Comparison between Machine Learning and Bivariate Statistical Models for Groundwater Recharge Zones

doi:10.21203/rs.3.rs-3089654/v1

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Comparison between Machine Learning and Bivariate Statistical Models for Groundwater Recharge Zones

https://doi.org/10.21203/rs.3.rs-3089654/v1

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Due to population growth and climate change, dependence on groundwater is expected to increase. This growth has put forth a major challenge of management for sustainable groundwater storage. This study illustrates a newly introduced bivariate statistical model with an ensembled data mining approach. Certainty factor (CF), evidential belief function (EBF), frequency ratio (FR) and convolutional neural network (CNN) are four bivariant statistical models. These four models are integrated with the logistic model tree (LMT) and random forest (RF). These models are used for preparing the groundwater potential map (GPM). The receiver operating characteristic (ROC) curve and area under the curve (AUC) were utilized for calculating the accuracy of the groundwater potential maps. The sequence and values of AUC obtained from the results are as CNN-RF (0.923), CF-RF (0.914), EBF-RF (0.911), FR-RF (0.904), CF-LMT (0.893), EBF-LMT (0.872) and FR-LMT (0.817). It can be concluded that the combination of bivariate statistic models and data mining techniques advance the method’s efficiency in creating a potential mapping of groundwater.

Hybrid models

geographic information system (GIS)

data mining techniques

groundwater potential mapping (GPM)

bivariate statistical models

Groundwater is a valuable natural resource that possesses a variety of qualities [1, 2]. The properties such as widespread availability, low development cost, consistent temperature, limited vulnerability to contamination, and reliability in droughts make it even more unique and useful [3, 4]. The growth of population and industrialization raised the required amount of water in Iran and some other countries. Globally, 50% of the drinking water needs, 40% of the industrial water needs and 20% of the agricultural water needs are fulfilled by groundwater resources [5, 6]. The demand for groundwater supplies has been increasing with rapid growth in the human population [7, 8]. Therefore, demarcations of potential zones of groundwater and their availability have become an essential means for executing an effective assessment of groundwater, and management system [9, 10]. In future assessing and mapping the groundwater potential zone is important for groundwater safety in the world. Identification of groundwater potential zones can be made with remote sensing (RS) and GIS technology [11, 12]. The studies related to groundwater potential target to identify the zones with optimal groundwater development. Groundwater potential has been described in broader spectrums but there is no fixed definition for this, neither a standard methodology nor units to measure the outputs [13]. Groundwater storage potential depends on the aquifer’s maximum permanent storage amount. Developing countries like Pakistan face hindrances in accessing hydrological information. Such information is crucial for the detection of the recent prominence of the groundwater structure [14]. Drilling, geophysical and geological methods are traditional groundwater exploration methods. These methods require time, human resources and high costs [6, 15]. Other than these conventional methods, RS and GIS methods are proved to be very efficient in groundwater potential mapping (GPM). They have improved the quality and accuracy of groundwater studies [16]. For hydrological investigation and monitoring, spatial and temporal domain information can be generated with remote sensing: analysis, prediction, and validation of data [11]. Large and complex geospatial databases are efficiently managed using GIS technology. Integration of GIS with RS and other geostatistical methods are used for many studies of groundwater potential plotting [3, 17–23].

To overcome the deficit between demand and supply, groundwater mapping is a significant method to figure out the areas which should be focused by management and policymakers. Anthropogenic activities contaminate the underground aquifers and fluctuation in water availability also affects the supply of water [24, 25]. Therefore, it is necessary to map the groundwater potential when surface water is not available enough to meet the requirements of water. It is observed that groundwater has better quality because of natural protection in aquifers, and it is easily available water source than surface water sources [26].

Proper mapping and planning are necessary to develop a sustainable supply of water, and research has explored rapid quantitative approaches to achieving this goal. For evaluating the safety and sustainability of groundwater, GIS and RS prove to be effective tools for the last two decades. Several studies regarding GPM involving bivariate and multivariate methods along with applications such as analytical hierarchy process (AHP) [27–30], evidential belief function (EBF) [31–33], frequency ratio (FR) [34–36], logistic regression (LR) [31, 37, 38] and weight of evidence (WOE) [33, 36]. At the same time, some alternatives have also been set up for assessing GPM by using machine learning methods involving tree-based methods like regression tree (RF) and classification and regression tree (CART) [39, 40]. Groundwater assessment can also be done by using an artificial neural network (ANN) [7].

