Prediction of groundwater drawdown using artificial neural networks

Groundwater drawdown is typically measured using pumping tests and field experiments; however, the traditional methods are time-consuming and costly when applied to extensive areas. In this research, a methodology is introduced based on artificial neural network (ANN)s and field measurements in an alluvial aquifer in the north of Iran. First, the annual drawdown as the output of the ANN models in 250 piezometric wells was measured, and the data were divided into three categories of training data, cross-validation data, and test data. Then, the effective factors in groundwater drawdown including groundwater depth, annual precipitation, annual evaporation, the transmissivity of the aquifer formation, elevation, distance from the sea, distance from water sources (recharge), population density, and groundwater extraction in the influence radius of each well (1000 m) were identified and used as the inputs of the ANN models. Several ANN methods were evaluated, and the predictions were compared with the observations. Results show that the modular neural network (MNN) showed the highest performance in modeling groundwater drawdown (Training R-sqr = 0.96, test R-sqr = 0.81). The optimum network was fitted to available input data to map the annual drawdown across the entire aquifer. The accuracy assessment of the final map yielded favorable results (R-sqr = 0.8). The adopted methodology can be applied for the prediction of groundwater drawdown in the study site and similar settings elsewhere.


Introduction
Groundwater is the major water resource in arid and semiarid areas of the world since these resources are less affected by evaporation and pollutants (Wada et al. 2010;Sahour et al., 2020a). Unfortunately, the increase in human population and agricultural and industrial developments has led to an increase in groundwater extraction, pollution, and depletion of these resources (Shivasorupy et al. 2012). Moreover, climate change and alteration of precipitation patterns have exerted extra pressure on groundwater resources in these regions making aquifers depletions a serious threat to human life (Abulibdeh et al. 2021). Therefore, access to groundwater fluctuations data and groundwater drawdown is essential for water resources management plans. Unfortunately, these data are often constrained by spatial and temporal gaps in many parts of the world. Even in areas with available groundwater observation networks, the estimation of groundwater drawdown is challenging when applied to a large domain.
The use of artificial intelligence (AI)-based models in groundwater studies has been growing in the past decade. methods of AI, including artificial neural networks (ANNs), fuzzy-neural networks, self-organized maps (SOM), and machine learning (ML), have been applied extensively in the groundwater modeling process. AI-based models have been used in groundwater quality studies (Chou 2006(Chou , 2007Han et al. 2011;Wang et al. 2014;Li et al. 2020;Maliqi et al. 2020;Pal and Chakrabarty 2020;Mosaffa et al. 2021), groundwater depth studies (Dixon 2004;Awasthi et al. 2005;Saemi and Ahmadi 2008;Shiri et al. 2013;Gong et al. 2018;Chen et al. 2020), and the other hydrological studies such as riverflow modeling, reservoir management, flood hazard, and sediment modeling (Smith and Eli 1995;Cheng et al. 2002;Wilby et al. 2003;Jain et al. 2004;Cheng et al. 2005;Peters et al. 2006;Demirel et al. 2009;Nourani et al. 2011;Can et al. 2012;Demirel et al. 2012;Kisi 2015;Taormina and Chau 2015;Nourani et al. 2019a, b a&b;Gholami and Sahour 2021). The results of previous research indicated that artificial intelligence methods are powerful tools for modeling hydrological parameters, but the accuracy of input data and the use of a suitable model structure is crucial for designing workflows of these studies. Ghose et al. (2010) used ANN for simulating water table in the region of Orissa, and they found that the ANN is very efficient in water table simulation. Wang et al. (2019) used a numerical model for evaluating the dewatering-induced groundwater drawdown. They simulated the relationship between groundwater drawdown and stratum deformation. They indicated that groundwater extraction caused a notable drawdown in the pumping location. Pradhan et al. (2019) evaluated the groundwater extraction status and predicted groundwater depth fluctuations using different AI methods such as radial basis function network (RBFN), neuro-fuzzy inference system, and fuzzy logic in an Indian inter-basin. Their results showed the higher performance of the fuzzy logic-based model over the neuro-fuzzy and RBFN models in water table modeling. Combining AI-based models with geographic information system (GIS) capabilities is a common exercise in groundwater modeling. Previous studies have shown the high performance of this exercise in modeling the quantity and quality of groundwater resources (Tweed et al. 2007;Ganapuram et al. 2009;Arslan 2012;Bradai et al. 2016;Haselbeck et al. 2019;Motevalli et al. 2019;Sahour et al. 2020b;Abulibdeh et al. 2021).
The aquifer type and conditions, including the hydrodynamic characteristics of an aquifer, determine the natural recharge potential and fluctuations of the groundwater depth (Rukundo and Dogan 2019;Abd-Elhamid et al. 2020;Hereher and Al-Awadhi 2020). Distance from water resources (such as lakes and rivers), the location of groundwater withdrawal sites, and precipitation values affect the amount of groundwater recharge (Guevara-Ochoa et al. 2018;Shi et al. 2021). Numerous studies have been performed to simulate the fluctuations of groundwater depth; however, estimation of annual drawdown values is challenging because of the complexity of the controlling factors and the needs for various inputs in the modeling process. This study aims to evaluate several ANN methods to predict the spatial variation of the annual groundwater drawdown using its affecting factors in an alluvial aquifer (unconfined aquifer) on the southern coasts of the Caspian Sea.

