# Statistical Analysis of the Potential of Landslides Induced by Combination between Rainfall and Earthquakes

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## Abstract

**:**

_{HERI}) was proposed, and an index for the degree of land disturbance (I

_{DLD}) was estimated to explore the characteristics of I

_{HERI}under specific natural environmental and slope land use conditions. The results revealed that among the investigated disaster-causing factors, the degree of slope land use disturbance, the slope of the natural environment, and rainfall exerted the strongest effect on landslide occurrence. When I

_{HERI}or I

_{DLD}was higher, the probability of a landslide also increased, and under conditions of a similar I

_{DLD}, the probability of landslides increased as the I

_{HERI}value increased, and vice versa. Thus, given the interaction between rainfall and earthquakes in the study area, the effect of the degree of slope land use disturbance on landslides should not be ignored. The results of a receiver operating characteristic (ROC) curve analysis indicated that the areas under the ROC curve for landslides induced by different trigger factors were all above 0.94. The results indicate that the area in which medium–high-level landslides are induced by an interaction between rainfall and earthquakes is large.

## 1. Introduction

## 2. Research Methods

#### 2.1. RF

#### 2.2. Texture Analysis

#### 2.3. Accuracy Assessment

#### 2.4. Receiver Operating Characteristic Curve

## 3. Study Areas

^{2}. Its main tributaries are the Tanaku River and Puyanu, Caolan, Houbori, Cailiao, and Guantian streams. Zengwen River is rich in water resources and flows through the Zengwen, Nanhua, and Wushantou reservoirs. This river is also used as a water supply and for power generation and attracts tourists to the local area [47].

## 4. Potential of the Induction of Landslides by the Interaction between Rainfall and Earthquakes

#### 4.1. Interpretation and Classification of Satellite Images before and after Rainfall or Earthquakes in the Study Area and Extraction of Landslide Data

#### 4.2. Selection of Landslide Hazard Factors

_{3Rmax}) were used as the rainfall indicator. Peak ground acceleration (PGA) was used as the earthquake indicator. The methods for estimating and grading the various hazard factors were in accordance with those reported by Tseng et al. [14] and are explained in the following.

#### 4.2.1. Natural Environmental Factors

- Elevation

- B.
- Slope

- C.
- Aspect

- D.
- Distance from the river

- E.
- Geology

- F.
- Distance from the fault

#### 4.2.2. Disturbance Factor of Slope Land Utilization

_{DC}) is the score of the aforementioned slope land use disturbance in each grid and the grade of the environmental conditions (G

_{EC}) is the score of the natural environment of the sloping land in each grid. G

_{DC}is the ratio of the area of each slope land use disturbance factor in the basic grid, and R

_{EC}represents the coding of the natural environmental factors of each slope land in the basic grid.

#### 4.2.3. Rain Trigger Factors

#### 4.2.4. Earthquake Trigger Factors

#### 4.3. Weight Analysis of Hazard-Causing Factors

_{3Rmax}-normalized data of each single rainfall occurrence and the PGA-normalized data of each single earthquake were integrated with the EAR × I

_{3Rmax}- and PGA-normalized data of postrainfall earthquakes and postearthquake rainfall. Then, an RF was used to analyze the degree of interpretation. Input data included the normalized values of EAR × I

_{3Rmax}and the PGA of each basic grid under each rainfall occurrence or each earthquake in the study area and the landslide condition of the corresponding basic grid after each rainfall occurrence or each earthquake. The mean reduction in precision was used to determine the explanatory degree of characteristic variables and estimate the explanatory power of different trigger factors. The degree of influence of EAR × I

_{3Rmax}and PGA characteristic variables under different trigger factors is summarized in Table 5. The explanatory power of each trigger factor item was set as the score value, and the postrainfall earthquake or postearthquake rainfall score value was obtained by adding up their individual explanatory powers. The effect of rainfall trigger factors on landslide occurrences in the study area was slightly higher than that of earthquake trigger factors.

