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Article

Regional Landslide Hazard and Risk Assessment Considering Landslide Spatial Aggregation and Hydrological Slope Units

by
Xuetao Yi
1,2,
Yanjun Shang
1,2,3,*,
He Meng
1,2,3,
Qingsen Meng
1,2,
Peng Shao
1,2 and
Izhar Ahmed
1,2
1
State Key Laboratory of Lithospheric and Environmental Coevolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2
College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
3
Xinjiang Key Laboratory of Geohazard Prevention, Xinjiang Institute of Engineering, Urumqi 830023, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(14), 8068; https://doi.org/10.3390/app15148068
Submission received: 20 June 2025 / Revised: 8 July 2025 / Accepted: 15 July 2025 / Published: 20 July 2025
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Abstract

Landslide risk assessment (LRA) is an important basis for disaster risk management. The widespread phenomenon of landslide spatial aggregation brings uncertainty to landslide hazard assessment (LHA) in LRA studies, but it is often overlooked. Based on the frequency ratio (FR) method, we proposed the dual-frequency ratio (DFR) method, which can quantitatively analyze the degree of landslide spatial aggregation. Using the analytic hierarchy process (AHP) and random forest (RF) models, we applied the DFR method to the LRA study of the Karakoram Highway section in China. According to the receiver operating characteristic (ROC) curve and the distribution characteristics of landslide hazard indices (LHIs), we evaluated the application effect of the DFR method. The results showed that the LHA models using the DFR method performed with higher accuracy and predicted more landslides in the zones with a high LHI. Moreover, the DFR-RF model had the best prediction performance, and its predictions were adopted together with vulnerability values to calculate the landslide risk. The zones with very high and high landslide risks were predominantly concentrated along highways in southern Aoyitake Town.

1. Introduction

A landslide is a common type of geological disaster in mountainous areas worldwide, often causing massive casualties and economic losses [1,2,3]. As human activities intensify and extreme climate events occur more frequently, landslides pose increasingly serious hazards [4,5,6,7]. Landslides have a wide distribution range and are highly sudden, posing serious challenges to disaster prevention and control [8,9,10]. Landslide risk assessment (LRA) is an important prerequisite for land use planning and actions of disaster risk reduction [11]. In recent years, it has also increasingly attracted the attention of researchers and government departments.
The landslide risk is commonly defined as the expected value of the losses caused by landslides to people’s lives, property, and economic activities in a specific area and during a specific period [12]. It possesses both disaster and social attributes, typically quantified as the product of landslide hazard and vulnerability [6]. Landslide hazard assessment (LHA) is the core procedure of LRA studies [13]. In existing studies, the landslide hazard usually represents the probability of a landslide event occurring in a certain area within a certain period of time [14]. At present, the most commonly used regional LHA models include heuristic models (such as the analytic hierarchy process (AHP)) [15,16,17], statistical models (such as the frequency ratio (FR) and statistical index (SI)) [18,19,20], and machine learning models (such as random forest (RF) and support vector machine (SVM)) [21,22,23,24]. These models can analyze the relationships between the landslide occurrence and predisposing factors involving geomorphology, geology, hydrology, and land cover [11].
Among these models, the FR method is computationally simple and can clearly reflect the correlations between predisposing factors and landslide occurrence [22]. Therefore, it is widely applied in LHA studies. Moreover, in combination with other models, it is often used as the input variable when calculating the landslide hazard index (LHI) [19,20]. However, the FR method does not take into account the phenomenon of landslide spatial aggregation, resulting in high uncertainty in its analysis results. In nature, the internal and external dynamic factors affecting the spatial distribution of landslides are anisotropic [25,26]. This leads to the existence of various degrees of landslide spatial aggregation in different regions. As a result, it is unreasonable to directly apply the FR method in the establishment of an LHR model without considering the spatial aggregation of landslides. This problem is very common in studies using the FR method. Additionally, some researchers have proposed quantitative indicators such as the CLAI to improve the FR method by quantitatively analyzing landslide spatial aggregation [19,20,21,22]. However, these indicators often ignore the differences in the coverage of predisposing factor classes, resulting in the uncertainty of the LHR model. In view of this situation, we propose the dual-frequency ratio (DFR) method, considering the spatial aggregation of landslides. It has shown excellent application effects in the LHR study of the northwestern region of China [20].
In this study, we applied the proposed DFR method to an LRA study in the section of the Karakoram Highway (KKH) between Kashi and Khunjerab. By combining the selected 10 predisposing factors and 356 landslide points, we used the original FR method and the DFR method to create spatial datasets for the LHA model. On this basis, we adopted the AHP model and RF model to generate landslide hazard maps. Based on the receiver operating characteristic (ROC) curve and the distribution characteristics of the LHIs, we evaluated the LHA model adopted in this study. Finally, the results of the LHA model with the best prediction performance were used to calculate the landslide risk in the study area.

