# Triggering Rainfall of Large-Scale Landslides in Taiwan: Statistical Analysis of Satellite Imagery for Early Warning Systems

^{*}

## Abstract

**:**

## 1. Introduction

^{3}, or a collapse depth deeper than 10 m [5]. Under the situation that epistemic conditions of LSLs are insufficient, in order to find a practical solution for early warning works, this study tries to find the most intuitive indicator, and rainfall and some other factors of LSLs seem to be the best choice. In order to establish the specific relationship between LSLs and triggering rainfall for the future LSL early warning predictions, LSL cases, satellite imagery, rainfall data, seismic data, and other support datasets were collected. In this study, two dimensionless factors, rainfall/landslide depth (R/D) and friction angle/slope (ϕ/θ), were assumed to have a linear relationship, and all factors, R, D, ϕ, θ, were assumed to have a nonlinear relationship, and the both linear and nonlinear regressions were analyzed statistically.

## 2. Literature Review

#### 2.1. Occurrence Mechanism-Related Research

#### 2.2. Monitoring-Related Research

- On-site monitoring

- 2.
- Remote Sensing

#### 2.3. Early Warning-Related Research

- Early warning indicators

- comprehensive indicators [59].

- 2.
- Early warning management values

- 3.
- Real-time simulation

## 3. Materials and Methods

#### 3.1. Case Collection and Screening

#### 3.2. Case Confirmation, Area Size, and Average Slope Identification of LSL

^{2}) of an LSL was calculated by the Calculate Geometry function of ESRI ArcMap

^{®}software. Based on 5 m resolution DEM data, the slope of each data grid was calculated first with the Slope function of the Surface tool in the Spatial Analyst Tools module of ArcToolbox, and the average slope θ (degree) for the corresponding range of each newborn LSL was calculated by the Zonal Statistics function in the Zonal tool module.

#### 3.3. The Occurrence Time Confirmation of LSL

#### 3.4. The Triggering Rainfall Analysis

- $R$ is the triggering rainfall for LSL (mm);
- ${R}_{0}$ is the accumulated rainfall from the beginning of the rainfall event that caused the LSL to the moment the landslide occurred (mm);
- $P$ is the antecedent rainfall (mm) $\approx \sum _{i=1}^{N}{\alpha}^{i}{R}_{i}$;
- ${R}_{i}$ is the rainfall on the i-th day (24 h) before the start of the rain field ${t}_{0}$ (mm);
- $N$ is the number of days to consider the antecedent rainfall (), generally N = 7;
- $\alpha $ is the daily (24 h) rainfall triggering landslide decay coefficient (), which can be 0.7 or 0.8. At present, α = 0.7 is used in this study to calculate the antecedent rainfall [62].

#### 3.5. The Linear Regression Analysis

^{3}) divided by the projected landslide area A as Equation (4). With an empirical volume–area relation [78] as Equation (4) from the SWCB, D can be evaluated as Equation (5).

#### 3.6. The Nonlinear Regression Analysis

- Step 1.
- Initial calculation

- ${\u2206}_{\mathrm{i}}$ is the residual of the i-th data [],
- ${p}_{i}$ is the landslide thickness of the i-th prediction (m),
- ${o}_{i}$ is the landslide thickness of the i-th observation (m),
- $n$ is the total number of observations ().

- Step 2.
- Solver

^{®}is used to find the optimized coefficients $a,b,c,d,e$. The sum of squared errors (SSE) as in Equation (10) is used as the target function, and the coefficients can be obtained by minimizing the SSE with Solver. Solver uses the GRG nonlinear solving method to solve the problem with an accuracy of the constraint of 0.000001.

- Step 3.
- SSE convergence

- Step 4.
- Bootstrap method processing

- Step 5.
- Solver

- Step 6.
- SSE convergence

- Step 7.
- Cumulative coefficient statistics

- $C{V}_{j}$ is coefficient of variation of the specific coefficient from the 1st to the j-th bootstrap resampling [],
- ${\sigma}_{1~j}$ is the standard deviation of the specific coefficient from the 1st to the j-th bootstrap resampling [],
- ${\mu}_{1~j}$ is the average value of the specific coefficient from the 1st to the j-th bootstrap resampling [].