#### 4.4. Establishment and Discussion of Hazard Indicators of the Interactive Correlation between Rainfall- and Earthquake-Induced Landslides

#### 4.4.1. Establishment of Hazard Indicators of Interaction between Rainfall and Earthquakes

_{HERI}of a basic grid number i after each rainfall occurrence or earthquake in the study area is defined as follows:

- F(T
_{R}): Standardized values of rainfall factors in each basic grid - F(T
_{E}): Standardized values of seismic factors in each basic grid - C
_{R}: Estimated score value for a single rainfall-induced landslide - C
_{E}: Estimated score value for a single earthquake-induced landslide - C
_{RE}: Score value calculated for a postrainfall earthquake-induced landslide - C
_{ER}: Score value calculated for a postearthquake rainfall-induced landslide

_{R}) or F(T

_{E}) can be obtained from the spatial distribution data of the trigger factors (EAR × I

_{3Rmax}or PGA) of each rainfall occurrence or each earthquake in the study area. The values of C

_{R}, C

_{E}, C

_{RE}, and C

_{ER}can be calculated separately using the aforementioned RF algorithm through a weight analysis. The trigger factors of single rainfall, single earthquake, earthquake after a previous rainfall event, and rainfall after a previous earthquake event induced landslides in the slope land in the study area. The larger the I

_{HERI}was, the higher the possibility of the interaction between rainfall and earthquakes inducing a landslide was.

_{HERI}, we first used SPSS Cluster Analysis [55] to categorize the I

_{HERI}values into five levels and then plotted the graph for the I

_{HERI}against the landslide grid ratio (Figure 2). The landslide grid ratio in the study area tended to increase with an increase in the degree of interaction between rainfall and earthquake events.

#### 4.4.2. Classification of Slope Land Use Disturbance Degree and Its Influence on Landslides in the Study Area

_{DLD}of each basic grid. By using SPSS Cluster Analysis, we categorized the I

_{DLD}values into five grades. We plotted the I

_{DLD}values against the 13 rainfall- or earthquake-induced landslide grid ratios in the study area (the number of basic grids with landslides divided by the number of basic grids where landslides occur) to determine the degree of slope land use disturbance (Figure 3). The landslide grid ratio of the slope land with a low degree of disturbance was 0.006, whereas that of the slope land with a high degree of disturbance was as high as 0.93. The results indicated that the landslide grid ratio of the slope land in the study area increased with the degree of slope land use disturbance.

#### 4.4.3. Interaction between the Hazard Indexes of Rainfall- and Earthquake-Induced Landslides and the Index of the Degree of Slope Land Use Disturbance

_{HERI}, I

_{DLD}, and landslide occurrence in each basic grid in the study area. A schematic of the interval settings is presented in Figure 4 and the schematic obtained after dividing the study area into 9 equidistant interval grids (from letter A to I) is presented in Figure 5. The red ○’s and gray ⨯’s in the figure represent basic grids with and without landslides, respectively. The basic grid with landslides represents the total number of landslides induced by all 13 rainfall or earthquake events in the study area, which yielded a total of 37,197 records. The grid points in the figure where a landslide did not occur were determined using a 1:1 ratio, which was obtained through random sampling from all basic grids where a landslide did not occur.

_{HERI}or I

_{DLD}was larger, the induced landslide ratio increased. When the degree of slope land use disturbance was similar in the study area, the landslide ratio, which indicated the probability of a landslide, increased with the I

_{HERI}value. Similarly, when the I

_{HERI}was similar in the study area, the probability of a landslide increased with the degree of slope land use disturbance. The interaction between rainfall and earthquake events in the study area indicates that the effect of the degree of slope land use disturbance on landslide occurrence is notable.

#### 4.5. Establishment and Verification of Rainfall- and Earthquake-Induced Landslide Potential Assessment Models and Potential Map Drawing

#### 4.5.1. Establishment of a Landslide Potential Assessment Model

#### 4.5.2. Verification of the Landslide Potential Assessment Model and Drawing of a Potential Map

_{3Rmax}or PGA) against the landslide area ratios of medium–high-level landslides induced by a single rainfall or a single earthquake event in the study area (Figure 14 and Figure 15, respectively). Irrespective of whether the average value of the EAR × I

_{3Rmax}of a single rainfall event was larger or the maximum value of the PGA of a single earthquake was larger, the landslide area ratio of the medium–high-level landslides exhibited an increasing trend. This finding indicates that the landslide potential estimated in this study is reasonable.

