Study on Landslide Susceptibility Based on Multi-Model Coupling: A Case Study of Sichuan Province, China

Abstract

Landslides are among the most prevalent geological hazards and are characterized by their high frequency, significant destructive potential, and considerable incident rate. Annually, these events lead to substantial casualties and property losses. Thus, conducting landslide susceptibility assessments in the regions vulnerable to such hazards has become crucial. In recent years, the coupling of traditional statistical methods with machine learning techniques has shown significant advantages in assessing landslide risk. This study focused on Sichuan Province, China, a region characterized by its vast area and diverse climatic and geological conditions. We selected 13 influencing factors for the analysis: elevation, slope, aspect, plan curve, profile curve, valley depth, precipitation, the stream power index (SPI), the topographic wetness index (TWI), the topographic position index (TPI), surface roughness, fractional vegetation cover (FVC), and slope height. This study incorporated the certainty factor method (CF), the information value method (IV), and their coupling with the decision tree C5.0 model (DT) and a logistic regression model (LR) as follows: IV-LR, IV-DT, CF-LR, and CF-DT. The results, validated by an ROC curve analysis, demonstrate that the evaluation accuracy of all six models exceeded 0.750 (AUC > 0.750). The IV-LR model exhibited the highest accuracy, with an AUC of 0.848. When comparing the accuracy among the models, it is evident that the coupling models outperformed the individual statistical models. Based on the results of the six models, a landslide susceptibility map was generated, categorized into five levels. High and very high landslide risk zones are mainly concentrated in the eastern and southeastern regions, covering nearly half of Sichuan Province. Medium-risk areas form linear distributions from northeast to southwest, occupying a smaller proportion of the area. Extremely low- and low-risk zones are predominantly located in the western and northwestern regions. The density of the landslide points increases with higher risk levels across the regions. This further validates the suitability of this research methodology for landslide susceptibility studies on a large scale. Consequently, this methodology can provide crucial insights for landslide prevention and mitigation efforts in this region.

1. Introduction

Geological disasters are occurring with increasing frequency on a global scale, causing ever-larger devastation and losses for local communities and governments. Landslides, a broad term encompassing the downward movement of rocks, soil, or debris, are triggered by various natural phenomena or human activities, including earthquakes, flash floods, road construction, deforestation, and mining [1]. As one of the most prevalent types of geological hazards, landslides pose a frequent threat to individuals residing in mountainous regions. Characterized by their extensive distribution, significant destructiveness, and high frequency of occurrence, landslides annually result in substantial casualties and property losses [2]. In China, the terrain exhibits a terraced distribution, with abundant mountains and plateaus in the western regions, making it a highly susceptible area for landslide disasters. Every year, landslide incidents occur frequently in these areas [3]. According to data from the “China Statistical Yearbook”, between 2000 and 2019, natural disasters occurred approximately 320,000 times, resulting in a total economic loss of approximately USD 9.894 billion for the country. Among these disasters, landslides stand out prominently, accounting for a staggering 220,000 occurrences and constituting 70.2% of the total occurrences of geological disasters. In Chongqing, one of the four major geological disaster-prone areas in China [4], geological hazards cause approximately 40–60 fatalities annually and result in direct economic losses of USD 40–55 million, accounting for over 20% of the city’s natural disaster-related losses. Given the significant adverse impacts of landslides in China and globally, predicting landslide probability and creating landslide susceptibility maps have become increasingly important. These tools are crucial for effective government management, future land use planning, and current risk mitigation efforts, serving as the primary means to avoid landslide risks [5].

In the past decade, the study of landslide susceptibility assessments has gained increasing attention. Generally, susceptibility models can be categorized into qualitative and quantitative analyses [6]. Qualitative methods, such as expert scoring and the Analytic Hierarchy Process (AHP) [7,8], require researchers to have extensive field investigation experience and a solid theoretical foundation. These methods are limited by subjectivity and perception, leading to discrepancies between theory and practice, but they were widely used in the early stages of landslide risk research [9,10]. In the early stages, quantitative methods primarily utilized mathematical and statistical models, including the frequency ratio method (FR) [11], certainty factor method [12], entropy value method [13], and information value method [14]. In the Shivalik region of Nepal, Bharat Prasad Bhandari et al. [15] studied landslide susceptibility using the frequency ratio method, the Shannon entropy method (SE), the weight of evidence (WoE), and the information value model. Validation and comparison through AUC curves indicated that the WoE model had a better predictive accuracy than the IV, FR, and SE models. The accuracy of the WoE model was 85%, while the accuracy of the other three models was below 79%, with an accuracy difference of about 6%. However, the accuracy difference between the other three models was not significant. All the models were suitable for assessing landslide susceptibility in the region, providing critical information related to the sustainability of roads and settlements in the study area. However, the models were relatively simplistic, relying only on traditional mathematical calculations and lacking advanced methodologies.

