# Rainfall-Induced Landslide Prediction Using Machine Learning Models: The Case of Ngororero District, Rwanda

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Area of Study

^{2}, and is composed of 13 administrative sectors, 73 administrative cells, and 419 villages. The district shares borders with five other districts. The district has a relief characterized by high mountains with very steep slopes that flow into valleys. The altitude varies between 1460 m and 2883 m above sea level, the highest point being on Bweru Mountain situated in Muhanda sector with 2883.4 m of altitude. The average annual temperature is 18 °C which varies with the altitude. The average altitude is 1500 m.

#### 2.2. Data Acquisition and Landslide Inventory

#### 2.2.1. Data Collection

#### 2.2.2. Dataset

#### 2.2.3. Rainfall

_{0}, Z(Si) represents the observed value at point Si, n is the number of observations, and λi is the weight. The weights decrease as the distance increases. The weights λi can be calculated as follows:

_{i0}is the distance between a target and observations. Rainfall data from the two weather stations in the study area and those in three neighboring districts (Figure 4) were used as input into the IDW model and GIS software tool was used for implementation.

#### 2.2.4. Antecedent Rainfall

#### 2.2.5. Slope

#### 2.2.6. Soil Type

#### 2.2.7. Soil Depth

#### 2.2.8. Land Cover

#### 2.2.9. Landslide Incidences

#### 2.2.10. Splitting Dataset into a Training and a Test Dataset

#### 2.2.11. Training and Testing the Models

#### 2.2.12. Results Analysis

#### 2.3. Machine Learning Models

#### 2.3.1. Random Forest

#### 2.3.2. Logistic Regression

#### 2.4. Re-Sampling

#### 2.5. Preliminary Analysis Using Exploratory Data Analysis (EDA)

#### 2.6. Models Evaluation

## 3. Results

#### 3.1. Preliminary Analysis: Correlation Among Features Used in the Models

#### 3.2. Models Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Geographical characteristics in the study area: (

**a**) slope, (

**b**) land cover, (

**c**) soil type, (

**d**) soil depth.

**Figure 7.**Random Forest decision tree [28].

**Figure 12.**ROC-AUC (

**a**) with no antecedent rainfall, (

**b**) 5-days antecedent rainfall taken into consideration.

Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | Total |
---|---|---|---|---|---|---|---|---|---|

Number of death | 19 | 14 | 31 | 0 | 10 | 64 | 7 | 77 | 222 |

**Table 2.**Summary of classification of key parameters in the study area and their standardized scores used in the model.

Slope | Soil | Land | |||||
---|---|---|---|---|---|---|---|

Slope Angle (Degree) | Score | Soil Type | Score | Soil Depth (cm) | Score | Land Cover | Score |

0–10 | 0 | Clay | 0 | <50 | 1 | Forest plantation | 3 |

>10–15 | 1 | Sand | 4 | >50–100 | 4 | Agriculture | 7 |

>15–20 | 4 | Silt | 6 | >100 | 10 | Open land | 10 |

>20–25 | 6 | ||||||

>25–45 | 10 |

1-Day Rainfall (Without Antecedent Rainfall) | 5-Days Antecedent Rainfall Included | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Fold | Accuracy (using cross-validation) | Accuracy (using train/test ratios) | Accuracy (using cross-validation) | Accuracy (using train/test ratios) | ||||||

RF | LR | Ratio | RF | LR | RF | LR | Ratio | RF | LR | |

1 | 0.9530 | 0.9466 | 0.80 & 0.20 | 0.9414 | 0.9322 | 0.9875 | 0.9877 | 0.80 & 0.20 | 0.9742 | 0.9836 |

2 | 0.9536 | 0.9466 | 0.75 & 0.25 | 0.9398 | 0.9330 | 0.9871 | 0.9882 | 0.75 & 0.25 | 0.9759 | 0.9835 |

