# Spatial Mapping of Groundwater Potentiality Applying Geometric Average and Fractal Models: A Sustainable Approach

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## Abstract

**:**

## 1. Introduction

^{3}/year [1]. Approximately 70% of this exploited resource is used both for agriculture (33%) and drinking water supply (37%) [2,3]. Continued overexploitation of this precious resource threatens future generations [4,5]. As pressure on this resource continually increases, the delineation of its potential areas becomes essential for its protection and better management [6].

- (1)
- Data-Driven-Model, which concerns statistical, probabilistic, and data mining techniques and the quality and quantity of data are the significant characteristics impacting the predictive precision. Various types of the first model have been employed for editing groundwater potential area maps, such as Dempster-Shafer theory [24,25], evidential belief function [26,27], frequency ratio [28,29], logistic regression [30,31], statistical index [25], certainty factor [32,33], the weight-of-evidence method [34] and index of entropy [35];
- (2)
- (3)
- Machine learning techniques (MLTs) have provided better accuracy in many situations due to their ability to handle, in a robust manner, data characterized by a non-linear format, representing different scales, and deriving from different sources [39,40]. The MLT includes several models such as aquifer sustainability factor [41], classification and regression tree [42], random forest [22,43], boosted regression tree [44], maximum entropy [22], artificial neural network model [45], and generalized additive model [46].

## 2. Study Area

^{2}, is located in the southeastern region of Morocco (Figure 1). It extends between X (250,000 to 350,000) and Y (31,000 to 374,000) Lambert Coordinates with a mountainous topography where altitudes vary from 564 to 2149 m. The climate is mainly arid and characterized by low rainfall, 100 mm on average, which generally faces summer temperatures exceeding 40 °C. More than 90% of the annual rainfall occurs from September to April. The hydrographic basin network, constituted by a set of tributaries (Assif N’Tamsoult and Assif Sidi Lahcen to the north and Assif N’Timguissint to the east), converges downstream at Tissent Foum. On the hydrogeological level, the Plio-quaternary filling of the beds of the Tissent wadi reaches several tens of meters, constituting in places alluvial aquifers captured by a set of boreholes whose maximum flow rates reach 25 L/s.

## 3. Materials and Methods

- (1)
- (2)
- Collect a geospatial database that influences groundwater availability from different sources and generate different map factors.
- (3)
- Assign a score to the classes of each factor according to their relative importance using the logistic function.
- (4)
- Select effective and ineffective factors by assigning weights using Concentration-Area (C-A) and Prediction-Area (P-A).
- (5)
- Generate the groundwater potential map by applying the Geometric Average Model (GAM).
- (6)
- Validate the efficiency and predictive ability of the model using 50% of the well locations.

#### 3.1. Datasetsproduction

#### 3.2. Methods Used

#### 3.2.1. Generation of Decision Factors with Logistic Transformation

_{X}and X are, respectively, the value transformed in the logistic space, and as the raw value of each pixel of the input factor, i and s are, respectively, the inflection point and the slope of the logistic function. Therefore, these two parameters can be computed using the following equations [48]:

#### 3.2.2. Identify the Best-Performing Factor

_{d}) and its weights (W

_{e}) [67,70]. N

_{d}is calculated as a ratio between the prediction rate and the corresponding occupied area using the following equation:

_{d}is the normalized density, P

_{r}and O

_{a}are the prediction rate and occupied area extracted from the P-A intersection point, respectively, and W

_{e}are the weight calculated by considering the ln of N

_{d}[70]. A value of N

_{d}> 1 (W

_{e}> 0) for a factor map indicates a positive association that meets the criteria for delineating target areas for further exploration.

#### 3.2.3. Integration of Transformed Factors

_{A}) model combining method was used to produce a potentiality model in a GIS environment. Due to the complexity of the numbers, it is not easy for anyone other than a mathematician to understand and calculate them [89]. It cannot be calculated in the case of a negative or zero value of any variable. G

_{A}model is defined as the nth root of the products of values where n is the count of values. The geometric average, G

_{A}of a data set {v

_{1}, v

_{2}, …, v

_{n}} is given by [47]:

#### 3.2.4. Model Validation

## 4. Results

#### 4.1. Identification of Decision Factors

#### 4.1.1. Drainage Density

#### 4.1.2. Lineament Density

#### 4.1.3. Slope

#### 4.1.4. Node Density

#### 4.1.5. Permeability

#### 4.1.6. Altitude

#### 4.1.7. Distance from Lineament

#### 4.1.8. Distance from Rivers

#### 4.2. Selecting Factors Influencing GWPA

_{d}) and its weight (W

_{e}). The C-A fractal model (Figure 5a–h) was applied to determine thresholds for discretizing factor values to obtain classified maps (Figure 6a–h). Based on these maps, the P-A graphs were edited (Figure 7a–h).

_{d}< 1 and W

_{e}< 0.

#### 4.3. Elaboration of Geometric Average Model

_{A GWPA}) can be computed as:

_{A GWPA}is the geometric average of groundwater potentiality, F

_{LD}, F

_{SP}, F

_{ND}, F

_{P}, F

_{AT}, F

_{DFR,}and F

_{DFL}are fuzzy scores of the lineament density, slope, node density, permeability, altitude, distance from rivers, and distance from lineament, computed using the logistic function. After the computation of G

_{A GWPA}values of the Tissent basin, a geometric average potentiality model was generated (Figure 8a).

#### 4.4. Evaluation of Geometric Average Model

_{d}= 1.70 (>1) and W

_{e}= 0.53 (>0). The geometric average model (Figure 8a) shows that 37% of the Tissent basin is a high-potential area, in which 63% of known training well are delineated, which illustrates the effectiveness of this model.

#### 4.5. Validation of the Geometric Average Model

_{A GWPA}model (Figure 8c, Table 3). The respective numbers of wells corresponding to very high, high, moderate, low, and very low groundwater potential areas are 1, 6, 5, 5, and 9. This result suggests a positive correlation between the wells location and the G

_{A GWPA}model, especially in Akka Ighane, El Ayn, and Imi-n-Talat regions.