With the advent of the big data era and the further development of computer science, remote sensing technology, and geographic information systems (GISs) [16], many researchers began to use machine learning models such as support vector machines (SVMs) [17], random forests [18], decision trees, BP neural networks, MaxEnt models, multilayer perceptrons (MLPs) [19], logistic regression models [20], and deep learning models to study landslide-prone areas. These methods have shown better performance compared to traditional mathematical and statistical models, with the research results demonstrating a certain level of reliability [21]. Osman Orhan et al. [22] utilized five machine learning techniques—artificial neural networks (ANNs), logistic regression (LR), support vector machines (SVMs), random forests (RFs), and classification and regression trees (CARTs)—to assess and map landslide susceptibility in the Alahavzi–Kabiser River basin in Turkey. They compared and validated the performances of these techniques using ROC curves and sensitivity and specificity tests. All the models demonstrated acceptable landslide susceptibility mapping performances, with the ANN model showing the highest landslide susceptibility prediction capability in this region. However, all five models belong to the same category of methods, resulting in a lack of comparison with different experimental approaches. As research progressed in the field of landslide prediction, researchers such as Can Yang and Lei-Lei Liu [23] moved beyond using single machine learning models and proposed a new approach that optimized models through Bayesian sample ratio optimization. This method considers the impacts of different proportions of training and testing sets on model performance, yielding an optimal positive-to-negative sample ratio. Furthermore, using this optimal signal-to-noise ratio, they developed improved models and generated corresponding landslide susceptibility maps. The experimental results indicated that optimizing the signal-to-noise ratio enhances the performance of support vector machines (SVMs), random forests (RFs), and gradient boosting decision trees (GBDTs). Although single models and their optimized applications often achieve a high accuracy, there are still limitations that can be addressed through further methodological improvements. In recent years, researchers have begun to couple statistical models with machine learning models [24] to enhance study precision. For instance, Haishan Wang et al. [25] combined the information value method with logistic regression to develop an evaluation model for landslide susceptibility in Shuangbai County. The use of coupled information enabled the logistic regression model to perform exceptionally well in assessing landslide susceptibility in Shuangbai County, surpassing the effectiveness of single information models. Notably, in high-risk areas, the coupled model can more accurately predict the likelihood of landslides, which is especially significant in regions with high densities of geological hazard points. Therefore, the authors concluded that coupled models are not only essential tools for evaluating landslide susceptibility but also provide a reliable basis for disaster mitigation planning by the relevant authorities. Although significant research has been conducted both domestically and internationally on landslide susceptibility mapping using machine learning methods [26,27,28], there is still no consensus among scholars on the most suitable approach. It is necessary to further compare the potential of coupling different machine learning methods with traditional statistical models in landslide susceptibility modeling and mapping. Additionally, the results of these coupled models should be compared with those of traditional models to determine the best approach. Currently, this comparative research is limited. Therefore, this paper analyzes the performance and applicability of different model choices in landslide susceptibility mapping by comparing the coupling of machine learning models with statistical models, as well as evaluating their respective advantages and limitations.

The area of this current study is Sichuan Province, which is located within the first and second steps of China’s three major topographic steps. It is situated in the transition zone between the Qinghai–Tibet Plateau (first step) and the middle and lower reaches of the Yangtze River Plain (third step) and is characterized by significant elevation differences, with higher altitudes in the west and lower altitudes in the east. This region features diverse geological types and lies on the Mediterranean–Himalayan volcanic seismic belt, which has experienced numerous destructive earthquakes and frequent moderate-to-minor seismic activity. The eastern part of the province is the Sichuan Basin, which experiences frequent foggy weather and high humidity, leading to soil loosening due to moisture infiltration. Compared to other regions, the unstable foundation in Sichuan makes it more prone to landslide disasters, with frequent small-to-medium size landslides [Appendix A]. Yingying Xue et al. [29] evaluated the social vulnerability of Sichuan Province by establishing a multidimensional indicator system, combining both quantitative and qualitative analysis models. They employed GIS technology for a spatial distribution analysis and validated the vulnerability results using historical disaster case studies. This study revealed the spatial pattern of natural disaster vulnerability in Sichuan Province: the northwest region exhibits lower vulnerability, while the southeast region shows higher vulnerability. Cities with high vulnerability are relatively concentrated, whereas those with low vulnerability are more dispersed. This study provides policy recommendations, including improvements to infrastructure and public services, to enhance disaster resilience in Sichuan Province. This landslide hazard analysis offers practical significance for mitigating vulnerability across various regions.

Most current research focuses on small areas, making it challenging to apply the findings in practice. This study area, covering a large portion of southwestern China, was used to create a landslide susceptibility map that will aid the Sichuan provincial government in macro-scale planning. This map will provide scientific and technical support for disaster early warning systems and resource protection.

2. Study Area and Methodology

2.1. Study Area

Sichuan Province, located in southwestern China, spans a vast inland area with geographical coordinates ranging from 92°21′ to 108°12′ E and from 26°03′ to 34°19′ N, stretching over 1075 km from east to west and 900 km from north to south, covering a total area of 486,000 square kilometers, as shown in Figure 1a. The geographical features of the Sichuan Basin are highly diverse. It connects with the Qinghai–Tibet Plateau in the northwest, borders the Hunan–Hubei mountainous area in the southeast, adjoins the Qinling Mountains and the Loess Plateau in the north, and neighbors the Yunnan–Guizhou Plateau in the south. The terrain includes mountains, plateaus, hills, and plains, with significant elevation variations ranging from 190 m to 7143 m and an average elevation of approximately 3750 m. The climate types are diverse, influenced by geographic location and topography, and can be classified into alpine, subtropical, and mid-subtropical humid climate zones. Sichuan Province is rich in water resources, with a dense river network and annual precipitation increasing from west to east. However, some areas within the Sichuan Basin receive less precipitation compared to the surrounding regions. This region’s complex geological structure and frequent seismic activity [30] have resulted in a high number of historical landslide disaster points, which are primarily distributed in the eastern and southern regions, as shown in Figure 1b.

2.2. Mathematical and Statistical Methods

The information value method and the certainty factor method are traditional geological hazard assessment techniques that are widely applied in landslide susceptibility studies. The IV model provides a measure of the relative importance of each factor and is used to construct landslide susceptibility maps. Its main advantage is its strong interpretability, clearly indicating the impact of each factor on landslide occurrence. The CF model builds on the IV model by offering a more precise normalization. These methods provide an intuitive understanding of the landslide triggering mechanisms by assessing the influence of various factors, thereby assisting in the identification of high-risk areas.