Study area
The study area includes a plain with an area of 10,000 square kilometers in the north of Iran. This plain is located on the southern coasts of the Caspian Sea, extending from 50°34' E to 54°10' E and 35°47' N to 37° N (Fig. 1). The mean annual precipitation of the study area varies from 1300 mm in the west to 600 mm in the east. Rainfall is a common type of precipitation in the Mazandaran plain, and snowfall is rare. The major types of land uses of the plain are agricultural lands (rice fields and gardens), residential areas (cities and villages), and water bodies (rivers and wetlands), forests, and industrial lands. Geologically, the plain is composed of Quaternary alluvial sediments, and there is an unconfined aquifer in an alluvial aquifer with shallow groundwater. Groundwater depth varies between 1 and 35 m. The agricultural section is the main consumer of water in the study area, and the main consumption is related to rice fields. The need for groundwater in the agricultural, residential, and industrial sectors in the region is very high. Due to the existence of more than 300,000 hectares of agricultural lands, the uncontrolled development of tourism and construction, and population growth, this region has faced an increase in water demand and groundwater extraction. This has led the groundwater resources to experience a significant drawdown and decline in water table across the region (Gholami et al. 2015a, b).

Measurement of annual groundwater drawdown
To measure the values of groundwater drawdown, 250 piezometric wells in the plain were selected. The depth of wells varies according to changes in the groundwater depth. These wells vary from 10 m in shallow aquifers to 100 m in the southern part of the study plain. The location of piezometric wells is shown in Fig. 1. The secondary data of monthly groundwater levels in those wells in a 5-year period (2015 to 2020) were obtained from Mazandaran Regional Water Company (MRWC 2020) and the Water Resources Research Organization of Iran (TAMAB 2020). The difference between groundwater level at its maximum (early spring) and minimum (early autumn) was determined as the values of the annual drawdown ( Fig. 2). At the beginning of spring, the water table is at its highest due to precipitation and pausing on agricultural activities during the cold seasons. The groundwater in the region is recharged during the six rainy months (Shiri et al. 2013). During the warm seasons (late summer and early fall), low precipitation rates and high agricultural activities, and extraction of groundwater lead to a decline in the water table (Yan et al. 2015). The study period was normal in terms of precipitation and climate without any drought period. The drawdown values of the examined wells have changed during the 5 years due to changes in precipitation values and agricultural lands as well as the development of residential areas. Therefore, the mean annual drawdown in this five-year period (2016-2020) was determined as the groundwater drawdown values at the location of each well, and the effective factors in groundwater drawdown were quantitatively estimated.

