# Guidance Index for Shallow Landslide Hazard Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Static Factors

#### 2.2. Dynamic Factors

#### 2.3. Shallow Landslide Index

^{2}pixel area and 1 m depth as rainfall thresholds alone do not provide information about the soil wetness profile with depth. Some studies [23,31] recommend that antecedent daily precipitation values be replaced by actual soil moisture observations because precipitation derived soil moisture proxies and actual observations are poorly correlated. This work adopts remotely sensed daily soil moisture values, and experimentally uses a 10-day time-lapse analysis. This time interval is based on studies by Glade (1997), Kanungo & Sharmana (2014), and Cain (1980).

#### 2.3.1. Shallow Landslide Index Modeling

#### 2.3.2. Assumptions and Limitations

- There are two known failure mechanisms associated with infiltration processes, in the first mechanism pore pressure increases due to liquefaction of the material, in the second mechanism, the soil remains in an unsaturated state but failure happens due to reduced suction [25]. This model assumes the first mechanism.
- As a data-driven model, β, the percentage of percolation is assumed to be intrinsic to all static variables in the model. It is assumed that the satellite values represent the actual moisture content in the soil after being affected by all the processes related to runoff, evaporation, suction, and percolation.
- Daily rainfall and soil moisture temporal resolutions are assumed because there is a date, not a time stamp for shallow landslide events listed in the inventory used in this study. At the moment, it is not possible to obtain a better temporal accuracy to build a large extent model based on the inventory limitations.
- Root-soil moisture (1 m) for AMSR-E and SMAP is the assumed soil moisture depth for this study.
- The L4_SM algorithm does not provide brightness temperature readings from SMAP in mountainous regions such as the Rocky Mountains or near water bodies. In areas where SMAP is not able to acquire data, root-soil moisture values are the result of forcing data and a catchment model.

#### 2.3.3. Model Evaluation

#### 2.3.4. Cut-off Probability

## 3. Results

#### 3.1. Shallow Landslide Index—AMSR-E/TRMM

#### 3.2. Shallow Landslide Index—SMAP/GPM

^{2}, the Pseudo R

^{2}or Nagelkerke R

^{2}(that ranges from 0 to 1) for each model describes the goodness of fit for each logistic model, in this case, all validation models are close to 1, therefore indicating a strong relationship (78.7%, 79.6%, and 76.8% respectively) between the predictors and the predicted value.

**Z**= ((2.4 × Slope) − (1.425 × Soil Type) + (5.136 × Land Cover) + (4.414 × SLI) − 46.6)

_{10-day}**Z**= ((2.6 × Slope) − (1.657 × Soil Type) + (5.609 × Land Cover) + (5.051 × SLI) − 50.2)

_{7-day}**Z**= ((3.1 × Slope) − (2.452 × Soil Type) + (6.793 × Land Cover) + (6.793 × SLI) − 56.4)

_{3-day}#### 3.3. SLI Application

## 4. Discussion

#### 4.1. Comparing AMSR-E/TRMM and SMAP/GPM

#### 4.2. Challenges and Limitations

## 5. Conclusions

^{2}pixel area. This index can serve as guidance for the assessment of shallow landslide hazards within susceptible areas in the Continental United States. AMSR-E and TRMM information are used at first as proxies for model development from where findings are as follows:

- The AMSR-E model predicts the highest number of cases correctly at 92.7% accuracy.
- The RMSE between the resulting SLI and the actual events is 0.83 in a scale from 1–13.
- The resulting index map is useful to have an understanding of hazardous areas as precedent soil moisture conditions and rainfall are taken into consideration. Nevertheless, as AMSR-E is no longer functional, current and future guidance is not possible.

- Slope is the variable with most influence over the model followed by soil moisture content and rainfall in the form of SLI, soil type, and land cover are subsequently in importance in the three models.
- The pseudo R
^{2}, the Nagelkerke R^{2}fit for a logistic regression for each model—10-day, 7-day, and 3-day—indicates a strong relationship (78.7%, 79.6%, and 76.8% respectively) between the predictors and the prediction. - The optimal cut-off value for these logistic regression models as indicated by the AUC is 0.2.
- The RMSE is used to understand the difference between the events and the predicted SLI value for the three models, as the RMSE is scale dependent, RMSE = 1.08, 0.84, 0.97 are considered a low error in the SLI scale of 1–13.
- Comparing AMSR-E’s performance to SMAP’s is not possible even though both models are built with the same predefined static variables. There is no overlap between AMRS-E and SMAP. In addition, the sample sizes of each instrument are very different, seven years of AMSR-E and TRMM versus nine months of SMAP and GPM. Nevertheless, the t-test of significant difference in means and the f-test for significant variance result in significant differences.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Shallow Landslide Index (SLI) Workflow. (

**Left**) static factors and methods used to establish susceptibility; (

**Right**) Dynamic and static factors integration to determine what combination results in a shallow landslide event. Such combination is expressed in the form of an index calculated for 10 or 7 days of root-soil moisture and rainfall conditions.

