*2.2. Reconstruction of the Empirical Thresholds*

Empirical rainfall thresholds were reconstructed by implementing CTRL-T tool, written in R open-source software and freely available at: http://geomorphology.irpi.cnr.it/tools/rainfall-eventsand-landslides-threshold. A detailed description of the algorithm is reported by Melillo et al. [8].

Figure 3 illustrates the logical framework of this method to assess the empirical rainfall threshold for a set of rain gauges and a multi-temporal shallow landslide inventory.


This radius was chosen according to the morphology of the study area (no significant variations on slope height, which could influence rainfall amount) and to the density of rain gauges in the study area (an average of one gauge per 13 km2).

3. Estimation of rainfall conditions leading to shallow landslide triggering. For each event in the inventory, the algorithm estimates possible rainfall conditions (in terms of duration and cumulated rainfall amount) leading to slope failure. This allows us to consider a possible inaccuracy in the estimation of the rain features triggering a landslide due to the distance between the slope failure and the related rain gauge. A weight, W, was assigned according to the inverse square distance between the rain gauge and the landslide (d<sup>−</sup>2), the cumulated rainfall amount (E), and the rainfall mean intensity (I) (Equation (1)):

$$\mathsf{W} = \mathsf{d}^{-2}\mathsf{E}^{2}\mathsf{I}^{-1} \tag{1}$$

Furthermore, a parameter, k, assumed equal to 0.84, allowed us to take into account the antecedent soil moisture condition depending on the amount of rain fallen in the previous days.

4. Reconstruction of rainfall threshold, based only on events triggering shallow landslides. Moreover, for each event, only the rainfall condition with the highest W value was selected. The threshold is defined as a power law curve which relates the cumulated rainfall amount (E) and the duration (D) of the events (Equation (2)):

$$\mathbf{E} = (\alpha \pm \Delta \alpha) \,\mathrm{D}^{(\omega \pm \Delta \omega)} \tag{2}$$

where α is the intercept of the curve;ω is the slope of the power law curve; and Δα and Δω are the uncertainties of α and ω, respectively.

The threshold was defined by means of a frequentist method for reconstructing a 5% exceedance probability threshold, according to Brunetti et al. [13]. The fitting parameters of the curve and the related uncertainties were estimated through the calculation of thresholds of 5000 synthetic series of rainfall events. These series contained the same number of rainfall events that triggered landslides, but selected randomly with replacement, according to a bootstrap technique [45]. Analysis of these series allowed us to estimate the final threshold, that had α and ω corresponding to the mean values of the different bootstrap thresholds with their respective uncertainties (Δα and Δω).

**Figure 3.** Flowchart of the methodology adopted for the reconstruction of the empirical thresholds.

**Figure 4.** (**a**) Average monthly potential and real evapotranspiration in the study area; (**b**) warm and cold periods identified through the trend of the aridity index.

**Table 1.** Parameters used in CTRL-T tool for reconstructing rainfall events and defining the empirical threshold. (CW) warm period in a year (May–September); (CC) cold period in a year (October–April); (Gs) resolution of the rain gauge; (P1, P2, and P4) time periods used to remove irrelevant amount of rain and to reconstruct rainfall events; (P3) irrelevant rainfall sub-events that had to be excluded in the calculation of the final events; (Rad) radius of the buffer to assign each landslide to the closest rain gauge.


The empirical threshold for the study area was assessed through this procedure, using hourly rainfall measurements collected in the period from January 2000 to December 2018, by a network of 19 rain gauges (blue circles in Figure 1), with a resolution (Gs) of 0.1 mm. Shallow landslides inventory of the same time span grouped the spatial and the temporal information of 143 triggering events. The spatial resolution of these events was about 1 km2. For 44% of the events, the exact triggering hour was known, while for the remaining 56%, only the part of the day (generally, each 6 h in a day), when slope failure occurred, was identified. Among the landslide inventories, 30 events (11% of the inventory) were located by using information related to field surveys, 155 events (55% of the inventory)by means of aerial or satellite images [1,24], and 96 events (34% of the inventory) from newspapers and online chronicles.