• Information Value Method

The information value method, which is based on information theory, is a statistical predictive approach primarily employed in environmental geological research, particularly in the spatial predictions of landslides and slope stability [31]. It converts the measured data of landslide-triggering factors such as elevation and slope into information values that reflect landslide susceptibility. These information values intuitively illustrate the specific roles and influences of different factors in the formation and development of landslides [32]. The formula is provided below:

$$I_j=\sum _{i=1}^n\mathit{ln}{\displaystyle \frac{\frac{N_i}{N}}{\frac{S_i}{S}}}$$

(1)

In this formula, $N_i$ represents the number of landslide points in the ith attribute category of a specific evaluation factor; $N$ denotes the total number of landslide points in the study area; $S_i$ represents the landslide area in the ith attribute category of a specific evaluation factor; and $S$ represents the total landslide area in the study area. $I_j$ represents the total information value of the evaluation factor unit, where a higher value indicates a higher landslide occurrence rate under the corresponding factor influence.

2.

Certainty Factor Model

The certainty factor model, which was proposed by Shortliffe, is a probability function within the realm of bivariate statistical analysis. It is utilized to assess the sensitivity of various factors, such as elevation, slope, and geological structure, to disaster events like landslides and slope instability. In this study, it was applied to analyze the sensitivity of various factors to landslide occurrence [33]. The calculation formula is as follows:

$$\begin{array}{c}CF=\left\{\begin{array}{c}{\displaystyle \frac{{PP}_a-{PP}_s}{{PP}_a\left(1-{PP}_s\right)}}{ PP}_a\ge {PP}_s\\ {\displaystyle \frac{{PP}_a-{PP}_s}{{PP}_s\left(1-{PP}_a\right)}}{ PP}_a>{PP}_s\end{array}\right.\end{array}$$

(2)

In this formula, ${PP}_a$ represents the conditional probability of landslide disasters occurring in evaluation factor category “a”. In this study [34], this is expressed as the ratio of the number (or area) of landslide disasters in evaluation factor category “a” to the total area of category “a”. ${PP}_s$ signifies the prior probability of landslide disasters occurring in the entire study area. In this research, this is represented as the ratio of the total number (or area) of all disasters in the study area to the total area of the study area. In a given study area, ${PP}_s$ is typically a constant value. $CF$ indicates the certainty factor of landslide disaster occurrence; a higher value indicates a higher certainty of landslide disaster occurrence.

2.3. Machine Learning Models

The selection of the logistic regression model is based on its ability to handle nonlinear relationships and assess the impact of various factors on the probability of landslide occurrence. This model is well-suited for managing large datasets with many variables, as it can evaluate each variable’s contribution to landslide risk while accommodating complex nonlinear relationships and high-dimensional data. The decision tree model was chosen because it effectively handles complex nonlinear relationships and provides clear classification rules. This model is particularly suitable for conducting layered assessments of landslide susceptibility, offering explicit decision-making criteria based on the data.

• Decision Tree C5.0 Model

A decision tree is a supervised learning method used for classification and regression that infers simple decision rules based on data features to predict the target variable. It consists of root nodes, internal nodes, and leaf nodes (terminal nodes), and the creation process involves multiple stages or layers of decision-making. Each node makes a binary decision based on data features, progressively splitting until reaching a leaf node, which separates the categories. As illustrated in Figure 2, the architecture of the decision tree model includes elements such as nodes, conditions, and productions [35]. The ID3 series (such as ID3, C4.5, and C5.0) contains renowned decision tree algorithms. In this study, the C5.0 algorithm was utilized. Each data tuple needed to contain both conditional attributes and category value attributes, where the conditional attributes could be discrete or continuous values and the categories needed to be discrete values. This study quantified the factors influencing landslides as raster image data, converting image pixels into tuples with pixel grayscale values as attribute values, and then applied the C5.0 algorithm [36].

In Figure 2, A represents a classification tree with a four-dimensional feature space and three classes, namely the feature values. The thresholds a, b, c, d, and e are represented by A, B, and C, which correspond to the class labels.

2.

Logistic regression model

Logistic regression is a machine learning algorithm with a simple principle and stable performance. It is mainly applied to solve binary classification problems [37]. In particular, it has been widely used in the field of landslide susceptibility assessments. The LR model uses a sigmoid function to restrict the output to the interval [0,1], thus establishing a predictive model for the probability of an event. Its advantage is that it accurately captures nonlinear relationships and requires relatively little in the way of tuning hyperparameters. By associating the likelihood of an event occurring with multiple features, LR is able to effectively characterize the complex relationships between data. The specific formula is as follows:

$$\begin{array}{c}P={\displaystyle \frac{1}{1+e^{{-\log }_{\mathit{it}}\left(p\right)}}}\end{array}$$

(3)

$${\mathit{log}}_{\mathit{it}}\left(P\right)=a_0+a_1{X}_1+a_2{X}_2+\dots +a_n{X}_n$$

(4)

where P is the probability of the occurrence of the landslide event, which is based on the value of 0~1 of the sigmoid curve; ${\mathit{log}}_{\mathit{it}}\left(P\right)$ is the logarithmic probability of the occurrence of the landslide event; $a_0$ is the intercept term; $a_1$, $a_2$, …, $a_n$ are the regression coefficients to be determined and the coefficients that correspond to each of the influencing factors; and $X_1$, $X_2$, …, $X_n$ are the independent variables.