## 5. Conclusions

_{HERI}) for landslides induced by postrainfall earthquakes and postearthquake rainfall and estimated the I

_{DLD}. This study then explored the characteristics of I

_{HERI}that affect landslides under specific natural environmental factor and slope land use disturbance conditions. The weight analysis results indicate that of the slope land use disturbance factors, bare land density exerted the strongest effect. Of the natural environmental factors, slope coding exerted the strongest effect. Compared with earthquakes, rainfall exerted a stronger effect. Irrespective of whether landslides were induced by a single rainfall event, a single earthquake, or both rainfall and earthquakes, the grid ratio for landslides in the study area tended to increase with an increase in the degree of slope land use disturbance. When I

_{HERI}or I

_{DLD}was larger, the induced landslide ratio increased. Thus, when the interaction between rainfall and earthquakes is considered, the impact of slope land use disturbance on landslide hazards should be noted. Moreover, regardless of whether single rainfall, single earthquake, or both rainfall and earthquake events were considered, the accuracy of each landslide potential model constructed using the RF method was above 83%, which is considered excellent. The AUC values in the assessment results for landslides induced by single rainfall, single earthquake, postrainfall earthquake, and postearthquake rainfall events were all above 0.94, indicating a higher risk of landslide induction by single rainfall and earthquake events. The forecasts had a high accuracy. With the exception of when the average rainfall in the study area was higher than that during the dual trigger events, the area ratio of medium–high-level landslides induced by the interaction between rainfall and earthquakes was large. According to the estimated landslide potential in this study, irrespective of whether the average EAR × I

_{3Rmax}value of a single rainfall event is larger or the maximum PGA value of a single earthquake is larger, the area of medium–high-level landslides tends to increase.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Schematic of the interval setting method of the relationships among the I

_{HERI}, I

_{DLD}, and landslide occurrence of each basic grid.

**Figure 5.**Relationships among the I

_{HERI}, I

_{DLD}, and landslide occurrence after various rainfall and earthquake events in the study area.

**Figure 10.**Landslide potential map of Alishan Township after rainfall and earthquakes overlapped by historical landslides.

**Figure 11.**Landslide potential map of Dapu Township after rainfall or earthquakes overlapped by historical landslides.

**Figure 12.**Landslide area ratio of medium–high-level landslides induced by rainfall and earthquakes in Alishan Township.

**Figure 13.**Landslide area ratio of medium–high-level landslides induced by rainfall and earthquakes in Dapu Township.

**Figure 14.**Landslide area ratios of medium–high-level landslides against average EAR × I

_{3Rmax}and maximum PGA induced by a single rainfall or a single earthquake event in Alishan Township.

**Figure 15.**Landslide area ratios of medium–high-level landslides against average EAR × I

_{3Rmax}and maximum PGA induced by a single rainfall or a single earthquake event in Dapu Township.

Satellite Image | Kappa | OA (%) | Kappa (Mosaic) | OA (%) (Mosaic) | ||||
---|---|---|---|---|---|---|---|---|

No | Year | Date | Before/After Event | Township | ||||

1 | 2004 | 10 Feb. | Before Typhoon Mindulle | Alishan | 0.60 | 65.7 | ||

2 | 2004 | 10 July | After Typhoon Mindulle | Alishan | 0.75 | 77.1 | ||

3 | 2008 | 5 Jan. | Before the 0305 Earthquake and Typhoon Kalmaegi | Alishan | 0.65 | 68.0 | 0.65 | 67.5 |

4 | 2008 | 10 Jan. | Before the 0305 Earthquake and Typhoon Kalmaegi | Alishan | 0.64 | 66.9 | ||

5 | 2008 | 21 July | After the 0305 Earthquake and Typhoon Kalmaegi | Alishan | 0.75 | 77.1 | ||

6 | 2008 | 5 Jan. | Before the 0305 Earthquake and Typhoon Kalmaegi | Dapu | 0.63 | 68.0 | ||

7 | 2008 | 21 July | After the 0305 Earthquake and Typhoon Kalmaegi | Dapu | 0.70 | 73.1 | ||

8 | 2009 | 12 Apr. | Before Typhoon Morakot and the 1105 earthquake | Dapu | 0.66 | 70.3 | ||

9 | 2009 | 6 Nov. | After Typhoon Morakot and the 1105 earthquake | Dapu | 0.62 | 66.9 | ||

10 | 2010 | 11 Apr. | Before the 0726 heavy rain | Dapu | 0.67 | 70.9 | ||

11 | 2010 | 4 Aug. | After the 0726 heavy rain | Dapu | 0.67 | 71.4 | ||

12 | 2010 | 4 Aug. | Before Typhoon Fanapi and the 1108 Earthquake | Dapu | 0.65 | 69.1 | ||