Chen, et al. [41] used the alternating decision tree (ADTree), RF and kernel logistic regression (KLR) models for assessing the groundwater spring potential mapping by considering fourteen factors. This study validated the use of an artificial intelligence approach for GPM. In a similar study by Kalantar, et al. [26] the RF, linear discriminant analysis (LDA) and mixture discriminant analysis (MDA) models for GPM were used in Iran. Results generated by RF were more reliable and accurate than LDA and MDA. Termeh R [42] used three ensemble bivariate models including EBF, certainty factor (CF) and FR with LMT and RF for GPM. In this study, 339 wells were chosen, and 15 different factors (hydrological and topographical) were considered. This study lacks to consider the temporal effect of conditioning factors and results generated by used optimizer models in this study were not more reliable. So, there is a need to focus on the temporal effect and enhance the optimizer accuracy for more reliable results. In a recent study, four bivariate statistical models (CNN, FR, EBF and CF) were used with data mining algorithm techniques of RF and LMT models to identify the locations where the potential of water recharge is available. Evaluation of the GIS-based (LMT) and RF models to identify the locations for groundwater recharge in the capital city of Pakistan, Islamabad. Factors that contribute to recharge and the best hybrid model was selected for the study region. The outputs of the current study will contribute towards a better understanding of systematic groundwater using RF and LMT models to outline and mapping of groundwater potential areas.

In this study, the process of GPM involves five different steps as shown in Fig. 1. In the first step, investigation region features were illustrated, and the wells present in the region were identified. In the second step, data collection was done, and a spatial database was created for effective criterion. Distribution maps of well data along with fifteen different considered factors were ready for modelling including plan curvature, drainage distance, distance to fault, rainfall, soil, TWI, land cover, slope, drainage density, elevation, slope length, fault density, profile curvature, lithology, and aspect. In the third step, the spatial correlation between effective criteria and available wells was estimated using bivariate models such as CF, EBF, FR and CNN. The fourth step involves the preparation of GPM by considering the weights of CF, EBF, FR and CNN models as input values for LMT and RF models. Finally, AUC and ROC were used to validate the GPM, and the most suitable model was chosen in the end.

2.1 Study area

Islamabad is the federal capital city of Pakistan. It is located at 33°28´ and 33°48´ north latitudes and 72°48´ and 73°22´ east longitudes as shown in Fig. 2. It is situated on the northern edge of the Pothohar plateau. Mountains and plains are spread over 1175 m in the city. There is a diversity in the seasonal conditions of the city. It has an average minimum temperature of 2°C and an average maximum of 45°C. Islamabad is a semi-arid city with an average monthly precipitation of 95.2 mm. In the monsoon season, the monthly average precipitation increases up to 267 mm and 309 mm in July and August, correspondingly.

The sudden trend of migration from rural to urban regions has been increased. The same is the case with this city. The population of the city has reached over 2 million. This rapid growth in population has put a burden on the natural resources and affected the environment adversely. In the city, the water demand is mainly fulfilled by surface water and groundwater. Moreover, the Rawal dam, Khanpur dam and Simli dam are the major water reservoirs of the region. Surface water and 180 tube wells are currently being used by the Capital Development Authority (CDA) for water supplies to the city. Some private companies are also supplying water to the inhabitants.

2.2 Good inventory

The Water Resources Administration of Islamabad published reports that provide the groundwater wells data. Based on water management reports and past research, in this study data of groundwater wells with high potential (≥ 11 m3/h) and electric conductivity (EC) and an average pH of 350 µmhos/cm and 6 was used, correspondingly. In the current study, wells were classified as random and divided into two testing and training datasets. Training includes 70% of the total locations (108 wells) and the remaining wells were 30% (34 wells) considered as validation. The station of water wells was already built-in, and these were picked up randomly to remove biasness. The location of the wells is demonstrated in Fig. 3a.

2.3 Conditioning Factors

There are mainly 5 parameters (hydrological, topographic, geological, climate and ecological parameters) involved in modelling which are subdivided into 15 factors according to the classification of each factor. The parameters are discussed in order of decreasing discriminatory value.

