Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

Alireza Arabameri; Jagabandhu Roy; Sunil Saha; Thomas Blaschke; Omid Ghorbanzadeh; Dieu Tien Bui

doi:10.3390/rs11243015

Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

Arabameri, Alireza;Roy, Jagabandhu;Saha, Sunil;Blaschke, Thomas;Ghorbanzadeh, Omid;Tien Bui, Dieu 2019-12-14 00:00:00 remote sensing Article Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran 1 2 2 3 Alireza Arabameri , Jagabandhu Roy , Sunil Saha , Thomas Blaschke , 3 4 , Omid Ghorbanzadeh and Dieu Tien Bui * Department of Geomorphology, Tarbiat Modares University, Tehran 14117-13116, Iran; [email protected] Department of Geography, University of Gour Banga, Malda, West Bengal 732103, India; [email protected] (J.R.); [email protected] (S.S.) Department of Geoinformatics – Z_GIS, University of Salzburg, 5020 Salzburg, Austria; [email protected] (T.B.); [email protected] (O.G.) Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam * Correspondence: [email protected] Received: 12 November 2019; Accepted: 10 December 2019; Published: 14 December 2019 Abstract: Groundwater is one of the most important natural resources, as it regulates the earth’s hydrological system. The Damghan sedimentary plain area, located in the region of a semi-arid climate of Iran, has very critical conditions of groundwater due to massive pressure on it and is in need of robust models for identifying the groundwater potential zones (GWPZ). The main goal of the current research is to prepare a groundwater potentiality map (GWPM) considering the probabilistic, machine learning, data mining, and multi-criteria decision analysis (MCDA) approaches. For this purpose, 80 wells collected from the Iranian groundwater resource department and ﬁeld investigation with global positioning system (GPS), have been selected randomly and considered as the groundwater inventory datasets. Out of 80 wells, 56 (70%) wells have been brought into play for modeling and 24 (30%) for validation purposes. Elevation, slope, aspect, convergence index (CI), rainfall, drainage density (Dd), distance to river, distance to fault, distance to road, lithology, soil type, land use/land cover (LU/LC), normalized dierence vegetation index (NDVI), topographic wetness index (TWI), topographic position index (TPI), and stream power index (SPI) have been used for modeling purpose. The area under the receiver operating characteristic (AUROC), sensitivity (SE), speciﬁcity (SP), accuracy (AC), mean absolute error (MAE), and root mean square error (RMSE) are used for checking the goodness-of-ﬁt and prediction accuracy of approaches to compare their performance. In addition, the inﬂuence of groundwater determining factors (GWDFs) on groundwater occurrence was evaluated by performing a sensitivity analysis model. The GWPMs, produced by technique for order preference by similarity to ideal solution (TOPSIS), random forest (RF), binary logistic regression (BLR), weight of evidence (WoE) and support vector machine (SVM) have been classiﬁed into four categories, i.e., low, medium, high and very high groundwater potentiality with the help of the natural break classiﬁcation methods in the GIS environment. The very high groundwater potentiality class is covered 15.09% for TOPSIS, 15.46% for WoE, 25.26% for RF, 15.47% for BLR, and 18.74% for SVM of the entire plain area. Based on sensitivity analysis, distance from river, and drainage density represent signiﬁcantly eects on the groundwater occurrence. validation results show that the BLR model with best prediction accuracy and goodness-of-ﬁt outperforms the other ﬁve models. Although, all models have very good performance in modeling of groundwater potential. Results of seed cell area index model that used for checking accuracy classiﬁcation of models show that all models have suitable performance. Therefore, these are promising models that can be applied for the GWPZs identiﬁcation, which will help for some needful action of these areas. Remote Sens. 2019, 11, 3015; doi:10.3390/rs11243015 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 3015 2 of 35 Keywords: groundwater potential mapping (GWPM); probabilistic models; machine learning algorithms; sensitivity analysis; Damghan sedimentary plain 1. Introduction Groundwater plays a crucial role in serving the heterogeneous need of human being such as drinking, agricultural, industrial, etc. [1]. In another way, groundwater availability and accessibility control sustainable development at a global, regional and local scale [2]. Large numbers of countries of the earth are facing the problem of water scarcity at the societal level [3]. In the arid and semi-arid regions, groundwater is the prime source of water and accounts for 80% groundwater resource [4]. Notably, in Iran, groundwater is more demanded source owing to its cleanness, tawdriness, constant chemical composition, constant temperature, lower pollution coecient, and a high certainty [4,5]. Groundwater extensively aects economic development, biological diversity and community health [6]. Similar to Iran country, a major part of the largely arid and semi-arid physiographic regions suers from the scarcity of water. Therefore, the groundwater is a main source of water to serve the dierent purpose and utilization of this region [7]. Iran has received average annual precipitation of 413 mm, and the evapo-transportation rate is 296 mm. Therefore, the 117 billion m of water is stored as groundwater over the whole country. The global per capita annual renewal water is 7600 m while the quantity of per capita global renewable water in Iran is 1900 m . In this region, the average yearly water consumption is 3.4 billion m , out of which about 65% is supplied from groundwater. In the present day, Iran is facing harsh water supply problems [8]. From these data, it is inevitable to implement water resource management policy for continuing the country’s economic and societal development. However, this issue can be short out by taking some necessary steps and decisions such as watershed management, artiﬁcial recharge, and management of soil and water [8]. In present the decades, groundwater recharge level has fallen due to unnecessary use and unscientiﬁc management plans [9]. Hence, aquifer potential determination through groundwater potentiality analysis is a good strategy in this ﬁeld [10,11]. Dierent methods and models, techniques and processes were induced and used for the groundwater potentiality map (GWPM) or identiﬁcation of areas having good potentiality of groundwater recharge. A few decades back, conventional techniques were applied for GWPM. Day by day improvement in technology with regarding scientiﬁc approach, the measuring instrument and computerized data analysis able to recognize the groundwater level, ﬂow and other aspects for GWPM. Comparatively, contemporary scientiﬁc methods are providing better outcomes than the conventional method. Recently, remote sensing (RS) and geographic information system (GIS) are playing important role in managing the groundwater resource without the computational requirements [12]. RS technique provides the spatial and non-spatial information—even over the inaccessible areas in a short duration [13]. Therefore, RS technique also a powerful, ecient, accurate tool for collecting, restoring, manipulating, analyzing the spatial data of the surface and sub-surface water research, e.g., groundwater recharge, potentiality, evaluation of water quality [2,14]. Speciﬁcally, satellite imagery can provide hydrological characteristics, i.e., drainage network, ﬂow accumulation, drainage density, recharge, and other geomorphologic characteristics [15]. The modeling of groundwater potential zones (GWPZ) is not only dependent on the single factors but also dependent on the dierent geo-environmental factors such as elevation, slope, aspect, rainfall, geology, fault, rainfall, drainage density (Dd), land use/land cover (LU/LC), normalized dierence vegetation index (NDVI), topographic wetness index (TWI), stream power index (SPI), soil permeability, topographic position index (TPI), convergence index (CI), inﬁltration rate, and soil texture. RS and GIS integration with modern groundwater mapping models such as probabilistic, knowledge-driven, machine learning, data mining could provide a powerful way to gain valuable decision-making information. The rapid development of probabilistic, machine learning, data mining, and ensemble models in recent decades is enhancing the basement to determine groundwater recharge opportunity, soil erosion susceptibility, gully erosion susceptibility, and other spatial modelings. Some Remote Sens. 2019, 11, 3015 3 of 35 new methods which were used by the researcher for spatial hazards probability and groundwater potentiality modeling are: evidential belief function (EBF), weights of evidence (WoE), frequency ratio (FR), classiﬁcation and regression tree (CART,), boosted regression tree (BRT), decision tree (DT), artiﬁcial neural network (ANN), multivariate adaptive regression splines (MARS), binary logistic regression (BLR), Shannon’s entropy (SE), analytic hierarchy process (AHP), maximum entropy (ME), random forest (RF), fuzzy logic (FL), support vector machine (SVM), multi-criteria decision analysis (MDCA), logistic model tree (LMT), quadratic discriminate analysis (QDA), K-nearest neighbor (KNN), and certainty factor (CF) [16–22]. In this work, we have used probabilistic, machine learning, data mining, and MDCA methods, namely WoE, BLR, SVM, RF, and a technique for order preference by similarity to ideal solution (TOPSIS). The outcomes of the same model vary depending on the physiographical situation in dierent regions. The suitable models help to demarcate the areas having groundwater potentiality. The models used in this research are accessible and eciently capable of groundwater modeling and are used in various areas for environmental management [23–26]. Thus, the study aims to recognize the GWPZ using ﬁve models (RF, TOPSIS, WoE, SVM, and BLR,) in the Damghan sedimentary plain of Semnan province in Iran. The current study will help in determining the proper groundwater resource and to the decision-maker for managing the water resources. 2. Materials and Methods 2.1. Study Area Damghan sedimentary plain, located within the Semnan province in Iran, covers an area of 2 0 0 0 1559 km . Geographically, this plain region stretches from 35 56 to 36 18 N latitude and 54 00 E to 54 40 E longitude (Figure 1). The long-term average of precipitation and long-term evaporation are about 151.01 and 3000 mm, respectively [27]. The arid climate prevails in this plain because the annual evaporation is greater than annual precipitation [28]. The average temperature in the mountainous portion of the study area is 9.8 ºC, and in the plain area, the mean temperature is 23.5 ºC. In the south of Alborz zone, the upland area of the watershed is extended, and the plain’s elevation ranges from 2860 m. a.s.l. in the northwest, to 1043 m a.s.l. in the southeast. Major portions of the study region are composed of Quaternary deposits [29]. The remaining parts of the plain are situated in the Alborz region and are covered by calcrete layers such as Cretaceous formations, as well as sandstone and Paleogene-related conglomerates. The low elevated area, composed of Quaternary deposits, has a high-water yield and recharge rate because of sediment nature and succession [30]. Nevertheless, the upland region in the Alborz zone is not suitable for recharge [31]. The mean depth of alluvial sediment varies from 150 m in north to 240 m in the south. In this area, the unconﬁned aquifer and bedrock consist of Neogene alluvium, such as marl and conglomerate, and the well logs set out the type of sediment. Remote Sens. 2018, 10, x FOR PEER REVIEW 4 of 37 Remote Sens. 2019, 11, 3015 4 of 35 Figure 1. Location of the study area in Iran and Semnan province and location of training and Figure 1. Location of the study area in Iran and Semnan province and location of training and validations wells in the study area. validations wells in the study area. The sedimentary plain of Damghan is located in arid and semi-arid regions and facing the problem 2.2. Methodology of water supply such as other arid regions. The main source of freshwater is sub-surface water storage For assessing the groundwater potentiality (GWP), some spatial and non-spatial data have been and undergoes the problems of over pumping and lowering of groundwater. In the recent decade, gathered to prepare different datasets for modeling and validation of results. The data consists of due to excessive groundwater exploitation for irrigation and industrial purposes combining with the two, i.e., primary and secondary, data. Primary data are pumping tests and yield measurements in decreasing amount of rainfall, the water table is coming down rapidly. Therefore, immediate planning the field. The secondary data are topographical map (scale 1:50000), lithological map (scale 1:100000), is needed to conserve the groundwater [30]. In this respect, the delineation of GWPZ is essential for Sentinel 2A, Phased Array type L-band synthetic aperture radar (PALSAR) digital elevation model proper planning and sustainable management of water. (DEM), rainfall of different metrological station of last 30 years, well location data from Water 2.2. Resou Methodology rce Management, Iran, soil data from soil department of Iran. Thematic maps of all the data were extracted and analyzed by the RS and GIS. The present work methodologically consists of four For assessing the groundwater potentiality (GWP), some spatial and non-spatial data have been phases (Figure 2) including; (1) preparation of groundwater inventory database thematic data layers gathered to prepare dierent datasets for modeling and validation of results. The data consists of of the groundwater conditioning factors including elevation, slope, aspect, CI, rainfall, lithology, soil two, i.e., primary and secondary, data. Primary data are pumping tests and yield measurements type, LU/LC, Dd, distance to river, distance to fault, distance to road, NDVI, TPI), TWI, and SPI; (2) in the ﬁeld. The secondary data are topographical map (scale 1:50,000), lithological map (scale multicollinearity assessment of the effective groundwater determining factors (GWDFs); (3) application of models and preparation of GWPMs. The GWPMs were classified according to the four Remote Sens. 2019, 11, 3015 5 of 35 1:100,000), Sentinel 2A, Phased Array type L-band synthetic aperture radar (PALSAR) digital elevation model (DEM), rainfall of dierent metrological station of last 30 years, well location data from Water Resource Management, Iran, soil data from soil department of Iran. Thematic maps of all the data were extracted and analyzed by the RS and GIS. The present work methodologically consists of four phases (Figure 2) including; (1) preparation of groundwater inventory database thematic data layers of the groundwater conditioning factors including elevation, slope, aspect, CI, rainfall, lithology, soil type, LU/LC, Dd, distance to river, distance to fault, distance to road, NDVI, TPI), TWI, and SPI; (2) multicollinearity assessment of the eective groundwater determining factors (GWDFs); (3) application of models and preparation of GWPMs. The GWPMs were classiﬁed according to the four classiﬁcation methods, namely quantile, natural breaks, equal interval, and geometrical interval, into four dierent groundwater susceptibility classes, including low, medium, high, and very high. By comparing the results of each classiﬁcation method and the distribution of training and validation wells on the high and very high groundwater susceptibility classes, it was found that the natural break classiﬁcation method gave the most accurate distribution. This agrees with the ﬁndings by Arabameri et al. [32], in that natural break method is a good classiﬁer in susceptibility mapping; and (4), evaluation of the models performances using area under receiver operating characteristics (AUROC) curve, sensitivity (SE), speciﬁcity (SP), accuracy (AC), mean absolute error (MAE), root mean square error (RMSE) and seed cell area index (SCAI) methods. 2.3. Data Preparation 2.3.1. Groundwater Inventory Map (GWIM) The groundwater inventory database is of a key role in groundwater potentiality mapping. An inventory map is a target variable for any spatial modeling [32]. The well inventory database was prepared after extensive ﬁeld visit with a hand GPS (global positioning system), and yield data were collected from the Department of Water Resources Management, Iran. Groundwater wells, with high yield of11 m h1 by pumping test analysis, have been considered for the GWPM. As a result, 80 wells have recognized in the study area. 56 wells (70%) of this dataset, were randomly selected to produce the GWPM models [32], whereas the remaining 24 (30%) wells were considered for validation of GWPMs [11]. The training and testing wells locations have been mentioned in Figure 1. Remote Remote Sens Sens. 2019 . ,2018 11, , 3015 10, x FOR PEER REVIEW 6 of 37 6 of 35 Figure 2. Methodological flowchart of the present work. Figure 2. Methodological ﬂowchart of the present work. 2.3.2. Groundwater Determining Factors (GWDFs) The dierent geo-environmental components play a crucial role in determining the status of groundwater. GWPM represents the association between GWDFs and well locations [21,22]. For the GWPM, 16 GWDFs have been selected including elevation, slope, aspect, CI, rainfall, lithology, soil type, LU/LC, NDVI, Dd, distance to the river, distance to fault, distance to road, TWI, SPI and TPI Remote Sens. 2019, 11, 3015 7 of 35 (Figure 3a–p). The PALSAR DEM (12.5 m resolution) downloaded from the Alaska Satellite Facility (ASF) Distributed Active Archive Center (DAAC). In this study, PALSAR DEM was used to extract the topographical, hydrological factors such as elevation, slope, aspect, CI, drainage, TWI, SPI, and TPI. The slope, aspect, and elevation are the major topographic components, used to determine the groundwater potentiality, erosion probability, etc. [21]. The DEM has been used as the elevation dataset (Figure 3a). The altitudinal ﬂuctuation controls climatic conditions and helps to induce various vegetation types and soil development [33]. The slope data layer has been derived from PALSAR DEM by spatial analysis in the GIS environment (Figure 3b). In the same way, the aspect map has also been extracted from PALSAR DEM imagery using a spatial analysis tool (Figure 3d). CI is an important terrain factor that demonstrates the arrangement of relief as a set of channels and ridges. It is developed by Kiss [34]. The convergence index (CI) has been calculated using Equation (1). CI = 90 , (1) i=1 where indicates the average angle between the aspect of adjacent cells and the direction to the central cell. The CI value ranges from100 to +100 (Figure 3c). The rainfall map was prepared by the kriging method considering the last 10-year annual rainfall of dierent stations (Figure 3e). The drainage was extracted from the topographical map and PALSAR DEM imagery. The Dd was computed based on Horton’s morphometric formula (Equation (2)). Dd = , (2) where Lu means the total length of all orders streams, A is the area in square kilometer. Finally, the spatial data layer of the Dd has been built using the IDW interpolation method in the GIS environment (Figure 3f). The fault layer has been taken out from Landsat 7 imagery in ENVI software. The road network has been taken o from the topographical map and Google Earth imagery. The distance to river, fault, road data layers have been built using the Euclidian distance buering tool and expressed in km (Figure 3g,h,i) [11]. The lithological information for the study area was gathered from the geological department of Iran [29]. The lithology map has been prepared by the digitization process (Figure 3j). Geologically, the region is composed of nine geological segments, namely A, B, C, D, E, F, G, H, and I (Figure 3j and Table 1). Soil data was collected from the soil department of Iranian and with the help of the digitized process, the thematic dataset of soil has been produced (Figure 3k). The LU/LC map has been produced from Sentinel 2A satellite image (12/08/2017) of 10 m, 20 m, and 60 m spatial resolution for each band using the supervised image classiﬁcation method (Figure 3l). NDVI has been computed from satellite image (Figure 3m) using Equation (3): NIR Red NDVI = , (3) NIR + Red where NIR is the near-infrared band or band 8 and red band or band 4. The TWI directly aects the topographic conditions, which control the hydrological process. TWI is the function of slope and the upstream area per unit width orthogonal to the direction of ﬂow [35]. TWI plays a major role in the spatial heterogeneity of hydrological conditions such as soil moisture, underwater ﬂow and slope steady-state [32]. The TWI has been introduced by Beven and Kirkby [36]. TWI is calculated from Equation (4): TWI = In(A / tan ), (4) 2 1 where AS represents the cumulative area of the catchment (m m ) and is the slope gradient (degrees). The TWI value ranges from 1.11 to 21.54 (Figure 3n). The SPI is a calculation of water ﬂow erosive power based on the assumption that discharge is commensurate with a given catchment