13 | 2010 | 27 Dec. | After Typhoon Fanapi and the 1108 Earthquake | Dapu | 0.65 | 69.1 | ||

14 | 2011 | 27 July | Before the Typhoon Nanmadol | Dapu | 0.71 | 74.9 | 0.68 | 72.0 |

15 | 2011 | 16 Aug. | Before the Typhoon Nanmadol | Dapu | 0.64 | 69.1 | ||

16 | 2011 | 27 Sep. | After the Typhoon Nanmadol | Dapu | 0.61 | 66.9 | ||

17 | 2012 | 10 Feb. | Before the 0226 earthquake | Dapu | 0.78 | 80.0 | ||

18 | 2012 | 7 Mar. | After the 0226 earthquake | Dapu | 0.66 | 70.2 | ||

19 | 2013 | 2 June | Before the 0602 earthquake | Alishan | 0.68 | 71.4 | ||

20 | 2013 | 29 June | After the 0602 earthquake | Alishan | 0.62 | 65.7 | 0.63 | 66.3 |

21 | 2013 | 4 July | After the 0602 earthquake | Alishan | 0.63 | 66.9 | ||

22 | 2015 | 28 Feb. | Before the 0520 heavy rain | Alishan | 0.66 | 68.6 | ||

23 | 2015 | 10 June | After the 0520 heavy rain | Alishan | 0.68 | 70.9 | ||

24 | 2015 | 5 Mar. | Before the 0520 heavy rain | Dapu | 0.73 | 74.9 | ||

25 | 2015 | 10 June | After the 0520 heavy rain | Dapu | 0.70 | 73.1 | ||

26 | 2015 | 28 Nov. | Before the 0206 earthquake | Alishan | 0.61 | 65.7 | ||

27 | 2016 | 14 Feb. | After the 0206 earthquake | Alishan | 0.64 | 66.9 | 0.68 | 70.3 |

28 | 2016 | 30 Mar. | After the 0206 earthquake | Alishan | 0.72 | 73.7 | ||

29 | 2015 | 28 Nov. | Before the 0206 earthquake | Dapu | 0.63 | 68.0 | ||

30 | 2016 | 30 Mar. | After the 0206 earthquake | Dapu | 0.66 | 70.3 | ||

31 | 2016 | 30 Mar. | Before Typhoon Megi | Dapu | 0.66 | 69.7 | ||

32 | 2016 | 19 Nov. | After Typhoon Megi | Dapu | 0.64 | 68.6 | ||

33 | 2017 | 18 Oct. | Before the 1122 earthquake | Alishan | 0.60 | 64.6 | 0.62 | 66.3 |

34 | 2017 | 17 Nov. | Before the 1122 earthquake | Alishan | 0.64 | 68.0 | ||

35 | 2018 | 16 Jan. | After the 1122 earthquake | Alishan | 0.66 | 69.7 | ||

36 | 2017 | 17 Nov. | Before the 0320 earthquake | Dapu | 0.65 | 68.6 | ||

37 | 2018 | 9 Apr. | After the 0320 earthquake | Dapu | 0.72 | 74.3 | ||

Total Average | Kappa = 0.66 OA = 70.1% |

**Table 2.**Effects of the characteristic variables of slope land use disturbance factors and natural environmental factors.

(a) Slope Land Use Disturbance Factor | |||
---|---|---|---|

Item | Degree of Influence of Characteristic Variables | ||

Mean Decrease Accuracy | Explanatory Power | Correlation Value | |

Road Density | 39.88 | 0.15 | 0.39 |

Building Density | 37.59 | 0.14 | 0.37 |

Bare Density | 48.00 | 0.18 | 0.42 |

Crop Density | 61.42 | 0.22 | −0.48 |

Green Coverage | 84.35 | 0.31 | −0.56 |

Total | 271.24 | 1 | |

(b) Natural Environment Factors | |||

Item | Degree of Influence of Characteristic Variables | ||

Mean Decrease Accuracy | Explanatory Power | Correlation Value | |

Elevation Code | 103.09 | 0.13 | −0.36 |

Slope Code | 235.93 | 0.29 | −0.54 |

Aspect Code | 90.90 | 0.11 | −0.33 |

Geology Code | 117.76 | 0.14 | 0.37 |

Distance Code from Water system | 150.72 | 0.18 | −0.42 |

Distance Code from Fault | 120.81 | 0.15 | 0.39 |

Total | 819.21 | 1 |

Slope Use Disturbance Factor | Green Coverage | Crop Density | Building Density | Road Density | Bare Density |
---|---|---|---|---|---|

