Rainfall-Induced Landslide Assessment under Different Precipitation Thresholds Using Remote Sensing Data: A Central Andes Case

: The determination of susceptibility to rainfall-induced landslides is crucial in developing a robust Landslide Early Warning System (LEWS). With the potential uncertainty of susceptibility changes in mountain environments due to different precipitation thresholds related to climate change, it becomes important to evaluate these changes. In this study, we employed a machine learning approach (logistic models) to assess susceptibility changes to landslides in the Central Andes. We integrated geomorphological features such as slope and slope curvature, and precipitation data on different days before the landslide. We then split the data into a calibration and validation database in a 50/50% ratio, respectively. The results showed an area under the curve (AUC) performance of over 0.790, indicating the model’s capacity to represent prone-landslide changes based on geo-morphological and precipitation antecedents. We further evaluated susceptibility changes using different precipitation scenarios by integrating Intensity/Duration/Frequency (IDF) products based on CHIRPS data. We concluded that this methodology could be implemented as a Rainfall-Induced Landslides Early Warning System (RILEWS) to forecast RIL occurrence zones and constrain precipitation thresholds. Our study estimates that half of the basin area in the study zone showed a 59% landslide probability for a return of two years at four hours. Given the extent and high population in the area, authorities must increase monitoring over unstable slopes or generate landslide early warning at an operational scale to improve risk management. We encourage decision-makers to focus on better understanding and analysing short-duration extreme events, and future urbanization and public infrastructure designs must consider RIL impact.


Introduction
The Central Andes (32-34 • S) experienced an intense activity of rainfall-induced landslides (RILs) associated with extreme hydrometeorological events [1][2][3].In South America, RILs commonly affect communities socially and economically, limiting the development of populations in the mountain environment [4].Stand-out variations in the frequency of RILs in the Andes have not been documented in detail, limiting the preparation plans of the competent authorities.Therefore, changes in RIL frequencies could negatively impact the Andes in future, increasing damage to the infrastructure.This work will analyse the variation in susceptibility to RILs in the Maipo River basin (as a representative case Water 2023, 15, 2514 2 of 17 study for Central Andes) using a Bayesian approach that integrates geomorphological and precipitation constraints.
Worldwide, changes in susceptibility to RIL have been documented in the literature [5,6].An accurate assessment of these changes necessitates the consideration of extreme precipitation events frequencies [7,8].Such events significantly impact slope stability and the likelihood of landslides, leading to a diminished quality of life for affected populations.Evaluating this issue requires utilizing historical global precipitation data and considering temporal and spatial coverage [9,10].Additionally, low-income countries face inherent limitations regarding instrumentation for RIL's comprehensive monitoring and early warning systems [11].The scarcity of precipitation data exacerbates the challenge of developing precise RIL susceptibility models.However, recent advancements in remote-sensing technology have enabled the estimation of global precipitation with reduced uncertainty [12,13].Hence, implementing integrated approaches incorporating local data, remote sensing and a susceptibility approach becomes imperative to obtain a more precise and comprehensive assessment of changes in RIL susceptibility on a global scale.
Strategies have been generated in recent decades to define susceptibility to RIL using different approaches worldwide [14][15][16][17][18]. Mainly, susceptibility landslide models underestimate the geomorphological conditions, prioritizing the regional and local precipitation thresholds [11] and limiting their application in public policies [19].Generally, methodological approaches are based on qualitative methods, semi-quantitative methods [20], statistical methods [18,21,22] and automatic-learning methods [21,23].An accurate estimation of RIL susceptibility becomes essential to understanding and assessing the risks associated.A deep understanding of the prone landslide under different precipitation thresholds allows for generating better operational procedures for decision-makers [24].A proper RIL susceptibility analysis provides robust information for the planning and implementation of mitigation and prevention measures, contributing to the protection of human life, infrastructure and the environment.These approaches are oriented toward understanding how slopes respond to RILs, enabling the creation of efficient early warning systems for RILEWS (Rainfall-Induced Landslide Early Warning Systems).At a regional scale, South America has shown an increase of human losses due to extreme precipitation events [25].The human casualties reach critical levels due to the lack of early warning systems.The countries with the most significant RIL-related loss of life in South America are Colombia and Perú [26][27][28][29].However, Ecuador and Chile have seen an increase in the rate of occurrence and damage caused to the population [30].RIL events in the Central Andes stand out, increasing their frequency in the province of Mendoza, Argentina [2,4,31].In Refs.[2,[32][33][34], the Central Andes stand out, a place with strong structural and lithological control [32,33,35].The Central Andes region, spanning from 28 • to 36 • S, exhibits a consistent lithological and structural pattern along its north-south distribution.Stand-out lithological variability with an east-west trend is primarily influenced by tectonic structures such as folds and faults [32,33].These structures allow the identification of deformation and collision processes influenced by regional orogenesis over time.These distinctive features will enable the selection of representative areas, which can provide substantial information for surface process studies and facilitate the establishment of generalizations based on these representative areas.
The article evaluates the spatial and temporal variability in RIL susceptibility in the Maipo River basin, a heavily populated Andean basin in the Central Andes.Analysing the likelihood of RIL events occurring under different precipitation thresholds makes it possible to determine RIL susceptibility.The study used probability functions (Probit/Logit models) based on a machine-learning approach (logistic models), using remote sensing, geomorphological and hydrometeorological data.This methodology can be integrated as RILEWS to assess the river basin's threat level and how this can be affected in the short and medium term by hydrometeorological events.The rest of the article is organised as follows: Section 2 presents the study zone's characteristics and its most characteristic features.Section 3 explains the methodology (for example, the Probit and Logit functions), databases and approaches used to evaluate the variation in RIL susceptibility.Section 4 provides the results obtained in the modelling and the spatial relationship present for the values obtained.Section 5 discusses the models' performance and the feasibility of being integrated into a future LEWS.Finally, in Section 5, there is a conclusion.

