Rain-Induced Shallow Landslide Susceptibility Under Multiple Scenarios Based on Effective Antecedent Precipitation

Abstract

Precipitation typically leads to the accumulation of soil moisture, which causes slope instability and triggers landslides. However, due to the lag nature of this process, landslides usually do not occur on the day of heavy rainfall. Therefore, it is essential to incorporate antecedent effective precipitation as a factor in landslide prediction models that allow for the creation of more comprehensive landslide susceptibility maps. In this study, six machine learning models are compared, with antecedent effective precipitation included as a conditioning factor for model training. The optimal model is selected to simulate landslide susceptibility maps under four return periods (5, 10, 20, and 50 years). Additionally, the mean decreases in the Gini and SHAP values are employed to identify the most significant factors contributing to landslides. The results indicate the following: (1) Effective antecedent precipitation is the most influential factor in landslide occurrence, ranging from one to two times higher than other factors. (2) Most meteorological stations in the study area show antecedent effective precipitation that follows a lognormal distribution, mainly in coastal areas, with a secondary fit to the general extreme value distribution. The spatial distribution of antecedent effective precipitation is more prominent in the coastal and western mountainous regions, with lower values that then increase with longer return periods in central areas. (3) The XGBoost model achieves the best performance, with an area under the curve of 0.96 and an accuracy of 89.02%. (4) The landslide susceptibility maps for the four return periods reveal three high-risk zones: the southern coastal mountains, the western Zhejiang mountains, and the areas surrounding the hilly region of Shaoxing to Taizhou in central Zhejiang. This study provides dynamic decision-making support for the prevention and control of rainstorm-induced landslide risks.

1. Introduction

Landslides occur worldwide every year at different scales. According to the NASA Goddard Space Flight Center’s Landslide Catalog, there were 15,455 landslide events worldwide between 1950 and 2022, causing over 59,862 deaths [1]. Due to the unique combination of geology and climate, China is highly prone to landslides [2]. In recent years, landslides have been responsible for as many as 70% of all geological disasters in China [3]. In particular, due to its major mountainous and hilly landform, as well as precipitation and topography, in Zhejiang Province, the occurrence of slope instability events is greatly enhanced. This underscores the importance of early identification and preventive measures to mitigate the severe effects of landslides on human lives and property.

Shallow landslide susceptibility research areas can be summarized into four broad categories: (1) The first is process-based prediction models of landslide instability mechanisms and physical processes [4,5]. These studies are founded on principles with respect to geology, soil mechanics, fluid dynamics, and geomechanics [6]. They consider precipitation infiltration [7], groundwater flow, and alterations in the strength of soil [8] by simulating and hypothesizing the ways in which landslide occurrence takes place. Additionally, current physics-based methods for predicting rainfall-induced shallow landslides rely on physical equations and principles from physics. These methods require only a limited set of input data, which is typically easy to obtain, making them highly suitable for rapid assessments in data-scarce regions. (2) The second type is physics-based models of landslide susceptibility prediction. These models rely on physics-based equations and principles to predict landslide occurrence. They require only a limited set of input data, which is typically easy to obtain, making them highly suitable for quick assessments in regions where data are scarce [9,10,11]. However, although these physical models can accurately predict the timing of landslides, especially for short-term monitoring and early warning [12], they are usually limited to small areas or single events [13]. Moreover, while they may not offer high-resolution predictions, their simplicity and the ease with which they can be applied make them valuable tools for rapid landslide risk assessments in many areas. (3) The third type comprises landslide susceptibility mapping, which is achieved using geographic information system (GIS) and remote sensing technologies. Geographic data relating to terrain, geology, precipitation, and land use are integrated to recognize areas that may turn out to be susceptible to landslides [14,15,16]. These models are mostly used for hazard zoning at macroscopic scales [17], as well as for identifying high-risk areas [18], incorporating ground observations to increase the accuracy of the results [19]. (4) The fourth type includes building landslide susceptibility assessment models that are then applied to historical landslide datasets [20]. These models use past landslide events to create a regression model or any other predictive model that can be used to evaluate susceptibility [21]. For example, precipitation threshold models, which relate rainfall intensity and duration to landslide occurrence [22], are widely used in shallow landslide disaster prediction research [23,24,25]. These methods are based on past events, have the advantages of simplicity and efficiency, and have been found to provide quick identification of probable landslide conditions.

There are three common approaches for developing predictive models using historical landslide events: (1) The first approach is expert assessment methods [26,27,28], which require expert knowledge for the analysis of landslide likelihood and severity; however, these methods are subjective and produce variable results. (2) The second approach is regression models [29,30,31], which are built on the basis of statistical analysis to identify relationships between susceptibility and influential factors. While very simple in their implementation and quantitatively accurate, they fail to represent complicated nonlinear relationships. (3) The third approach is machine learning models, which require large datasets and the proper selection of factors, ratios, and algorithms [32]. Common models include support vector machines (SVMs) [33], random forests (RFs) [34], neural networks [35], Bayesian networks [36], k-nearest neighbors (KNNs) [37], and XGBoost (XGB) [38,39]. All these models are able to handle nonlinear relations and large datasets fairly well, and they demonstrate excellent generalizability if they are well fitted.