3. Data and Impact Factors

3.1. Data Sources

Statistical analysis indicated that the study area is home to 6314 avalanches, nine ground collapses, 14,041 landslides, 3203 debris flows, and 2972 slopes that present geological hazards. According to the broad definition of landslides, the total number of collapses, debris flows, and landslides in the study area is 23,558 [38]. In this study, we obtained STRM-DEM data at a resolution of 90 m from the Geospatial Data Cloud (http://www.gscloud.cn, accessed on 3 April 2024). We also obtained precipitation data from the National Meteorological Science Data Center (http://data.cma.cn, accessed on 3 April 2024) at a resolution of 1 km. Finally, we obtained STRM-DEM data at a resolution of 1000 m from the Resource Environment Science Data Platform (http://www.resdc.cn, accessed on 3 April 2024) for the vegetation cover.

The slope, aspect, plan curve, profile curve, surface roughness, and TWI were obtained from the raw DEM data and calculated using the ArcGIS 10.8.1 surface analysis tool. The FVC was calculated from the NDVI data. The SPI, TPI, slope height, and valley depth were analyzed using open-source software for geographic information (SAGA-9.3.2). Finally, the raster images of various impact factors were transformed into uniform cells using ArcGIS per mask extraction, projection, and resampling, among other techniques. The coordinate system was unified as WGS_1984_UTM_Zone_50N, with a spatial resolution of 120 m × 120 m.

3.2. Selection of Impact Factors

In this study, we selected elevation, slope, aspect, plan curvature, profile curvature, valley depth, precipitation, the SPI, the TWI, the TPI, surface roughness, FVC, slope height, the terrain ruggedness index (TRI), and topographic relief as the evaluation factors, considering the topographic and climatic characteristics of the study area. Based on the characteristics of these evaluation factors, we employed the natural breaks method [39] to categorize the 15 influencing factors into three to ten distinct levels.

3.3. Covariance Diagnostics

The selection of hazard-inducing factors is crucial in landslide sensitivity assessments [40]. However, using too many factors may cause covariance, which can lead to redundant information in a model, thereby affecting the reliability of the assessment results. On the contrary, using too few factors may ignore some important influencing factors, leading to less accurate assessment results. Therefore, it is necessary to test the covariance of the chosen factors before conducting the landslide susceptibility assessment.

Typically, we use two indicators, the Variance Inflation Factor (VIF) and tolerance, to assess the collinearity among factors [5]. When the tolerance is less than 0.1 or the VIF is less than 10, it indicates a high degree of collinearity, necessitating the exclusion of such factors. An initial analysis using SPSS 27 software revealed issues with the TRI and topographic relief, with tolerances of 0.092 and 0.067 and VIFs of 10.836 and 14.956, respectively. These values did not meet the standard criteria. After excluding these two factors, we conducted another collinearity diagnosis, and the results, as shown in

Table 1. Collinearity diagnostic results.

Factor	Tolerance	VIF	Factor	Tolerance	VIF
Elevation	0.583	1.717	SPI	0.312	3.205
Slope	0.220	4.545	TWI	0.326	3.066
Aspect	0.992	1.008	TPI	0.705	1.419
Plan curve	0.634	1.577	Surface roughness	0.304	3.291
Profile curve	0.601	1.663	TWI	0.838	1.193
Valley depth	0.607	1.646	Slope height	0.603	1.658
Precipitation	0.597	1.675

, indicated that the thirteen remaining evaluation factors met the diagnostic requirements of collinearity, allowing us to construct a landslide susceptibility model. This analysis provided robust support, enabling us to more accurately assess landslide susceptibility in subsequent studies. Additionally, it ensured that our model possessed high reliability and predictive capability, improving its guidance of practical disaster prevention and mitigation efforts.

• Elevation

Diverse topography across various elevations results in contrasting surface water retention capacities, thereby influencing the probability of landslides. Additionally, elevation plays a pivotal role in shaping the characteristics of landslides, such as their extent of movement and spatial reach [41]. Within the study area, elevations range from 190 to 7143 m, as illustrated in Figure 3a, and they were categorized into six classes using the natural breaks method. The analysis of the data presented in

Table 2. The grading status of each landslide evaluation factor and the IV and CF values.