2. Methodology

2.1. Modelling Process of LRA

The main objective of this study was to analyze the impact of landslide spatial aggregation on landslide hazard evaluation and to conduct an LRA study for the KKH. The process of an LRA study consists of six steps, as shown in Figure 1.
(1)
Establishment of landslide database. We identified the predisposing factors for the formation of landslides in the study area by field investigations and literature research. Based on remote sensing interpretation and field investigation data, a database containing information on the spatial distribution of landslides and the characteristics of related predisposing factors was established. In this study, the hydrological slope unit was adopted as the basic evaluation unit.
(2)
Analysis of correlations between landslide occurrence and predisposing factors. We established the connection between landslide occurrence and the predisposing factors through the DFR method. Based on this, an index system for landslide risk assessment was established.
(3)
Landslide hazard map. We conducted the LHA of the study area using the AHP and RF methods. In the process of calculating the landslide hazard, the frequency ratio and the dual-frequency ratio were the input variables.
(4)
Evaluation of LHA models. Based on the ROC curve and distribution characteristics of various levels of landslide hazard, we analyzed the LHA outputs obtained by different methods for the study area.
(5)
Vulnerability assessment. We used the AHP method to obtain the vulnerability zoning map of the study area for the calculation of the landslide risk.
(6)
Landslide risk map. Based on the above assessment of the landslide hazard and vulnerability, we calculated the landslide risk of the study area. During this procedure, the landslide hazard data with the highest accuracy were selected as the input variables for landslide risk calculation.

2.2. Analysis of Landslide Spatial Aggregation

The frequency ratio (FR) method is one of the most widely used statistical models in LHA studies [5,11,18]. It has the advantages of reliable results and convenient use. The FR values indicate the spatial correlations between landslide occurrence and the predisposing factors and can quantitatively reflect the degree of influence of different landslide predisposing factors. It can be calculated by Equation (1):
FRij = (lij/sij)/(L/S)
where FRij is the frequency ratio of class i under the j predisposing factor, lij is the number of occurred landslides in the above class i, sij is the area of class i, L is the total number of occurred landslides in the study area, and S is the total size of the study area. When the FR value is greater than 1, the relevant predisposing factors play a positive role in landslide occurrence. The higher the frequency ratio, the higher the probability of landslide occurrence.
Some studies have found that the FR method has the limitation of not considering the spatial aggregation of landslides [19,20,22,27,28]. As shown in Figure 2, the size of the selected area in each case is S, and the total number of landslides in it is L. In the selected area of each case, class i is split into the same evaluation unit with an area of Su. Regarding case 1 and case 2, class i in each case has the same FR value of (10/(5·Su))/(L/S). However, in case 1, landslides occur in only one evaluation unit, and the degree of landslide spatial aggregation is significantly higher. Thus, the FR value of class i in case 1 should be lowered by considering landslide spatial aggregation. Furthermore, the degree of landslide spatial aggregation is not only related to the proportion of evaluation units with occurred landslides but also to the average number of landslide points in each evaluation unit. For example, in case 2 and case 3, each evaluation unit of class i is connected with an occurred landslide. However, in case 2, each evaluation unit has 2 landslide points, while, in case 3, each evaluation unit has only 1 landslide point. This indicates that the degree of landslide spatial aggregation in case 3 is lower. Similarly, in case 4, only one evaluation unit has a landslide point, and the total number of landslides is 1. The proportion of evaluation units with a landslide in case 4 is the lowest, but its degree of spatial aggregation is also the lowest.
According to the main cases of landslide spatial aggregation phenomena (Figure 2), we propose the DFR method to improve the FR method’s analysis [20]. In this improved method, an index named LAIFR, reflecting the degree of landslide spatial aggregation, is defined as in Equation (2):
LAIFR = (UL/UT)/(lij/UT)
where LAIFR is the index denoting the landslide spatial aggregation degree, UL is the number of evaluation units with occurred landslides under class i of predisposing factor j, UT is the total number of evaluation units under class i of predisposing factor j, and lij is the number of occurred landslides in class i.
Usually, the higher the LAIFR value is, the lower the spatial aggregation degree of landslides is in a certain class of a factor. When there is no landslide in a certain class, the LAIFR value is equal to 0. Based on Equation (3), the FR value is optimized using LAIFR:
DFRij = FRij × LAIFR
where DFRij is the improved frequency ratio of a certain class i of factor j. In this study, we also uniformly refer to the values of DFR and FR as FRs.

