*3.5. Validation of the Reconstructed Thresholds*

For the validation period of August 1992–August 1997, 488 rainfall events were identified (Figure 11a). Twenty of these events represented conditions able to trigger shallow landslides in the study area. The triggering events occurred in the cold period of the year, especially in November and in February–March and were classified as light–moderate (B), moderate–heavy (C1), or heavy (C2) rainfalls according to Alpert et al.'s [64] classification, with a duration between 9 and 218 h and cumulated amount between 38.0 and 129.4 mm.

During the modelled time-span, evapotranspiration rates (Figure 11b) ranged between 0 and 12 mm/day. Values close to 0 mm/day occurred in cold winter months, while summer dry months were characterized by a warmer condition that allowed evapotranspiration.

Pore-water pressure trend at typical depths of the sliding surfaces (Figure 11c) was characterized by the typical hydrological behaviors of the soil layers at the same depth, as inferred by field data at the test-site slope during the monitoring period since March 2012 [24,47]. These soil layers reached the driest condition during warm months of the year, especially between June and October, when few thunderstorms were interspersed by prolonged periods without rain and with significant evapotranspiration rates. The first significant rainfall events of October–November, characterized by at least 30 mm of rain fallen in 24 h, caused a slight increase in pore-water pressure. A more evident pore-water pressure increase was observed in the following wet period, between November and January, when rainfall events of at least 20–30 mm/day were rather close to each other, and evapotranspiration rates were limited (<1 mm/day) (Figure 11c). During both cold and wet months, pore-water pressure generally remained lower than –20 kPa, reaching saturated conditions in correspondence of other important rainfall events of at least 20 mm/day. Saturated conditions and the development of positive pressures (corresponding to the formation of a perched water table) were most probable till the end of March. In April, pore-water pressure began to decrease down to values lower than –20 kPa, due to an increase in evapotranspiration rates (about 4–5 mm/day) and to an increase in dry days between two different rainfalls. Instead, till the end of June, after very intense events of at least 50 mm of rain fallen in 12 h, a transient increase of pore-water-pressure till values of about −10 kPa was observed. Pore-water pressure tended to decrease very fast, till the driest soil conditions, since the end of June-beginning of July.

**Figure 11.** Rainfall amounts (**a**), evapotranspiration rates (**b**), and modeled pore-water pressure at the typical depth (1.0–1.2 m form ground) of the shallow-landslide sliding surface (**c**) for the time span August 1992–August 1997.

The distribution of the modeled values of pore-water pressure (Table 6 and Figure 12) was similar to that observed in the field since March 2012, confirming the reliability of the model in representing the real soil hydrological conditions. Main significant differences between monitored and modeled distributions regarded the lowest value of pore-water pressure (−993 and −1483 kPa for monitored and modeled trends, respectively) and the first quartile (−846 and −484 for monitored and modeled trends, respectively), together with the degree of gaussianity, which was not shown in the distribution of the modeled values (skewness of −1.18; WS-W statistic of Shapiro–Wilk test of 0.71, *p*-value < 0.01; Table 6 and Figure 12). Instead, the third quartile of the distribution of the modeled pore-water pressure was equal to −22 kPa, which is very similar to that one of the monitored values (−20 kPa). These results confirm the reasonable choice of considering initial conditions of pore-water pressure higher than −20 kPa for the reconstruction of the physicallybased thresholds. The modeled value of pore-water pressure at the sliding surface depth at the beginning of a triggering event in the time span of the

validation phase was around 0 kPa every time, which is also in agreement with the initial conditions in correspondence of the monitored triggering event of 28 February–2 March 2014 at the test-site slope [24].

**Table 6.** Main statistics of the distribution of the pore-water pressure values at typical depth of shallow landslides sliding surface (1.0–1.2 m from the ground level), modeled for the period August 1992–August 1997 at the test-site slope: (Sd) standard deviation; (Min) minimum value; (Max) maximum value; (I quart) first quartile; (III quart) third quartile; (Skew) skewness; (WS-W) statistic of the Shapiro–Wilk test, applied to test the gaussianity of the distribution; (*p*-value) confidence level of the statistic of the Shapiro–Wilk test.


**Figure 12.** Histogram of distribution of the pore-water pressure values at typical depth of shallow-landslide sliding surface (1.0–1.2 m from the ground level) for the modeled time span (August 1992–August 1997) at the test-site slope.

Pore-water pressure at the beginning of each identified rainfall was linked to each reconstructed rainfall scenario. This was done to relate rainfall events with a certain initial pore-water pressure to the correct physicallybased threshold. For the validation of the empirical thresholds, all the rainfall events considered for the validation of each physicallybased threshold (TRIGRS/–20, TRIGRS/–10, and TRIGRS/0) were used, in order to make homogeneous the comparison between the validation phases of all the defined thresholds (Figure 13).

Table 7 Listingof the results of the validation phase. All the thresholds correctly identified the rainfall events able to trigger shallow landslides (true positives), as testified by TP values of 95 ± 2% and 100 ± 0% and by FN values of 5 ± 2% and 0 ± 0% for empirical and TRIGRS/0 thresholds, respectively.TP and FN indexes were not calculated for both TRIGRS/–10 and TRIGRS/–20, because no events triggered shallow landslides, starting from initial conditions of pore-water pressure equal to either −10 or −20 kPa. Instead, the reliability of these thresholds in identifying non-triggering rainfall events was assessed by means of TN and FP values. For events with initial pore-water pressure conditions of −20 or −10 kPa, the respective thresholds are characterized by TN of 100 ± 0% and by FP of 0 ± 0%, confirming the capability of these models in distinguishing events able to trigger or not trigger shallow landslides. Moreover,the TRIGRS/0 threshold assessed the conditions which could not trigger slope instabilities well, as testified by TN of 93 ± 1% and by FP of 7 ± 1%. Instead, the empirical threshold was characterized by a lower ability in distinguishing triggering or non-triggering events. Its TN was of 76 ± 3%, while its FP was of 24 ± 3%. In these terms, these thresholds overestimated the conditions able to trigger shallow landslides, classifying 24 ± 3% of real non-triggering events as able to cause shallow landsliding (false positives).

**Figure 13.** Duration(D) and Cumulated amount (E) conditions for the rainfall events recorded in the period August 1992–August 1997 and used for the validation phase, and the corresponding thresholds: (**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 7.** Mean ± standard deviation of the statistical indexes used in the validation phase of the reconstructed thresholds. (TP) true positives; (TN) true negatives; (FP) false positives; and (FN) false negatives.

