# Using Deep Learning to Formulate the Landslide Rainfall Threshold of the Potential Large-Scale Landslide

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Materials and Methods

#### 3.1. Data Collection

#### 3.2. Preprocess

#### 3.3. Multicollinearity Analysis

_{i}

^{2}is the coefficient of multiple determination of regression i.

#### 3.4. The Framework of Deep Learning Model

_{j}is the raw output value of the layer j, and K is the total number of labels. The total percent of the output value in the classification model must be equal to 1.

#### 3.5. Hyperparameter Tuning

#### 3.6. Model Evaluate

_{1}score, as well as the harmonic mean of the precision and recall [53].

## 4. Results and Discussion

#### 4.1. Correlation and Multicollinearity between Factors

#### 4.2. Result of Hyperparameter Tuning

#### 4.3. Training and Evaluated Results

#### 4.4. Predicting and Revising Landslide Rainfall Threshold

#### 4.5. Establishing Recurrence Interval Distribution of Revised Landslide Rainfall Threshold

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Location of the influence area of Alishan D098; (

**b**) the historical landslide areas by years.

**Figure 3.**(

**a**) The new landslide distribution; (

**b**) the number of grid points by year in the sub-basin.

**Figure 4.**Spatial distribution of maximum daily rainfall in 2009. (

**a**) Tsengwen Reservoir Watershed; (

**b**) sub-basin where the study area is located.

**Figure 5.**Topographic factors: (

**a**) elevation; (

**b**) slope; (

**c**) aspect; (

**d**) plan curvature; (

**e**) profile curvature; (

**f**) Topographic Wetness Index (TWI); (

**g**) Stream Power Index (SPI); (

**h**) distance from fault; (

**i**) distance from river; (

**j**) distance from road; (

**k**) lithology. 1. Thick-bedded massive sandstone and argillaceous sandstone; 2. sandstone and sand-shale interbedding; 3. bodies of water; 4. massive shale, occasionally with thin-bedded siltstone; 5. siltstone and shale thin interbedding.

**Figure 7.**Pearson correlation coefficient between factors for training datasets. (

**a**) Landslide susceptibility classification model; (

**b**) rainfall threshold regression model.

**Figure 8.**The accuracy and loss trend of training and validation dataset. (

**a**) Landslide susceptibility classification model; (

**b**) rainfall threshold regression model.

**Figure 10.**The prediction result of the sub-basin and Alishan D098 influence area. (

**a**) Landslide susceptibility classification model; (

**b**) rainfall threshold regression model.

**Figure 11.**The spatial distribution of landslide rainfall threshold in Alishan D098 influence area. (

**a**) Original result, which did not take the landslide susceptibility into account; (

**b**) revised result, which did take the landslide susceptibility into account.

**Figure 13.**The distribution of recurrence interval of revised landslide rainfall threshold in the influence area.

Topography Factors | Data Source | Data Type | Value Range |
---|---|---|---|

Elevation | DEM | Continuous | 384.70–1238.10 |

Slope | DEM | Continuous | 0.00–64.89 |

Aspect | DEM | Continuous | −1.00–360.00 |

Plan curvature | DEM | Continuous | −27.07–25.72 |

Profile curvature | DEM | Continuous | −31.32–30.42 |

Topographic Wetness Index (TWI) | DEM | Continuous | 2.65–20.51 |

Stream Power Index (SPI) | DEM | Continuous | 0–4,388,483 |

Distance to fault | CGS | Continuous | 0.00–1646.15 |

Distance to river | DEM | Continuous | 0.00–680.66 |

Distance to road | OpenStreetMap | Continuous | 0.00–610.98 |

Lithology | CGS | Categorical | n/a |

Hyperparameters | Type | Defined Parameters |
---|---|---|

Counts of Hidden Layer | Integer | 2–10 |

Neurons of Hidden Layer | Integer | 4, 8, 12, …, 124, 128 |

Dropout Rate | Real | 0.00, 0.05, 0.10, …, 0.85, 0.90 |

Stepsize of Adam Optimizer | Float | 0.0001–0.1 |

**Table 3.**The VIF results of each factor for training datasets of landslide susceptibility and rainfall threshold regression model.