- Step 8.
- Statistics converged

- Step 9.
- Coefficient statistical analysis

- Step 10.
- Outcome estimation

## 4. Results

#### 4.1. Linear Regression Analysis Results

#### 4.2. Nonlinear Regression Analysis Results

^{®}was used to perform the nonlinear fit analysis between the predictions and the observations according to Equation (8). The results are shown in Table 4 and Figure 8. From the value of R square and the adjusted R square, it was found that Equation (8) has a good degree of model fit, and F is very different from the significance F (last two columns of ANOVA). This indicates that each parameter has large differences between groups, and small differences within groups. From the results in Figure 8b, it was found that the predicted value and the observed value have similar trends, and the function described by Equation (8) is reasonable.

## 5. Discussion

#### 5.1. Prediction Ability

- ${R}_{LT}$ is the predicted rainfall by the linear regression trend line (m),
- ${R}_{LU}$ is the predicted rainfall by the linear regression upper boundary line (m),
- ${R}_{LL}$ is the predicted rainfall by the linear regression lower boundary line (m),
- ${R}_{NT}$ is the predicted rainfall by the nonlinear regression trend line (m),
- ${R}_{NU}$ is the predicted rainfall by the nonlinear regression upper boundary line (m),
- ${R}_{NL}$ is the predicted rainfall by the nonlinear regression lower boundary line (m).

#### 5.2. Limitations

#### 5.3. Early Warning Application

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Landslide types of satellite images: newborn landslide (

**a**,

**b**) and expanded landslide (

**c**,

**d**). (modified from: [66]). (

**a**) Xiaolin Village Landslide (pre-event), (

**b**) Xiaolin Village Landslide (post-event), (

**c**) Shanping Landslide (pre-event), (

**d**) Shanping Landslide (post-event).

**Figure 2.**Schematic diagram of rain field cutting (modified from: [76]).

**Figure 3.**Nonlinear regression workflow. The numbered items are the key steps of the process, detailed in the following text.

**Figure 8.**The results of the fit analysis between the nonlinear predicted value and the observed value, where (

**a**) is the residual of each parameter, (

**b**) is the sample regression line of each parameter, and (

**c**) is the normal probability. D is the thickness of the sliding soil layer, R is the landslide triggering rainfall, θ is the slope of sliding surface, and ϕ is the equivalent friction angle.

**Figure 9.**Comparison between predicted and estimated values of collapse thickness in 149 potential LSL areas.

**Table 1.**Comparison table of on-site monitoring programs (modified from [21]).

Investigation Item | Instruments | Investigation Objects | Accuracy | |
---|---|---|---|---|

Surface changes | Surface inclinometer | Tilting direction and amount of ground surface | 1” | |

Surface extensometer | Fracture displacement and velocity | 0.2 mm | ||

Surface measurement | Optical measuring instruments | Tilting direction and amount of ground surface | 1~10 mm | |

GNSS | Displacement of the ground surface | NA | ||

LiDAR scanner | Terrain 3D variation | NA | ||

Underground changes | In-place inclinometer | Sliding surface position and variation | 5~10” | |

Pipe strain gauge | Sliding surface position and variation | 1 × 10^{−6} | ||

Borehole extensometer | Sliding surface dislocation rate | 0.2 mm | ||

Multipoint borehole extensometer | Sliding surface position and dislocation rate | 0.3 mm | ||

Surface hydrology | Rain gauge | Rainfall amount | 0.5 mm | |

Underground hydrology | Water level gauge | Variation of water level in the hole | 0.05%FS | |

Pore pressure gauge | Variation of water pressure of the sliding surface | 0.05%FS | ||

Soil moisture meter | Variation of soil saturation | NA | ||

Flowmeter | Variation of discharge | NA | ||

Structures | Earth pressure gauge | Earth pressure acting on retaining walls, deep foundation piles | 0.1%FS | |

Load cell | Tension acting on the ground anchor | 0.1%FS | ||

Strain gauge | Deformation of the structure | 1 × 10^{−6} | ||

Rebar gauge | Stress acting on the rebar gauge | 0.1%FS | ||

Inclinometer | Tilt variation of structure | 1~10” | ||

In-place inclinometer | Bending deformation of steel pipe piles | 5~10” |

No. | ID | Event | Area Size (ha) | Occurrence Time | Cited From |
---|---|---|---|---|---|