Score | 1 | 2 | 3 | 4 | 5 |

Natural Environment Factors | Distance Code from Fault | Geology Code | Aspect Code | Elevation Code | Distance Code from Water System | Slope Code |
---|---|---|---|---|---|---|

Score | 1 | 2 | 3 | 4 | 5 | 6 |

Trigger Factor | Index | Influence Degree of Characteristic Variables | ||
---|---|---|---|---|

Mean Decrease Accuracy | Explanatory Power | Score | ||

Single Rain | EAR × I_{3Rmax} | 90.97 | 0.27 | 0.27 |

Single Earthquake | PGA | 54.28 | 0.16 | 0.16 |

Post-Earthquake Rainfall | EAR × I_{3Rmax} | 48.34 | 0.14 | 0.32 |

PGA | 60.88 | 0.18 | ||

post-rainfall Earthquake | EAR × I_{3Rmax} | 45.50 | 0.13 | 0.25 |

PGA | 39.34 | 0.12 | ||

Total | 339.31 | 1 |

**Table 6.**The I

_{HERI}, I

_{DLD}, and number of grids with and without landslides and the ratio of the landslide grids in each interval corresponding to the occurrence of landslides.

Interval No. | Number of Grids with Landslide | Number of Grids without Landslide | Landslide Grid Ratio | |
---|---|---|---|---|

Number of Grids with Landslide/ Number of Grids without Landslide | Number of Grids with Landslide/ Total Number of Grids in the Interval | |||

A | 16,373 | 33,326 | 0.49 | 0.33 |

B | 1656 | 2297 | 0.72 | 0.42 |

C | 644 | 489 | 1.32 | 0.57 |

D | 14,795 | 1001 | 14.80 | 0.94 |

E | 1132 | 47 | 24.10 | 0.96 |

F | 216 | 6 | 36.00 | 0.97 |

G | 2205 | 30 | 73.50 | 0.99 |

H | 176 | 1 | 176.00 | 0.99 |

I | 0 | 0 | — | — |

Trigger Factor | (a) Single Rainfall | (b) Single Earthquake | |||
---|---|---|---|---|---|

Accuracy | Training | Testing | Training | Testing | |

PA of Grids with Landslide | 91.61% | 83.14% | 98.66% | 95.96% | |

PA of Grids without Landslide | 99.40% | 92.17% | 99.90% | 95.63% | |

Overall Accuracy | 100% | 89.84% | 99.92% | 95.70% | |

Trigger Factor | (c) Post-rainfall Earthquake | (d) Post-earthquake Rainfall | |||

Accuracy | Training | Testing | Training | Testing | |

PA of Grids with Landslide | 98.23% | 87.02% | 96.26% | 89.99% | |

PA of Grids without Landslide | 99.68% | 88.01% | 98.21% | 92.22% | |

Overall Accuracy | 100% | 88.27% | 99.84% | 91.67% |

Single Typhoon or Rainfall | Typhoon Mindulle | 0726 Heavy Rain | Typhoon Nanmadol | ||||
---|---|---|---|---|---|---|---|

Coverage | Alishan Township | Dapu Township | Dapu Township | ||||

Evaluation Result | |||||||

Landslide | Non-landslide | Landslide | Non-landslide | Landslide | Non-landslide | ||

Actual Situation | Landslide | 6083 | 919 | 697 | 2 | 522 | 1 |

Non-landslide | 20,948 | 225,031 | 3993 | 77,505 | 2279 | 76,647 | |

PA of Grids with Landslide | 86.88% | 99.71% | 99.81% | ||||

PA of Grids without Landslide | 91.48% | 95.10% | 97.11% | ||||

Overall Accuracy | 91.36% | 95.14% | 97.13% | ||||

Single Rainfall or Earthquake | 0520 Heavy Rain | 0520 Heavy Rain | Typhoon Megi | ||||

Coverage | Alishan Township | Dapu Township | Dapu Township | ||||

Evaluation Result | |||||||

Landslide | Non-landslide | Landslide | Non-landslide | Landslide | Non-landslide | ||