Remote Sens. 2019, 11, 3015 8 of 35 area [37]. One of the most important factors in controlling slope erosion processes is SPI. Regions with high stream power have high erosion potentiality [38]. From Equation (5), SPI has been calculated: SPI = A tan , (5) where A is the upstream contributing area and is slope gradient (in degrees). The spatial allocation of SPI ranges from 6.27 to 24.44 (Figure 3o) in the research area. TPI is deﬁned as the dierence between the middle point elevation (Z ) and the average elevation (Z) in a predetermined radius around it (R) [39]: TPI = Z Z, (6) Z = Z . (7) i2R The TPI has positive and negative value; a positive value demonstrates that the midpoint is located at a higher place than its average while a negative value indicates a lower place than the average. The TPI range depends not only on variations in altitude but also on landscape units (R) [40]. Where large R values mainly depend on the main units of landscape, and small R values show up lower valleys such as small valleys and ridges. The TPI value ranges from 12.16 to 14.67 in this plain (Figure 3p). Spatial resolutions of the selected GWDFs are not the same. For preparing the groundwater potential maps of the study area the resolution of PALSAR DEM, i.e., 12.5 m* 12.5 m has been selected as the base scale and all the GWCFs of which scale are greater or lesser than the PALSAR DEM have been resembled into a 12.5 m* 12.5 m resolution. The data layers of elevation (Figure 3a), slope (Figure 3b), CI (Figure 3c), rainfall (Figure 3e), Dd (Figure 3f), distance to river (Figure 3g), distance to fault (Figure 3h), distance to road (Figure 3i), TWI (Figure 3n), SPI (Figure 3p), TPI (Figure 3o), and NDVI (Figure 3m) have been categorized into ﬁve sub-classes using the natural break classiﬁcation method in GIS environment (Table 2). Aspect (Figure 3d), lithology (Figure 3j), soil type (Figure 3k), and LU/LC (Figure 3l) are the categorical factors. The categorical factors are also mentioned in Table 2. Table 1. Description of lithology units in the study area. Group Unit Description COm Dolomite platy and ﬂaggy limestone containing trilobite; sandstone and shale (MILA FM). Cl Dark red medium-grained arkosic to subarkosic sandstone and micaceous siltstone (LALUN FM). Yellowish, thin to thick-bedded, fossiliferous argillaceous limestone, dark grey limestone, greenish DCkh marl and shale, locally including gypsum Db Grey and black, partly nodular limestone with intercalations of calcareous shale (BAHRAM FM). E1s Sandstone, conglomerate, marl and sandy limestone. Ek Well bedded green tu and tuaceous shale (KARAJ FM). D Jl Light grey, thin-bedded to massive limestone (LAR FM). K2m,l Marl, shale and detritic limestone. K Cretaceous rocks in general. Murmg Gypsiferous marl. Murc Red conglomerate and sandstone. Plc Polymictic conglomerate and sandstone. PlQc Fluvial conglomerate, Piedmont conglomerate and sandstone. P Undierentiated Permian rocks. Pr Dark grey medium-bedded to massive limestone (RUTEH LIMESTONE). Qft2 Low level piedmont fan and valley terrace deposits. Qft1 High level piedmont fan and valley terrace deposits. Qcf Clay ﬂat. Qal Stream channel, braided channel and ﬂood plain deposits. I TRJs Dark grey shale and sandstone (SHEMSHAK FM). Remote Sens. 2018, 10, x FOR PEER REVIEW 10 of 37 Remote Sens. 2019, 11, 3015 9 of 35 Figure 3. Cont. Remote Sens. Remote Sens 2019, . 11 2018 , 3015 , 10, x FOR PEER REVIEW 11 of 10 37 of 35 Figure 3. Groundwater determining factors: (a) elevation, (b) slope, (c) aspect, (d) convergence index, (e) rainfall, Figure 3. Groundwater determining factors: (a) elevation, (b) slope, (c) aspect, (d) convergence index, (f) drainage density, (g) distance to river, (h) distance to fault, (i) distance to road, (j) lithology, (k) soil type, (l) (e) rainfall, (f) drainage density, (g) distance to river, (h) distance to fault, (i) distance to road, (j) land use/land cover (LULC), (m) normalized difference vegetation index (NDVI), (n) topographic wetness index lithology, (k) soil type, (l) land use/land cover (LULC), (m) normalized dierence vegetation index (TWI), (O) topographic position index (TPI), (p) stream power index (SPI). (NDVI), (n) topographic wetness index (TWI), (O) topographic position index (TPI), (p) stream power index (SPI). Remote Sens. 2019, 11, 3015 11 of 35 Table 2. Computation of statistics and classes of groundwater determining factors (GWDFs). Factors Min. Max. Classes Methods (1.) <1155, (2.) 1155 –1297, (3.) 1297–1512, (4.) Natural break Elevation (m) 1043 2869 1512–1993, (5.) >1993 (Jenks) (1.) <2.55, (2.) 2.55–9.35, (3.) 9.35–20.70, Natural break Slope (degree) 0 72.32 (4.) 20.70–34.03, (5.) >34.03 (Jenks) (1.) Flat (1), (2.) North (0–22.5), (3.) Northeast (22.5–67.5), (4.) East (67.5–112.5), (5.) Southeast Aspect - - (112.5–157.5), (6.) South (157.5–202.5), (7.) Directional units Southwest (202.5–247.5), (8.) West (247.5–292.5), (9.) Northwest (292.5–337.5) (1.) <59.21, (2.) 59.21—18.43, (3.) Natural break Convergence index -100 100 18.43–17.64, (4.) 17.64–57.64, (5.) >57.64 (Jenks) (1.) <132.95, (2.) 132.95–170.69, (3.) Natural break Rainfall (mm) 96 406 170.69–226.68, (4.) 226.68–305.81, (5.) >305.81 (Jenks) (1.) A, (2.) B, (3.) C, (4.) D, (5.) E, (6.) F, (7.) G, Lithological Lithology - - (8.) H, (9.) I Units (1.) Aridisols, (2.) Rock outcrops/entisols, Soil types/ Soil type - - (3.) Salt ﬂats Orders (1.) Bare land, (2.) Agriculture land, (3.) Supervised LULC - - Rangeland, (4.) Urban Classiﬁcation Drainage density (1.) <1.12, (2.) 1.12 –1.54, (3.) 1.54–1.88, Natural break 0.15 3.18 (km/km ) (4.) 1.88–2.24, (5.) >2.24 (Jenks) Distance to river (1.) <0.10, (2.) 0.10–0.21, (3.) 0.21–0.37, (4.) Natural break 0 1.35 (km) 0.37–0.57, (5.) >0.57 (Jenks) Distance to fault (1.) <2.20, (2.) 2.20–4.85, (3.) 4.85–7.75, Natural break 0 16.08 (km) (4.) 7.75–10.91, (5.) >10.91 (Jenks) Distance to road (1.) <2.78, (2.) 2.78–6.09, (3.) 6.09–9.91, Natural break 0 22.18 (km) (4.) 9.91–14.44, (5.) >14.44 (Jenks) (1.) <0.01, (2.) 0.01–0.07, (3.) 0.07–0.12, Natural break NDVI 0.24 0.54 (4.) 0.12–0.21, (5.) >0.21 (Jenks) (1.) <5.51, (2.) 5.51–7.44, (3.) 7.44–9.76, Natural break TWI 1.11 21.54 (4.) 9.76–13.21, (5.) >13.21 (Jenks) (1.) <2.06, (2.) 2.06–0.58, (3.) 0.58–0.56, Natural break TPI 12.16 14.67 (4.) 0.56–2.56, (5.) >2.56 (Jenks) (1.) <8.05, (2.) 8.05–9.83, (3.) 9.83–11.97, Natural break SPI 6.27 24.44 (4.) 11.97–14.89, (5.) >14.89 (Jenks) 2.4. Models 2.4.1. Weight of Evidence (WoE) Model The WoE model is the main Bayesian probability system model in linear logic form and uses non-conditional and conditional probabilities [41]. WoE reveals the spatial association between dependent variable, i.e., well locations and independent variables, i.e., GWDFs. The weight of each class has been assigned by this method using the following equations (Equations (8)–(14)) [42]: W = , (8) WoE S(C) C = W W , (9) i i P(B/D) W = In , (10) P(B/D) P(B/D) W = In , (11) P(B/D) 2 + 2 S(C) = S (W ) + S (W ), (12) 1 1 2 + S (W ) = + , (13) P(B/D) P(B/D) Remote Sens. 2019, 11, 3015 12 of 35 1 1 S (W ) = + , (14) P(B/D) P(B/D) where P(B|D) is the conditional probability of B occurring given the presence of D, B is the datasets of GWDFs related to the presence of groundwater well and B indicates the groundwater is absent of the datasets of groundwater conditioning factors. D indicates the presence of well while D stand for the absence of a well, and P is the probability. Whereas, W is a positive weight of GWDFs for groundwater occurrence. Conversely, W is a negative weight with respect to the absence of groundwater well (unfavorable factors). WoE computation has been started by the pixels counting process between groundwater well locations and GWDFs. The weighted GWDFs factors have been summed up in the raster calculation to generate the single layer of GWPM in the GIS environment using the following Equation (15). GWMP = (W Elevation) + (W Slope) + (W Aspect) + (W Convergence Index) WoE WoE WoE WoE WoE + (W Rainfall) + (W Drainage Density) + (W Distance to River)+ WoE WoE WoE (W Distance to Fault) + (W Distance to Road) + (W Lithology)+ WoE WoE WoE (W Soil Type) + (W LULC) + (W NDVI) + (W TWI)+ WoE WoE WoE WoE (W TPI) + (W SPI) WoE WoE (15) 2.4.2. Random Forest (RF) RF is the non-parametric multivariate model [43], which can be used for the analysis of regression and classiﬁcation and variable selections. RF model creates thousands of trees, forming a ‘forest’ based on the decision rule. Each tree in the RF model depends on a sample of bootstrapped of data using a CART process with a random subset of variables selected at each node. The ﬁnal decision of the class membership and model (output) has determined according to the majority priority of all decision trees [44]. The trees’ ensembles would have performed much better than a single tree. It is important to know that the program can be run by a large number of trees with taking large and too many computational requirements [45]. RF is a very reliable and ﬂexible ensemble classiﬁer, which depends upon the decision trees, that have so many attractive performances such a minimum costly, minimum tendencies for overﬁtting and also capability of the work with very high dimensional data [46]. The RF model is also a very fast machine learning solution, allowing a highly accurate classiﬁcation with internal unbiased generalizability estimation during the process of forest construction [47]. The basic merits of RF model arise when the program proceeds including (i) no need of any assumptions regarding the data distribution, (ii) no overﬁtting problem, (iii) in case of single tree, a low correlation estimated, while the diversity of forest increases the usages of a number of factors, (iv) helps to estimate negative or error using ‘out-of-bag’(OOB) data, (v) averages a large number of trees, resulting the low bias and low variance, subsequently, (f), resulting in the excellent prediction for performances [43,48]. Besides, the numerical and categorical data can be incorporated in the RF model. Using the OOB error-index, the variance and covariance between the grids cells can be estimated [48]. The predication values of this model are estimated by the huge amount of decision trees [43]. The presence and absence groundwater wells among the GWDFs can easily be estimated by RF model. In this algorithm, the mean decrease accuracy and Gini are estimated by the RF model to analysis the variable importance of the GWDFs [30]. This algorithm calculates untouched the proper count, the amount of correct classiﬁcation applying the data out-of-bag as its test sample. In the out-of-bag instances, the values of the attributes are then randomly permuted. A new set of data will then be checked for proper classiﬁcation. The average of this number is the raw importance score for the speciﬁc attribute over all trees in the forest. Therefore, factors importance in RF model is computed for variable Yi by out of bag error (OOB) [49]. Factors importance of Yi can be calculated using the Equation (16): VImp(Y ) = errOOB errOOB , (16) ntree Remote Sens. 2019, 11, 3015 13 of 35 where ntree stands for the number of trees, VImp(Yi) denotes variable importance for variable Yj, errOOB is an error when all the factors are included, and errOOB denotes an error after the removal of the variable j. The Gini index was used to measure the variable signiﬁcance based on the number of times that variable is picked by all trees [47,50]. In this study, the ‘randomForest’ package in R program has been installed and run the RF model for estimating the GWPZ [51]. Finally, the RF model-based GWPM has been produced in the GIS environment. 2.4.3. Binary Logistic Regression (BLR) BLR model is the most common statistical model which considers both dichotomous and continuous variables. However, the practical dependent variable must be in binary form, i.e., 1 and 0. Where, 0 represents the absence of groundwater well and 1 stands for the presence of the groundwater well [37,52]. For GWPM, it corresponds with the Bernoulli method, which determines the high groundwater potentiality over space depending on the Bernoulli probability [32]. The main target of the BLR analysis is to chalk out the correct and appropriate prediction of samples and probe the correlation between a dependent variable with a set of independent variables [32]. Among the dierent methods of the regressions, the BLR is ﬁtting a logistic curve or function concerning data. As a result, BLR estimates the values that vary from 0 to 1, while 1 means the presence of groundwater well, conversely 0 means the chances of occurrence of groundwater well is nil. In this method, the target value is calculated using Equation (17): ( ) Y = Logit P = Ln = C + C X + C X + ::::::::: C X , (17) 0 1 1 2 2 n n 1 p where Logit is the link function, P is the probability of occurrence of groundwater well (y), p = 1 p are the odds of groundwater occurrence (or probability of presence divided by the probability of absence) the, C0 is the model intercept and (C1, ::: , Cn) are the regression coecients for each GWCF (X1, ::: , Xn) [32]. In this contribution, the BLR model has been applied in R by using the ‘glm’ function based on the “stats” package [32]. In this study, the random point’s values have been extracted from each variable of GWCFs for presence and absence condition of the groundwater. Finally, GWPM by BLR model has been produced in GIS with regarding the prediction database. 2.4.4. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) The TOPSIS method was introduced by Hwang and Yoon [53]. Presently, it is an important multi-criteria decision approach among the several MCDA processes utilized for water management practices [54]. This approach relies on the premise that the best alternative solution should have the shortest distance Euclidean from the positive ideal solution and the longest distance from the negative solution [32]. The ideal solution in GWPM is the best model to distinguish between groundwater well presences and absences. TOPSIS is a method that cannot understand categorical properties [55]. That is why the AHP has been used to assign the weight to each GWDF. The computation of the entire TOPSIS model was carried out step by step as follows: Step 1: Preparation of a decision matrix with m criteria and n alternatives using Equation (18): 2 3 a a a 6 11 12 1n 7 6 7 6 7 6 7 6 7 a a a 6 22 7 21 1n 6 7 A = 6 7. (18) ij 6 7 6 7 . . . . 6 7 6 7 4 5 a a a m2 mn m1 Step 2: Normalization of decision matrix using Equation (19): ij r = q , (19) ij i=1 ij Remote Sens. 2019, 11, 3015 14 of 35 where i = 1, ::: , m; j = 1 ::: n. Step 3: Determine the weight of criteria using the AHP model: AHP, ﬁrst implemented by Saaty [56] is one of the most comprehensive MDCA approaches. This method assists decision-makers in receiving quantitative and qualitative parameters. The pairwise comparisons help for the judgment and computation of GWCFs [57]. After preparing paired comparisons, the resulting paired comparison matrix is normalized using Equation (20) and then the ﬁnal weight (W ) of each parameter is obtained using Equation (21). ij r = q , (20) ij ij i=1 ij i=1 W = . (21) One of the advantages of this method is to show the inconsistency [58]. To assess the degree of weighting precision, an Inconsistency Index is used. The consistency test shows how much trust can be put in the priorities of a matrix. If this value is >0.1, this means that it is not consistent with the speciﬁed weights and should be checked. Inconsistency ratio is often being used to calculate the Inconsistency in judgments, Equations (22) and (24) have been used for its calculation: I.I IR = , (22) I.I.R max n I.I = , (23) n 1 a W 1 (i,j) = , (24) max n W (i,j) i=1 where IR refers to the inconsistency ratio, I.I. is an inconsistency index, n is the number of criteria, a is the geometric mean of matrix and W is weight vector. (i,j) Step 4: Calculation of the weighted normalized decision matrix using Equation (25): V = r W , (25) ij ij j where W represents the weight of the criteria. Step 5: Calculation of the positive and negative ideal solution using Equations (26) and (27), respectively: n o + < A = maxV /j 2 J , minV /j 2 J i = 1, 2,::: .m ij ij , (26) + + + + = V , V ,::: , V ,::: , V 1 2 j n o A = minV /j 2 J , maxV /j 2 J i = 1, 2,::: .m ij ij n o (27) = V , V ,::: , V ,::: , V 1 2 j where, j and J’ are related to increasing and decreasing criteria, respectively, where J is associated with the positive criteria and J’ is associated with the negative criteria. Step 6: Calculation of the distance from the positive and negative ideal solution using Equations (28) and (29), respectively: d = V V ; i = 1, 2,::: ., m, (28) i+ ij j=1 d = V V ; i = 1, 2,::: ., m. (29) i ij j=1 Remote Sens. 2019, 11, 3015 15 of 35 Step 7: Calculation of the relative closeness to the ideal solution using Equation (30): cl = ; 0 cl 1; i = 1, 2,::: , m, (30) i+ i+ d + d i+ i where cl is the closeness coecient, di+ is a positive ideal solution (PIS), and d is negative ideal i+ i solution (NIS). The value of cl ranges between 0 and 1. The larger the cl value indicates the better the i+ i+ performance of the alternatives. In this contribution, to perform the Mathematical calculation, 500 points have been randomly selected and derived the values of GWDFs for each point, then a table was made, consisting of 16 GWDFs columns and 500 rows. Subsequently, these values have entered into SPSS and done the process. Ultimately, the TOPSIS based GWPM has been prepared considering the point values using the IDW method in the GIS environment. 2.4.5. Support Vector Machine (SVM) SVM is the supervised learning system of machine learning associated with learning algorithms that analyze the data used for classiﬁcation and regression analysis. It is developed by Bai et al. [59]. SVM helps in the transformations of nonlinear covariates into a higher dimensional feature space [60]. SVM is also a statistical learning theory associated with a training phase in which a training dataset of related input and target output values trains the model. The trained model will then be used to analyze a separate set of test data. SVM has two main underlying concepts for discriminating the problems, i.e., the optimum linear separating hyper-plane that separates patterns of data, and another is the kernel functions that convert the original nonlinear data pattern to a linearly separable format in a high-dimensional feature space [60]. A set of linear separable training vectors x (i = 1, 2, ::: , n) consists of two classes, which are denoted as y = 1. The SVM’s goal is to ﬁnd an n-dimensional hyperplane that dierentiates the two groups by the total distance. Mathematically, it can be minimized as: kwk , (31) Subject to the following constraints: y = ((wx ) + b) 1, (32) i i where kwk is the norm of the normal hyper-plane, b is a scalar base, and (wx ) denotes the scalar product operation. Introducing the Lagrangian multiplier, the cost function can be deﬁned as: L = kwk (y ((wx ) + b) 1), (33) i i i i=1 where is the Lagrangian multiplier. It is possible to achieve the solution by double minimizing Equation (32). The standard procedures for w and b and detailed discussions can be found in Vapnik [61], Tax and Duin [62] and Yao et al. [60]. For non-separable case, one can change the constraints by setting up slack variables : y ((wx ) + b) 1 . (34) i i i Equation (32) will be modiﬁed as: 1 1 L = kwk , (35) 2 n i=1 Remote Sens. 2019, 11, 3015 16 of 35 where [0, 1] was introduced to account for misclassiﬁcation [63]. Besides, a kernel function K (x , x ) i j was introduced by Vapnik [61] to account for the nonlinear decision boundary [63]. The two-class SVM method was used in this study because it was reported that Yao et al. [60] produced a more accurate map of susceptibility from the two classes of SVM. That’s why Radial Basis Function (RBF) was used for kernel in this study and the two-class SVM model was ﬁrst trained and then used to construct a GWPM. In this method, 1 and 0 values indicate the positive and negative relationship of groundwater occurrence. To perform the GWP mapping using the SVM, we used the ENVI 4.3. The default RBF kernel, which works well in most cases, has been used. In addition, in many studies and cases (especially in nonlinear problems), RBF provides better prediction results compared to other kernels [64]. Finally, the GWPM by SVM has been produced in the GIS. 2.5. Validation of Models In this study, to analyze the potentiality and performance of the selected models, we have used two thresholds dependent methods i.e., ROC curve and SCAI. The ROC curve and SCAI are the signiﬁcant and accurate justiﬁcation methods of dierent models [65]. For this purpose, 30% validation and 70% training datasets have been considered by the ROC curve and SCAI methods (11). The area under curve (AUC) of the ROC method range between 0.5 to 1. If the value is nearest to 1, it indicates excellent prediction accurateness of the models [66]. The accuracy value that is AUC of the ROC is mentioned in Table 3. The AUC values have been calculated using the Equation (36). In the case of SCAI method, if the sub-class values of models decrease from very low to very high sub-classes, it indicates that models are suitable and acceptable [67]. P P TP+ TN AUC = . (36) P + N Table 3. Area under curve (AUC) values and statements. AUC Values Accuracy Statements 0.5–0.6 Low 0.6–0.7 Moderate 0.7–0.8 High 0.8–0.9 Very high 0.9–1 Excellent Source: Yesilnacar [66]. We also used ﬁve statistical techniques in this analysis to test models’ performance, including SE, SP, AC, MAE, and RMSE. Based on four possible consequences i.e., true positive (TP), false positive (FP), true negative (TN) and false negative (FN), sensitivity (Equation (37)), speciﬁcity (Equation (38)) and accuracy (Equation (39)) have been measured: TP and FP are the counts of well pixel that are correctly identiﬁed as well pixel and non-well pixel, respectively. On the other hand, TN and FN are the numbers of well pixel which are correctly classiﬁed and incorrectly classiﬁed as non-well class. SE is the ratio of the number of well pixels properly classiﬁed to the total number of well pixels predicted. SP is the ratio between the number of well pixels wrongly classiﬁed and the total non-well pixels predicted. AC is the ratio between the number of properly classiﬁed well and non-well pixels. MAE (Equation (40)) and RMSE (Equation (42)) indices have been considered to assess the disparity between the observed and predicted data. The high values of Sensitivity, Speciﬁcity, and Accuracy and low value of MAE and RMSE value indicate the good capability of the models [68–72]. The following ﬁve formulas have been used for statistical measures. TP SE = , (37) TP + FN Remote Sens. 2019, 11, 3015 17 of 35 TN SP = , (38) TN + FP TP + TN AC = , (39) TP + TN + FP + FN MAE = X X , (40) predicted actual i=1 RMSE = (X X ) , (41) predicted actual i=1 where X and X is the predicted and real values in the training dataset or testing dataset of predicted actual the groundwater potentiality models and n is the total number of samples in the training data set or testing dataset. 