1 | SR-3 | Typhoon Morakot (200908) | 19 | 09 August 2009 17:00 | Interviews with local residents |

2 | SR-5 | 238 | 09 August 2009 17:00 | ||

3 | SR-6 | 142 | 10 August 2009 12:00 | ||

4 | SR-7 | 130 | 09 August 2009 02:00 | ||

5 | SR-8 | 88 | 09 August 2009 02:00 | ||

6 | SR-9 | 74 | 09 August 2009 04:00 | ||

7 | SR-11 | 40 | 08 August 2009 16:00 | ||

8 | SR-12 | 32 | 09 August 2009 07:00 | ||

9 | SR-16 | 26 | 09 August 2009 07:00 | ||

10 | SR-19 | 23 | 08 August 2009 15:00 | ||

11 | SR-42 | 15 | 09 August 2009 07:00 | ||

12 | SR-43 | 15 | 09 August 2009 07:00 | ||

13 | SR-46 | 15 | 09 August 2009 05:00 | ||

14 | SR-53 | 14 | 09 August 2009 00:00 | ||

15 | SR-94 | 351 | 09 August 2009 10:00 | ||

16 | SR-95 | 249 | 09 August 2009 06:00 | ||

17 | SR-96 | 81 | 09 August 2009 10:00 | ||

18 | SR-97 | 61 | 09 August 2009 09:00 | ||

19 | SR-98 | 52 | 09 August 2009 06:00 | ||

20 | SR-99 | 15 | 09 August 2009 04:00 | ||

21 | SR-100 | 11 | 08 August 2009 10:00 | ||

22 | SR-101 | 10 | 09 August 2009 09:00 | ||

23 | 2005_002 | Typhoon Haitang (200505) | 18 | 21 July 2005 14:33 | The evaluation results of the LSL occurrence time and location from the BATS |

24 | 2006_002 | 0609 Torrential Rain | 12 | 10 Jun 2006 00:53 | |

25 | 2008_002 | Typhoon Sinlaku (200813) | 89 | 18 September 2008 02:50 | |

26 | 2008_003 | Typhoon Kamaegi (200807) | 10 | 19 July 2008 05:30 | |

27 | 2012_002 | Typhoon Saola (201209) | 19 | 03 August 2012 09:02 | |

28 | 2012_004 | 25 | 03 August 2012 03:00 |

Cases | Landslide or Not | Rainfall Type Used | |
---|---|---|---|

107 newborn LSLs | 28 occurrence-time-known cases | Yes | Triggering rainfall |

79 occurrence-time-unknown cases | Yes | Total event rainfall | |

149 potential LSL areas | No | Total rainfall of Typhoon Morakot |

Regression Statistics | ||||||
---|---|---|---|---|---|---|

Multiple R | 0.9569 | |||||

R Square | 0.9157 | |||||

Adjusted R Square | 0.9052 | |||||

Standard Error | 2.8447 | |||||

Observations | 28 | |||||

ANOVA | ||||||

df | SS | MS | F | Significance F | ||

Regression | 3 | 2109.4427 | 703.1476 | 86.8894 | 4.9903 × 10^{−13} | |

Residual | 24 | 194.2187 | 8.0924 | |||

Total | 27 | 2303.6614 | ||||

Coefficients | Standard Error | t-Test | p-value | Lower 95% | Upper 95% | |

Intercept | 66.7058 | 6.1858 | 10.7838 | 1.10 × 10^{−10} | 53.9390 | 79.4725 |

R(m) | −2.2273 | 2.8034 | −0.7945 | 0.4347 | −8.0133 | 3.5587 |

θ(degree) | 0.0043 | 0.1279 | 0.0334 | 0.9737 | −0.2597 | 0.2682 |

$\varphi $(degree) | −2.2251 | 0.1456 | −15.2793 | 7.26 × 10^{−14} | −2.5257 | −1.9246 |

