**4. Discussion**

Rainfall thresholds can be considered a fundamental tool for assessing hazard toward slope instabilities and for defining reliable early warning system tools for their prediction [65].

One of the major challenges in establishing effective thresholds is obtaining a threshold able to correctly distinguish the triggering scenarios (true positives) from the events which cannot cause the development of slope failures (true negatives), also avoiding numerous erroneous alerts, corresponding to rainfall conditions that could not cause real instabilities (false positives).

Rainfall thresholds answering these issues are mostly reconstructed through an empirical/statistical approach, exploiting past inventories formed by the events able to or not able to trigger shallow landslides [4,5]. Uncertainties and limitations of these thresholds (i.e., availability and quality of rainfall data and landslides information, correct definition of the triggering times, and neglecting the antecedent soil hydrological conditions) induce researchers in order to verify the possibility of using physicallybased procedures that can provide the assessment of the link between rainfall features, soil

hydromechanical conditions before a rainfall event, and shear strength response of soils during the rainwater infiltration.

Mirus et al. [32] and Fusco et al. [30] aimed to perform a robust comparison between these two types of approach, in steep slopes covered by colluvial soils derived from glacial and till deposits in the coastal area of the Northwestern United States [32], and in steep slopes covered by thick pyroclastic deposits in Southern Italy [30], respectively. The present paper compares empirical and physicallybased rainfall thresholds estimated for a wide area of Northern Italy (Oltrepò Pavese), significantly prone to shallow landslides and representative of the typical geological, geomorphological, and environmental features of Apennine area [66].

Empirical thresholds of the study area were reconstructed by means of the typical exploitation of a long multi-temporal inventory (2000–2018) of rainfall events able to trigger or not shallow landslides. Instead, the second type of thresholds were estimated through a physicallybased slope model (TRIGRS), representative of the real geological and geomorphological conditions where shallow landslides develop in the study area, allowing to couple the monitoring of soil hydrological responses toward atmosphere-soil interface, the modeling of slope hydrological responses, and the slope stability analysis. In this way, the estimation of rainfall thresholds was performed by considering not only rainfall attributes, but also the typical antecedent soil hydrological conditions.

Monitoring data acquired during a significant time span, covering more than seven years (March 2012–October 2019) [24,45], and the modeled ones for a five-year period (August 1992–August 1997) demonstrate variations of soil pore-water pressure trends in deep soil horizons, where sliding surface could form. Monitoring and modeling data confirm that the soil pore-water pressure regime is linked to the seasonal and interannual meteorological variability, showing similar trends during warm/dry and cold/wet months across different years. Unsaturated conditions are typical of warm months in the year, especially between May and September. A certain increase of pore-water pressure till values close to 0 kPa was observed only after the most intense events, of at least 50 mm of rain fallen in at least 12 h. After re-wetting events in the first weeks of Autumn months (at least 30 mm of rain fallen in at least 24 h), the coldest time of the year, which lasts from October to April, is characterized by pore-water pressure closer to saturated conditions, generally in the order of −20 and −10 kPa. Development of nil or positive values in correspondence of other important rainfall events, corresponding to the formation of a perched water table, occurs when further strong rainfall events, of at least 20 mm/day, or prolonged rainy periods, affect the study slope.

Such a seasonal hydrological behavior explains why shallow-landslide-triggering events occurred mostly during cold months between October and April. Antecedent pore-water pressure close to 0 kPa in soil horizons where shallow landslides develop, combined with further heavy rainfall events or a prolonged rainy period (duration between 4 and 105 h, with cumulated amount between 30.4 and 133.7 mm), cause the typical scenario which induces widespread slope instabilities in the study area. This scenario also confirms the monitored conditions of triggering during 28 February–2 March 2014 event that is shown in Bordoni et al. [23].

Conversely, in warm months between May and September, only heavy–torrential (D1) or torrential (D2) rainfalls, according to Alpert et al.'s [64] classification (duration between 5 and 15 h and cumulated amounts between 106.8 and 155.2 mm), have the potential to trigger shallow failures, only when they are preceded by other rainfalls which cause the increase in pore-water pressure to go up to around −20 kPa.

Triggering conditions in cold months of the study area are similar to those identified in different contexts all over the world, which are characterized by a cold and wet season in a year like in the study area [32,67–71]. Instead, triggering events of warm months have features similar to those commonly occurring in the coastal zones of the Mediterranean region [16,28,30,51,63,72,73], when strong convective thunderstorms affect those areas especially at the end of summer (September) or in the first weeks of autumn (October–November).

The differences in triggering conditions and the significant effect of soil hydrological conditions at the beginning of a rainfall event influence the reconstructed thresholds for shallow landslides' occurrence. By comparing the different physicallybased thresholds, it is clear that the drier the soil is, the bigger the amount of rain required to trigger a landslide is, considering the same duration of the event. For a certain temporal length of the rainfall, the cumulated amount able to trigger shallow landslides for an initial pore-water pressure condition of −20 kPa is about 20–25 times higher than that required if the initial pore-water pressure is of 0 kPa. This amount decreases if the initial pore-water pressure is of −10 kPa, even if it is still 6–8 times higher than that obtained considering an initial pore-water pressure of 0 kPa. This estimation matches with the datasets of triggering events analyzed for the study area, where rainfalls able to trigger shallow landslides were more severe, in terms of cumulated amount (higher than 100 mm), when they occurred in periods with soil in unsaturated conditions. Instead, the amount of rain able to trigger shallow landslides decreased significantly, till more than 3 times, when the soil was saturated.