2.6. Sensitivity Analysis (SA) It is very dicult to completely remove the uncertainty in the preparation of data layers [73–75]. Refsgaard et al. [75] was used dierent techniques e.g., Monte Carlo analysis, error propagation equations, sensitivity analysis (SA), scenario analysis, etc. for measuring the uncertainty. Sensitive analysis has been used in various studies [75–77] for the measurement of the eect of variable variations on model outputs, allowing then a quantitative assessment of the relative importance of uncertainty sources. In the present study, map removal sensitivity analysis (MRSA) method has been used, which was developed by Lodwick et al. [78]. The MRSA method would help to evaluate the sensitivity of the groundwater potentiality maps by removing one or more parameters from the groundwater potentiality maps. This technique has been used by several researchers to address the signiﬁcant role of the eective factors [79–81]. It helps to identify the quantitative contribution of each groundwater conditioning factor to the uncertainty of the model output [72,82]. The percentage of contribution (PC) of each groundwater conditioning factor has been estimated by the MRSA method to explore the relative importance on the model output using the following Equation (42) [83]: (AUC AUC ) all i PC = 100, (42) AUC where AUC and AUC indicate the AUC values obtained from modeling groundwater potential all i model using all GWDFs and the model when the ith GWDF has been excluded. 3. Results 3.1. Analyzing the Multi-Collinearity (MC) of Groundwater Determining Factors The MC problem reduces some linear models’ predictive accuracy [84]. Techniques were applied in this study to assess the MC problem between GWDFs, namely tolerance (TOL) and inﬂation factor variance (VIF) [85]. Tolerance values of <0.1 and VIF of <10 reveal no MC problem among the GWDFs [86]. Roy and Saha [87] and Arabameri et al. [32] were used the MC test for the landslide susceptibility and groundwater potentiality mapping. The selected 16 GWDFs have been tested by SPSS. No MC problem has been found among the GWDFs, as no one value of tolerance and VIF does exceed the threshold limit (Table 4). Therefore, the selected GWDFs are suitable for the prediction of groundwater potentiality. Here, maximum tolerance and VIF values are 0.91 and 5.91 (Table 4). Remote Sens. 2019, 11, 3015 18 of 35 Table 4. Multi-collinearity test of groundwater conditioning factors. Collinearity Statistics Conditioning Factors Tolerance VIF Elevation 0.281 4.275 Slope 0.256 3.908 Convergence Index 0.816 1.226 Rainfall 0.202 4.792 Drainage Density 0.542 1.846 Distance to River 0.855 1.170 Distance to Fault 0.527 1.897 Distance to Road 0.485 2.061 NDVI 0.704 1.420 TWI 0.201 4.911 TPI 0.891 1.122 SPI 0.202 4.713 Aspect 0.916 1.092 Lithology 0.580 1.724 LULC 0.612 1.634 Soil Type 0.492 2.032 3.2. Application of the Weight of Evidence (WoE) Groundwater potentiality reclines on the positive and negative eects of the eective groundwater determining factors. The positive value of WoE indicates the chances of storage of groundwater and vice-versa. The zero value of WoE means the sub-class of factors has no role in determining the groundwater occurrence [88]. The results of WoE model have been put in Table 5. The low altitudinal zone is more potential for the accumulation of groundwater than abrupt slope and higher altitudinal areas due to the high inﬁltration rate and less surface runo [89]. For elevation, 1043–1155 m altitude with a value of 4.88 is showing the strongest positive eects among these GWDFs in making the areas potential to groundwater. On the contrary, the others sub-layers such as 1155–1297 m (WoE = 3.05), 1297–1512 m (WoE = 0), 1512–1993 m (WoE = 0), and >1993 m (WoE = 0) altitudinal levels are representing the negative and less eect in the presence of the groundwater (Table 5). Among the ﬁve slope classes, the <2.55-degree class has the maximum value of WoE i.e., 2.97 which depicts the strong control on the occurrence of groundwater. On the other hand, the remaining four sub-classes of slope have no control over the groundwater at all (Table 5). The north-east aspect has the highest WoE value (WoE = 1.84), which indicates the strong positive eects on the storage of groundwater. CI is the parameters of topography that reﬂect the elevation as a collection of convergent (channel) and divergent (ridge) areas. The CI value ranges from +100 to100. Among the ﬁve classes, the two sub-class of CI such as <59.21 (WoE = 2.02) and >57.64 (WoE = 2.02) has the strongest positive relationship, while others sub-layers have a negative relationship with groundwater storage (Table 5). Rainfall is an important groundwater potentiality determining factor. Rainfall classes <132 mm (WoE = 2.47) and 132 mm–170 mm (WoE = 0.40) have the strongest positive relationship. Lithologoically, the region is composed of nine geological regions, namely A, B, C, D, E, F, G, H, and I. Only the H geological region (quaternary sediments) with WoE of 2.64 has a strong positive eect on the groundwater formation. Among the GWDFs, the soil is of crucial part in the groundwater recharge. Pedologically, the region is composed of three soil orders i.e., aridisols, entisols or rock outcrops, and salt ﬂats. Comparatively, aridisols have a great contribution (WoE = 3.50) in the storage of groundwater. The LU/LC are categories into four types namely rangeland, bare land, agriculture and urban. Only agriculture land with WoE = 8.80 has a strong positive relationship, indicating the high potential of groundwater comparatively the bare land, urban and rangeland areas. Among the other GWDFs, the sub-classes of 1.88–2.24 km/km (WoE = 1.62) of drainage density, <0.10 km (WoE = 0.74) of distance to river, 7.75 –10.91km (WoE = 3.25) of distance to fault, 2.78–6.09km (WoE = 2.25) of distance to road, 0.12–0.21 (WoE = 6.08) of NDVI, Remote Sens. 2019, 11, 3015 19 of 35 5.51–7.44 (WoE = 1.69) of TWI,0.58–0.56 (WoE = 1.44) of TPI and <8.05 (WoE = 1.60) of SPI have the strong positive inﬂuence on the recharge of groundwater (Table 5). Subsequently, weights have been assigned to the sub-layers of GWDFs and converted as weighted WoE layers. All weighted GWDFs have been summed up and generated a single layer of GWPM (Figure 4c). The prepared GWPM has been classiﬁed into four categories i.e., low, medium, high and very high potential zones with the help of the natural break classiﬁcation method (Figure 4c). The results of GWMP by WoE model are showing that only 297.33 km (15.46%) area is of very high groundwater potentiality, followed by the 2 2 2 583.90 km (30.36%) for high, 617.37 km (32.1%) for medium and 424.85 km (22.09%) for low GWPZs (Table 6 and Figure 5). Table 5. The spatial relation between conditioning factors and well locations by weight of evidence model. % of % of Elevation (m) Pixels Well W+ W C S2W+ S2W S© C/S© Pixel Well <1043–1155 855,560 49.36 53 94.64 0.65 2.25 2.90 0.02 0.33 0.59 4.88 1155–1297 446,173 25.74 3 5.36 1.57 0.24 1.81 0.33 0.02 0.59 3.05 1297–1512 303,221 17.50 0 0.00 0.00 0.19 0.00 0.00 0.02 0.00 0.00 1512–1993 101,149 5.84 0 0.00 0.00 0.06 0.00 0.00 0.02 0.00 0.00 >1993 27,036 1.56 0 0.00 0.00 0.02 0.00 0.00 0.02 0.00 0.00 Slope (degree) <2.55 126,724,5 73.12 55 98.21 0.30 2.71 3.01 0.02 1.00 1.01 2.98 2.55–9.35 335,864 19.38 1 1.79 2.38 0.20 2.58 1.00 0.02 1.01 2.56 9.35–20.70 638,68 3.69 0 0.00 0.00 0.04 0.00 0.00 0.02 0.00 0.00 20.70–34.03 44,815 2.59 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 >34.03 21,347 1.23 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 Aspect F 82,884 4.78 3 5.36 0.11 0.01 0.12 0.33 0.02 0.59 0.20 N 89,279 5.15 3 5.36 0.04 0.00 0.04 0.33 0.02 0.59 0.07 NE 154,448 8.91 9 16.07 0.59 0.08 0.67 0.11 0.02 0.36 1.85 E 296,877 17.13 10 17.86 0.04 0.01 0.05 0.10 0.02 0.35 0.14 SE 431,538 24.90 8 14.29 0.56 0.13 0.69 0.13 0.02 0.38 1.80 S 359,878 20.76 12 21.43 0.03 0.01 0.04 0.08 0.02 0.33 0.12 SW 167,965 9.69 7 12.50 0.25 0.03 0.29 0.14 0.02 0.40 0.71 W 853,21 4.92 3 5.36 0.08 0.00 0.09 0.33 0.02 0.59 0.15 NW 64,949 3.75 1 1.79 0.74 0.02 0.76 1.00 0.02 1.01 0.75 Convergence Index <59.21568627 145,566 8.40 9 16.07 0.65 0.09 0.74 0.11 0.02 0.36 2.02 59.21–18.43 368,782 21.28 14 25.00 0.16 0.05 0.21 0.07 0.02 0.31 0.68 18.43–17.64 707,982 40.85 14 25.00 0.49 0.24 0.73 0.07 0.02 0.31 2.36 17.64–57.64 364,974 21.06 10 17.86 0.16 0.04 0.20 0.10 0.02 0.35 0.59 >57.64 145,835 8.41 9 16.07 0.65 0.09 0.73 0.11 0.02 0.36 2.02 Rainfall (mm) <132 429,194 24.76 22 39.29 0.46 0.21 0.68 0.05 0.03 0.27 2.47 132–170 100,66,02 58.08 34 60.71 0.04 0.06 0.11 0.03 0.05 0.27 0.40 170–226 166,770 9.62 0 0.00 0.00 0.10 0.00 0.00 0.02 0.00 0.00 226–305 77,365 4.46 0 0.00 0.00 0.05 0.00 0.00 0.02 0.00 0.00 >305 53,208 3.07 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 Lithology A 7093 0.41 0 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 B 35,899 2.07 0 0.00 0.00 0.02 0.00 0.00 0.02 0.00 0.00 C 57,180 3.30 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 D 72,339 4.17 0 0.00 0.00 0.04 0.00 0.00 0.02 0.00 0.00 E 23,837 1.38 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 F 24,485 1.41 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 G 86,958 5.02 2 3.57 0.34 0.02 0.36 0.50 0.02 0.72 0.49 H 138,8009 80.09 54 96.43 0.19 1.72 1.90 0.02 0.50 0.72 2.64 I 37,340 2.15 0 0.00 0.00 0.02 0.00 0.00 0.02 0.00 0.00 Aridisols 118,6872 68.48 54 96.43 0.34 2.18 2.52 0.02 0.50 0.72 3.50 Rock Outcrops/Entisols 392,588 22.65 0 0.00 0.00 0.26 0.00 0.00 0.02 0.00 0.00 Salt Flats 153,679 8.87 2 3.57 0.91 0.06 0.97 0.50 0.02 0.72 1.34 Remote Sens. 2019, 11, 3015 20 of 35 Table 5. Cont. % of % of Elevation (m) Pixels Well W+ W C S2W+ S2W S© C/S© Pixel Well LULC Bareland 654,072 37.74 4 7.14 1.66 0.40 2.06 0.25 0.02 0.52 3.98 Agriculture 206,538 11.92 52 92.86 2.05 2.51 4.57 0.02 0.25 0.52 8.80 Rangeland 777,361 44.85 0 0.00 0.00 0.60 0.00 0.00 0.02 0.00 0.00 Urban 95,167 5.49 0 0.00 0.00 0.06 0.00 0.00 0.02 0.00 0.00 Drainage Density (km/square km) <1.12 125,010 7.21 0 0.00 0.00 0.07 0.00 0.00 0.02 0.00 0.00 1.12–1.54 360,107 20.78 6 10.71 0.66 0.12 0.78 0.17 0.02 0.43 1.81 1.54–1.88 480,396 27.72 19 33.93 0.20 0.09 0.29 0.05 0.03 0.28 1.03 1.88–2.24 452,295 26.10 20 35.71 0.31 0.14 0.45 0.05 0.03 0.28 1.62 >2.24 315,331 18.19 11 19.64 0.08 0.02 0.09 0.09 0.02 0.34 0.28 Distance to River (km) <0.10 629,316 36.31 23 41.07 0.12 0.08 0.20 0.04 0.03 0.27 0.74 0.10–0.21 519,863 30.00 19 33.93 0.12 0.06 0.18 0.05 0.03 0.28 0.64 0.21–0.37 360,248 20.79 9 16.07 0.26 0.06 0.32 0.11 0.02 0.36 0.87 0.37–0.57 170,585 9.84 4 7.14 0.32 0.03 0.35 0.25 0.02 0.52 0.67 >0.57 53,127 3.07 1 1.79 0.54 0.01 0.55 1.00 0.02 1.01 0.55 Distance to Fault (km) <2.20 634,007 36.58 7 12.50 1.07 0.32 1.40 0.14 0.02 0.40 3.45 2.20–4.85 339,860 19.61 12 21.43 0.09 0.02 0.11 0.08 0.02 0.33 0.34 4.85–7.75 295,667 17.06 14 25.00 0.38 0.10 0.48 0.07 0.02 0.31 1.56 7.75–10.91 272,734 15.74 18 32.14 0.71 0.22 0.93 0.06 0.03 0.29 3.25 >10.91 190,871 11.01 5 8.93 0.21 0.02 0.23 0.20 0.02 0.47 0.50 Distance to Road (km) <2.78 584,777 33.74 22 39.29 0.15 0.09 0.24 0.05 0.03 0.27 0.88 2.78–6.09 503,128 29.03 24 42.86 0.39 0.22 0.61 0.04 0.03 0.27 2.25 6.09–9.91 341,304 19.69 8 14.29 0.32 0.07 0.39 0.13 0.02 0.38 1.01 9.91–14.44 216,429 12.49 2 3.57 1.25 0.10 1.35 0.50 0.02 0.72 1.87 >14.44 87,501 5.05 0 0.00 0.00 0.05 0.00 0.00 0.02 0.00 0.00 NDVI <0.01 946 0.05 0 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.0–0.07 995,879 57.46 8 14.29 1.39 0.70 2.09 0.13 0.02 0.38 5.48 0.07–0.12 614,296 35.44 28 50.00 0.34 0.26 0.60 0.04 0.04 0.27 2.24 0.12–0.21 95,540 5.51 15 26.79 1.58 0.26 1.84 0.07 0.02 0.30 6.08 >0.21 26,478 1.53 5 8.93 1.77 0.08 1.84 0.20 0.02 0.47 3.93 TWI <5.51 315,821 18.22 0 0.00 0.00 0.20 0.00 0.00 0.02 0.00 0.00 5.51–7.44 793,998 45.81 32 57.14 0.22 0.23 0.46 0.03 0.04 0.27 1.69 7.44–9.76 391,225 22.57 14 25.00 0.10 0.03 0.13 0.07 0.02 0.31 0.43 9.76–13.21 174,040 10.04 8 14.29 0.35 0.05 0.40 0.13 0.02 0.38 1.05 >13.21 58,055 3.35 2 3.57 0.06 0.00 0.07 0.50 0.02 0.72 0.09 <2.06 11,457 0.66 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 2.06–0.58 55,078 3.18 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 0.58–0.56 160,7635 92.76 55 98.21 0.06 1.40 1.46 0.02 1.00 1.01 1.44 0.56–2.56 47,227 2.72 1 1.79 0.42 0.01 0.43 1.00 0.02 1.01 0.43 >2.56 11,742 0.68 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 SPI <8.05 538,726 31.08 23 41.07 0.28 0.16 0.44 0.04 0.03 0.27 1.60 8.05–9.83 595,727 34.37 20 35.71 0.04 0.02 0.06 0.05 0.03 0.28 0.21 9.83 11.97 329,339 19.00 6 10.71 0.57 0.10 0.67 0.17 0.02 0.43 1.55 11.97–14.89 171,410 9.89 4 7.14 0.33 0.03 0.36 0.25 0.02 0.52 0.69 >14.89 95,996 5.54 3 5.36 0.03 0.00 0.04 0.33 0.02 0.59 0.06 Remote Sens. 2018, 10, x FOR PEER REVIEW 23 of 37 >2.56 11,742 0.68 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 SPI <8.05 538,726 31.08 23 41.07 0.28 -0.16 0.44 0.04 0.03 0.27 1.60 8.05–9.83 595,727 34.37 20 35.71 0.04 -0.02 0.06 0.05 0.03 0.28 0.21 9.83- 11.97 329,339 19.00 6 10.71 -0.57 0.10 -0.67 0.17 0.02 0.43 -1.55 11.97–14.89 171,410 9.89 4 7.14 -0.33 0.03 -0.36 0.25 0.02 0.52 -0.69 Remote Sens. 2019, 11, 3015 21 of 35 >14.89 95,996 5.54 3 5.36 -0.03 0.00 -0.04 0.33 0.02 0.59 -0.06 Figure 4. Groundwater potentiality maps showing: (a), binary logistic regression (BLR); (b), technique Figure 4. Groundwater potentiality maps showing: (a), binary logistic regression (BLR); (b), technique for order preference by similarity to ideal solution (TOPSIS); (c), weight of evidence (WoE); (d), for order preference by similarity to ideal solution (TOPSIS); (c), weight of evidence (WoE); (d), random random forest (RF); (e), support vector machine (SVM). forest (RF); (e), support vector machine (SVM). Remote Sens. 2019, 11, 3015 22 of 35 Table 6. Areal distribution of groundwater potentiality maps. Models Potentiality Classes Area in Square km % of Area Low 446.1995 23.2 Medium 787.3882 40.94 TOPSIS High 399.4639 20.77 Very high 290.222 15.09 Low 424.8511 22.09 Medium 617.3708 32.1 WoE High 583.9059 30.36 Very high 297.3381 15.46 Low 1064.34 55.34 Medium 198.6742 10.33 RF High 174.4409 9.07 Very high 485.8189 25.26 Low 744.3069 38.7 Medium 594.4839 30.91 BLR High 286.9524 14.92 Very high 297.5304 15.47 Low 248.6793 12.93 Medium 569.0967 29.59 SVM High 744.8839 38.73 Very high 360.4215 18.74 3.3. Application of Random Forest (RF) Model The RF model has been used in the present study to identify GWPZ. For carrying out the RF model, the point values based on well and non-well locations have been derived from GWDFs. The out-of-bag (OOB) of RF model is 3.32% (Table 7). The results depict that elevation (385.72), rainfall (281.63), drainage density (152.98), distance to fault (258.36), NDVI (262.47), distance to the road (189.28) and LULC (137.42) factors have great contribution in the RF process (Figure 6). Conversely, factors such as lithology, soil type and convergence index have a tiny role in the RF process. Finally, GWPM by RF model has been prepared and classiﬁed into four classes such as low, medium, high and very GWPZs (Figure 4d). According to the GWPM, only 485.81 km (25.26%) areas have very high groundwater potentiality. Other potentiality zones such as high, medium and low GWPZs are covered 9.07%, by 10.33% and 55.34% of the study area respectively (Table 6) Table 7. Confusion matrix from random forest model (0 = non-well or negative, 1 = well or positive). Predicted Observation Class Error OOB (%) 0 1 0 8273 149 0.018 3.32 1 180 1319 0.120 Remote Sens. 2018, 10, x FOR PEER REVIEW 24 of 37 Remote Sens. 2019, 11, 3015 23 of 35 Figure 5. Areal distribution of groundwater potentiality maps. Figure 5. Areal distribution of groundwater potentiality maps. Remote Sens. 2018, 10, x FOR PEER REVIEW 26 of 37 Remote Sens. 2019, 11, 3015 24 of 35 Figure 6. Determining the weight of conditioning factors using random forest (RF). Figure 6. Determining the weight of conditioning factors using random forest (RF). 3.4. Application of Binary Logistic Regression (BLR) The BLR probabilistic model has been used for GWPZ estimation. The point base data for well 3.4. Application of Binary Logistic Regression (BLR) and non-well locations have been extracted from each GWDF. Here, BLR is expressed with binary value, i.e., 0 and 1. 1 means that the presence of well and 0 means absence of well. The coecients of The BLR probabilistic model has been used for GWPZ estimation. The point base data for well regression values have been obtained by the BLR. The results of BLR (Table 8) show that slope (0.577), and non-well locations have been extracted from each GWDF. Here, BLR is expressed with binary soil type (6.808), lithology (2.553) and LULC (2.2942) have the reciprocal and positive impacts on the value, i.e., 0 and 1. 1 means that the presence of well and 0 means absence of well. The coefficients of occurrence of groundwater. Among the GWCFs, elevation (0.0237), convergence index (0.0029), rainfall regression values have been obtained by the BLR. The results of BLR (Table 8) show that slope (0.577), (0.0131), distance to fault (0.0001), distance to road (0.0002), TWI (0.2892) and TPI (0.0426) have less soil type (6.808), lithology (2.553) and LULC (2.2942) have the reciprocal and positive impacts on the importance for the formation of groundwater. Conversely, Dd, distance to the river, NDVI and SPI occurrence of groundwater. Among the GWCFs, elevation (0.0237), convergence index (0.0029), have negative impacts on the groundwater occurrence. Afterward, the weights have been assigned to rainfall (0.0131), distance to fault (0.0001), distance to road (0.0002), TWI (0.2892) and TPI (0.0426) GWCFs by BLR. Finally, GWPM by BLR has been built and categorized into four categories such as low, have less importance for the formation of groundwater. Conversely, Dd, distance to the river, NDVI medium, high and very high GWPZs using the natural break method. According to this classiﬁcation, and SPI have negative impacts on the groundwater occurrence. Afterward, the weights have been 15.47% of the Damghan plain has very high groundwater potentiality, followed by 38.7%, 30.91%, and assigned to GWCFs by BLR. Finally, GWPM by BLR has been built and categorized into four 14.92% for low, moderate and high GWPZs (Figure 4a and Table 6). categories such as low, medium, high and very high GWPZs using the natural break method. According to this classification, 15.47% of the Damghan plain has very high groundwater potentiality, followed by 38.7%, 30.91%, and 14.92% for low, moderate and high GWPZs (Figure 4a and Table 6). Remote Sens. 2018, 10, x FOR PEER REVIEW 27 of 37 Remote Sens. 2019, 11, 3015 25 of 35 Table 8. Determining the weight of conditioning factors using logistic regression. Table 8. Determining the weight of conditioning factors using logistic regression. Parameters Weight Parameters Weight Elevation 0.0237 Elevation 0.0237 Slope 0.5778 Slope 0.5778 CI 0.0029 CI 0.0029 Rainfall 0.0131 Rainfall 0.0131 Drain Drainage age Density Density 1.739−1.739 Distance to River 0.0008 Distance to River −0.0008 Distance to Fault 0.0001 Distance to Fault 0.0001 Distance to Road 0.0002 Distance to Road 0.0002 NDVI 7.633 NDVI −7.633 TWI 0.2892 TWI 0.2892 TPI 0.0426 TPI 0.0426 SPI 0.1487 SPI −0.1487 Aspect 1.3488 Aspect −1.3488 Lithology 2.5531 Lithology 2 LULC 2.2942.5531 Soil types 6.8088 LULC 2.2942 Soil types 6.8088 3.5. Application of TOPSIS The TOPSIS an important MDCA approach used to delineate the GWPZs. In this research, 500 3.5. Application of TOPSIS points were selected randomly and extracted point values from GWCFs. The AHP is an important The TOPSIS an important MDCA approach used to delineate the GWPZs. In this research, 500 knowledge-driven MDCA model, used to assign weights to GWCFs for performing the TOPSIS model. points were selected randomly and extracted point values from GWCFs. The AHP is an important The weights of GWCFs are 0.082 (elevation), 0.088 (slope), 0.057 (aspect), 0.058 (convergence index), knowledge-driven MDCA model, used to assign weights to GWCFs for performing the TOPSIS 0.092 (rainfall), 0.067 (drainage density), 0.063 (distance to river), 0.070 (distance to fault), 0.059 (distance model. The weights of GWCFs are 0.082 (elevation), 0.088 (slope), 0.057 (aspect), 0.058 (convergence to index) road), , 0. 