# Application of Fuzzy Logic and Fractal Modeling Approach for Groundwater Potential Mapping in Semi-Arid Akka Basin, Southeast Morocco

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## Abstract

**:**

_{d}), and its weight (W

_{e}) were applied to estimate the capacity of each model to predict the target area. The analysis shows that the expected value model (N

_{d}= 1.86 and W

_{e}= 0.62) is more efficient than the geometric average model (Nd = 0.96 and We = −0.04). The results of the expected value model can be used in the future planning and management of water resources in the Akka basin.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The altitude varies from 549 to 2104 m. The prevailing climate is arid, characterized by heat in summer and cold in winter with an average temperature of 23°C and average annual precipitation of about 95.72 mm. The “Bani chain” dominating the landscape of this region is dug perpendicular to its direction by the tributaries of Drâa River, giving rise to a more or less broad water gap called “Foum” according to local nomenclature.

#### 2.2. Datasets Preparation

#### 2.3. Fuzzy Logic Function

_{X}and X are the fuzzy scores and the raw value of each pixel of the transformed input factor in the range [0, 1], and i and s are the inflection point and slope of the logistic function. These parameters are defined according to the following equations [55]:

#### 2.4. Factors Influencing Groundwater

#### 2.4.1. Lineament Density

#### 2.4.2. Node Density

#### 2.4.3. Drainage Density

#### 2.4.4. Distance from Rivers

#### 2.4.5. Distance from Lineament

#### 2.4.6. Permeability

#### 2.4.7. Slope

#### 2.4.8. Topographic Witness Index (TWI)

#### 2.4.9. Plan Curvature and Profile Curvature

#### 2.5. Integration of Transformed Factors

#### 2.5.1. Geometric Average Model

_{A GP}, can be calculated as follows:

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

_{LD}, F

_{ND}, F

_{DD}, F

_{DFR}, F

_{DFL}, F

_{P}, F

_{S}, F

_{TWI}, F

_{PL}, and F

_{PR}are fuzzy scores of transformed values of the lineament density, the node density, the drainage density, the distance from rivers, the distance from lineament, the permeability, the slope, the TWI, the plan curvature, and the profile curvature computed using the Equation (1). The final groundwater potential map obtained using the geometric average model (G

_{A GP}) is illustrated in Figure 5a.

#### 2.5.2. Expected Value Model

_{P GP}is the expected value of groundwater potentiality, I

_{LD}is the lineament density value, I

_{ND}is the node density value, I

_{DD}is the drainage density value, I

_{DFR}is the distance from rivers value, I

_{DFL}is the distance from lineament value, I

_{P}is the permeability value, I

_{S}is the slope value, I

_{TWI}is the TWI value, T

_{PL}is the plan curvature and I

_{PR}is the profile curvature value and F

_{LD}, F

_{ND}, F

_{DD}, F

_{DFR}, F

_{DFL}, F

_{P}, F

_{S}, F

_{TWI}, F

_{PL}, F

_{PR}are corresponding fuzzy scores computed using Equation (1).

_{pGP}values in the Akka basin, areas of hydrogeological interest can be identified and mapped for further exploration (Figure 6).

## 3. Results and Discussion

#### 3.1. Elaborated Model Assessment

_{d}) and its weight (W

_{e}) [21,22]. N

_{d}is computed as the prediction rate divided by the corresponding occupied area extracted from the intersection point of the P–A graph and W

_{e}are calculated considering the ln of N

_{d}[30,83]. A model with an N

_{d}> 1 and W

_{e}> 0 is considered a satisfying result for a hydrogeological prospection [83].

_{d}and W

_{e}for the expected value model are greater than those of the geometric average model, 1.86 > 0.96 and 0.62 > −0.04 (Figure 5d and Figure 6d, Table 1).

#### 3.2. Groundwater Potential Map

_{d}computed for the expected value model is 1.86 (Table 1), far greater than that of the geometric average model (0.96). This comparison shows that the expected value is the best model for the target area, presenting a high groundwater potential.