## 5. Discussion

_{A GWPA}map edit was classified into five categories (Figure 8c): very high, high, moderate, low, and very low. Its analysis shows that the areas of high and very high potentiality are related to the formation permeability factor, especially in the regions of El Ayn in the north, Akka Ighane in the southeast, Tilaffou in the west, and downstream of the basin. Arnous et al. [93] showed a strong relationship between high permeability formations and areas with high groundwater potentiality since it facilitates rain and wadi water infiltration. Deleting this factor at the mapping model level reduces the high and moderate potential regions alarmingly [104].

_{A GWPA}map shows low groundwater reserves due to steep slopes preventing water’s gradual infiltration into deep reservoirs. On the other hand, porous alluvial formations characterize the downstream part of the basin with low gradients and longer water-formation contact time. The interconnection of these several factors led to the recharge of deep reservoirs and, thus, high groundwater potentiality. According to Ajay Kumar et al. [114], excluding the influence of slope in the mapping models has led to a significant increase in areas of low groundwater potentiality. Apart from these high potential areas, the rest of the basin is characterized by low geological formations permeability, high elevations inducing steep slopes, and low density of lineaments. These negatively impact water availability in these areas.

_{A GWPA}in delineating potential groundwater areas shows an N

_{d}greater than 1 and W

_{e}greater than 0. However, all the factors used present prediction rates (P

_{r}) less (45 < P

_{r}< 59) than the geometric average model (P

_{r}= 63) (Figure 8d). Therefore, the target areas developed by these methods present positive associations with the existing wells. The validation results showed that approximately 46.16% of the well corresponds to areas of moderate to very high groundwater potentiality.

_{A GWPA}map, although validated by existing wells, may have limitations due to the resolution of the data used in a study area. The application of satellite images and a high-resolution digital elevation model (DEM) allows better extraction of the factors influencing G

_{A GWPA}[16,61,115,116]. Consequently, the high resolution of these data improves the final G

_{A GWPA}map. The lack of a climatological station limits the integration of the precipitation factor. Therefore, it is important to equip the basin with a set of stations to fill this data gap.

## 6. Conclusions

_{A GWPA}map, which was classified into five classes: very high, high, moderate, low, and very low, covering 4.82%, 10.99%, 21.36%, 14.49%, and 48.34% of the basin area. The P-A graph validated the G

_{A GWPA}.

