# Groundwater-Potential Mapping Using a Self-Learning Bayesian Network Model: A Comparison among Metaheuristic Algorithms

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Spring Inventory Map

^{3}/h and a mean pH and electrical conductivity (EC) of 7.1 and 490 μmhos/cm, respectively. In this study, the locations of the springs were provided by the Water Resources Management Organization (WRMO) of Iran. Google Earth was used to verify the locations of the springs. Of the locations, 70% (131 locations) were randomly used for modeling (i.e., training), and 30% (56 locations) were randomly used for the modeling evaluation (i.e., validation).

#### 2.3. Criteria Affecting the Potential of Groundwater

#### 2.4. CF Method

#### 2.5. Baysian Network (BayesNet) Machine-Learning Model

#### 2.6. Genetic Algorithm (GA)

#### 2.7. Simulated Annealing (SA) Algorithm

#### 2.8. Tabu Search (TS) Algorithm

#### 2.9. Hybrid Model

#### 2.10. OneR Technique

#### 2.11. Validation Indices

## 3. Results and Discussion

#### 3.1. Determining the Important Criteria

#### 3.2. Results of the CF Method

#### 3.3. Results of the Hybrid Models

#### 3.4. GPM Using Hybrid Models

#### 3.5. Validation of GPM

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Factors | Source | Scale | Classification Method |
---|---|---|---|

Altitude | Natural breaks | ||

Slope angle | Natural breaks | ||

Slope aspect | Manual | ||

Plan curvature | SRTM DEM | 1:60,000 | Manual |

Profile curvature | Natural breaks | ||

TWI | Natural breaks | ||

Distance to river | Manual | ||

Drainage density | Natural breaks | ||

Lithology | Geological Survey of Iran | 1:100,000 | Lithological units |

Distance to fault | Manual | ||

Soil | Khuzestan Natural Resources Organization | 1:100,000 | Soil units |

Land use/cover | Landsat-8 image | 1:60,000 | Land use/cover units |

Rainfall | The annual average of 22 meteorological stations in Khuzestan | 1:60,000 | Natural breaks |

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**Figure 1.**Research methodology. TWI: topographic wetness index, GA: genetic algorithm, SA: simulated annealing, TS: Tabu search, RMSE: root mean square error, MAE: mean absolute error, ROC: receiver operating characteristic, AUC: area under the curve.

**Figure 3.**Maps of affecting factors: (

**a**) altitude, (

**b**) slope angle, (

**c**) slope aspect, (

**d**) topographic wetness index (TWI), (

**e**) plan curvature, (

**f**) profile curvature, (

**g**) distance to river, (

**h**) distance to fault, (

**i**) drainage density, (

**j**) rainfall, (

**k**) lithology, (

**l**) soil and (

**m**) land use/cover.

Class | No. of Pixels in Domain | No. of Springs | CF | Class | No. of Pixels in Domain | No. of Springs | CF |
---|---|---|---|---|---|---|---|

