Cost-sensitive rainfall thresholds for shallow landslides

The risk management of rainfall-induced landslides requires reliable rainfall thresholds to issue early warning alerts. The practical application of these thresholds often leads to misclassifications, either false negative or false positive, which induce costs for the society. Since missed-alarm (false negative) and false-alarm (false positive) cost may be significantly different, it is necessary to find an optimal threshold that accounts for and minimises such costs, tuning the false-alarm and missed-alarm rates. In this paper, we propose a new methodology to develop cost-sensitive rainfall thresholds, and we also analyse several factors that produce uncertainty, such as the accuracy of rainfall intensity values at landslide location, the time of occurrence, the minimum rainfall amount to define the non-triggering event, and the variability of cost scenarios. Starting from a detailed mapping of landslides that occurred during five large-scale rainfall events in the Italian Central Alps, we first developed rainfall threshold curves with a ROC-based approach by using both rain gauge and bias-adjusted weather radar data. Then, based on a reference cost scenario in which we quantified several cost items for both missed alarms and false alarms, we developed cost-sensitive rainfall threshold curves by using cost-curve approach (Drummond and Holte 2000). Finally, we studied the sensitivity of cost items. The study confirms how important is the information regarding rainfall intensity at the landslide site for the development of rainfall thresholds. Although the use of bias-corrected radar strongly improves these values, a large uncertainty related to the exact time of landslide occurrence still remains, negatively affecting the analysis. Accounting for the different missed-alarm and false-alarm misclassification costs is important because different combinations of these costs make an increase or decrease of the rainfall thresholds convenient. In our reference cost scenario, the most convenient threshold is lower than ROC-based thresholds because it seeks to minimise the number of missed alarms, whereas the missed-alarm costs are almost seven times greater than false-alarm costs. However, for different cost scenarios, threshold may vary significantly, as much as half an order of magnitude.