0.063 092 (r(lithology), ainfall), 0.067 (dr 0.050 ain(soil age dty ensi pe), ty), 0. 0.060 063 (di (LULC), stance to 0.061 river), (NDVI), 0.070 (di0.045 stance to (TWI), fault)0.04(TPI) , 0.059 and (distance to road), 0.063 (lithology), 0.050 (soil type), 0.060 (LULC), 0.061 (NDVI), 0.045 (TWI), 0.045 (SPI) (Figure 7). The weights of GWCFs by AHP and point base values of GWCFs have been 0.04(TPI) and 0.045 (SPI) (Figure 7). The weights of GWCFs by AHP and point base values of GWCFs computed using the Equations (17)–(26) and then, calculated the ﬁnal weight. The GWPM by TOPSIS have been computed using the Equations (17)–(26) and then, calculated the final weight. The GWPM has been built considering the points values of GWCFs weights with the help of the inverse distance by TOPSIS has been built considering the points values of GWCFs weights with the help of the weighted (IDW) interpolation method (Figure 4b). The GWPM by TOPSIS has been classiﬁed into four inverse distance weighted (IDW) interpolation method (Figure 4b). The GWPM by TOPSIS has been classes such as low, medium, high and very high GWPZs with the help of natural break method. The classified into four classes such as low, medium, high and very high GWPZs with the help of natural results of GWMP by WoE model shows that only 290.22 km (15.09%) area is very high groundwater break method. The results of GWMP by WoE model shows that only 290.22 km2 (15.09%) area is very 2 2 2 potential, followed by the 399.46 km (20.77%), 787.38 km (40.94%) and 446.19 km (23.2%) areas are high groundwater potential, followed by the 399.46 km2 (20.77%), 787.38 km2 (40.94%) and 446.19 high, medium and low groundwater potential (Table 6) km2 (23.2%) areas are high, medium and low groundwater potential (Table 6) Figure 7. Determining the weight of conditioning factors using analytic hierarchy process (AHP) method. Remote Sens. 2019, 11, 3015 26 of 35 3.6. Application of Support Vector Machine (SVM) SVM is a vital machine learning data mining technique, used to recognize the potentiality of groundwater. All data layers have been reclassiﬁed into dierent classes using the SVM method. The SVM classiﬁcation value ranges from 0 to 1, 0 indicating the absence of groundwater well in GWCFs and Conversely 1 value also indicates the presence and potentiality of groundwater formation. Among the GWDFs, the low altitude, low slopping, high rainfall, nearest distance to river, high Dd, nearest distance to road, far distance to fault, high vegetation index, H lithological units, agriculture land, arid soils, high TWI and low SPI have been considered as sub-layers of high groundwater potential, marked by the 1 values. Conversely, high altitude, slopping, low drainage density, far distance to a river, low fault distance, low vegetation index, rangeland, bare land, urban, entisols, salt ﬂats, low TWI, and low rainfall have been identiﬁed as the 0 values because these conditions are not suitable for groundwater recharge. Thus, all GWDFs have been weighted by SVM and summed up in GIS to generate a single data layer of groundwater potential map (GWPM). The GWPM by SVM has been classiﬁed into four classes such as low, medium, high and very high GWPZs with the help of the natural break classiﬁcation method (Figure 4e). The results of GWMP by WoE model show that only 2 2 360.42 km (18.74%) area has very high groundwater potentiality and 248.67 km (12.93%) area has low groundwater potentiality (Table 6). 3.7. Validations and Comparison of Models Sometimes a single method of validation is not sucient for judging the potentiality and performance of models because of the concentration of samples within a few places. Methods of AUROC, SE, SP, AC, MAE, RMSE, and SCAI were used to test the performance of models. Both training (goodness of ﬁt) and validation (prediction accuracy) datasets have been used for judging the capability of models in producing the GWPMs of the study area. Considering the training dataset ROC curves (Figure 8) showing the AUC values of WoE, RF, TOPSIS, SVM, and BLR models are 0.914, 0.846, 0.924, 0.833, and 0.933, respectively (Figure 8). The SE values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.807, 0.800, 0.833, 0.792, and 0.852, respectively. The SP values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.818, 0.789, 0.810, 0.789, and 0.828, respectively (Table 9) The accuracy values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.813, 0.795, 0.821, 0.791, and 0.839, respectively. The RMSE values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.317, 0.367, 0.316, 0.377, and 0.314, respectively. MAE values of the WoE, RF, TOPSIS, SVM and BLR models are 0.221, 0.275, 0.219, 0.269 and 0.216, respectively. AUCROC, sensitivity, speciﬁcity, accuracy, MAE, and MRSE are depicting the consistency between the trained models and actual situation of groundwater. In the validation data context, the AUC values WoE, RF, TOPSIS, SVM, and BLR are 0.898, 0.816, 0.901, 0.851, and 0.943, respectively. The SE values of the WoE, RF, TOPSIS, SVM and BLR models are 0.800, 0.783, 0.870, 0.773 and 0.909, respectively. The SP values of the WoE, RF, TOPSIS, SVM and BLR models are 0.826, 0.760, 0,840, 0.760, and 0.846 respectively (Table 9). The accuracy value of the WoE, RF, TOPSIS, SVM, and BLR models are 0.813, 0.771, 0.854, 0.766 and 0.875, respectively. On the other hand the RMSE values of the WoE, RF, TOPSIS, SVM and BLR models are 0.332, 0.383, 0.321, 0.409, and 0.311 and MAE values are 0.235, 0.288, 0.233, 0.311, and 0.214, respectively (Table 9). Remote Sens. 2018, 10, x FOR PEER REVIEW 29 of 37 predictability to evaluate the groundwater potentiality of the Damghan sedimentary plain, although other models have good capability in mapping the groundwater potentiality. Remote Sens. 2019, 11, 3015 27 of 35 Figure 8. Validation of results using the area under the curve of the receiver operating characteristic Figure 8. Validation of results using the area under the curve of the receiver operating characteristic (AUROC). (a) Training dataset (success rate curve) and (b) validation dataset (prediction rate curve). (AUROC). (a) Training dataset (success rate curve) and (b) validation dataset (prediction rate curve). Table Table 9. 9. Analysis Analysis of performa of performances nces usin using g training dataset an training dataset and d validat validation ion dataset for dataset the m for the odels. models. Training Dataset Validation Dataset Training Dataset Validation Dataset Measures WoE RF TOPSIS SVM BLR WoE RF TOPSIS SVM BLR True positive 46 44 45 42 46 20 17 20 18 20 True negative 45 45 47 45 48 19 19 21 19 22 Measures False positive 10 12 11 12 10 4 6 4 6 4 False negative 11 11 9 11 8 5 5 3 5 2 Sensitivity 0.807 0.800 0.833 0.792 0.852 0.800 0.773 0.870 0.783 0.909 True positive 46 44 45 42 46 20 17 20 18 20 Speciﬁcity 0.818 0.789 0.810 0.789 0.828 0.826 0.760 0.840 0.760 0.846 Accuracy 0.813 0.795 0.821 0.791 0.839 0.813 0.766 0.854 0.771 0.875 True negative RMSE 0.317 45 0.367 45 0.316 47 0.377 45 48 0.314 19 0.332 19 0.383 21 0.321 19 0.409 22 0.311 MAE 0.221 0.275 0.219 0.269 0.216 0.235 0.288 0.233 0.311 0.214 AUC 0.914 0.846 0.924 0.833 0.933 0.898 0.81 0.901 0.851 0.943 False positive 10 12 11 12 10 4 6 4 6 4 False negative 11 11 9 11 8 5 5 3 5 2 All the statistical techniques and ROC curves used in this study for evaluating the performance of the models have judged all the models as good for mapping the groundwater potentiality in this Sensitivity 0.807 0.800 0.833 0.792 0.852 0.800 0.773 0.870 0.783 0.909 plain. SCAI is another important validation method, used to validate the models. The SCAI values of Specificity 0.818 0.789 0.810 0.789 0.828 0.826 0.760 0.840 0.760 0.846 sub-classes of all models have decreased from low potentiality to very high potentiality, indicating the appropriateness and suitability for the groundwater potentiality evaluation (Table 10). Above Accuracy 0.813 0.795 0.821 0.791 0.839 0.813 0.766 0.854 0.771 0.875 all, according to the threshold dependent, SCAI and statistical methods the BLR has the strongest RMSE predictability to evaluate 0.317 the 0.gr 36oundwater 7 0.316 0. potentiality 377 0.314 of the 0.332 Damghan 0.383 sedimentary 0.321 0.40 plain, 9 0. although 311 other models have good capability in mapping the groundwater potentiality. MAE 0.221 0.275 0.219 0.269 0.216 0.235 0.288 0.233 0.311 0.214 AUC 0.914 0.846 0.924 0.833 0.933 0.898 0.81 0.901 0.851 0.943 WoE RF TOPSIS SVM BLR WoE RF TOPSIS SVM BLR Remote Sens. 2019, 11, 3015 28 of 35 Table 10. Computation sheet of seed cell area index (SCAI) methods. Training Datasets Validation Datasets Groundwater Models Potentiality % of Pixels No of % of No of % of Sum SCAI Classes Wells Wells Wells Wells Low 23.20 0 0.00 0 0.00 0.00 0.00 Medium 40.94 0 0.00 0 0.00 0.00 0.00 TOPSIS High 20.77 2 3.57 4 16.67 20.24 1.03 Very high 15.09 54 96.43 20 83.33 179.76 0.08 Low 22.09 0 0.00 0 0.00 0.00 0.00 Medium 32.10 2 3.57 1 4.17 4.17 7.70 WoE High 30.36 5 8.93 2 8.33 11.90 2.55 Very high 15.46 49 87.50 21 87.50 96.43 0.16 Low 55.34 1 1.79 0 0.00 1.79 30.99 Medium 10.33 4 7.14 1 4.17 11.31 0.91 RF High 9.07 8 14.29 3 12.50 26.79 0.34 Very high 25.26 43 76.79 20 83.33 160.12 0.16 Low 38.70 0 0.00 1 4.17 4.17 9.29 Medium 30.91 0 0.00 23 95.83 95.83 0.32 BLR High 14.92 2 3.57 0 0 3.57 4.18 Very high 15.47 54 96.43 0 0 96.43 0.16 Low 12.93 0 0.00 0 0.00 0.00 0.00 Medium 29.59 1 1.79 6 25.00 26.79 1.10 SVM High 38.73 14 25.00 18 75.00 100.00 0.39 Very high 18.74 41 73.21 73.21 0.26 3.8. Sensitivity Analysis To assess the inﬂuence of GWDFs on groundwater potentiality occurrence and to explore the eective factors with the strongest eect on the result of the groundwater potentiality prediction, a sensitivity analysis has been carried out (Table 11 and Figure 9). The results of sensitivity analysis showed in percentage contribution (PC) values of factors attained. The Pc values of the GWDFs are 7.5% (elevation), 11.35% (convergence index), 13.68% (drainage density), 11.81% (distance to road), 7.18% (distance to fault), 16.10% (distance to river), 6.19% (land use/land cover), 8.66% (lithology), 6.91% (NDVI), 9.67% (Rainfall), 7.86% (slope), 5.52% (soil), 10.10% (SPI), 12.58% (TPI), 9.51% (TWI) and 0.41% (aspect). The only slope aspect has very little contribution to the occurrence of groundwater potentiality. The results indicated that the groundwater potentiality maps of the study area are highly sensitive to elevation, lithology, drainage density, rainfall, distance to river, TPI, TWI, SPI, and distance to road. The sensitive analysis would help to reduce the variation in the model and to understand the signiﬁcant geo-environmental factors that are vital for understanding the structure of model. Table 11. Sensitivity result when each factor is excluded in the binary logistic regression model. GWDFs Decrease of AUC (in Percentage) Elevation 7.5 CI 11.35 Drainage density 13.68 Distance from road 11.81 Distance from fault 7.18 Distance from river 16.10 LULC 6.19 Lithology 8.66 NDVI 6.91 Rainfall 9.67 Slope 7.86 Soil 5.52 SPI 10.70 TPI 12.58 TWI 9.51 Aspect 0.41 Remote Sens. 2018, 10, x FOR PEER REVIEW 31 of 37 Distance from road 11.81 Distance from fault 7.18 Distance from river 16.10 LULC 6.19 Lithology 8.66 NDVI 6.91 Rainfall 9.67 Slope 7.86 Soil 5.52 SPI 10.70 TPI 12.58 TWI 9.51 Aspect 0.41 Remote Sens. 2019, 11, 3015 29 of 35 GWDFs Figure 9. Sensitivity result when each factor is excluded in the binary logistic regression model. Figure 9. Sensitivity result when each factor is excluded in the binary logistic regression model. 4. Discussion 4. Discussion In the recent decade, the demand for water has signiﬁcantly increased because of the rapid growth In the recent decade, the demand for water has significantly increased because of the rapid of population, especially in arid and semi-arid areas. The large part of Damghan sedimentary plain growth of population, especially in arid and semi-arid areas. The large part of Damghan sedimentary covering the arid and semi-arid environments groundwater is the main source of water for living. In plain covering the arid and semi-arid environments groundwater is the main source of water for this region, groundwater planning and sustainable management are necessary. The hydrogeologist, living. In this region, groundwater planning and sustainable management are necessary. The engineers and decision need some basic tools for managing the groundwater. GWPM may meet the hydrogeologist, engineers and decision need some basic tools for managing the groundwater. GWPM basic tool of groundwater management. may meet the basic tool of groundwater management. GWPM is the outcome of the lithology, tectonics, topography, vegetation, rainfall, and hydrology, GWPM is the outcome of the lithology, tectonics, topography, vegetation, rainfall, and which are available and accessible everywhere in the environment. In this research, a dierent hydrology, which are available and accessible everywhere in the environment. In this research, a type of data has been used as the input datasets. DEMs based study provides more accurate and different type of data has been used as the input datasets. DEMs based study provides more accurate signiﬁcant results [90–92]. Dierent DEMs provide dierent results, e.g., ALOS DEM with 30 m spatial and significant results (90–92). Different DEMs provide different results, e.g., ALOS DEM with 30 m resolution provide suitable and excellent results, comparatively the ASTER and SRTM DEMs with 30 m spatial resolution provide suitable and excellent results, comparatively the ASTER and SRTM DEMs resolution [93]. Here, the authors combined the geomorphology, geology and hydrology parameters with 30 m resolution [93]. Here, the authors combined the geomorphology, geology and hydrology to recognize the spatial groundwater potential. Spatial analysis is the core matter of the research for adopting the most performing approach and models for GWPMs, considering the argument topic [12–15]. Geo-environmental factors (i.e., elevation, slope, aspect, rainfall, lithology, land use/land cover, soil type, drainage density, distance to river, distance to fault, distance to road, NDVI, TWI, TPI, and SPI) were considered as the GWDFs that have been tested for the multi-collinearity problem by VIF and tolerance, and are the most eective for groundwater storage. The categorical variables such as aspect, lithology, soil type, LU/LC factors have been converted into the quantity continuous data through assigning the weight by the WoE and TOPSIS method. For the LR and RF, these GWDFs have been evaluated to prepare GWPMs taking the extracted values of GWDFs of the 500 points. The results of these models are more accurate than previous works [32]. In this work, we applied probabilistic (WoE, BLR), machine learning (SVM and RF) and multi-criteria decision approach (TOPSIS) models for building the GWPMs of Damghan sedimentary plain. These models have represented the excellent results as other works were done by Mohammady et al. [94] and Arabameri et al. [25,26]. All models, however, have very few variations in groundwater potential modeling accuracy. According to the AUROC, SE, SP, Accuracy, MAE and MRSE among the ﬁve models, the BLR models (for training dataset AUC = 0.933, SE = 0.852, SP = 0.828, AC = 0.839, MAE = 0.216 and RMSE = 0.314 and for Percantage change in AUC Elevation CI Dd Distance from Road Distance from Fault Distance from River LULC Lithology NDVI Rainfall Slope Soil SPI TPI TWI Aspect Remote Sens. 2019, 11, 3015 30 of 35 validation dataset AUC = 0.943, SE = 0.909, SP = 0.846, AC = 0.875, MAE = 0.214 and RMSE = 0.311) have better capability for mapping the groundwater potentiality than other models. Recognizing the signiﬁcance of each variable for groundwater storage is very dicult. The soil, lithology, altitude, rainfall, LU/LC, NDVI, Dd, distance to fault factors are dominant factors among 16 GWDFs for the formation of groundwater. The SA is depicting the contribution in producing the uncertainty in the GWPM and the factor distance from the river has the highest contribution to the variation of output of model. Similar to the Shahroud plain, the Damghan sedimentary plain regions consists of the large bare land, rangeland, and urban land, interrupting the water inﬁltration into sub-surface layer, while agriculture land with aquifer locations are receiving the larger water into the sub-surface and also signify the hydrologic properties [95]. According to TOPSIS model, the rainfall, slope, elevation, LU/LC, soil type factors have been highly prioritized by the AHP model, suggesting the most potential for groundwater formation. Such ﬁndings are conﬁrmed with the work of Arabameri et al. [32]. Among the 16 GWDFs, the elevation is the most important topographic component that inﬂuences the groundwater recharge. In fact, at a lower segment, the Damghan sedimentary plain is almost ﬂat, where water stagnation and associated inﬁltration of water is maximized. On the contrary, high altitudes, associated with open and v-shaped slopes promote runo due to local physiography. The methods applied for validating the GWPMs are showing outstanding accuracy, and ensemble models have better capabilities than the individual modes. Such ensemble models have been shown to be more reliable in this analysis than the other models used by the researchers for GWPM in various other locations [96,97]. The proper methods can have the ability to produce GWPMs, and that can be used for planning purposes. The used probabilistic, machine learning and ensemble models have excellent accuracy and may be used for groundwater management in this plain region. 5. Conclusions Today, GWPM is an eective groundwater resource management method. Through the Over-extraction of groundwater in the low groundwater, the potential region can be limited by the GWPM. With the advancement in the technical ﬁeld, dierent techniques for the spatial modeling of groundwater are introducing day by day. So, it very dicult to say what method would be best for spatial modeling. However, in the present research, ﬁve methods (BLR, TOPSIS, WoE, RF, and SVM) have been used for modeling the groundwater and the compared among them to answer the question of what model is relatively better for the Damghan sedimentary plain. The GWPM approaches are more appropriate to predict the potential of groundwater. The GWPMs have been produced with the help of RS and GIS techniques. RS and GIS both combinedly helped to perform the works such as identiﬁcation of well, thematic data generation, classiﬁcation, and ﬁnal map generations. The RS and GIS-based study are cost and time saving, accurate, and provide meaningful results. The R studio is an important machine learning program that helps to perform dierent kinds of models such as logistic regression, random forest, naive Bayes tree, support vector machine, artiﬁcial neural network, and several other methods. R program based model performance is more easy, accurate, eciency and perfect. The GWPMs, produced by the selected methods have been categorized into four categories i.e., low, medium, high and very high potential classes. The results of GWPMs show that the very 2 2 high potentiality zones are covered with by an area of 290.22 km (15.09% by TOPSIS), 297.34 km 2 2 2 (15.46% by WoE), 485 km (25.26% by RF), 297.53 km (15.47% by BLR) and 360.42 km (18.74% by SVM) out of 1923.27 km areas. The worthiness of GWPMs has been signiﬁcantly validated by the ROC and SCAI methods and ﬁve statistical measures i.e., SE, SP, AC, MAE, and MRSE. According to the results of the ROC, SCAI methods and statistical measures, these models are excellent for the prediction of GWPZ. The very high or excellent GWPZs have been found in the low elevated and less sloppy area. The arid soils are covered by high potentiality of groundwater. In the case of the LU/LC and vegetation index, the agriculture land and high vegetation density areas have high potentiality of groundwater. Conversely, high altitude, sloppy land, urban area, rangeland, salt ﬂats, entisols soil type have the low potentiality of groundwater formation. The GWPMs may be used as tool in Remote Sens. 2019, 11, 3015 31 of 35 this study area for managing and developing the groundwater. The resulting maps can also assist decision-makers, planners, and engineers in choosing the ideal location, groundwater distribution for further groundwater exploration. 