# Comparison of Different Machine Learning Methods for Debris Flow Susceptibility Mapping: A Case Study in the Sichuan Province, China

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Materials and Methods

#### 3.1. Preparation of Data Sets

#### 3.1.1. Compilation of Debris Flow Inventory

#### 3.1.2. Selection of Debris Flow Causal Factors

^{2}to 1829.68 km

^{2}. We excluded a few regions (e.g., plateau and plain areas) of the Sichuan Province in susceptibility mapping because of the inadequate conditions to trigger a debris flow.

#### 3.1.3. Partition of Data Sets

#### 3.2. Model Construction Using Machine Learning Algorithms

#### 3.2.1. Logistic Regression (LR)

_{1}, …, X

_{p}) are the debris flow causal factors, β

_{0}represents the intercept, (β

_{1}, …, β

_{p}) are the regression coefficients. LR uses the maximum likelihood method to estimate (β

_{1}, …, β

_{p}). Finally, the probability of a debris flow occurring varies from 0 to 1.

#### 3.2.2. Random Forest (RF)

#### 3.2.3. Support Vector Machines (SVM)

_{1}, ε

_{2}, …, ε

_{n}are slack variables. Later, to classify new data, the decision function can be written as below:

_{i}are positive real constants. The radial basis kernel function was adopted in this study due to its robustness, as reported by Rahmati et al. [30] and Kavzoglu et al. [45]. The core parameters of SVM modeling included gamma and cost.

#### 3.2.4. Boosted Regression Trees (BRT)

#### 3.3. Evaluation and Comparison Methods

## 4. Results

#### 4.1. Development of Debris Flow Susceptibility Maps

#### 4.2. Evaluation and Comparison of Machine Learning Models

#### 4.3. Assessment of Factor Importance

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Study area and debris flow location map. Each dot represents the geographic coordinate of a debris flow.

**Figure 4.**Optimal causal factors used for final debris flow susceptibility mapping. (

**a**) mean slope angle, (

**b**) mean altitude, (

**c**) altitude difference, (

**d**) groove gradient, (

**e**) seismic intensity, (

**f**) area of moderately hard lithology in each watershed, (

**g**) clay content of each watershed, (

**h**) area of moderate soil erosion in each watershed, (

**i**) area of severe soil erosion in each watershed, (

**j**) NDVI, (

**k**) moisture index, (

**l**) aridity index, (

**m**) accumulated temperature of 10 °C, (

**n**) population density, and (

**o**) road density.

**Figure 5.**The debris flow susceptibility maps of the Sichuan Province based on the (

**a**) Logistic Regression (LR), (

**b**) Random Forest (RF), (

**c**) Support Vector Machines (SVM), and (

**d**) Boosted Regression Trees (BRT) models.

**Figure 7.**The ROC curves of four debris flow susceptibility models using (

**a**) training set and (

**b**) validation set.

**Figure 8.**Importance of causal factors in the RF model. Values are arranged based on the mean decrease in Gini index and the expressed relative to the maximum value.

**Figure 9.**Distribution of watersheds with high and very high debris flow susceptibility derived from the BRT model on (

**a**) mean altitude map, (

**b**) altitude difference map, (

**c**) aridity index map, and (

**d**) groove gradient map.

No. | Causal Factors | Clusters | Sources |
---|---|---|---|

1 | Mean slope angle | Topographic | ASTER GDEM (Spatial resolution of 30 m × 30 m) (http://earthexplorer.usgs.gov) |

2 | Slope aspect | ||

3 | Mean altitude | ||

4 | Altitude difference | ||

5 | Groove gradient | ||

6 | Seismic intensity * | Geological | China seismic information (Scale of 1:4,000,000) (http://www.csi.ac.cn) |

7 | Lithology * | Lithological composition map of Sichuan Province (Scale of 1:200,000) (http://www.csi.ac.cn) | |

