this model, two-phase structures, the Tsukamoto model and the Sugeno model, were used (Aytek 2009). The Tsukamoto structure is more complicated than the Sugeno model (Bayatvarkeshi et al. 2020). The TSK structure with Bell and Gaussian MFs and the number of MFs were also applied in this research work. Tangent hyperbolic (Tan), Sigmoid (Sig), Levenberg–Marquardt (LM), and Conjugate Gradient learning rules (Conj) were used to simulate the spring discharge.

NeuroSolutions 5 software was used to simulate ANN, CANFIS, and PCA-ANN models. Parameters such as porosity, hydraulic conductivity, and specific yield were measured by frequent field visits and precipitation data of five meteorological stations such as Varayaneh (St1), Faresban (St2), Synoptic (St3), Giyan (St4), and Barzool (St5) and elevations were used as input data. The discharge of springs, namely: Famaseb karst springs (Sp1), Faresban (Sp2), Ghale Baroodab (Sp3), Gian (Sp4), and Gonbad Kabood (Sp5) for the years 1994–2020 were obtained from the Hamadan Regional Water Organization (HMRW 2023). The positions of all springs are presented in Figure 1. The data were divided into two categories: train data (70%) and test data (30%), and this percentage is acceptable in various research work related to neural models (Coulibaly et al. 2001; Guzman et al. 2019; Bayatvarkeshi et al. 2020; Di Nunno & Granata 2020; Mohammadi et al. 2021). The division of training and test sets was selected randomly with the aid of the black box of Neurosolution 5 software which is commonly available in the software itself. Among the data sets, 30% was considered as the test data set and the remaining 70% was considered as the training set. The three intelligent models used are based on the error measurement indicators.

For each neural intelligence model, three models (ANN, PCA-ANN, and CANFIS) were implemented for 20 neurons with activation and MFs, learning rules, and other information. Figure 6 shows the results of these performances in the test phase. The value of the correlation coefficient in the test phase is less than 0.7 in all executions; the maximum value for the three ANN models is 0.645 with the Sigmoid activation function, in the CANFIS model, is 0.654 with the activation function Tangent hyperbolic (Tan) and Gaussian membership function. Finally, for the PCA model, the r value is 0.652 with the Sigmoid activation function and Sanger's implementation, which is preferred for PCA-ANN because it naturally divides the PCA components based on the magnitude (Bayatvarkeshi et al. 2020), was calculated. The Levenberg–Marquardt was introduced and preferred as the best learning rule for all three models, which is also mentioned based on previous research (Zare Abyaneh et al. 2016; Bayatvarkeshi et al. 2020). The value of the nRMSE coefficient of all three models is 0.094. A summary of the execution based on the best neuron that has the highest accuracy among 20 neurons separately for each learning rule, activation function, and membership of ANN and PCA-ANN models is presented in Tables 2 and 3. A summary of all CANFIS models simulated is given in Table 4.

Among the 20 implemented neurons: n = 2, with the Tangent hyperbolic activation function, the Levenberg–Marquardt learning rules, and the Conjugate Gradient. The Sigmoid activation function and the learning rules of Levenberg–Marquardt are n = 16. The Sigmoid activation function and the Conjugate Gradient learning rules are n = 7. The separation of the activation function and different learning rules was considered based on the error measurement indicators. Finally, the implemented model with the value of n = 16, the MBE value equal to 24.740 (l/s), and the highest correlation coefficient value was selected as the best model for discharge simulation with the ANN model.

Table 3 presents the best neuron separated by MFs, activation functions, and learning rules. In this table, the best value of n for Sanger's membership function, two learning rules (Levenberg–Marquardt and Conjugate Gradient), and two activation functions (Tangent hyperbolic and sigmoid) equal to 3, 4, 11, and 13 were selected based on higher accuracy and less error among 20 neurons. The executions based on Oja's membership function with the mentioned statistical functions and rules showed that the best value of n equals 2, 3, 12, and 18 among 20 executed neurons.

Finally, Sanger's membership function, Levenberg–Marquardt learning rules, and Sigmoid activation function with the value of n = 13 became the best neuron and execution with a high accuracy of 9.4% and correlation coefficient of 0.652 for simulating the discharge of karstic springs in the area.

Two Bell and Gaussian MFs were implemented in the CANFIS model separately with different learning rules and activation functions. The results of the performances are presented in Table 4. Based on the three error measurement indicators examined, the model with Gaussian membership function, Levenberg–Marquardt learning rules, and Tangent function has higher accuracy and less error among other implementations used for the simulation of spring discharges.

The average percentage of the simulated discharge rate changes compared with the observed discharge rate of the springs during the statistical period under investigation in the two stages of test and train is shown in Figure 7. The highest average percentage of the simulated discharge increases compared with the value observed in the test phase. This was observed for May in the period of 27 years, which has a value of 24.20%. The lowest fluctuation percentage was observed, with a value of −24.61% for December. The results in the train stage also indicate that October and April had the maximum fluctuation with an average value of 23 and 22%, respectively, compared with the observed value.

At this stage, the minimum average reduction percentage was also achieved, with the amount of −0.61% in January. In general, in the wet seasons, November, December, and January, the average percentage of fluctuation is the lowest compared with the dry seasons (June, July, and August).

Prediction of surface flow, including spring discharge, assists in providing reliable and useful information in managing and planning water resources. Using selected intelligent models has helped us significantly to interpret. In this research, five hydraulic parameters were measured in the field with precipitation and elevation data, and five parameters were considered as input to simulate the discharge of five karstic springs in Nahavand Plain, Hamedan Province, located in the west of Iran. Three ANN, PCA-ANN, and CANFIS intelligent models were implemented to simulate the discharge of selected springs. According to the analysis of results, the CANFIS model is the best model based on the r, nRMSE, and MBE index to simulate spring discharge. The value of the correlation coefficient computed in the ANN model is 0.645; in the CANFIS model, it is 0.654; and in the PCA-ANN model, it is 0.652. Leven-Marquardt learning rules were preferred as the best learning rules for all three models. The value of nRMSE of all three models is 9.4%. Finally, the CANFIS model was preferred for simulating karstic spring discharge due to its higher accuracy than the other two models. The average amount of the simulated discharge fluctuation percentage compared with the observed value during the investigated period in the months of the wet seasons of the year, including November, December, and January, has the lowest value compared with the dry seasons.

In this research, precipitation as time series data was used for the first time as input data to simulate the discharge of five karstic springs in the region and four hydrogeological parameters were also measured by attempting field visits.

For further studies, we suggest using satellite data of groundwater level as input for future research to improve the model's performance.

This research was not funded by any organization.

The data sets generated during and analysed during the current study are available from the corresponding author on reasonable request.

The authors declare there is no conflict.