A landslide susceptibility assessment by means of machine learning models involves extracting relevant factors from many domains, such as geology, topography, hydrology, vegetation, soil, and human activities [40]. Precipitation is the primary natural trigger of landslides, as it increases soil moisture, softens the soil, reduces shear strength, and causes slope instability. Landslides often have a close relationship with extreme rainfall or prolonged precipitation events [41]. While climate change enhances the uncertainty of extreme precipitation events, it also increases the probability and magnitude of landslides [42]. Although the importance of precipitation in landslide prediction is widely recognized, most previous machine learning studies either focused on annual precipitation, which has a low correlation with landslide occurrence [43], or used daily precipitation data to explore the relationship between landslides and precipitation [44]. In fact, landslide occurrence is often closely linked to extreme rainfall or prolonged rainfall events, meaning that effective antecedent precipitation (EAP) has a strong correlation with landslide occurrence compared to other precipitation indices. Considering EAP during landslide susceptibility assessments is crucial for improving the accuracy of landslide prediction. By capturing the cumulative effects of precipitation, EAP enhances the accuracy and reliability of landslide predictions. Considering precipitation intensity and duration, along with their spatial correlation with landslides, will lead to more precise prediction models. Compared to other factors, the variability of EAP is substantial, adding significant uncertainty to landslide susceptibility assessments. Thus, it is essential to account for landslide susceptibility under various antecedent precipitation probability scenarios.

This study proposes an innovative approach to landslide susceptibility assessments by integrating cumulative rainfall effects through the effective antecedent precipitation (EAP). Specifically, we conducted the following:

• Based on EAP data from 2064 historical landslides, a high-precision landslide prediction model was developed. Compared to coarse-grained precipitation metrics, the EAP data more accurately capture the mechanism of rainfall-triggered landslides, significantly improving the model’s predictive accuracy. Additionally, the analyses of both the mean decreases in the Gini and SHAP values indicate that EAP is a key factor contributing to landslides.
• Using daily precipitation records from 69 meteorological stations, we evaluate eight probability distribution models to characterize EAP across various return periods, thereby quantifying multiple antecedent rainfall scenarios for hazard analysis.
• We generate dynamic landslide susceptibility maps under different rainfall return periods (5, 10, 20, and 50 years), which identify high-risk zones and illustrate how extreme precipitation probability scenarios impact landslide spatial patterns.

These contributions demonstrate a more accurate and scenario-inclusive framework for rain-induced landslide prediction, providing valuable insights for early warning and risk management in mountainous regions.

The structure of this study is organized as follows: Section 1 presents the introduction and reviews the current state of research. Section 2 describes the study area, data sources, data processing, and research methodology. Section 3 presents the results of the landslide susceptibility assessment in Zhejiang Province under different rainfall return periods. Section 4 discusses the implications of the findings. Finally, Section 5 summarizes the main contributions of this study.

2. Materials and Methods

2.1. Landslide in Zhejiang

The study area is in the southeastern coastal region of China, which features a subtropical monsoon climate characterized by hot, rainy summers and cold, dry winters, with precipitation concentrated in the summer months. The terrain is complex, consisting predominantly of mountains and hills, with mountainous regions covering 70.4% of the province’s total area. The elevation gradually decreases from the southwest to the northeast. The geological structure of Zhejiang Province is dominated by the Jiangshan-Shaoxing fault zone, which is marked by extensive faults and folds. This complex geological setting, combined with the province’s concentrated monsoonal precipitation, makes Zhejiang a hotspot for landslide disasters.

For this study, we collected a dataset of 2064 landslide points from the study area and daily precipitation data from 69 meteorological stations (Figure 1a). The temporal span of the landslide dataset is from 1974 to 2015, during which the annual number of landslide occurrences was recorded (Figure 1b). The daily precipitation data cover the period from 1961 to 2024. Most shallow landslides in the study area are triggered by precipitation, with approximately 80% occurring during the peak precipitation period from May to September, which is consistent with the monsoonal distribution in Zhejiang. Landslide occurrence is positively correlated with the precipitation level (Figure 1c). However, the relationship between precipitation and landslides is not strictly linear. For example, let us consider a specific landslide event, which occurred on 26 July 2010. For this landslide, we have compared the daily precipitation data from local meteorological stations and the EAP for the 10 days leading up to the event (Figure 1d). We found that an extreme precipitation event of 106.2 mm was recorded on 24 July 2010, but this event did not immediately trigger a landslide. Instead, the subsequent increase in precipitation over the following 2 days ultimately caused the landslide, as the gradual accumulation of EAP increased the soil moisture, significantly increasing the likelihood of landslide occurrence.

2.2. Framework

The assessment process is divided into four main parts:

• Daily precipitation data processing: Data gathered from meteorological stations over multiple years are employed, and various distribution functions are applied for fitting, where the optimal distribution function is chosen to calculate the return period values for each station in the study area. Interpolation is then performed to generate distribution maps of the EAP under different return periods, which are subsequently used for prediction by the following models.
• Additional data processing: First, it is necessary to collect data related to the topography, geology, hydrology, and other relevant factors of the study area, and a landslide inventory is compiled for the region. In this study, 14 conditioning factors from the research area were collected and subjected to multicollinearity analysis to select the appropriate factors.
• Model training: A set of negative samples equal in number to the 2064 landslide points was created, excluding points located within water systems. These negative samples, together with the positive samples, form the training and validation datasets for the model. The random forest (RF), XGBoost, multilayer perceptron (MLP), k-nearest neighbor (KNN), support vector machine (SVM), and gradient boosting machine (GBM) models are trained. A total of 70% of the landslide points are used for training, while the remaining 30% are used for validation.
• Landslide analysis and mapping: In this phase, the importance of each conditioning factor is calculated. In this study, various methods, including SHAP values and the mean decrease in Gini, are employed to compare the different models and assess the importance of the multifactorial variables.

This framework (Figure 2) describes the steps that were carried out to assess landslide susceptibility in the study area.

