Freshwater scarcity is an ever-increasing problem throughout the arid and semi-arid countries, and it often results in poverty. Thus, it is necessary to enhance understanding of freshwater resources availability, particularly for groundwater, and to be able to implement functional water resources plans. This study introduces a novel statistical approach combined with a data-mining ensemble model, through implementing evidential belief function and boosted regression tree (EBF-BRT) algorithms for groundwater potential mapping of the Lordegan aquifer in central Iran. To do so, spring locations are determined and partitioned into two groups for training and validating the individual and ensemble methods. In the next step, 12 groundwater-conditioning factors (GCFs), including topographical and hydrogeological factors, are prepared for the modeling process. The mentioned factors are employed in the application of the EBF model. Then, the EBF values of the GCFs are implemented as input to the BRT algorithm. The results of the modeling process are plotted to produce spring (groundwater) potential maps. To verify the results, the receiver operating characteristics (ROC) test is applied to the model’s output. The findings of the test indicated that the areas under the ROC curves are 75 and 82% for the EBF and EBF-BRT models, respectively. Therefore, it can be inferred that the combination of the two techniques could increase the efficacy of these methods in groundwater potential mapping.
Introduction
Groundwater could be regarded as the water in the saturated parts of the Earth that fills the pore section of geologic formations and soil beneath the water table (Freeze and Cherry 1979). Groundwater has broad advantages over surface water as a resource, including its capability to be utilized when needed, and it is less vulnerable to catastrophic incidents (Naghibi and Pourghasemi 2015). Furthermore, groundwater contributes the most in meeting freshwater demand in arid and semi-arid areas such as the Middle East (Chezgi et al. 2015). Groundwater potential mapping is one of the well-studied subjects in the literature and has attracted many researchers over the years.
Many researchers have used statistical and data mining algorithms to map groundwater potential. Some of them have used spring locations as groundwater resource indicators, while others used qanat and well locations. According to the literature, the frequency ratio (Oh et al. 2011; Pourtaghi and Pourghasemi 2014; Naghibi et al. 2015), weights-of-evidence (Ozdemir 2011a; Corsini et al. 2009; Razandi et al. 2015; Tahmassebipoor et al. 2016), and index of entropy (Naghibi et al. 2015) are among the most popular methods used by the scholars. Moreover, other data mining methods such as classification and regression tree, random forest, and boosted regression tree (BRT) are widely used to assess the potential of groundwater (e.g. Naghibi and Pourghasemi 2015; Naghibi et al. 2016; Zabihi et al. 2016; Rahmati et al. 2016; Mousavi et al. 2017; Golkarian et al. 2018). Although data mining techniques have proved to be reliable in working with nonlinear and complex data (Naghibi et al. 2016), one of the drawbacks is overfitting, which impacts the models’ estimation quality and prediction validity. In two recent papers, by Naghibi and Moradi Dashtpagerdi (2016) and Naghibi et al. (2018), various data mining algorithms, including random forest, BRT, support vector machine, artificial neural network, quadratic discriminant analysis, linear discriminant analysis, flexible discriminant analysis, penalized discriminant analysis, k-nearest neighbors, and multivariate adaptive regression splines, were employed for groundwater assessment taking into account spring and qanat locations. Other techniques include the evidential belief function (EBF) method to map the potentiality of groundwater (Nampak et al. 2014; Rahmati and Melesse 2016). Nampak et al. (2014) used EBF to map groundwater potential and compared its performance with a logistic regression model; the results indicated the superior performance of the EBF model. In another research project, Naghibi and Pourghasemi (2015) examined the efficacy of the EBF model and compared the results with classification and regression tree, random forest, BRT, and generalized linear model. Their findings also yielded an acceptable performance of the EBF model.
