# A Landslide Numerical Factor Derived from CHIRPS for Shallow Rainfall Triggered Landslides in Colombia

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### Framework

## 2. Data

#### 2.1. Geological and Climatological Settings

#### 2.2. Landslide Inventory

#### 2.3. Static Parameters

#### 2.4. Dynamic Parameters

## 3. Methods

#### 3.1. Dynamic Factors Modeling—Soil Moisture and Rainfall

#### 3.2. Logistic Modeling—Dynamic and Static Factors

#### 3.3. Landslide Thresholds

#### 3.3.1. Landslide Triggering Factor—LTF

#### 3.3.2. Cumulative Rainfall Event-Duration (E-D) Threshold

^{−b}, where I is the rainfall mean intensity in mm/h; D is the duration of the rainfall event expressed hourly or daily; α is the scaling constant; and b represents the slope) [9].

#### 3.4. Assumptions

- Both the logistic regression model and the LTF threshold are data driven approaches.
- We assume that pore pressure increases due to liquefaction of the material.
- We suppose that soil moisture content for a specific location is dependent on the amount and duration of the rainfall that occurs before the landslide event and on the non-rain (dry) period between the two events. We do not incorporate root uptake or evapotranspiration information.
- Daily rainfall temporal resolution is used because the landslide inventory lists a date, not a timestamp of when the event occurred.
- It is understood that a landslide changes the physical characteristics of the area. It may flatten the slope and remove the weak soil layer, which in return may change the landcover. Under these circumstances, the calculated LTF for that location no longer applies because conditions have changed.

## 4. Results

#### 4.1. Logistic Regression—Dynamic and Static Factors

#### 4.2. Landslide Triggering Factor (LTF) Thresholds—Dynamic Factors and Slope

^{2}) for the LTF threshold-Slope relationship as per Equation (7) is R

^{2}= 0.836. Figure 6 shows that the LTF-Slope angle relation rapidly changes in smaller slope angles, whereas it barely fluctuates in larger ones. Slopes greater than 25° show an asymptote average threshold value of 1.227 with a standard deviation of 0.104.

#### Landslide Triggering Factor Error—False Positive Rate (FPR)

#### 4.3. Accumulated Rainfall Duration (E-D) Threshold—Dynamic Factors and Slope

^{2}= 0.68), thus, we use this form.