Features | Landslide Susceptibility (n = 62,252) | Rainfall Threshold (n = 31,126) |
---|---|---|

Elevation | 2.916 | 3.330 |

Slope | 1.359 | 1.502 |

Aspect | 1.435 | 1.381 |

Plan Curvature | 1.548 | 1.548 |

Profile Curvature | 1.246 | 1.252 |

TWI | 1.963 | 2.293 |

SPI | 1.279 | 1.447 |

Distance to fault | 2.444 | 2.492 |

Distance to river | 2.094 | 2.491 |

Distance to road | 1.060 | 1.041 |

Lithology | 1.346 | 1.423 |

Hyperparameters | Landslide Susceptibility Classification | Rainfall Threshold Regression | ||||
---|---|---|---|---|---|---|

1st | 2nd | 3rd | 1st | 2nd | 3rd | |

Counts of hidden layer | 4 | 4 | 3 | 4 | 4 | 3 |

Neurons of hidden layer 1 | 108 | 108 | 108 | 124 | 120 | 120 |

Rate of dropout layer 1 | 0.05 | 0.05 | 0.30 | 0.20 | 0.20 | 0.45 |

Neurons of hidden layer 2 | 84 | 84 | 96 | 128 | 108 | 84 |

Rate of dropout layer 2 | 0.25 | 0.25 | 0.45 | 0.20 | 0.70 | 0.05 |

Neurons of hidden layer 3 | 100 | 100 | 60 | 36 | 28 | 88 |

Rate of dropout layer 3 | 0.45 | 0.45 | 0.10 | 0.25 | 0.05 | 0.00 |

Neurons of hidden layer 4 | 112 | 112 | - | 72 | 28 | - |

Rate of dropout layer 4 | 0.30 | 0.30 | - | 0.10 | 0.40 | - |

Stepsize of Adam Optimizer | 0.000874 | 0.000874 | 0.000383 | 0.001889 | 0.000669 | 0.000507 |

Initial epoch | 67 | 23 | 67 | 67 | 67 | 67 |

Epochs | 200 | 67 | 200 | 200 | 200 | 200 |

Best step | 91 | 41 | 127 | 83 | 120 | 99 |

Validation accuracy | 0.8916 | 0.8683 | 0.8652 | n/a | n/a | n/a |

Score (Validation loss) | 0.0801 | 0.0977 | 0.0998 | 0.0675 | 0.0704 | 0.0710 |

Models | Evaluate | Train Dataset | Test Dataset |
---|---|---|---|

Landslide Susceptibility Classification | Overall accuracy | 0.9094 | 0.8959 |

Precision | 0.9118 | 0.8985 | |

Recall | 0.9094 | 0.8959 | |

ROC AUC | 0.9633 | 0.9550 | |

F_{1} score | 0.9092 | 0.8957 | |

Cohen’s kappa | 0.8187 | 0.7918 | |

MCC | 0.8211 | 0.7944 | |

Rainfall Threshold Regression | MAE | 180.09 | 185.98 |

RMSE | 228.03 | 233.97 | |

MAPE | 0.2631 | 0.2716 |

Recurrence Interval | p-Value | RMSE |
---|---|---|

Extreme-value Type I Distribution | 0.9995 | 0.0424 |

Normal Distribution | 0.8510 | 0.0555 |

Pearson Type III Distribution | 0.9725 | 0.0441 |

Log-Normal Distribution | 0.9725 | 0.0437 |

Log-Pearson Type III Distribution | 0.8510 | 0.0840 |

Regions | Condition | Rainfall Threshold (mm/day) | Recurrence Interval (Year) |
---|---|---|---|

Northeast Alishan D098 Downstream of Alishan D098 Longmei Settlement | Non-managed | 780 | 20 |

Has been managed | 820 | 25 | |

Whole Area | n/a | 980 | 64 |

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**MDPI and ACS Style**

Chiang, J.-L.; Kuo, C.-M.; Fazeldehkordi, L.
Using Deep Learning to Formulate the Landslide Rainfall Threshold of the Potential Large-Scale Landslide. *Water* **2022**, *14*, 3320.
https://doi.org/10.3390/w14203320

**AMA Style**

Chiang J-L, Kuo C-M, Fazeldehkordi L.
Using Deep Learning to Formulate the Landslide Rainfall Threshold of the Potential Large-Scale Landslide. *Water*. 2022; 14(20):3320.
https://doi.org/10.3390/w14203320

**Chicago/Turabian Style**

Chiang, Jie-Lun, Chia-Ming Kuo, and Leila Fazeldehkordi.
2022. "Using Deep Learning to Formulate the Landslide Rainfall Threshold of the Potential Large-Scale Landslide" *Water* 14, no. 20: 3320.
https://doi.org/10.3390/w14203320