Landslides due to rainfall are phenomena that dislocate a mass of soil from its natural position, which then slides downward along a slope due to gravity forces. Intense or long-duration rainfall infiltrates the soil and increases the pore pressure, resulting in soil saturation that leads to slope failure. The saturated soil becomes weak and loses cohesion, and the slope fails when rainfall crosses a certain threshold (Bernardie et al., 2014; Martinović et al., 2018; Lee et al., 2021). The heavy rainfall saturates a slope and triggers a landslide due to the reduction in the soil's shear strength and the increase in pore water pressure (Tsai and Chen, 2010; Lacerda et al., 2014; Chatra et al., 2019; Chen et al., 2021; Luino et al., 2022). For example, steep slopes with loose soils and even moderate rainfall can lead to the displacement of an enormous quantity of soil mass. On the contrary, in slopes with more stable, cohesive soils, the surface failure might be smaller (Tsai and Chen, 2010). The rainfall quantity and duration influence the volume of the landslides; the higher the intensity and the longer the duration of rainfall, the larger the resulting surface failure (Chang and Chiang, 2009; Bernardie et al., 2014; Chen et al., 2017). The landslide occurrences can also be influenced by human activities that weaken the slope, such as excavation at the slope toe and loading caused by construction and land use such as agriculture or mining (Rosi et al., 2016). Rapid-urbanization activities in mountainous regions affect topography through hill cutting, deforestation, and water drainage (Rahman et al., 2017); these activities disturb the slope structure and change the water flow, which exacerbates the effect of landslides in regions where human engineering activities are mostly located (Holcombe et al., 2016; Chen et al., 2019). Therefore, to mitigate landslide-induced risks in runout regions, estimation of the volume of landslides due to rainfall (VLDR) plays a crucial role.

The quantification of VLDR is essential for effective risk management (Tacconi Stefanelli et al., 2020), emergency response, engineering design (Cheung, 2021), economic assessment, and environmental protection (Alcántara-Ayala and Sassa, 2023). With estimates of VLDR, morphologists can update hazard maps (Van Westen, 2000) to reflect the scale of potential mass movement in various regions and obtain regions with similar likelihoods of landslides of similar soil mass, highlighting risk zone levels, i.e., low, moderate, and high. These classifications help engineers to apply appropriate slope stabilization techniques depending on the level of risk (Dahal and Dahal, 2017). Additionally, enhancing the precision of VLDR estimations and improving predictive capabilities are essential for understanding and monitoring landscape evolution. Montgomery et al. (2009) emphasized that the volume of landslides is a key factor in determining the extent of downstream damage, particularly for large debris flows or rock avalanches, which can drastically alter the landscape and affect surrounding ecosystems and infrastructure. Similarly, Korup (2004) further explored the long-term geomorphological effects of large-volume landslides, highlighting their importance in reshaping mountainous terrains and influencing sediment transport, which is critical for understanding both immediate and future landscape changes. However, the existing landslide susceptibility models, which are mostly used for the identification of regions susceptible to landslides (i.e., landslide zonation) (Kim et al., 2014; Gutierrez-Martin, 2020; Chen et al., 2021; Li et al., 2022), are essential in emergency management because they provide a general overview of zones with a higher probability of landslide occurrence, but they do not emphasize the determination of the approximate value of the volume of failing mass in relation to excessive-rainfall events.