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remote sensing Article Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran 1 2 2 3 Alireza Arabameri , Jagabandhu Roy , Sunil Saha , Thomas Blaschke , 3 4 , Omid Ghorbanzadeh and Dieu Tien Bui * Department of Geomorphology, Tarbiat Modares University, Tehran 14117-13116, Iran; [email protected] Department of Geography, University of Gour Banga, Malda, West Bengal 732103, India; [email protected] (J.R.); [email protected] (S.S.) Department of Geoinformatics – Z_GIS, University of Salzburg, 5020 Salzburg, Austria; [email protected] (T.B.); [email protected] (O.G.) Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam * Correspondence: [email protected] Received: 12 November 2019; Accepted: 10 December 2019; Published: 14 December 2019 Abstract: Groundwater is one of the most important natural resources, as it regulates the earth’s hydrological system. The Damghan sedimentary plain area, located in the region of a semi-arid climate of Iran, has very critical conditions of groundwater due to massive pressure on it and is in need of robust models for identifying the groundwater potential zones (GWPZ). The main goal of the current research is to prepare a groundwater potentiality map (GWPM) considering the probabilistic, machine learning, data mining, and multi-criteria decision analysis (MCDA) approaches. For this purpose, 80 wells collected from the Iranian groundwater resource department and ﬁeld investigation with global positioning system (GPS), have been selected randomly and considered as the groundwater inventory datasets. Out of 80 wells, 56 (70%) wells have been brought into play for modeling and 24 (30%) for validation purposes. Elevation, slope, aspect, convergence index (CI), rainfall, drainage density (Dd), distance to river, distance to fault, distance to road, lithology, soil type, land use/land cover (LU/LC), normalized dierence vegetation index (NDVI), topographic wetness index (TWI), topographic position index (TPI), and stream power index (SPI) have been used for modeling purpose. The area under the receiver operating characteristic (AUROC), sensitivity (SE), speciﬁcity (SP), accuracy (AC), mean absolute error (MAE), and root mean square error (RMSE) are used for checking the goodness-of-ﬁt and prediction accuracy of approaches to compare their performance. In addition, the inﬂuence of groundwater determining factors (GWDFs) on groundwater occurrence was evaluated by performing a sensitivity analysis model. The GWPMs, produced by technique for order preference by similarity to ideal solution (TOPSIS), random forest (RF), binary logistic regression (BLR), weight of evidence (WoE) and support vector machine (SVM) have been classiﬁed into four categories, i.e., low, medium, high and very high groundwater potentiality with the help of the natural break classiﬁcation methods in the GIS environment. The very high groundwater potentiality class is covered 15.09% for TOPSIS, 15.46% for WoE, 25.26% for RF, 15.47% for BLR, and 18.74% for SVM of the entire plain area. Based on sensitivity analysis, distance from river, and drainage density represent signiﬁcantly eects on the groundwater occurrence. validation results show that the BLR model with best prediction accuracy and goodness-of-ﬁt outperforms the other ﬁve models. Although, all models have very good performance in modeling of groundwater potential. Results of seed cell area index model that used for checking accuracy classiﬁcation of models show that all models have suitable performance. Therefore, these are promising models that can be applied for the GWPZs identiﬁcation, which will help for some needful action of these areas. Remote Sens. 2019, 11, 3015; doi:10.3390/rs11243015 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 3015 2 of 35 Keywords: groundwater potential mapping (GWPM); probabilistic models; machine learning algorithms; sensitivity analysis; Damghan sedimentary plain 1. Introduction Groundwater plays a crucial role in serving the heterogeneous need of human being such as drinking, agricultural, industrial, etc. [1]. In another way, groundwater availability and accessibility control sustainable development at a global, regional and local scale [2]. Large numbers of countries of the earth are facing the problem of water scarcity at the societal level [3]. In the arid and semi-arid regions, groundwater is the prime source of water and accounts for 80% groundwater resource [4]. Notably, in Iran, groundwater is more demanded source owing to its cleanness, tawdriness, constant chemical composition, constant temperature, lower pollution coecient, and a high certainty [4,5]. Groundwater extensively aects economic development, biological diversity and community health [6]. Similar to Iran country, a major part of the largely arid and semi-arid physiographic regions suers from the scarcity of water. Therefore, the groundwater is a main source of water to serve the dierent purpose and utilization of this region [7]. Iran has received average annual precipitation of 413 mm, and the evapo-transportation rate is 296 mm. Therefore, the 117 billion m of water is stored as groundwater over the whole country. The global per capita annual renewal water is 7600 m while the quantity of per capita global renewable water in Iran is 1900 m . In this region, the average yearly water consumption is 3.4 billion m , out of which about 65% is supplied from groundwater. In the present day, Iran is facing harsh water supply problems [8]. From these data, it is inevitable to implement water resource management policy for continuing the country’s economic and societal development. However, this issue can be short out by taking some necessary steps and decisions such as watershed management, artiﬁcial recharge, and management of soil and water [8]. In present the decades, groundwater recharge level has fallen due to unnecessary use and unscientiﬁc management plans [9]. Hence, aquifer potential determination through groundwater potentiality analysis is a good strategy in this ﬁeld [10,11]. Dierent methods and models, techniques and processes were induced and used for the groundwater potentiality map (GWPM) or identiﬁcation of areas having good potentiality of groundwater recharge. A few decades back, conventional techniques were applied for GWPM. Day by day improvement in technology with regarding scientiﬁc approach, the measuring instrument and computerized data analysis able to recognize the groundwater level, ﬂow and other aspects for GWPM. Comparatively, contemporary scientiﬁc methods are providing better outcomes than the conventional method. Recently, remote sensing (RS) and geographic information system (GIS) are playing important role in managing the groundwater resource without the computational requirements [12]. RS technique provides the spatial and non-spatial information—even over the inaccessible areas in a short duration [13]. Therefore, RS technique also a powerful, ecient, accurate tool for collecting, restoring, manipulating, analyzing the spatial data of the surface and sub-surface water research, e.g., groundwater recharge, potentiality, evaluation of water quality [2,14]. Speciﬁcally, satellite imagery can provide hydrological characteristics, i.e., drainage network, ﬂow accumulation, drainage density, recharge, and other geomorphologic characteristics [15]. The modeling of groundwater potential zones (GWPZ) is not only dependent on the single factors but also dependent on the dierent geo-environmental factors such as elevation, slope, aspect, rainfall, geology, fault, rainfall, drainage density (Dd), land use/land cover (LU/LC), normalized dierence vegetation index (NDVI), topographic wetness index (TWI), stream power index (SPI), soil permeability, topographic position index (TPI), convergence index (CI), inﬁltration rate, and soil texture. RS and GIS integration with modern groundwater mapping models such as probabilistic, knowledge-driven, machine learning, data mining could provide a powerful way to gain valuable decision-making information. The rapid development of probabilistic, machine learning, data mining, and ensemble models in recent decades is enhancing the basement to determine groundwater recharge opportunity, soil erosion susceptibility, gully erosion susceptibility, and other spatial modelings. Some Remote Sens. 2019, 11, 3015 3 of 35 new methods which were used by the researcher for spatial hazards probability and groundwater potentiality modeling are: evidential belief function (EBF), weights of evidence (WoE), frequency ratio (FR), classiﬁcation and regression tree (CART,), boosted regression tree (BRT), decision tree (DT), artiﬁcial neural network (ANN), multivariate adaptive regression splines (MARS), binary logistic regression (BLR), Shannon’s entropy (SE), analytic hierarchy process (AHP), maximum entropy (ME), random forest (RF), fuzzy logic (FL), support vector machine (SVM), multi-criteria decision analysis (MDCA), logistic model tree (LMT), quadratic discriminate analysis (QDA), K-nearest neighbor (KNN), and certainty factor (CF) [16–22]. In this work, we have used probabilistic, machine learning, data mining, and MDCA methods, namely WoE, BLR, SVM, RF, and a technique for order preference by similarity to ideal solution (TOPSIS). The outcomes of the same model vary depending on the physiographical situation in dierent regions. The suitable models help to demarcate the areas having groundwater potentiality. The models used in this research are accessible and eciently capable of groundwater modeling and are used in various areas for environmental management [23–26]. Thus, the study aims to recognize the GWPZ using ﬁve models (RF, TOPSIS, WoE, SVM, and BLR,) in the Damghan sedimentary plain of Semnan province in Iran. The current study will help in determining the proper groundwater resource and to the decision-maker for managing the water resources. 2. Materials and Methods 2.1. Study Area Damghan sedimentary plain, located within the Semnan province in Iran, covers an area of 2 0 0 0 1559 km . Geographically, this plain region stretches from 35 56 to 36 18 N latitude and 54 00 E to 54 40 E longitude (Figure 1). The long-term average of precipitation and long-term evaporation are about 151.01 and 3000 mm, respectively [27]. The arid climate prevails in this plain because the annual evaporation is greater than annual precipitation [28]. The average temperature in the mountainous portion of the study area is 9.8 ºC, and in the plain area, the mean temperature is 23.5 ºC. In the south of Alborz zone, the upland area of the watershed is extended, and the plain’s elevation ranges from 2860 m. a.s.l. in the northwest, to 1043 m a.s.l. in the southeast. Major portions of the study region are composed of Quaternary deposits [29]. The remaining parts of the plain are situated in the Alborz region and are covered by calcrete layers such as Cretaceous formations, as well as sandstone and Paleogene-related conglomerates. The low elevated area, composed of Quaternary deposits, has a high-water yield and recharge rate because of sediment nature and succession [30]. Nevertheless, the upland region in the Alborz zone is not suitable for recharge [31]. The mean depth of alluvial sediment varies from 150 m in north to 240 m in the south. In this area, the unconﬁned aquifer and bedrock consist of Neogene alluvium, such as marl and conglomerate, and the well logs set out the type of sediment. Remote Sens. 2018, 10, x FOR PEER REVIEW 4 of 37 Remote Sens. 2019, 11, 3015 4 of 35 Figure 1. Location of the study area in Iran and Semnan province and location of training and Figure 1. Location of the study area in Iran and Semnan province and location of training and validations wells in the study area. validations wells in the study area. The sedimentary plain of Damghan is located in arid and semi-arid regions and facing the problem 2.2. Methodology of water supply such as other arid regions. The main source of freshwater is sub-surface water storage For assessing the groundwater potentiality (GWP), some spatial and non-spatial data have been and undergoes the problems of over pumping and lowering of groundwater. In the recent decade, gathered to prepare different datasets for modeling and validation of results. The data consists of due to excessive groundwater exploitation for irrigation and industrial purposes combining with the two, i.e., primary and secondary, data. Primary data are pumping tests and yield measurements in decreasing amount of rainfall, the water table is coming down rapidly. Therefore, immediate planning the field. The secondary data are topographical map (scale 1:50000), lithological map (scale 1:100000), is needed to conserve the groundwater [30]. In this respect, the delineation of GWPZ is essential for Sentinel 2A, Phased Array type L-band synthetic aperture radar (PALSAR) digital elevation model proper planning and sustainable management of water. (DEM), rainfall of different metrological station of last 30 years, well location data from Water 2.2. Resou Methodology rce Management, Iran, soil data from soil department of Iran. Thematic maps of all the data were extracted and analyzed by the RS and GIS. The present work methodologically consists of four For assessing the groundwater potentiality (GWP), some spatial and non-spatial data have been phases (Figure 2) including; (1) preparation of groundwater inventory database thematic data layers gathered to prepare dierent datasets for modeling and validation of results. The data consists of of the groundwater conditioning factors including elevation, slope, aspect, CI, rainfall, lithology, soil two, i.e., primary and secondary, data. Primary data are pumping tests and yield measurements type, LU/LC, Dd, distance to river, distance to fault, distance to road, NDVI, TPI), TWI, and SPI; (2) in the ﬁeld. The secondary data are topographical map (scale 1:50,000), lithological map (scale multicollinearity assessment of the effective groundwater determining factors (GWDFs); (3) application of models and preparation of GWPMs. The GWPMs were classified according to the four Remote Sens. 2019, 11, 3015 5 of 35 1:100,000), Sentinel 2A, Phased Array type L-band synthetic aperture radar (PALSAR) digital elevation model (DEM), rainfall of dierent metrological station of last 30 years, well location data from Water Resource Management, Iran, soil data from soil department of Iran. Thematic maps of all the data were extracted and analyzed by the RS and GIS. The present work methodologically consists of four phases (Figure 2) including; (1) preparation of groundwater inventory database thematic data layers of the groundwater conditioning factors including elevation, slope, aspect, CI, rainfall, lithology, soil type, LU/LC, Dd, distance to river, distance to fault, distance to road, NDVI, TPI), TWI, and SPI; (2) multicollinearity assessment of the eective groundwater determining factors (GWDFs); (3) application of models and preparation of GWPMs. The GWPMs were classiﬁed according to the four classiﬁcation methods, namely quantile, natural breaks, equal interval, and geometrical interval, into four dierent groundwater susceptibility classes, including low, medium, high, and very high. By comparing the results of each classiﬁcation method and the distribution of training and validation wells on the high and very high groundwater susceptibility classes, it was found that the natural break classiﬁcation method gave the most accurate distribution. This agrees with the ﬁndings by Arabameri et al. [32], in that natural break method is a good classiﬁer in susceptibility mapping; and (4), evaluation of the models performances using area under receiver operating characteristics (AUROC) curve, sensitivity (SE), speciﬁcity (SP), accuracy (AC), mean absolute error (MAE), root mean square error (RMSE) and seed cell area index (SCAI) methods. 2.3. Data Preparation 2.3.1. Groundwater Inventory Map (GWIM) The groundwater inventory database is of a key role in groundwater potentiality mapping. An inventory map is a target variable for any spatial modeling [32]. The well inventory database was prepared after extensive ﬁeld visit with a hand GPS (global positioning system), and yield data were collected from the Department of Water Resources Management, Iran. Groundwater wells, with high yield of11 m h1 by pumping test analysis, have been considered for the GWPM. As a result, 80 wells have recognized in the study area. 56 wells (70%) of this dataset, were randomly selected to produce the GWPM models [32], whereas the remaining 24 (30%) wells were considered for validation of GWPMs [11]. The training and testing wells locations have been mentioned in Figure 1. Remote Remote Sens Sens. 2019 . ,2018 11, , 3015 10, x FOR PEER REVIEW 6 of 37 6 of 35 Figure 2. Methodological flowchart of the present work. Figure 2. Methodological ﬂowchart of the present work. 2.3.2. Groundwater Determining Factors (GWDFs) The dierent geo-environmental components play a crucial role in determining the status of groundwater. GWPM represents the association between GWDFs and well locations [21,22]. For the GWPM, 16 GWDFs have been selected including elevation, slope, aspect, CI, rainfall, lithology, soil type, LU/LC, NDVI, Dd, distance to the river, distance to fault, distance to road, TWI, SPI and TPI Remote Sens. 2019, 11, 3015 7 of 35 (Figure 3a–p). The PALSAR DEM (12.5 m resolution) downloaded from the Alaska Satellite Facility (ASF) Distributed Active Archive Center (DAAC). In this study, PALSAR DEM was used to extract the topographical, hydrological factors such as elevation, slope, aspect, CI, drainage, TWI, SPI, and TPI. The slope, aspect, and elevation are the major topographic components, used to determine the groundwater potentiality, erosion probability, etc. [21]. The DEM has been used as the elevation dataset (Figure 3a). The altitudinal ﬂuctuation controls climatic conditions and helps to induce various vegetation types and soil development [33]. The slope data layer has been derived from PALSAR DEM by spatial analysis in the GIS environment (Figure 3b). In the same way, the aspect map has also been extracted from PALSAR DEM imagery using a spatial analysis tool (Figure 3d). CI is an important terrain factor that demonstrates the arrangement of relief as a set of channels and ridges. It is developed by Kiss [34]. The convergence index (CI) has been calculated using Equation (1). CI = 90 , (1) i=1 where indicates the average angle between the aspect of adjacent cells and the direction to the central cell. The CI value ranges from100 to +100 (Figure 3c). The rainfall map was prepared by the kriging method considering the last 10-year annual rainfall of dierent stations (Figure 3e). The drainage was extracted from the topographical map and PALSAR DEM imagery. The Dd was computed based on Horton’s morphometric formula (Equation (2)). Dd = , (2) where Lu means the total length of all orders streams, A is the area in square kilometer. Finally, the spatial data layer of the Dd has been built using the IDW interpolation method in the GIS environment (Figure 3f). The fault layer has been taken out from Landsat 7 imagery in ENVI software. The road network has been taken o from the topographical map and Google Earth imagery. The distance to river, fault, road data layers have been built using the Euclidian distance buering tool and expressed in km (Figure 3g,h,i) [11]. The lithological information for the study area was gathered from the geological department of Iran [29]. The lithology map has been prepared by the digitization process (Figure 3j). Geologically, the region is composed of nine geological segments, namely A, B, C, D, E, F, G, H, and I (Figure 3j and Table 1). Soil data was collected from the soil department of Iranian and with the help of the digitized process, the thematic dataset of soil has been produced (Figure 3k). The LU/LC map has been produced from Sentinel 2A satellite image (12/08/2017) of 10 m, 20 m, and 60 m spatial resolution for each band using the supervised image classiﬁcation method (Figure 3l). NDVI has been computed from satellite image (Figure 3m) using Equation (3): NIR Red NDVI = , (3) NIR + Red where NIR is the near-infrared band or band 8 and red band or band 4. The TWI directly aects the topographic conditions, which control the hydrological process. TWI is the function of slope and the upstream area per unit width orthogonal to the direction of ﬂow [35]. TWI plays a major role in the spatial heterogeneity of hydrological conditions such as soil moisture, underwater ﬂow and slope steady-state [32]. The TWI has been introduced by Beven and Kirkby [36]. TWI is calculated from Equation (4): TWI = In(A / tan ), (4) 2 1 where AS represents the cumulative area of the catchment (m m ) and is the slope gradient (degrees). The TWI value ranges from 1.11 to 21.54 (Figure 3n). The SPI is a calculation of water ﬂow erosive power based on the assumption that discharge is commensurate with a given catchment Remote Sens. 2019, 11, 3015 8 of 35 area [37]. One of the most important factors in controlling slope erosion processes is SPI. Regions with high stream power have high erosion potentiality [38]. From Equation (5), SPI has been calculated: SPI = A tan , (5) where A is the upstream contributing area and is slope gradient (in degrees). The spatial allocation of SPI ranges from 6.27 to 24.44 (Figure 3o) in the research area. TPI is deﬁned as the dierence between the middle point elevation (Z ) and the average elevation (Z) in a predetermined radius around it (R) [39]: TPI = Z Z, (6) Z = Z . (7) i2R The TPI has positive and negative value; a positive value demonstrates that the midpoint is located at a higher place than its average while a negative value indicates a lower place than the average. The TPI range depends not only on variations in altitude but also on landscape units (R) [40]. Where large R values mainly depend on the main units of landscape, and small R values show up lower valleys such as small valleys and ridges. The TPI value ranges from 12.16 to 14.67 in this plain (Figure 3p). Spatial resolutions of the selected GWDFs are not the same. For preparing the groundwater potential maps of the study area the resolution of PALSAR DEM, i.e., 12.5 m* 12.5 m has been selected as the base scale and all the GWCFs of which scale are greater or lesser than the PALSAR DEM have been resembled into a 12.5 m* 12.5 m resolution. The data layers of elevation (Figure 3a), slope (Figure 3b), CI (Figure 3c), rainfall (Figure 3e), Dd (Figure 3f), distance to river (Figure 3g), distance to fault (Figure 3h), distance to road (Figure 3i), TWI (Figure 3n), SPI (Figure 3p), TPI (Figure 3o), and NDVI (Figure 3m) have been categorized into ﬁve sub-classes using the natural break classiﬁcation method in GIS environment (Table 2). Aspect (Figure 3d), lithology (Figure 3j), soil type (Figure 3k), and LU/LC (Figure 3l) are the categorical factors. The categorical factors are also mentioned in Table 2. Table 1. Description of lithology units in the study area. Group Unit Description COm Dolomite platy and ﬂaggy limestone containing trilobite; sandstone and shale (MILA FM). Cl Dark red medium-grained arkosic to subarkosic sandstone and micaceous siltstone (LALUN FM). Yellowish, thin to thick-bedded, fossiliferous argillaceous limestone, dark grey limestone, greenish DCkh marl and shale, locally including gypsum Db Grey and black, partly nodular limestone with intercalations of calcareous shale (BAHRAM FM). E1s Sandstone, conglomerate, marl and sandy limestone. Ek Well bedded green tu and tuaceous shale (KARAJ FM). D Jl Light grey, thin-bedded to massive limestone (LAR FM). K2m,l Marl, shale and detritic limestone. K Cretaceous rocks in general. Murmg Gypsiferous marl. Murc Red conglomerate and sandstone. Plc Polymictic conglomerate and sandstone. PlQc Fluvial conglomerate, Piedmont conglomerate and sandstone. P Undierentiated Permian rocks. Pr Dark grey medium-bedded to massive limestone (RUTEH LIMESTONE). Qft2 Low level piedmont fan and valley terrace deposits. Qft1 High level piedmont fan and valley terrace deposits. Qcf Clay ﬂat. Qal Stream channel, braided channel and ﬂood plain deposits. I TRJs Dark grey shale and sandstone (SHEMSHAK FM). Remote Sens. 2018, 10, x FOR PEER REVIEW 10 of 37 Remote Sens. 2019, 11, 3015 9 of 35 Figure 3. Cont. Remote Sens. Remote Sens 2019, . 