# Analysis and Mapping of Rainfall-Induced Landslide Susceptibility in A Luoi District, Thua Thien Hue Province, Vietnam

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, based on the interpretation of aerial photographs and field research. A study area of 263 km

^{2}was selected for assessing the landslide susceptibility covering the main mountain ranges and all observed landslides (Figure 1). The observed landslide density in this area is about 2.7%. Unfortunately, no details were found or noted about the width, depth, types or causes of the landslides. Such data are often missing or incomplete, especially in remote and rural regions such as this study area.

#### 2.2. Data Sources

- Slope: a digital slope angle map was derived from the DEM and a slope class map by separating the slope angles into six classes: (1) flat-gentle (<5°), (2) fair (5–15°), (3) moderate (15–25°), (4) fairly moderate (25–35°), (5) steep (35–45°), and (6) very steep (>45°).
- Fault density: faults were digitized from the geological map and the fault density was derived as total length of faults per 1 km
^{2}; a categorical fault density map was obtained by classifying the fault density in intervals of 500 m/km^{2}(Table 1). - Weathering crust: a digital categorical map was derived from fieldwork in Thua Thien Hue Province carried out by Văn et al. [51], indicating Quaternary deposits and four types of weathering crusts: Sialite, Sialferrite, Ferrosialite, and mixtures of Silixite.
- Land use: a digital map was derived from a Landsat TM5 image of 20 February 1999 (Path/row: 125/48); four land uses were identified and verified in the field by Văn et al. [51], resulting in four land use classes: agriculture, forest, shrub and bare hills, and build-up land.
- Drainage distance: a digital map of the shortest distance to a watercourse was derived from the topographic map and a drainage distance class map was obtained by subdividing the values into classes <50 m, 50–200 m and >200 m (adapted from the literature, e.g., reference [20]).
- Precipitation: average annual precipitation was selected as rainfall causative factor for landslide analysis, because precise information about the intensity of individual storms is not available in the study area; the precipitation map was derived by spatial interpolation (inverse distance weighting) of the average annual precipitation observed from 1976 to 2003 in three climate stations in the A Luoi district [52]; the values range from about 2900 mm/year to 3500 mm/year and because this is a rather small range the precipitation class map was derived by dividing the values into just three classes: <3100 mm/year, 3100–3300 mm/year and >3300 mm/year.

#### 2.3. Methods for Landslide Susceptibility Analysis

_{ij}is the weight of class j of parameter i, f

_{ij}the landslide density within class j of parameter i, and f the landslide density within the entire map. Statistically, f

_{ij}is the conditional probability of a landslide event occurring in class j of parameter i and f is the prior probability of a landslide event occurring in the entire study area. Thus, each causative factor map is overlaid with the landslide map and the landslide frequency ratio f

_{ij}/f and weight value in each class of the factor map is determined. The weight value is calculated only for classes with landslide occurrences and a zero value is assigned otherwise [17,20], which implies that the related parameter class has no impact on the landslide susceptibility. By overlying all causative factor class maps and adding the weights, a landslide susceptibility map is obtained that expresses the relative likelihood for landslide occurrence.

_{i}are causative factors, and a

_{i}are regression coefficients. The coefficients are estimated by non-linear regression, imposing $p=1$ in known landslide areas and $p=0$ elsewhere. Then the probability for landslides in each mapping unit is predicted with Equation (2) to obtain a landslide susceptibility map. One of the advantages of LR over other methods is that the probabilities always fall between 0 and 1. Equation (2) implies that all causative factors are numerical variables. Thus, in the case of categorical maps, the classes can be substituted by their corresponding landslide frequency ratios f

_{ij}/f. In this study, the SAS 9.1 software (SAS Institute Inc., Cary, NC, USA) [53] is used to process the data and estimate the regression coefficients.

