*6.1. First Test: Sensitivity to New Data on Landslide Occurrence*

The modified *AR-S* method with no bootstrap is tested firstly by using the recent addition to the WEAR data set of dated landslide events. Taking into account their date uncertainty, the 39 landslide events constituting this validation set yield 117 new weighted event dates, of which four are discarded from the analysis because they do not meet the *AR* ≥ 5 mm requirement. The 113 remaining data instances (constituting *Q*, Figure 4) are distributed in the log(*AR*)–log(*S*) space in such a manner that 6% of them are located below the 5% threshold line derived from the calibration (Equation (8)) and 8% below the 10% threshold line (Equation (9)), indicating a good performance of the calculated thresholds (Figure S2) considering the small sample size.

Another test using the validation set, which in the same time should improve the accuracy of the calibrated thresholds, has consisted in combining the data of the calibration and validation sets into a larger data set of 540 event dates in order to recalculate the thresholds. The new thresholds read as

$$AR\left(5\%\right) = 4.5 \times S^{-1.14} \text{ (}R^2 = 0.66\text{)}\tag{10}$$

$$AR\left(10\%\right) = 6.1 \times S^{-1.08}\ \left(R^2 = 0.59\right) \tag{11}$$

and do not much differ from those derived from the calibration set only (Equations (8) and (9)) (Figure 6b), confirming the relevance of the modified *AR*-*S* method. Though slightly decreased by additional noise brought in the middle- to low-*S* classes by the new data (Figure S2), their coefficients of determination remain highly significant. Likewise, their FNRs (0.04 and 0.06 for the 5% and 10% thresholds, respectively) are slightly degraded mainly as a result of an increased deficit in data in these *S* classes. Owing to the larger size of the data set, we nevertheless consider these thresholds (Equations (10) and (11)) more reliable than those based only on the calibration set, especially the 5% threshold, for which FNR ≈ TPE.
