*2.4. Corroboration of the Reconstructed Threshold*

A comparison between empirical and physicallybased thresholds estimated for Oltrepò Pavese area was performed in order to evaluate the predictive capability of both these models, as well as their advantages and limitations. Their validation was carried out through a dataset of events that took place during the period of August 1992–August 1997. For this time span, rainfall data were collected in correspondence of 3 rain gauges (black circles in Figure 1), while location and triggering moment of shallow landslides were recorded from local newspapers and information of fire brigades.

CTRL-T tool was used to reconstruct the different rainfall events also for this dataset, using the same required input parameters listed in Table 1. For the empirical thresholds, the final position on the graph below or above the defined thresholds was evaluated. In regard to the physicallybased thresholds, similarly to what done for their definition, the identified rainfall conditions were used as input data to apply the TRIGRS model and to assess slope Fs at the representative testsite. Thus, each event was estimated as responsible to trigger or not to trigger shallow landslides based on the assessed values of Fs in correspondence of the sectors typically affected by shallow landslides. Then, the position on the graph below or above the defined physicallybased thresholds was evaluated.

In the case of the estimated physicallybased thresholds validation, it is required to assess the pore-water pressure condition at the same depth of the observed sliding surfaces (1.0 m). For these reasons, time series of pore-water pressures at 1.0 m were modeled through HYDRUS-1D [60] software, considering the same physical and hydrological boundary conditions used for TRIGRS implementation. This model was chosen because it can assess long time series of soil hydrological parameters influenced by intermittent dry and rainy periods in a reliable way [60]. HYDRUS-1D was implemented for each of the 3 meteorological stations included in the validation dataset. Soil hydrological properties (Table 2) and boundary conditions corresponded to those used for the application of the TRIGRS model. Meteorological conditions required by the model were the rainfall amounts and air temperatures that were used to model the evapotranspiration effects through Hargreaves et al.'s [61] equation. Modeled time spans started from a significant dry period of a year, corresponding to 1 August 1992. In Oltrepò Pavese, early August is characterized every year by dry conditions of soils, which keep steady along depth, due to low rainfalls and high evapotranspiration rates in the previous summer months (June–July). In particular, a pore-water pressure equal to −993 kPa was assumed, according to the field measurements reported in Bordoni et al. [24,47]. This modeling approach was already implemented for the estimation of time series of soil hydrological parameters in other Italian regions prone to shallow landslides [53,62], obtaining a good estimation of the initial pore-water pressure conditions of a triggering event.

Statistical indexes were then calculated to evaluate the predictive capabilities of both types of thresholds for the validation dataset. Considering a rainfall threshold as a binary classifier of rainfall conditions leading to shallow landslides, its performance can be assessed by computing a 2 × 2 a posteriori contingency table [15]. Thus, each rainfall event can correspond to occurrence (true) or nonoccurrence (false) of shallow landslides, while the model can be considered as positive (successful prediction) or negative (wrong prediction). Accordingly, the following indexes can be classified [17,63]: true positives (TP), i.e., rainfall conditions exceeding the threshold causing shallow landslides; false positives (FP), i.e., rainfall conditions exceeding the threshold but without real triggering of shallow landslides; true negatives (TN), i.e., rainfall conditions below the threshold and without shallow landslides occurrence; false negatives (FN), i.e., rainfall conditions below the threshold but causing shallow landslides.