Study Zone
The Maipo basin is located in the Central Andes (33 • S/70 • W) (Figure 1).The zone has high summits and extensive valleys resulting from the action of different climate controls, particularly glacial and erosional processes related to the Andes Mountains rivers [36,37].The zone presents uneven terrain, which exposes geological processes like kilometres-long deformations and faulting, volcanism, zones with hydrothermal alteration and geothermal centres.These properties generate RIL in the area due to modifying the terrain features, emphasizing topographic changes and soils with clay due to hydrothermal alteration [38].From the above, the site is highly susceptible to RIL, but without knowing its impact beyond a qualitative analysis.
relationship present for the values obtained.Section 5 discusses the models' performance and the feasibility of being integrated into a future LEWS.Finally, in Section 5, there is a conclusion.

Study Zone
The Maipo basin is located in the Central Andes (33 °S/70 °W) (Figure 1).The zone has high summits and extensive valleys resulting from the action of different climate controls, particularly glacial and erosional processes related to the Andes Mountains rivers [36,37].The zone presents uneven terrain, which exposes geological processes like kilometres-long deformations and faulting, volcanism, zones with hydrothermal alteration and geothermal centres.These properties generate RIL in the area due to modifying the terrain features, emphasizing topographic changes and soils with clay due to hydrothermal alteration [38].From the above, the site is highly susceptible to RIL, but without knowing its impact beyond a qualitative analysis.
Lithologies of the area could be separated into two rock sets.The eastern boundary of the Maipo River basin exhibits sedimentary, volcanic and highly deformed volcanosedimentary units from the Mesozoic Era [34].In contrast, over the central and western areas of the basin, volcanic and volcano-sedimentary units from the Cenozoic Era emerge with less deformation.This group also includes the current volcanic and sedimentary products.The emplacement of the different bodies was controlled by the inversion of normal faults and by the Aconcagua fold and thrust belt, which affected both basement blocks and sedimentary cover [35] (Figure 1).Lithologies of the area could be separated into two rock sets.The eastern boundary of the Maipo River basin exhibits sedimentary, volcanic and highly deformed volcanosedimentary units from the Mesozoic Era [34].In contrast, over the central and western areas of the basin, volcanic and volcano-sedimentary units from the Cenozoic Era emerge with less deformation.This group also includes the current volcanic and sedimentary products.The emplacement of the different bodies was controlled by the inversion of normal faults and by the Aconcagua fold and thrust belt, which affected both basement blocks and sedimentary cover [35] (Figure 1).The area's climate is warm and temperate, showing rainier winters than summers, classified as Csb (Mediterranean) according to the Köppen-Geiger system.The precipitation stations installed in the Maipo basin show annual values of 1177 mm [39].Moreover, the driest months run between November to March, with an average value of 29 mm.The highest precipitation occurs between April and September, with monthly precipitation averaging nearly 100 mm [39].The precipitation patterns of the last few decades have gradually decreased with extreme precipitation events.Hydrometeorological events with precipitation peaks exceeding 160 mm have increased, generating RILs and floods in the Maipo River [19,40,41].However, in the last 60 years, the zone has experienced devastating landslides, which have had a significant economic and social impact on Chile as a nation [19,27,42].Some registered events correspond to the 2013, 2016 and 2021 RILs [3,19,42].The fast vertical changes of the 0 isotherms generate liquid precipitation over snow-covered soil, triggering landslides, mudflow and debris flow in the area [19,42].These events are relevant due to their proximity to densely populated communities.A good example corresponds to the extreme precipitation events of the year 2013, where intense precipitation generated favourable conditions to saturate the soil and lose slope stability (Figure 2).The results of this event were numerous landslides and debris flows, generating damages in public infrastructure.These cases, without notice, increase the infrastructure damage and economic losses, reducing the inhabitants' quality of life.
The area's climate is warm and temperate, showing rainier winters than summ classified as Csb (Mediterranean) according to the Köppen-Geiger system.precipitation stations installed in the Maipo basin show annual values of 1177 mm [ Moreover, the driest months run between November to March, with an average valu 29 mm.The highest precipitation occurs between April and September, with mon precipitation averaging nearly 100 mm [39].The precipitation patterns of the last decades have gradually decreased with extreme precipitation eve Hydrometeorological events with precipitation peaks exceeding 160 mm have increa generating RILs and floods in the Maipo River [19,40,41].However, in the last 60 years, zone has experienced devastating landslides, which have had a significant economic social impact on Chile as a nation [19,27,42].Some registered events correspond to 2013, 2016 and 2021 RILs [3,19,42].The fast vertical changes of the 0 isotherms gene liquid precipitation over snow-covered soil, triggering landslides, mudflow and de flow in the area [19,42].These events are relevant due to their proximity to den populated communities.A good example corresponds to the extreme precipitation eve of the year 2013, where intense precipitation generated favourable conditions to satu the soil and lose slope stability (Figure 2).The results of this event were numer landslides and debris flows, generating damages in public infrastructure.These ca without notice, increase the infrastructure damage and economic losses, reducing inhabitants' quality of life.