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The aforementioned studies mostly used single models in the groundwater-related research; however, the ensemble models have been used in other fields of study including landslides (Lee et al. 2012; Umar et al. 2014) and flood susceptibility modelling (Tehrany et al. 2013, 2014). Very recently, Naghibi et al. (2017b) introduced a novel ensemble model, which was constructed based on four data mining models and the frequency ratio in a groundwater-related study. The findings of their research indicated that the produced ensemble model showed a better performance than a single application of the models. Similarly, Pourghasemi and Kerle (2016) combined EBF and random forest models to achieve better model performance and their results indicated a higher efficacy of the ensemble method.
Boosted regression tree as a data mining technique was selected for this purpose as it has the capability for feature selection (Naghibi et al. 2016) as well as implementing stochastic gradient boosting to diminish variance and bias (Abeare 2009). The BRT model also defines the importance of the impacting factors in the modelling procedure. Considering the aforementioned strong features of the BRT model, this model was chosen to be combined with the EBF model to improve its prediction accuracy. In this research, the proposed ensemble method (EBF-BRT) improves on the weak points of each method and combines their advantages by analyzing the relationships of groundwater with each independent layer and with each class of independent layers; furthermore, groundwater-related independent variables can be assessed. Since this combined approach is almost new in groundwater potential assessment, through this research its efficiency and capability can be examined. This research aims to improve the performance of statistical techniques through the extension of a data-mining ensemble model in groundwater potential mapping. Thus, the aims of this study are: (1) evaluating the performance of the EBF-BRT model in groundwater potentiality assessment, (2) ranking the importance of groundwater-conditioning factors (GCFs) and the relationship between groundwater potential and the GCFs, and (3) providing spatial information and guidance to support decision-making processes concerning groundwater management in the Lordegan aquifer in central Iran.
Materials and methods
A spring can be defined as a feature by which groundwater flows from an aquifer to the land surface. Based on the physiographical and hydrological characteristics of the study area, this study assumes that the natural spring occurrences and their discharge rates can be related to the potential of groundwater resources in the studied basin. To quantify this relationship, a groundwater potential map (GPM) is proposed as a tool for providing spatial information and for determining the relationship between the spring occurrence and effective factors, here called ‘conditioning factors’.
For modelling of groundwater potential, two datasets were prepared, including a springs location inventory and the GCFs. Using the mentioned datasets, the EBF model was implemented, and the resultant GPM was plotted using ArcGIS 10.4. In the next step, EBF values were extracted and then used as an input to the BRT model, and the ensemble EBF-BRT model was trained. Finally, by implementing a receiver operating characteristics (ROC) plot, the efficacy of the EBF and EBF-BRT methods were validated. Figure 1 shows the methodology flowchart implemented in this research.
Fig. 1
Flowchart of the methodology implemented in this study
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Study area and preparation of the conditioning factors
Study area
The Lordegan Basin covers the areas between 31°19′09″ and 31°38′06″ north latitudes and 50°28′02″ and 51°13′13″ east longitudes, and is located in Chaharmahal-e-Bakhtiari Province, Iran. Lordegan Basin covers an area of 1,486 km2. The topographic elevation in Lordegan Basin ranges between 850 and 3,640 m above mean sea level (amsl) with a mean elevation of 2,044 m amsl. The lithology of the Lordegan Basin is mainly composed of sedimentary and tertiary rocks and Quaternary deposits, and about 33.3% of its area is classified under group 5, including low-level piedmont fan and valley terraces deposits (GSI 1997; Table 1). The dominant land use is rangeland, which covers approximately 44% of the basin floor. Other types of land use encompass forest, agriculture, orchard, and residential area. Spring occurrence is not limited to the plain areas and it can be seen on different slopes and elevations; hence, the study was carried out at the basin scale.
