# Forecasting of Landslides Using Rainfall Severity and Soil Wetness: A Probabilistic Approach for Darjeeling Himalayas

^{1}

^{2}

^{3}

^{4}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. The town is getting densely populated and expanded along the roads without proper planning. Multi-storied buildings are getting constructed along the streets and on steeper slopes.

#### 2.1. Geology

#### 2.2. Geohydrology

## 3. Landslides in Kalimpong

#### 3.1. Rainfall

#### 3.2. Drainage System

#### 3.3. Data for the Hydrological Simulation

^{2}and spatializing the data within this small area may cause overfitting problems. To overcome this limitation, the parameters used were calibrated using moisture content values collected from a different database, called the Modern Era Retrospective-Analysis for Research and Applications (MERRA) using Goddard Earth Observing System Data Assimilation System Version 5 (GEOS 5) [54]. The data provides hourly surface data with 30′ horizontal resolution. The data is also a reanalysis product that has been validated.

## 4. Methodology of Study

#### 4.1. Simulation of Soil Moisture

- (a)
- Penman–Monteith equation [57] for evapotranspiration;
- (b)
- Saint–Venant equations, two dimensional diffusion wave approximation [57] for overland flow;
- (c)
- Saint–Venant equations, one dimensional diffusion wave approximation [57] for channel flow;
- (d)
- Rutter equation [57] for canopy drip and interception;
- (e)
- Variably saturated flow equation (3D) [58] for subsurface flow;

#### 4.2. Rainfall Events and Empirical Thresholds

^{γ}

_{f}was calculated. By using a kernel density estimation [64], the probability density function of the distribution of δE was determined. The result fitted with a Gaussian function in the form

#### 4.3. Bayes’ Theorem

_{min}, T

_{5}, T

_{10}, T

_{20}and T

_{50}) six categories were defined. Hence, 30 cells (5 by 6) were available for the two-dimensional Bayesian analysis.

- N
_{A}= The total number of landslide events (If n number of landslides occur on the same day, it is considered as one landslide event) - N
_{R}= The total number of rainfall events during the study period - N
_{B,C}= The number of events in each cell condition - N
_{(B,C|A)}= The number of rainfall events that resulted in landslides while satisfying a cell condition

## 5. Results and Discussion

#### 5.1. Soil Moisture Estimation

^{2}value of 0.84. The calibrated parameters are listed in Table 2 below:

#### 5.2. Rainfall Thresholds

_{min}, T

_{5}, T

_{10}, T

_{20}, and T

_{50}). The defined thresholds and data points are plotted in Figure 5.

_{min}threshold is the threshold below which no landslides are expected to occur. The obtained results are found to be in good agreement with the ID thresholds defined for the area [44]. The variation in duration was found to be relatively less, from one to eight days while the event rainfall values varied the order of tens to hundreds. Out of the 61 events, 5% of the events are expected to fall below the T

_{5}line, 10% below the T

_{10}line, and so on. The T

_{50}line is the best fit line where 50% of the data points are expected to be below the line and 50% above the line. The equation of the minimum threshold has been obtained as E = 1.50D

^{0.65}and the best fit line is defined as E = 6.03D

^{0.65}. The values of α and γ of different thresholds are tabulated in Table 3.

#### 5.3. Probabilistic Thresholds

_{min}, T

_{min}–T

_{5}, T

_{5}–T

_{10}, T

_{10}–T

_{20}, T

_{20}–T

_{50}, and greater than T

_{50}. The classification of soil wetness values are 0–0.2, 0.2–0.4, 0.4–0.6, 0.6–0.8, and 0.8–1.0. For certain cases, the probability of occurrence of landslide was obtained as zero where either $P\left(B,C|A\right)\text{}or\text{}P\left(A\right)$ is becoming zero. The probabilistic thresholds are plotted in Figure 6.

- (a)
- the severity of a rainfall event exceeds 50% and the soil wetness is between 0.4 and 0.6
- (b)
- the severity of a rainfall event between 20% and 50% and the soil wetness is between 0.6 and 0.8
- (c)
- the severity of a rainfall event between 5% and 10% and the soil wetness is between 0.6 and 0.8.

## 6. Validation

_{min}threshold is considered. While increasing the threshold level, the value of specificity is increased, but at the cost of many missed alarms, reducing the value of sensitivity in both cases. The term likelihood ratio is the ratio of sensitivity to the false positive rate and can be used to evaluate the model performance. The more the likelihood ratio, the better is the model. The likelihood ratio is also the highest for the minimum thresholds considered in both cases. The relative values of likelihood ratio for two-dimensional probabilistic model is higher than those of an empirical model in all the cases, assuring the better performance of the probabilistic model. The lesser values of sensitivity are expected as the total number of displacement events considered for validation is as less than seven and even single missed alarms can have a significant effect on the term.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Drainage map of Kalimpong, overlaid on a digital elevation model [43].

