*4.3. Temporal Probability of Landslide Initiation*

The temporal probability of landslide incident is determined as the product of annual exceedance probability (AEP) and probability of landslide occurrence [16]. AEP is defined as the probability of the threshold being exceeded in a given year [46], and is determined using the Poisson probability model defined as [16]

$$P(\mathbf{N}(\mathbf{t})=\mathbf{n}) = \mathbf{e}^{-\lambda\mathbf{t}} \frac{(-\lambda\mathbf{t})^{\mathbf{n}}}{\mathbf{n}!} \tag{1}$$

where N(t) represents the number of landslide incidences during time t and λ is landslide occurrence rate. The exceedance probability for time t is calculated as [13]

$$P[\text{N}(\mathbf{t}) \ge 1] = 1 - \exp\left(-\mathbf{t}/\mu\right) \tag{2}$$

where μ is the mean recurrence interval between subsequent landslides determined from landslide inventory.

The determination of temporal probability was based on the following assumptions: (i) probability of landslide incidence is correlated to the probability of rainfall threshold being reached or exceeded, and (ii) landslides will not or will seldom occur when precipitation value is less than the threshold value [13,16,47].

The annual temporal probabilities for different zones of the study region are depicted in Figure 8, and their distribution along with the threshold equations is presented in Table 1. For Zone 1, the threshold value was exceeded 55 times during the simulation period, and out of these 55 cases, landslides were triggered in 16. The estimated probability P[L|(R > RT)] for Zone 1 was 0.29. Similarly, for Zone 2 and 3, the threshold value was exceeded 76 and 64 times in the 4 year period, leading to 31 and 21 landslides being triggered and contributing temporal probability values of 0.41 and 0.33, respectively. The probability of having one or more rainfall events in any given year varied from 0.29 to 0.41. The highest probability values were obtained for Zone 2, followed by Zone 3 and Zone 1. This variation was also observed in the number of landslide incidences for each zone. These precipitation events were also capable of triggering multiple landslides during the monsoon period.

**Figure 8.** Annual exceedance probability (AEP) of landslide occurrences along the Samdrup Jongkhar–Trashigang Highway.