Methodology
We used geomorphological and precipitation forcing in the Central Andes evaluate the spatial and temporal variability in RIL susceptibility.The study propo that the occurrence of RILs could be assessed by logistic distributions, allowing analysis of RIL's probability under scarce dataset availability.Geomorpholog indicators and spatially distributed precipitation data are used, and the probabi establishes "landslide likely" or "landslide not likely".Next, we present methodological scheme where the input data is used along the implementation sta

Methodology
We used geomorphological and precipitation forcing in the Central Andes to evaluate the spatial and temporal variability in RIL susceptibility.The study proposes that the occurrence of RILs could be assessed by logistic distributions, allowing the analysis of RIL's probability under scarce dataset availability.Geomorphological indicators and spatially distributed precipitation data are used, and the probability establishes "landslide likely" or "landslide not likely".Next, we present a methodological scheme where the input data is used along the implementation stages (cal/val) to evaluate the susceptibility of RIL occurrences according to different precipitation scenarios based on intensity/duration/frequency (IDF) curves.

Data
The in situ evidence shows that precipitation and topography promote generation of RILs in the study zone [19,42].A complete database was created using CHIRPS data on topography and daily precipitation.The topographic data include elevation and slope angle values derived from 1-arc second SRTM, RIL spatial and temporal distributions, and slope standard dispersion along the material release area.To assess the performance using external data from the Bayesian models, the initial database was separated into calibration and validation databases.
The study area has 14 weather stations, of which most have fewer than 15 years of data with a high presence of gaps.Moreover, the stations are placed in the lower parts of the basin, not being suitable to measure the precipitation in the generation zone of the RIL.Therefore, a low temporal extension of the weather stations becomes difficult to use as reference stations.Moreover, many landslides have no weather data in older periods (previous to 2000).To overpass this limitation, several satellite precipitation products such as PERSIAN, TMPA, CMORPH or CHIRPS allow one to reduce the spatial coverage of estimates, reaching the 0.05 degree.The CHIRPS product utilized daily estimations to constrain precipitation values for each RIL event with exact dates and localization.This approach proved instrumental in addressing the area's limited availability of hydrometeorological data.Sub-daily scale analysis was not feasible due to the absence of landslide occurrence timestamps in the historical databases.Previous studies established that CHIRPS has lower uncertainty metrics becoming suitable for hydrological applications.The precipitation data were correlated using a point-pixel approach with the spatial location of the existing RILs in the registry.In the same way, a library of intensity/duration/frequency (IDF) curves of precipitation events were considered from CHIRPS products [12].The IDF product has intensity values under different return periods of 2, 5, 10 and 25 years with durations of 4, 8, 12 and 24 h.The IDF dataset has a spatial coverage that accurately estimates the impact of different extreme precipitation events in the river basin by evaluating its degree susceptibility changes.
Geomorphological characteristics were integrated using the SRTM (Shuttle Radar Topography Mission), forcing the spatial resolution at 30 m.In recent decades, SRTM products have been used by the geoscientific community to perform complex treatments of the spatial data [11,44,45].SRTM is suitable to understand the geomorphological features of the terrain, becoming a useful support in landslide assessment.RIL assessment was carried out using SRTM in numerical modelling [16,46,47], or predictive models [48].We used two geomorphological features in our approach.First, we utilised surface slope values as a proxy to assess steepness, and second, we considered the standard deviation of the slope within a 60 m radius of each pixel.This comprehensive approach allowed us to capture the dispersion of elevations over a short distance, revealing the soil's predisposition to generate RIL (Rainfall-Induced Landslide) events.
We used RIL registry, provided by the National Geology and Mining Service (SER-NAGEOMIN) previously used by [11].The dataset has 500 events in the Central Andes; however, 100 RILs are emplaced inside the basin, and just 58 had an exact date.The final database includes mudflows, debris flows and landslides.This catalogue of landslides is the most complete to date, being improved by the integration of global sources such as the Global Landslide Catalogue (GLC) [11] and the Global Fatal Landslide Database (GFLD) [49] used in other studies [9,50].
It is important to note that integrating CHIRPS and SRTM may introduce uncertainties due to the different spatial resolutions of these two products.However, despite this consideration, numerous hydrological [51,52] and natural hazard studies [53][54][55] have consistently demonstrated that integrating these sources allows for rigorous analyses with scientific validity.

Model Training and Validation
To generate a spatially distributed susceptibility model, a logistic model will be maintained.The database is integrated into a Bayesian inference model.Bayesian models are useful tools for establishing models with limited data and low computational consumption, allowing operational functionality in LEWS.As the primary approach, this work will consider implementing a statistical model based on the Logit and Probit probability models (Figure 3), which have demonstrated promising results in the Southern Andes [11,15,16].The database was separated into a calibration database (SDB1) and a validation database, independent from the calibration database (SDB2).The separation rate is 50/50%.