2.3.1 Hydrological parameters

Drainage distance, drainage density and TWI play a significant role in hydrological factors. Drainage distance was obtained by forming a 300 m buffer Polygon around the streams. Drainage density was extracted from SRTM-based DEM. TWI was calculated from bands of Landsat satellite. In hydrological processes, topographic control is illustrated by the TWI factor. Moore, et al. [43] introduced an equation to find TWI:

$$TWI=\text{ln}\left(As|tan\alpha \right)$$

Where, As represents the cumulative upslope area and α is the slope angle. TWI, as shown in Fig. 3h, is classified into ranges from low (1.85) to high (7.16). Areas with higher values of drainage density are unsuitable for the production of groundwater resources because it increases the surface runoff and decreases the infiltration process [44]. Figure 3b and Fig. 3i shows the classification of drainage distance in meter (< 100, 100–200, 200–500, > 500) and drainage density in ${m}^{2}$ (< 1, 1−1.84, 1.84–2.68, 2.68–3.53, > 3.53) respectively.

2.3.2 Topographic Parameters

Different topographical parameters considered in this study including slope, slope length, profile curvature, elevation, aspect, and plan curvature were extricated from ASTER digital elevation model (DEM) with a spatial resolution of 30m. SAGA GIS®2.1.2 and ArcGIS®10.3 software were used to create these layers. Previous literature, natural break technique and features of the study area define the classification of maps. Terrain surface crossing with a horizontal plane made counter line curvature termed as plane curvature while surface crossing vertical plane made flow line curvature known as profile curvature [45]. Figure 3c and Fig. 3d show the classification of plan and profile curvature in the study region. Both plan and profile curvatures include five classes in radian/sec: <−2.34,−2.34-(−0.6),−0.6−0.6, 0.6–2.6, > 2.6 and <−3.14,−3.14-(−1.1),−1.1−0.7, 0.7–2.9,>2.9, respectively.

The slope is responsible for the speed of groundwater runoff and infiltration [46]. This factor is classified into five classes including, < 12, 12–24, 24–36, 36–48, > 48 (degrees) as shown in Fig. 3j. Moore and ID.Burch [47] presented an equation to determine the potential of soil loss by combining slope steepness and slope length, collectively known as the LS factor:

$$LS={\left(Bs|22.13\right)}^{0.6}{\left(\text{sin}\alpha |0.0896\right)}^{1.3}$$

Where Bs signifies the particular catchment area and α angle of slope. Figure 3k shows the five classes (< 10, 10–20, 20–30, 30–40, > 40) of slope length in meters.

At different elevations, soil type and vegetation vary due to climatic changes [48]. Study area, as shown in Fig. 3m, includes different elevations in meters, < 531, 531–617, 617–756, 756–994, > 994. The slope aspect is another factor that influences the vegetation and rainfall intensity. Figure 3p illustrate the 9 classifications of slope aspect in the investigation region, including flat, north, north-east, east, south-east, south, south-west, west, north-west, and north.

2.3.3 Geological parameters

Geological parameters include two factors: lithology, fault density and distance from faults. Lithology and faults data was obtained from the Geological Map of Pakistan issued by the Government of Pakistan. Through hydraulic conductivity, the potential of groundwater is influenced by lithology. The map shows that lithology has three classes: sandstone, limestone, and unconsolidated deposits. Spatial network distribution and groundwater accumulation are controlled by faults [49]. Fault density in kilometer Square and distance from fault in kilometers are classed into various classes (100, 100–200, 200–500, 500–1000, 1000–2000, 2000–5000, > 5000) and (< 15, 15–41, 41–65, 65–91, > 91) as shown in Fig. 3n and Fig. 3e, respectively.

2.3.4 Climate parameters

The climate parameter includes rain which influences the recharge of groundwater [50]. Rainfall data is acquired by interpolation of annual rainfall records and then it was blended with the rainfall map issued by Pakistan Metrological Department (PMD). It significantly assesses the flow of water and the nutritional status of the basin. ArcGIS®10.3 is used to generate a map as shown in Fig. 3f, of rainfall in millimeters and divided into five different classes: <882, 882–999, 999–1116, 1116–1233, 1233–1350.

2.3.5 Ecological parameters

Soil and land use are considered among the most important ecological factors. The source of soil and land use is FAO land cover. Soil is an important parameter defining the surface and subsurface runoff generation and accumulation [51]. Soil map, as shown in Fig. 3g, is classified into seven different types of soil including, calcareous loamy soil piedmont, calcareous silty soil-gullied land complex, rough broken land, mountainous land with nearly continuous soil, mountainous soil with patchy soil, urban and calcareous loamy soil. Land use indirectly or directly influenced evapotranspiration, runoff, and permeability [51]. Figure 3i shows the four classifications of land use including bare area, built-up, vegetation and water.