Table 1
Lithology characteristics of Lordegan Basin, Iran
Lithology group
Lithology characteristics
1
Anhydrite, salt, grey and red marl, alternating with anhydrite, argillaceous limestone and limestone
2
Blue and purple shale and marl inter-bedded with the argillaceous limestone
3
Bluish grey marl and shale with subordinate thin-bedded argillaceous-limestone
4
Brown to grey, calcareous, feature-forming sandstone and low-weathering, gypsum-veined, red marl and siltstone
5
Low-level piedmont fan and valley terrace deposits
6
Low-weathering grey marls alternating with bands of more resistant shelly limestone
7
Pale red marl, marlstone, limestone, gypsum and dolomite
8
Cream to brown color, weathering, feature-forming, well-jointed limestone with intercalations of shale
9
Dark red, medium-grained arkosic to subarkosic sandstone and micaceous siltstone
10
Limestone, dolomite, dolomitic limestone and thick layers of anhydrite in alternation with dolomite in middle part
Undivided Bangestan group, mainly limestone and shale, Albian era
13
Undivided Eocene rock
Data preparation
In this study, a spring inventory dataset including 94 springs (in 2014) was prepared based on the field surveys (Fig. 2). The dataset was then split into two subsets for training (70% of the dataset: 66 springs) and validating (30% of the dataset: 28 springs) the models (Pourghasemi and Beheshtirad 2015). It should be noted that the division of the spring dataset into two subsets was conducted on the basis of a random algorithm in ArcGIS 10.4.
Fig. 2
Locations of the study area in Iran, and the training and validation springs
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Based on the literature (Ozdemir 2011a, b) and availability of data, 12 GCFs were selected for the modelling process. The GCFs are composed of eight topographical factors, two river-related factors, and two physical factors including land use and lithology. It should be noted that as the EBF works with classified factors, the GCFs were classified based on the literature (Ozdemir 2011a, b; Naghibi et al. 2018).
In the first step, a 20-m resolution digital elevation model (DEM) of the studied basin was derived from a 1:50,000-scale topographic map. The slope angle derived from the DEM was split into four ranges of 0–5, 5–15, 15–30, and >30° (Fig. 3a). Slope aspect was also derived from DEM data and then classified into nine classes (Fig. 3b). Elevation is another important GCF (Ozdemir 2011a, b) that was employed in this investigation (Fig. 3c). The elevation of the studied basin was partitioned into five equal classes.
Fig. 3
The groundwater-conditioning factors (GCFs) considered in this study: a slope angle, b slope aspect, c elevation, d plan curvature, e profile curvature, f slope length, g stream power index (SPI), h topographic wetness index (TWI), i distance from rivers, j rivers density, k land use, and l lithology
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Plan curvature is a topographical-based variable, which shows the direction of flow (Ozdemir 2011a; Fig. 3d). Profile curvature clarifies at which rate the slope changes in the maximum slope direction (Ozdemir 2011b; Fig. 3e). Slope length (LS) is considered as a mixture of the two variables of slope steepness and slope length (Naghibi et al. 2016) and is calculated as follows (Moore et al. 1991; Fig. 3f):
where, As depicts the specific watershed area and α is the estimated slope gradient (degree).
The stream power index (SPI) could be implemented to show potential flow erosion at a specific location of the basin (Moore and Burch 1986; Fig. 3g). Further, the topographic wetness index (TWI) was taken into account in this investigation. TWI denotes the spatial changes of soil moisture (Moore and Burch 1986; Fig. 3h).
Distance from rivers and river density are two crucial GCFs that affect the groundwater potentiality (Naghibi et al. 2015). These two layers were calculated in ArcGIS 10.4 using Euclidean distance and line density functions. Concerning the distance from rivers, 100 m-intervals were chosen, and the distances were then classified into five groups (Fig. 3i). A rivers density map was partitioned into four categories by a natural break classification method (Fig. 3j).
A land use map was produced by implementing Landsat 8/Enhance Thematic Mapper Plus (ETM+) images for the year 2015 based on a likelihood algorithm. The land use map contained five different land use classes: orchard, residential area, rangeland, agriculture, and forest (Fig. 3k).