11 2018 , 3015 , 10, x FOR PEER REVIEW 11 of 10 37 of 35 Figure 3. Groundwater determining factors: (a) elevation, (b) slope, (c) aspect, (d) convergence index, (e) rainfall, Figure 3. Groundwater determining factors: (a) elevation, (b) slope, (c) aspect, (d) convergence index, (f) drainage density, (g) distance to river, (h) distance to fault, (i) distance to road, (j) lithology, (k) soil type, (l) (e) rainfall, (f) drainage density, (g) distance to river, (h) distance to fault, (i) distance to road, (j) land use/land cover (LULC), (m) normalized difference vegetation index (NDVI), (n) topographic wetness index lithology, (k) soil type, (l) land use/land cover (LULC), (m) normalized dierence vegetation index (TWI), (O) topographic position index (TPI), (p) stream power index (SPI). (NDVI), (n) topographic wetness index (TWI), (O) topographic position index (TPI), (p) stream power index (SPI). Remote Sens. 2019, 11, 3015 11 of 35 Table 2. Computation of statistics and classes of groundwater determining factors (GWDFs). Factors Min. Max. Classes Methods (1.) <1155, (2.) 1155 –1297, (3.) 1297–1512, (4.) Natural break Elevation (m) 1043 2869 1512–1993, (5.) >1993 (Jenks) (1.) <2.55, (2.) 2.55–9.35, (3.) 9.35–20.70, Natural break Slope (degree) 0 72.32 (4.) 20.70–34.03, (5.) >34.03 (Jenks) (1.) Flat (1), (2.) North (0–22.5), (3.) Northeast (22.5–67.5), (4.) East (67.5–112.5), (5.) Southeast Aspect - - (112.5–157.5), (6.) South (157.5–202.5), (7.) Directional units Southwest (202.5–247.5), (8.) West (247.5–292.5), (9.) Northwest (292.5–337.5) (1.) <59.21, (2.) 59.21—18.43, (3.) Natural break Convergence index -100 100 18.43–17.64, (4.) 17.64–57.64, (5.) >57.64 (Jenks) (1.) <132.95, (2.) 132.95–170.69, (3.) Natural break Rainfall (mm) 96 406 170.69–226.68, (4.) 226.68–305.81, (5.) >305.81 (Jenks) (1.) A, (2.) B, (3.) C, (4.) D, (5.) E, (6.) F, (7.) G, Lithological Lithology - - (8.) H, (9.) I Units (1.) Aridisols, (2.) Rock outcrops/entisols, Soil types/ Soil type - - (3.) Salt ﬂats Orders (1.) Bare land, (2.) Agriculture land, (3.) Supervised LULC - - Rangeland, (4.) Urban Classiﬁcation Drainage density (1.) <1.12, (2.) 1.12 –1.54, (3.) 1.54–1.88, Natural break 0.15 3.18 (km/km ) (4.) 1.88–2.24, (5.) >2.24 (Jenks) Distance to river (1.) <0.10, (2.) 0.10–0.21, (3.) 0.21–0.37, (4.) Natural break 0 1.35 (km) 0.37–0.57, (5.) >0.57 (Jenks) Distance to fault (1.) <2.20, (2.) 2.20–4.85, (3.) 4.85–7.75, Natural break 0 16.08 (km) (4.) 7.75–10.91, (5.) >10.91 (Jenks) Distance to road (1.) <2.78, (2.) 2.78–6.09, (3.) 6.09–9.91, Natural break 0 22.18 (km) (4.) 9.91–14.44, (5.) >14.44 (Jenks) (1.) <0.01, (2.) 0.01–0.07, (3.) 0.07–0.12, Natural break NDVI 0.24 0.54 (4.) 0.12–0.21, (5.) >0.21 (Jenks) (1.) <5.51, (2.) 5.51–7.44, (3.) 7.44–9.76, Natural break TWI 1.11 21.54 (4.) 9.76–13.21, (5.) >13.21 (Jenks) (1.) <2.06, (2.) 2.06–0.58, (3.) 0.58–0.56, Natural break TPI 12.16 14.67 (4.) 0.56–2.56, (5.) >2.56 (Jenks) (1.) <8.05, (2.) 8.05–9.83, (3.) 9.83–11.97, Natural break SPI 6.27 24.44 (4.) 11.97–14.89, (5.) >14.89 (Jenks) 2.4. Models 2.4.1. Weight of Evidence (WoE) Model The WoE model is the main Bayesian probability system model in linear logic form and uses non-conditional and conditional probabilities [41]. WoE reveals the spatial association between dependent variable, i.e., well locations and independent variables, i.e., GWDFs. The weight of each class has been assigned by this method using the following equations (Equations (8)–(14)) [42]: W = , (8) WoE S(C) C = W W , (9) i i P(B/D) W = In , (10) P(B/D) P(B/D) W = In , (11) P(B/D) 2 + 2 S(C) = S (W ) + S (W ), (12) 1 1 2 + S (W ) = + , (13) P(B/D) P(B/D) Remote Sens. 2019, 11, 3015 12 of 35 1 1 S (W ) = + , (14) P(B/D) P(B/D) where P(B|D) is the conditional probability of B occurring given the presence of D, B is the datasets of GWDFs related to the presence of groundwater well and B indicates the groundwater is absent of the datasets of groundwater conditioning factors. D indicates the presence of well while D stand for the absence of a well, and P is the probability. Whereas, W is a positive weight of GWDFs for groundwater occurrence. Conversely, W is a negative weight with respect to the absence of groundwater well (unfavorable factors). WoE computation has been started by the pixels counting process between groundwater well locations and GWDFs. The weighted GWDFs factors have been summed up in the raster calculation to generate the single layer of GWPM in the GIS environment using the following Equation (15). GWMP = (W Elevation) + (W Slope) + (W Aspect) + (W Convergence Index) WoE WoE WoE WoE WoE + (W Rainfall) + (W Drainage Density) + (W Distance to River)+ WoE WoE WoE (W Distance to Fault) + (W Distance to Road) + (W Lithology)+ WoE WoE WoE (W Soil Type) + (W LULC) + (W NDVI) + (W TWI)+ WoE WoE WoE WoE (W TPI) + (W SPI) WoE WoE (15) 2.4.2. Random Forest (RF) RF is the non-parametric multivariate model [43], which can be used for the analysis of regression and classiﬁcation and variable selections. RF model creates thousands of trees, forming a ‘forest’ based on the decision rule. Each tree in the RF model depends on a sample of bootstrapped of data using a CART process with a random subset of variables selected at each node. The ﬁnal decision of the class membership and model (output) has determined according to the majority priority of all decision trees [44]. The trees’ ensembles would have performed much better than a single tree. It is important to know that the program can be run by a large number of trees with taking large and too many computational requirements [45]. RF is a very reliable and ﬂexible ensemble classiﬁer, which depends upon the decision trees, that have so many attractive performances such a minimum costly, minimum tendencies for overﬁtting and also capability of the work with very high dimensional data [46]. The RF model is also a very fast machine learning solution, allowing a highly accurate classiﬁcation with internal unbiased generalizability estimation during the process of forest construction [47]. The basic merits of RF model arise when the program proceeds including (i) no need of any assumptions regarding the data distribution, (ii) no overﬁtting problem, (iii) in case of single tree, a low correlation estimated, while the diversity of forest increases the usages of a number of factors, (iv) helps to estimate negative or error using ‘out-of-bag’(OOB) data, (v) averages a large number of trees, resulting the low bias and low variance, subsequently, (f), resulting in the excellent prediction for performances [43,48]. Besides, the numerical and categorical data can be incorporated in the RF model. Using the OOB error-index, the variance and covariance between the grids cells can be estimated [48]. The predication values of this model are estimated by the huge amount of decision trees [43]. The presence and absence groundwater wells among the GWDFs can easily be estimated by RF model. In this algorithm, the mean decrease accuracy and Gini are estimated by the RF model to analysis the variable importance of the GWDFs [30]. This algorithm calculates untouched the proper count, the amount of correct classiﬁcation applying the data out-of-bag as its test sample. In the out-of-bag instances, the values of the attributes are then randomly permuted. A new set of data will then be checked for proper classiﬁcation. The average of this number is the raw importance score for the speciﬁc attribute over all trees in the forest. Therefore, factors importance in RF model is computed for variable Yi by out of bag error (OOB) [49]. Factors importance of Yi can be calculated using the Equation (16): VImp(Y ) = errOOB errOOB , (16) ntree Remote Sens. 2019, 11, 3015 13 of 35 where ntree stands for the number of trees, VImp(Yi) denotes variable importance for variable Yj, errOOB is an error when all the factors are included, and errOOB denotes an error after the removal of the variable j. The Gini index was used to measure the variable signiﬁcance based on the number of times that variable is picked by all trees [47,50]. In this study, the ‘randomForest’ package in R program has been installed and run the RF model for estimating the GWPZ [51]. Finally, the RF model-based GWPM has been produced in the GIS environment. 2.4.3. Binary Logistic Regression (BLR) BLR model is the most common statistical model which considers both dichotomous and continuous variables. However, the practical dependent variable must be in binary form, i.e., 1 and 0. Where, 0 represents the absence of groundwater well and 1 stands for the presence of the groundwater well [37,52]. For GWPM, it corresponds with the Bernoulli method, which determines the high groundwater potentiality over space depending on the Bernoulli probability [32]. The main target of the BLR analysis is to chalk out the correct and appropriate prediction of samples and probe the correlation between a dependent variable with a set of independent variables [32]. Among the dierent methods of the regressions, the BLR is ﬁtting a logistic curve or function concerning data. As a result, BLR estimates the values that vary from 0 to 1, while 1 means the presence of groundwater well, conversely 0 means the chances of occurrence of groundwater well is nil. In this method, the target value is calculated using Equation (17): ( ) Y = Logit P = Ln = C + C X + C X + ::::::::: C X , (17) 0 1 1 2 2 n n 1 p where Logit is the link function, P is the probability of occurrence of groundwater well (y), p = 1 p are the odds of groundwater occurrence (or probability of presence divided by the probability of absence) the, C0 is the model intercept and (C1, ::: , Cn) are the regression coecients for each GWCF (X1, ::: , Xn) [32]. In this contribution, the BLR model has been applied in R by using the ‘glm’ function based on the “stats” package [32]. In this study, the random point’s values have been extracted from each variable of GWCFs for presence and absence condition of the groundwater. Finally, GWPM by BLR model has been produced in GIS with regarding the prediction database. 2.4.4. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) The TOPSIS method was introduced by Hwang and Yoon [53]. Presently, it is an important multi-criteria decision approach among the several MCDA processes utilized for water management practices [54]. This approach relies on the premise that the best alternative solution should have the shortest distance Euclidean from the positive ideal solution and the longest distance from the negative solution [32]. The ideal solution in GWPM is the best model to distinguish between groundwater well presences and absences. TOPSIS is a method that cannot understand categorical properties [55]. That is why the AHP has been used to assign the weight to each GWDF. The computation of the entire TOPSIS model was carried out step by step as follows: Step 1: Preparation of a decision matrix with m criteria and n alternatives using Equation (18): 2 3 a a a 6 11 12 1n 7 6 7 6 7 6 7 6 7 a a a 6 22 7 21 1n 6 7 A = 6 7. (18) ij 6 7 6 7 . . . . 6 7 6 7 4 5 a a a m2 mn m1 Step 2: Normalization of decision matrix using Equation (19): ij r = q , (19) ij i=1 ij Remote Sens. 2019, 11, 3015 14 of 35 where i = 1, ::: , m; j = 1 ::: n. Step 3: Determine the weight of criteria using the AHP model: AHP, ﬁrst implemented by Saaty [56] is one of the most comprehensive MDCA approaches. This method assists decision-makers in receiving quantitative and qualitative parameters. The pairwise comparisons help for the judgment and computation of GWCFs [57]. After preparing paired comparisons, the resulting paired comparison matrix is normalized using Equation (20) and then the ﬁnal weight (W ) of each parameter is obtained using Equation (21). ij r = q , (20) ij ij i=1 ij i=1 W = . (21) One of the advantages of this method is to show the inconsistency [58]. To assess the degree of weighting precision, an Inconsistency Index is used. The consistency test shows how much trust can be put in the priorities of a matrix. If this value is >0.1, this means that it is not consistent with the speciﬁed weights and should be checked. Inconsistency ratio is often being used to calculate the Inconsistency in judgments, Equations (22) and (24) have been used for its calculation: I.I IR = , (22) I.I.R max n I.I = , (23) n 1 a W 1 (i,j) = , (24) max n W (i,j) i=1 where IR refers to the inconsistency ratio, I.I. is an inconsistency index, n is the number of criteria, a is the geometric mean of matrix and W is weight vector. (i,j) Step 4: Calculation of the weighted normalized decision matrix using Equation (25): V = r W , (25) ij ij j where W represents the weight of the criteria. Step 5: Calculation of the positive and negative ideal solution using Equations (26) and (27), respectively: n o + < A = maxV /j 2 J , minV /j 2 J i = 1, 2,::: .m ij ij , (26) + + + + = V , V ,::: , V ,::: , V 1 2 j n o A = minV /j 2 J , maxV /j 2 J i = 1, 2,::: .m ij ij n o (27) = V , V ,::: , V ,::: , V 1 2 j where, j and J’ are related to increasing and decreasing criteria, respectively, where J is associated with the positive criteria and J’ is associated with the negative criteria. Step 6: Calculation of the distance from the positive and negative ideal solution using Equations (28) and (29), respectively: d = V V ; i = 1, 2,::: ., m, (28) i+ ij j=1 d = V V ; i = 1, 2,::: ., m. (29) i ij j=1 Remote Sens. 2019, 11, 3015 15 of 35 Step 7: Calculation of the relative closeness to the ideal solution using Equation (30): cl = ; 0 cl 1; i = 1, 2,::: , m, (30) i+ i+ d + d i+ i where cl is the closeness coecient, di+ is a positive ideal solution (PIS), and d is negative ideal i+ i solution (NIS). The value of cl ranges between 0 and 1. The larger the cl value indicates the better the i+ i+ performance of the alternatives. In this contribution, to perform the Mathematical calculation, 500 points have been randomly selected and derived the values of GWDFs for each point, then a table was made, consisting of 16 GWDFs columns and 500 rows. Subsequently, these values have entered into SPSS and done the process. Ultimately, the TOPSIS based GWPM has been prepared considering the point values using the IDW method in the GIS environment. 2.4.5. Support Vector Machine (SVM) SVM is the supervised learning system of machine learning associated with learning algorithms that analyze the data used for classiﬁcation and regression analysis. It is developed by Bai et al. [59]. SVM helps in the transformations of nonlinear covariates into a higher dimensional feature space [60]. SVM is also a statistical learning theory associated with a training phase in which a training dataset of related input and target output values trains the model. The trained model will then be used to analyze a separate set of test data. SVM has two main underlying concepts for discriminating the problems, i.e., the optimum linear separating hyper-plane that separates patterns of data, and another is the kernel functions that convert the original nonlinear data pattern to a linearly separable format in a high-dimensional feature space [60]. A set of linear separable training vectors x (i = 1, 2, ::: , n) consists of two classes, which are denoted as y = 1. The SVM’s goal is to ﬁnd an n-dimensional hyperplane that dierentiates the two groups by the total distance. Mathematically, it can be minimized as: kwk , (31) Subject to the following constraints: y = ((wx ) + b) 1, (32) i i where kwk is the norm of the normal hyper-plane, b is a scalar base, and (wx ) denotes the scalar product operation. Introducing the Lagrangian multiplier, the cost function can be deﬁned as: L = kwk (y ((wx ) + b) 1), (33) i i i i=1 where is the Lagrangian multiplier. It is possible to achieve the solution by double minimizing Equation (32). The standard procedures for w and b and detailed discussions can be found in Vapnik [61], Tax and Duin [62] and Yao et al. [60]. For non-separable case, one can change the constraints by setting up slack variables : y ((wx ) + b) 1 . (34) i i i Equation (32) will be modiﬁed as: 1 1 L = kwk , (35) 2 n i=1 Remote Sens. 2019, 11, 3015 16 of 35 where [0, 1] was introduced to account for misclassiﬁcation [63]. Besides, a kernel function K (x , x ) i j was introduced by Vapnik [61] to account for the nonlinear decision boundary [63]. The two-class SVM method was used in this study because it was reported that Yao et al. [60] produced a more accurate map of susceptibility from the two classes of SVM. That’s why Radial Basis Function (RBF) was used for kernel in this study and the two-class SVM model was ﬁrst trained and then used to construct a GWPM. In this method, 1 and 0 values indicate the positive and negative relationship of groundwater occurrence. To perform the GWP mapping using the SVM, we used the ENVI 4.3. The default RBF kernel, which works well in most cases, has been used. In addition, in many studies and cases (especially in nonlinear problems), RBF provides better prediction results compared to other kernels [64]. Finally, the GWPM by SVM has been produced in the GIS. 2.5. Validation of Models In this study, to analyze the potentiality and performance of the selected models, we have used two thresholds dependent methods i.e., ROC curve and SCAI. The ROC curve and SCAI are the signiﬁcant and accurate justiﬁcation methods of dierent models [65]. For this purpose, 30% validation and 70% training datasets have been considered by the ROC curve and SCAI methods (11). The area under curve (AUC) of the ROC method range between 0.5 to 1. If the value is nearest to 1, it indicates excellent prediction accurateness of the models [66]. The accuracy value that is AUC of the ROC is mentioned in Table 3. The AUC values have been calculated using the Equation (36). In the case of SCAI method, if the sub-class values of models decrease from very low to very high sub-classes, it indicates that models are suitable and acceptable [67]. P P TP+ TN AUC = . (36) P + N Table 3. Area under curve (AUC) values and statements. AUC Values Accuracy Statements 0.5–0.6 Low 0.6–0.7 Moderate 0.7–0.8 High 0.8–0.9 Very high 0.9–1 Excellent Source: Yesilnacar [66]. We also used ﬁve statistical techniques in this analysis to test models’ performance, including SE, SP, AC, MAE, and RMSE. Based on four possible consequences i.e., true positive (TP), false positive (FP), true negative (TN) and false negative (FN), sensitivity (Equation (37)), speciﬁcity (Equation (38)) and accuracy (Equation (39)) have been measured: TP and FP are the counts of well pixel that are correctly identiﬁed as well pixel and non-well pixel, respectively. On the other hand, TN and FN are the numbers of well pixel which are correctly classiﬁed and incorrectly classiﬁed as non-well class. SE is the ratio of the number of well pixels properly classiﬁed to the total number of well pixels predicted. SP is the ratio between the number of well pixels wrongly classiﬁed and the total non-well pixels predicted. AC is the ratio between the number of properly classiﬁed well and non-well pixels. MAE (Equation (40)) and RMSE (Equation (42)) indices have been considered to assess the disparity between the observed and predicted data. The high values of Sensitivity, Speciﬁcity, and Accuracy and low value of MAE and RMSE value indicate the good capability of the models [68–72]. The following ﬁve formulas have been used for statistical measures. TP SE = , (37) TP + FN Remote Sens. 2019, 11, 3015 17 of 35 TN SP = , (38) TN + FP TP + TN AC = , (39) TP + TN + FP + FN MAE = X X , (40) predicted actual i=1 RMSE = (X X ) , (41) predicted actual i=1 where X and X is the predicted and real values in the training dataset or testing dataset of predicted actual the groundwater potentiality models and n is the total number of samples in the training data set or testing dataset. 