2.3. Data

The correct selection of conditioning factors is necessary to derive an accurate landslide susceptibility spatial distribution map [45]. Most previous studies categorized conditioning factors into five primary types: geological, hydrological, land cover, topographical, and other variables [46]. Therefore, we selected 14 conditioning factors that consider the environmental characteristics of the study area. All data were standardized to a common coordinate system and processed into aligned 1 km × 1 km raster grids.

These factors include two geological factors: the distance to faults and lithology. The hydrological factors include the distance to rivers, EAP, the stream power index (SPI), the sediment transport index (STI), and the topographic wetness index (TWI). The topographical factors include a digital elevation model (DEM), the slope, the topographic ruggedness index (TRI), and the slope aspect. The land cover factors include the normalized difference vegetation index (NDVI) and soil texture. In addition, human activities also play a major role in landslide activities [47], such as making any slopes progressively less stable during activities such as cutting of the slope, artificial filling, excavation, and the construction of terrace roads. Therefore, to consider the impact of human activities, the index for the distance to roads was selected. The data sources are listed in

Table 1. Environmental data used in the landslide analysis.

Data	Time	Resolution	Source
Precipitation	1961–2024	Text data	China Meteorological Administration (CMA)
River	–	Line data	Chinese Academy of Sciences, Resource and Environment Science Data Center
Landslide location	1974–2015	Point data	China Water Resources Authority (CWRA)
Road	-	Line data	Chinese Academy of Sciences, Resource and Environment Science Data Center
NDVI	2000–2022	1000 m	National Tibetan Plateau Data Center
Elevation	-	30 m	Shuttle Radar Topography Mission (NASA SRTM)
Soil texture	-	1000 m	Harmonized World Soil Database (HWSD)
Fault	-	Line data	Geoscientific Data & Discovery Publishing System

, where the lithology data are from the Global Lithological Map database, which was compiled by Hartmann and Moosdorf [48].

Two of the variables are directly extracted from the DEM datasets: the slope and the slope aspect. TWI is a commonly used topographic indicator that describes the potential for water accumulation and soil moisture in a given terrain. It combines the terrain’s ability to accumulate water flow in relation to its surface drainage efficiency, making it a key factor in studying hydrological processes and surface moisture distribution. SPI is used to measure the erosive power of flowing water. It reflects the ability of water flow to interact with the terrain and is primarily used to study processes such as river sedimentation, erosion, and soil loss. TRI is used to measure the complexity or roughness of the terrain in an area, which is calculated as the difference in elevation between the highest and lowest pixel values. STI [49] is used to describe the ability of sediment to move under the influence of water flow. It combines flow velocity, discharge, slope, and other topographic features to assess the capacity of the water flow to transport sediment under different conditions. The formulas for these four indicators are as follows:

$$\mathrm{T}\mathrm{WI}=\mathrm{In}\left({\displaystyle \frac{{\mathit{A}}_{\mathit{S}}}{\tan \left(\beta \right)}}\right)$$

(1)

$$\mathrm{SPI}={\mathit{A}}_{\mathit{S}} \times \tan \left(\beta \right)$$

(2)

$$\mathrm{TRI}={\mathrm{DEM} }_{\max }– {\mathrm{DEM}}_{\min }$$

(3)

$$\mathrm{STI}={\left({\displaystyle \frac{{\mathit{A}}_{\mathit{S}}}{22.13}}\right)}^{0.6}\times {\left({\displaystyle \frac{\sin \beta }{0.0896}}\right)}^{1.3}$$

(4)

where the specific catchment area ${\mathit{A}}_{\mathit{S}}$ refers to the catchment area per unit width, β represents the slope, and ${\mathrm{DEM} }_{\mathrm{m}\mathrm{ax}}$ and ${\mathrm{DEM}}_{\min }$ denote the maximum and minimum values of the pixel elevation, respectively.

This study uses 2064 landslide points, which serve as positive samples. An equal number of random points were also generated within the study area to act as negative samples. To avoid sampling areas potentially affected by landslides, all negative samples within a 500 m buffer of known landslide points were excluded. Additionally, all points located within water bodies were removed, as such areas typically lack the geomorphological conditions necessary for landslide occurrence.

To address the different measurement units and spatial resolutions of each conditioning factor, it is essential to standardize the data to eliminate any dimensional differences that could affect the model results. As such, the raster resolution was standardized to 1 km × 1 km. Using well-defined positive and negative samples, along with a multisource database structure, specific target data were extracted at various levels to construct the training and prediction samples for the model.

Accurate discretization of the data is also critical, as it directly influences the quality and depth of subsequent analyses [50]. This study accounts for the characteristics of each factor’s data and categorizes most conditioning factors into five or six levels (

Table 2. Landslide influencing factors and their classes.