Model Training and Validation
To generate a spatially distributed susceptibility model, a logistic model will be maintained.The database is integrated into a Bayesian inference model.Bayesian models are useful tools for establishing models with limited data and low computational consumption, allowing operational functionality in LEWS.As the primary approach, this work will consider implementing a statistical model based on the Logit and Probit probability models (Figure 3), which have demonstrated promising results in the Southern Andes [11,15,16].The database was separated into a calibration database (SDB1) and a validation database, independent from the calibration database (SDB2).The separation rate is 50/50%.The Logit distribution model fits the occurrence probability of an event by a logistic curve.The Logit (L) distribution model is given by Equation (1).
where L (l i = 1) is the RIL occurrence probability, N is the number of predictors used (X K ), β K is the coefficient of the function and β o is the intercept.A Probit distribution also uses binary dependent variables; its main difference with the logit distribution is the inverse normal distribution [56].The Probit (P) distribution is given by Equation (2).
Water 2023, 15, 2514 where k, β and X k refer to the same variables as the logit distribution, is the error in the fit with the standard normal distribution, and φ −1 denotes an inverse normal probability function [57].The two distributions were implemented using three predictors that correspond to daily precipitation, slope and dispersion of the slope in a range of 90 m.A calibration set was selected 100 times to obtain β k and their standard deviations are denoted by ∑ k , respectively.
A Receiver Operating Characteristic (ROC) analysis was performed from the results obtained to evaluate the model's performance.A ROC analysis assesses the model's capacity to correctly classify RIL events under the geomorphological and precipitation conditions that triggered them in space and time.Thus, it is possible to determine the ability to fit the calibration data with the validation values as a future prognosis tool, for example, in the case of future RILEWS.
ROC analysis evaluated each regression's quality using the independent database DB2 (Figure 3).The DB2 georeferenced to the initial Rainfall-Induced Landslide initiation area.The landslide susceptibility zones were compared with the pixel of the generated model (the pixel that includes the point).Thus, the degree of accuracy in identifying a new RIL under different slopes and precipitation conditions was determined.A probability threshold (tolerance) was established to define the moment at which the models correctly identify a RIL event.
We evaluated the sensitivity (S) using the validation database.Thus, the sensitivity of the RIL prediction can be characterised by its operational implementation in future RILEWS.Then, the sensitivity of each iteration was estimated (Equation ( 3)), which represents the capacity of the set of estimators to correctly detect RIL events [58].In addition, the specificity (E) was calculated (Equation ( 4)) to evaluate the ability to detect non-RIL events or true negatives (TN) to avoid false positives (FP) [58].

Spatial and Temporal Assessment
Following the model validation by ROC analysis, a basin's response under different precipitation thresholds was assessed (Figure 3).We used IDF curves generated in previous studies [12] for Chile's entire central zone by considering a daily temporal resolution.The IDF curve maps are resampled from the original 10 km to values of 30 m according to the native resolution of the logistic model.Thus, the impact of different precipitation intensities can be evaluated on the slopes of the river basin to understand the most susceptible zones and if they change under different precipitation conditions.From this, the probability changes in the river basin were analysed.

Results
The section provides the results obtained from the modelling strategy.We used predictive Logit and Probit models to determine the probability distribution of RIL occurrence (Section 3.1).Additionally, we evaluated the variation in RIL occurrence probabilities considering hydrometeorological scenarios (Section 3.2).

Model Training and Validation
The estimators selected for the Logit and Probit models are the variables precipitation, slope, standard deviation of the slope (Slope std) and intercept (Figure 4).For the Logit model, the precipitation estimator presented a median of −0.042963 with a 75th percentile Water 2023, 15, 2514 8 of 17 of −0.034747 and a 25th percentile of −0.051299.For the slope estimator, a median of 0.0012559 was obtained, with a 75th percentile of 0.0074464 and a 25th percentile equal to −0.0038287.Moreover, the slope standard deviation estimator showed an estimated median equal to −0.0094525 and 75th percentile of 0.027428, and a 25th percentile of −0.033528.Additionally, the intercept estimator had a median of 0.52208, with 75th and 25th percentiles of 0.74902 and 0.39865, respectively (Figure 4).75th percentile of −0.034747 and a 25th percentile of −0.051299.For the slope estimator, a median of 0.0012559 was obtained, with a 75th percentile of 0.0074464 and a 25th percentile equal to −0.0038287.Moreover, the slope standard deviation estimator showed an estimated median equal to −0.0094525 and 75th percentile of 0.027428, and a 25th percentile of −0.033528.Additionally, the intercept estimator had a median of 0.52208, with 75th and 25th percentiles of 0.74902 and 0.39865, respectively (Figure 4).
Moreover, for the Probit model, the estimator precipitation presented a median equal to −0.026656, with the 75th percentile equal to −0.019658 and the 25th percentile equal to −0.031279.The variable slope presented a median of 0.00046619, 75th percentile of 0.0035535 and 25th percentile equal to −0.0027549.The standard deviation of the slope had a median equal to −0.0037141.Meanwhile, the 75th percentile showed a value of 0.020158, and the 25th percentile reached −0.017904.Finally, the intercept estimator presented a median of 0.32954, with 75th and 25th percentiles equal to 0.46231 and 0.22477, respectively.The validation and calibration curves obtained for the Logit and Probit models show results that exceed 0.79 for calibration and 0.60 for validation.Table 1 summarises the calibration and validation values for the Logit and Probit models, respectively.The calibration value obtained for the Logit function was 0.7965, while the Probit function reached 0.7908.The validation values slightly decrease to 0.6021 for the Logit function and 0.6055 for the Probit model.The ROC curve shows differences between the validation and calibration curves of the Logit and Probit models (Figure 5).The Moreover, for the Probit model, the estimator precipitation presented a median equal to −0.026656, with the 75th percentile equal to −0.019658 and the 25th percentile equal to −0.031279.The variable slope presented a median of 0.00046619, 75th percentile of 0.0035535 and 25th percentile equal to −0.0027549.The standard deviation of the slope had a median equal to −0.0037141.Meanwhile, the 75th percentile showed a value of 0.020158, and the 25th percentile reached −0.017904.Finally, the intercept estimator presented a median of 0.32954, with 75th and 25th percentiles equal to 0.46231 and 0.22477, respectively.
The validation and calibration curves obtained for the Logit and Probit models show results that exceed 0.79 for calibration and 0.60 for validation.Table 1 summarises the calibration and validation values for the Logit and Probit models, respectively.The calibration value obtained for the Logit function was 0.7965, while the Probit function reached 0.7908.The validation values slightly decrease to 0.6021 for the Logit function and 0.6055 for the Probit model.The ROC curve shows differences between the validation and calibration curves of the Logit and Probit models (Figure 5).The calibration curves of the Logit and Probit models exhibit a better fit, emphasizing the low values in false positive rate cases and high values in true positive rate cases.In contrast, the validation curves of the Probit and Logit models always have higher rates of false positives and lower rates of true positives (Figure 5).calibration curves of the Logit and Probit models exhibit a better fit, emphasizing the low values in false positive rate cases and high values in true positive rate cases.In contrast, the validation curves of the Probit and Logit models always have higher rates of false positives and lower rates of true positives (Figure 5).

