# Rainfall Induced Landslide Susceptibility Mapping Based on Bayesian Optimized Random Forest and Gradient Boosting Decision Tree Models—A Case Study of Shuicheng County, China

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}and the population is about 754,900 [34] (Figure 1). Shuicheng County is one of the most landslide-prone areas in China, one of the reasons is because it is karst landscape with easily leaking surface water and high soil moisture content. The annual average precipitation (AAP) of study area is about 1100 mm, precipitation is the major inducing factor for landslides. On 23 July 2019, a rainfall induced landslide occurred in the study area, which caused the destruction of many houses and roads and the death of villagers [35,36]. According to the Guizhou Meteorological Bureau, between 18 and 23 July, Jichang Town experienced three periods of heavy rain shortly before the landslide: the night of 18 July from 19 July to 20 July and the night of 22 July. The cumulative rainfall at this site reached 189.1 mm for 18–23 July and 98 mm for 22–23 July. [35].

#### 2.2. Data

^{2}/m), $\beta $ is the slope of each grid [44], $DE{M}_{MAX}$ and $DE{M}_{MIN}$ are the maximum and minimum DEM value of eight grids around each grid, respectively. All the variables in those equations can be extracted by DEM data using “Fill,” “Flow Accumulation,” “Flow Direction,” “Neighborhood Statistics” and “Raster Calculator” tools in ArcGIS.

## 3. Methods

#### 3.1. Data Pretreatment

#### 3.2. Imbalanced Sample Problem and Sample Preparation

#### 3.3. RF Model

#### 3.4. GBDT Model

#### 3.5. Bayesian Optimization

#### 3.6. Model Evaluation

## 4. Results

#### 4.1. Feature Importance

#### 4.2. Results of Bayesian Optimization

#### 4.3. LSMs Based Multiple Models

_{li}) is over 63% for all models in both the high and very high grades and very few in both the low and very low areas. This indicates the good accuracy of all four models. Compared to the RF model, the GBDT model has a higher P

_{li}at both very low and very high levels, indicating that the GBDT model is more sensitive to positive samples and less effective than RF in predicting negative samples. Comparing the four models, GBDT_B has the best P

_{li}distribution, which also indicates that it may be the best model and the specific model validation results are compared and analyzed in 4.4.

#### 4.4. Model Comparison and Validation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Data and Code Availability

## References

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**Figure 2.**Thematic maps of conditioning factors. (

**a**) Elevation, (

**b**) Slope, (

**c**) Aspect, (

**d**) Plan curvature, (

**e**) Profile curvature, (

**f**) Lithology, (

**g**) Geological age, (

**h**) Distance to faults, (

**i**) Distance to roads, (

**j**) Distance to rivers, (

**k**) Stream power index (SPI), (

**l**) Sediment transport index (STI), (

**m**) Topographic relief index (TRI), (

**n**) Topographic wetness index (TWI), (

**o**) Land cover, (

**p**) Normalized difference vegetation index (NDVI), (

**q**) Annual average precipitation (AAP).

Conditioning Factor | Data Structure | Data Summary |
---|---|---|

Elevation | Raster | Height above sea level |

Slope | Raster | Calculated by DEM |

Aspect | Raster | Calculated by DEM |

Plan curvature | Raster | Calculated by DEM |

Profile curvature | Raster | Calculated by DEM |

Lithology | Polygon | Digitized from lithology map |

Geological age | Polygon | Digitized from geological age map |

Faults | Line | Distance to faults |

Roads | Line | Distance to roads |

Rivers | Line | Distance to rivers |

SPI | Raster | Calculated by DEM |

STI | Raster | Calculated by DEM |

TRI | Raster | Calculated by DEM |

TWI | Raster | Calculated by DEM |

Land cover | Raster | The category of land cover |

NDVI | Raster | The Vegetation cover index |

Precipitation | Raster | Annual average precipitation |

**Table 2.**Hyperparameters, default values and search spaces of random forest (RF) and gradient boosting decision tree (GBDT) models.