Numerous researchers have used landslide inventories, remote sensing data, and numerical techniques to establish the relationship between landslide geometry and influencing factors to determine landslide volumes quantitatively. For example, Saito et al. (2014) studied the relationship between rainfall-triggered landslides to test whether the volume of landslides across Japan that occurred between 2001 and 2011 could be directly predicted from rainfall metrics. The findings revealed that larger landslides occurred when rainfall exceeded certain thresholds, but there were significant discrepancies between the peaks of rainfall metrics and maximum landslide volumes, and total rainfall was found to be a suitable predictor of landslides. Dai and Lee (2001) established the frequency–volume relation for landslides in Hong Kong SAR and noticed that the relation for shallow landslides above 4 m³ followed the power law. The 12 h rolling rainfall contributed most to the prediction of the volume of landslides. Jaboyedoff et al. (2012) contributed by demonstrating the value of remote sensing technologies such as light detection and ranging (lidar) in conjunction with field data to improve the accuracy of volume estimates and capture the geomorphological changes associated with landslides. Ju et al. (2023) constructed an area–volume power law model for the estimation of the volume of landslides using high-resolution lidar data collected between 2010 and 2020 in Hong Kong SAR. Their aim was to accurately estimate the volume of small-scale landslides. Their reliance on localized datasets limits the model's applicability in regions with different geological settings, and the model does not consider all variabilities in landslide characteristics. Razakova et al. (2020) calculated landslide volume using remote sensing data to assess the efficiency of aerial photographs in environmental impact assessment and ground-based measurement. The study did not consider the effect of vegetation and topography and only focused on a single landslide case, which may be a source of bias due to differences in soil composition and environmental factors. Hovius et al. (1997) analyzed multiple sets of aerial photos and frequency–magnitude relations for landslides in Aotearoa / New Zealand. Their findings precisely determined that the landslide frequency–magnitude relationship followed a power law and their infrequent large magnitude contributed to landscape change. The study highlighted the importance of soil composition for landslide size, but the reliance on aerial photos, which may be inaccurate in dense forest areas, and the omission of climatic factors limit the generality of the findings. Guzzetti et al. (2008) applied statistical methods to regional landslide inventories and antecedent rainfall data ranging between 10 min and 35 d. Their findings revealed that the slope angle and soil type significantly influence landslide volume estimates and that the rainfall intensity is more important than duration. Chatra et al. (2019) applied numerical methods to study the effect of rainfall duration and intensity on the generation of pore pressure in the soil; their findings revealed higher instability in loose soil compared to medium-compacted soil slopes. Huang et al. (2020) introduced a hybrid machine learning model combining support vector regression (SVR) with a genetic algorithm to estimate debris-flow volumes. The model was tested on real-world case studies, showing improved accuracy in volume predictions compared to traditional methods. However, it was noticed that the study relied on a limited dataset, which may reduce the model's generalizability to other regions of different geomorphology and environmental settings. Shirzadi et al. (2017) compared the effectiveness of statistical and machine learning models in simulating landslide volume–areal relations, demonstrating that machine learning techniques outperform traditional statistical methods in terms of accuracy. The study did not consider the climatic and geomorphic factors such as rainfall, vegetation, or soil type that trigger and influence factors in landslide occurrence. It was noted that existing models only treated the interaction of soil and rainfall without considering environmental factors, human activity, and the non-linear behavior of the triggering and influencing factors.

In the present study, the volume of landslides due to rainfall is predicted using ordinary least-squares or linear regression (OLS), random forest (RF), support vector machine (SVM), extreme gradient boosting (EGB), generalized linear model (GLM), decision tree (DT), deep neural network (DNN), k-nearest-neighbor (KNN), and ridge regression (RR) algorithms, considering the details of triggering factors (i.e., rainfall) and predisposing factors (i.e., geomorphological, soil, and environmental). Here, we aim to construct a data-driven algorithm that combines input parameters for physically based and empirical models and incorporates more complex non-linear features of input variables to predict the occurrence of associated events more accurately. The main assumption behind the data-driven algorithm is that the considered feature input of the model produces a similar volume of landslides due to rainfall and follows the same pattern in a particular region with the same features under the same quantity of rainfall. Here, we examine different machine learning (ML) algorithms and compare their performance using the coefficient of determination (R2), mean square error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and symmetric mean absolute percentage error (SMAPE) of the predicted volume of landslides. The focus is to optimize the predictions of the volume of landslides due to rainfall, taking into account triggering and influencing factors with higher accuracy.

In this paper, we consider nine data-driven models, namely OLS, RF, SVM, EGB, GLM, DT, DNN, KNN, and RR, to predict the volume of landslides due to rainfall. The model is tested on South Korean landslide inventories and predisposing factors coupled with triggering factors, i.e., rainfall data. Our detailed workflow is summarized in Fig. 3. The steps for construction of these models can be briefly summarized as follows: (a) the dataset for landslide inventories is cleaned and combined with the rainfall dataset; (b) collinearity analysis is performed using the variance inflation factor; (c) continuous features are scaled (Z score) (Bonamutial and Prasetyo, 2023) to facilitate algorithms in fast convergence; (d) the dataset is split into training and test set; (e) all models are tested on the same training set and the model is evaluated on the test set using mean absolute error (MAE), coefficient of determination (R2), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), and mean absolute percentage error (MAPE) for the comparison of actual and predicted volume by each model; (f) variable importance is calculated for the optimal model; and (g) the distance correlation is calculated for each continuous feature and the Kruskal–Wallis and Dunn tests are conducted to examine the similarity of the effects of each category on the landslide volume.