Conditioning Factor	Class	Classification Standard
DEM/(m)	6	<100; 100–200; 200–400; 400–600; 600–800; >800
Slope/(°)	6	<2°; 2–5°; 5–10°; 10–15°; 15–20°; >20°
Slope aspect	9	North; northeast; east; southeast; south; southwest; west; northwest; flat
Topographic Wetness Index (TWI)	6	<6; 6–8; 8–10; 10–12; 12–15; >15
Distance to fault(m)	6	<500; 500–1000; 1000–3000; 3000–5000; 5000–10,000; >10,000
NDVI	5	<0.2; 0.2–0.4; 0.4–0.6; 0.6–0.8; >0.8
Distance to river(m)	6	<500; 500–1000; 1000–3000; 3000–5000; 5000–8000; >8000
Effective antecedent precipitation/ (mm)	6	< 25; 25–50; 50–100; 100–200; 200–300; >300
Soil texture	3	Coarse textured; medium textured; fine textured
Distance to road/(m)	6	<100; 100–300; 300–500; 500–1000; 1000–3000; >3000
Terrain Ruggedness Index (TRI)	6	0–73; 73–176; 176–275; 275–382; 382–516; >516
Sediment Transport Index (STI)	6	<1.77; 1.77–7.97; 7.97–22.15; 22.15–44.75; 44.75–77.09; >77.09
Stream power index	6	<−10; −10–−7; −7–−3; −3–−1; −1–1; >1
Lithology	13	Acid plutonics; acid volcanic; basic plutonics; basic volcanics; carbonate sedimentary rock; intermediate plutonics; intermediate volcanics; metamorphics; mixed sedimentary rock; pyroclastics; siliciclastic sedimentary; unconsolidated sediment; undefined

). The spatial distributions of 13 conditioning factors, excluding EAP, are illustrated in Figure 3.

2.4. Methods

2.4.1. Effective Antecedent Precipitation

Not all precipitation prior to a landslide directly triggers such events, meaning that there may be a time lag between precipitation and landslide occurrence. During this interval, precipitation may evaporate, infiltrate, or be absorbed, leading to a reduction in effective precipitation. The remaining precipitation, which is crucial for triggering landslides, is termed EAP [51].

The concept of EAP was first introduced by Kohler and Linsley [52] to predict storm runoff and was later adapted by Crozier and Eyles [53] for landslide forecasting. The basic formula for calculating EAP is as follows:

$${\mathit{R}}_{\mathit{c}}={\mathit{R}}_0+\sum _{\mathit{i}=1}^{\mathrm{n}}{\alpha }^{\mathit{i}}{\mathit{R}}_{\mathit{i}}$$

(5)

where ${\mathit{R}}_{\mathit{c}}$ represents EAP, ${\mathit{R}}_0$ represents the precipitation on the day of the landslide, i represents the number of precipitation days, α represents the effective precipitation coefficient reflecting the constant decay factor of weathered layers, and ${\mathit{R}}_{\mathit{i}}$ represents the precipitation on the ith day before the landslide event. In this research, the topography and precipitation conditions of Zhejiang Province were considered, and a 10 day time scale in the computation of EAP was chosen, which should ensure that we include every relevant intense precipitation event while making sure that interference from unrelated precipitation is minimal. A correlation analysis between different precipitation coefficients and landslide incidence was conducted to select the optimal precipitation coefficient (

Table 3. Correlation analysis of the precipitation coefficient.

Precipitation Coefficient	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
Pearson correlation	0.3093	0.3130	0.3168	0.3207	0.3247	0.3288	0.3325	0.3352	0.3348	0.3278

). The table shows that the highest correlation occurs when the coefficient is 0.8, which is consistent with previous studies [54].

2.4.2. Optimal Probability Distribution Model for Effective Antecedent Precipitation

By examining the recurrence patterns of historical precipitation events, the potential for future precipitation-induced landslides can be assessed [55,56]. Eight kinds of maximum 10 day EAP probability distribution models are used in this research: normal Gaussian, lognormal, gamma, generalized extreme values, Rayleigh, Weibull, exponential, and Pearson type III, each of which is tested to determine its fitness at each meteorological station. In this framework, three validation methods are used for finding the optimal distribution function: the Akaike information criterion (AIC), the Kolmogorov–Smirnov test, and the root mean square error (RMSE), allowing us to calculate EAP at different return periods for each site. These methods jointly evaluate model performance from two perspectives: goodness of fit and predictive accuracy, thereby supporting the selection of the optimal distribution for each station. In cases where the three methods yield different results, a majority-voting strategy was adopted; i.e., the distribution supported by at least two of the three criteria was selected. When no consensus could be reached, due to each criterion favoring a different distribution, RMSE was used as the final determining metric, as it more directly reflects the predictive error in estimating antecedent effective precipitation.

The AIC, a statistical method for model selection introduced by Akaike [57], is expressed as

$$\mathrm{AIC}=2\mathit{k}-2\ln \left({\mathit{L}}^{^}\right)$$

(6)

where $\mathit{k}$ is the number of parameters in the model and ${\mathit{L}}^{^}$ is the likelihood estimate.

In statistical analysis, the Kolmogorov-Smirnov test is a significant nonparametric method for comparing the distributions of two samples [58]. The statistic D represents the Kolmogorov-Smirnov test statistic, which calculates the maximum difference between the cumulative distribution functions (CDFs) of two samples, and is defined as

$$\mathit{D}={ \max }_{\mathrm{x}}\left|{\mathit{F}}_1\left(\mathit{x}\right)-{ \mathit{F}}_2\left(\mathit{x}\right)\right|$$

(7)

where ${\mathit{F}}_1\left(\mathit{x}\right)$ and ${\mathit{F}}_2\left(\mathit{x}\right)$ are the CDFs of the two samples.

The spatial distribution of EAP was fitted using the ANUSPLIN interpolation method, a commonly used interpolation technique developed by the Australian National University [59,60]. This method effectively balances interpolation accuracy and smoothness, combining topography and climate for accurate interpolation [61].

2.4.3. Model Performance Evaluation Methods

This research employs six distinct machine learning models for landslide susceptibility assessments: the RF [62], SVM [63] MLP [64], XGB [65], gradient boosting [66], and KNN [67].

