An analysis of robustness, sampling variation and performances of landslide triggering thresholds determined by different approaches

Rainfall intensity-duration landslide-triggering thresholds have been proposed as a possible component for the implementation of territorial landslide early warning systems. Given a set of rainfall and landslide data, three approaches can be distinguished to determine thresholds: (i) methods based on triggering events only, (ii) methods based on the non-triggering events only, and (iii) methods based on both type of rainfall events. The aim of the present research is to compare these three possible approaches based on statistical criteria: robustness, sampling variation, and performance. This comparison can provide an insight on which of the three approaches is more appropriate based on the dataset that happens to be available for the area of interest.

We address these aspects by setting up a virtual simulation framework combining a stochastic rainfall model with a hydrological and slope stability model, which allows to make repeated experiments and to simulate different uncertainty conditions.

Our analysis shows that methods based on triggering rainfall only can be the worst with respect to the three investigated statistical properties. Methods based on both triggering and non-triggering rainfall have the highest performances in terms of the ROC true skill statistic; they are also robust, but still require a quite large sample to sufficiently limit the sampling variation of the threshold parameters. On the other side, methods based on non-triggering rainfall only, which are mostly overlooked up, are characterized by good robustness and low sampling variation. It can also be shown that in realistic scenarios their performances can be acceptable and even higher than thresholds derived from triggering events only. Indeed, the use of triggering rainfall only, a common practice in the past literature, yields to thresholds with the worse statistical properties, except when there is a clear separation between triggering and non-triggering events.

Based on these results, it can be stated that methods based on non-triggering rainfall only deserve wider attention, as they have also the practical advantage that can be in principle used where limited information on landslide occurrence is available. The fact that relatively large samples (about 200 landslides events) are needed for a sufficiently precise estimation of threshold parameters when using triggering rainfall, provides a possible insight on the level of uncertainty of thresholds proposed in the past literature.