This section details how all analyses and model development were performed in R using various libraries. The DNN regression model was constructed using the dnn() function from the cito library (Amesoeder et al., 2024), with two hidden layers of (50, 50) nodes. The model was trained for 1500 epochs (iterations), with a learning rate of 0.01 and the MAE as the loss function. The DT regression model was constructed with tree() function from the tree library, with the recursive-partition method. The RR model was constructed using glmnet() from the glmnet package (Friedman et al., 2010), with a ridge penalty (alpha = 0). The optimal lambda was obtained by performing 10-fold cross-validation. The EGB model was built using the xgboost() function in the xgboost package (Chen et al., 2022). The optimal model was obtained at the 524th boosting iteration with max depth = 5 and other parameters set to default. The GLM regression model was constructed using the glm() function (R Core Team, 2022) with the Gaussian family and log link to constrain the model to predicting positive outcomes. KNN regression was constructed using the knnreg() function from the caret package (Kuhn, 2022), with the number of neighbors, k, at 17. The OLS model was constructed with lm() from the stats package (R Core Team, 2022). The RF model was run using randomForest() from the randomForest package (Liaw and Wiener, 2002) with default parameters, and the optimal model was reached at the 256th iteration. The SVM regression model with a linear kernel was built using the e1071 package (Meyer et al., 2021) and other parameters set to default.

The predictive performance of all tested models on the holdout dataset is depicted by the scatterplot (Fig. 5) of the actual volume as recorded in the test set and predicted outcome values of each model. The red line represents the perfect prediction. The scatterplot of actual and predicted values of tested models shows that OLS performed least well compared to other models, with R2 = 0.2744; that is, 27 % of variances in the model were explained by predictors. The second-worst-performing model was RR, with R2 = 0.3034, which is a 3.6 % improvement compared to OLS. Among all models, three out of nine, namely OLS, SVM, and RR, performed at below 50 %; however, these models predicted small values of volume (below 2000 m³) well. The MAE of these three models was higher than that of the remaining six models, namely DNN, DT, GLM, KNN, RF, and EGB. Among these last models, the best performing was EGB, with R2 = 0.88 being the proportion of the variance explained by predictors and MAE = 146.6 m³. The evaluation metrics for the training and test models are summarized in Table 4. Considering R2, three models, namely EGB, RF, and DNN, had a value of R2 above 80 % on the holdout set.

Regarding the prediction on the training set, GLM had an R2 of 83 %. Nevertheless, the prediction on the holdout set was 51.9 %; this large variation in variance explained by predictors indicates that the GLM model did not catch all non-linear patterns in the holdout set. Notably, the prediction difference in R2 on both the training and the test sets for the random forest exhibited a very small difference compared to EGB and DNN, that is, 1.75 % compared to 12.17 % and 7.72 % for DNN and EGB, respectively. Despite the stable prediction of RF, for the performance in terms of SMAPE, DNN gave the second-lowest symmetric mean absolute percentage error: 43.83 and 39.79 m³ on the training and test sets, respectively. According to Chicco et al. (2021), R2 is more informative in regression modeling; thus, RF had better predictions than DNN.

To dive deep into the prediction performance of the EGB model, we analyzed variables' importance for the prediction of the volume. It was observed that slope length was the predictor that contributed the most to the performance of the EGB model, followed by maximum hourly rainfall and slope aspect. The altitude, 3 h rainfall, slope angle, and age of timber contributed moderately to the prediction of the outcome volumes, with gains above 0.01 and less than 0.2. The antecedent rainfall from 3 d and above and continuous rainfall made minor contributions, with a gain of less than 0.01 for each. The presence of rainwater drainage channels made a moderate contribution, with a gain close to 0.01. On the other hand, the contribution of soil depth and forest density in the models was insignificant and far below 0.01. Though Fig. 2a depicts the association between larger volumes and fire history, the variable importance indicates that this relation was not significant. Some variables made minor contributions, depending on the case, and the contribution of those variables may also increase depending on other regional settings. Therefore, all variables with GVIF below 10 were kept in the model. Figure 6 illustrates the variables' importance for the EGB model. The vertical red line splits landslides prediction features into two groups, the first (to the right of the line) containing features that contributed a gain above 0.01 and the other (to the left of the line) containing those that made minor contributions.