Parameter | Max | Min | Mean | Median | 40% | 60% |
---|---|---|---|---|---|---|

a | 24,469.2875 | 648.5690 | 6095.1517 | 4438.0571 | 3576.8579 | 5539.8139 |

b | −0.0229 | −0.3621 | −0.1647 | −0.1604 | −0.1744 | −0.1460 |

c | 0.1614 | −0.4220 | −0.1339 | −0.1298 | −0.1492 | −0.1089 |

d | 2.4898 | 0.8831 | 1.6260 | 1.6288 | 1.5488 | 1.7067 |

e | 5.0123 | −22.1158 | −4.4903 | −3.5814 | −4.7650 | −2.5826 |

**Table 6.**The landslide thickness of the prediction minus the observation for 28 occurrence-time-known cases. (Unit: m, % relative to the observation).

ΔD_{max} | ΔD_{min} | ΔD_{mean} | ΔD_{median} | ΔD_{40%} | ΔD_{60%} | |
---|---|---|---|---|---|---|

Standard deviation | 9.18 (15%) | 6.85 (35%) | 3.52 (9%) | 1.38 (6%) | 1.65 (6%) | 1.77 (7%) |

Mean of absolute values | 15.03 (72%) | 31.00 (167%) | 8.03 (41%) | 1.07 (5%) | 2.20 (11%) | 2.87 (15%) |

Maximum value | 42.61 (99%) | −23.20 (−117%) | 16.15 (55%) | 2.38 (12%) | 0.02 (0%) | 6.63 (26%) |

Mean value | 15.03 (72%) | −31.00 (−167%) | 8.03 (41%) | 0.16 (1%) | −2.20 (−11%) | 2.82 (15%) |

Median value | 11.38 (76%) | −28.18 (−163%) | 6.94 (43%) | 0.45 (3%) | −1.85 (−10%) | 2.84 (17%) |

Minimum value | 6.38 (37%) | −50.56 (−231%) | 3.69 (21%) | −4.00 (−13%) | −7.11 (−23%) | −0.36 (−2%) |

**Table 7.**The landslide thickness of the prediction minus the observation for 79 occurrence-time-unknown cases. (Unit: m, % relative to the observation).

ΔD_{max} | ΔD_{min} | ΔD_{mean} | ΔD_{median} | ΔD_{40%} | ΔD_{60%} | |
---|---|---|---|---|---|---|

Standard deviation | 1.42 (4%) | 1.60 (20%) | 1.20 (8%) | 0.65 (5%) | 0.69 (6%) | 0.67 (5%) |

Mean of absolute values | 9.26 (75%) | 26.47 (216%) | 4.39 (35%) | 0.63 (5%) | 2.13 (17%) | 1.48 (12%) |

Maximum value | 16.21 (83%) | −22.69 (−150%) | 8.71 (61%) | 1.62 (15%) | 0.13 (1%) | 3.36 (30%) |

Mean value | 9.26 (75%) | −26.47 (−216%) | 4.39 (35%) | −0.39 (−3%) | −2.13 (−17%) | 1.48 (12%) |

Median value | 8.81 (75%) | −26.41 (−219%) | 4.19 (35%) | −0.43 (−3%) | −2.17 (−18%) | 1.42 (12%) |

Minimum value | 7.46 (62%) | −32.25 (−254%) | 1.85 (17%) | −1.72 (−16%) | −3.55 (−32%) | 0.02 (0%) |

$\mathit{R}$ | ${\mathit{R}}_{\mathit{L}\mathit{T}}$ | ${\mathit{R}}_{\mathit{L}\mathit{L}}$ | ${\mathit{R}}_{\mathit{L}\mathit{U}}$ | ${\mathit{R}}_{\mathit{N}\mathit{T}}$ | ${\mathit{R}}_{\mathit{N}\mathit{L}}$ | ${\mathit{R}}_{\mathit{N}\mathit{U}}$ | |

Maximum value (mm) | 1271.3 | 1599.1 | 1147.8 | 2554.0 | 1425.8 | 804.3 | 3069.4 |

Minimum value (mm) | 501.6 | 571.4 | −198.5 | 955.9 | 277.0 | 178.7 | 507.4 |

Error sum of squares (m^{2}) | 2.3922 | 9.0971 | 19.3008 | 2.1096 | 4.3647 | 55.0174 | |