**Figure 6.**Histogram of conditional probability of occurrence of landslides based on rainfall severity and antecedent soil moisture.

**Table 1.**The monthly rainfall data (mm) during monsoon season in Kalimpong town (2010–2017) [42].

Month | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 |

June | 316.8 | 337.0 | 354.9 | 248.0 | 396.4 | 568.0 | 327.2 | 153.7 |

July | 665.4 | 678.0 | 433.1 | 424.6 | 371.2 | 534.4 | 869.8 | 811.5 |

August | 425.3 | 525.6 | 250.8 | 401.0 | 571.8 | 242.3 | 262.6 | 432.1 |

September | 268.2 | 384.1 | 467.9 | 113.0 | 265.4 | 331.2 | 366.8 | 287.6 |

Parameters | Calibrated Value |
---|---|

Canopy storage | 5 mm |

AE/PE at field capacity | 1 |

Maximum Rooting Depth | 1.6 m |

Saturated water content | 0.40 |

Strickler overland flow coefficient | 0.50 m^{1/3}s^{−1} |

Saturated hydraulic conductivity | 1.14 m/day |

Leaf Area Index | 1 |

Residual water content | 0.08 |

vanGenuchten-n | 1.17 |

vanGenuchten-alpha | 0.03 cm^{−1} |

Exceedance Probability (%) | α | γ |
---|---|---|

50 | 6.03 | 0.65 |

20 | 4.08 | 0.65 |

10 | 3.31 | 0.65 |

5 | 2.38 | 0.65 |

min | 1.50 | 0.65 |

Statistical Attributes | TP | FP | FN | TN | Sensitivity = TP/(TP + FN) | Specificity = TN/(FP + TN) | False Positive Rate = FP/(FP + TN) | Likelihood Ratio = Sensitivity/(1 − Specificity) | |
---|---|---|---|---|---|---|---|---|---|

Empirical Thresholds | Tmin | 5 | 67 | 2 | 291 | 0.7143 | 0.8128 | 0.1872 | 3.8166 |

T5 | 2 | 47 | 5 | 311 | 0.2857 | 0.8687 | 0.1313 | 2.1763 | |

T10 | 1 | 37 | 6 | 321 | 0.1429 | 0.8966 | 0.1034 | 1.3822 | |

T20 | 1 | 27 | 6 | 331 | 0.1429 | 0.9246 | 0.0754 | 1.8942 | |

T50 | 1 | 15 | 6 | 343 | 0.1429 | 0.9581 | 0.0419 | 3.4095 | |

Probabilistic Thresholds | P > 0.1 | 6 | 41 | 1 | 317 | 0.8571 | 0.8855 | 0.1145 | 7.4843 |

P > 0.2 | 2 | 27 | 5 | 331 | 0.2857 | 0.9246 | 0.0754 | 3.7884 | |

P > 0.4 | 2 | 26 | 5 | 332 | 0.2857 | 0.9274 | 0.0726 | 3.9341 | |

P > 0.6 | 2 | 25 | 5 | 333 | 0.2857 | 0.9302 | 0.0698 | 4.0914 | |

P > 0.8 | 2 | 17 | 5 | 341 | 0.2857 | 0.9525 | 0.0475 | 6.0168 |

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**MDPI and ACS Style**

Abraham, M.T.; Satyam, N.; Pradhan, B.; Alamri, A.M. Forecasting of Landslides Using Rainfall Severity and Soil Wetness: A Probabilistic Approach for Darjeeling Himalayas. *Water* **2020**, *12*, 804.
https://doi.org/10.3390/w12030804

**AMA Style**

Abraham MT, Satyam N, Pradhan B, Alamri AM. Forecasting of Landslides Using Rainfall Severity and Soil Wetness: A Probabilistic Approach for Darjeeling Himalayas. *Water*. 2020; 12(3):804.
https://doi.org/10.3390/w12030804

**Chicago/Turabian Style**

Abraham, Minu Treesa, Neelima Satyam, Biswajeet Pradhan, and Abdullah M. Alamri. 2020. "Forecasting of Landslides Using Rainfall Severity and Soil Wetness: A Probabilistic Approach for Darjeeling Himalayas" *Water* 12, no. 3: 804.
https://doi.org/10.3390/w12030804