3 | 0.9531 | 0.9459 | 0.70 & 0.30 | 0.9399 | 0.9352 | 0.9876 | 0.9878 | 0.70 & 0.30 | 0.9744 | 0.9838 |

4 | 0.952 | 0.9457 | 0.65 & 0.35 | 0.9394 | 0.9392 | 0.9870 | 0.9879 | 0.65 & 0.35 | 0.9767 | 0.9838 |

5 | 0.9530 | 0.9467 | 0.60 & 0.40 | 0.9469 | 0.9413 | 0.9876 | 0.9879 | 0.60 & 0.40 | 0.9740 | 0.9840 |

Av. | 0.9530 | 0.9463 | 0.55 & 0.45 | 0.9409 | 0.9415 | 0.9874 | 0.9879 | 0.55 & 0.45 | 0.9744 | 0.9837 |

Std | 0.0003 | 0.0004 | 0.0028 | 0.0041 | 0.0002 | 0.0001 | 0.001 | 0.0001 |

Performance Metric | 1-Day Rainfall, Antecedent Rainfall Excluded (%) | 5-Days Antecedent Rainfall Included (%) | ||
---|---|---|---|---|

RF | LR | RF | LR | |

Recall (TPR) | 84.61 | 90.38 | 95.19 | 96.15 |

Specificity (TNR) | 93.91 | 93.92 | 97.64 | 98.38 |

False Positive Rate (FPR) | 6.08 | 6.07 | 2.35 | 1.61 |

False Negative Rate (FNR) | 15.38 | 9.61 | 4.80 | 3.84 |

Intercept | Daily Rainfall | Antecedent Rainfall (5-Days) | Slope | Soil Type | Soil Depth | Land Cover |
---|---|---|---|---|---|---|

−7.06 | 1.32 | 2.47 | −9.34 | −2.90 | −4.10 | −4.37 |

−9.29 | −5.39 | −1.85 | −1.12 | |||

1.20 | 1.23 | −1.10 | −1.56 | |||

3.87 | ||||||

6.49 |

Random Forest | Logistic Regression | |||||
---|---|---|---|---|---|---|

Correct Predictions (%) | ||||||

Performance Metric | Without Antecedent Rainfall | With Antecedent Rainfall | Improvement (%) | Without Antecedent Rainfall | With Antecedent Rainfall | Improvement (%) |

Recall (TPR) | 84.61 | 95.19 | 10.58 | 90.38 | 96.15 | 5.77 |

Specificity (TNR) | 93.91 | 97.64 | 3.73 | 93.92 | 98.38 | 4.46 |

Incorrect Predictions (%) | ||||||

False Positives | 6.08 | 2.35 | 3.73 | 6.07 | 1.61 | 4.46 |

False Negatives | 15.38 | 4.80 | 10.58 | 9.61 | 3.84 | 5.77 |

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## Share and Cite

**MDPI and ACS Style**

Kuradusenge, M.; Kumaran, S.; Zennaro, M.
Rainfall-Induced Landslide Prediction Using Machine Learning Models: The Case of Ngororero District, Rwanda. *Int. J. Environ. Res. Public Health* **2020**, *17*, 4147.
https://doi.org/10.3390/ijerph17114147

**AMA Style**

Kuradusenge M, Kumaran S, Zennaro M.
Rainfall-Induced Landslide Prediction Using Machine Learning Models: The Case of Ngororero District, Rwanda. *International Journal of Environmental Research and Public Health*. 2020; 17(11):4147.
https://doi.org/10.3390/ijerph17114147

**Chicago/Turabian Style**

Kuradusenge, Martin, Santhi Kumaran, and Marco Zennaro.
2020. "Rainfall-Induced Landslide Prediction Using Machine Learning Models: The Case of Ngororero District, Rwanda" *International Journal of Environmental Research and Public Health* 17, no. 11: 4147.
https://doi.org/10.3390/ijerph17114147