The RF, XGB, and GBM are tree-based ensemble methods that improve model robustness by combining multiple decision trees. The SVM is a kernel-based classifier designed to find the optimal separating hyperplane. The KNN is a distance-based non-parametric method that assigns class labels based on majority voting among the nearest neighbors. MLP belongs to neural network models and is a feedforward network with multiple hidden layers; it is capable of modeling nonlinear relationships.

To ensure stable performance and fair comparison among different machine learning models, hyperparameter tuning was conducted separately for each model using the GridSearchCV method. All models were trained and validated using 5-fold cross-validation to mitigate the risk of overfitting. During training, feature data were standardized using StandardScaler, and sample imbalance was addressed using the synthetic minority over-sampling technique (SMOTE). All computations and experiments were performed in the Python 3.11.7 environment.

To evaluate model performance comprehensively, several metrics are utilized, including accuracy, recall, the area under the curve (AUC) value, and receiver operating characteristic (ROC) curve analysis. Ideally, the ROC curve should closely approach the y-axis; if the ROC curve falls below the y = x line, it indicates poor model performance. The AUC value reflects the model’s discriminative ability, with an ideal value of 1.

This study also uses five metrics—accuracy, recall, the F1 score, precision, and logarithmic loss—to evaluate model performance. Their respective formulas are as follows:

$$\mathrm{Accuracy}={\displaystyle \frac{\mathit{TP}+\mathit{TN}}{\mathit{TP}+\mathit{TN}+\mathit{FP}+\mathit{FN}}}$$

(8)

$$\mathrm{Recall}={\displaystyle \frac{\mathit{TP}}{\mathit{TP}+\mathit{FN}}}$$

(9)

$$\mathit{F}1=2 \times {\displaystyle \frac{\mathrm{Precision} \times \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}}$$

(10)

$$\mathrm{Precision}={\displaystyle \frac{\mathit{TP}}{\mathit{TP}+\mathit{FP}}}$$

(11)

$$\mathrm{Log} \mathrm{Loss}=-{\displaystyle \frac{1}{N}}\sum _{\mathit{i}=1}^N[y_i\times \log \left(y_i^{^}\right)+(1-y_i)\times \log \left(1-y_i^{^}\right)]$$

(12)

where TP is the number of true positive cases, TN is the number of true negative cases, FP is the number of false positive cases, FN is the number of false negative cases, $N$ represents the total number of samples, $y_i$ is the true label of the$i$th sample (either 0 or 1), and $y_i^{^}$ is the model’s predicted probability that the $i$th sample belongs to class 1, which also ranges from 0 to 1.

3. Results

3.1. Effective Antecedent Precipitation Analysis

The optimal distribution models of EAP at the meteorological stations revealed distinct spatial variations (Figure 4a). The generalized extreme value distribution and lognormal distribution dominate the study area, with the former primarily prevailing in the northern coastal region of Zhejiang, while the latter is more prevalent in the southern coastal region of Zhejiang. Frequency cumulative distribution graphs for various optimal distribution functions are presented in Figure 4b–e, which show good fits between the selected models and the data, indicating statistical validity and minimal prediction errors. Figure 5 presents a comparison of probability density histograms for various fitted distributions at the four representative stations shown in Figure 4. Based on the optimal distribution functions for each station, the EAP for different return periods was calculated and visualized through ANUSPLIN interpolation.

The results reveal substantial regional variation in the EAP distribution across Zhejiang (Figure 6). The north–central region shows relatively low EAP values, whereas the western, southwestern, and coastal areas exhibit relatively high EAP values, which are consistent with the province’s precipitation patterns. The mountainous and hilly terrain in the western and southwestern regions leads to enhanced uplift and condensation of moisture due to the complex topography, resulting in increased precipitation. Additionally, coastal areas, including the Zhoushan Islands, Ningbo, and Taizhou, benefit from their proximity to the ocean, where marine moisture transport and topographic factors further increase precipitation. In contrast, northern Zhejiang, predominantly the Hangjiahu Plain, experiences less precipitation due to minimal topographic influence and greater distance from the ocean. As the return period increases, the cumulative range and intensity of the EAP significantly increase, with maximum EAP values reaching 426.65 mm for the 50-year return period.

3.2. Model Comparison and Validation

Given the numerous factors involved in evaluating geological disasters, statistical multicollinearity is often unavoidable, potentially hindering the accurate analysis of the relationships between susceptibility models and geological disasters. Therefore, prior to model establishment, correlation and multicollinearity analyses were conducted on the 14 selected factors to ensure their appropriateness. The multicollinearity analysis was conducted using Stata 18, and the results indicated no significant multicollinearity issues among the 14 factors. Specifically, the variance inflation factors for all 14 influencing factors were well below the threshold of 10, and the tolerance values were above 0.1.

In the landslide susceptibility assessment, the contribution of each factor to the model can be analyzed using the mean decrease in Gini and SHAP values. The mean decrease in Gini determines the contribution of each feature to the model by evaluating the improvement in purity brought by each feature to the model, thereby measuring the importance of the features. This indicator is commonly used in RF models [68].

The SHAP value model was used to assess the performance of the XGB and GBM models by ranking the importance of the factors (Figure 7a). EAP shows the highest contribution, followed by the TRI, the slope, the SPI, and the distance to roads. The SHAP visualizations (Figure 7b,c), shown by the red points, are concentrated on the right side, indicating a strong positive influence of the EAP on landslide occurrence. The TRI, SPI, and slope also have positive impacts, while the distance to roads, the NDVI, and the distance to fault lines mostly show negative effects. This suggests that areas with higher EAP values, more rugged terrain, higher SPI values, steeper slopes, proximity to roads, less vegetation, and proximity to fault lines are more susceptible to landslides. The results indicate that EAP has a significant impact on the prediction outcomes, which are clearly related to the widespread spatiotemporal distribution of rainfall-induced landslides in the study area, where high-frequency rainfall events are common [69,70]. Under the monsoon climate conditions in Zhejiang Province, rainfall is concentrated in the summer, with precipitation from May to September accounting for 69% of the annual total. Particularly during the typhoon season and the plum rain season, such heavy rainfall/prolonged precipitation greatly contributes to the occurrence of landslides. This further emphasizes the importance of considering EAP in landslide susceptibility assessments.