_{d}= 1.70 and W

_{e}= 0.53, confirming the model’s validity. The model results were compared with the 26 existing wells; 46.16% of them corresponded to areas of moderate to very high potential regions. These results confirm the suitability of the Geometric Average model for mapping potential groundwater zones. It can easily be applied in other similar areas to optimize future well locations.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Margat, J.; van der Gun, J. Groundwater around the World; CRC Press/Balkema: Leiden, Netherlands, 2013. [Google Scholar]
- Smith, M.; Cross, K.; Paden, M.; Laban, P. Spring—Managing Groundwater Sustainability; IUCN: Gland, Switzerland, 2016. [Google Scholar]
- Kostyuchenko, Y.; Artemenko, I.; Abioui, M.; Benssaou, M. Global and Regional Climatic Modeling. In Encyclopedia of Mathematical Geosciences; Sagar, B.D., Cheng, Q., McKinley, J., Agterberg, F., Eds.; Springer: Cham, Switzerland, 2022; pp. 1–5. [Google Scholar] [CrossRef]
- Todd, D.K.; Mays, L.W. Groundwater Hydrology; Wiley: New York, NY, USA, 2005. [Google Scholar]
- Rekha, V.B.; Thomas, A.P. Integrated Remote Sensing and GIS for Groundwater Potentially Mapping in Koduvan Àr-Sub-Watershed of Meenachil River Basin, Kottayam District; School of Environmental Sciences, Mahatma Gandhi University: Kerala, India, 2007. [Google Scholar]
- Ozdemir, A. GIS-based groundwater spring potential mapping in the Sultan Mountains (Konya, Turkey) using frequency ratio, weights of evidence and logistic regression methods and their comparison. J. Hydrol.
**2011**, 411, 290–308. [Google Scholar] [CrossRef] - Fankhauser, K.; Macharia, D.; Coyle, J.; Kathuni, S.; McNally, A.; Slinski, K.; Thomas, E. Estimating groundwater use and demand in arid Kenya through assimilation of satellite data and in-situ sensors with machine learning toward drought early action. Sci. Total. Environ.
**2022**, 831, 154453. [Google Scholar] [CrossRef] - Aissa, R.B.; Boutoutaou, D. Characterization of groundwater in arid zones (case of Ouargla basin). Energy Procedia
**2017**, 119, 556–564. [Google Scholar] [CrossRef] - Hssaisoune, M.; Bouchaou, L.; Sifeddine, A.; Bouimetarhan, I.; Chehbouni, A. Moroccan Groundwater Resources and Evolution with Global Climate Changes. Geosciences
**2020**, 10, 81. [Google Scholar] [CrossRef] - Golkarian, A.; Rahmati, O. Use of a maximum entropy model to identify the key factors that influence groundwater availability on the Gonabad Plain, Iran. Environ. Earth Sci.
**2018**, 77, 369. [Google Scholar] [CrossRef] - Naghibi, S.A.; Ahmadi, K.; Daneshi, A. Application of Support Vector Machine, Random Forest, and Genetic Algorithm Optimized Random Forest Models in Groundwater Potential Mapping. Water Resour. Manag.
**2017**, 31, 2761–2775. [Google Scholar] [CrossRef] - Naghibi, S.A.; Pourghasemi, H.R.; Pourtaghi, Z.S.; Rezaei, A. Groundwater qanat potential mapping using frequency ratio and Shannon’s entropy models in the Moghan watershed, Iran. Earth Sci. Inform.
**2015**, 8, 171–186. [Google Scholar] [CrossRef] - Rahmati, O.; Naghibi, S.A.; Shahabi, H.; Bui, D.T.; Pradhan, B.; Azareh, A.; Rafiei-Sardooi, E.; Samani, A.N.; Melesse, A.M. Groundwater spring potential modelling: Comprising the capability and robustness of three different modeling approaches. J. Hydrol.
**2018**, 565, 248–261. [Google Scholar] [CrossRef] - Aouragh, M.H.; Essahlaoui, A.; El Ouali, A.; El Hmaidi, A.; Kamel, S. Groundwater potential of Middle Atlas plateaus, Morocco, using fuzzy logic approach, GIS and remote sensing. Geomat. Nat. Hazards Risk
**2017**, 8, 194–206. [Google Scholar] [CrossRef] - Hamdani, N.; Baali, A. Characterization of groundwater potential zones using analytic hierarchy process and integrated geomatic techniques in Central Middle Atlas (Morocco). Appl. Geomat.
**2020**, 12, 323–335. [Google Scholar] [CrossRef] - Echogdali, F.Z.; Boutaleb, S.; Bendarma, A.; Saidi, M.E.; Aadraoui, M.; Abioui, M.; Ouchchen, M.; Abdelrahman, K.; Fnais, M.S.; Sajinkumar, K.S. Application of Analytical Hierarchy Process and Geophysical Method for Groundwater Potential Mapping in the Tata Basin, Morocco. Water
**2022**, 14, 2393. [Google Scholar] [CrossRef] - Echogdali, F.Z.; Boutaleb, S.; Kpan, R.B.; Ouchchen, M.; Bendarma, A.; El Ayady, H.; Abdelrahman, K.; Fnais, M.S.; Sajinkumar, K.S.; Abioui, M. Application of Fuzzy Logic and Fractal Modeling Approach for Groundwater Potential Mapping in Semi-Arid Akka Basin, Southeast Morocco. Sustainability
**2022**, 14, 10205. [Google Scholar] [CrossRef] - Souissi, D.; Msaddek, M.H.; Zouhri, L.; Chenini, I.; El May, M.; Dlala, M. Mapping groundwater recharge potential zones in arid region using GIS and Landsat approaches, southeast Tunisia. Hydrol. Sci. J.
**2018**, 63, 251–268. [Google Scholar] [CrossRef] - Mallick, J.; Khan, R.A.; Ahmed, M.; Alqadhi, S.D.; Alsubih, M.; Falqi, I.; Hasan, M.A. Modeling Groundwater Potential Zone in a Semi-Arid Region of Aseer Using Fuzzy-AHP and Geoinformation Techniques. Water
**2019**, 11, 2656. [Google Scholar] [CrossRef] - Machiwal, D.; Jha, M.K.; Mal, B.C. Assessment of Groundwater Potential in a Semi-Arid Region of India Using Remote Sensing, GIS and MCDM Techniques. Water Resour. Manag.