Factors affecting groundwater drawdown
In this study, the factors affecting groundwater drawdown including extraction values, the transmissivity of aquifer formation, depth to the water table, topography (slope and elevation), location in the watershed, distance from water resources (groundwater recharge), annual precipitation, annual evaporation, and distance from industries and residential centers were used as the inputs of the modeling process (Awasthi et al. 2005;Shiri et al. 2013;Gong et al. 2018;Guevara-Ochoa et al. 2018, Pradhan et al. 2019Abd-Elhamid et al. 2020;Shi et al. 2021). Examples of inputs are shown in Table 1.

Groundwater depth
Groundwater depth is one of the main factors affecting the groundwater extraction values because shallow aquifers are easier and more accessible for extraction (Adamowski and Chan 2011). Based on the secondary data of the observed groundwater depth (water table) in the examined wells, the mean groundwater levels were determined. Then, using the interpolation of the mean values at each point and the interpolation capabilities of the GIS, the spatial distribution of annual groundwater depth in the Mazandaran plain was estimated.

Transmissivity of aquifer formations
Transmissivity of aquifer formations affects the permeability and the influence radius of the wells (Shie et al. 2016). The aquifer transmissivity in each well was determined using pumping tests conducted by MRWC. Then, the mean transmissivity map of the entire aquifer was provided using the values of each well and determination of homogeneous areas of transmissivity using geological and hydrogeological maps. The homogeneous areas of transmissivity were prepared and confirmed by MRWC.

Groundwater extraction
Determining groundwater extraction is one of the most challenging inputs. Access to accurate data on extraction, especially in the case of agricultural wells in the region, was difficult due to the lack of automatic gauges. For this purpose, data of all rural and urban drinking and industrial water wells and their annual extraction values were provided. Further, a digital  cadastral map of the region (accuracy = 1 m meter) showing major landuses such as rice farms and citrus gardens was prepared. The maximum influence radius of the wells is considered to be 1000 m (Shi et al. 2016). Finally, the summation of the groundwater extraction (drinking water, industry, and agriculture) was considered as the annual extraction values. It is noteworthy that according to studies, the water need for one hectare of rice field and one hectare of the garden is about 11,000 and 5,000 m 3 /year, respectively (MRWC). As noted above, measuring groundwater extraction is very difficult and requires extensive data. In this study, extensive groundwater extraction data from drinking, agricultural, and industrial water wells within the influence radius of the wells were provided. To prepare a map of groundwater extraction within the influence radius of the well, digital layers of agricultural land (rice lands and gardens) and the location and wells pumping rates were provided in GIS. Since the maximum influence radius of the wells is 1000 m, therefore, for a 2000 m pixel (sides 1000 m), the area of agricultural lands was multiplied by their water consumption. Then, the map of annual groundwater extraction within the influence radius was provided as the total consumption rate (sum of drinking water, industry, and agricultural lands).

Annual precipitation and evaporation
Precipitation and evaporation are two affecting factors in groundwater recharge (Guevara-Ochoa et al. 2018). To estimate the spatial distribution of precipitation and evaporation in the study area, the field-based precipitation and evaporation data (climatology stations) were interpolated in the GIS environment to provide the raster layers of annual mean precipitation and evaporation rates.

Topography (elevation and slope)
Slope affects the hydrogeological conditions in a coastal aquifer (Abd-Elhamid et al. 2020). A 10 m digital elevation model (DEM) was generated using 10-m contour lines in GIS. Then, a slope map was provided using DEM and GIS. The study area includes a plain with a very gentle slope where topographic changes are less than one hundred meters in the whole plain surface. The spatial distribution of wells was provided based on the distance from the Caspian Sea as the watershed outlet.

Distance from water resources
All rivers, wetlands, and lakes of the study site were surveyed based on topographic maps and satellite images, and the distance from the water resources was prepared in the GIS environment. The distance from water resources can be effective in groundwater recharge and depletion (Awasthi et al. 2005).