#### Accumulated Rainfall Duration (E-D) Thresholds Error—False Positive Rate (FPR)

#### 4.4. LTF Threshold vs. E-D Threshold

#### 4.5. Landslide Triggering Factor—(LTF) Thresholds Hazard Map

#### 4.6. Challenges and Limitations

## 5. Conclusions

^{2}mark this as the region with the least precipitation (in two rainfall episodes) necessary to trigger a landslide. And although the DM map could serve as a guide for vulnerability and risk, several challenges should be resolved to “fine-tune” the thresholds. These include introducing a “time of event” parameter and physical or reliable satellite-based antecedent soil moisture information when it becomes available.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Girty, G.H. Perilous Earth: Understanding Processes behind Natural Disasters, ver. 1.0 Chapter 8 Landslides. 2009. Available online: http://www.sci.sdsu.edu/visualgeology/naturaldisasters/ (accessed on 1 July 2021).
- Petley, D. Global patterns of loss of life from landslides. Geology
**2012**, 40, 927–930. [Google Scholar] [CrossRef] - Kim, H.G.; Lee, D.K.; Park, C. Assessing the cost of damage and effect of adaptation to landslides considering climate change. Sustainability
**2018**, 10, 1628. [Google Scholar] [CrossRef] [Green Version] - Cruden, D.J.; Varnes, D.M. Landslides: Investigation and Mitigation. Transp. Res. Board Spec. Rep.
**1996**, 247, 36–75. [Google Scholar] - Sidle, R.C.; Ochiai, H. Landslides: Processes, Prediction, and Land Use; American Geophysical Union: Washington, DC, USA, 2006; Volume 18. [Google Scholar] [CrossRef]
- Kirschbaum, D.B.; Adler, R.; Hong, Y.; Lerner-Lam, A. Evaluation of a preliminary satellite-based landslide hazard algorithm using global landslide inventories. Nat. Hazards Earth Syst. Sci.
**2009**, 9, 673–686. [Google Scholar] [CrossRef] [Green Version] - Aristizábal, E.; García, E.; Martínez, C. Susceptibility assessment of shallow landslides triggered by rainfall in tropical basins and mountainous terrains. Nat. Hazards
**2015**, 78, 621–634. [Google Scholar] [CrossRef] - Aristizábal, E.; Velez, J.; Martínez, C.; Jaboyedoff, M. SHIA_Landslide: A distributed conceptual and physically based model to forecast the temporal and spatial occurrence of shallow landslides triggered by rainfall in tropical and mountainous basins. Landslides
**2015**, 13, 497–517. [Google Scholar] [CrossRef] - Cullen, C.A.; Al-Suhili, R.; Khanbilvardi, R. Guidance index for shallow landslide hazard analysis. Remote Sens.
**2016**, 8, 866. [Google Scholar] [CrossRef] [Green Version] - Collins, B.D.; Znidarcic, D. Stability Analyses of Rainfall Induced Landslides. J. Geotech. Geoenviron. Eng.
**2004**, 130, 362. [Google Scholar] [CrossRef] - Glade, T.; Anderson, M.; Crozier, M. Landslide Hazard and Risk; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2004; Available online: https://books.google.com/books?id=UFQk0I4EUiwC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false (accessed on 22 March 2022).
- Caine, N. The rainfall intensity-duration control of shallow landslides and debris flows. Geogr. Ann. Ser. A Phys. Geogr.