Geology is composed of three GCFs including lithological classes, and fault-related factors such as distance and density maps (Naghibi et al. 2016). After investigating the fault layer of the studied region, it was found that only a tiny portion of the studied region is affected by faults; therefore, fault-related factors were not considered in the current research. Based on a 1:100,000-scale geological map, the geological units were partitioned into thirteen units including groups 1–13 (Table 1; Fig. 3l).
Modelling process
In this section, a description of the models is presented and then the process of applying a novel data-mining model (EBF-BRT) is explained.
Evidential belief function (EBF) model
The EBF model is developed based on the Dempster–Shafer approach of evidence (Dempster 1967; Shafer 1976), which includes uncertainty (Unc), belief (Bel), plausibility (Pls), and disbelief (Dis) that change from 0 to 1 (Carranza and Hale 2003). This model has a relative flexibility and is able to work with uncertain conditions (Nampak et al. 2014). In the Dempster–Shafer theory, Bel and Pls define the lower and upper probabilities of the generalized Bayesian theorem, respectively (Nampak et al. 2014). Therefore, it can be inferred that Bel is greater than or equal to Pls. Unc could be calculated by differentiating Pls and Bel values (Naghibi and Pourghasemi 2015). Based on the evidential data, disbelief depicts the belief in the false proposition. For calculating the Bel value, first, a frame of discernment could be calculated (Dempster 1967; Shafer 1976; Pourghasemi and Beheshtirad 2015):
where TP shows the pixels that include springs, \( \overline{T_{\mathrm{P}}} \) shows the pixels that do not include springs, and ϕ represents the empty set.
From Eq. (1), the Bel function could be computed as follows (Park 2011; Pourghasemi and Beheshtirad 2015):
where \( {N}_{\left(\mathrm{S}\cap {A}_{ij}\right)} \) denotes the density of spring pixels incidence in Aij, N(S) denotes the total density of all springs in the studied basin, \( {N}_{\left({A}_{ij}\right)} \) represents the density of pixels in Aij, and N(P) is the density of pixels in the whole studied basin. More descriptions and information about EBF algorithm could be found in Carranza and Hale (2003).
The novel data-mining ensemble model
The BRT is a data-mining/machine-learning approach, which comprises of both decision trees and boosting techniques and could be employed for both regression and classification issues (Youssef et al. 2015). It aims to increase the efficacy as well as prediction capability of single methods by combining several fitted models (Naghibi et al. 2016). Boosting is applied in order to combine the results of the decision trees, which is similar to model averaging. There are some parameters that require optimizing in this model such as a number of trees, shrinkage (or learning rate), and interaction depth. Shrinkage or learning rate defines the importance of trees in the built model (Naghibi et al. 2016). Interaction depth or complexity determines the number of nodes in trees.
The BRT model can be explained as follows (Elith et al. 2008; Naghibi et al. 2016):
Starting weights to be equal to fi = 1/n.
For m = 1 to iteration classifier Cm):
1.
Run classifier Cm to the weighted data
2.
Calculate misclassification rate rm
3.
Consider the classifier weight \( {\alpha}_m\log \left(\frac{\left(1-{r}_{\mathrm{m}}\right)}{r_{\mathrm{m}}}\right) \)
4.
Recalculate weights wi = wi exp[αmI(yi ≠ Cm)]
Finally, the majority vote can be obtained by: \( \operatorname{sign}=\left[{\sum}_{m-1}^M{\alpha}_m{C}_m(X)\right] \)
It is noted that the best set of parameters in BRT were selected by using the accuracy index and Cohen’s kappa index, which can be calculated as follows:
where n is the ratio of cells that are correctly categorized, and N shows the number of total training cells, while TP, FP, TN, and FN represent true positive, false positive, true negative, and false negative, respectively (Naghibi and Moradi Dashtpagerdi 2016).
