**7. Relevance to Landslide Hazard and Early Warning Studies**

The modified *AR-S* approach is relevant for the increased accuracy of the resulting *AR* thresholds, which is partly also on account of the regional-scale *S* data [49] and the enlarged landslide inventory. In particular, the conservative low-exceedance probability thresholds are most reliable, being least affected by a degraded distribution of data used for the threshold calibration (FNR ≈ TPE). Depending on the local susceptibility, thresholds at the 5% exceedance probability range from *AR* = 62 mm in the least susceptible areas to *AR* = 7 mm in the highest susceptibility pixels, respectively, for which landslide have been reported (Equation (10)). These triggering *AR* conditions might seem low at first sight when compared to values obtained in other studies that look into antecedent rainfall conditions based on gauge measurements, e.g., a required minimum of 139 mm cumulated over 20 days to trigger landslides in the NE Himalaya [68]; a mean triggering rainfall accumulation of 376 mm for periods ranging between 15 and 40 days in NW Spain [69]; a critical rainfall amount of 450 mm over a two-week period in the greater Durban region in South Africa [70]. However, the triggering values obtained in our study are conceivable given the following main factors contributing to their relative lower values: (1) the exponential decay function applied in our *AR* calculation (Equation (1)) in contrast to the values obtained in the above cited studies through mere accumulation; (2) the high weathering

conditions in the tropical context of the WEAR that may increase the sensitivity to landsliding [50]; and (3) the underestimation of the area-averaged SRE [33,56] used in the calculation of *AR* (Equation (1)). The latter is not necessarily an issue when thresholds are evaluated with the same SRE used for their calibration [32]. To date, SRE-based studies form only a small fraction in landslide threshold research [3,32]. A TMPA-RT-based threshold was established for Italy at the 20% exceedance probability, obtaining a critical rainfall accumulation of 189 mm for an extrapolated duration of 42 days [32]. However, the extrapolation is doubtful, given the limited threshold calibration range of ~11 days [32]. In addition, no decay function is applied to this extrapolated value for accumulated antecedent rainfall and the higher exceedance probability level obviously renders an elevated threshold compared to the 5% and 10% levels deployed in our study. On the other hand, the 5% thresholds calibrated for central Italy by [71] based on TMPA (Research Version) data, estimate critical accumulated rainfall in the order of 30 mm over an extrapolated duration of 42 days, which falls in our estimated triggering range at the 5% exceedance probability.

Furthermore, the modified *AR-S* threshold method is relevant in the context of landslide hazard analysis when rainfall data are only available for conditions that triggered landslides, for it proved to be a robust alternative for frequentist-based threshold approaches [9,40] when the method's assumptions (i.e., large and well-spread data set [40]) are not met. To the authors' knowledge, it is the first time that a stratified data selection technique is adopted in the threshold calibration approach, which effectively showed to enhance the data distribution over the whole range of the causative threshold variable (*S*). This allows the method to be transferable not only to other data sets for *S* (and hence other study areas), but to any parameter that might be considered as a possible cause for landsliding [34] without the requirement of the data to be homogeneously distributed, to which further research should be carried out. This is significant in the context of the 'trigger-cause' conceptual framework of threshold definition as proposed by [34], in response to the shortcomings of the rainfall-only thresholds with regard to their limited physical meaning [34]. The framework was designed to introduce hydrological information on different timescales, with the choice of the parameters and timescales depending on their expected significance for slope failure given the physiographic context and considered landslide types [34]. In the *AR-S* approach, the causative hydrological status of the slope is substituted by information on spatially varying predisposing ground conditions, while *AR* presents the progressive build-up of the landslide trigger [35]. We could anticipate, however, that improvements in satellite-based soil moisture data, with regard to their spatial resolution and performance over dense vegetated areas or complex topography [72–74], would allow in the future to replace the static *S* variable by a dynamic causative hydrological factor over data-scarce regions.

In addition, the enhanced relation between *AR* threshold values and *S* renders a potential landslide early warning system more efficient. In this respect, the integrated spatial component of the *AR-S* approach (Figure 8) has a clear advantage over traditional thresholds, such as rainfall intensity-duration thresholds, the latter only informing 'when' the probability of a landslide occurrence increases but not 'where' [65]. The spatial component furthermore avoids data to be partitioned according to homogeneous physiographic units to enhance the accuracy of thresholds [9,75], which is of particular relevance in data-scarce contexts. Finally, the method was designed to use area-averaged SRE, allowing its adoption in regions where a dense rain gauge network is absent and evaluate hazard in near-real time.

However, the efficient use of the *AR-S* approach in hazard or early warning studies is hampered by a number of factors that might contribute to an obscured relation between *AR* and *S*, including: (1) the level of accuracy and completeness of the landslide inventory [28,42]; (2) a lack of differentiation in landslide processes whose triggering conditions are different [63]; (3) the accuracy of *S* and SRE data [33,49]; (4) the resampling of *S* data to the coarser SRE data resulting in inaccurate *S*-classifications of landslide data; (5) the anthropogenic influence on the environment, such as in the context of exponential demographic pressure in the WEAR [76,77]; and (6) the empirically defined parameters in

the *AR* equation (Equation (1)) by [35]. The highlighted obstacles and limitations serve as pathways for further investigation and improvements in the *AR-S* threshold approach.