**1980**, 62, 23–27. [Google Scholar] - Maturidi, A.M.A.M.; Kasim, N.; Taib, K.A.; Azahar, W.N.A.W. Rainfall-Induced Landslide Thresholds Development by Considering Different Rainfall Parameters: A Review. J. Ecol. Eng.
**2021**, 22, 85–97. [Google Scholar] [CrossRef] - Dikshit, A.; Satyam, N.; Pradhan, B.; Kushal, S. Estimating rainfall threshold and temporal probability for landslide occurrences in Darjeeling Himalayas. Geosci. J.
**2020**, 24, 225–233. [Google Scholar] [CrossRef] - Naidu, S.; Sajinkumar, K.S.; Oommen, T.; Anuja, V.J.; Samuel, R.A.; Muraleedharan, C. Early warning system for shallow landslides using rainfall threshold and slope stability analysis. Geosci. Front.
**2018**, 9, 1871–1882. [Google Scholar] [CrossRef] - Mandal, P.; Sarkar, S. Estimation of rainfall threshold for the early warning of shallow landslides along National Highway-10 in Darjeeling Himalayas. Nat. Hazards
**2021**, 105, 2455–2480. [Google Scholar] [CrossRef] - Kirschbaum, D.B.; Stanley, T.; Simmons, J. A dynamic landslide hazard assessment system for Central America and Hispaniola. Nat. Hazards Earth Syst. Sci.
**2015**, 15, 2257–2272. [Google Scholar] [CrossRef] [Green Version] - Brunetti, M.T.; Melillo, M.; Gariano, S.L.; Ciabatta, L.; Brocca, L.; Amarnath, G.; Peruccacci, S. Satellite rainfall products outperform ground observations for landslide prediction in India. Hydrol. Earth Syst. Sci.
**2021**, 25, 3267–3279. [Google Scholar] [CrossRef] - Rossi, M.; Luciani, S.; Valigi, D.; Kirschbaum, D.; Brunetti, M.T.; Peruccacci, S.; Guzzetti, F. Statistical approaches for the definition of landslide rainfall thresholds and their uncertainty using rain gauge and satellite data. Geomorphology
**2017**, 285, 16–27. [Google Scholar] [CrossRef] - Marin, R.J.; Velásquez, M.F.; García, E.F.; Alvioli, M.; Aristizábal, E. Assessing two methods of defining rainfall intensity and duration thresholds for shallow landslides in data-scarce catchments of the Colombian Andean Mountains. Catena
**2021**, 206, 105563. [Google Scholar] [CrossRef] - van Westen, C.J.; Castellanos, E.; Kuriakose, S.L. Spatial data for landslide susceptibility, hazard, and vulnerability assessment: An overview. Eng. Geol.
**2008**, 102, 112–131. [Google Scholar] [CrossRef] - Vallejo-Zamudio, L.E. El incierto crecimiento económico colombiano. Apuntes Cenes
**2017**, 36, 9–10. [Google Scholar] [CrossRef] [Green Version] - Aristizábal, E.; Sánchez, O. Spatial and temporal patterns and the socioeconomic impacts of landslides in the tropical and mountainous Colombian Andes. Disasters
**2020**, 44, 596–618. [Google Scholar] [CrossRef] [PubMed] - Poveda, G.; Vélez, J.I.; Mesa, O.J.; Cuartas, A.; Barco, J.; Mantilla, R.I.; Mejía, J.F.; Hoyos, C.D.; Ramírez, J.M.; Ceballos, L.I.; et al. Linking Long-Term Water Balances and Statistical Scaling to Estimate River Flows along the Drainage Network of Colombia. J. Hydrol. Eng.
**2007**, 12, 4–13. [Google Scholar] [CrossRef] [Green Version] - Álvarez-Villa, O.D.; Vélez, J.I.; Poveda, G. Improved long-term mean annual rainfall fields for Colombia. Int. J. Climatol.
**2011**, 31, 2194–2212. [Google Scholar] [CrossRef] - NOAA—Physical Science Laboratory. Multivariate ENSO Index Version 2 (MEI.v2). NOAA ENSO. 2022. Available online: https://psl.noaa.gov/enso/mei/ (accessed on 25 February 2022).
- Poveda, G. Diagnóstico del Ciclo Anual y Efectos del ENSO Sobre la Intensidad Máxima de Lluvias de Duración Entre 1 y 24 Horas en los Andes de Colombia. Meteorol. Colomb.
**2002**, 5, 67–74. [Google Scholar] - El Espectador. Avalancha en Mocoa, una de las Peores Tragedias de 2017. 2017. Available online: https://www.elespectador.com/noticias/nacional/avalancha-en-mocoa-una-de-las-peores-tragedias-de-2017/ (accessed on 19 October 2020).
- Benfield, A. Global Catastrophe Recap. 2019. Available online: http://thoughtleadership.aonbenfield.com/Documents/20190508-analytics-if-april-global-recap.pdf (accessed on 4 July 2020).