Actual | Landslide | 3958 | 467 | 1012 | 177 | 577 | 38 |

Non-landslide | 18,868 | 242,051 | 5341 | 70,094 | 3296 | 78,541 | |

PA of Grids with Landslide | 89.45% | 85.11% | 93.82% | ||||

PA of Grids without Landslide | 92.77% | 92.92% | 95.96% | ||||

Overall Accuracy | 92.71% | 92.80% | 95.96% |

Single Earthquake | 0226 Earthquake | 0602 Earthquake | 0206 Earthquake | ||||
---|---|---|---|---|---|---|---|

Coverage | Dapu Township | Alishan Township | Alishan Township | ||||

Evaluation Result | |||||||

Landslide | Non-landslide | Landslide | Non-landslide | Landslide | Non-landslide | ||

Actual Situation | Landslide | 687 | 22 | 6602 | 157 | 3839 | 122 |

Non-landslide | 3155 | 76,990 | 10,587 | 236,645 | 11,263 | 249,499 | |

PA of Grids with Landslide | 96.90% | 97.68% | 96.92% | ||||

PA of Grids without Landslide | 96.06% | 95.72% | 95.68% | ||||

Overall Accuracy | 96.07% | 95.77% | 95.70% | ||||

Single Earthquake | 0206 Earthquake | 1122 Earthquake | 0320 Earthquake | ||||

Coverage | Dapu Township | Alishan Township | Dapu Township | ||||

Evaluation Result | |||||||

Landslide | Non-landslide | Landslide | Non-landslide | Landslide | Non-landslide | ||

Actual Situation | Landslide | 475 | 27 | 3139 | 6 | 484 | 5 |

Non-landslide | 2197 | 79,731 | 14,714 | 253,350 | 3219 | 76,404 | |

PA of Grids with Landslide | 94.62% | 99.81% | 98.98% | ||||

PA of Grids without Landslide | 97.32% | 94.51% | 95.96% | ||||

Overall Accuracy | 97.30% | 94.57% | 95.98% |

Post-Rainfall Earthquake | 1105 Earthquake after Typhoon Morakot | 1108 Earthquake after Typhoon Fanapi | |||
---|---|---|---|---|---|

Coverage | Dapu Township | Dapu Township | |||

Evaluation Result | |||||

Landslide | Non-landslide | Landslide | Non-landslide | ||

Actual Situation | Landslide | 1568 | 116 | 962 | 24 |

Non-landslide | 12,975 | 67,610 | 5102 | 74,832 | |

PA of Grids with Landslide | 93.11% | 97.57% | |||

PA of Grids without Landslide | 83.90% | 93.62% | |||

Overall Accuracy | 84.09% | 93.67% |

Post-Earthquake Rainfall | Typhoon Kalmaegi after 0305 Earthquake | Typhoon Kalmaegi after 0305 Earthquake | |||
---|---|---|---|---|---|

Coverage | Alishan Township | Dapu Township | |||

Evaluation Result | |||||

Landslide | Non-landslide | Landslide | Non-landslide | ||

Actual Situation | Landslide | 3348 | 184 | 910 | 67 |

Non-landslide | 15,377 | 221,588 | 10,275 | 52,018 | |

PA of Grids with Landslide | 94.79% | 93.14% | |||

PA of Grids without Landslide | 93.51% | 83.51% | |||

Overall Accuracy | 93.53% | 83.65% |

**Table 12.**Landslide area ratios of medium–high-level landslides induced by rainfall and earthquakes in Alishan Township.

Trigger | Single Rainfall | Single Earthquake | Post-Earthquake Rainfall | ||||
---|---|---|---|---|---|---|---|

Landslide Area or Area Ratio | Typhoon Mindulle | 0520 Heavy Rainfall | 0602 Earthquake | 0206 Earthquake | 1122 Earthquake | Typhoon Kalmaegi after 0305 Earthquake | |

Total area of historical disaster areas (hectares) | 1394.6 | 1394.6 | 1394.6 | 1394.6 | 1394.6 | 1394.6 | |

Area (hectares) in historical disaster area with medium-high landslide potential | 627.9 | 480.1 | 441.4 | 397.3 | 414.7 | 509.1 | |

Landslide area ratio of medium-high landslide potential | 0.45 | 0.344 | 0.317 | 0.285 | 0.297 | 0.365 |