2.4 Models

In this study, on training data four bivariate statistical models including CNN, CF, FR and EBF are applied and points of all considered factors are calculated. After that, on these values, two hybrid models i.e. RF and LMT are applied over each point individually. In the first step, CNN, CF, FR and EBF are used to prepare the input file and then run this input file on RF and LMT model. Detail of each model is given below.

2.4.1 CNN Model

DLAs (Deep Learning Algorithms) are being developed on structure human brain. These are based on computational system like Artificial Neutral System (ANN) [52]. CNN has been adopted by many research scholars. CNN based classification and prediction has been employed to earth sciences and many other disciplines [53–55]. The features like Local connections, pooling, shared weights, and especially multiple layers make CNN recognizable and distinctive. Input data in CNN are images or they might be explained as images. This the main concept in CNN which makes it differentiable. This distinctive feature reduces the parameters which speeds up the process. Normally, CNN architecture is composed of different layers such as pooling layers (PLs),including convolutional layers (CLs), and the rectified linear unit (ReLU). PLs monitors overfitting, allow stable conversion, and reduces the convulsion structures which improves computational resulting from the convolutions. CLs identifies the Obscurities are identified by CLs. It provides the best results for data classification [56]. The property of ReLU activation enhances the nonlinear characteristics of the network through the ReLU activation function. For studies, scholars use different structures on the basis of the the data type, the image, and the objective. Some popular examples of structures are GoogleNet [57], ZFNet [58] and VGGNet [59]. Many previously published research articles and papers have explained in detail the types of layers, Primary Parameters of learning, and handling of training data in CNN [60].

2.4.2 FR Model

The FR shows the occurrence probability of a specific action or a factor. It determines the relationship between wells and effective factors of groundwater [35]. The FR is the proportion of the area with wells to the total investigation region. The below equation is used for the calculation of this factor:

$$FR= \frac{\frac{\text{N}\text{p}\text{i}\text{x} \left(\text{S}\text{X}\text{i}\right)}{{\sum }_{i=1}^{m}\text{N}\text{p}\text{i}\text{x} \left(\text{S}\text{X}\text{i}\right)}}{\frac{\text{N}\text{p}\text{i}\text{x}\left(\text{X}\text{j}\right)}{{\sum }_{j=1}^{n}\text{N}\text{p}\text{i}\text{x}\left(\text{X}\text{j}\right)}}$$

The numerator represents the ratio of wells number to the number of the total well in a class while denominators are the proportion of the number of the pixels in that class to the number of the total pixels. 15 groundwater affecting parameters are used in this study. Each parameter is termed as criteria, and each criterion is classified into various subcategories. Each subcategory is known as a class. Simple and easy concepts are used in the FR model. It is also capable of analyzing bivariate statistical models and classification of each factor. This method ignores the relationship between variables, which is counted as a drawback of this method [61].

2.4.3 CF Model

The CF model, as a bivariate statistical model, was introduced in 1975 by Shortliffe and Buchanan. This model was later modified in1986 by Longman [62, 63]. GIS is used to integrate the results in a spatial database in this model. Well outcomes frequency in layers each class is the base for calculation of this factor. It is calculated by the following equation [64]:

$$\left\{\begin{array}{c}cf= \frac{\text{p}\text{p}\text{a}-\text{p}\text{p}\text{s}}{\text{p}\text{p}\text{a}(1-\text{p}\text{p}\text{s})}, if ppa \ge pps\\ cf= \frac{\text{p}\text{p}\text{a}-\text{p}\text{p}\text{s}}{\text{p}\text{p}\text{s}(1-\text{p}\text{p}\text{a})}, if<pps\end{array}\right.$$

The proportion of well-pixels number in a division to the total pixels of the same division is called ppa. The proportion of the total pixels with wells of the study region to the total pixels of the generated map is called pps. The values of the CF model range from−1 to + 1. Positive values are indicators of an increase in precision, and less certainty is indicated by negative values [65].