- Farr, T.G.; Rosen, P.A.; Caro, E.; Crippen, R.; Duren, R.; Hensley, S.; Kobrick, M.; Paller, M.; Rodriguez, E.; Roth, L.; et al. The shuttle radar topography mission. Rev. Geophys.
**2007**, 45, 2. [Google Scholar] [CrossRef] [Green Version] - Buchhorn, M.; Bertels, L.; Smets, B.; De Roo, B.; Lesiv, M.; Tsendbazar, N.E.; Masiliunas, D.; Linlin, L. Copernicus Global Land Service: Land Cover 100m: Version 3 Globe 2015–2019: Algorithm Theoretical Basis Document; Zenodo: Geneve, Switzerland, 2020. [Google Scholar] [CrossRef]
- Eswaran, H.; Reich, P.; Padmanabhan, E. World soil resources opportunities and challenges. In World Soil Resources and Food Security; CRC Press, Taylor and Francis Group: Boca Raton, FL, USA, 2016; pp. 29–52. [Google Scholar]
- Instituto Geográfico Agustín Codazzi- Subdirección de Agrología—Grupo Interno de Trabajo Geomática. Mapas de Suelos del Territorio Colombiano a Escala 1:100.000. 31 December 2017. Available online: http://metadatos.igac.gov.co/geonetwork/srv/spa/catalog.search#/metadata/b857e651-b8d2-4bf2-9e03-41a038c7206a (accessed on 14 August 2020).
- Lehmann, P.; Gambazzi, F.; Suski, B.; Baron, L.; Askarinejad, A.; Springman, S.M.; Holliger, K.; Or, D. Evolution of soil wetting patterns preceding a hydrologically induced landslide inferred from electrical resistivity survey and point measurements of volumetric water content and pore water pressure. Water Resour. Res.
**2013**, 49, 7992–8004. [Google Scholar] [CrossRef] - Funk, C.; Peterson, P.; Landsfeld, M.; Pedreros, D.; Verdin, J.; Shukla, S.; Husak, G.; Rowland, J.; Harrison, L.; Hoell, A.; et al. The climate hazards infrared precipitation with stations—A new environmental record for monitoring extremes. Sci. Data
**2015**, 2, 150066. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gorsevski, P.V.; Gessler, P.E.; Foltz, R.B.; Elliot, W.J. Spatial prediction of landslide hazard using logistic regression and ROC analysis. Trans. GIS
**2006**, 10, 395–415. [Google Scholar] [CrossRef] - Guns, M.; Vanacker, V. Logistic regression applied to natural hazards: Rare event logistic regression with replications. Nat. Hazards Earth Syst. Sci.
**2012**, 12, 1937–1947. [Google Scholar] [CrossRef] - Thomas, D.R.; Zumbo, B.D.; Dutta, S. On Measuring the Relative Importance of Explanatory Variables in a Logistic Regression. J. Mod. Appl. Stat. Methods
**2008**, 7, 4. [Google Scholar] [CrossRef] [Green Version] - Zhu, L.; Huang, J. GIS-based logistic regression method for landslide susceptibility mapping in regional scale. J. Zhejiang Univ. Sci. A
**2006**, 7, 2007–2017. [Google Scholar] [CrossRef] - Akbari, A.; Bin, F.; Yahaya, M.; Azamirad, M.; Fanodi, M. Landslide Susceptibility Mapping Using Logistic Regression Analysis and GIS Tools. Electron. J. Geotech. Eng.
**2014**, 19, 1687–1696. [Google Scholar] - Regmi, N.R.; Giardino, J.R.; McDonald, E.V.; Vitek, J.D. A comparison of logistic regression-based models of susceptibility to landslides in western Colorado, USA. Landslides
**2014**, 11, 247–262. [Google Scholar] [CrossRef] - Lee, S. Cross-verification of spatial logistic regression for landslide susceptibility analysis: A case study of Korea. In Proceedings of the 31st International Symposium on Remote Sensing of Environment, ISRSE 2005: Global Monitoring for Sustainability and Security, St. Petersburg, Russia, 20–24 June 2005; Available online: http://www.scopus.com/inward/record.url?eid=2-s2.0-84879728712&partnerID=tZOtx3y1 (accessed on 4 March 2020).
- Kavzoglu, T.; Sahin, E.K.; Colkesen, I. Landslide susceptibility mapping using GIS-based multi-criteria decision analysis, support vector machines, and logistic regression. Landslides