**2010**, 25, 1359–1386. [Google Scholar] [CrossRef] - Castillo, J.L.U.; Cruz, D.A.M.; Leal, J.A.R.; Vargas, J.T.; Tapia, S.A.R.; Celestino, A.E.M. Delineation of Groundwater Potential Zones (GWPZs) in a Semi-Arid Basin through Remote Sensing, GIS, and AHP Approaches. Water
**2022**, 14, 2138. [Google Scholar] [CrossRef] - Rahmati, O.; Pourghasemi, H.R.; Melesse, A.M. Application of GIS-based data driven random forest and maximum entropy models for groundwater potential mapping: A case study at Mehran Region, Iran. Catena
**2016**, 137, 360–372. [Google Scholar] [CrossRef] - Naghibi, S.A.; Vafakhah, M.; Hashemi, H.; Pradhan, B.; Alavi, S.J. Groundwater Augmentation through the Site Selection of Floodwater Spreading Using a Data Mining Approach (Case study: Mashhad Plain, Iran). Water
**2018**, 10, 1405. [Google Scholar] [CrossRef] - Rahmati, O.; Melesse, A.M. Application of Dempster–Shafer theory, spatial analysis and remote sensing for groundwater potentiality and nitrate pollution analysis in the semi-arid region of Khuzestan, Iran. Sci. Total. Environ.
**2016**, 568, 1110–1123. [Google Scholar] [CrossRef] - Haghizadeh, A.; Moghaddam, D.D.; Pourghasemi, H.R. GIS-based bivariate statistical techniques for groundwater potential analysis (an example of Iran). J. Earth Syst. Sci.
**2017**, 126, 109. [Google Scholar] [CrossRef] - Kordestani, M.D.; Naghibi, S.A.; Hashemi, H.; Ahmadi, K.; Kalantar, B.; Pradhan, B. Groundwater potential mapping using a novel data-mining ensemble model. Hydrogeol. J.
**2019**, 27, 211–224. [Google Scholar] [CrossRef] - Pourghasemi, H.R.; Beheshtirad, M. Assessment of a data-driven evidential belief function model and GIS for groundwater potential mapping in the Koohrang Watershed, Iran. Geocarto Int.
**2014**, 30, 662–685. [Google Scholar] [CrossRef] - Oh, H.-J.; Kim, Y.-S.; Choi, J.-K.; Park, E.; Lee, S. GIS mapping of regional probabilistic groundwater potential in the area of Pohang City, Korea. J. Hydrol.
**2011**, 399, 158–172. [Google Scholar] [CrossRef] - Moghaddam, D.D.; Rezaei, M.; Pourghasemi, H.R.; Pourtaghie, Z.S.; Pradhan, B. Groundwater spring potential mapping using bivariate statistical model and GIS in the Taleghan Watershed, Iran. Arab. J. Geosci.
**2015**, 8, 913–929. [Google Scholar] [CrossRef] - Ozdemir, A. Using a binary logistic regression method and GIS for evaluating and mapping the groundwater spring potential in the Sultan Mountains (Aksehir, Turkey). J. Hydrol.
**2011**, 405, 123–136. [Google Scholar] [CrossRef] - Chen, W.; Li, H.; Hou, E.; Wang, S.; Wang, G.; Panahi, M.; Li, T.; Peng, T.; Guo, C.; Niu, C.; et al. GIS-based groundwater potential analysis using novel ensemble weights-of-evidence with logistic regression and functional tree models. Sci. Total. Environ.
**2018**, 634, 853–867. [Google Scholar] [CrossRef] [PubMed] - Razandi, Y.; Pourghasemi, H.R.; Neisani, N.S.; Rahmati, O. Application of analytical hierarchy process, frequency ratio, and certainty factor models for groundwater potential mapping using GIS. Earth Sci. Inform.
**2015**, 8, 867–883. [Google Scholar] [CrossRef] - Hou, E.; Wang, J.; Chen, W. A comparative study on groundwater spring potential analysis based on statistical index, index of entropy and certainty factors models. Geocarto Int.
**2018**, 33, 754–769. [Google Scholar] [CrossRef] - Corsini, A.; Cervi, F.; Ronchetti, F. Weight of evidence and artificial neural networks for potential groundwater spring mapping: An application to the Mt. Modino area (Northern Apennines, Italy). Geomorphology
**2009**, 111, 79–87. [Google Scholar] [CrossRef] - Al Abadi, A.M.A.; Shahid, S. A comparison between index of entropy and catastrophe theory methods for mapping groundwater potential in an arid region. Environ. Monit. Assess.
**2015**, 187, 1–21. [Google Scholar] [CrossRef] - Rahmati, O.; Samani, A.N.; Mahdavi, M.; Pourghasemi, H.R.; Zeinivand, H. Groundwater potential mapping at Kurdistan region of Iran using analytic hierarchy process and GIS. Arab. J. Geosci.
**2014**, 8, 7059–7071. [Google Scholar] [CrossRef] - Yin, H.; Shi, Y.; Niu, H.; Xie, D.; Wei, J.; Lefticariu, L.; Xu, S. A GIS-based model of potential groundwater yield zonation for a sandstone aquifer in the Juye Coalfield, Shangdong, China. J. Hydrol.
**2017**, 557, 434–447. [Google Scholar] [CrossRef] - Moghaddam, D.D.; Rahmati, O.; Haghizadeh, A.; Kalantari, Z. A Modeling Comparison of Groundwater Potential Mapping in a Mountain Bedrock Aquifer: QUEST, GARP, and RF Models. Water
**2020**, 12, 679. [Google Scholar] [CrossRef] - Pham, B.T.; Son, L.H.; Hoang, T.-A.; Nguyen, D.-M.; Bui, D.T. Prediction of shear strength of soft soil using machine learning methods. Catena
**2018**, 166, 181–191. [Google Scholar] [CrossRef] - Tien Bui, D.; Shahabi, H.; Shirzadi, A.; Chapi, K.; Hoang, N.-D.; Pham, B.T.; Bui, Q.-T.; Tran, C.-T.; Panahi, M.; Bin Ahmad, B.; et al. A Novel Integrated Approach of Relevance Vector Machine Optimized by Imperialist Competitive Algorithm for Spatial Modeling of Shallow Landslides. Remote Sens.
**2018**, 10, 1538. [Google Scholar] [CrossRef] - Smith, A.J.; Walker, G.; Turner, J. Aquifer sustainability factor: A review of previous estimates. In International Association of Hydrogeologists (AIH) and the Geological Society of Australia (GSA); CSIRO: Canberra, Australia, 2010; p. EP104589. [Google Scholar]
- Naghibi, S.A.; Pourghasemi, H.R. A Comparative Assessment Between Three Machine Learning Models and Their Performance Comparison by Bivariate and Multivariate Statistical Methods in Groundwater Potential Mapping. Water Resour. Manag.