2.4.4 EBF Model

In 1967, Dempster proposed the Dempster-Shafer theory of evidence. It was later advanced by Shafer in 1976. On the basis of this theory, a statistical bivariate technique, i.e. the EBF model was developed [66]. Four basic EBFs are used which include the rank of belief (Bel), ambiguity level (Unc), rank of disbelief (Dis), and rank of plausibility (Pls). Bel parameter is considered pessimistic mode and has a low probability. State of high probability and optimistic mode are considered by Pls parameter. In this model, Pls parameter value is greater or equal to the Bel factor value. These two parameters differences give the third parameter i.e., Unc. The spatial relationship of the active parameters and well occurrence is estimated from the extracted data by this model. This model also estimates the spatial relationship between each class factor as well. The following equations were used for this model [67]:

$${Bel}_{{c}_{ij}}= \frac{{w}_{{c}_{ij}D}}{{\sum }_{f=0}^{m}{w}_{{c}_{ij}D}}$$

$${w}_{{c}_{ij}D}= \frac{N({C}_{ij}\cap )/N\left({C}_{ij}\right)}{N\left(D\right)-N({C}_{ij}\cap D)/N\left(T\right)-N\left({C}_{ij}\right)}$$

Equation 6 demonstrates the conditional existing well probability (i.e., the occurrence of groundwater) in the nonexistence of ${C}_{ij}$ (each division of each parameter). ${W}_{{C}_{ij}D}$ (Weight of ${C}_{ij}$.) shows the belief that there is a well instead of it being lacking. Here, $m$ shows the considered number of criteria for modelling, each class of each criterion is represented by $i$, each criterion is represented by $j$. In these relations, N (T) shows the total pixels in the investigation region and N (D) represent the total well-pixels.

2.4.5 RF Model

The RF model is a well-known data mining algorithm. Different classification trees use this model. A significant number of decision trees are generated by switching and changing the target affecting variables. Then all trees are integrated by the algorithm in a prediction [68]. Then each tree’s original data is randomly chosen in the training process [69]. A number of tree depths are selected to start a for loop and divide dataset for validation inside it. After training the decision tree with that depth on training data and testing it on the validation set, keep validation error, plot it and find the global minimum of a validation error. Afterwards, three user-defined parameters are included in the RF model. It includes the number of factors used for constructing each tree, tree’s number, and minimum node number. Strength enhancement of independent trees and power reduction of the relationship between them improves the forecast of the RF model [70]. All accessible information for its tree growth is not used by the RF model. Only 66% of Bootstrap information is utilized. A forecast variable is randomly implemented during the growing phase. In the same phase, this predictor variable is used for node generation in a tree. Now the maximum size of the decision tree is produced [71]. The remaining 33% of the information is used for the evaluation of the fitted tree. This procedure is repeated numerous times. All likely values average are used as the final forecast of algorithms [70].

2.4.6 LMT Model

The nature of the logistic model tree (LMT) is a non-parametric classification model. It is associated with a supervised training algorithm combining decision tree learning and logistic regression (LR). Quantitative variables or classified variables are predicted in this model on the basis of qualitative and quantitative predictor variables collection. In reality, the hierarchical model’s decision tree includes decisive means that decompose into homogeneous regions of independent variables [72]. Interpretation of a set of laws is made by decision trees that lead to a category or value. Measurement of distance is a distinction between building techniques of a decision tree. Decision trees are known as classification trees, and they are applied to predict discrete variables. Those decision trees which are applied for forecasting continuous variables are called regression trees [73]. The objective of a decision tree is discovering methodology in the way of a series of procedures for presenting the prediction results which are extricated from input parameters. For the isolation of an increment in logistic type data, the LR model is produced in each tree leaf using the Logit Boost algorithm. The CART algorithm is used to cut the tree. LR of an additive in the Logit Boost algorithm is used for each C class (non-well or well) with least squares, where C class defines the drilling of water wells for the purpose of obtaining groundwater data as shown in the equation [74]:

$${L}_{c}\left(X\right)={\beta }_{0}+\sum _{i=0}^{D}{\beta }_{i}$$

$$\left(C|X\right)=\frac{\text{e}\text{x}\text{p}\left({L}_{c}\left(X\right)\right)}{{\sum }_{{c}^{{\prime }}=1}^{C}\text{e}\text{x}\text{p}\left({L}_{{c}^{{\prime }}}\left(X\right)\right)}$$

Where C shows the class number in the equation.