Spatial and Temporal Assessment
The median values obtained for the probability of RIL occurrence have a strong impact on the basin during short-duration extreme events, reaching over 0.8 (or 80%) (Figure 5).The Logit model curves show slightly higher probabilities of RIL occurrence than the Probit models (0.79 vs. 0.78, respectively, for 30 min of duration, Figure 6).The trend values of the Logit and Probit models indicate that the cases with the highest values correspond to those with return periods of 25, 50 and 100 years, with precipitation thresholds of 0.5 hr, and median values ranging from 0.726023 to 0.791746 (Figure 6).
It was mainly observed that half of the basin area has a probability of RIL occurrence during durations of 30 to 60 min for both the logit and probit models.Additionally, the median probability decreased for return periods longer than four years (see Figure 6).Hence, the basin is highly vulnerable to short-term events, with more than half of the catchment area exceeding a median probability value of 0.55 for all cases.The probability of RIL occurrence decreased for durations exceeding eight hours, as shown in Figure 6.
The Logit models exhibited slightly higher values than the Probit models (Figure 6).We compared the models without identifying significant discrepancies.For each particular hydrometeorological event, the most significant discrepancies were found for events with a return period of ten years and thresholds of 1 and 4 h.For a return period of one hundred years, with a precipitation threshold of 2 h, there was a difference in

Spatial and Temporal Assessment
The median values obtained for the probability of RIL occurrence have a strong impact on the basin during short-duration extreme events, reaching over 0.8 (or 80%) (Figure 5).The Logit model curves show slightly higher probabilities of RIL occurrence than the Probit models (0.79 vs. 0.78, respectively, for 30 min of duration, Figure 6).The trend values of the Logit and Probit models indicate that the cases with the highest values correspond to those with return periods of 25, 50 and 100 years, with precipitation thresholds of 0.5 hr, and median values ranging from 0.726023 to 0.791746 (Figure 6).probability of 0.02.In contrast, the least significant discrepancies between the values of both models in each hydrometeorological event studied were identified for a return period of 2, 5, 10 and 25 years, with a difference of less than 0.02 (Figure 6).

Analysis and Discussion
We compared two logistic models around three variables as forcing variables to estimate the probability of RIL occurrence in the Maipo River basin (33.59 °S/70.38°W), one of the most populated basins in the Central Andes.We integrated geomorphological It was mainly observed that half of the basin area has a probability of RIL occurrence during durations of 30 to 60 min for both the logit and probit models.Additionally, the median probability decreased for return periods longer than four years (see Figure 6).Hence, the basin is highly vulnerable to short-term events, with more than half of the catchment area exceeding a median probability value of 0.55 for all cases.The probability of RIL occurrence decreased for durations exceeding eight hours, as shown in Figure 6.
The Logit models exhibited slightly higher values than the Probit models (Figure 6).We compared the models without identifying significant discrepancies.For each particular hydrometeorological event, the most significant discrepancies were found for events with a return period of ten years and thresholds of 1 and 4 h.For a return period of one hundred years, with a precipitation threshold of 2 h, there was a difference in probability of 0.02.In contrast, the least significant discrepancies between the values of both models in each hydrometeorological event studied were identified for a return period of 2, 5, 10 and 25 years, with a difference of less than 0.02 (Figure 6).