Distance from industries and residential centers
A database of the plain's industries has been prepared and checked on satellite images. Residential areas were prepared based on remote sensing and topographic maps with a scale of 25,000. Then, distance from industries and residential areas was prepared in the GIS environment. The wells near industrial and residential areas have a high pumping discharge and can affect the groundwater depth (Gholami et al. 2015a).

Prediction of groundwater drawdown by using ANN
ANN is a black box modeling method that has a structure similar to the human brain. The main components of an ANN include input data, neurons learning algorithm or technique, transfer functions, and number of training epoch. Using accurate and effective inputs in a phenomenon such as groundwater depth fluctuations and identify and communicate between inputs and outputs, several models can be presented. The first step is to normalize the data and was randomly divided into three classes: training class (65 percent of the data), cross-validation class (10 percent of the data), and test class (25 percent of the data). Correlation analysis between groundwater drawdown and its affecting factors was conducted to evaluate the network inputs and determine the main factors of groundwater drawdown. NeuroSolutions software was used for the modeling process with different ANNs. In the neural network environment, different structures of inputs were used using the trial-error method and evaluation of network performance. Moreover, the trial-error method was used to determine the optimal architecture of the selected networks, including optimal transfer function, learning technique, neurons number, and number of training epochs.
Moreover, sensitivity analysis was performed to evaluate the optimal inputs. Evaluation criteria of the network performance were the correlation between the predicted and the measured values as well as the error indices such as the coefficient of determination (R-sqr) and the mean squared error (MSE).
Different structure of ANNs including multilayer perceptron (MLP), Jordan and Elman Network (JEN), generalized feed-forward (GFF), radial basis function (RFB), time-lagged recurrent (TLRN), principal component analysis (PCA), and modular neural network (MNN) were used for modeling groundwater drawdown. The MLP network typically uses a backpropagation algorithm (BP). BP is used to train feed-forward neural networks (FNN). In FNNs, the connections between constituent units do not form a cycle, making them different from recursive neural networks. The FNN is the first and simplest type of ANNs, in which, data move only in a forward direction. In fact, the data initially move from the input nodes (neurons) and pass through the hidden layers to reach the output nodes. The main problems of MLP network are low training speed and need to a large number of training data (Gholami et al. 2015b). The JE network develops the MLP with processing elements (PEs). PEs create a network with the ability to extract temporal data from the input data (Mohamed and Atta 2010). The GFF network has a similar structure to the MLP network how connections can go through one or more layers. In fact, the ability of the MLP network to solve problems is not the secret of the GFF network. But, GFF is often much more efficient in solving problems (Beghdad 2008). An MNN is an ANN specialized through a series of independent ANNs moderated by a number of intermediaries. The intermediaries take the module output and processes them to create an output of the ANN as a whole. Further, the intermediaries only receive the outputs of the modules and does not respond to the modules that do not interact with each other (Bart and Jacob 1994). The RBF includes a nonlinear hybrid network that is typically comprised of a single hidden layer of the PEs. One of the advantages of this network is its faster processing compared to the MLP network. The TLRN network includes an algorithm with short memory. The TLRN network is developed in nonlinear time series predicting, temporal pattern classification, and identification systems (Sattari et al. 2011). Supervised and unsupervised learning techniques are integrated in the same topology in a PCA network. In fact, the PCA finds a series of uncorrelated features among the inputs and that is an unsupervised linear procedure (Beghdad 2008).

Performance evaluation of the models
The source of uncertainty in this study can be divided into two categories of measurements' uncertainties and model uncertainty. The uncertainty introduced by measurements is those that can occur due to human and instrument errors for measuring input parameters. Uncertainty of the model can be reflected in predictive power of the model. Both uncertainties (introduced by model and the inputs) can be reflected in prediction values. In fact, by comparing the observed values with predicted values as we performed in this study. Finally, statistical indices such as the coefficient of determination (R-sqr), the mean absolute error (MAE), the mean squared error (MSE), the Nash-Sutcliffe efficiency (NSE), and matching and correlation between the measured and predicted rates in modeling stages have been used to evaluate the performance of the used networks. Moreover, the observed and predicted values of groundwater drawdown layers were displayed in GIS for comparison and visual evaluation.

