## 3 Materials and Methods
### A Methodology for the Assessment of Warning Thresholds  
After the setup of the GNSS, we also improved a methodology for effective use of GNSS measurements. The developed system divided in a sequence of steps that starts from the acquisition and processing of data and ends with a dedicated dissemination procedure of obtained results. The flowchart of Figure 7 shows the proposed procedure that, in this case, it is focused on GNSS data, but it could be applied to a generic landslide monitoring system. The main steps of the monitoring management procedure are:  
(i) The statistical control of raw data. We used an algorithm that detects signal-noise ratio, called a Ratio test (R), developed by [32]. Only raw data with a minimum acceptable quality (empirically fixed at R \(\geq\) 4) pass to the further phase of processing. If the raw data have an R \(<\) 4 (low quality), no further elaborations are possible and the procedure starts again with new data. (ii) The thresholds assessment. In this step, an automatic algorithm checks if the movement overpasses the statistical and the geological thresholds. The statistical threshold (ST) is related to the accuracy of the instrument: in our case, it is twice the standard deviation (2\(\sigma\)) around the value foreseen by the regression line. The geological threshold (GT) is based on the geological model, and it is related to the movement rate that, according to expert studies, could indicate an incipient paroxysmal phase. It is important to remark that the GT must be higher, or at least equal, than the ST. If the model shows that the GT is below instrument accuracy, probably our monitoring system is not adequate for the considered slope instability. In the case of Madonna del Sasso, the GT for short-term displacement was not yet determined, but we can consider that it can be very close to the ST. According to long-term monitoring results, the long-term threshold was empirically fixed at 3 mm/100 days (or 11 mm per year). This threshold has been defined considering the analysis of long (2006-2019) topographic monitoring sequence. On short period, measurements that overcome the ST have to be carefully considered to check if this result can be considered a spike or the beginning of a critical phase. To solve this problem, the system required a double validation before declare and alarm: (i) firstly, the monitoring result must be statistically validated (R \(>\) 4); (ii) then, it should be analyzed and also validated from the geological point of view. If the displacement is statically validated, an automatic warning report is daily generated: the procedure considers, as usual, three levels of warning:1. Greenlight that means regular conditions (i.e., the ST and GT are not overpassed (Figure 8 and Table 3);
2. Yellow light (warning level), if the GT has been overcome for one day (\(\geq\)24 h). In this phase, we can also consider the possibility that it could be an error in the system and, for this reason, we have to wait for the second cycle of measurement to obtain a validation of the trend,
3. Red light (alarm level) if the GT has been overcome for consecutive two days (\(\geq\)48 h). In this condition, monitoring results should also be evaluated and validated from the geological point of view. This procedure has been implemented to be totally automatized and requires the human check only at the end of a quality control procedure, for the last validation of the alert. Figure 7: Flowchart of the proposed procedure to define and test the alert threshold based on continuous and low-cost GNSS monitoring. The chart is focused on daily processing, but the same schema could be applied to long-term thresholds. (iii) The validation of the alert. This is a human-based procedure in which experts, on the base of automatic alert messages that coming from the monitoring systems, decide the congruency of the alert messages and they activate alert communication procedure to the authorities and the public.