Analysis and Discussion
We compared two logistic models around three variables as forcing variables to estimate the probability of RIL occurrence in the Maipo River basin (33.59 • S/70.38 • W), one of the most populated basins in the Central Andes.We integrated geomorphological features (slope, slope dispersion) of the SRTM digital elevation model and precipitation data on different days (CHIRPS database) before the landslide.We established a Bayesian relation between conditioning factors (topography/geomorphology) and triggers (precipitation at different intensities).The results allowed quantification for the first time of the degree of susceptibility to RIL in a basin of the Central Andes, showing that the half-area basin has RIL probability over 50% in short-duration events (less than one hour of duration).This study improves preliminary results that have only established qualitative limits [29,59].The high reliability of the calibration (AUC > 0.79), obtained through the ROC analysis [59][60][61][62], will open the door to RILEWS in future work [48,63].

Modeling
The good agreement between the validation and calibration results (ROC values) demonstrates the feasibility of both models (Table 1).The results of the estimators showed a low interquartile range in the inversions, suggesting a good agreement (less than 0.06 of difference for predictive variables, Figure 4).The results were interpreted as a stable model, not depending on the randomness of the database.Moreover, the intercept must be evaluated with caution for operational scale models such as RILEWS.The dispersion degree of intercept reached a difference of 2.3 for logit and probit.Nevertheless, both models have high rates of True Positives and low False Positive values, reaching 0.9 (Figure 5).A solid ability to differentiate true positives from true negatives can correctly generate a good separation of periods with RIL probability from periods without RIL probability spatially [59][60][61].The implementation proposal of this methodology as a RILEWS would make it possible to forecast RIL occurrence zones, constraining how the precipitation thresholds under a RIL could take place.Our results could suit an operational RILEWS scale considering the geomorphological features and the distributed precipitation values above the place as a proxy [8,11,24,64].
The prediction capacity of Logit showed a better performance than the Probit distribution.Despite the quantitative performance, the values of AUC could be negligible at an operational level as RILEWS.The values of the ROC curve show a better fit for the Logit/Probit calibration models, providing AUC over 0.7 in both cases (Table 1).The AUC reported was similar or greater than similar studies [48,61,62].The quality of the calibration and validation values suggests that this model could be integrated into warning systems before landslides (RILEWS) [63].From this, it is proposed that both models be used due to the excellent performance during the validation stage [8].Refs.[15,16] demonstrated that for the Biobío zone (Southern Andes), AUC of 0.6 was sufficient to generate probability models for RIL by using climate indicators.From this, it is proposed that the results generated could have the same performance.The results of this study showed the possibility of introducing a simple Bayesian model compared to other methods, such as neural networks [55,65,66] or deep learning approaches [67,68], requiring a more robust landslide inventory, which is not available currently.Although remote sensing data could allow delimitating of the spatial distribution of landslides, the temporal identification is unsuitable due to the long revisit time of satellite products in the Central Andes.Accurate time delimitation of the landslide generation is essential to improve landslide susceptibility models.

Spatial and Temporal Assessment
The most contrastive probability difference of the Logit/Probit models is identified for precipitation thresholds of 0.5 h and return periods of 25, 50 and 100 years (example in Figure 7).Our results show that short and intense events must be evaluated in detail for the Central Andes zone.The soil hydraulic properties of the zone, mainly permeability, are susceptible to fast events, concordant with the Bayesian approach derived in the present manuscript.Extreme events in the Central and Southern Andes have been shown to activate RILs, causing severe damage to the population and infrastructure [29,59,69].The abrupt changes for 30 min precipitation events highlight the importance of having precipitation estimation/forecast systems in the Central Andes.The present study allowed one for the first time to identify the spatial and temporal distribution of RIL in a highly populated basin in the Central Andes.Our results introduce quantitative information for better decision-making, showing that more than half of the basin is landslide-prone, susceptible to short-duration precipitation, reaching over 70% for a return period over ten years (Figure 6).The landslide-prone zones showed a correlation with the existing lithological units.The areas with mapped RIL and RIL-prone zones are related to volcanogenic units from the Cenozoic Era.Moreover, the marine and continental sedimentary units show a lower predisposition to landslide.In the Maipo basin, the lithologies show the impact of hydrothermal fluids [38,71]; in addition, at the regional scale, at least two deformation events are noted with evident folding and faulting on the rocky units of the zone [33][34][35]70], which, together with the climate action, are evidenced in the weak mechanical integrity of rocks [24].The slopes of the valleys in the area expose a wide variety of unconsolidated deposits of diverse selection on the surface.In turn, these unstable [33,35,37].The main mechanism of RIL activation is due to the low water infiltration capacity in the volcanogenic and carbonate units, partially preventing the effective The zone is highly complex due to the heterogeneity of soil/rock formations.The relief formation related to the active tectonism favoured geomorphological conditions in RIL activation [37].Heavy rains can affect the mechanical integrity of the soil/rock due to fast water content variations [24,70].Water content variations predispose the formation of noticeable gully incisions in the study zone, characterised by its sharp relief (Figure 1).Moreover, the zone ends up reflecting the degree of soil weathering.The high presence of rock/soil discontinuities allows water infiltration to decrease the medium's cohesion [19,30].
The landslide-prone zones showed a correlation with the existing lithological units.The areas with mapped RIL and RIL-prone zones are related to volcanogenic units from the Cenozoic Era.Moreover, the marine and continental sedimentary units show a lower predisposition to landslide.In the Maipo basin, the lithologies show the impact of hydrothermal fluids [38,71]; in addition, at the regional scale, at least two deformation events are noted with evident folding and faulting on the rocky units of the zone [33][34][35]70], which, together with the climate action, are evidenced in the weak mechanical integrity of rocks [24].The slopes of the valleys in the area expose a wide variety of unconsolidated deposits of diverse selection on the surface.In turn, these unstable [33,35,37].The main mechanism of RIL activation is due to the low water infiltration capacity in the volcanogenic and carbonate units, partially preventing the effective infiltration of rainwater into the lithologies, so that preferably, the water runs off in a superficial way, predisposing the transport of the debris arranged sequentially on the surface.
It is crucial to consider the different geological processes in the zone to significantly estimate the mechanical properties of rocks affected by deformation processes.The competitive difference among the different units is noteworthy and conditions the erosive processes that further trigger later movements of rocks and soils.