Landslide Evaluation Factors	Classification	Number of Landslide Points/pts	Classified Area/km2	IV	CF
Elevation (m)	190~947	13,838	139,307.13	0.76731	0.56164
	947~1894	5864	52,958.20	0.87591	0.61173
	1894~2862	2490	54,838.27	−0.01553	−0.01614
	2862~3649	964	70,326.52	−1.21324	−0.71253
	3649~4261	298	94,711.69	−2.68492	−0.93471
	4261~7143	61	97,758.19	−4.30280	−0.98709
Slope (°)	0~7.56	6344	133,091.41	0.03179	0.03280
	7.56~16.33	7590	122,597.76	0.29324	0.26646
	16.33~25.09	5335	117,720.17	−0.01871	−0.01941
	25.09~34.77	2997	92,670.65	−0.35612	−0.30963
	34.77~77.10	1245	43,090.92	−0.46886	−0.38542
Aspect	−1~34.39	1997	44,950.31	−0.03860	−0.03962
	34.39~69.77	2309	48,636.40	0.02776	0.02870
	69.77~105.17	2737	55,293.06	0.06953	0.07042
	105.17~141.97	2822	55,917.75	0.08888	0.08916
	141.97~178.77	2594	51,414.75	0.08859	0.08888
	178.77~215.58	2183	48,367.48	−0.02281	−0.02362
	215.58~250.97	2090	49,126.10	−0.08191	−0.08214
	250.97~286.36	2250	54,098.21	−0.10456	−0.10358
	286.36~321.74	2202	50,808.30	−0.06338	−0.06419
	321.74~359.96	2327	50,558.54	−0.00324	−0.00339
Plan curve	−8.15~−0.27	1870	46,660.81	−0.14039	−0.13645
	−0.27~0.14	15,420	324,460.31	0.03008	0.03106
	0.14~6.63	6225	138,778.88	−0.02773	−0.02864
Profile curve	−6.01~−0.24	2277	70,903.92	−0.36189	−0.31372
	−0.24~0.19	14,813	325,580.89	−0.01353	−0.01408
	0.19~6.26	6425	113,415.19	0.20572	0.19493
Valley depth	−585~−276.43	934	104,816.84	−1.64392	−0.81403
	−276.43~519.09	3355	135,899.21	−0.62489	−0.47644
	519.09~749.61	6953	135,408.95	0.10745	0.10680
	749.61~1004.40	5149	81,580.20	0.31379	0.28235
	1004.40~1344.12	4370	39,889.34	0.86523	0.60704
	1344.12~2508.88	2754	12,305.46	1.57959	0.83232
Precipitation (mm)	303.25~732.01	1554	44,519.13	−0.27837	−0.25177
	732.01~886.36	2685	102,990.07	−0.57023	−0.44624
	886.36~1017.85	5470	129,631.35	−0.08870	−0.08862
	1017.85~1149.34	6068	104,914.83	0.22660	0.21256
	1149.34~1309.40	5270	86,028.96	0.28407	0.25924
	1309.40~1761.03	2466	41,845.09	0.24534	0.22808
SPI	−13.81~−10.28	1660	45,712.77	−0.23991	−0.22134
	−10.28~−5.83	6010	134,011.18	−0.02884	−0.02977
	−5.83~−1.61	4883	107,532.39	−0.01638	−0.01702
	−1.61~0.44	6767	155,616.51	−0.05968	−0.06057
	0.44~3.52	2843	54,786.87	0.11706	0.11582
	3.52~15.26	1349	11,705.66	0.91495	0.62847
TWI	2.05~5.20	7430	196,949.33	−0.20177	−0.18988
	5.20~6.97	9709	190,209.15	0.10058	0.10032
	6.97~9.53	3752	81,459.60	−0.00216	−0.00227
	9.53~13.36	1701	31,524.24	0.15611	0.15153
	13.36~27.12	920	9223.06	0.77057	0.56325
TPI	−310.39~−14.75	1386	25,236.75	0.17461	0.16796
	−14.75~−6.76	6377	111,620.64	0.21408	0.20203
	−6.76~1.23	10,301	243,522.16	−0.08648	−0.08650
	1.23~11.89	4663	106,020.09	−0.04748	−0.04850
	11.89~368.80	790	23,499.23	−0.31620	−0.28052
Surface roughness	1~1.06	14,575	265,304.23	0.17413	0.16754
	1.06~1.15	5766	138,199.78	−0.10102	−0.10027
	1.15~1.30	2472	84,701.59	−0.45841	−0.37876
	1.30~1.56	624	19,267.98	−0.35435	−0.30836
	1.56~5.72	74	1892.43	−0.16586	−0.15905
FVC	0~0.50	180	18,681.15	−1.56552	−0.79872
	0.50~0.73	1516	57,141.71	−0.55266	−0.43616
	0.73~0.88	9286	189,037.80	0.06336	0.06436
	0.88~1	12,528	245,042.68	0.10333	0.10291
Slope height	0~84.55	18,467	302,731.60	0.27971	0.25580
	84.55~225.46	4140	139,212.17	−0.43873	−0.36603
	225.46~469.70	795	55,600.24	−1.17102	−0.69996
	469.70~2395.49	113	12,355.98	−1.61793	−0.80909

revealed a general decrease in the number of landslide incidents with increasing elevation. The majority of landslide occurrences, approximately 83.78%, were concentrated between 190 and 1894 m, indicating a heightened susceptibility to landslide disasters in the low-elevation regions of Sichuan.

2.

Slope

Slope is one of the critical factors influencing landslides, as the presence of a slope gradient facilitates the downslope movement of materials. However, the occurrence of landslides does not exhibit a direct linear relationship with the slope gradient [42,43]; instead, there is a specific range within which the probability of occurrence peaks. As shown in Figure 3b, the slopes in the study area range from 0 to 77°, and they were classified into five categories using the natural breaks method. According to the data in Table 2, the majority of the landslide points are concentrated within the 8–16° range, with IV and CF values of 0.29324 and 0.26646, respectively.

3.

Aspect

Aspect plays a crucial role in mountain ecology, influencing the duration of sunlight exposure and the intensity of solar radiation. These differences in radiation create distinct microclimates, which affect water evaporation and vegetation density on slopes, thereby increasing the variability in landslide risk [44]. In the study area, aspect ranges from −1° to 360°, as shown in Figure 3c, and it was classified into ten categories using the natural breaks method. According to Table 2, the distribution of landslides across different aspect intervals is relatively uniform. The highest concentration of landslides, totaling 2822, occurred within the 105.17–141.97° range, with IV and CF values of 0.08888 and 0.08916, respectively.

4.

Plan and profile curves

In the field of digital terrain analysis, plan curvature and profile curvature are among the key topographic features. Plan curvature describes the curvature characteristics of the terrain in the horizontal direction. The magnitude of its value reflects the degree of the curvature variation on the terrain’s surface in the horizontal direction, thereby revealing the steepness of the terrain. The calculation results of this feature have wide-ranging applications in slope calculation, hydrological modeling, and land use planning.

