*4.2. Threshold Calculation*

Using CTRL-T we reconstructed 1315 rainfall conditions responsible for the occurrence of landslides in the observed period. For 281 landslides it was not possible to determine the triggering rainfall event for three main reasons: (i) the distance between the landslide and the rain gauges exceeded 15 km (chosen according to the morphology and the rain gauge density of the study area); (ii) the delay between the end of the rainfall condition and the occurrence of the landslide exceeded 48 h; (iii) accurate landslide information or rainfall data were lacking. These landslides were excluded from the calculation. Several landslides occurring on the same day and near the same rain gauges were presumably triggered by the same amount of rainfall. In this case, CTRL-T selected only the rainfall condition corresponding to the first triggered landslide. As a result of the analysis, out of 1315 rainfall events, only 368 survived the selection criteria (Figures 1 and 3).

The values of 15 km and 48 h for maximum distance and delay, respectively, were selected in accordance with previous works [32,33,35,38] and should be considered as conservative upper limits. Most of the landslides (305 out of 368, 83%) were associated with rain gauges located at a maximum distance of 10 km, and half of them within 6 km; in 48 cases the distance was shorter than 2 km. Regarding the delay between the end of the rainfall and the occurrence landslide time, the majority of the landslides (299 out of 368, 81%) that were associated with rainfall conditions ended within a delay of 24 h. Specifically, half of them had a delay of less than 10 h and in 60 cases the delay was null.

Based on the 368 rainfall conditions, the algorithm included in CTRL-T calculated *ED* (cumulated event rainfall—duration) thresholds at different non-exceedance probabilities (Table 1). As a reference with previous works (e.g., [32–35,38,46,47]), Figure 3 shows the rainfall conditions and the threshold at 5% NEP. According to the frequentist method [46,47], the 5% NEP threshold leaves 5% of the empirical *ED* conditions below itself. The relative uncertainties of the parameters of the thresholds were also calculated. The 5% NEP threshold has low relative uncertainties (0.7/6.8 = 10.3%; 0.02/0.4 = 5%), which means a better distribution of the rainfall conditions.

**Figure 3.** (**a**) Log-log plot with the cumulated event rainfall—duration *ED*, conditions that triggered landslides in Slovenia and the corresponding 5% *ED* threshold (T5,SVN). (**b**) T5,SVN threshold in the range 1 h ≤ *D* ≤ 120 h, in linear coordinates. The shaded areas represent the threshold uncertainty.


**Table 1.** Main characteristics of rainfall thresholds defined in this study.

\* MPRC—Maximum Probability Rainfall Condition.

#### 4.2.1. Thresholds for Different Mean Annual Rainfall Classes

To investigate the role of the rainfall regime for the landslide triggering conditions in Slovenia, we used data on mean annual rainfall (MAR) provided by ARSO [42], which were divided into three classes. Figure 4 shows that the eastern part of Slovenia (32% of the total national territory) is characterized by low values of MAR (800 ≤ MAR ≤ 1300 mm), the central part (30%) by medium values (1300 < MAR ≤ 1600 mm) and the western part (38%) by high values (1600 < MAR ≤ 4000 mm). The number of landslides in the region characterized by a low, medium and high MAR class is 137, 127 and 104, respectively. The lowest density of landslides (one landslide every 74 km2) is found in the area with high MAR values, while the other two areas are characterized by a similarly higher value of landslide density (one every 47 km2).

**Figure 4.** Subdivision of Slovenia based on different mean annual rainfall (MAR) between 1981 and 2010 [42] into three classes, with indication of the landslides used in the analysis. The donut chart shows the number of landslides in each class.

Figure 5a shows the MPRCs classified into three MAR classes, with the corresponding 5% *ED* thresholds, T5,L, T5,M and T5,H (Table 1). The three thresholds are also shown in Figure 5b, in linear coordinates and in the range of duration 1 ≤ *D* ≤ 120 h, with the shaded areas representing the

uncertainty associated to each threshold. Inspection of Figure 5a and Table 1 reveals that the three point-clouds have different distributions and the subsets have diverse duration ranges, and the resulting thresholds have different parameters. In particular, α increases from 7.2 to 8.3, and γ decreases from 0.41 to 0.34 moving from T5,H to T5,L. Therefore, the curves become higher and steeper with an increasing MAR (Table 1), ranging from α = 8.3 ± 1.1 and γ = 0.34 ± 0.02 for the low MAR region to α = 7.1 ± 1.6 and γ = 0.41 ± 0.05 for the high MAR region. This behavior is in accordance with the findings of Peruccacci et al. [39] in the nearby Italian territory: the rainfall required to trigger landslides increases with the MAR, which proves a sort of adaptation of the landscape to the average rainfall conditions. The relative uncertainty of α increases as the MAR class increases, while Δγ/γ remains stable.

**Figure 5.** (**a**) Log-log plot with the *ED* (cumulated event rainfall—duration) conditions that triggered landslides in Slovenia classified according to three classes of mean annual rainfall (MAR) and corresponding 5% *ED* thresholds (T5,H, T5,M, T5,L). (**b**) Same thresholds and related uncertainties (shaded areas) in the range 1 h≤ *D* ≤120 h, in linear coordinates. Legend: L, 800 mm ≤ MAR ≤ 1300 mm; M, 1300 mm < MAR ≤ 1600 mm; H, 1600 mm < MAR ≤ 4000 mm.