To apply a novel data-mining ensemble model, first, the EBF model was applied and belief values were assigned to different classes of the GCFs. Then, new maps of each factor were produced by the lookup function in ArcGIS 10.4. A new dataset was provided for training of the data-mining model (i.e. BRT). In this dataset, 1 was assigned to the spring and 0 was assigned to nonspring locations. It is noted that the nonspring locations were randomly defined using ArcGIS 10.4. Using the new training dataset and new GCFs layers with Bel values, the BRT model was conducted using R open-source software via the gbm package (Ridgeway 2006). The BRT model was run using a 10-fold cross-validation, deemed to be a sufficient number of runs for optimization of the assigned parameters. It needs to be clarified that the GPMs produced by the EBF and BBF-BRT methods are classified into four classes—low, moderate, high, and very high—by the natural break classification method (Naghibi et al. 2018).
Results and discussion
GPM production by evidential belief function
The results of the EBF model are presented in Table 2 where the values of the Bel, Dis, and Unc are reported. As mentioned in the methodology section, a class with high Bel value has a high potential for the occurrence of the event, which in this case is the existence of a spring (Nampak et al. 2014; Pourghasemi and Beheshtirad 2015). Based on the results, it can be observed that there is an inverse relationship between slope angle and the Bel value, which means that the groundwater potential decreases with the increase in slope angle. Regarding the results of slope aspect, flat and north-east classes show the highest Bel values. In contrast, south-east and south-west classes have Bel value of zero, which indicates their low potential of spring incidence. This finding can be related to the less sunshine duration over the north slope aspects in the northern hemisphere. In the case of elevation, the results indicated that an inverse relationship exists between GCF and spring incidence. At lower elevations, water has concentrated near the rivers and, therefore, the wetness index is higher in these areas which can result in the higher potential of groundwater. The flat characteristic of the plan curvature had the highest Bel value (Bel = 0.54). The highest Bel value was observed in the (−0.001)–(0.001) category of the profile curvature. An inverse relationship was observed between the slope length and spring incidence. In the case of SPI, the results indicated that <200 and 400–600 categories have the highest Bel value of 0.34 and 0.24, respectively. The findings of TWI signified a direct relationship between TWI and spring incidence. Regarding the distance from rivers, an inverse relationship between the distance from river and the spring occurrence was observed. Regarding river density, the 0.86–1.46 class has the highest Bel value of 0.40 followed by >1.46, 0.31–0.86, and <0.31 classes. The modeling results with respect to land use showed that agriculture has the highest Bel value, followed by forest and rangeland. Regarding lithology, the highest values of Bel were observed for group 2 and group 10 with values of 0.22 and 0.17, respectively.
Table 2
Spatial relationship between GCFs and springs using the EBF model
Factor
Class
% of pixels in domain
No. of springs
Bel
Dis
Unc
Slope angle (degree)
0–5
29.46