Normalized error sum of squares | 4.1646 | 9.9850 | 34.2229 | 3.2921 | 4.8297 | 70.8433 | |

Standard deviation (mm) | 297.7 | 580.5 | 845.5 | 279.5 | 402.1 | 1427.5 | |

Normalized standard deviation | 0.3927 | 0.6081 | 1.1258 | 0.3492 | 0.4229 | 1.6198 |

$\mathit{R}$ | ${\mathit{R}}_{\mathit{L}\mathit{T}}$ | ${\mathit{R}}_{\mathit{L}\mathit{L}}$ | ${\mathit{R}}_{\mathit{L}\mathit{U}}$ | ${\mathit{R}}_{\mathit{N}\mathit{T}}$ | ${\mathit{R}}_{\mathit{N}\mathit{L}}$ | ${\mathit{R}}_{\mathit{N}\mathit{U}}$ | |

Maximum value (mm) | 1994.4 | 1544.9 | 1174.1 | 1987.9 | 1688.7 | 950.8 | 3589.9 |

Minimum value (mm) | 779.2 | 464.8 | 132.2 | 862.1 | 872.7 | 470.0 | 1966.4 |

Error sum of squares (m^{2}) | 11.2251 | 26.5031 | 3.7198 | 4.1568 | 18.3132 | 40.8837 | |

Normalized error sum of squares | 4.5775 | 12.7829 | 1.9193 | 1.5839 | 7.6505 | 31.4102 | |

Standard deviation (mm) | 644.8 | 990.8 | 371.2 | 392.4 | 823.6 | 1230.5 | |

Normalized standard deviation | 0.4117 | 0.6881 | 0.2666 | 0.2422 | 0.5323 | 1.0786 |

$\mathit{R}$ | ${\mathit{R}}_{\mathit{L}\mathit{T}}$ | ${\mathit{R}}_{\mathit{L}\mathit{L}}$ | ${\mathit{R}}_{\mathit{L}\mathit{U}}$ | ${\mathit{R}}_{\mathit{N}\mathit{T}}$ | ${\mathit{R}}_{\mathit{N}\mathit{L}}$ | ${\mathit{R}}_{\mathit{N}\mathit{U}}$ | |

Maximum value (mm) | 2267.9 | 3016.4 | 2685.2 | 3412.0 | 2739.7 | 1575.6 | 5647.8 |

Minimum value (mm) | 822.3 | 804.5 | 511.1 | 1037.4 | 1144.4 | 591.5 | 2583.9 |

Error sum of squares (m^{2}) | 10.0854 | 20.0943 | 8.5405 | 6.1552 | 23.6371 | 94.8223 | |

Normalized error sum of squares | 3.1882 | 5.8767 | 3.4506 | 2.3811 | 6.6163 | 44.9751 | |

Standard deviation (mm) | 611.2 | 862.7 | 562.4 | 477.5 | 935.7 | 1874.0 | |

Normalized standard deviation | 0.3436 | 0.4665 | 0.3575 | 0.2970 | 0.4950 | 1.2906 |

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## Share and Cite

**MDPI and ACS Style**

Tsai, T.-T.; Tsai, Y.-J.; Shieh, C.-L.; Wang, J.H.-C.
Triggering Rainfall of Large-Scale Landslides in Taiwan: Statistical Analysis of Satellite Imagery for Early Warning Systems. *Water* **2022**, *14*, 3358.
https://doi.org/10.3390/w14213358

**AMA Style**

Tsai T-T, Tsai Y-J, Shieh C-L, Wang JH-C.
Triggering Rainfall of Large-Scale Landslides in Taiwan: Statistical Analysis of Satellite Imagery for Early Warning Systems. *Water*. 2022; 14(21):3358.
https://doi.org/10.3390/w14213358

**Chicago/Turabian Style**

Tsai, Tsai-Tsung, Yuan-Jung Tsai, Chjeng-Lun Shieh, and John Hsiao-Chung Wang.
2022. "Triggering Rainfall of Large-Scale Landslides in Taiwan: Statistical Analysis of Satellite Imagery for Early Warning Systems" *Water* 14, no. 21: 3358.
https://doi.org/10.3390/w14213358