*6.2. Second Test: Robustness to Di*ff*erent S Data Sets*

We test the modified *AR-S* approach for the adoption of a different data set for *S*, using the continental-scale *S* data [45] and the complete (calibration+validation) data set of landslide events, obtaining the following *AR* thresholds (Figure 7)

$$AR\ (5\%) = 5.7 \times S^{-2.10}\ \left(\mathbb{R}^2 = 0.73\right) \tag{12}$$

$$AR\left(10\%\right) = 7.6 \times \text{S}^{-2.08} \text{ (R}^2 = 0.61\text{)}\tag{13}$$

with significant and meaningful values for R2 and threshold parameters α, and β. Moreover, these thresholds show a stronger relation between threshold *AR* values and *S* with increased values for parameters (α*,*) β and *R*2, explained by the increased dispersion of the data over the *S* range (Figure 7) relative to when the regional-scale *S* data was applied (Figure 6b). Where the *AR-S* approach developed by [35] posed problems for adopting a different *S* model than that used for its development (Figure 3), these results show that the modified *AR-S* approach proved to solve this matter. The threshold at the higher exceedance probability remains affected by a bias similar to that in Equation (11) with the actual FNR lower than the TPE (FNRs equal 0.05 and 0.07 for the 5% and 10% thresholds, respectively).

**Figure 7.** Log–log plot of antecedent rain (mm) vs. landslide susceptibility (continental-scale [45]) for the landslide events on the reported day and the days prior and after that date (with the point size relative to their attributed weights, i.e., 0.67 and 0.17 respectively). The green and red curves are the *AR* thresholds at 5% and 10% exceedance probability levels respectively, obtained with the modified *AR-S* method (Figure 4) without the bootstrapping statistical technique. Ndata is the number of data in the expanded (calibration+validation) data set. The dashed lines delimit the log(*S*) classes.

Another indicator for the robustness of the modified *AR-S* method is the generally satisfying correspondence between *AR* threshold results for the continental- and regional-scale *S* models (Table 2). The single main discrepancy is observed for the 10% threshold in the low *S* data range, related to the actual FNRs of these thresholds being significantly smaller than their TPE. The latter is explained by the sensitivity of the threshold slope to the deficient number and exact location of data in the low-*S* classes, causing the largest threshold difference to appear for the 10% threshold (implying a greater lack of data in low-*S* classes) at the low end of the *S* range. By contrast, the intercept of the threshold equations, being located in the *AR-S* space with the highest density of data, remains quasi stable for different *S* models (Figure 6b, Figure 7).

**Table 2.** *AR* threshold values (in mm) calculated using continental- (Equations (12) and (13)) vs. regional-scale (Equations (10) and (11)) *S* data, provided at 5% and 10% exceedance probability for the extreme susceptibility values *S* observed in the data sets. The estimations are based on the complete calibration+validation data set of landslide events.


Because of the enhanced relation between threshold *AR* values and *S* in Equations (12) and (13), it is tempting to suggest that thresholds based on the continental-scale *S* data would be more efficient when adopted in a landslide early warning system. However, the spatial pattern of the *AR* thresholds based on the regional-scale *S* data are closer to the reality, given that this regional-scale *S* model has a higher predictive power and geomorphological plausibility as compared to the continental-scale model [49]. The respective *AR* threshold maps are presented at the 5% probability of exceedance level in Figure 8. In general, we observe lower *AR* thresholds within the Rift. Nevertheless, there are some major differences between the two threshold maps, caused by differences in the quality of the susceptibility models. First, the threshold model using the continental susceptibility map of [45] assigns low *AR* thresholds to the rainforest in DR Congo south of the equator, despite the fact that the area is characterized by high amounts of rain and few landslides [29,35]. Second, the regional susceptibility data of [49] overall shows a much lower threshold in Uganda. In conclusion, we confirm the earlier observation that the *AR* thresholds based on the regional-scale *S* data and the currently most extensive landslide event inventory are to date the most accurate available thresholds for landsliding in the WEAR (Equations (10) and (11)).

**Figure 8.** Antecedent rainfall (*AR*) threshold maps (0.25◦ resolution) at 5% exceedance probability, based on the complete (calibration+validation) landslide inventory, and the (**a**) continental-scale *S* model [45] (Figure 7, Equation (12)) and (**b**) regional-scale *S* model [49] (Figure 6b, Equation (10)). *AR* threshold values are only shown for the *S* range covered by the 184 landslide events used for the threshold estimations (i.e., (**a**): *S* 0.31–0.97; (**b**): *S* 0.10–0.72). 1: Lake Albert; 2: Lake Edward; 3: Lake Kivu; 4: Lake Tanganyika. Background hillshade 3 arc-second SRTM (±90 m).