38
0.54
0.15
0.31
5–15
22.58
20
0.37
0.23
0.41
15–30
35.25
8
0.09
0.34
0.57
>30
12.71
0
0.00
0.29
0.71
Slope aspect
Flat
8.70
10
0.22
0.19
0.59
North
13.59
8
0.11
0.21
0.68
Northeast
14.69
13
0.17
0.19
0.64
East
8.65
4
0.09
0.21
0.70
Southeast
8.66
6
0.00
0.00
1.00
South
10.47
4
0.07
0.21
0.72
Southwest
13.60
10
0.00
0.00
1.00
West
11.17
8
0.14
0.00
0.86
Northwest
10.47
3
0.06
0.00
0.94
Elevation (m)
<1400
1.63
4
0.61
0.24
0.15
1400–1900
40.15
36
0.22
0.19
0.58
1900–2500
45.22
25
0.14
0.29
0.57
2500–3000
9.22
1
0.03
0.28
0.70
>3000
3.79
0
0.00
0.00
1.00
Plan curvature (100/m)
Concave
29.54
16
0.28
0.36
0.36
Flat
37.60
39
0.54
0.22
0.24
Convex
32.86
11
0.18
0.42
0.41
Profile curvature (100/m)
< (−0.001)
35.30
23
0.33
0.34
0.33
(−0.001)-(0.001)
32.79
30
0.46
0.27
0.27
> (0.001)
31.91
13
0.21
0.39
0.40
Slope length (m)
<20
38.46
40
0.41
0.16
0.43
20–40
16.73
12
0.29
0.25
0.47
40–60
14.23
8
0.22
0.26
0.52
>60
30.58
6
0.08
0.33
0.59
Stream power index
<200
30.62
27
0.34
0.21
0.45
200–400
12.96
7
0.21
0.26
0.54
400–600
9.55
6
0.24
0.25
0.51
>600
46.87
26
0.21
0.28
0.50
Topographic wetness index
<8
19.44
2
0.05
0.39
0.56
8–12
56.23
32
0.29
0.38
0.33
>12
24.33
32
0.66
0.22
0.12
Distance from rivers (m)
<100
4.69
27
0.71
0.17
0.12
100–200
4.15
5
0.15
0.27
0.58
200–300
4.10
2
0.06
0.28
0.66
300–400
4.03
1
0.03
0.28
0.69
>400
83.04
31
0.00
0.00
1.00
River density (km/km2)
<0.31
60.74
18
0.08
0.42
0.50
0.31–0.86
11.82
8
0.18
0.23
0.60
0.86–1.46
21.94
33
0.40
0.14
0.45
>1.46
5.50
7
0.34
0.21
0.45
Land use
Agriculture
24.58
33
0.61
0.16
0.23
Forest
30.83
11
0.16
0.30
0.54
Orchard
0.04
0
0.00
0.25
0.75
Rangeland
43.99
22
0.23
0.29
0.48
Residential area
0.57
0
0.00
0.00
1.00
Lithology
Group 1
3.25
4
0.16
0.07
0.76
Group 2
4.22
7
0.22
0.07
0.71
Group 3
0.22
0
0.00
0.08
0.92
Group 4
4.44
5
0.15
0.07
0.78
Group 5
33.32
26
0.10
0.07
0.82
Group 6
8.23
2
0.03
0.08
0.89
Group 7
1.53
0
0.00
0.08
0.92
Group 8
28.52
17
0.08
0.08
0.84
Group 9
2.39
1
0.06
0.08
0.87
Group 10
1.60
2
0.17
0.08
0.76
Group 11
0.02
0
0.00
0.08
0.92
Group 12
1.40
0
0.00
0.08
0.92
Group 13
10.86
2
0.03
0.08
0.89
Bel belief, Dis disbelief, Unc uncertainty
Overall, these findings signified that a direct relationship exists between spring incidence and TWI factor. In contrast, an inverse relationship was observed between the groundwater potentiality and three GCFs including elevation, slope length, and distance from rivers. Naghibi and Pourghasemi (2015) obtained the same relationship between elevation, TWI, and distance from rivers and spring occurrence. However, in some other factors such as LS, the findings of this study differ from the findings of Naghibi and Pourghasemi (2015). These differences can be due to the different properties of the studied regions (i.e. topographical and hydrological characteristics). Furthermore, the results of the EBF-BRT model revealed that the distance from rivers, lithology, river density, and plan curvature had the highest importance in the groundwater potential mapping of the studied basin.
The GPM produced by the EBF model in the current study is presented in Fig. 4a and Table 3. It should be noted that the final EBF map was obtained by summing all the Bel values. Based on the findings, the value of GPM in this model ranges from 0.88 to 5.29. Low, moderate, high, and very high potential categories composed 34, 28, 20, and 18% of the studied basin, respectively.