Similarly, profile curvature describes the curvature characteristics of the terrain in the direction perpendicular to the horizontal plane. Typically, we measure profile curvature based on the curvature of the terrain’s surface in the direction of the maximum slope. The value of the profile curvature reflects the degree of the curvature change in the vertical direction, which directly influences the terrain’s bending degree. The results of the profile curvature calculations play significant roles in groundwater flow simulation, karst topography studies, and soil erosion modeling [45]. In our study area, as shown in Figure 3d,e, the ranges of plan curvature and profile curvature were divided into three classes. According to Table 2, the region with plan curvature values between −0.27 and 0.14 had the highest number of landslide points, accounting for 65.58% of the total. Similarly, the region with profile curvature values between −0.24 and 0.19 contained the most landslide points, accounting for 62.99% of the total.

5.

Valley Depth (the elevation difference between valleys and upstream ridges)

The depth of valleys affects slope stability and, consequently, influences the probability of landslide occurrence, which is also one of the important influencing factors [46]. As shown in Figure 3f, when classified into six categories, the number of landslide points first increases and then decreases. However, according to the IV and CF values, it gradually increases with an increase in valley depth, indicating that the significance of its impact on landslides becomes more pronounced.

6.

Precipitation

Rainfall is one of the main triggering factors for landslides and serves as an important indicator for assessing the climate and water resources in this region. Rainfall can increase soil saturation, thereby reducing soil stability and increasing the risk of landslides [47]. The multi-year average precipitation in the study area of Sichuan Province is approximately 488,975 million cubic meters. Water resources are most abundant in the river runoff, with nearly 1400 rivers of various sizes within the borders of this province, making it the “Province of a Thousand Rivers”. As shown in Figure 3g, precipitation was divided into six classes using the natural breaks method. According to Table 2, under the influence of precipitation, the landslide points are mainly concentrated in the range of 886.36 mm to 1309.40 mm, accounting for 71.48% of the total.

7.

SPI

The SPI is a crucial indicator for measuring the river erosion capacity and stability of the study area. It represents the erosive power of the water flow, which is influenced by gravitational forces and aligned with the movement of solid particles [13]. The calculation formula is as follows:

$$\begin{array}{c}SPI=AS\times \mathit{tan}\beta \end{array}$$

(5)

where $\beta$ is the local gradient of the slope and $AS$ is the area of the particular catchment. As shown in Figure 3h, the $\mathrm{S}\mathrm{P}\mathrm{I}$ map of the study area was classified into six categories, reflecting varying levels of erosive power. This classification aids in better understanding the spatial variation and distribution of the runoff intensity. According to Table 2, the landslide points are predominantly concentrated in the range of −10.28 to 0.44, accounting for 75.11% of the total.

8.

TWI

The TWI describes the influence of topography on the location and size of the saturated source areas generated by the runoff [48]. Similar to the SPI, it is a standard index representing the combined impact of watershed hydrology and topography on soil erosion and protection. The calculation formula is as follows:

$$\begin{array}{c}\mathit{TWI}=\mathit{ln}\left({\displaystyle \frac{AS}{\mathit{tan}\beta }}\right)\end{array}$$

(6)

where $\beta$ is the local gradient of the slope and $AS$ is the area of the particular catchment. As shown in Figure 3i, the TWI map of this region was divided into five categories, reflecting different levels of slope erosion sensitivity. According to Table 2, the landslide points are primarily concentrated in the range of 2.05 to 6.97, accounting for 72.89% of the total. The number of landslide points is approximately inversely proportional to the TWI value, indicating that the frequency of landslides is inversely related to the topographic wetness index.

9.

TPI

The TPI is a topographic indicator used to describe the relative elevation of a surface location [49]. It assesses the relative position of a surface point on the terrain based on the elevation of the point and the elevation of its surrounding neighboring points. The TPI is commonly used to identify various landforms, such as valleys, ridges, and slopes. Higher TPI values generally indicate that a surface point is located at a higher elevation, while lower TPI values suggest the point is at a lower elevation. The calculation formula [50] is as follows:

$$\begin{array}{c}TPI=T_0-{\displaystyle \frac{\sum _{i=1}^n{T}_n}{n}}\end{array}$$

(7)

Here, $T_0$ represents the elevation of the unit being evaluated, $T_n$ denotes the elevation of the grid cells, and $n$ is the total number of units in the specified neighborhood used for the calculation. As shown in Figure 3j, the TPI was classified into five categories. According to Table 2, the distribution of the landslide points follows a roughly normal distribution, with the highest concentration of landslide points (43.80%) falling within the range of −6.76 to 1.23.

10.

Surface roughness

Surface roughness is used as an indicator to quantify the degree of ruggedness of a terrain’s surface [49]. The greater the surface roughness, the higher the degree of surface fragmentation and erosion and the more pronounced the negative effects of rainfall on the surface. As shown in Figure 3k, it was divided into five classes. According to Table 2, the landslide points are primarily distributed within the range of 1.0 to 1.15, accounting for 86.51% of the total, and there is a negative correlation between the number of landslide points and the surface roughness value, indicating an inverse relationship between the landslide occurrence frequency and surface roughness.

11.

FVC

The FVC is typically described as the ratio of the vertical projection area of vegetation on the ground to the total area of the statistical region, with values ranging from 0 to 1. Higher values indicate greater vegetation coverage. This index directly reflects the vegetation cover status of an area and has a significant impact on this region’s hydrological conditions [51]. The calculation formula is as follows:

$$\begin{array}{c}FVC={\displaystyle \frac{NDVI-{NDVI}_{min}}{NDVI-{NDVI}_{max}}}\end{array}$$

(8)

The $\mathrm{F}\mathrm{V}\mathrm{C}$ represents vegetation coverage, ${NDVI}_{max}$ is the NDVI value for pure green pixels, and ${NDVI}_{min}$ is the NDVI value for the pixels showing pure bare soil. As shown in Figure 3l, this region was divided into four categories. According to Table 2, the area with an FVC range of 0.88~1.0 has the highest distribution of landslide points, accounting for 53.28% of the total. Additionally, the number of landslide points is positively correlated with the FVC value, indicating that the frequency of landslides increases with higher vegetation coverage.