Implications of the Study
The present study analyses the impact of short precipitation in the Central Andes zone.We perform a Bayesian analysis to understand the RIL probability based on geomorphological features along a representative area of the Central Andes.The landslide triggering conditions in the study area depended on several variables such as lithology, geomorphology, and exogenous agents.RILs can transport large volumes of material, affecting extensive areas in the foothills [30].The forced logistic model using IDF curves shows that in extreme cases, the median susceptibility of the river basin reaches 80% (Figure 6).This value is high; therefore, a constant monitoring and/or mitigation measures must be taken when considering the precipitation as forcing.Our estimations determined that half of the area could become landslide-prone under short periods during a return period of fewer than five years (Figure 7).The recurrence of precipitation events predisposes the zone to be affected by new and extreme landslides, increasing the population's vulnerability due to the increased urbanisation in Central Chile.Therefore, a new constraint for decision-makers must be considered, suggesting that civil infrastructure design would be involved in future events.From the results, we propose that efforts should focus on understanding and analysing short-duration extreme events.These results have deep implications for sediment generation and erosion for a sediment source that reaches the subduction trench.Therefore, this study allows us to understand that the Central Andes could generate sediment.

Future Outlook
The present study introduces a novel susceptibility approach for a basin situated in the Central Andes.Our research not only opens up new possibilities in terms of landslide mitigation strategies but also takes a Bayesian perspective into account.However, further improvement of the model can be achieved by incorporating additional geomechanical features such as soil/rock cohesion and other relevant rheological properties in a more comprehensive manner.It is important to note that the zone under investigation has experienced significant alteration due to the influence of hydrothermal fluids, resulting in the weakening of rocks and soil bodies [38].The structural control observed in the Maipo basin indicates a pronounced alteration caused by the ascent of hydrothermal fluids, affecting various lithologies [38,41].Looking ahead, we encourage the exploration of alternative approaches to susceptibility assessment that consider the spatial distribution of lithology and the mechanical qualities of rocks and soils, thereby enhancing the accuracy and reliability of the results obtained.
Moreover, the high variability of the soil geotechnical features become essential fully understanding the interaction between the rheological properties and the generation of RILs in the Central Andes.A wide variety of gravitational events differ widely from each other.This first approach allows one for the first time to understand the impact of different precipitation thresholds over a densely populated basin in the Central Andes.Future studies must improve the soil variability to improve the quality of decision-makers over the territory.
The model carried out in this study demonstrated that the logistic model is suitable to establish rainfall-induced landslides probabilities.Our study complements previous studies to develop a robust rainfall early warning system in the Southern Andes [9,11].Recent studies of precipitation quality suggest that in situ weather stations could be replaced by numerical models [16] or remotely sensed measures [11,13,29,44,59] in South America.Future phases could introduce the use of operational precipitation forecasts such as GFS [72], Weather Research Forecast (WRF) [73] and CHIRPS-GEFS [10].
The performance of predictive models relies heavily on the quantity and quality of input data [11].Regarding natural hazard planning, decision-makers often require preliminary estimates of the size or volume of landslides that could occur under specific precipitation events.However, the available database for the study zone is inadequate for determining this information.This limitation stems from the limited number of variables and the absence of previous measurements of size or volume.In the future, additional data on size or volume in preliminary reports could contribute to developing more accurate models.In the meantime, decision-makers must consider using physical-based models only if the zone has an accurate geotechnical characterization.These models could provide valuable support for decision-making processes.
Despite the number of landslides in the database being comparable with other studies [11,16], we suggest increasing the inventory in future studies.A deep and accurate determination of landslides will increase the AUC values and sensibility of the models.It is worth noting that there is only one way to divide the calibration and validation databases.Previous studies used logistic models and divided the calibration and validation database (50/50) to obtain predictive models that exceed 87% in performance [11].In contrast, ref. [74] divided their databases into 80/20 for the calibration and validation stages, reaching an AUC performance between 0.839 and 0.898 for four different models.The division of the cal/val databases is constrained by the availability and quality of the data.
In the future, conditioning and conditioning variables of RILs will be integrated to improve the performance of the present results.The wide soil variability showed that the RIL distribution in the basin is inhomogeneous.The soil variability will impact the conditioning factors.An integration of new variables such as soil moisture and textural properties will make it possible to implement RILEWS at the operational level in future instances.It is suggested that future studies evaluate the presence of sectors with slow deformations using other methodologies to identify RIL reactivation.A long-term surface deformation monitoring is allowed in similar zones to constrain and forecast slope failure, improving landslide-early warning systems.