**2013**, 11, 425–439. [Google Scholar] [CrossRef] - Pourghasemi, H.R.; Moradi, H.R.; Aghda, S.M.F. Landslide susceptibility mapping by binary logistic regression, analytical hierarchy process, and statistical index models and assessment of their performances. Nat. Hazards
**2013**, 69, 749–779. [Google Scholar] [CrossRef] - Shahabi, H.; Khezri, S.; Ahmad, B.B.; Hashim, M. Landslide susceptibility mapping at central Zab basin, Iran: A comparison between analytical hierarchy process, frequency ratio and logistic regression models. Catena
**2014**, 115, 55–70. [Google Scholar] [CrossRef] - Ayalew, L.; Yamagishi, H. The application of GIS-based logistic regression for landslide susceptibility mapping in the Kakuda-Yahiko Mountains, Central Japan. Geomorphology
**2005**, 65, 15–31. [Google Scholar] [CrossRef] - Chawla, N.V.; Bowyer, K.W.; Hall, L.O.; Kegelmeyer, W.P. SMOTE: Synthetic Minority Over-sampling Technique. J. Artif. Intell. Res.
**2002**, 16, 321–357. [Google Scholar] [CrossRef] - Segoni, S.; Rossi, G.; Rosi, A.; Catani, F. Landslides triggered by rainfall: A semi-automated procedure to define consistent intensity–duration thresholds. Comput. Geosci.
**2014**, 63, 123–131. [Google Scholar] [CrossRef] - Valenzuela, P.; Zêzere, J.L.; Domínguez-Cuesta, M.J.; García, M.A.M. Empirical rainfall thresholds for the triggering of landslides in Asturias (NW Spain). Landslides
**2019**, 16, 1285–1300. [Google Scholar] [CrossRef] - Mathew, J.; Babu, D.G.; Kundu, S.; Kumar, K.V.; Pant, C.C. Integrating intensity-duration-based rainfall threshold and antecedent rainfall-based probability estimate towards generating early warning for rainfall-induced landslides in parts of the Garhwal Himalaya, India. Landslides
**2014**, 11, 575–588. [Google Scholar] [CrossRef] - Glade, T.; Crozier, M.; Smith, P. Applying probability determination to refine landslide-triggering rainfall thresholds using an empirical ‘Antecedent Daily Rainfall Model. Pure Appl. Geophys.
**2000**, 157, 1059–1079. Available online: http://link.springer.com/article/10.1007/s000240050017 (accessed on 14 August 2014). [CrossRef] - Liao, Z.; Hong, Y.; Wang, J.; Fukuoka, H.; Sassa, K.; Karnawati, D.; Fathani, F. Prototyping an experimental early warning system for rainfall-induced landslides in Indonesia using satellite remote sensing and geospatial datasets. Landslides
**2010**, 7, 317–324. [Google Scholar] [CrossRef] - Godt, J.W.; Baum, R.L.; Chleborad, A.F. Rainfall characteristics for shallow landsliding in Seattle, Washington, USA. Earth Surf. Processes Landf.
**2006**, 31, 97–110. [Google Scholar] [CrossRef] - Baum, R.L.; Godt, J.W. Early warning of rainfall-induced shallow landslides and debris flows in the USA. Landslides
**2009**, 7, 259–272. [Google Scholar] [CrossRef] - Guzzetti, F.; Stark, C.P.; Salvati, P. Evaluation of flood and landslide risk to the population of Italy. Environ. Manag.
**2005**, 36, 15–36. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**Datasets used for the study area and corresponding landslide events happening between 2016 and 2019: (