The empirical threshold is very close to the physicallybased one estimated based on an initial pore-water pressure condition of 0 kPa. For the same duration, the amount of triggering cumulated rainfall for an initial pore-water pressure of 0 kPa is 5.3–10.5 mm higher than that estimated by the empirical threshold. This is in agreement with comparisons between physicallybased and empirical thresholds performed in other areas prone to shallow landsliding worldwide [28,30,32].

In the dataset used to validate the reconstructed thresholds, triggering events occurred only in conditions of pore-water pressure equal to 0 kPa. Both empirical threshold and TRIGRS/0 threshold correctly identified rainfall events able to trigger shallow landslides (TP higher than 95%, FN lower than 5%), although only the TRIGRS/0 threshold recognized all the triggering events. However, the empirical threshold significantly overestimated the rainfall conditions able to trigger shallow landslides, as testified by FP = 24±3%. Instead, TRIGRS/0 threshold worked well for assessing the conditions which could not trigger slope instabilities, strongly limiting the false positives (FP = 7±1%).

These results confirm the fundamental role played by the soil hydrological conditions present at the beginning of a rainfall event on the development of shallow slope failures. All the false positives identified by the empirical threshold correspond to rainfall event occurred when the soil was not completely saturated, especially (90%) when pore-water pressure was lower than −10 kPa (Figure 14). These results are confirmed also by an event that occurred on 21 October 2019, when a strong thunderstorm hit the northern portion of the study area, in particular close to rain gauges 3 and 6 (Figure 1). In total, 118 mm of rain fell in 24 h, with a peak of 97 mm of cumulated rain in 6 h, between 5:00 p.m. and 11:00 p.m. local time. These rainfall conditions are located above the empirical thresholds, but they did not cause any triggering of shallow failures due to pore-water pressure conditions, at the beginning of the rainfall, of −800 kPa, as measured by the monitoring station in the study area.

**Figure 14.** Modeled values of initial pore-water pressure conditions in correspondence of the false positives of empirical thresholds for the validation dataset.

Empirical threshold causes an overestimation of triggering events, determining false positives in correspondence of rainfall conditions similar to the ones that provoked observed shallow failures, but with an initial soil condition drier than that corresponding to the real triggering events. Thus, physicallybased thresholds which also take into account the antecedent soil conditions in terms of pore-water pressure can represent an improvement, both in terms of objectively predicting shallow-landslide occurrence and also limiting false positives.

Reconstructed rainfall thresholds for the Oltrepò Pavese area were then compared with other duration(D) and cumulated amount (E) thresholds of other Italian areas (Figure 15). Regional and national thresholds in Italy [8,74–76] were derived by using an empirical approach similar to that adopted for the empirical thresholds of the Oltrepò Pavese area. Thresholds for Oltrepò Pavese were also compared to a world threshold defined by Innes [77] for the occurrence of debris flows.

**Figure 15.** Comparison between the reconstructed thresholds for Oltrepò Pavese area, with some regional, national, and world thresholds. Source: (1) empirical threshold (mean fitting parameters) of Oltrepò Pavese area; (2) physicallybased threshold for initial pore-water pressure of −20 kPa (mean fitting parameters) of Oltrepò Pavese area (TRIGRS/–20); (3) physicallybased threshold for initial pore-water pressure of −10 kPa (mean fitting parameters) of Oltrepò Pavese area (TRIGRS/–10); (4) physicallybased threshold for initial pore-water pressure of 0 kPa (mean fitting parameters) of Oltrepò Pavese area (TRIGRS/0); (5) world [77]; (6) Italy [74]; (7) Liguria [8]; Sicily [75]; and (9) Italian Alps [76].

Physicallybased thresholds obtained on the basis of antecedent pore-water pressure equal to −20 kPa (TRIGRS/–20) or −10 kPa (TRIGRS/–10) are located above all the other thresholds, in agreement with the need of a higher amount of rain to trigger shallow landslides in unsaturated soil conditions. TRIGRS/0 threshold and the empirical thresholds are located close to each other, with the former slightly above the empirical curves. Physicallybased thresholds reconstructed for completely saturated soils (TRIGRS/0) intercept all other considered thresholds (at world, Italian, and regional scale) for an event duration of 40 h,whereas the empirical thresholds intercept world and some regional (Sicily, Italian Alps) thresholds at the same duration. Moreover, both these thresholds show a lower steepness, which implies that the rainfall amount required to trigger shallow landslides for event with duration less than 40 h is higher than the one of the compared world, Italian, and regional thresholds. Instead, for event longer than 40 h, TRIGRS/0 thresholds and the empirical thresholds are below the other thresholds. For these rainfall features, the cumulated amount able to trigger shallow failures is lower if compared to the other analyzed thresholds. The Oltrepò Pavese area is, then, more susceptible to shallow landsliding for long-duration [64] events. For short and medium events [64], the amount of rainfall able to trigger shallow landslides is higher, thus reducing the proneness of the territory in correspondence of such events.

According to the achieved results of this paper, the main relevance of this work and of the reconstructed thresholds are as follows: (i) empirically and physicallybased thresholds for a representative area of the Italian Apennines; (ii) different physicallybased thresholds according to different soil hydrological conditions and considering rainfall scenarios already measured in the study area; (iii) implementation of a physicallybased slope model allowing to couple the monitoring of soil hydrological responses toward atmosphere-soil interface, the modeling of slope hydrological responses, and the slope stability analysis; (iv) robust evaluation of the threshold's predictive capability through a different dataset with respect to that used in the reconstruction of the models; and (vi) determination of advantages and constraints in the use of empirically or physicallybased thresholds.