**2015**, 29, 5217–5236. [Google Scholar] [CrossRef] - Zabihi, M.; Pourghasemi, H.R.; Pourtaghi, Z.S.; Behzadfar, M. GIS-based multivariate adaptive regression spline and random forest models for groundwater potential mapping in Iran. Environ. Earth Sci.
**2016**, 75, 1–19. [Google Scholar] [CrossRef] - Chen, W.; Zhao, X.; Tsangaratos, P.; Shahabi, H.; Ilia, I.; Xue, W.; Wang, X.; Bin Ahmad, B. Evaluating the usage of tree-based ensemble methods in groundwater spring potential mapping. J. Hydrol.
**2020**, 583, 124602. [Google Scholar] [CrossRef] - Lee, S.; Hong, S.-M.; Jung, H.-S. GIS-based groundwater potential mapping using artificial neural network and support vector machine models: The case of Boryeong city in Korea. Geocarto Int.
**2018**, 33, 847–861. [Google Scholar] [CrossRef] - Naghibi, S.A.; Moghaddam, D.D.; Kalantar, B.; Pradhan, B.; Kisi, O. A comparative assessment of GIS-based data mining models and a novel ensemble model in groundwater well potential mapping. J. Hydrol.
**2017**, 548, 471–483. [Google Scholar] [CrossRef] - Yousefi, M.; Carranza, E.J.M. Geometric average of spatial evidence data layers: A GIS-based multi-criteria decision-making approach to mineral prospectivity mapping. Comput. Geosci.
**2015**, 83, 72–79. [Google Scholar] [CrossRef] - Yousefi, M.; Nykänen, V. Data-driven logistic-based weighting of geochemical and geological evidence layers in mineral prospectivity mapping. J. Geochem. Explor.
**2016**, 164, 94–106. [Google Scholar] [CrossRef] - Echogdali, F.Z.; Boutaleb, S.; Abia, E.H.; Ouchchen, M.; Dadi, B.; Id-Belqas, M.; Abioui, M.; Pham, L.T.; Abu-Alam, T.; Mickus, K.L. Mineral prospectivity mapping: A potential technique for sustainable mineral exploration and mining activities—A case study using the copper deposits of the Tagmout basin, Morocco. Geocarto Int.
**2021**, 1–22. [Google Scholar] [CrossRef] - Afzal, P.; Mirzaei, M.; Yousefi, M.; Adib, A.; Khalajmasoumi, M.; Zarifi, A.Z.; Foster, P.; Yasrebi, A.B. Delineation of geochemical anomalies based on stream sediment data utilizing fractal modeling and staged factor analysis. J. Afr. Earth Sci.
**2016**, 119, 139–149. [Google Scholar] [CrossRef] - Choubert, G. Histoire géologique du précambrien de l’Anti–Atlas. Notes Mem. Serv. Geol. Maroc.
**1963**, 162, 352. [Google Scholar] - Soulaimani, A.; Burkhard, M. The Anti-Atlas chain (Morocco): The southern margin of the Variscan belt along the edge of the West African craton. Geol. Soc. Lond. Spec. Publ.
**2008**, 297, 433–452. [Google Scholar] [CrossRef] - Benssaou, M.; Hamoumi, N. The western Anti-Atlas of Morocco: Sedimentological and palæogeographical formation studies in the Early Cambrian. J. Afr. Earth Sci.
**2001**, 32, 351–372. [Google Scholar] [CrossRef] - Benssaou, M.; Hamoumi, N. Le graben de l’Anti-Atlas occidental (Maroc): Contrôle tectonique de la paléogéographie et des séquences au Cambrien inférieur. C. R. Geosci.
**2003**, 335, 297–305. [Google Scholar] [CrossRef] - Echogdali, F.Z.; Boutaleb, S.; Jauregui, J.; Elmouden, A. Cartography of Flooding Hazard in Semi-Arid Climate: The Case of Tata Valley (South-East of Morocco). J. Geogr. Nat. Disasters
**2018**, 8, 1–11. [Google Scholar] [CrossRef] - Ouchchen, M.; Boutaleb, S.; Abia, E.H.; El Azzab, D.; Abioui, M.; Mickus, K.L.; Miftah, A.; Echogdali, F.Z.; Dadi, B. Structural interpretation of the Igherm region (Western Anti Atlas, Morocco) from an aeromagnetic analysis: Implications for copper exploration. J. Afr. Earth Sci.
**2021**, 176, 104140. [Google Scholar] [CrossRef] - Echogdali, F.Z.; Boutaleb, S.; Taia, S.; Ouchchen, M.; Id-Belqas, M.; Kpan, R.B.; Abioui, M.; Aswathi, J.; Sajinkumar, K.S. Assessment of soil erosion risk in a semi-arid climate watershed using SWAT model: Case of Tata basin, South-East of Morocco. Appl. Water Sci.
**2022**, 12, 1–15. [Google Scholar] [CrossRef] - Choubert, G. L’accident majeur de l’Anti–Atlas. C. R. Acad. Sci. Paris
**1947**, 224, 1172–1173. [Google Scholar] - Thomas, R.; Chevallier, L.; Gresse, P.; Harmer, R.; Eglington, B.; Armstrong, R.; de Beer, C.; Martini, J.; de Kock, G.; Macey, P.; et al. Precambrian evolution of the Sirwa Window, Anti-Atlas Orogen, Morocco. Precambrian Res.
**2002**, 118, 1–57. [Google Scholar] [CrossRef] - Pham, B.T.; Jaafari, A.; Prakash, I.; Singh, S.K.; Quoc, N.K.; Bui, D.T. Hybrid computational intelligence models for groundwater potential mapping. Catena
**2019**, 182, 104101. [Google Scholar] [CrossRef] - Benjmel, K.; Amraoui, F.; Boutaleb, S.; Ouchchen, M.; Tahiri, A.; Touab, A. Mapping of Groundwater Potential Zones in Crystalline Terrain Using Remote Sensing, GIS Techniques, and Multicriteria Data Analysis (Case of the Ighrem Region, Western Anti-Atlas, Morocco). Water
**2020**, 12, 471. [Google Scholar] [CrossRef] - Bhattacharya, S.; Das, S.; Das, S.; Kalashetty, M.; Warghat, S.R. An integrated approach for mapping groundwater potential applying geospatial and MIF techniques in the semiarid region. Environ. Dev. Sustain.
**2020**, 23, 495–510. [Google Scholar] [CrossRef] - Micheli-Tzanakou, E. Supervised and Unsupervised Pattern Recognition; CRC Press: Boca Raton, FL, USA, 1999. [Google Scholar]
- Berthold, M.; Hand, D.J. Intelligent Data Analysis: An Introduction; Springer: Berlin, Germany, 2003. [Google Scholar]
- Bishop, C.M. Pattern Recognition and Machine Learning; Weller: New York, NY, USA, 2006. [Google Scholar]
- Yousefi, M.; Kamkar-Rouhani, A.; Carranza, E.J.M. Application of staged factor analysis and logistic function to create a fuzzy stream sediment geochemical evidence layer for mineral prospectivity mapping. Geochem. Explor. Environ. Anal.