12.

Slope Height

Slope height refers to the vertical height variation of the surface or terrain. In landslide susceptibility studies, slope height typically denotes the height variation of the terrain or surface features along a certain direction (usually horizontal). It is of significant value for landslide hazard mapping [52]. As illustrated in Figure 3m, slope height was categorized into four classes. According to Table 2, the majority of the landslide points, comprising 78.53% of the total, are concentrated in the range of 0~84.55. Furthermore, the number of landslide points is inversely proportional to the slope height value, indicating a negative correlation between the landslide occurrence frequency and slope height.

4. Results Analysis and Accuracy Validation

In this study, a susceptibility analysis and an evaluation were conducted across the entirety of Sichuan Province using both mathematical statistical models (IV and CF) and models coupled with machine learning (IV-DT, IV-LR, CF-DT, and CF-LR). The results of each model were then classified into five categories (very high, high, moderate, low, and very low susceptibility) using the natural breaks method (as shown in Figure 4 and

Table 3. Evaluation results of six models.

Models	Susceptibility Level	Classified Area/km2	Proportion of Classified Area/%	Classified Area/km2	Proportion of the Number of Landslide Points/%	Density of Landslide Points/(pts/km2)
IV	Very low	58,864.954	0.116	52	0.002	0.00088
	Low	88,686.691	0.174	174	0.007	0.00196
	Moderate	100,583.107	0.198	803	0.034	0.00798
	High	96,681.758	0.190	4703	0.200	0.04864
	Very high	163,505.722	0.322	17,760	0.756	0.10862
IV-LR	Very low	97,641.331	0.192	61	0.003	0.00062
	Low	94,576.997	0.186	297	0.013	0.00314
	Moderate	69,544.901	0.137	896	0.038	0.01288
	High	62,252.741	0.122	3032	0.129	0.04870
	Very high	185,138.611	0.364	19,225	0.818	0.10384
IV-DT	Very low	73,635.941	0.145	55	0.002	0.00075
	Low	76,111.474	0.150	161	0.007	0.00212
	Moderate	91,643.112	0.180	532	0.023	0.00581
	High	91,303.704	0.180	3684	0.157	0.04035
	Very high	175,628.002	0.346	19,060	0.811	0.10852
CF	Very low	57,115.022	0.112	129	0.005	0.00226
	Low	113,965.819	0.224	612	0.026	0.00537
	Moderate	123,232.536	0.242	2585	0.110	0.02098
	High	99,130.810	0.195	7003	0.298	0.07064
	Very high	114,878.045	0.226	13,163	0.560	0.11458
CF-LR	Very low	97,641.331	0.192	61	0.003	0.00069
	Low	94,576.997	0.186	297	0.013	0.00244
	Moderate	69,544.901	0.137	896	0.038	0.01512
	High	62,252.741	0.122	3032	0.129	0.04765
	Very high	185,138.611	0.364	19,225	0.818	0.10299
CF-DT	Very low	73,635.941	0.145	55	0.002	0.00166
	Low	76,111.474	0.150	161	0.007	0.00404
	Moderate	91,643.112	0.180	532	0.023	0.01515
	High	91,303.704	0.180	3684	0.157	0.06848
	Very high	175,628.002	0.346	19,060	0.811	0.11182

).

4.1. Mathematical Statistical Models

The determination of the information values (IVs) and certainty factors (CFs) for 13 factors influencing landslides, such as elevation and precipitation, in the study area was carried out using ArcGIS operations to obtain the number of landslide points and the area for each factor’s partition. Subsequently, the values were calculated using the formulae mentioned in Section 2. Finally, the information value and certainty factor of each influencing factor were equally weighted and overlaid using a raster calculator, resulting in landslide susceptibility assessment maps based on the IV and CF models for the study area. These results are illustrated in Figure 4a,d.

4.2. Coupled Models

The coupled models integrated conventional statistical models with machine learning models, leveraging the strengths of each to compensate for their respective weaknesses. Traditional statistical models provide an intuitive understanding of the relationship between the factors and landslide occurrence but may struggle with complex nonlinear relationships. Machine learning models excel 2021 at handling nonlinear relationships and high-dimensional data, thereby uncovering more potential complex associations. By combining these models, the goal is to create more accurate landslide susceptibility maps. In Sichuan Province, where the geological and climatic conditions are complex, different areas may exhibit significantly different landslide-triggering mechanisms. Coupled models can more comprehensively capture these complexities, offering more precise risk zoning.

To build the coupled models, it was necessary to first determine the range of levels for each factor using the natural breaks method and record the number of landslide points and the area within each range. Subsequently, the information values (IVs) and certainty factors (CFs) for each part were calculated using the formulae mentioned earlier. These values were then added to the attribute tables of each factor range. After converting the vectors to rasters, the IV and CF model maps were generated by equally weighting and overlaying the data using a raster calculator. The coupled models integrated conventional statistical models with machine learning models to establish landslide susceptibility maps with a higher accuracy. To train and build the models for machine learning, it was necessary to establish a dataset of landslide disaster training samples. The samples consisted of the attributes of the landslide evaluation factors (13 attributes of the factors influencing landslide susceptibility) and the landslide properties (the landslide points and non-landslide points). In the study area, there were a total of 23,558 landslide points. Regarding the selection of the points for the landslide susceptibility evaluation modeling, the non-landslide points were selected at least 1000 m from the known landslide points, and the distances between all the non-landslide units were at least 1000 m. An equal number of non-landslide points were generated using ArcGIS software. Using the “Extract Values to Points” function, the IV and CF values for the 13 influencing factors were assigned to the sampled data as input variables. Landslide points (with a value of 1) and non-landslide points (with a value of 0) were used as the output variables for the model. The landslide sample dataset was randomly divided into the training and testing sets at a ratio of 7:3. This study employed SPSS Modeler software to build the machine learning models and obtained the influence weights of the 13 factors affecting landslide occurrence in both the decision tree C5.0 and logistic regression models. Finally, the influence factor maps with the IV and CF values were overlaid according to their respective weights, resulting in four output maps based on the coupled models (IV-LR, IV-DT, CF-LR, and CF-DT), as shown in Figure 4b,c,e and f, respectively.