2.6. Sensitivity Analysis (SA) It is very dicult to completely remove the uncertainty in the preparation of data layers [73–75]. Refsgaard et al. [75] was used dierent techniques e.g., Monte Carlo analysis, error propagation equations, sensitivity analysis (SA), scenario analysis, etc. for measuring the uncertainty. Sensitive analysis has been used in various studies [75–77] for the measurement of the eect of variable variations on model outputs, allowing then a quantitative assessment of the relative importance of uncertainty sources. In the present study, map removal sensitivity analysis (MRSA) method has been used, which was developed by Lodwick et al. [78]. The MRSA method would help to evaluate the sensitivity of the groundwater potentiality maps by removing one or more parameters from the groundwater potentiality maps. This technique has been used by several researchers to address the signiﬁcant role of the eective factors [79–81]. It helps to identify the quantitative contribution of each groundwater conditioning factor to the uncertainty of the model output [72,82]. The percentage of contribution (PC) of each groundwater conditioning factor has been estimated by the MRSA method to explore the relative importance on the model output using the following Equation (42) [83]: (AUC AUC ) all i PC = 100, (42) AUC where AUC and AUC indicate the AUC values obtained from modeling groundwater potential all i model using all GWDFs and the model when the ith GWDF has been excluded. 3. Results 3.1. Analyzing the Multi-Collinearity (MC) of Groundwater Determining Factors The MC problem reduces some linear models’ predictive accuracy [84]. Techniques were applied in this study to assess the MC problem between GWDFs, namely tolerance (TOL) and inﬂation factor variance (VIF) [85]. Tolerance values of <0.1 and VIF of <10 reveal no MC problem among the GWDFs [86]. Roy and Saha [87] and Arabameri et al. [32] were used the MC test for the landslide susceptibility and groundwater potentiality mapping. The selected 16 GWDFs have been tested by SPSS. No MC problem has been found among the GWDFs, as no one value of tolerance and VIF does exceed the threshold limit (Table 4). Therefore, the selected GWDFs are suitable for the prediction of groundwater potentiality. Here, maximum tolerance and VIF values are 0.91 and 5.91 (Table 4). Remote Sens. 2019, 11, 3015 18 of 35 Table 4. Multi-collinearity test of groundwater conditioning factors. Collinearity Statistics Conditioning Factors Tolerance VIF Elevation 0.281 4.275 Slope 0.256 3.908 Convergence Index 0.816 1.226 Rainfall 0.202 4.792 Drainage Density 0.542 1.846 Distance to River 0.855 1.170 Distance to Fault 0.527 1.897 Distance to Road 0.485 2.061 NDVI 0.704 1.420 TWI 0.201 4.911 TPI 0.891 1.122 SPI 0.202 4.713 Aspect 0.916 1.092 Lithology 0.580 1.724 LULC 0.612 1.634 Soil Type 0.492 2.032 3.2. Application of the Weight of Evidence (WoE) Groundwater potentiality reclines on the positive and negative eects of the eective groundwater determining factors. The positive value of WoE indicates the chances of storage of groundwater and vice-versa. The zero value of WoE means the sub-class of factors has no role in determining the groundwater occurrence [88]. The results of WoE model have been put in Table 5. The low altitudinal zone is more potential for the accumulation of groundwater than abrupt slope and higher altitudinal areas due to the high inﬁltration rate and less surface runo [89]. For elevation, 1043–1155 m altitude with a value of 4.88 is showing the strongest positive eects among these GWDFs in making the areas potential to groundwater. On the contrary, the others sub-layers such as 1155–1297 m (WoE = 3.05), 1297–1512 m (WoE = 0), 1512–1993 m (WoE = 0), and >1993 m (WoE = 0) altitudinal levels are representing the negative and less eect in the presence of the groundwater (Table 5). Among the ﬁve slope classes, the <2.55-degree class has the maximum value of WoE i.e., 2.97 which depicts the strong control on the occurrence of groundwater. On the other hand, the remaining four sub-classes of slope have no control over the groundwater at all (Table 5). The north-east aspect has the highest WoE value (WoE = 1.84), which indicates the strong positive eects on the storage of groundwater. CI is the parameters of topography that reﬂect the elevation as a collection of convergent (channel) and divergent (ridge) areas. The CI value ranges from +100 to100. Among the ﬁve classes, the two sub-class of CI such as <59.21 (WoE = 2.02) and >57.64 (WoE = 2.02) has the strongest positive relationship, while others sub-layers have a negative relationship with groundwater storage (Table 5). Rainfall is an important groundwater potentiality determining factor. Rainfall classes <132 mm (WoE = 2.47) and 132 mm–170 mm (WoE = 0.40) have the strongest positive relationship. Lithologoically, the region is composed of nine geological regions, namely A, B, C, D, E, F, G, H, and I. Only the H geological region (quaternary sediments) with WoE of 2.64 has a strong positive eect on the groundwater formation. Among the GWDFs, the soil is of crucial part in the groundwater recharge. Pedologically, the region is composed of three soil orders i.e., aridisols, entisols or rock outcrops, and salt ﬂats. Comparatively, aridisols have a great contribution (WoE = 3.50) in the storage of groundwater. The LU/LC are categories into four types namely rangeland, bare land, agriculture and urban. Only agriculture land with WoE = 8.80 has a strong positive relationship, indicating the high potential of groundwater comparatively the bare land, urban and rangeland areas. Among the other GWDFs, the sub-classes of 1.88–2.24 km/km (WoE = 1.62) of drainage density, <0.10 km (WoE = 0.74) of distance to river, 7.75 –10.91km (WoE = 3.25) of distance to fault, 2.78–6.09km (WoE = 2.25) of distance to road, 0.12–0.21 (WoE = 6.08) of NDVI, Remote Sens. 2019, 11, 3015 19 of 35 5.51–7.44 (WoE = 1.69) of TWI,0.58–0.56 (WoE = 1.44) of TPI and <8.05 (WoE = 1.60) of SPI have the strong positive inﬂuence on the recharge of groundwater (Table 5). Subsequently, weights have been assigned to the sub-layers of GWDFs and converted as weighted WoE layers. All weighted GWDFs have been summed up and generated a single layer of GWPM (Figure 4c). The prepared GWPM has been classiﬁed into four categories i.e., low, medium, high and very high potential zones with the help of the natural break classiﬁcation method (Figure 4c). The results of GWMP by WoE model are showing that only 297.33 km (15.46%) area is of very high groundwater potentiality, followed by the 2 2 2 583.90 km (30.36%) for high, 617.37 km (32.1%) for medium and 424.85 km (22.09%) for low GWPZs (Table 6 and Figure 5). Table 5. The spatial relation between conditioning factors and well locations by weight of evidence model. % of % of Elevation (m) Pixels Well W+ W C S2W+ S2W S© C/S© Pixel Well <1043–1155 855,560 49.36 53 94.64 0.65 2.25 2.90 0.02 0.33 0.59 4.88 1155–1297 446,173 25.74 3 5.36 1.57 0.24 1.81 0.33 0.02 0.59 3.05 1297–1512 303,221 17.50 0 0.00 0.00 0.19 0.00 0.00 0.02 0.00 0.00 1512–1993 101,149 5.84 0 0.00 0.00 0.06 0.00 0.00 0.02 0.00 0.00 >1993 27,036 1.56 0 0.00 0.00 0.02 0.00 0.00 0.02 0.00 0.00 Slope (degree) <2.55 126,724,5 73.12 55 98.21 0.30 2.71 3.01 0.02 1.00 1.01 2.98 2.55–9.35 335,864 19.38 1 1.79 2.38 0.20 2.58 1.00 0.02 1.01 2.56 9.35–20.70 638,68 3.69 0 0.00 0.00 0.04 0.00 0.00 0.02 0.00 0.00 20.70–34.03 44,815 2.59 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 >34.03 21,347 1.23 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 Aspect F 82,884 4.78 3 5.36 0.11 0.01 0.12 0.33 0.02 0.59 0.20 N 89,279 5.15 3 5.36 0.04 0.00 0.04 0.33 0.02 0.59 0.07 NE 154,448 8.91 9 16.07 0.59 0.08 0.67 0.11 0.02 0.36 1.85 E 296,877 17.13 10 17.86 0.04 0.01 0.05 0.10 0.02 0.35 0.14 SE 431,538 24.90 8 14.29 0.56 0.13 0.69 0.13 0.02 0.38 1.80 S 359,878 20.76 12 21.43 0.03 0.01 0.04 0.08 0.02 0.33 0.12 SW 167,965 9.69 7 12.50 0.25 0.03 0.29 0.14 0.02 0.40 0.71 W 853,21 4.92 3 5.36 0.08 0.00 0.09 0.33 0.02 0.59 0.15 NW 64,949 3.75 1 1.79 0.74 0.02 0.76 1.00 0.02 1.01 0.75 Convergence Index <59.21568627 145,566 8.40 9 16.07 0.65 0.09 0.74 0.11 0.02 0.36 2.02 59.21–18.43 368,782 21.28 14 25.00 0.16 0.05 0.21 0.07 0.02 0.31 0.68 18.43–17.64 707,982 40.85 14 25.00 0.49 0.24 0.73 0.07 0.02 0.31 2.36 17.64–57.64 364,974 21.06 10 17.86 0.16 0.04 0.20 0.10 0.02 0.35 0.59 >57.64 145,835 8.41 9 16.07 0.65 0.09 0.73 0.11 0.02 0.36 2.02 Rainfall (mm) <132 429,194 24.76 22 39.29 0.46 0.21 0.68 0.05 0.03 0.27 2.47 132–170 100,66,02 58.08 34 60.71 0.04 0.06 0.11 0.03 0.05 0.27 0.40 170–226 166,770 9.62 0 0.00 0.00 0.10 0.00 0.00 0.02 0.00 0.00 226–305 77,365 4.46 0 0.00 0.00 0.05 0.00 0.00 0.02 0.00 0.00 >305 53,208 3.07 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 Lithology A 7093 0.41 0 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 B 35,899 2.07 0 0.00 0.00 0.02 0.00 0.00 0.02 0.00 0.00 C 57,180 3.30 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 D 72,339 4.17 0 0.00 0.00 0.04 0.00 0.00 0.02 0.00 0.00 E 23,837 1.38 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 F 24,485 1.41 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 G 86,958 5.02 2 3.57 0.34 0.02 0.36 0.50 0.02 0.72 0.49 H 138,8009 80.09 54 96.43 0.19 1.72 1.90 0.02 0.50 0.72 2.64 I 37,340 2.15 0 0.00 0.00 0.02 0.00 0.00 0.02 0.00 0.00 Aridisols 118,6872 68.48 54 96.43 0.34 2.18 2.52 0.02 0.50 0.72 3.50 Rock Outcrops/Entisols 392,588 22.65 0 0.00 0.00 0.26 0.00 0.00 0.02 0.00 0.00 Salt Flats 153,679 8.87 2 3.57 0.91 0.06 0.97 0.50 0.02 0.72 1.34 Remote Sens. 2019, 11, 3015 20 of 35 Table 5. Cont. % of % of Elevation (m) Pixels Well W+ W C S2W+ S2W S© C/S© Pixel Well LULC Bareland 654,072 37.74 4 7.14 1.66 0.40 2.06 0.25 0.02 0.52 3.98 Agriculture 206,538 11.92 52 92.86 2.05 2.51 4.57 0.02 0.25 0.52 8.80 Rangeland 777,361 44.85 0 0.00 0.00 0.60 0.00 0.00 0.02 0.00 0.00 Urban 95,167 5.49 0 0.00 0.00 0.06 0.00 0.00 0.02 0.00 0.00 Drainage Density (km/square km) <1.12 125,010 7.21 0 0.00 0.00 0.07 0.00 0.00 0.02 0.00 0.00 1.12–1.54 360,107 20.78 6 10.71 0.66 0.12 0.78 0.17 0.02 0.43 1.81 1.54–1.88 480,396 27.72 19 33.93 0.20 0.09 0.29 0.05 0.03 0.28 1.03 1.88–2.24 452,295 26.10 20 35.71 0.31 0.14 0.45 0.05 0.03 0.28 1.62 >2.24 315,331 18.19 11 19.64 0.08 0.02 0.09 0.09 0.02 0.34 0.28 Distance to River (km) <0.10 629,316 36.31 23 41.07 0.12 0.08 0.20 0.04 0.03 0.27 0.74 0.10–0.21 519,863 30.00 19 33.93 0.12 0.06 0.18 0.05 0.03 0.28 0.64 0.21–0.37 360,248 20.79 9 16.07 0.26 0.06 0.32 0.11 0.02 0.36 0.87 0.37–0.57 170,585 9.84 4 7.14 0.32 0.03 0.35 0.25 0.02 0.52 0.67 >0.57 53,127 3.07 1 1.79 0.54 0.01 0.55 1.00 0.02 1.01 0.55 Distance to Fault (km) <2.20 634,007 36.58 7 12.50 1.07 0.32 1.40 0.14 0.02 0.40 3.45 2.20–4.85 339,860 19.61 12 21.43 0.09 0.02 0.11 0.08 0.02 0.33 0.34 4.85–7.75 295,667 17.06 14 25.00 0.38 0.10 0.48 0.07 0.02 0.31 1.56 7.75–10.91 272,734 15.74 18 32.14 0.71 0.22 0.93 0.06 0.03 0.29 3.25 >10.91 190,871 11.01 5 8.93 0.21 0.02 0.23 0.20 0.02 0.47 0.50 Distance to Road (km) <2.78 584,777 33.74 22 39.29 0.15 0.09 0.24 0.05 0.03 0.27 0.88 2.78–6.09 503,128 29.03 24 42.86 0.39 0.22 0.61 0.04 0.03 0.27 2.25 6.09–9.91 341,304 19.69 8 14.29 0.32 0.07 0.39 0.13 0.02 0.38 1.01 9.91–14.44 216,429 12.49 2 3.57 1.25 0.10 1.35 0.50 0.02 0.72 1.87 >14.44 87,501 5.05 0 0.00 0.00 0.05 0.00 0.00 0.02 0.00 0.00 NDVI <0.01 946 0.05 0 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.0–0.07 995,879 57.46 8 14.29 1.39 0.70 2.09 0.13 0.02 0.38 5.48 0.07–0.12 614,296 35.44 28 50.00 0.34 0.26 0.60 0.04 0.04 0.27 2.24 0.12–0.21 95,540 5.51 15 26.79 1.58 0.26 1.84 0.07 0.02 0.30 6.08 >0.21 26,478 1.53 5 8.93 1.77 0.08 1.84 0.20 0.02 0.47 3.93 TWI <5.51 315,821 18.22 0 0.00 0.00 0.20 0.00 0.00 0.02 0.00 0.00 5.51–7.44 793,998 45.81 32 57.14 0.22 0.23 0.46 0.03 0.04 0.27 1.69 7.44–9.76 391,225 22.57 14 25.00 0.10 0.03 0.13 0.07 0.02 0.31 0.43 9.76–13.21 174,040 10.04 8 14.29 0.35 0.05 0.40 0.13 0.02 0.38 1.05 >13.21 58,055 3.35 2 3.57 0.06 0.00 0.07 0.50 0.02 0.72 0.09 <2.06 11,457 0.66 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 2.06–0.58 55,078 3.18 0 0.00 0.00 0.03 0.00 0.00 0.02 0.00 0.00 0.58–0.56 160,7635 92.76 55 98.21 0.06 1.40 1.46 0.02 1.00 1.01 1.44 0.56–2.56 47,227 2.72 1 1.79 0.42 0.01 0.43 1.00 0.02 1.01 0.43 >2.56 11,742 0.68 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 SPI <8.05 538,726 31.08 23 41.07 0.28 0.16 0.44 0.04 0.03 0.27 1.60 8.05–9.83 595,727 34.37 20 35.71 0.04 0.02 0.06 0.05 0.03 0.28 0.21 9.83 11.97 329,339 19.00 6 10.71 0.57 0.10 0.67 0.17 0.02 0.43 1.55 11.97–14.89 171,410 9.89 4 7.14 0.33 0.03 0.36 0.25 0.02 0.52 0.69 >14.89 95,996 5.54 3 5.36 0.03 0.00 0.04 0.33 0.02 0.59 0.06 Remote Sens. 2018, 10, x FOR PEER REVIEW 23 of 37 >2.56 11,742 0.68 0 0.00 0.00 0.01 0.00 0.00 0.02 0.00 0.00 SPI <8.05 538,726 31.08 23 41.07 0.28 -0.16 0.44 0.04 0.03 0.27 1.60 8.05–9.83 595,727 34.37 20 35.71 0.04 -0.02 0.06 0.05 0.03 0.28 0.21 9.83- 11.97 329,339 19.00 6 10.71 -0.57 0.10 -0.67 0.17 0.02 0.43 -1.55 11.97–14.89 171,410 9.89 4 7.14 -0.33 0.03 -0.36 0.25 0.02 0.52 -0.69 Remote Sens. 2019, 11, 3015 21 of 35 >14.89 95,996 5.54 3 5.36 -0.03 0.00 -0.04 0.33 0.02 0.59 -0.06 Figure 4. Groundwater potentiality maps showing: (a), binary logistic regression (BLR); (b), technique Figure 4. Groundwater potentiality maps showing: (a), binary logistic regression (BLR); (b), technique for order preference by similarity to ideal solution (TOPSIS); (c), weight of evidence (WoE); (d), for order preference by similarity to ideal solution (TOPSIS); (c), weight of evidence (WoE); (d), random random forest (RF); (e), support vector machine (SVM). forest (RF); (e), support vector machine (SVM). Remote Sens. 2019, 11, 3015 22 of 35 Table 6. Areal distribution of groundwater potentiality maps. Models Potentiality Classes Area in Square km % of Area Low 446.1995 23.2 Medium 787.3882 40.94 TOPSIS High 399.4639 20.77 Very high 290.222 15.09 Low 424.8511 22.09 Medium 617.3708 32.1 WoE High 583.9059 30.36 Very high 297.3381 15.46 Low 1064.34 55.34 Medium 198.6742 10.33 RF High 174.4409 9.07 Very high 485.8189 25.26 Low 744.3069 38.7 Medium 594.4839 30.91 BLR High 286.9524 14.92 Very high 297.5304 15.47 Low 248.6793 12.93 Medium 569.0967 29.59 SVM High 744.8839 38.73 Very high 360.4215 18.74 3.3. Application of Random Forest (RF) Model The RF model has been used in the present study to identify GWPZ. For carrying out the RF model, the point values based on well and non-well locations have been derived from GWDFs. The out-of-bag (OOB) of RF model is 3.32% (Table 7). The results depict that elevation (385.72), rainfall (281.63), drainage density (152.98), distance to fault (258.36), NDVI (262.47), distance to the road (189.28) and LULC (137.42) factors have great contribution in the RF process (Figure 6). Conversely, factors such as lithology, soil type and convergence index have a tiny role in the RF process. Finally, GWPM by RF model has been prepared and classiﬁed into four classes such as low, medium, high and very GWPZs (Figure 4d). According to the GWPM, only 485.81 km (25.26%) areas have very high groundwater potentiality. Other potentiality zones such as high, medium and low GWPZs are covered 9.07%, by 10.33% and 55.34% of the study area respectively (Table 6) Table 7. Confusion matrix from random forest model (0 = non-well or negative, 1 = well or positive). Predicted Observation Class Error OOB (%) 0 1 0 8273 149 0.018 3.32 1 180 1319 0.120 Remote Sens. 2018, 10, x FOR PEER REVIEW 24 of 37 Remote Sens. 2019, 11, 3015 23 of 35 Figure 5. Areal distribution of groundwater potentiality maps. Figure 5. Areal distribution of groundwater potentiality maps. Remote Sens. 2018, 10, x FOR PEER REVIEW 26 of 37 Remote Sens. 2019, 11, 3015 24 of 35 Figure 6. Determining the weight of conditioning factors using random forest (RF). Figure 6. Determining the weight of conditioning factors using random forest (RF). 3.4. Application of Binary Logistic Regression (BLR) The BLR probabilistic model has been used for GWPZ estimation. The point base data for well 3.4. Application of Binary Logistic Regression (BLR) and non-well locations have been extracted from each GWDF. Here, BLR is expressed with binary value, i.e., 0 and 1. 1 means that the presence of well and 0 means absence of well. The coecients of The BLR probabilistic model has been used for GWPZ estimation. The point base data for well regression values have been obtained by the BLR. The results of BLR (Table 8) show that slope (0.577), and non-well locations have been extracted from each GWDF. Here, BLR is expressed with binary soil type (6.808), lithology (2.553) and LULC (2.2942) have the reciprocal and positive impacts on the value, i.e., 0 and 1. 1 means that the presence of well and 0 means absence of well. The coefficients of occurrence of groundwater. Among the GWCFs, elevation (0.0237), convergence index (0.0029), rainfall regression values have been obtained by the BLR. The results of BLR (Table 8) show that slope (0.577), (0.0131), distance to fault (0.0001), distance to road (0.0002), TWI (0.2892) and TPI (0.0426) have less soil type (6.808), lithology (2.553) and LULC (2.2942) have the reciprocal and positive impacts on the importance for the formation of groundwater. Conversely, Dd, distance to the river, NDVI and SPI occurrence of groundwater. Among the GWCFs, elevation (0.0237), convergence index (0.0029), have negative impacts on the groundwater occurrence. Afterward, the weights have been assigned to rainfall (0.0131), distance to fault (0.0001), distance to road (0.0002), TWI (0.2892) and TPI (0.0426) GWCFs by BLR. Finally, GWPM by BLR has been built and categorized into four categories such as low, have less importance for the formation of groundwater. Conversely, Dd, distance to the river, NDVI medium, high and very high GWPZs using the natural break method. According to this classiﬁcation, and SPI have negative impacts on the groundwater occurrence. Afterward, the weights have been 15.47% of the Damghan plain has very high groundwater potentiality, followed by 38.7%, 30.91%, and assigned to GWCFs by BLR. Finally, GWPM by BLR has been built and categorized into four 14.92% for low, moderate and high GWPZs (Figure 4a and Table 6). categories such as low, medium, high and very high GWPZs using the natural break method. According to this classification, 15.47% of the Damghan plain has very high groundwater potentiality, followed by 38.7%, 30.91%, and 14.92% for low, moderate and high GWPZs (Figure 4a and Table 6). Remote Sens. 2018, 10, x FOR PEER REVIEW 27 of 37 Remote Sens. 2019, 11, 3015 25 of 35 Table 8. Determining the weight of conditioning factors using logistic regression. Table 8. Determining the weight of conditioning factors using logistic regression. Parameters Weight Parameters Weight Elevation 0.0237 Elevation 0.0237 Slope 0.5778 Slope 0.5778 CI 0.0029 CI 0.0029 Rainfall 0.0131 Rainfall 0.0131 Drain Drainage age Density Density 1.739−1.739 Distance to River 0.0008 Distance to River −0.0008 Distance to Fault 0.0001 Distance to Fault 0.0001 Distance to Road 0.0002 Distance to Road 0.0002 NDVI 7.633 NDVI −7.633 TWI 0.2892 TWI 0.2892 TPI 0.0426 TPI 0.0426 SPI 0.1487 SPI −0.1487 Aspect 1.3488 Aspect −1.3488 Lithology 2.5531 Lithology 2 LULC 2.2942.5531 Soil types 6.8088 LULC 2.2942 Soil types 6.8088 3.5. Application of TOPSIS The TOPSIS an important MDCA approach used to delineate the GWPZs. In this research, 500 3.5. Application of TOPSIS points were selected randomly and extracted point values from GWCFs. The AHP is an important The TOPSIS an important MDCA approach used to delineate the GWPZs. In this research, 500 knowledge-driven MDCA model, used to assign weights to GWCFs for performing the TOPSIS model. points were selected randomly and extracted point values from GWCFs. The AHP is an important The weights of GWCFs are 0.082 (elevation), 0.088 (slope), 0.057 (aspect), 0.058 (convergence index), knowledge-driven MDCA model, used to assign weights to GWCFs for performing the TOPSIS 0.092 (rainfall), 0.067 (drainage density), 0.063 (distance to river), 0.070 (distance to fault), 0.059 (distance model. The weights of GWCFs are 0.082 (elevation), 0.088 (slope), 0.057 (aspect), 0.058 (convergence to index) road), , 0. 