_{ij}is the certainty factor of class j of parameter i. The values range between −1 and +1, whereby −1 means definitely false and +1 means definitely true. Positive values indicate an increasing certainty in causality, while negative values correspond to the opposite. A value equal to or close to zero means that it is difficult to give any indication about causality. A combination of two CF values, x and y, is a CF value, z, calculated as follows [40,43]

#### 2.4. Model Verification

## 3. Results

## 4. Discussion

#### 4.1. Statistical Index Model

_{ij}/f. Factor classes that contribute strongly to landslides can be identified by frequency ratios larger than 2, which means that the landslide susceptibility is more than double the overall average. There are only four classes that strongly promote landslides: geology classes Dai Loc Complex (magmatic rock) and Lower A Vuong Formation (schist), both fairly soft rock types, and the highest fault density class and the geomorphology erosional-denudational slope class, both for obvious reasons. Factor classes that strongly avert landslides have frequency ratios of less than 0.5, which means that the landslide susceptibility is less than halve of the overall average. There are six classes that fall into this category: the smallest slope class, geomorphology classes Alluvial deposits and Planation surface and the smallest drainage distance class (river banks), which all relate directly to nearly flat areas, and the geological classes Lower Nui Vu Formation and Upper A Lin formation, which also occur predominantly in flat areas.

#### 4.2. Logistic Regression Model

#### 4.3. Certainty Factor Model

#### 4.4. Optimal Model

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Receiver operating characteristic (ROC) curves and area under the curve (AUC) values showing the accuracy of the models for predicting landslide susceptibility (SI: statistical index model, LR: logistic regression model, CF: certainty factor model) and the optimum threshold point for the CF model.

**Table 1.**Causative factors for landslide, classes in each factor, and associated area ratios, landslide frequency ratios, SI weights and CF values (significant values are indicated in bold).

Factor | Class | Area (%) | f_{ij}/f | W_{ij} | CF_{ij} |
---|---|---|---|---|---|