Model | Hyperparameter | Default Value | Search Space |
---|---|---|---|

RF | N_Estimators | 100 | (50, 500) |

Max_Depth | None | (1, 100) | |

Min_Sample_Leaf | 1 | (1, 100) | |

Max_Leaf_Nodes | Max Value (factor number) | (2, 17) | |

GBDT | N_Estimators | 100 | (50, 500) |

Max_Depth | None | (1, 100) | |

Min_Sample_Leaf | 1 | (1, 100) | |

Max_Leaf_Nodes | Max Value (factor number) | (2, 17) | |

Learning_Rate | 1.0 | (0.1, 1.0) | |

Subsample | 1.0 | (0.5, 1.0) |

Model | Hyperparameter | Bayesian Optimization Result |
---|---|---|

RF | N_Estimators | 252 |

Max_Depth | 42 | |

Min_Sample_Leaf | 1 | |

Max_Leaf_Nodes | 17 | |

GBDT | N_Estimators | 310 |

Max_Depth | 47 | |

Min_Sample_Leaf | 2 | |

Max_Leaf_Nodes | 17 | |

Learning_Rate | 0.30346 | |

Subsample | 0.95475 |

**Table 4.**Quantitative results for the comparison of historical landslides of each grade in LSMs (P

_{li}is the percentage of historical landslides in each grade to total landslides).

RF | GBDT | RF_B | GBDT_B | |||||
---|---|---|---|---|---|---|---|---|

LSM Grade | Count | P_{li} (%) | Count | P_{li} (%) | Count | P_{li} (%) | Count | P_{li} (%) |

Very Low | 7 | 2.92 | 21 | 8.75 | 8 | 3.33 | 17 | 7.08 |

Low | 31 | 12.92 | 19 | 7.92 | 33 | 13.75 | 7 | 2.92 |

Medium | 50 | 20.83 | 34 | 14.12 | 49 | 20.42 | 5 | 2.08 |

High | 85 | 35.42 | 62 | 25.84 | 77 | 32.08 | 12 | 5.00 |

Very High | 67 | 27.93 | 94 | 39.17 | 73 | 30.42 | 199 | 82.92 |

Model | Test Data Set | Validation Methods | Results | |
---|---|---|---|---|

RF | TP | 116 | Precision | 0.739 |

Recall | 0.806 | |||

TN | 103 | F1 | 0.771 | |

Accuracy | 0.760 | |||

FP | 41 | OPR | 0.261 | |

UPR | 0.194 | |||

FN | 28 | MCC | 0.523 | |

AUC | 0.845 | |||

GBDT | TP | 116 | Precision | 0.707 |

Recall | 0.806 | |||

TN | 96 | F1 | 0.753 | |

Accuracy | 0.736 | |||

FP | 48 | OPR | 0.293 | |

UPR | 0.194 | |||

FN | 28 | MCC | 0.477 | |

AUC | 0.796 | |||

RF_B | TP | 119 | Precision | 0.744 |

Recall | 0.826 | |||

TN | 103 | F1 | 0.783 | |

Accuracy | 0.771 | |||

FP | 41 | OPR | 0.256 | |

UPR | 0.174 | |||

FN | 25 | MCC | 0.545 | |

AUC | 0.860 | |||

GBDT_B | TP | 115 | Precision | 0.782 |

Recall | 0.799 | |||

TN | 112 | F1 | 0.790 | |

Accuracy | 0.788 | |||

FP | 32 | OPR | 0.218 | |

UPR | 0.201 | |||

FN | 29 | MCC | 0.576 | |

AUC | 0.866 |

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**MDPI and ACS Style**

Rong, G.; Alu, S.; Li, K.; Su, Y.; Zhang, J.; Zhang, Y.; Li, T.
Rainfall Induced Landslide Susceptibility Mapping Based on Bayesian Optimized Random Forest and Gradient Boosting Decision Tree Models—A Case Study of Shuicheng County, China. *Water* **2020**, *12*, 3066.
https://doi.org/10.3390/w12113066

**AMA Style**

Rong G, Alu S, Li K, Su Y, Zhang J, Zhang Y, Li T.
Rainfall Induced Landslide Susceptibility Mapping Based on Bayesian Optimized Random Forest and Gradient Boosting Decision Tree Models—A Case Study of Shuicheng County, China. *Water*. 2020; 12(11):3066.
https://doi.org/10.3390/w12113066

**Chicago/Turabian Style**

Rong, Guangzhi, Si Alu, Kaiwei Li, Yulin Su, Jiquan Zhang, Yichen Zhang, and Tiantao Li.
2020. "Rainfall Induced Landslide Susceptibility Mapping Based on Bayesian Optimized Random Forest and Gradient Boosting Decision Tree Models—A Case Study of Shuicheng County, China" *Water* 12, no. 11: 3066.
https://doi.org/10.3390/w12113066