**2014**, 14, 45–58. [Google Scholar] [CrossRef] - Yousefi, M.; Carranza, E.J.M. Prediction–area (P–A) plot and C–A fractal analysis to classify and evaluate evidential maps for mineral prospectivity modeling. Comput. Geosci.
**2015**, 79, 69–81. [Google Scholar] [CrossRef] - Porwal, A.; Carranza, E.J.M.; Hale, M. A Hybrid Neuro-Fuzzy Model for Mineral Potential Mapping. J. Int. Assoc. Math. Geol.
**2004**, 36, 803–826. [Google Scholar] [CrossRef] - Porwal, A.; Carranza, E.J.M.; Hale, M. A Hybrid Fuzzy Weights-of-Evidence Model for Mineral Potential Mapping. Nat. Resour. Res.
**2006**, 15, 1–14. [Google Scholar] [CrossRef] - Mihalasky, M.J.; Bonham-Carter, G.F. Lithodiversity and Its Spatial Association with Metallic Mineral Sites, Great Basin of Nevada. Nat. Resour. Res.
**2001**, 10, 209–226. [Google Scholar] [CrossRef] - Daya, A.A. Comparative study of C–A, C–P, and N–S fractal methods for separating geochemical anomalies from background: A case study of Kamoshgaran region, northwest of Iran. J. Geochem. Explor.
**2015**, 150, 52–63. [Google Scholar] [CrossRef] - Heidari, S.M.; Afzal, P.; Ghaderi, M.; Sadeghi, B. Detection of mineralization stages using zonality and multifractal modeling based on geological and geochemical data in the Au-(Cu) intrusion-related Gouzal-Bolagh deposit, NW Iran. Ore Geol. Rev.
**2021**, 139, 104561. [Google Scholar] [CrossRef] - Afzal, P.; Alghalandis, Y.F.; Khakzad, A.; Moarefvand, P.; Omran, N.R. Delineation of mineralization zones in porphyry Cu deposits by fractal concentration–volume modeling. J. Geochem. Explor.
**2011**, 108, 220–232. [Google Scholar] [CrossRef] - Mandelbrot, B.B. The Fractal Geometry of Nature; Freeman: San Francisco, CA, USA, 1983. [Google Scholar]
- Zissimos, A.M.; Cohen, D.R.; Christoforou, I.C.; Sadeghi, B.; Rutherford, N.F. Controls on soil geochemistry fractal characteristics in Lemesos (Limassol), Cyprus. J. Geochem. Explor.
**2021**, 220, 106682. [Google Scholar] [CrossRef] - Li, C.; Ma, T.; Shi, J. Application of a fractal method relating concentrations and distances for separation of geochemical anomalies from background. J. Geochem. Explor.
**2003**, 77, 167–175. [Google Scholar] [CrossRef] - Zuo, R.; Cheng, Q. Mapping singularities—A technique to identify potential Cu mineral deposits using sediment geochemical data, an example for Tibet, west China. Miner. Mag.
**2008**, 72, 531–534. [Google Scholar] [CrossRef] - Zuo, R. Decomposing of mixed pattern of arsenic using fractal model in Gangdese belt, Tibet, China. Appl. Geochem.
**2011**, 26, S271–S273. [Google Scholar] [CrossRef] - Cheng, Q.; Agterberg, F.; Ballantyne, S. The separation of geochemical anomalies from background by fractal methods. J. Geochem. Explor.
**1994**, 51, 109–130. [Google Scholar] [CrossRef] - Asl, R.A.; Afzal, P.; Adib, A.; Yasrebi, A.B. Application of multifractal modeling for the identification of alteration zones and major faults based on ETM+ multispectral data. Arab. J. Geosci.
**2015**, 8, 2997–3006. [Google Scholar] [CrossRef] - A Gonçalves, M.; Mateus, A.; Oliveira, V. Geochemical anomaly separation by multifractal modelling. J. Geochem. Explor.
**2001**, 72, 91–114. [Google Scholar] [CrossRef] - Cheng, Q.; Li, Q. A fractal concentration–area method for assigning a color palette for image representation. Comput. Geosci.
**2002**, 28, 567–575. [Google Scholar] [CrossRef] - Yousefi, M.; Carranza, E.J.M. Fuzzification of continuous-value spatial evidence for mineral prospectivity mapping. Comput. Geosci.
**2015**, 74, 97–109. [Google Scholar] [CrossRef] - Zuo, R.; Wang, J. Arc Fractal: An ArcGIS Add-In for Processing Geoscience Data Using Fractal/Multifractal Models. Nat. Resour. Res.
**2020**, 29, 3–12. [Google Scholar] [CrossRef] - Nazarpour, A.; Omran, N.R.; Paydar, G.R.; Sadeghi, B.; Matroud, F.; Nejad, A.M. Application of classical statistics, log ratio transformation and multifractal approaches to delineate geochemical anomalies in the Zarshuran gold district, NW Iran. Geochemistry
**2015**, 75, 117–132. [Google Scholar] [CrossRef] - Ouchchen, M.; Boutaleb, S.; Abia, E.; El Azzab, D.; Miftah, A.; Dadi, B.; Echogdali, F.; Mamouch, Y.; Pradhan, B.; Santosh, M.; et al. Exploration targeting of copper deposits using staged factor analysis, geochemical mineralization prospectivity index, and fractal model (Western Anti-Atlas, Morocco). Ore Geol. Rev.
**2022**, 143, 104762. [Google Scholar] [CrossRef] - Wang, Y.M.; Chin, K.-S.; Yang, J.B. Measuring the performances of decision-making units using geometric average efficiency. J. Oper. Res. Soc.
**2007**, 58, 929–937. [Google Scholar] [CrossRef] - Wei, G. Some Arithmetic Aggregation Operators with Intuitionistic Trapezoidal Fuzzy Numbers and Their Application to Group Decision Making. J. Comput.
**2010**, 5, 345–351. [Google Scholar] [CrossRef] - Tothill, P. Limitations of the use of the geometric mean to obtain depth independence in scanning and whole body counting. Phys. Med. Biol.
**1974**, 19, 382–385. [Google Scholar] [CrossRef] - Chung, C.-J.F.; Fabbri, A.G. Validation of Spatial Prediction Models for Landslide Hazard Mapping. Nat. Hazards
**2003**, 30, 451–472. [Google Scholar] [CrossRef] - Magesh, N.S.; Chandrasekar, N.; Soundranayagam, J.P. Delineation of groundwater potential zones in Theni district, Tamil Nadu, using remote sensing, GIS and MIF techniques. Geosci. Front.
**2012**, 3, 189–196. [Google Scholar] [CrossRef] - Arnous, M.O.; Sultan, Y.M. Geospatial technology and structural analysis for geological mapping and tectonic evolution of Feiran–Solaf metamorphic complex, South Sinai, Egypt. Arab. J. Geosci.
**2014**, 7, 3023–3049. [Google Scholar] [CrossRef] - Arnous, M.O. Groundwater potentiality mapping of hard-rock terrain in arid regions using geospatial modelling: Example from Wadi Feiran basin, South Sinai, Egypt. Hydrogeol. J.
**2016**, 24, 1375–1392. [Google Scholar] [CrossRef] - Jasrotia, A.S.; Bhagat, B.D.; Kumar, A.; Kumar, R. Remote Sensing and GIS Approach for Delineation of Groundwater Potential and Groundwater Quality Zones of Western Doon Valley, Uttarakhand, India. J. Indian Soc. Remote. Sens.