Elevation | <250 m | 14.6 | 0.53 | −0.63 | −0.47 |

250–500 m | 21.1 | 1.46 | 0.38 | 0.33 | |

500–750 m | 48.9 | 0.81 | −0.21 | −0.20 | |

>750 m | 15.4 | 1.42 | 0.35 | 0.30 | |

Slope | <5° | 21.6 | 0.10 | −2.30 | −0.90 |

5–15° | 19.5 | 0.57 | −0.55 | −0.43 | |

15–25° | 23.4 | 1.42 | 0.35 | 0.30 | |

25–35° | 21.1 | 1.52 | 0.42 | 0.35 | |

35–45° | 11.2 | 1.46 | 0.38 | 0.32 | |

>45° | 3.3 | 1.55 | 0.44 | 0.37 | |

Geology | Dai Loc Complex (igneous) | 8.8 | 2.16 | 0.77 | 0.55 |

Lower A Lin (sedimentary) | 11.6 | 0.97 | −0.03 | −0.03 | |

Lower A Vuong (metamorphic) | 5.8 | 2.19 | 0.78 | 0.56 | |

Lower Ben Giang - Que Son (igneous) | 13.9 | 1.00 | 0.00 | 0.00 | |

Lower Long Dai (metamorphic) | 8.4 | 1.12 | 0.11 | 0.11 | |

Lower Nui Vu (metamorphic) | 10.5 | 0.47 | −0.76 | −0.54 | |

Middle A Vuong (metamorphic) | 0.8 | 0 | 0 | −1.00 | |

Middle Long Dai (metamorphic) | 17.6 | 1.26 | 0.23 | 0.21 | |

Middle-upper Pleistocene | 2.1 | 0 | 0 | −1.00 | |

Upper A Lin (sedimentary) | 8.0 | 0.25 | −1.37 | −0.75 | |

Upper Ben Giang - Que Son (igneous) | 1.3 | 0 | 0 | −1.00 | |

Upper Long Dai (metamorphic) | 9.3 | 0.52 | −0.67 | −0.49 | |

Upper Nui Vu (metamorphic) | 1.9 | 0 | 0 | −1.00 | |

Fault density | <500 m/km^{2} | 5.1 | 1.20 | 0.17 | 0.16 |

500–1000 m/km^{2} | 60.0 | 0.96 | −0.04 | −0.04 | |

1000–1500 m/km^{2} | 28.0 | 0.74 | −0.30 | −0.26 | |

>1500 m/km^{2} | 6.8 | 2.28 | 0.83 | 0.58 | |

Geomorphology | Alluvium deposits | 6.3 | 0.11 | −2.27 | −0.90 |

Erosional channels and riverbeds | 10.7 | 0 | 0 | −1.00 | |

Early Quaternary valley pediment | 22.5 | 0.54 | −0.62 | −0.47 | |

Wash slope | 5.5 | 0.53 | −0.64 | −0.48 | |

Erosional-denudational slope | 7.1 | 2.01 | 0.71 | 0.52 | |

Quick gravity slope (debris flow) | 11.8 | 1.23 | 0.21 | 0.19 | |

Slow gravity slope (earth flow) | 28.5 | 1.82 | 0.60 | 0.46 | |

Planation surface | 7.6 | 0.47 | −0.73 | −0.53 | |

Weathering crust | Quaternary deposit | 2.1 | 0 | 0 | −1.00 |

Ferrosialite | 20.9 | 0.67 | −0.39 | −0.33 | |

Mixtures of Silixite | 28.5 | 0.90 | −0.10 | −0.10 | |

Sialferrite | 35.1 | 1.22 | 0.20 | 0.18 | |

Sialite | 13.3 | 1.32 | 0.27 | 0.24 | |

Land use | Agriculture | 4.2 | 0 | 0 | −1.00 |

Forest | 27.2 | 1.20 | 0.18 | 0.17 | |

Shrub and bare hill | 67.1 | 1.01 | 0.01 | 0.01 | |

Built-up area | 1.5 | 0 | 0 | −1.00 | |

Distance to river | ≤50 m | 8.7 | 0.21 | −1.59 | −0.80 |

50–200 m | 22.7 | 0.64 | −0.44 | −0.36 | |

>200 m | 68.6 | 1.22 | 0.20 | 0.18 | |

Precipitation | <3100 mm/y | 32.8 | 0.92 | −0.08 | −0.08 |

3100–3300 mm/y | 39.0 | 1.23 | 0.20 | 0.19 | |

>3300 mm/y | 28.1 | 0.78 | −0.25 | −0.23 |

**Table 2.**Estimated coefficients of the logistic regression model, with standard error and corresponding Student’s t-statistic and p-value.

Parameter | Coefficient | Standard Error | t-Score | p-Value |
---|---|---|---|---|

Intercept | −6.88 | 0.366 | −18.8 | <10^{−4} |

Elevation | 4.29 × 10^{−4} | 0.44 × 10^{−4} | 9.75 | <10^{−4} |

Slope | 0.018 | 0.001 | 18.0 | <10^{−4} |

Geology | 0.660 | 0.021 | 31.3 | <10^{−4} |

Fault density | 7.90 × 10^{−5} | 3.30 × 10^{−5} | 2.39 | 0.008 |

Geomorphology | 0.774 | 0.021 | 37.8 | <10^{−4} |

Land use | −0.134 | 0.061 | −2.21 | 0.014 |

Weathering crust | −0.141 | 0.057 | −2.47 | 0.007 |

Distance to river | 3.06 × 10^{−4} | 0.30 × 10^{−4} | 10.2 | <10^{−4} |

Precipitation | −1.87 × 10^{−3} | 0.03 × 10^{−3} | −69.3 | <10^{−4} |

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**MDPI and ACS Style**

Long, N.T.; De Smedt, F.
Analysis and Mapping of Rainfall-Induced Landslide Susceptibility in A Luoi District, Thua Thien Hue Province, Vietnam. *Water* **2019**, *11*, 51.
https://doi.org/10.3390/w11010051

**AMA Style**

Long NT, De Smedt F.
Analysis and Mapping of Rainfall-Induced Landslide Susceptibility in A Luoi District, Thua Thien Hue Province, Vietnam. *Water*. 2019; 11(1):51.
https://doi.org/10.3390/w11010051

**Chicago/Turabian Style**

Long, Nguyen Thanh, and Florimond De Smedt.
2019. "Analysis and Mapping of Rainfall-Induced Landslide Susceptibility in A Luoi District, Thua Thien Hue Province, Vietnam" *Water* 11, no. 1: 51.
https://doi.org/10.3390/w11010051