2.4.7 Validation

Estimating the classification results and evaluating its competence to recognize a particular class is done with the help of the ROC curve and is defined as a probability curve. AUC (area under ROC curve) is used for validation of the method’s sensitivity [36]. The relation of classified and unclassified values is justified by the concept of sensitivity. The efficiency of a classifier in identifying the class is directly proportional to the baseline change for a specific class in the ROC curve. The AUC is also calculated considering the trend diagram of the ROC curve [75]. AUC gives a total performance measure across all possible classification thresholds. The higher the value of the AUC, the greater that method's reliability as a predictor [76]. This index is used to assess the assigned values of the objective class properly (True Positive), assigned incorrect class values (False Positive), the non-allocated values to the specified class (True Negative) and non-allocated incorrect class values (False Negative). X-axis and Y-axis of the equation are calculated in Equations [77]:

$$X=1-\frac{TN}{TN+FP{\prime }}$$

$$Y=\frac{TP}{TP+FN}$$

The state of actual positive output is called True positive (TP). The state of actual positive output and negative predictive value is termed as False negative (FN). The situation of actual negative output and negative predictive value is known as True negative (TN). The situation of actual negative output and positive predictive value is presented by False positive (FP). The mentioned indices come from the confusion matrix. This is the base for the calculation of the ROC curve. The validation of the model is carried out by calculating ROC Curves. Such curves explain how accurate the model is which means how reliable the results are.

3.1 Result of FR, CF, and Bel

As indicated in Appendix A, the Aspect parameter includes high weights for EBF, CF and FR in the southwest direction. According to the results of the landcover factor vegetation areas include the maximum probability of water existence. Rainfall class < 882 have the highest values for FR (1.15), CF (0.18) and Bel (0.29) ,because more rainfall classes indicate more occurrence of groundwater. The drainage distance is a strong contributor to correctly identifying areas of groundwater potential. Weights are high in less than 100m class for FR (1.087), CF (0.16) and Bel (0.25). TWI represent the topography effect on the size and location of runoff saturation zones [78]. High weights for TWI parameter is in less than 2 class which includes 1.13, 0.28 and 0.17 for FR, CF and Bel. The drainage density factor significantly identifies resources of groundwater and the structure of lithology for an area is represented by this factor. Class of fault density factor less than 15 includes high weights for EBF (0.46), FR (1.42) and CF (0.29). In lithology, sandstone has the highest number of well. Less distance to fault affects the groundwater existence positively because it controls the exchange of water between basement and ground [35]. In profile curvature 1.1–0.7 class have high weight. In the elevation parameter, FR model outcomes (1.016) illustrated that class of elevation more than 617m have less correspondence with groundwater while groundwater has high correspondence. Low elevation regions are more pervious against overflow. In high slope areas, groundwater runoff increases so groundwater has less correspondence with low slopes and high with high slope regions. The highest weights for three factors in the slope parameter is for the 36–48 degrees class. It has been observed that with an increase in slope length, the weights decrease in each class. Incidence of groundwater is greatly affected by plan curvature, and a class of this factor 0.6 to−0.6 have the highest weights for EBF, CF and FR. Long term water holding capacity of this type of class is high. Mountainous land with nearly continuous soil has high weights for CF, EBF and FR in the soil factor. The highest weights were given to those who contribute more to groundwater potential mapping.

3.2 Application of Ensemble Models

An ensemble model is used to prepare the GPM by LMT and RF models operating the bivariate statistic model weights, as shown in Appendix A. Waikato Environment for Knowledge Analysis (WEKA) data mining software is used to implement the LMT and RF model [79, 80]. In RF modelling, the process explains the importance and values of each factor as shown in Fig. 4. FR-RF model outcomes illustrate that aspect, drainage distance, rainfall and landcover have the greatest importance while slope length and lithology constitute the least importance. According to the CF-RF model, drainage density (0.33), then landcover (0.32), rainfall and aspect have the highest importance while elevation (0.18) and plan curvature (0.2) showed the least importance in the current study. In EBF-RF, the greatest importance is related to elevation, aspect, drainage distance and land cover. Slope length (0.2), plan curvature (0.19) and slope (0.2) showed least importance. In CNN, aspect,landuse and rainfall have highest importance while plan curvature (0.15) and profile curvature (0.2) showed the least importance. It has been observed that all four models showed the greatest values for aspect, drainage density, drainage distance, landcover and rainfall. The slope aspect is influenced by the more rainfall in the southwest direction and groundwater potential increases in more rainfall areas. Drainage density shows the lithological features and less distance from drainage facilitate the water exchange between ground and streams. In agricultural areas, groundwater potential increases because aquifers get charged by irrigation water.