**2013**, 41, 365–377. [Google Scholar] [CrossRef] - Haris, K.; Efstratiadis, S.; Maglaveras, N.; Katsaggelos, A. Hybrid image segmentation using watersheds and fast region merging. IEEE Trans. Image Process.
**1998**, 7, 1684–1699. [Google Scholar] [CrossRef] - Boutaleb, S.; Boualoul, M.; Oudra, M.; Bouchaou, L.; Dindane, K. Apports du traitement d’image et de la géophysique à l’étude des ressources en eau en milieu fissuré: Cas de l’Anti–Atlas marocain. Afr. Geosci. Rev.
**2008**, 15, 129–141. [Google Scholar] - Boutaleb, S.; Boualoul, M.; Bouchaou, L.; Oudra, M. Application of remote-sensing and surface geophysics for groundwater prospecting in a hard rock terrain, Morocco. In Applied Groundwater Studies in Africa; CRC Press: London, UK, 2008; pp. 215–230. [Google Scholar] [CrossRef]
- Boutaleb, S.; El Hammichi, F.; Tabyaoui, H.; Bouchaou, L.; Dindane, K. Détermination des écoulements préférentiels en zone karstique (Tafrata, Maroc), Apport des données satellitaires SAR ERS-1 et Landsat ETM+ et de la prospection géophysique. Rev. Sci. Eau
**2009**, 22, 407–419. [Google Scholar] [CrossRef] - Hssaisoune, M.; Boutaleb, S.; Bouchaou, L.; Benssaou, M.; Tagma, T. Use of remote sensing and electrical resistivity tomography to determine Tidsi spring recharge and underground drainage. Eur. Water
**2017**, 57, 429–434. [Google Scholar] - Rahman, M.A.; Rusteberg, B.; Gogu, R.; Ferreira, J.L.; Sauter, M. A new spatial multi-criteria decision support tool for site selection for implementation of managed aquifer recharge. J. Environ. Manag.
**2012**, 99, 61–75. [Google Scholar] [CrossRef] - Naghibi, S.A.; Pourghasemi, H.R.; Dixon, B. GIS-based groundwater potential mapping using boosted regression tree, classification and regression tree, and random forest machine learning models in Iran. Environ. Monit. Assess.
**2016**, 188, 1–27. [Google Scholar] [CrossRef] - Acharya, T. Study of Groundwater Prospects of the Crystalline Rocks in Purulia District, West Bengal, India Using Remote Sensing Data. Earth Resour.
**2013**, 1, 54. [Google Scholar] [CrossRef] - Saranya, T.; Saravanan, S. Groundwater potential zone mapping using analytical hierarchy process (AHP) and GIS for Kancheepuram District, Tamilnadu, India. Model. Earth Syst. Environ.
**2020**, 6, 1105–1122. [Google Scholar] [CrossRef] - Patra, S.; Mishra, P.; Mahapatra, S.C. Delineation of groundwater potential zone for sustainable development: A case study from Ganga Alluvial Plain covering Hooghly district of India using remote sensing, geographic information system and analytic hierarchy process. J. Clean. Prod.
**2018**, 172, 2485–2502. [Google Scholar] [CrossRef] - Ganapuram, S.; Kumar, G.V.; Krishna, I.M.; Kahya, E.; Demirel, M.C. Mapping of groundwater potential zones in the Musi basin using remote sensing data and GIS. Adv. Eng. Softw.
**2009**, 40, 506–518. [Google Scholar] [CrossRef] - Solomon, S.; Quiel, F. Groundwater study using remote sensing and geographic information systems (GIS) in the central highlands of Eritrea. Hydrogeol. J.
**2006**, 14, 1029–1041. [Google Scholar] [CrossRef] - Aswathi, J.; Sajinkumar, K.S.; Rajaneesh, A.; Oommen, T.; Bouali, E.H.; Kumar, R.B.B.; Rani, V.R.; Thomas, J.; Thrivikramji, K.P.; Ajin, R.S.; et al. Furthering the precision of RUSLE soil erosion with PSInSAR data: An innovative model. Geocarto Int.
**2022**, 1–24. [Google Scholar] [CrossRef] - Caine, J.S.; Evans, J.P.; Craig, B.F. Fault zone architecture and permeability structure. Geology
**1996**, 24, 1025–1028. [Google Scholar] [CrossRef] - Faulkner, D.; Jackson, C.; Lunn, R.; Schlische, R.; Shipton, Z.; Wibberley, C.; Withjack, M. A review of recent developments concerning the structure, mechanics and fluid flow properties of fault zones. J. Struct. Geol.
**2010**, 32, 1557–1575. [Google Scholar] [CrossRef] - Goldscheider, N.; Neukum, C. Fold and fault control on the drainage pattern of a double-karst-aquifer system, Winterstaude, Austrian Alps. Acta Carsologica
**2010**, 39, 173–186. [Google Scholar] [CrossRef] - Evans, J.P.; Forster, C.B.; Goddard, J.V. Permeability of fault-related rocks, and implications for hydraulic structure of fault zones. J. Struct. Geol.
**1997**, 19, 1393–1404. [Google Scholar] [CrossRef] - Medici, G.; Smeraglia, L.; Torabi, A.; Botter, C. Review of Modeling Approaches to Groundwater Flow in Deformed Carbonate Aquifers. Groundwater
**2020**, 59, 334–351. [Google Scholar] [CrossRef] [PubMed] - Jothibasu, A.; Anbazhagan, S. Modeling groundwater probability index in Ponnaiyar River basin of South India using analytic hierarchy process. Model. Earth Syst. Environ.
**2016**, 2, 1–14. [Google Scholar] [CrossRef] - Kumar, V.A.; Mondal, N.C.; Ahmed, S. Identification of Groundwater Potential Zones Using RS, GIS and AHP Techniques: A Case Study in a Part of Deccan Volcanic Province (DVP), Maharashtra, India. J. Indian Soc. Remote. Sens.
**2020**, 48, 497–511. [Google Scholar] [CrossRef] - Mohammadzadeh, A.; Zoej, M.J.V.; Tavakoli, A. Automatic main road extraction from high resolution satellite imageries by means of particle swarm optimization applied to a fuzzy-based mean calculation approach. J. Indian Soc. Remote. Sens.
**2009**, 37, 173–184. [Google Scholar] [CrossRef] - Benjmel, K.; Amraoui, F.; Aydda, A.; Tahiri, A.; Yousif, M.; Pradhan, B.; Abdelrahman, K.; Fnais, M.S.; Abioui, M. A Multidisciplinary Approach for Groundwater Potential Mapping in a Fractured Semi-Arid Terrain (Kerdous Inlier, Western Anti-Atlas, Morocco). Water
**2022**, 14, 1553. [Google Scholar] [CrossRef]

