# Optimizing Rotation Forest-Based Decision Tree Algorithms for Groundwater Potential Mapping

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The topographical elevation of the study area varies between 1230 m and 1800 m above sea level (a.s.l.) [26].

^{2}, out of which 516 rivers have drainage areas between 1 and 10 km

^{2}, 93 rivers have drainage areas between 10 and 50 km

^{2}, 33 rivers have drainage areas between 50 and 100 km

^{2}, and 10 rivers have drainage areas larger than 100 km

^{2}. The total length of rivers is 3255.96 km, and the river network density is 0.86 km/km

^{2}.

^{2}is 0.9 km/km

^{2}. The relative height difference of ravines is 120–567 m, and the average longitudinal gradient of tributaries is between 2.5‰ and 9.13‰.

#### 2.2. Data Processing

## 3. Methodology

#### 3.1. Multicollinearity among Factors

#### 3.2. Evidential Belief Function (EBF)

_{ij}represents the jth class of the ith evaluation factor, and A represents the evaluation area; N(T) represents the total number of dependent variables; N(A

_{ij}) represents the number of evaluation units in the jth class of the ith evaluation factor; N(T∩A

_{ij}) represents the number of dependent variables in the jth class of the ith evaluation factor; and N(A) represents the total number of evaluation units in the evaluation area.

_{ij}to the conditional probability that D exists given the absence of A

_{ij}; ${{\displaystyle W}}_{{{\displaystyle A}}_{ij}}(\overline{D})$ is the ratio of the conditional probability that D does not exist given the presence of A

_{ij}to the conditional probability that D does not exist given the absence of A

_{ij}.

#### 3.3. Rotation Forest (RF)

#### 3.4. Best-First Decision Tree Classifier (BFTree)

#### 3.5. Classification and Regression Tree (CART)

#### 3.6. Functional Trees (FT)

#### 3.7. Performance Evaluation of Models

## 4. Results

#### 4.1. Correlation Analysis

#### 4.2. Configuration and Training of the Models

#### 4.3. Model Performance and Validation

#### 4.4. Comparison of the Hybrid Model with Benchmark Models

#### 4.5. Generation of Groundwater Potential Maps

## 5. Discussion

## 6. Concluding Remarks

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**(

**a**) Optimization of RFBFT method; (

**b**) Optimization of RFCART method; (

**c**) Optimization of RFFT method.

**Figure 10.**Point density figure: (

**a**) geometrical interval, (

**b**) natural breaks, (

**c**) quantile, (

**d**) equal interval.

**Figure 11.**Groundwater potential maps: (

**a**) EBF model; (

**b**) BFT model; (

**c**) CART model; (

**d**) FT model; (

**e**) RFBFT model; (

**f**) RFCART model; (

**g**) RFFT model.

Methods | Algorithms | Parameter | AUC |
---|---|---|---|

Base classifier | BFT | seed, 8; numFoldsPruning, 6; pruning used. | 0.784 |

CART | seed, 2; numFoldsPruning, 3. | 0.801 | |

FT | FT Leaves; numBoostingIterations, 20; FT and FT Inner used. | 0.854 | |

Ensembles | RF | Use a base classifier, BFT; seed, 9; numIteration, 32. | 0.911 |

Use a base classifier, CART; seed, 37; numIteration, 15. | 0.894 | ||

Use a base classifier, FT; seed, 43; numIteration, 16. | 0.898 |

Test Variables | BFTree | RF-BFT | EBF | CART | RF-CART | FT | RF-FT |
---|---|---|---|---|---|---|---|

AUC | 0.784 | 0.911 | 0.824 | 0.801 | 0.894 | 0.852 | 0.898 |

SE | 0.026 | 0.016 | 0.022 | 0.025 | 0.018 | 0.021 | 0.017 |

95% CI | 0.733–0.836 | 0.880–0.942 | 0.780–0.868 | 0.753–0.849 | 0.859–0.928 | 0.811–0.893 | 0.865–0.932 |

p Value | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 | <0.0001 |

Test Variables | BFTree | RF-BFT | EBF | CART | RF-CART | FT | RF-FT |
---|---|---|---|---|---|---|---|

AUC | 0.659 | 0.807 | 0.725 | 0.669 | 0.808 | 0.705 | 0.800 |

SE | 0.046 | 0.037 | 0.042 | 0.045 | 0.037 | 0.044 | 0.037 |

95% CI | 0.569–0.748 | 0.735–0.879 | 0.642–0.807 | 0.580–0.757 | 0.736–0.880 | 0.619–0.791 | 0.727–0.873 |

p Value | 0.0012 | <0.0001 | <0.0001 | 0.0006 | <0.0001 | <0.0001 | <0.0001 |

Pairwise Comparison | Chi-Square | Significance Level p | Significance |
---|---|---|---|

RF-BFT vs. EBF | 10.84 | 9.958 × 10^{−4} | Yes |

RF-BFT vs. BFT | 28.667 | <0.0001 | Yes |

RF-BFT vs. CART | 26.923 | <0.0001 | Yes |

RF-BFT vs. FT | 13.823 | 2.008 × 10^{−4} | Yes |

RF-CART vs. EBF | 6.693 | 0.010 | Yes |

RF-CART vs. BFT | 20.891 | <0.0001 | Yes |

RF-CART vs. CART | 19.630 | <0.0001 | Yes |

RF-CART vs. FT | 6.551 | 0.010 | Yes |

RF-FT vs. EBF | 7.533 | 6.057 × 10^{−3} | Yes |

RF-FT vs. BFT | 21.464 | <0.0001 | Yes |

RF-FT vs. CART | 18.642 | <0.0001 | Yes |

RF-FT vs. FT | 8.988 | 2.718 × 10^{−3} | Yes |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, W.; Wang, Z.; Wang, G.; Ning, Z.; Lian, B.; Li, S.; Tsangaratos, P.; Ilia, I.; Xue, W.
Optimizing Rotation Forest-Based Decision Tree Algorithms for Groundwater Potential Mapping. *Water* **2023**, *15*, 2287.
https://doi.org/10.3390/w15122287

**AMA Style**

Chen W, Wang Z, Wang G, Ning Z, Lian B, Li S, Tsangaratos P, Ilia I, Xue W.
Optimizing Rotation Forest-Based Decision Tree Algorithms for Groundwater Potential Mapping. *Water*. 2023; 15(12):2287.
https://doi.org/10.3390/w15122287

**Chicago/Turabian Style**

Chen, Wei, Zhao Wang, Guirong Wang, Zixin Ning, Boxiang Lian, Shangjie Li, Paraskevas Tsangaratos, Ioanna Ilia, and Weifeng Xue.
2023. "Optimizing Rotation Forest-Based Decision Tree Algorithms for Groundwater Potential Mapping" *Water* 15, no. 12: 2287.
https://doi.org/10.3390/w15122287