Fig. 4
Groundwater potential map produced by the a EBF and b EBF-BRT models
Table 3
Range and area of different classes of the groundwater potential map (GPM) produced by the EBF and EBF-BRT models
Class
EBF
EBF-BRT
Range of the values
Area %
Range of the values
Area %
Low
0.88–1.91
34
0–0.23
32
Moderate
1.91–2.60
28
0.23–0.41
28
High
2.60–3.41
20
0.41–0.61
25
Very high
3.41–5.29
18
0.61–0.96
15
×
GPM production by the novel data-mining ensemble model
The findings of the application of BRT algorithm are presented in Fig. 5. The final BRT model was applied with the minimum terminal node size of 10, shrinkage value of 0.1, 50 number of trees, and interaction depth of 1 (accuracy index = 0.66 and Cohen’s Kappa index = 0.33). The contribution of the GCFs to the modelling process is presented in Fig. 6. The results indicated that the distance from rivers, lithology, river density, and plan curvature have the highest contribution to groundwater potential estimated by the EBF-BRT model (Fig. 6). The land use and profile curvature showed the lowest contribution and SPI showed no effect on groundwater potential. The GPM obtained from the EBF-BRT method is presented in Fig. 4b and Table 3. The GPM produced by the EBF-BRT model resulted in low, moderate, high, and very high potential categories, which composed 32, 28, 25, and 15% of the studied basin, respectively.
Fig. 5
Results of the EBF-BRT application
Fig. 6
Importance of the grGCFs in the BRT model (RiverDist distance from rivers; Litho lithology; RiverDens rivers density; PlanC plan curvature; TWI topographic wetness index; SlopeAngle slope angle; SlopeAspect slope aspect; LS slope length; Altitude elevation; Landuse land use; ProfileC profile curvature; SPI stream power index)
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Validation and verification of the GPMs
This section includes two steps: (1) validation of the maps using the validation dataset and ROC curve and (2) verifying the results by taking the observed spring discharges into account. Chung and Fabbri (2003) stated that the validation is regarded as a very necessary stage in the modeling procedure. To do so, the ROC curve was implemented to define the accuracy of the GPMs produced by the EBF and EBF-BRT models. The GPMs were verified employing training and validation datasets. The area under the curve of ROC varies between 0.5 and 1 (Sangchini et al. 2016; Hong et al. 2017; Kalantar et al. 2018). A larger area under the curve of ROC denotes higher efficacy of the models in spatial modeling (Jaafari and Gholami 2017; Pham et al. 2018) such as groundwater potential mapping. Figure 7 presents the prediction performance of the produced GPMs by EBF and EBF-BRT models implementing the ROC curve. Accordingly, the area under the curve of ROC for the validation dataset was defined as 75.5 and 82.1% for EBF and EBF-BRT models, respectively. Further, the area under the ROC curve for the training dataset was calculated as 77.2 and 83% for EBF and EBF-BRT, respectively. It was assumed that the values of more than 70% indicate an acceptable performance of the model (Naghibi et al. 2016).
Fig. 7
Receiver operating characteristics (ROC) curve calculated for the EBF and EBF-BRT models for a training and b validation datasets
×
To verify the resulting groundwater potential map of the basin, the spring discharge record was used. For this, the observed discharge values higher than the median discharge, 0.75 L/s, were selected for the models’ verification. Distribution of the selected springs in different potential zones produced by EBF and EBF-BRT is presented in Table 4. As can be seen in the table that, among 47 high-discharge springs, 15 and 16 springs were located in the very high potential zone produced by EBF and EBF-BRT, respectively. According to the modeling results, very few springs with high discharge were located in the low potential zone (Table 4). The distribution of the high-discharge springs in the identified groundwater potential zones, as well as the computed area under the ROC curve, confirm the satisfying performance of the models in this study.