8 | Soil texture * | Edaphic | Spatial distribution datasets of soil texture in China (Spatial resolution of 1 km × 1 km) (http://www.resdc.cn) |

9 | Soil erosion * | Spatial distribution datasets of soil erosion in China (Spatial resolution of 1 km × 1 km) (http://www.resdc.cn) | |

10 | Moisture index (Calculated by Thornthwaite method) | Meteorological | Meteorological datasets in China (Spatial resolution of 500 m × 500 m) (http://www.resdc.cn) |

11 | Aridity index | ||

12 | Mean annual temperature | ||

13 | Accumulated temperature of 10 °C | ||

14 | Annual precipitation | ||

15 | Population density | Sociometric | Spatial distribution datasets of population in China (Spatial resolution of 1 km × 1 km) (http://www.resdc.cn) |

16 | Road density | OpenStreetMap Data (http://planet.openstreetmap.org) | |

17 | Normalized Difference Vegetation Index (NDVI) | Land cover | MODIS images (Spatial resolution of 500 m × 500 m) (https://modis.gsfc.nasa.gov) |

18 | Land use * | The land use and land cover change database in China (Spatial resolution of 1 km × 1 km) (http://www.resdc.cn) |

^{1}The factors with “*” in the table have the following sub-factors: (1) The seismic intensity was reclassified into five groups (<VI, VI, VII, VIII, and ≥IX), and the area of each group was also taken as a factor. (2) The lithology was constructed with five groups based on hardness (extremely soft, soft, moderate hard, hard, and extremely hard), and the area of each group was also taken as a factor. (3) The soil texture included three factors—clay content, sand content, and silt content. (4) Soil erosion was reclassified into six groups (micro, mild, moderate, serious, drastic, and very drastic), and the area of each group was also taken as a factor. (5) Land use was interpreted as six groups (cropland, woodland, grassland, waterbody, construction land, and unused land), and the area of each type was also taken as a factor.

Observed | Predicted | |
---|---|---|

Debris-Flow | Non-Debris-Flow | |

Debris-flow | True positive (TP) | False negative (FN) |

Non-debris-flow | False positive (FP) | True negative (TN) |

Evaluation Criteria | Models | |||
---|---|---|---|---|

LR | RF | SVM | BRT | |

ACC | 0.762 | 0.791 | 0.785 | 0.823 |

AUC | 0.843 | 0.870 | 0.865 | 0.907 |

Evaluation Criteria | Models | |||
---|---|---|---|---|

LR | RF | SVM | BRT | |

ACC | 0.762 | 0.779 | 0.781 | 0.781 |

AUC | 0.829 | 0.849 | 0.849 | 0.852 |

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**MDPI and ACS Style**

Xiong, K.; Adhikari, B.R.; Stamatopoulos, C.A.; Zhan, Y.; Wu, S.; Dong, Z.; Di, B. Comparison of Different Machine Learning Methods for Debris Flow Susceptibility Mapping: A Case Study in the Sichuan Province, China. *Remote Sens.* **2020**, *12*, 295.
https://doi.org/10.3390/rs12020295

**AMA Style**

Xiong K, Adhikari BR, Stamatopoulos CA, Zhan Y, Wu S, Dong Z, Di B. Comparison of Different Machine Learning Methods for Debris Flow Susceptibility Mapping: A Case Study in the Sichuan Province, China. *Remote Sensing*. 2020; 12(2):295.
https://doi.org/10.3390/rs12020295

**Chicago/Turabian Style**

Xiong, Ke, Basanta Raj Adhikari, Constantine A. Stamatopoulos, Yu Zhan, Shaolin Wu, Zhongtao Dong, and Baofeng Di. 2020. "Comparison of Different Machine Learning Methods for Debris Flow Susceptibility Mapping: A Case Study in the Sichuan Province, China" *Remote Sensing* 12, no. 2: 295.
https://doi.org/10.3390/rs12020295