**Figure 2.**Antecedent Soil moisture $\mathsf{\theta}$ and accumulated rainfall depth in d-days over the pixel area Vwd as the total volume of water content of the Shallow Landslide Index (SLI).

**Figure 3.**The Shallow Landslide Index (SLI)—for each pixel that contains information about static factors and their corresponding initial soil moisture, the algorithm incrementally tries rainfall values (starting at 0) until it finds the value that makes the logistic regression equation equal to 1.

**Figure 5.**Normalized importance analysis of each variable in the three models indicating the percentage effect of each variable on the dependent variable.

**Figure 6.**ROC Curve SMAP/GPM models showing the resulting AUC values for all three different time periods tested, SLI 10, 7, and 3 days respectively.

**Figure 7.**(

**Top**) SLI for 10 days calculated with AMSR-E/TRMM information; (

**Bottom**) SLI for 10 days calculated with SMAP/GPM information. The color bar represents the index number associated to the minimum amount of moisture and rainfall depth accumulation necessary to trigger a shallow landslide at each location. Any new calculated values that are equal or greater to the SLI shall be considered for further investigation, as it is likely that a shallow landslide event could happen.

Soil Type | Shape Area km^{2} | Number of Events | Random Points |
---|---|---|---|

Cambisols | 718,950 | 65 | 400 |

Luvisols | 2,953,072 | 60 | 591 |

Acrisols | 1,746,111 | 44 | 110 |

Phaeozems | 1,188,000 | 17 | 202 |

Kastanozems | 2,427,042 | 13 | 316 |

Andosols | 318,317 | 12 | 50 |

Podzols | 699,157 | 10 | 44 |

Regosols | 761,849 | 9 | 40 |

Total Cases | 1753 | ||||
---|---|---|---|---|---|

Event | Number of Cases | Total % of Data | % Cases Modeled | % Event Model Cases | Number of Cases |

1 | 141 | 8 | 141/1263 = 11 | 141/204 = 69 | 1263 |

0 | 1122 | 64 | 1122/1263 = 89 | 1122/1549 = 72 | |

1263 | 72 | 72% | |||

Event | Number of Cases | % Total | % Cases Validated | % Event Validated Cases | Number of Cases |

1 | 63 | 3.6 | 63/490 = 12.8 | 63/204 = 31 | 490 |

0 | 427 | 24.3 | 427/490 = 87.2 | 427/1549 = 27.6 | |

490 | 27.9 | 28% |

Shallow Landslide Event | ||||
---|---|---|---|---|

Predicted | Not Predicted | Total | ||

Landslide | 116 true positive | 8 false positive | 128 | |

Not landslide | 12 false negative | 1103 true negative | 1111 | |

Total | 128 | 1111 | 1239 |

Model | Chi-Square | Df. | Sig. |
---|---|---|---|

10-day | 155.484 | 4 | 0.000 |

7-day | 156.208 | 4 | 0.000 |

3-day | 156.552 | 4 | 0.000 |

Descriptive Statistics | |||||||||
---|---|---|---|---|---|---|---|---|---|

N | Min. | Max. | Mean | Std. | Var. | Skewness | |||

ST | ST | ST | ST | Std. Error | ST | ST | ST | Std. Error | |

SLI_10_Day | 3837 | 6 | 13 | 9.48 | 0.025 | 1.54 | 2.373 | 0.222 | 0.04 |

AMSR-E | 3837 | 1 | 13 | 9.08 | 0.026 | 1.63 | 2.656 | −0.803 | 0.04 |

Mean | Std. Dev. | Std. Error Mean | t. | Df. | Sig. (2-Tailed) | |
---|---|---|---|---|---|---|

Models | 0.39927 | 1.356 | 0.0218 | 18.238 | 3836 | 0.000 |

© 2016 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 (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Avalon Cullen, C.; Al-Suhili, R.; Khanbilvardi, R.
Guidance Index for Shallow Landslide Hazard Analysis. *Remote Sens.* **2016**, *8*, 866.
https://doi.org/10.3390/rs8100866

**AMA Style**

Avalon Cullen C, Al-Suhili R, Khanbilvardi R.
Guidance Index for Shallow Landslide Hazard Analysis. *Remote Sensing*. 2016; 8(10):866.
https://doi.org/10.3390/rs8100866

**Chicago/Turabian Style**

Avalon Cullen, Cheila, Rafea Al-Suhili, and Reza Khanbilvardi.
2016. "Guidance Index for Shallow Landslide Hazard Analysis" *Remote Sensing* 8, no. 10: 866.
https://doi.org/10.3390/rs8100866