_{LD}, I

_{ND}, I

_{DD}, I

_{DFR}, I

_{DFL}, I

_{P}, I

_{S}, I

_{TWI}, I

_{PL}, I

_{PR}) is multiplied by its probability of occurrence (here, fuzzy score) and then divided by the sum of the probabilities (here, fuzzy scores) [21]. The geometric average model, on the other hand, uses only the transformed factors in the fuzzy logic, with no respect to the respective weight of those factors, thus affecting the model’s result compared to the expected value model.

#### 3.3. Validation of Model

## 4. Conclusions

_{d}(normalized density) and W

_{e}(weight of N

_{d}) for the expected value model are greater than those of the geometric average model, 1.86 > 0.96 and 0.62 > −0.04. The spatial relationship established between the well locations and the final maps shows that of the 32 known well occurrences, approximately 22 and 6 wells coincide with high- and very-high-potential areas produced by the expected value model and the geometric average model, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Fuzzy scores of transformed values of (

**a**) lineament density (LD); (

**b**) node density (DN); (

**c**) drainage density (DD); (

**d**) distance from rivers (DFR); (

**e**) distance from lineament (DFL); (

**f**) permeability (P); (

**g**) slope (S); (

**h**) TWI; (

**i**) plan curvature (PL); (

**j**) profile curvature (PR).

**Figure 5.**(

**a**) Geometric average map; (

**b**) concentration-area model (C–A), log–log plot for a geometric average model; (

**c**) classified geometric average model; (

**d**) prediction area (P–A) plot for the classified geometric average model.

**Figure 6.**(

**a**) Expected value map; (

**b**) concentration-area model (C–A), log–log plot for expected value model; (

**c**) classified expected value model; (

**d**) prediction area (P–A) plot for the classified expected value model.

**Table 1.**Extracted prediction rate (P

_{r}), occupied area (O

_{a}), normalize density (N

_{d}), and the weight (W

_{e}) of a different model.

Model | P_{r} (%) | O_{a} (%) | N_{d} | W_{e} |
---|---|---|---|---|

Expected value | 65 | 35 | 1.86 | 0.62 |

Geometric average | 49 | 51 | 0.96 | −0.04 |

**Table 2.**The distribution of wells and percentage of areas in potential groundwater zones generated by the geometric average and expected value models.

Class | Expected Value | Geometric Average | ||||
---|---|---|---|---|---|---|

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

Very high | 450.15 | 21.78 | 13 | 83.93 | 4.06 | 4 |

High | 381.58 | 18.47 | 9 | 130.36 | 6.31 | 2 |

Moderate | 439.45 | 21.27 | 3 | 381.95 | 18.48 | 2 |

Low | 412.95 | 19.98 | 4 | 1185.25 | 57.36 | 21 |

Very low | 382.23 | 18.50 | 3 | 284.90 | 13.79 | 3 |

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## Share and Cite

**MDPI and ACS Style**

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.
https://doi.org/10.3390/su141610205

**AMA Style**

Echogdali FZ, Boutaleb S, Kpan RB, Ouchchen M, Bendarma A, El Ayady H, Abdelrahman K, Fnais MS, Sajinkumar KS, Abioui M.
Application of Fuzzy Logic and Fractal Modeling Approach for Groundwater Potential Mapping in Semi-Arid Akka Basin, Southeast Morocco. *Sustainability*. 2022; 14(16):10205.
https://doi.org/10.3390/su141610205

**Chicago/Turabian Style**

Echogdali, Fatima Zahra, Said Boutaleb, Rosine Basseu Kpan, Mohammed Ouchchen, Amine Bendarma, Hasna El Ayady, Kamal Abdelrahman, Mohammed S. Fnais, Kochappi Sathyan Sajinkumar, and Mohamed Abioui.
2022. "Application of Fuzzy Logic and Fractal Modeling Approach for Groundwater Potential Mapping in Semi-Arid Akka Basin, Southeast Morocco" *Sustainability* 14, no. 16: 10205.
https://doi.org/10.3390/su141610205