Results
The mean annual drawdown rates of groundwater in the study region according to the statistics of groundwater depth fluctuations in 250 piezometric wells were between 0.15 and 4.37 m per year. The average drawdown in these wells was 1.75 m per year. A drawdown of about seven meters in a particular year has been observed in some wells. The elevation of the Mazandaran plain varies between -27 and 30 m with an average slope of less than 5 percent. The model inputs such as distance from water resources, distance from industrial centers and population centers vary from zero to several kilometers. Further, the mean annual depth to the water table in the studied plain varies from 0.5 to 40 m (Fig. 3). The shallow groundwater is observed on the coasts of the Caspian Sea or the outlet of watersheds, and the deepest groundwater is observed in the southern border of Mazandaran plain. The mean annual precipitation and evaporation vary between 600 to 1300 mm and 875 to 1000 mm, respectively.
The annual groundwater extraction within the influence radius of the sampling wells was estimated between 0.1 and 3.66 million m 3 /year (average 2 million m 3 /year). The maximum extraction values occur around rice lands and drinking water supply wells (Fig. 2). An example of the estimated data on the inputs and output of neural networks is presented in Table 1. Correlation analysis between inputs and network output was used to find the optimal inputs and the main factors of groundwater drawdown in the region (Table 2). According to Table 2, factors such as groundwater extraction values, depth to groundwater, and transmissivity of aquifer formations have the highest correlation coefficients. Therefore, these three factors will be the most important factors in the drawdown of groundwater depth (Pradhan et al. 2019;Abd-Elhamid et al. 2020;Shi et al. 2021).
The results also indicated that the hyperbolic tangent transfer function or sigmoid function and LM learning technique are the best selections for the optimal network structure, which in previous studies were also among the optimum options . Different results were obtained during the trial-error procedure with different neural network structures, transfer functions, learning techniques, and the number of neurons. Neural network training in two stages of cross-validation and training yielded favorable results (Table 3). According to the results, all tested neural networks showed acceptable performance in simulating groundwater drawdown. However, the MNN and MLP networks have the highest correlation between the measured and predicted values and the lowest error in the predicted values. Results of the evaluation on the test stage are presented in Table 4. According to the statistical criteria in Table 4, the MNN network is the most efficient network among the tested networks in predicting the water table drawdown.
The comparison between the predicted and the observed values of groundwater drawdown in the test stage in different structures of the neural network is presented in Fig. 4. As can be seen, the MNN network has the highest correlation between the predicted and the observed values. As we mentioned before, the raster layers of optimal network inputs (depth to groundwater, transmissivity, and annual extraction values) were prepared in the GIS environment. The values were converted to numerical format to predict the groundwater drawdown values across the entire studied plain. Finally, the predicted values were converted back to raster format in GIS. The predicted values were presented as a map of the annual groundwater drawdown values (Fig. 5).
The comparison of the predicted and observed groundwater drawdown values (Fig. 4) indicates the accuracy of the results and the performance of the used methodology. Based on the results, the MNN network has the highest performance and the lowest error in the modeling process (training and testing stages).