**a**) CHIRPS rainfall (mm)—used in the logistic model and LTF method; (

**b**) slope angle derived from SRTM V3—used in the logistic model and LTF method. (

**c**) USDA Soils Classification—used in the logistic model; (

**d**) Copernicus Landcover 2019—used in the logistic model.

**Figure 3.**Monthly rainfall-triggered landslide events during the study period 2016–1019 and monthly cumulative rainfall data for the same timeframe from CHIRPS.

**Figure 4.**An example of rainfall characteristics for two successive rainfall/dry periods at one landslide location. PR1 and RS1 represent the very first rainfall recorded at one location: (PR1) number of days that the rainfall (intermittently lasted) and (RS1) the total amount of rainfall in that period. Then, there was no rain for 2 days (DT), but later it rained for 2 extra days (PR2) amounting to the triggering rainfall (RS2). These rainfall/dry pairs start at the beginning of the rainfall time series (01/01/2016) until the time of the landslide as listed in the inventory. Each pair is stored as a “running” data line where PR2 and RS2 become PR1 and RS1 of the following line.

**Figure 6.**Calculated LTF threshold values (

**blue**) fitted with Equation (7) (

**red**) for the training dataset.

**Figure 7.**E-D threshold values for the training dataset with corresponding equations and determination coefficients: (

**a**) Equation (5a)—power form and (

**b**) Equation (5b)—linear form.

**Figure 8.**(

**a**) E-D and LTF threshold values with corresponding false positive rate for the training dataset (65%) and (

**b**) for the testing dataset (35%).

**Figure 9.**DynamicMap quantities between two rainfall episodes that will trigger a landslide once exceeded at that specific slope angle. Days are expressed as (day

^{2}) as per Equation (12) where the two rainfalls average is measured in mm/day and then are divided by the dry period between the two rainfalls, also measured in days.

Data Type | Dataset | Resolution/Accuracy | Extent | Source |
---|---|---|---|---|

Slope | SRTM | 30 m | Global | NASA/USGS/JPL-Caltech |

Landcover | Copernicus | 100 m | Global | Copernicus |

Soils | USDA | 1:5,000,000 | Global | USDA |

Rainfall | CHIRPS | 0.05° × 0.05° | Global | UCSB/CHG |

Landslide inventory | Universidad Nacional De Colombia/SGC | Various mapping scales and survey types | National | Universidad Nacional De Colombia/SGC |

**Table 2.**Variables created to track rainfall days, dry days, and rainfall amounts leading to a landslide event in the inventory.

Variable Name | Represents |
---|---|

PR1 | Total number of days of Precedent Rainfall event |

RS1 | Rainfall Sum during PR1 in mm |

PR2 | Total number of days of rainfall event following PR1 |

RS2 | Rainfall Sum during PR2 in mm |

DT | Non-rainfall day period between two consecutive rainfall events |

**Table 3.**Example of rainfall/dry periods for one location from the beginning of the time series until the moment of the event—one landslide.

PR1 (Days) | RS1 (mm/Day) | DT (Days) | PR2 (Days) | RS2 (mm/Day) |
---|---|---|---|---|

1 | 34.30 | 2 | 1 | 34.30 |

1 | 34.30 | 1 | 3 | 52.31 |

3 | 52.31 | 27 | 1 | 11.87 |

1 | 11.87 | 3 | 1 | 6.00 |

1 | 6.00 | 2 | 1 | 8.17 |

… | … | … | … | … |

Event | Cases | Under SMOTE | Cases Training | Cases Testing |
---|---|---|---|---|

1 | 346 | 346 | 241 | 105 |

0 | 125,901 | 346 | 238 | 108 |

Percentage | 100% | 100% | ~70% | ~30% |

Class | Precision | Recall | F1-Score |
---|---|---|---|

0 | 0.71 | 0.79 | 0.75 |

1 | 0.75 | 0.67 | 0.71 |

Variable | Coefficients | OR |
---|---|---|

PR1 | −0.33 | 0.718 |

RS1 | 0.01 | 1.013 |

DT | −1.87 | 0.153 |

PR2 | −0.33 | 0.715 |

RS2 | 0.01 | 1.011 |

Slope | −0.20 | 0.851 |

Soil Type | −0.90 | 0.404 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 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**

Cullen, C.A.; Al Suhili, R.; Aristizabal, E.
A Landslide Numerical Factor Derived from CHIRPS for Shallow Rainfall Triggered Landslides in Colombia. *Remote Sens.* **2022**, *14*, 2239.
https://doi.org/10.3390/rs14092239

**AMA Style**

Cullen CA, Al Suhili R, Aristizabal E.
A Landslide Numerical Factor Derived from CHIRPS for Shallow Rainfall Triggered Landslides in Colombia. *Remote Sensing*. 2022; 14(9):2239.
https://doi.org/10.3390/rs14092239

**Chicago/Turabian Style**

Cullen, Cheila Avalon, Rafea Al Suhili, and Edier Aristizabal.
2022. "A Landslide Numerical Factor Derived from CHIRPS for Shallow Rainfall Triggered Landslides in Colombia" *Remote Sensing* 14, no. 9: 2239.
https://doi.org/10.3390/rs14092239