Table 4
Distribution of the high-discharge springs in the identified groundwater potential zones
Potential zones
EBF
BRT
No. of springs
Springs (%)
No. of springs
Springs (%)
Low
8
17.02
4
8.52
Moderate
10
21.28
12
25.53
High
14
29.79
15
31.91
Very high
15
31.91
16
34.04
Performance comparison
The findings of this study indicated superior performance of the EBF-BRT to EBF model in producing groundwater potential maps; therefore, it can be observed that making the ensemble EBF-BRT model increased the efficacy of the GPM in this research. The validation results also indicated an acceptable capability of the EBF model in producing GPM. Naghibi and Pourghasemi (2015) and Nampak et al. (2014) employed the EBF model for producing GPMs. Their results depicted acceptable performance of the EBF, which is in agreement with the findings of this study. Other researchers have employed different methods to improve the performance of the EBF model. Tien Bui et al. (2015) employed an EBF-fuzzy logic hybrid method for modelling landslides. Their findings showed the higher efficacy of the hybrid method relative to the EBF model. In another research project, Pourghasemi and Kerle (2016) employed an EBF-random forest model to map landslide susceptibility, and their findings depicted a better performance of the EBF-random forest model than the EBF model. In a related work, Naghibi et al. (2017a) used an ensemble model comprised of four data-mining models and frequency ratio. Their results indicated a better performance of the ensemble model by the reduction of overfitting. Moreover, Naghibi et al. (2017b) used a genetic algorithm to optimize random forest as an ensemble model, and this combination yielded a better performance. In the current research, the more accurate results of the EBF-BRT model could be due to the strong features of the single BRT and EBF models. The BRT model is capable of coping with nonlinear relationships (Naghibi et al. 2016). Boosted regression tree applies a combination of boosting and regression techniques, which results in a better performance (Elith et al. 2008). The EBF, on the other hand, is proved to be a robust model for managing uncertainties in spatial modelling and can deal with missing values.
Conclusions
Groundwater potential mapping has been considered as an important aspect of groundwater-related studies and has attracted many scholars worldwide. In this study, a novel ensemble EBF-BRT model was introduced, and its performance was assessed in groundwater potential mapping. The EBF-BRT model was applied using a training dataset of the belief values extracted from EBF model results. Using the ROC curve, performance of the EBF and EBF-BRT models was evaluated. The findings indicated that the EBF-BRT model yielded better performance than the simple EBF model. Therefore, it can be concluded that application of the BRT model can enhance the prediction strength of the EBF model; however, both of the models had acceptable performance in this study. The better performance of the EBF-BRT model could be due to stronger features of the BRT model such as its capability to cope with phenomena in which there are nonlinear relationships. Regarding the conditioning factors, it was observed that the distance from rivers, lithology, rivers density, and plan curvature have the highest importance in the GPMs by the EBF-BRT model. Considering the findings of this study, the implemented methodology can be recommended for other areas with similar geological and hydrological setting. GPMs can be regarded as a guiding tool for freshwater professionals to properly manage land and water resources. GPMs would also provide superior insight of groundwater condition in various parts of a basin that would subsequently lead to efficient exploitation of groundwater.
The GPMs can be employed for functional water resources management especially through land use planning. Those activities with high water requirements, i.e. irrigated agriculture, can be located in areas with higher groundwater potential. However, the rate of exploitation should be monitored and controlled. The GPMs can also support decision-making processes in the land use and water resources planning that ultimately leads to environmental sustainability, which is very crucial in the Middle Eastern countries such as Iran. It is evident that overexploitation issue causes many problems for people and the government in most of the aquifers in Iran. The outputs of this study could be channeled to the relevant agencies/organizations and result in a better aquifer management strategy through defining the places where groundwater extraction can be more productive. Better land use planning could lead to lower pressure on aquifers. However, it is the first step and there need to be more remediation steps, such as artificial recharge through water harvesting, and flood spreading.
Acknowledgements
The authors would like to appreciate the editor Dr. Martin Appold for handling the paper and two anonymous reviewers for their constructive comments on the previous version of the paper.
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