# 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

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**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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**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.;
et al. 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,
et al. 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,
and et al. 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