The variable importance plot depicts the overall contribution of a given feature; however, it does not provide detailed information. To gain more insight into the relationship between the volume of landslides and predictors, statistical tests for normality, namely the Shapiro–Wilk test and Dunn's test, were conducted. The Shapiro–Wilk test (Dudley, 2023) results revealed that the distribution of volume was non-normal (W = 0.40642, p value < 0.001). Noting that the volume distribution was non-normal, we opted for the non-parametric tests, which do not rely on normality to conduct the distance correlation (Székely et al., 2007) test (dcor) for continuous independent features. Figure 7 illustrates that the slope length exhibited a higher value (dcor = 0.56), followed by continuous rainfall, altitude, and 3 h rainfall, and the values kept decreasing up to timber diameter, with a distance correlation of 0.08. Overall, the distance correlation between the volume of landslides shows a moderate strength of association between continuous predictors.

Furthermore, to test for categorical features, the Kruskal–Wallis test (McKight and Najab, 2010) was used to check whether the volume of the landslide was different in each category and Dunn's tests (Dinno, 2015) were applied to examine which categories had similar means of the volume of landslides due to rainfall in different categories. The null hypothesis (H₀) was that the mean volume of landslides in different categories is the same, and the alternative hypothesis (H₁) was that the means of landslides are different in some categories. For the slope aspect, the second-most-significant predictor for the EGB model according to the results of the Kruskal–Wallis test (χ2=20.889, df = 7, p value = 0.003938), showed that there is a significant difference in the median of the volume in some categories of slope aspects. To know which classes of slope aspects had significantly different mean volumes, Dunn's test results at the 95 % confidence interval applied to pairs (east–southwest, east–southeast, east–south, east–northwest, and northwest–southeast) had significantly different means of landslides' volume (with p value < 0.05). Figure 8 shows that the southwest and southeast aspects had a higher frequency of landslides.

The Kruskal–Wallis test for the difference in the mean of drainage classes gave results of χ2=15.792, df = 2, and p value = 0.000372, which shows that the means of the volume per class were different. This was clarified by Dunn's test results: p values were less than 0.05 in all pairwise mean difference comparisons. The results of these tests highlighted that drainage has a remarkable influence on the occurrence of rainfall-induced landslides on the Korean Peninsula.

Numerical models have traditionally been employed due to their foundation in physical principles such as slope stability and hydrological dynamics (Glade et al., 2005). These models are valuable for understanding the underlying mechanisms of landslide processes but often face limitations when applied to regions with complex or heterogeneous terrain, as they require detailed, high-quality input data that may not always be available (Caine, 1980). In the same way, statistical models, which use historical rainfall and landslide data to establish correlations, can offer useful predictions of VLDR in regions with extensive historical records (Chung and Fabbri, 2003). However, these models may struggle to account for local variations in topography or rapidly changing weather patterns, limiting their general applicability. Additionally, ML techniques have shown significant promise in improving predictive accuracy at the regional level due to the capability of processing large diverse datasets and capturing complex non-linear relationships that traditional models might fail to capture (Pourghasemi and Rahmati, 2018). Further, ML models can adapt to regional variations and continuously improve as new data are introduced, offering a more flexible and dynamic approach to predicting VLDR on a regional scale (Liu et al., 2021b). Subsequently, the aim of this study was to construct a data-driven algorithm that accurately predicts VLDR. The results of nine different tested algorithms revealed a tremendous difference between classical regression models (OLS, RR, and GLM) and other data-driven machine learning models. In this study, apart from SVM regression, DT, and KNN, the machine learning models (DNN, DT, RF, and EGB) exhibited high prediction capability with R2 above 50 % (Fig. 5). The DNN, EGB, and RF models achieved R2 > 0.8 on both training and test sets, with accuracy reduced to R2 values of 1.75 %, 7.72 %, and 12.17 % for RF, EGB, and DNN, respectively, on the holdout set, indicating that the model could yield reliable volume estimates in adjacent areas with similar geological and environmental conditions. The random forest model performed well in predicting smaller volumes; however, as the volume increased, the model underpredicted volume values. The DNN model, with low MAE, performed quite well compared to random forest; however, the model did not perform well on moderate volume values, resulting in reduced R2. The EGB model tested on the South Korean landslide inventory coupled with rainfall data at the time of landslide events and antecedent rainfall within 1 month of the event exhibited more accurate predictions compared to other constructed algorithms. The difference in performance may be due to the internal structure of each algorithm; the RF builds multiple decision trees and averages predictions to improve accuracy (Breiman, 2001), while EGB builds sequential trees in a recursive order, where the newly built tree improves error that occurred while building the previous decision tree and optimizes the loss function through a gradient descent (Chen et al., 2022).