Altitude (m) | Distance to river (m) | ||||||

<724 | 864,512 | 39 | −0.076 | 0–100 | 151,724 | 29 | 0.744 |

724–1084 | 962,838 | 73 | 0.355 | 100–200 | 137,908 | 22 | 0.693 |

1084–1566 | 432,096 | 4 | −0.810 | 200–300 | 142,610 | 7 | 0.0031 |

1566–2162 | 271,106 | 14 | 0.053 | 300–400 | 126,125 | 3 | −0.513 |

>2162 | 150,608 | 1 | −0.864 | >400 | 211,880 | 70 | −0.324 |

Slope angle | Distance to fault (m) | ||||||

0–8 | 973,112 | 61 | 0.220 | 0–300 | 53,716 | 5 | 0.474 |

8–16 | 691,532 | 38 | 0.110 | 300–600 | 52,757 | 1 | −0.612 |

16–25 | 528,894 | 18 | −0.303 | 600–900 | 51,893 | 0 | −1.000 |

25–37 | 349,366 | 11 | −0.355 | 900–1200 | 53,661 | 0 | −1.000 |

>37 | 138,256 | 3 | −0.555 | >1200 | 246,514 | 125 | 0.035 |

TWI | Drainage density | ||||||

<3.48 | 655,123 | 12 | −0.625 | 0–0.243 | 130,811 | 27 | −0.570 |

3.48–4.31 | 775,835 | 28 | −0.261 | 0.243–0.487 | 936,236 | 51 | 0.101 |

4.31–5.15 | 645,477 | 51 | 0.381 | 0.487–0.731 | 366,305 | 47 | 0.618 |

5.15–6.1 | 457,665 | 35 | 0.361 | 0.731–0.974 | 62,963 | 6 | 0.486 |

>6.1 | 147,060 | 5 | −0.304 | >0.974 | 3556 | 0 | −1.000 |

Profile curvature | Rainfall (mm) | ||||||

<−0.0054 | 160,359 | 20 | 0.608 | < 450 | 466,347 | 0 | −1.000 |

-0.0054–0.0017 | 601,468 | 35 | 0.160 | 450–500 | 818,925 | 49 | 0.180 |

-0.0017–0.0011 | 101,300 | 46 | −0.070 | 500–550 | 497,838 | 48 | 0.490 |

0.0011–0.0048 | 716,132 | 27 | −0.220 | 550–600 | 426,536 | 18 | −0.137 |

>0.0048 | 190,193 | 3 | −0.670 | >600 | 468,081 | 16 | −0.301 |

Plan curvature | Soil | ||||||

Concave | 644,059 | 55 | 0.427 | Bad lands | 123,049 | 61 | 0.014 |

Flat | 136,304 | 60 | −0.099 | Inceptisols | 579,991 | 45 | 0.370 |

Convex | 674,060 | 16 | −0.514 | Entisols | 871,261 | 25 | −0.410 |

Lithology | Slope aspect | ||||||

Qft2 | 484,268 | 43 | 0.449 | F | 1623 | 0 | −1.000 |

MuPlaj | 118,043 | 16 | 0.639 | N | 312,384 | 12 | −0.213 |

Mgs | 953,888 | 32 | −0.313 | NE | 324,921 | 10 | −0.370 |

Kgu | 35,391 | 0 | −1.000 | E | 242,263 | 11 | −0.070 |

OMas | 598,244 | 14 | −0.520 | SE | 243,474 | 9 | −0.243 |

Kbgp | 53,728 | 0 | −1.000 | S | 373,092 | 30 | 0.392 |

Mmn | 1,07201 | 3 | −0.420 | SW | 482,906 | 24 | 0.016 |

Plbk | 114,957 | 12 | 0.530 | W | 392,328 | 21 | 0.087 |

PeEpd | 114,465 | 11 | 0.490 | NW | 308,169 | 14 | −0.070 |

JKkgp | 399 | 0 | −1.000 | ||||

KEpd-gu | 101,159 | 0 | −1.000 | ||||

Land use/cover | |||||||

Forest | 468,449 | 18 | −0.213 | ||||

Agriculture | 117,252 | 75 | 0.347 | ||||

Pasture | 100,168 | 36 | −0.371 | ||||

Bare land | 7285 | 0 | −1.000 | ||||

Urban area | 4071 | 0 | −1.000 | ||||

Water body | 27,672 | 2 | 0.324 |

GA | SA | TS |
---|---|---|

Iterations = 200 Population Size = 50 Mutation Rate = 0.2 | Iterations = 200 Subiterations = 10 Initial temperature = 10 Temperature reduction rate = 0.99 | Iterations = 200 Tabu list = 5 Maximum number of parents = 2 |

Index | BayesNet-GA | BayesNet-SA | BayesNet-TS | BayesNet | ||||
---|---|---|---|---|---|---|---|---|

Training | Validation | Training | Validation | Training | Validation | Training | Validation | |

RMSE | 0.2633 | 0.334 | 0.2844 | 0.3502 | 0.3415 | 0.427 | 0.3621 | 0.44 |

MAE | 0.2178 | 0.288 | 0.2238 | 0.3112 | 0.297 | 0.349 | 0.3123 | 0.3721 |

Kappa | 0.885 | 0.75 | 0.8168 | 0.7321 | 0.725 | 0.5 | 0.711 | 0.5 |

Precision | 0.947 | 0.877 | 0.909 | 0.867 | 0.863 | 0.787 | 0.8321 | 0.7468 |

Recall | 0.943 | 0.875 | 0.908 | 0.866 | 0.863 | 0.75 | 0.8321 | 0.7212 |

ROC-AUC | 0.987 | 0.948 | 0.974 | 0.939 | 0.944 | 0.892 | 0.9212 | 0.8732 |

Model | ROC–AUC | SE | 95% CI |
---|---|---|---|

BayesNet-GA | 0.830 | 0.0378 | 0.748 to 0.895 |

BayesNet-SA | 0.818 | 0.0393 | 0.734 to 0.884 |

BayesNet-TS | 0.810 | 0.0419 | 0.725 to 0.878 |

BayesNet | 0.792 | 0.0428 | 0.705 to 0.863 |

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**MDPI and ACS Style**

Karimi-Rizvandi, S.; Goodarzi, H.V.; Afkoueieh, J.H.; Chung, I.-M.; Kisi, O.; Kim, S.; Linh, N.T.T.
Groundwater-Potential Mapping Using a Self-Learning Bayesian Network Model: A Comparison among Metaheuristic Algorithms. *Water* **2021**, *13*, 658.
https://doi.org/10.3390/w13050658

**AMA Style**

Karimi-Rizvandi S, Goodarzi HV, Afkoueieh JH, Chung I-M, Kisi O, Kim S, Linh NTT.
Groundwater-Potential Mapping Using a Self-Learning Bayesian Network Model: A Comparison among Metaheuristic Algorithms. *Water*. 2021; 13(5):658.
https://doi.org/10.3390/w13050658

**Chicago/Turabian Style**

Karimi-Rizvandi, Sadegh, Hamid Valipoori Goodarzi, Javad Hatami Afkoueieh, Il-Moon Chung, Ozgur Kisi, Sungwon Kim, and Nguyen Thi Thuy Linh.
2021. "Groundwater-Potential Mapping Using a Self-Learning Bayesian Network Model: A Comparison among Metaheuristic Algorithms" *Water* 13, no. 5: 658.
https://doi.org/10.3390/w13050658