Machine learning involves both training and validation phases. For this study, the research samples were randomly divided at a 70:30 ratio, with 70% of the data used for training and 30% for validation. The testing dataset includes 640 landslide points and 599 non-landslide points. Model performance was evaluated using the accuracy, recall, F1 score, log loss, and AUC values. Model evaluation results and optimized hyperparameters are presented in

Table 4. Performance comparison and hyperparameter settings of machine learning models.

Model	Accuracy	Recall	F1 Score	Log Loss	Optimized Hyperparameters
RF	89.02%	89.66%	0.8909	0.2844	n_estimators = 500; max_depth = 20; min_samples_split = 2; min_samples_leaf = 1; max_features = ‘sqrt’
XGB	89.02%	89.82%	0.8910	0.2417	n_estimators = 200; max_depth = 3; learning_rate = 0.2; subsample = 0.9; colsample_bytree = 0.8
MLP	81.60%	83.20%	0.8188	0.3836	hidden_layer_sizes = (64, 32); activation = ‘relu’; solver = ‘adam’; alpha = 0.01; learning_rate_init = 0.001; max_iter = 1000; batch_size = ‘auto’; early_stopping = True
KNN	84.26%	83.04%	0.8406	0.4056	n_neighbors = 10; weights = ‘distance’; metric = ‘manhattan’
GBM	89.35%	90.15%	0.8942	0.2548	n_estimators = 500; max_depth = 3; learning_rate = 0.1; min_samples_split = 2; subsample = 0.9
SVM	86.28%	86.75%	0.8633	0.3130	kernel = ‘rbf’; C = 10; gamma = ‘scale’

. The receiver operating characteristic curve is shown in Figure 8.

The models generally perform well in terms of accuracy and ROC. Among them, the decision tree models XGB, GBM, and RF outperformed the others, all with accuracy, recall, and F1 scores exceeding 89% and relatively low log loss scores. The SVM model also performed reasonably well, with accuracy, recall, and F1 scores above 86% and a relatively low log loss. However, the KNN and MLP models performed poorly. Although their accuracy is acceptable, their high log loss indicates that their predictions deviate significantly from the actual distribution.

3.3. Landslide Results Under Different Return Periods

Using the trained RF model, predictions were made for a 1 km × 1 km grid across the entire study area. Landslide susceptibility probabilities were categorized into six levels using the natural breaks method: extremely low risk (0–0.18), low risk (0.18–0.33), moderate risk (0.33–0.50), elevated risk (0.50–0.67), high risk (0.67–0.84), and extremely high risk (0.84–1). These results are illustrated in Figure 9.

From the results, we identify three distinct high-susceptibility zones in Zhejiang Province: the southern coastal mountainous region, the western mountainous area, and the hilly region of Shaoxing–Taizhou in central Zhejiang. In contrast, the Hangjiahu Plain, the Ningshao Plain, and the Jinqu Basin are mostly categorized as low-risk zones. The rugged and undulating terrain of the southern mountainous region aligns with higher susceptibility levels, demonstrating a consistent relationship between landslide susceptibility and fundamental geographic patterns.

Next, we further examined the landslide susceptibility map generated by the XGB model for the 20-year return period. To evaluate the accuracy of the susceptibility map rigorously, we overlaid confirmed landslide points for the 20-year return period, with the aim of verifying the alignment between the mapped landslide areas and actual landslide events. The verification results, as shown in Figure 10, highlight four notable landslide clusters: Region 1 near Huzhou–Anji; Region 2 in Quzhou, western Zhejiang; Region 3 in the eastern part of the province (Shaoxing–Shengzhou); and Region 4 in the southern mountainous area around Wenzhou. The analysis reveals that most landslide points fall within high-risk or extremely high-risk zones, with high-risk levels for Regions 1, 2, 3, and 4 of 60.7%, 68.95%, 94.25%, and 98.60%, respectively. The close correspondence between actual landslide locations and the predicted susceptibility map underscores the XGB model’s effectiveness in forecasting landslide susceptibility and provides valuable insights for geological disaster risk assessments and management.

4. Discussion

4.1. Importance of Effective Antecedent Precipitation in Landslide Disaster Prediction

According to the literature review in Section 1, previous research on landslide susceptibility assessments identified that precipitation and particularly its complex spatiotemporal distribution are an important triggering factor of landslide disasters [71]. Most previous studies have incorporated annual average precipitation into landslide susceptibility assessments [72,73]. While this approach captures the spatial distribution of precipitation, it fails to reveal the impact of specific landslide events. Other studies have considered daily and hourly precipitation as influencing factors [74] to analyze individual landslide events, but they do not account for large-scale landslide hazards. In contrast, EAP, combined with different return periods, reflects the cumulative impact of precipitation on landslides across various temporal scales. Specifically, it accounts for the temporal decay of rainfall, providing a more accurate assessment of its effect on slope stability.