**Figure 4.**Maps of transformed values: (

**a**) drainage density map; (

**b**) lineament density map; (

**c**) slope map; (

**d**) node density map; (

**e**) permeability map; (

**f**) altitude map; (

**g**) distance from rivers map; (

**h**) distance from lineament map.

**Figure 5.**Concentration-area (C-A) log-log plots for the transformed values: (

**a**) drainage density map; (

**b**) lineament density map; (

**c**) slope map; (

**d**) node density map; (

**e**) permeability map; (

**f**) altitude map; (

**g**) distance from rivers map; (

**h**) distance from lineament map.

**Figure 6.**Classified map for the transformed values: (

**a**) drainage density map; (

**b**) lineament density map; (

**c**) slope map; (

**d**) node density map; (

**e**) permeability map; (

**f**) altitude map; (

**g**) distance from rivers map; (

**h**) distance from lineament map.

**Figure 7.**Prediction-area (P-A) plot for the classified map: (

**a**) drainage density map; (

**b**) lineament density map; (

**c**) slope map; (

**d**) node density map; (

**e**) permeability map; (

**f**) altitude map; (

**g**) distance from rivers map; (

**h**) distance from lineament map.

**Figure 8.**(

**a**) Groundwater potentiality map of Tissent basin using the geometric average model; (

**b**) Concentration-area (C-A) log-log plots of G

_{A GWPA}; (

**c**) Classified map of G

_{A GWPA}; (

**d**) Prediction–area (P-A) plot for the classed map of G

_{A GWPA}.

Category | Factor | Data Type | Scale | Source |
---|---|---|---|---|

Topographical | Slope | Raster | 30 m × 30 m | DEM (http://earthexplorer.usgs.gov/ (accessed on 23 September 2014)) |

Altitude | Raster | 30 m × 30 m | DEM (http://earthexplorer.usgs.gov/ (accessed on 23 September 2014)) | |

Hydrological | Distance from rivers | Raster | 30 m× 30 m | DEM (http://earthexplorer.usgs.gov/ (accessed on 23 September 2014)) |

Drainage density | Raster | 30 m× 30 m | DEM (http://earthexplorer.usgs.gov/ (accessed on 23 September 2014)) | |

Geological | Permeability | Raster | 1:1,000,000 | Geological map of Morocco (Ministry of Energy and Mines of Morocco) |

Lineament density | Raster | 30 m× 30 m | Landsat 8 OLI (http://earthexplorer.usgs.gov/ (accessed on 30 December 2021)) | |

Node density | Raster | 30 m× 30 m | Landsat 8 OLI (http://earthexplorer.usgs.gov/ (accessed on 30 December 2021)) | |

Distance from lineament | Raster | 30 m× 30 m | Landsat 8 OLI (http://earthexplorer.usgs.gov/ (accessed on 30 December 2021)) | |

Groundwater Point | Well | Vector | - | The Souss Massa Hydraulic Basin Agency (Agadir, Morocco) |

Evidential Map | Prediction Rate (P_{r}) (%) | Occupied Area (O_{a}) (%) | Normalized Density (N_{d}) | Weight (W_{e}) |
---|---|---|---|---|

Permeability | 59 | 41 | 1.44 | 0.36 |

Altitude | 59 | 41 | 1.44 | 0.36 |

Slope | 57 | 43 | 1.33 | 0.28 |

Distance from lineament | 56 | 44 | 1.27 | 0.24 |

Distance from rivers | 54 | 46 | 1.17 | 0.16 |

Lineament density | 52 | 48 | 1.08 | 0.08 |

Node density | 51 | 49 | 1.04 | 0.04 |

Drainage density | 45 | 55 | 0.82 | −0.20 |

**Table 3.**The distribution of wells and percentage of areas in potential groundwater zones generated by the G

_{A GWPA}model.

Class | Geometric Average Model (G_{A GWPA}) | |||
---|---|---|---|---|

Area (km^{2}) | Area % | Number of Wells | Wells % | |

Very high | 172.76 | 4.82 | 1 | 3.85 |

High | 395.07 | 10.99 | 6 | 23.08 |

Moderate | 767.77 | 21.36 | 5 | 19.23 |

Low | 521.12 | 14.49 | 5 | 19.23 |

Very low | 1737.56 | 48.34 | 9 | 34.61 |

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## Share and Cite

**MDPI and ACS Style**

Echogdali, F.Z.; Boutaleb, S.; Abioui, M.; Aadraoui, M.; Bendarma, A.; Kpan, R.B.; Ikirri, M.; El Mekkaoui, M.; Essoussi, S.; El Ayady, H.; Abdelrahman, K.; Fnais, M.S. Spatial Mapping of Groundwater Potentiality Applying Geometric Average and Fractal Models: A Sustainable Approach. *Water* **2023**, *15*, 336.
https://doi.org/10.3390/w15020336

**AMA Style**

Echogdali FZ, Boutaleb S, Abioui M, Aadraoui M, Bendarma A, Kpan RB, Ikirri M, El Mekkaoui M, Essoussi S, El Ayady H, Abdelrahman K, Fnais MS. Spatial Mapping of Groundwater Potentiality Applying Geometric Average and Fractal Models: A Sustainable Approach. *Water*. 2023; 15(2):336.
https://doi.org/10.3390/w15020336

**Chicago/Turabian Style**

Echogdali, Fatima Zahra, Said Boutaleb, Mohamed Abioui, Mohamed Aadraoui, Amine Bendarma, Rosine Basseu Kpan, Mustapha Ikirri, Manal El Mekkaoui, Sara Essoussi, Hasna El Ayady, Kamal Abdelrahman, and Mohammed S. Fnais. 2023. "Spatial Mapping of Groundwater Potentiality Applying Geometric Average and Fractal Models: A Sustainable Approach" *Water* 15, no. 2: 336.
https://doi.org/10.3390/w15020336