Conclusions
To understand the spatial and temporal variability of susceptibility to RILs, we performed a Bayesian analysis based on logistic regressions.Our validation results demonstrated that logit and probit distributions can spatially represent RIL-prone zones with an ROC value of 0.79.The good agreement between validation and calibration results suggests that the models are stable and do not depend on the data-driven model variability.The results might be limited to the size of the RIL catalog, due to the variability of the intercept requiring a future increase of the RIL database with additional features such as geomechanical properties.We conclude that it is possible to apply this methodology as an early warning system for rain-induced landslides (RILEWS), since from this approach, it is possible to delimit the zones most prone to suffer RIL in a highly populated area due to their true positive rates and low false positive values suggesting that the model is suitable to future RILEWS.
The estimation of probable RIL zones at a spatial and temporal scale under different rainfall durations showed a strong influence of short-period duration, these types of events becoming relevant in future mitigation plans to decision-makers.The results of the study could be useful in an operational scale RILEWS considering as a proxy the geomorphological characteristics and precipitation values distributed over the site.The importance of implementing RILEWS for mountain areas is that it is possible to delimit the zones prone to suffer RIL in a highly populated area.In the same way, our study allows one to estimate probable RIL zones at a spatial and temporal level under different precipitation durations.
The present study analyzed the impact of short-and long-duration precipitation in the Central Andes area.We determined that half of the area could become prone to landslides induced by short-duration precipitation during a return period of fewer than five years, increasing the vulnerability of the population due to increased urbanization in Central Chile.We encourage decision-makers to focus on a better understanding and analysis of short-duration extreme events.Our article addresses a priority case study at the Chilean level.The approach we use will generate key tools for national and international decisionmaking in geohazard risk management.In the future, this will provide a solid basis for the implementation of land-use planning policies, the design of building codes and the elaboration of disaster response and recovery plans.
Our results showed that the Maipo basin has a wide variability to susceptibility of the RIL under different precipitation thresholds.The study area showed a landslide probability of 59% for half of the basin area (two-year 4 h return).The probability implies that the area is highly susceptible, introducing a new degree of freedom in public policies.Authorities should monitor or generate RILEWS on a permanent operational basis.The results of this study could be used in the future to support decision-making by public entities.In addition, the application of this approach will allow one in the future to optimally redistribute economic and human resources to improve risk management in years with high risk of RIL occurrence, as well as to make estimates related to the amount of sediment generated at the basin level and its possible influence on tectonism.
Finally, future studies should be oriented to restrict the values of soil variability, in addition to expanding the catalog of RILs in the area, which will improve the quality of decision-making on the territory.In addition, future developments and public infrastructures should take into account the impact of RILs in their design.The performance of predictive models depends on the quantity and quality of input data.In the future, it is suggested to integrate conditioning variables of the RILs to improve the performance of the current results.

Figure 1 .
Figure 1.(a) Relief map with the location of RILs of the study zone.(b) CHIRPS product with IDF of 2 years and duration of 4 h.

Figure 1 .
Figure 1.(a) Relief map with the location of RILs of the study zone.(b) CHIRPS product with IDF of 2 years and duration of 4 h.

Figure 2 .
Figure 2. RIL was activated in the Maipo river basin on 21 January 2013.(a) Proximal and mid zone of a debris flow, located over ancient alluvial deposits.(b) Debris-flow deposits with me blocks immersed in sandy to silty material.(c) The channel after the erosion of the debris-f deposits (Estero San Alfonso).(d) Partial obstruction of Rio Maipo caused by the debris-f deposit of a tributary.Based from [42,43].

Figure 2 .
Figure 2. RIL was activated in the Maipo river basin on 21 January 2013.(a) Proximal and middle zone of a debris flow, located over ancient alluvial deposits.(b) Debris-flow deposits with metric blocks immersed in sandy to silty material.(c) The channel after the erosion of the debris-flow deposits (Estero San Alfonso).(d) Partial obstruction of Rio Maipo caused by the debris-flow deposit of a tributary.Based from [42,43].

Figure 3 .
Figure 3. Methodological approach, in the section "Predictor dataset".The Logit distribution model fits the occurrence probability of an event by a logistic curve.The Logit (L) distribution model is given by Equation (1).

Figure 4 .
Figure 4. Comparison of estimators used for the configuration of the Logit and Probit models.

Figure 4 .
Figure 4. Comparison of estimators used for the configuration of the Logit and Probit models.

Figure 5 .
Figure 5. Validation and calibration curves for the Logit and Probit functions.

Figure 5 .
Figure 5. Validation and calibration curves for the Logit and Probit functions.

Figure 6 .
Figure 6.Comparison between IDF values for median probability of the RIL occurrence.

Figure 6 .
Figure 6.Comparison between IDF values for median probability of the RIL occurrence.

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Figure 7 .
Figure 7.Comparison between IDF values for median probability of the RIL occurrence.

Figure 7 .
Figure 7.Comparison between IDF values for median probability of the RIL occurrence.

Table 1 .
Calibration and validation values for the Logit and Probit models.

Table 1 .
Calibration and validation values for the Logit and Probit models. A.U.C.