EAP is a precipitation gauging measure, which considers its cumulative effects and measures the degree of soil moisture saturation. According to He [75], there is a strong exponential relationship between soil moisture and antecedent precipitation during the early stages of landslides. This further emphasizes that EAP is indispensable for landslide prediction. Abraham [76] improved landslide early warning performance by including antecedent soil moisture. In particular, it was shown that, in cases where the soil moisture has a very low initial value, intense precipitation is able to trigger a landslide, while less intense precipitation can trigger landslides once the soil is already wet. In this study, the RF analysis identified EAP as the most influential factor in landslide susceptibility, surpassing all other variables. This finding supports the hypothesis that EAP is a crucial component in landslide susceptibility mapping.

The present study further adds innovation to the field of landslide susceptibility mapping by introducing return periods and making susceptibility assessments for the 5-year, 10-year, 20-year, and 50-year intervals. This is an approach that accounts for the local geographic conditions and the spatial distribution characteristics of landslide events for different precipitation intensities. In particular, by developing multitemporal susceptibility maps, we gain insight into the dynamic evolution of landslide risk, which helps identify potential high-risk areas under different precipitation scenarios.

The approach used in this paper is particularly well suited to hilly and mountainous regions with lush vegetation and abundant rainfall. In such environments, intense and frequent precipitation events gradually saturate the soil, and EAP indicators help effectively capture this process [77,78]. As a result, the landslide susceptibility model incorporating EAP performs optimally in these humid, vegetated, and hilly terrains, where the cumulative antecedent rainfall plays a decisive role in slope stability [79,80]. The selection of the EAP time window also plays a critical role in landslide prediction. Although there is currently no universally accepted standard for determining the optimal window length, existing studies suggest that a 10-day window performs well in humid subtropical regions. For instance, Zhao [81] adopted a 10-day EAP window in a study on landslide disasters in Sichuan Province and achieved favorable results. Similarly, Ma [82], using data from Zhejiang Province, proposed a method based on a power-law relationship between precipitation and landslide occurrence, confirming the applicability and accuracy of the 10-day window for landslide prediction.

Regions characterized by heavy monsoonal rains and thick vegetation cover can therefore expect more reliable predictions from our model, whereas drier or sparsely vegetated areas might require the calibration of the EAP parameters [83,84]. Overall, the proposed framework achieves its best adaptability and predictive power in precipitation-rich, forested hill countries, which are common in many subtropical and tropical mountainous regions.

4.2. Model Interpretation and Technical Limitations

This study compares six traditional machine learning models for landslide prediction in terms of a binary classification problem: whether a landslide occurs or not. The XGB model was selected based on its good performance, and its confusion matrix shows that it produced 556 TPs, 73 FPs, 63 FNs, and 547 TNs. This indicates that the model correctly identified 556 landslide events and successfully excluded 547 non-landslide areas. However, the model incorrectly classified 63 non-landslide points as landslide points and 73 landslide points as non-landslide points. Overall, the model performs well in landslide detection tasks, exhibiting high accuracy and strong discriminative ability.

By contrast, the KNN and MLP models showed weaker performance, there are several potential reasons that might explain the suboptimal performance of the KNN and MLP models. For the KNN model, although increasing the value of k generally reduces model complexity, its performance still lags behind that of decision trees. This may be due to the high dimensionality of the features or the unclear classification boundary at the 0.5 probability threshold between the landslide and non-landslide classes. As a result, the model struggles to form stable and representative neighborhoods in a high-dimensional space [85,86]. Increasing k can therefore introduce more noisy samples rather than meaningful neighbors, further degrading generalization [87]. As for the MLP model, the loss function converged during training, and the performance difference between the training and validation sets was minimal, indicating no clear overfitting or underfitting. However, overall predictive accuracy remained relatively low, possibly due to several factors: a limited training sample size inadequate for the effective generalization of deep networks and the limited expressive power of input features failing to provide sufficient discriminatory information [88,89]. Future work could focus on improving feature engineering, expanding the training dataset, or optimizing the network structure to enhance model performance.

The selection of analysis units plays a critical role in landslide susceptibility modeling. To better represent spatial heterogeneity, some studies have adopted geomorphology-based units, such as sub-watersheds or slope segments, which reflect terrain-driven spatial processes and help to reveal the geomorphic controls and distribution patterns of landslides. In this study, a regular grid with a resolution of 1 km² was used as the basic analysis unit. This approach offers two key advantages: it enables good spatial resolution compatibility with multi-source datasets such as climate, soil, topography, and vegetation, thereby facilitating data integration and regional-scale modeling; the regular grid structure provides a uniform spatial framework, which is beneficial for conducting consistent analyses and risk comparisons across large areas.

For the return period calculations, we selected the maximum value of the moving sequence of the EAP for each meteorological station and year for the fitting of the return period. Although this reflects the precipitation trends under extreme precipitation scenarios, it still has certain limitations. The moving sequence’s maximum value only considers extreme values within a single time window and does not fully capture precipitation variations over longer timescales, leading to an increase in the landslide susceptibility probability at different return periods. Furthermore, the spatial heterogeneity of precipitation and climate differences across different regions may affect the accuracy of the return period calculation. Therefore, future studies could introduce more complex spatiotemporal analysis methods by incorporating additional meteorological factors and regional climate characteristics to improve the accuracy of precipitation return period assessments.

4.3. Uncertainty of Different Precipitation Types on Landslide Disasters

The rainfall process is an essential factor in determining regional susceptibility to landslides because it affects the moisture content of rocks and soil, reducing their shear strength and thus promoting landslides. However, the diverse and complex nature of rainfall and soil moisture has introduced significant uncertainties into the model’s outputs when simulating the various factors influencing landslide risk.