Discussion
The measured values of groundwater in the wells showed a decline of more than 1.7 m in most parts of the area of the study. The maximum groundwater drawdown values occur in places with high groundwater depth, high transmissivity (coarse texture), and high groundwater extraction.
According to Table 1, depth to groundwater, extraction values, the transmissivity of aquifer formations, annual precipitation, and evaporation, location elevation, distance from industries and residential centers have a significant relationship with drawdown. The three factors of transmissivity of aquifer formations, extraction values , and groundwater depth with correlation coefficients of 0.8, 0.7, and 0.6, respectively, were the most effective controlling factors in groundwater drawdown in the study area. The higher the transmissivity or permeability of the aquifer, the higher the possibility of extraction with higher pumping discharge, and as a result, we will see a higher decline in the water table (Pradhan et al. 2019). In fact, high transmissivity leads to a larger influence radius in a well. Therefore, groundwater extraction, even at a further distance, affects the water table in adjacent areas. According to the results, the amount of groundwater extraction is also directly related to the decline of the groundwater table (Awasthi et al. 2005;Saemi et al. 2008;Gong et al. 2018).
Precipitation is one of the major factors of the groundwater natural recharge. A significant and inverse relationship between precipitation and groundwater drawdown values was reported in previous studies (Shiri et al. 2013). Precipitation showed a significant spatial changes across the study area. But the amount of groundwater recharge is affected by factors such as precipitation values, location in the watershed and distance from surface water resources. Extraction is another important factor in the groundwater drawdown. As a result, changes in precipitation do not determine the amount of groundwater drawdown. In fact, there is no strong relationship between the annual precipitation of each place and the rate of groundwater drawdown in the study area. There are many places that have a higher precipitation, but a higher drawdown has been recorded, and vice versa.
Evaporation can affect near surface groundwater or in the areas where groundwater meet surface water such as wetlands. However, evaporation is not correlated with groundwater drawdown in the studied plain. The elevation is an effective factor in the water table in unconfined aquifers. Low lands have more water recharge capacity, and the water table is higher in them causing lower decline in water table. The precipitation in these area are high and the gentle topography cause water to have enough time to recharge the groundwater. Also, the areas closer to the Caspian Sea coasts are affected by surface water discharges.
Distance from industries and residential centers is two factors that have a significant relationship.
Because these areas are the place of drilling wells and they reflect the density of extraction sites and the extraction values of groundwater (Gholami et al. 2015a). The presence of surface water can reduce the reliance and pressure on groundwater resources. Therefore, distance from water resources (rivers, wetlands, freshwater lakes) can play an important role in water table fluctuations. However, no significant relationship between this parameter and groundwater drawdown values was observed in the studied plain.
The process of predicting groundwater drawdown was performed using different neural networks in which most of them showed an acceptable performance. Among the various neural network structures used, the MNN network showed the highest efficiency, and the TLRN network had the lowest performance in predicting groundwater drawdown. According to Table 3, there was not much difference between the performance of the tested networks. Correct prediction of the maximum drawdown values is important in water resources management planning. The adopted The study also showed that using only three main inputs (transmissivity of aquifer formation, depth to the water table, and extraction rate), and an efficient neural network structure, groundwater drawdown can be predicted with acceptable accuracy.
Providing a reliable groundwater drawdown map can help water resource managers adopt strategies to mitigate the impacts of groundwater depletion. The adopted methodology can be used for investigating different scenarios of groundwater extraction and climate variability (increased groundwater withdrawal during droughts). The methodology presented in this study can be tested with other input parameters. The adopted methodology can also be used in other plains with similar or different variables. Such practices can also provide insights on water needs for future population, industrial, and agricultural growth.

Conclusion
Assessment of groundwater drawdown is complex and challenging task due to the presence of various climatic and anthropogenic factors. Traditional field-based measurement of groundwater drawdown requires a dense network of observational wells, which is not available in many   . 4 Comparison of the measured and predicted annual groundwater drawdown in the test stages of the different used ANNs countries. We adopted a feasible conventional methodology to map a large-scale prediction of groundwater drawdown in an alluvial and coastal aquifer. The relationship between groundwater drawdown and its affecting factors in 250 wells was established using ANN-based models. Using available input data in the study area, the spatial changes of the annual groundwater drawdown were mapped across the entire study area. In the modeling process, different neural network structures with different inputs can be used. However, the most challenging step is to quantify the parameters that explain the groundwater drawdown in an aquifer in order to train an ANN. Theadvantages of using artificial intelligence in predicting the groundwater drawdown are speed of operation, high performance, low cost, and connectivity with other systems such as GIS. The adopted methodology can be used to predict changes in groundwater drawdown in the study area and in similar settings elsewhere. This can be performed under different scenarios of climate and groundwater extraction. To complete future studies, we suggest using other methods of artificial intelligence and machine learning, as well as different input parameters for the prediction of drawdown values.