The slope aspect played an important role in the prediction of the volume, and the landslides mostly occurred in locations oriented toward the south-southwest and southeast. This may be due to the direction taken by typhoons, which hit the southwest versants of mountains upon landfall on the Korean Peninsula and travel toward the northeast Pacific (Lee et al., 2013; Ha, 2022). The findings of this research are congruent with those of Lee et al. (2013), who also highlighted that the mountain versant oriented to strong wind directions may face more landslides. The study also highlighted that a moderate rainwater drainage channel plays an important role in the prevention of landslides due to its stabilizing effect. The landslide location and pattern follow the rainfall climate scenario, which highlighted a higher intensity of rainfall in the northeastern region of South Korea (Lee, 2016). In addition, the findings of this study are congruent with Zhang et al. (2019) observations that highlighted the low influence of soil type in landslide modeling and showed that the maximum rainfall and cumulative 3 h of rainfall were the most contributing rainfall types, which indicated that the shallow landslides of interest may have been triggered by sudden rainfall concentrated in a few hours before the occurrence of the events. The occurrence of landslides triggered by rainfall is a complex phenomenon that involves many interrelated environmental settings, human activities, geological conditions, and climatic conditions. Moreover, the occurrence of typhoons is known to aggravate the landslides' impacts on communities (Chang et al., 2008); incorporating typhoon variables in future studies to customize regional settings may improve the accuracy of models. The advantage of this research is that the constructed model has high predictive accuracy and can handle the non-linearity of predisposing factors. The model came to fill the gap in a few fields related to the prediction of the volume of landslides using data-driven techniques. This model can serve as an effective tool for policymakers to incorporate landslide volume risks into policies aimed at protecting infrastructure and residents dwelling in landslide high-risk zones.

To understand the applicability of the developed models, the trained model was tested using unknown data (test data), with volume predictions generated solely based on the predictor variables; actual volume values were utilized only for evaluating model prediction accuracy. The outcome exhibited a difference in R2 on the training and holdout set of 7.72 % for the optimal model (i.e., EGB), highlighting that the model can be applied to other regions of with similar settings. It was noted that without proper model calibration with the independent dataset, it is difficult to determine whether these discrepancies in performance are due to model limitations or data differences in different regions (Huang et al., 2020). Therefore, future research will focus on developing an independent database containing recent landslide geometry data from various regions of the Korean Peninsula to enhance model accuracy, along with calibrating region-specific parameters to ensure the model's transferability to other regions.

The major limitation of this study is that the analysis is solely focused on shallow-seated landslides, specifically translational slope failures with volumes below 13 000 m³. Thus, the analysis may not fully capture the variability in landslide characteristics across different geomorphological and geological contexts. Deep-seated landslides, for instance, often exhibit distinct failure mechanisms, material compositions, and depositional patterns that influence their volumetric characteristics, and these were not considered in this investigation. Similarly, debris flows, known for their unique channelization and entrainment behaviors, were not included, potentially limiting the applicability of the optimized models to other landslide types. Further, this study was performed using point-based landslide inventory data, which may not capture all variability in influencing factors and their exact state. The incorporation of high-resolution data from remote sensing and other sources may also improve the efficiency of the predictions. These limitations may impact the broader applicability of the proposed model; however, future studies will aim to address this by conducting separate analyses for deep-seated landslides and debris flows, allowing for a more comprehensive understanding of landslide volume predictions across diverse landslide types and geomorphological settings.

In this paper, the aim was to construct a data-driven model that predicts the volume of landslides due to rainfall. To this end, nine different classical regression models and machine learning algorithms were tested on a South Korean landslide dataset containing features of landslides that occurred between 2011 and 2012. Among the tested models, the EGB model produced the most accurate prediction. This is proven by the evaluation of the difference between actual and predicted values, such as R2 = 88.41 % and MAE = 146.6120 m³ on the holdout set. The analysis of feature variables in the contribution to the prediction of the model revealed that the slope length was the most influential predictor. The EGB model can be seen as a promising tool for the prediction of the volume of landslides due to its high predictive performance. The model can be customized in different environmental settings. The model can be applied to estimate the expected volume of landslides based on forecasted rainfall once the model has been well adjusted to fit the geomorphological and environmental settings of the region of interest after re-training on the regional historical data to include regional variability. Therefore, this model can be a good tool for planning for resilience and infrastructure pre-construction risk assessment to ensure that new infrastructure is placed in stable regions free from severe landslides.