The geographical location of Zhejiang Province is characterized by frequent typhoons and monsoon precipitation, which are characterized by extremely heavy, short-duration precipitation events (typhoons) and continuously long events, such as plum rains [90]. Typhoon precipitation generally saturates soil, destabilizing the geological formations of slope surfaces, and induces landslides. Deformations due to landslides are linked closely to the intensity and duration of typhoon-induced precipitation events [19]. As well as being characterized by very high precipitation intensities over short durations, typhoons have an uneven spatial distribution and unpredictable landfall locations and paths. These factors also contribute to the suddenness and unpredictability of landslide occurrence. Moreover, plum rain season precipitation is mediated by the East Asian summer monsoon, and its year-to-year variability adds even more uncertainty to landslide susceptibility assessments [91].

Furthermore, soil moisture exists in a variety of forms. However, in Central Asian countries, including Tajikistan and Kazakhstan, the water content is influenced not only by precipitation but also by snowmelt from local mountains and thawing permafrost [92]. The melting of snow in the mountains releases large volumes of water, which rapidly infiltrate the ground, increasing saturation and, consequently, reducing shear strength. This, in turn, heightens the risk of landslides, particularly in mountainous regions [93]. The rate of snowmelt is by far influenced by many aspects relative to temperature change, the incidence of sunlight, micro-topography, and the physical properties of the snow itself, complicating landslide prediction and assessments.

In conclusion, many uncertainties exist in the prediction of landside disaster events due to the interaction among diverse precipitation types and forms of soil moisture. Several precipitation types and soil-moisture forms may co-occur in space and time, which will enhance the highly complex, nonlinear mechanisms of landslide initiation. Therefore, future landslide risk assessments should ideally be multidimensional in their approach in order to outline the combined effects of various precipitation types and soil environments with a view of formulating detailed, targeted prevention and evaluation strategies.

4.4. Landslide Disasters in the Context of Future Climate Change

Research indicates that with global warming, the frequency and intensity of extreme weather events have increased globally, and future climate changes are likely to lead to significant increases in extreme precipitation levels worldwide [11]. Studies have shown that various precipitation indices used to study Central Asia exhibit spatial diversity and heterogeneity, with a general trend toward increased moisture [94]. This trend is not limited to Central Asia: China Climate Change Blue Book (2021) reports that the average annual precipitation in China has shown an increasing trend over the past 40 years, exacerbating the risks associated with extreme weather events. Recent studies have clearly indicated that daily precipitation intensity in southeastern China is projected to increase significantly during 2041–2060 under both RCP4.5 and RCP8.5 emission scenarios, reflecting the region’s heightened hydrological sensitivity to climate change [95]. Qin employed the RegCM4 regional climate model driven by GFDL_ESM2M to simulate changes in the frequency and intensity of extreme precipitation events across major river basins in China under the RCP4.5 scenario. Qin’s findings suggest that, compared to the historical period, southeastern China will likely experience a substantial increase in extreme precipitation occurrences, with the annual total precipitation from very wet days (R95p) increasing by more than 10 mm and the maximum 5-day precipitation value (RX5day) rising by over 4 mm [96]. These changes contribute to enhanced soil moisture accumulation and saturation, thereby increasing antecedent effective precipitation, which plays a crucial role in hydrological triggering mechanisms. Moreover, the rise in antecedent effective precipitation has been identified as a key contributing factor to shallow landslides, as increased precipitation elevates both surface and groundwater levels. Intense rainfall events can generate rapid runoff, alter slope stability, and significantly raise soil moisture content, thereby elevating landslide risks [97]. Additionally, climate change can cause the permafrost in plateau areas to melt, leading to ground subsidence and sliding and accelerating mountain snowmelt, which further increase soil moisture and slope instability, ultimately triggering landslides [98].

To predict and manage landslide disasters accurately in the context of future climate change, enhancing the predictive capabilities of climate models and improving early warning systems for extreme weather events are crucial. In particular, integrating high-resolution climate projections under various shared socioeconomic pathway (SSP) scenarios can help assess the sensitivity of landslide-prone areas to changes in precipitation patterns. Moreover, coupling climate outputs with physics-based or machine learning-based landslide susceptibility models allows for a more comprehensive risk assessment, enabling targeted mitigation strategies and adaptive planning.

5. Conclusions

This study evaluates landslide susceptibility based on EAP for different return periods by incorporating 14 factors related to geology, topography, and hydrology. Six machine learning models were trained to assess landslide risk. The following conclusions are drawn.

The best-fit distribution models for most stations in the study area are the generalized extreme value and lognormal distributions. The spatial distribution maps of EAP for the different return periods show higher values in coastal and western Zhejiang mountainous regions and lower values in the central and northern Zhejiang areas. As the return period increases, EAP generally shows an upward trend.

Among the six machine learning models used here, XGB outperformed the others with an AUC of 0.96 and an accuracy of 89%. Feature importance assessments using methods such as SHAP values and the mean decrease in Gini indicate that the most significant contributing factor to the model is EAP, followed by the TRI, the slope, the distance to roads, and the SPI.

From the landslide susceptibility assessments under varying return periods (5, 10, 20, and 50 years), we identified three high-susceptibility zones: the southern coastal areas, the western mountainous region, and the hilly Shaoxing–Taizhou area in central Zhejiang. In contrast, the central and northeastern plains predominantly fall within lower-risk zones.

Overall, this study combined the recurrence period of EAP with landslide susceptibility maps, offering a fresh perspective that contributes to a more comprehensive assessment of landslide disaster risk. Future work could explore more advanced, interpretable, and integrated machine learning models to advance the field further.