0.063 092 (r(lithology), ainfall), 0.067 (dr 0.050 ain(soil age dty ensi pe), ty), 0. 0.060 063 (di (LULC), stance to 0.061 river), (NDVI), 0.070 (di0.045 stance to (TWI), fault)0.04(TPI) , 0.059 and (distance to road), 0.063 (lithology), 0.050 (soil type), 0.060 (LULC), 0.061 (NDVI), 0.045 (TWI), 0.045 (SPI) (Figure 7). The weights of GWCFs by AHP and point base values of GWCFs have been 0.04(TPI) and 0.045 (SPI) (Figure 7). The weights of GWCFs by AHP and point base values of GWCFs computed using the Equations (17)–(26) and then, calculated the ﬁnal weight. The GWPM by TOPSIS have been computed using the Equations (17)–(26) and then, calculated the final weight. The GWPM has been built considering the points values of GWCFs weights with the help of the inverse distance by TOPSIS has been built considering the points values of GWCFs weights with the help of the weighted (IDW) interpolation method (Figure 4b). The GWPM by TOPSIS has been classiﬁed into four inverse distance weighted (IDW) interpolation method (Figure 4b). The GWPM by TOPSIS has been classes such as low, medium, high and very high GWPZs with the help of natural break method. The classified into four classes such as low, medium, high and very high GWPZs with the help of natural results of GWMP by WoE model shows that only 290.22 km (15.09%) area is very high groundwater break method. The results of GWMP by WoE model shows that only 290.22 km2 (15.09%) area is very 2 2 2 potential, followed by the 399.46 km (20.77%), 787.38 km (40.94%) and 446.19 km (23.2%) areas are high groundwater potential, followed by the 399.46 km2 (20.77%), 787.38 km2 (40.94%) and 446.19 high, medium and low groundwater potential (Table 6) km2 (23.2%) areas are high, medium and low groundwater potential (Table 6) Figure 7. Determining the weight of conditioning factors using analytic hierarchy process (AHP) method. Remote Sens. 2019, 11, 3015 26 of 35 3.6. Application of Support Vector Machine (SVM) SVM is a vital machine learning data mining technique, used to recognize the potentiality of groundwater. All data layers have been reclassiﬁed into dierent classes using the SVM method. The SVM classiﬁcation value ranges from 0 to 1, 0 indicating the absence of groundwater well in GWCFs and Conversely 1 value also indicates the presence and potentiality of groundwater formation. Among the GWDFs, the low altitude, low slopping, high rainfall, nearest distance to river, high Dd, nearest distance to road, far distance to fault, high vegetation index, H lithological units, agriculture land, arid soils, high TWI and low SPI have been considered as sub-layers of high groundwater potential, marked by the 1 values. Conversely, high altitude, slopping, low drainage density, far distance to a river, low fault distance, low vegetation index, rangeland, bare land, urban, entisols, salt ﬂats, low TWI, and low rainfall have been identiﬁed as the 0 values because these conditions are not suitable for groundwater recharge. Thus, all GWDFs have been weighted by SVM and summed up in GIS to generate a single data layer of groundwater potential map (GWPM). The GWPM by SVM has been classiﬁed into four classes such as low, medium, high and very high GWPZs with the help of the natural break classiﬁcation method (Figure 4e). The results of GWMP by WoE model show that only 2 2 360.42 km (18.74%) area has very high groundwater potentiality and 248.67 km (12.93%) area has low groundwater potentiality (Table 6). 3.7. Validations and Comparison of Models Sometimes a single method of validation is not sucient for judging the potentiality and performance of models because of the concentration of samples within a few places. Methods of AUROC, SE, SP, AC, MAE, RMSE, and SCAI were used to test the performance of models. Both training (goodness of ﬁt) and validation (prediction accuracy) datasets have been used for judging the capability of models in producing the GWPMs of the study area. Considering the training dataset ROC curves (Figure 8) showing the AUC values of WoE, RF, TOPSIS, SVM, and BLR models are 0.914, 0.846, 0.924, 0.833, and 0.933, respectively (Figure 8). The SE values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.807, 0.800, 0.833, 0.792, and 0.852, respectively. The SP values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.818, 0.789, 0.810, 0.789, and 0.828, respectively (Table 9) The accuracy values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.813, 0.795, 0.821, 0.791, and 0.839, respectively. The RMSE values of the WoE, RF, TOPSIS, SVM, and BLR models are 0.317, 0.367, 0.316, 0.377, and 0.314, respectively. MAE values of the WoE, RF, TOPSIS, SVM and BLR models are 0.221, 0.275, 0.219, 0.269 and 0.216, respectively. AUCROC, sensitivity, speciﬁcity, accuracy, MAE, and MRSE are depicting the consistency between the trained models and actual situation of groundwater. In the validation data context, the AUC values WoE, RF, TOPSIS, SVM, and BLR are 0.898, 0.816, 0.901, 0.851, and 0.943, respectively. The SE values of the WoE, RF, TOPSIS, SVM and BLR models are 0.800, 0.783, 0.870, 0.773 and 0.909, respectively. The SP values of the WoE, RF, TOPSIS, SVM and BLR models are 0.826, 0.760, 0,840, 0.760, and 0.846 respectively (Table 9). The accuracy value of the WoE, RF, TOPSIS, SVM, and BLR models are 0.813, 0.771, 0.854, 0.766 and 0.875, respectively. On the other hand the RMSE values of the WoE, RF, TOPSIS, SVM and BLR models are 0.332, 0.383, 0.321, 0.409, and 0.311 and MAE values are 0.235, 0.288, 0.233, 0.311, and 0.214, respectively (Table 9). Remote Sens. 2018, 10, x FOR PEER REVIEW 29 of 37 predictability to evaluate the groundwater potentiality of the Damghan sedimentary plain, although other models have good capability in mapping the groundwater potentiality. Remote Sens. 2019, 11, 3015 27 of 35 Figure 8. Validation of results using the area under the curve of the receiver operating characteristic Figure 8. Validation of results using the area under the curve of the receiver operating characteristic (AUROC). (a) Training dataset (success rate curve) and (b) validation dataset (prediction rate curve). (AUROC). (a) Training dataset (success rate curve) and (b) validation dataset (prediction rate curve). Table Table 9. 9. Analysis Analysis of performa of performances nces usin using g training dataset an training dataset and d validat validation ion dataset for dataset the m for the odels. models. Training Dataset Validation Dataset Training Dataset Validation Dataset Measures WoE RF TOPSIS SVM BLR WoE RF TOPSIS SVM BLR True positive 46 44 45 42 46 20 17 20 18 20 True negative 45 45 47 45 48 19 19 21 19 22 Measures False positive 10 12 11 12 10 4 6 4 6 4 False negative 11 11 9 11 8 5 5 3 5 2 Sensitivity 0.807 0.800 0.833 0.792 0.852 0.800 0.773 0.870 0.783 0.909 True positive 46 44 45 42 46 20 17 20 18 20 Speciﬁcity 0.818 0.789 0.810 0.789 0.828 0.826 0.760 0.840 0.760 0.846 Accuracy 0.813 0.795 0.821 0.791 0.839 0.813 0.766 0.854 0.771 0.875 True negative RMSE 0.317 45 0.367 45 0.316 47 0.377 45 48 0.314 19 0.332 19 0.383 21 0.321 19 0.409 22 0.311 MAE 0.221 0.275 0.219 0.269 0.216 0.235 0.288 0.233 0.311 0.214 AUC 0.914 0.846 0.924 0.833 0.933 0.898 0.81 0.901 0.851 0.943 False positive 10 12 11 12 10 4 6 4 6 4 False negative 11 11 9 11 8 5 5 3 5 2 All the statistical techniques and ROC curves used in this study for evaluating the performance of the models have judged all the models as good for mapping the groundwater potentiality in this Sensitivity 0.807 0.800 0.833 0.792 0.852 0.800 0.773 0.870 0.783 0.909 plain. SCAI is another important validation method, used to validate the models. The SCAI values of Specificity 0.818 0.789 0.810 0.789 0.828 0.826 0.760 0.840 0.760 0.846 sub-classes of all models have decreased from low potentiality to very high potentiality, indicating the appropriateness and suitability for the groundwater potentiality evaluation (Table 10). Above Accuracy 0.813 0.795 0.821 0.791 0.839 0.813 0.766 0.854 0.771 0.875 all, according to the threshold dependent, SCAI and statistical methods the BLR has the strongest RMSE predictability to evaluate 0.317 the 0.gr 36oundwater 7 0.316 0. potentiality 377 0.314 of the 0.332 Damghan 0.383 sedimentary 0.321 0.40 plain, 9 0. although 311 other models have good capability in mapping the groundwater potentiality. MAE 0.221 0.275 0.219 0.269 0.216 0.235 0.288 0.233 0.311 0.214 AUC 0.914 0.846 0.924 0.833 0.933 0.898 0.81 0.901 0.851 0.943 WoE RF TOPSIS SVM BLR WoE RF TOPSIS SVM BLR Remote Sens. 2019, 11, 3015 28 of 35 Table 10. Computation sheet of seed cell area index (SCAI) methods. Training Datasets Validation Datasets Groundwater Models Potentiality % of Pixels No of % of No of % of Sum SCAI Classes Wells Wells Wells Wells Low 23.20 0 0.00 0 0.00 0.00 0.00 Medium 40.94 0 0.00 0 0.00 0.00 0.00 TOPSIS High 20.77 2 3.57 4 16.67 20.24 1.03 Very high 15.09 54 96.43 20 83.33 179.76 0.08 Low 22.09 0 0.00 0 0.00 0.00 0.00 Medium 32.10 2 3.57 1 4.17 4.17 7.70 WoE High 30.36 5 8.93 2 8.33 11.90 2.55 Very high 15.46 49 87.50 21 87.50 96.43 0.16 Low 55.34 1 1.79 0 0.00 1.79 30.99 Medium 10.33 4 7.14 1 4.17 11.31 0.91 RF High 9.07 8 14.29 3 12.50 26.79 0.34 Very high 25.26 43 76.79 20 83.33 160.12 0.16 Low 38.70 0 0.00 1 4.17 4.17 9.29 Medium 30.91 0 0.00 23 95.83 95.83 0.32 BLR High 14.92 2 3.57 0 0 3.57 4.18 Very high 15.47 54 96.43 0 0 96.43 0.16 Low 12.93 0 0.00 0 0.00 0.00 0.00 Medium 29.59 1 1.79 6 25.00 26.79 1.10 SVM High 38.73 14 25.00 18 75.00 100.00 0.39 Very high 18.74 41 73.21 73.21 0.26 3.8. Sensitivity Analysis To assess the inﬂuence of GWDFs on groundwater potentiality occurrence and to explore the eective factors with the strongest eect on the result of the groundwater potentiality prediction, a sensitivity analysis has been carried out (Table 11 and Figure 9). The results of sensitivity analysis showed in percentage contribution (PC) values of factors attained. The Pc values of the GWDFs are 7.5% (elevation), 11.35% (convergence index), 13.68% (drainage density), 11.81% (distance to road), 7.18% (distance to fault), 16.10% (distance to river), 6.19% (land use/land cover), 8.66% (lithology), 6.91% (NDVI), 9.67% (Rainfall), 7.86% (slope), 5.52% (soil), 10.10% (SPI), 12.58% (TPI), 9.51% (TWI) and 0.41% (aspect). The only slope aspect has very little contribution to the occurrence of groundwater potentiality. The results indicated that the groundwater potentiality maps of the study area are highly sensitive to elevation, lithology, drainage density, rainfall, distance to river, TPI, TWI, SPI, and distance to road. The sensitive analysis would help to reduce the variation in the model and to understand the signiﬁcant geo-environmental factors that are vital for understanding the structure of model. Table 11. Sensitivity result when each factor is excluded in the binary logistic regression model. GWDFs Decrease of AUC (in Percentage) Elevation 7.5 CI 11.35 Drainage density 13.68 Distance from road 11.81 Distance from fault 7.18 Distance from river 16.10 LULC 6.19 Lithology 8.66 NDVI 6.91 Rainfall 9.67 Slope 7.86 Soil 5.52 SPI 10.70 TPI 12.58 TWI 9.51 Aspect 0.41 Remote Sens. 2018, 10, x FOR PEER REVIEW 31 of 37 Distance from road 11.81 Distance from fault 7.18 Distance from river 16.10 LULC 6.19 Lithology 8.66 NDVI 6.91 Rainfall 9.67 Slope 7.86 Soil 5.52 SPI 10.70 TPI 12.58 TWI 9.51 Aspect 0.41 Remote Sens. 2019, 11, 3015 29 of 35 GWDFs Figure 9. Sensitivity result when each factor is excluded in the binary logistic regression model. Figure 9. Sensitivity result when each factor is excluded in the binary logistic regression model. 4. Discussion 4. Discussion In the recent decade, the demand for water has signiﬁcantly increased because of the rapid growth In the recent decade, the demand for water has significantly increased because of the rapid of population, especially in arid and semi-arid areas. The large part of Damghan sedimentary plain growth of population, especially in arid and semi-arid areas. The large part of Damghan sedimentary covering the arid and semi-arid environments groundwater is the main source of water for living. In plain covering the arid and semi-arid environments groundwater is the main source of water for this region, groundwater planning and sustainable management are necessary. The hydrogeologist, living. In this region, groundwater planning and sustainable management are necessary. The engineers and decision need some basic tools for managing the groundwater. GWPM may meet the hydrogeologist, engineers and decision need some basic tools for managing the groundwater. GWPM basic tool of groundwater management. may meet the basic tool of groundwater management. GWPM is the outcome of the lithology, tectonics, topography, vegetation, rainfall, and hydrology, GWPM is the outcome of the lithology, tectonics, topography, vegetation, rainfall, and which are available and accessible everywhere in the environment. In this research, a dierent hydrology, which are available and accessible everywhere in the environment. In this research, a type of data has been used as the input datasets. DEMs based study provides more accurate and different type of data has been used as the input datasets. DEMs based study provides more accurate signiﬁcant results [90–92]. Dierent DEMs provide dierent results, e.g., ALOS DEM with 30 m spatial and significant results (90–92). Different DEMs provide different results, e.g., ALOS DEM with 30 m resolution provide suitable and excellent results, comparatively the ASTER and SRTM DEMs with 30 m spatial resolution provide suitable and excellent results, comparatively the ASTER and SRTM DEMs resolution [93]. Here, the authors combined the geomorphology, geology and hydrology parameters with 30 m resolution [93]. Here, the authors combined the geomorphology, geology and hydrology to recognize the spatial groundwater potential. Spatial analysis is the core matter of the research for adopting the most performing approach and models for GWPMs, considering the argument topic [12–15]. Geo-environmental factors (i.e., elevation, slope, aspect, rainfall, lithology, land use/land cover, soil type, drainage density, distance to river, distance to fault, distance to road, NDVI, TWI, TPI, and SPI) were considered as the GWDFs that have been tested for the multi-collinearity problem by VIF and tolerance, and are the most eective for groundwater storage. The categorical variables such as aspect, lithology, soil type, LU/LC factors have been converted into the quantity continuous data through assigning the weight by the WoE and TOPSIS method. For the LR and RF, these GWDFs have been evaluated to prepare GWPMs taking the extracted values of GWDFs of the 500 points. The results of these models are more accurate than previous works [32]. In this work, we applied probabilistic (WoE, BLR), machine learning (SVM and RF) and multi-criteria decision approach (TOPSIS) models for building the GWPMs of Damghan sedimentary plain. These models have represented the excellent results as other works were done by Mohammady et al. [94] and Arabameri et al. [25,26]. All models, however, have very few variations in groundwater potential modeling accuracy. According to the AUROC, SE, SP, Accuracy, MAE and MRSE among the ﬁve models, the BLR models (for training dataset AUC = 0.933, SE = 0.852, SP = 0.828, AC = 0.839, MAE = 0.216 and RMSE = 0.314 and for Percantage change in AUC Elevation CI Dd Distance from Road Distance from Fault Distance from River LULC Lithology NDVI Rainfall Slope Soil SPI TPI TWI Aspect Remote Sens. 2019, 11, 3015 30 of 35 validation dataset AUC = 0.943, SE = 0.909, SP = 0.846, AC = 0.875, MAE = 0.214 and RMSE = 0.311) have better capability for mapping the groundwater potentiality than other models. Recognizing the signiﬁcance of each variable for groundwater storage is very dicult. The soil, lithology, altitude, rainfall, LU/LC, NDVI, Dd, distance to fault factors are dominant factors among 16 GWDFs for the formation of groundwater. The SA is depicting the contribution in producing the uncertainty in the GWPM and the factor distance from the river has the highest contribution to the variation of output of model. Similar to the Shahroud plain, the Damghan sedimentary plain regions consists of the large bare land, rangeland, and urban land, interrupting the water inﬁltration into sub-surface layer, while agriculture land with aquifer locations are receiving the larger water into the sub-surface and also signify the hydrologic properties [95]. According to TOPSIS model, the rainfall, slope, elevation, LU/LC, soil type factors have been highly prioritized by the AHP model, suggesting the most potential for groundwater formation. Such ﬁndings are conﬁrmed with the work of Arabameri et al. [32]. Among the 16 GWDFs, the elevation is the most important topographic component that inﬂuences the groundwater recharge. In fact, at a lower segment, the Damghan sedimentary plain is almost ﬂat, where water stagnation and associated inﬁltration of water is maximized. On the contrary, high altitudes, associated with open and v-shaped slopes promote runo due to local physiography. The methods applied for validating the GWPMs are showing outstanding accuracy, and ensemble models have better capabilities than the individual modes. Such ensemble models have been shown to be more reliable in this analysis than the other models used by the researchers for GWPM in various other locations [96,97]. The proper methods can have the ability to produce GWPMs, and that can be used for planning purposes. The used probabilistic, machine learning and ensemble models have excellent accuracy and may be used for groundwater management in this plain region. 5. Conclusions Today, GWPM is an eective groundwater resource management method. Through the Over-extraction of groundwater in the low groundwater, the potential region can be limited by the GWPM. With the advancement in the technical ﬁeld, dierent techniques for the spatial modeling of groundwater are introducing day by day. So, it very dicult to say what method would be best for spatial modeling. However, in the present research, ﬁve methods (BLR, TOPSIS, WoE, RF, and SVM) have been used for modeling the groundwater and the compared among them to answer the question of what model is relatively better for the Damghan sedimentary plain. The GWPM approaches are more appropriate to predict the potential of groundwater. The GWPMs have been produced with the help of RS and GIS techniques. RS and GIS both combinedly helped to perform the works such as identiﬁcation of well, thematic data generation, classiﬁcation, and ﬁnal map generations. The RS and GIS-based study are cost and time saving, accurate, and provide meaningful results. The R studio is an important machine learning program that helps to perform dierent kinds of models such as logistic regression, random forest, naive Bayes tree, support vector machine, artiﬁcial neural network, and several other methods. R program based model performance is more easy, accurate, eciency and perfect. The GWPMs, produced by the selected methods have been categorized into four categories i.e., low, medium, high and very high potential classes. The results of GWPMs show that the very 2 2 high potentiality zones are covered with by an area of 290.22 km (15.09% by TOPSIS), 297.34 km 2 2 2 (15.46% by WoE), 485 km (25.26% by RF), 297.53 km (15.47% by BLR) and 360.42 km (18.74% by SVM) out of 1923.27 km areas. The worthiness of GWPMs has been signiﬁcantly validated by the ROC and SCAI methods and ﬁve statistical measures i.e., SE, SP, AC, MAE, and MRSE. According to the results of the ROC, SCAI methods and statistical measures, these models are excellent for the prediction of GWPZ. The very high or excellent GWPZs have been found in the low elevated and less sloppy area. The arid soils are covered by high potentiality of groundwater. In the case of the LU/LC and vegetation index, the agriculture land and high vegetation density areas have high potentiality of groundwater. Conversely, high altitude, sloppy land, urban area, rangeland, salt ﬂats, entisols soil type have the low potentiality of groundwater formation. The GWPMs may be used as tool in Remote Sens. 2019, 11, 3015 31 of 35 this study area for managing and developing the groundwater. The resulting maps can also assist decision-makers, planners, and engineers in choosing the ideal location, groundwater distribution for further groundwater exploration. 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Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

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Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

Application of Probabilistic and Machine Learning Models for Groundwater Potentiality Mapping in Damghan Sedimentary Plain, Iran

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