WEKA software is used to implement hybrid models with bivariate models. After this, by using ArcGIS 10.3 software, the generalization of the model is made to the total pixel of the investigation region, and each calculated pixel represents the pixel consequence on groundwater. The weight of each pixel represents the likelihood of groundwater existence. The investigation region is classed into different classes: Very high, high, medium, low and very low potential. Very high and high potential regions signify the maximum existence of water while very low and low potential regions have less chance of water availability. Figure 5 shows the high potential areas which are more appropriate for groundwater occurrence.

3.3 Model’s validation

ROC curve is presented in Fig. 6 for ensemble models generated in the study. Table 1 shows the accuracy of models ranges from highest value of CNN-RF (0.923), CF-RF (0.914), EBF-RF (0.911), FR-RF (0.904), CF-LMT (0.893), EBF-LMT (0.872) and FR-LMT (0.817) models, correspondingly. Uncertainty in groundwater existence explains the high precision of CNN, EBF and CF models than the FR model. Values of the X-axis and Y-axis signifies the sensitivity and specificity. The value of AUC lies between 0 and 1, where values greater than 0.5 shows high accuracy while values less than 0.5 show the integrity of the model. The prepared map of groundwater potential by using an RF model integrating with the bivariate model has high accuracy as illustrated in results.

Table 1. Results of ROC, area under the curve (AUC) of four GPM models

Test Result Variable(s)	AUC	Std. Error	Asymptotic Sig.	Asymptotic 95% Conﬁdence Interval
Test Result Variable(s)	AUC	Std. Error	Asymptotic Sig.	Lower Bound	Upper Bound
CF-RF	0.914	0.022	0	0.889	0.958
EBF-RF	0.911	0.025	0	0.881	0.96
FR-RF	0.904	0.024	0	0.874	0.952
CF-LMT	0.893	0.025	0	0.862	0.942
EBF-LMT	0.872	0.027	0	0.838	0.924
FR-LMT	0.817	0.033	0	0.77	0.881
CNN-RF	0.923	0.019	0	0.893	0.965

GIS-based model’s applications for exploring the potential map of groundwater are very useful and less time and cost consuming. All considered parameters play a significant role in the potential mapping of groundwater as discussed above in the results. However, a mixture of data mining techniques and bivariate statistical models are used for the determination of potential mapping with more precision. One of the widely used non-parametric learning algorithm for supervision and classification is the decision tree. The concept of overfitting should be considered in decision trees. There is an imbalance in the concept of bias and variance. This is another disadvantage of this method. The difference between the system outputs and the actual expected value is referred to as the concept of bias. The variation in the system by altering the sample or using out-data samples is referred to as variance [10]. The selection of a low depth tree becomes the reason for bias errors and reduces variance. On the other hand, the selection of a high depth tree will show high variance and reduced bias. So, a balance between the bias and variance of a tree should be maintained. The bagging method is applied for reducing variance. This study is conducted by combining bivariate statistical models of CNN, FR, CF, and EBF integrated with data mining methods of RF and LMT models. These models were utilized for preparing groundwater potential maps for Islamabad city, Pakistan.

The base of difference between the mentioned models and data mining techniques is hypothesis or type of the processed data, respectively. Generally, the hypothesis of a statistical technique is reality-based. It shows that the information distribution is normal and clear. Initial assumptions affect the validity of the precision of the outcomes [81]. On the other hand, no hypothesis is used in data mining techniques. Data mining techniques are better than bivariate statistical models. Contradictory and incomplete data works very well in data mining models. Based on the data pattern, the lost data can be retrieved in data mining models [74]. However, any lost parameter can lead to the ineffectiveness of data in bivariate statistical. The ability of the statistical model to find patterns is lost due to an increased number of factors. Bivariate statistical models are not able to discover the complex and non-linear relationships of included parameters. The reason for this lies in their linear nature. But the task of finding a complex relationship between parameters can be easily completed using data mining techniques. These techniques are designed to do the task for all the included parameters of the database.

The outcomes of the ROC curve are based on the accuracy of AUC. The AUC hierarchal order of models in terms of accuracy is CNN-RF (0.923), CF-RF (0.914), EBF-RF (0.911), FR-RF (0.904), CF-LMT (0.893), EBF-LMT (0.872) and FR-LMT (0.817). CF-RF model shows more accuracy, and the calculation for input and output of this model is easy and simple [77], while the input and the output of the EBF model have more computational complexity as compared to the FR model. The calculation of the FR model’s output and input is an easy process. EBF and CF models show complexity against uncertainty. These models are well suited for combining the confidence of different sources [82].