**Table 13.**Landslide area ratios of medium–high-level landslides induced by rainfall and earthquakes in Dapu Township.

Trigger | Single Rainfall | Single Earthquake | Post-Earthquake Rainfall | Post-Rainfall Earthquake | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Landslide Area or Area Ratio | 0726 Heavy Rain | Typhoon Nanmadol | 0520 Heavy Rain | Typhoon Megi | 0226 Earthquake | 0206 Earthquake | 0320 Earthquake | Typhoon Kalmaegi after 0305 Earthquake | 1105 Earthquake after Typhoon Morakot | 1108 Earthquake after Typhoon Fanapi | |

Total area of historical disaster areas (hectares) | 482.6 | 482.6 | 482.6 | 482.6 | 482.6 | 482.6 | 482.6 | 482.6 | 482.6 | 482.6 | |

Area (hectares) in historical disaster area with medium-high landslide potential | 78 | 68.2 | 100.8 | 91.3 | 72.4 | 78.3 | 84.7 | 152.9 | 132.9 | 99.4 | |

Landslide area ratio of medium-high landslide potential | 0.162 | 0.141 | 0.209 | 0.189 | 0.15 | 0.162 | 0.176 | 0.317 | 0.275 | 0.206 |

(a) Alishan Township | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Rainfall or (and) Earthquake | EAR × I_{3Rmax} (mm^{2}/3-h) | PGA (gal) | ||||||||||

Maximum | Minimum | Mean | Maximum | Minimum | Mean | |||||||

Typhoon Mindulle | 138,449 | 39,993 | 86,407 | |||||||||

0520 Heavy Rainfall | 85,608 | 19,767 | 45,671 | |||||||||

0602 Earthquake | 445 | 34 | 116 | |||||||||

0206 Earthquake | 212 | 52 | 126 | |||||||||

1122 Earthquake | 318 | 32 | 94 | |||||||||

Typhoon Kalmaegi after 0305 Earthquake | 131,572 | 18,518 | 82,081 | 88 | 7 | 35 | ||||||

(b) Dapu Township | ||||||||||||

Rainfall or (and) Earthquake | EAR × I_{3Rmax} (mm^{2}/3-h) | PGA (gal) | ||||||||||

Maximum | Minimum | Mean | Maximum | Minimum | Mean | |||||||

0726 Heavy Rainfall | 23,269 | 4713 | 11,161 | |||||||||

Typhoon Nanmadol | 10,299 | 4856 | 7259 | |||||||||

0520 Heavy Rainfall | 67,375 | 40,667 | 58,007 | |||||||||

Typhoon Megi | 78,593 | 20,659 | 39,822 | |||||||||

0226 Earthquake | 68 | 25 | 55 | |||||||||

0206 Earthquake | 185 | 72 | 138 | |||||||||

0320 Earthquake | 243 | 77 | 146 | |||||||||

Typhoon Kalmaegi after 0305 Earthquake | 193,711 | 115,644 | 164,877 | 169 | 13 | 55 | ||||||

1105 Earthquake After Typhoon Morakot | 437,136 | 158,541 | 295,497 | 68 | 16 | 35 | ||||||

1108 Earthquake after Typhoon Fanapi | 35,863 | 9268 | 20,962 | 208 | 23 | 69 |

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© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tseng, C.-M.; Chen, Y.-R.; Chang, C.-M.; Yang, Y.-L.; Chen, Y.-R.; Hsieh, S.-C. Statistical Analysis of the Potential of Landslides Induced by Combination between Rainfall and Earthquakes. *Water* **2022**, *14*, 3691.
https://doi.org/10.3390/w14223691

**AMA Style**

Tseng C-M, Chen Y-R, Chang C-M, Yang Y-L, Chen Y-R, Hsieh S-C. Statistical Analysis of the Potential of Landslides Induced by Combination between Rainfall and Earthquakes. *Water*. 2022; 14(22):3691.
https://doi.org/10.3390/w14223691

**Chicago/Turabian Style**

Tseng, Chih-Ming, Yie-Ruey Chen, Chwen-Ming Chang, Ya-Ling Yang, Yu-Ru Chen, and Shun-Chieh Hsieh. 2022. "Statistical Analysis of the Potential of Landslides Induced by Combination between Rainfall and Earthquakes" *Water* 14, no. 22: 3691.
https://doi.org/10.3390/w14223691