*3.4. Reconstruction of Empirical and Physicallybased Thresholds*

Rainfall thresholds reconstructed with different methodologies are shown in Figure 10. All of these functions were characterized by a low uncertainty of the two fitting parameters (0.2–1.9 for α, 0.01–0.04 for ω). Instead, equations of the reconstructed thresholds were very different from each other. Average values of the α parameter ranged between 11.2 and 225.0, while mean values of the ω parameter ranged between 0.08 and 0.30. Empirical threshold and physicallybased threshold considering initial pore-water pressure of −20 kPa (TRIGRS/-20) were steeper than the other two functions, as testified by significantly higher values of the ω parameter (0.25–0.30 against 0.08–0.12, respectively). The empirical threshold had the lowest value of intercept α (11.2 ± 0.2). Within physicallybased thresholds, the lower was the value of α the higher is the initial pore-water pressure used to reconstruct the threshold. The α parameter of TRIGRS/0 was about 5 times and 10 times lower than the values for the thresholds TRIGRS/–10 and TRIGRS/–20, respectively.

The practical effects of these differences are clearer when the cumulated amount of rain able to trigger shallow landslides is calculated for different rainfall durations (between 10 and 50 h), based on the defined thresholds (Table 5). For the same duration, the amount of rainfall able to trigger shallow landslides was lower by considering the empirical threshold than physicallybased threshold.

**Figure 10.** Rainfall thresholds (black line for the average function, gray dot lines for the average functions plus or minus the uncertainties) for the occurrence of shallow landslides in the study area: (**a**) threshold reconstructed through the empirical method; (**b**) threshold reconstructed through the physicallybased method considering an initial pore-water pressure of −20 kPa at the depth of the sliding surface (TRIGRS/–20); (**c**) threshold reconstructed through the physicallybased method considering an initial pore-water pressure of −10 kPa at the depth of the sliding surface (TRIGRS/–10); (**d**) threshold reconstructed through the physicallybased method considering an initial pore-water pressure of 0 kPa at the depth of the sliding surface (TRIGRS/0).


**Table 5.** Ranges of different rainfall cumulated amount enough to trigger shallow landslides for different rainfall duration, calculated using the different reconstructed thresholds.

Using the TRIGRS/0 threshold, the amount of critical cumulated rainfall increases of 5.3–10.5 mm, for the same rainfall duration. For the other physicallybased thresholds, the increase of the critical cumulated amount was more significant. Considering the TRIGRS/-20 threshold, the critical cumulated rain was about 22–25 times higher than that defined by using empirical threshold, for the same duration. Instead, considering the TRIGRS/-10 threshold, the required rainfall able to trigger shallow landslides was about 6–9 times higher than that defined using empirical threshold, for the same duration.

For the empirical thresholds, it is important to highlight that 26.2% of the rainfall events which did not cause the real triggering of shallow landslides (green circles in Figure 10a) was located above the defined thresholds (false positives). Instead, the percentage of rainfall events modeled as not able to trigger landslides but located above the thresholds was lower than 0.5% for all types of physicallybased thresholds. Considering the only triggering event when also the initial pore-water pressure at the depth of the sliding surface was known (28 February–2 March 2014 event at the testsite, 68.9 mm of rain fallen in 42 h), the empirical threshold and the TRIGRS/0 threshold correctly identified this rainfall scenario as a triggering event, since it was located above the defined thresholds (blue square in Figure 10a,d).

To verify the reliability of a rainfall threshold, it is required to quantify its effectiveness in distinguishing rainfall events able to or not able to trigger shallow landslides. This procedure could not be performed for both empirically and physicallybased thresholds by using only the database of the events already utilized to build these models. In fact, a direct comparison between the reliability of different types of thresholds could not be performed, due to the intrinsic outputs of the methods used to reconstruct each threshold. In particular, in the definition of each physicallybased threshold, all the modeled events whose Fs was lower than 1.0 potentially represented a triggering event. Instead, in the database of the triggering events that occurred between 2000 and 2018 and were used as input to build the different thresholds, the initial pore-water pressure at the depth of the sliding surface was measured only for the event of 28 February–2 March 2014 monitored at the testsite. Thus, it is not possible to link an initial pore-water pressure to all the events, neglecting the possibility to quantify the predictive capability of the different thresholds in identifying triggering or non-triggering events.

For these reasons, the validation and the evaluation of the predictive capability of the thresholds were performed by using an external database of rainfall and shallow-landslide events available for another period.