The results interpret that CNN, CF and EBF model are better in terms of accuracy than FR. These models include uncertainty in their results. The accuracy of groundwater potential mapping has been increased due to the combination of data mining algorithms and bivariate statistical models. Such an increase can be seen in previous studies [16, 83]. Termeh R [42] had similar study but results are less reliable (AUC obtained using the CF-RF, EBF-RF, FR-RF, CF-LMT, EBF-LMT and FR-LMT methods were 0.927, 0.924, 0.917, 0.906, 0.885 and 0.83, respectively), because the weights of factors were directly used in this study which lacks to show their significance. In recent study, it is to be noted that every factor has its individual contribution and an additional CNN model is used which shows highest accuracy. To identify this significance of each factor bivariate statistics as input for RF is used. Temporal effect of these factors is also considered and average of last 10 years is taken, so it results in true prediction by removing temporal errors. In this study, different optimizer model and activation functions are used to enhance the accuracy of model, and Gradient Descent optimizer proves to be best possible model, which helps to generate more meaningful results than in recent previous studies. All previously published studies usually used statistical techniques for groundwater potential mapping but MLs techniques provide accurate results by identifying two variable relationship [84–86]. Interpretation of results illustrates that the accuracy of the RF model is more than the LMT model. The reason for higher accuracy lies in the fact that assumption is not needed on the factor’s distribution in the RF model and the calculation of the relationship between factors. RF model has another advantage to overcome the overfitting problem and managing with respect to the partiality in the data. At the same time, the LMT model cannot perform these functions. Another benefit of the RF model currently dominated by the machine learning system is its use for issues of both classification and regression. Execution and acceptance of input variables, not deleting anyone from thousands of inputs are done in the RF model. This model can also determine important variables in the prediction of the model as well. The RF algorithms are easy to use and very useful. The default hyperparameters of the RF algorithm often produce a better prediction of results. Some hyperparameters are low and difficult to understand. In the present study after validation of this model and accuracy check of the final map, it has been observed that in this area RF model is best, but it can change from area to area.

The study aimed to prepare a groundwater potential map for Islamabad city using a combination of bivariate statistical models (CNN, FR, EBF and CF) with RF and LMT models. Obtained outcomes of the ROC curve and AUC helps to determine that the CNN-RF model is better for more accuracy and improved GPM. The CF-RF, EBF-RF and FR-RF models also provide accuracy but less than the CNN-RF model. It is evident from the outcomes that CNN, CF and EBF models are better and improved in terms of accuracy than FR in combination with the technique of the random forest model. Distance from the waterway, Slope aspect, topography and rainfall curve parameters are the most important factors. The least important factors are lithology,plan curvature and soil parameters. Combined models assist in calculating the significance of parameters. On the basis of the results of the CNN, FR and CF model, the maximum number of wells are observed on the basis of a different parameter, drainage distance, plan curvature, profile curvature, distance from the fault, rainfall factor, soil factor, TWI, land cover, slope, slope length, drainage density, elevation, fault density, lithology and aspect.

5.1 Contributions and future implications

The present study is helpful to identify the wells in Islamabad city and provide the details of the potential of groundwater by mapping the study region using machine learning methods. It has never been used before in this region, so it provides baseline study for developing countries facing water crisis. Due to the increase in population day by day, people are suffering from the unavailability of safe water. The maps generated may be helpful to meet the requirements of the residents, and in future, data may be useful for management and policy-makers in case of scarcity issues. This study also validates the ensembling of four bivariate statistical models with two hybrid models by using their advanced optimizers which in result generated more reliable outputs.. Additionally, multiple datasets by considering their temporal effect, were used which are responsible for recharge, so ultimately accuracy with more datasets increased. In future, it is suggested to implement the present study to new locations with water scarcity problems for assessment of the potential of groundwater. Some other model can also be integrated to get more meaningful results in the investigation region. Planners and managing authorities can implement other methods of finding groundwater potential to make the outputs more certain.

Author Contributions: All the authors contributed equally to this study.

Funding: N/A

Acknowledgements: The authors would like to thank Quaid-i-Azam University, COMSATS University Islamabad Wah Campus and Universiti Teknologi PETRONAS (UTP) for the support provided for this research.

Conflicts of Interest: The authors declare that they have no conflict of interest.

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No competing interests reported.

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Comparison between Machine Learning and Bivariate Statistical Models for Groundwater Recharge Zones

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