4.3. Distribution of Landslide Conditions

The analysis of the distribution of the landslide conditions served as the foundation for this study of landslide susceptibility. This analysis could initially demonstrate the accuracy of the models and the distribution of the grades. In this study, the map of the landslide susceptibility results based on the six models was analyzed in conjunction with the landslide hazard sites. This analysis allowed for the comparison of the area shares of the landslide areas and the densities of the landslide sites with different grades, as illustrated in Figure 5 and Figure 6.

As shown in Figure 5, in the extremely high-risk areas, the CF-LR model occupies the largest area, accounting for 37.08% of the total area, while the CF model covers the lowest proportion of the area at 22.6%. In the extremely low-risk areas, the CF model occupies the smallest area at 11.24% of the total area, and the distribution of the area between the CF-DT model and the CF model is similar. The IV-LR model has the highest proportion, at 19.18%. All the models except for the CF model demonstrate that the proportion of the area in the very high-risk zone is greater than the proportions in the extremely low-risk, low-risk, medium-risk, and high-risk zones.

According to Figure 6, the density distributions of the landslide disaster points among the six models demonstrate consistency. With increasing risk levels, the density of the landslide points notably increases. In particular, the extremely high-risk and high-risk areas account for the vast majority of the landslide points. The CF model exhibits the highest landslide point density, reaching 0.18522 points/square kilometer, while the IV-DT model has the lowest density at 0.14887 points/square kilometer. In the low-risk and extremely low-risk areas, the IV model has the lowest landslide point density at 0.00284 points/square kilometer, while the CF model has the highest density at 0.00313 points/square kilometer.

4.4. ROC Curve Accuracy Validation

To assess the accuracy of the six models in predicting landslide susceptibility in the study area, ROC curves were adopted. This method plots the true positive rate against the false positive rate, forming a curve where the area under the curve (AUC) represents the area under the ROC curve, primarily measuring the model’s generalization performance [53]. The AUC value ranges from 0 to 1, with higher values indicating a greater model accuracy. In this paper, the study area landslide disaster point data were combined with a certain limit range of random non-landslide disaster points as a basis and the use of multi-value extraction to the point, resulting in a landslide susceptibility map of the landslide points and non-landslide points. For the evaluation of the index data, the disaster point data target value was set to 1 and the non-disaster point data target value was set to 0. The data were processed and imported into SPSS to obtain the current ROC curve of susceptibility, as shown in Figure 7.

Based on the ROC curve analysis, the AUC values of the six models all exceeded 0.750, indicating the reliability of the models. The AUC values of the IV, IV-DT, IV-LR, CF, CF-DT, and CF-LR models were 0.842, 0.847, 0.848, 0.815, 0.828, and 0.846, respectively. Moreover, the accuracy of the coupled models based on single mathematical statistical methods was higher. Among them, the CF model had the lowest accuracy, while the IV-LR model had the highest accuracy at 0.848, indicating that this model is most suitable for landslide susceptibility studies in this research area. These results are consistent with the findings in reference [22], which indicate that combining statistical models with machine learning models generally yields a higher accuracy compared to using a single model alone. In our study, the higher accuracy demonstrated by the IV-LR model suggests that it performs well in predicting landslide risk, aligning with the advantages highlighted in the introduction.

5. Conclusions

This study evaluated landslide susceptibility in Sichuan Province using the information value method, the certainty factor method, and their coupling with machine learning models (IV-LR, IV-DT, CF-LR, CF-DT). Based on thirteen key factors, including elevation, slope, and precipitation, we generated landslide susceptibility maps and classified the region into five risk levels. The main findings are as follows:

(1)

Risk Distribution: High- and very high-risk zones are mainly in the eastern and southeastern parts of Sichuan, covering nearly half of the province. Moderate-risk areas are distributed in a northeast–southwest linear pattern, while extremely low- and low-risk zones are concentrated in the western and northwestern regions. The models show a high consistency in risk prediction, indicating their reliability. Furthermore, the density of the landslide points increases with the elevation of the risk area.

(2)

Model Performance: The IV-LR model achieved the highest AUC value (0.848), while the CF model had the lowest (0.815). The coupling methods, compared to the individual models, demonstrated a superior accuracy, suggesting that combining methods improves the landslide susceptibility assessment.

(3)

Based on the results of this study, the landslide susceptibility analysis holds significant implications for disaster prevention and mitigation efforts. By identifying high-risk and very high-risk areas within Sichuan Province, the relevant authorities can prioritize the allocation of resources to these critical regions, thereby enhancing the monitoring of and early warning capabilities for landslides. Notably, the IV-LR model demonstrated a high predictive accuracy, providing robust support for developing scientifically grounded prevention strategies. Furthermore, the increase in the landslide point density with rising risk levels underscores the necessity of strengthening the control measures in high-risk areas. Integrating the model results, future efforts should focus on optimizing disaster prevention strategies according to specific geological and climatic conditions, thereby improving landslide risk management, reducing disaster losses, and safeguarding public safety and property.