2.3. Modeling Approaches

2.3.1. AHP Model

The AHP model is a semi-quantitative method for solving decision-making problems and is widely used in LHA studies [11,29,30]. In this model, predisposing factors are compared in pairs to evaluate the degree of influence of each factor on landslide occurrence [16,17,19]. Then, based on the comparison results, a judgment matrix is established to obtain the weight value of each factor. The degree of influence can be classified into different levels ranging from 1 to 9 [31]. In the AHP model, the consistency ratio (CR) is used to check the consistency of the judgment matrix and is calculated by Equation (4). Generally, when the CR value is less than 0.1, the judgment matrix satisfies the calculation requirements [16].
CR = CI/RI
where CI is the consistency index of the judgment matrix and can be obtained by Equation (5), and RI is the random index of the judgment matrix and can be found in Table 1 [32,33,34].
CI = (λmax − n)/(n − 1)
where λmax is the principal eigenvalue of the judgment matrix, and n is the total number of selected factors.
Finally, the landslide hazard can be calculated using Equation (6):
LHIAHP = w1 × PF1 + w2 × PF2 + w3 × PF3 + … + wj × PFj
where LHIAHP is the landslide hazard index obtained by the AHP model, wj is the weight value of predisposing factor j, and PFj is the FR of predisposing factor j.

2.3.2. RF Model

The RF model is commonly used in LHA studies [3,20,22,35,36]. Proposed by Breiman (2001) for multi-class classification and prediction tasks, this ensemble model is composed of a battery of tree classifiers [37,38,39]. It combines a random subspace with bagging ensemble learning, which can effectively reduce the overfitting risk of a single tree and significantly improve the model’s accuracy and generalization ability [21]. The principal process of the RF model is carried out by the following steps [37,40]: (1) adopt the Pearson correlation coefficient to analyze the multicollinearity of the data and utilize stratified sampling to generate the training set and test set; (2) use bootstrap sampling to randomly select samples with replacement from the original training set to generate multiple training subsets; (3) randomly select some features to construct decision trees and assign multiple decision trees to different computing nodes for parallel training; (4) obtain the prediction results by the majority voting method. During this process, the accuracy of the model is calculated using the test set, and parameters such as the number of trees and the maximum depth are optimized through cross-validation.

2.4. Model Evaluation

The ROC curve is a tool used to evaluate the performance of binary classification models, and it is also widely adopted in LHA studies. The vertical axis of this curve represents the true positive rate (TPR) of the model, indicating the ability to identify the evaluation units with landslides. Its horizontal axis is the false positive rate (FPR), which reflects the situation wherein evaluation units with landslides are wrongly classified as non-landslide evaluation units. TFR and FPR can be obtained by Equations (7) and (8), respectively. The more closely the curve approaches the upper-left corner, the better the model’s ability to distinguish positive and negative samples.
TPR = TP/(TP + FN)
FPR = FP/(FP + TN)
where TP is the number of correctly predicted landslide samples, FN is the number of non-landslide samples misjudged by the selected model, FP is the number of landslide samples misjudged by the selected model, and TN is the number of correctly predicted non-landslide samples.
The predictive performance of the model is generally quantitatively analyzed using the area under the ROC curve (AUC). Based on the AUC value, the model performance can be classified into the following levels [5,11,41]: very low (0.5–0.6), low (0.6–0.7), moderate (0.7–0.8), good (0.8–0.9), and excellent (0.9–1.0). Generally, the AUC value is calculated by Equation (9) [20]:
AUC = (ΣTP + ΣFN)/(TP + TN + FP + FN)
In addition, the distribution characteristics of LHIs can be used to analyze the performance of LHA models [11,42]: (1) the coverage of a landslide hazard level usually increases as the hazard level lowers, and the zones with high landslide hazards should constitute a very small proportion of the whole area; (2) landslides are mainly distributed in zones with high hazard levels, and they rarely occur in low-hazard zones.

3. Study Area and Data

3.1. Study Area

The KKH is one of the highest mountainous highways in the world. Its section within China starts from Kashi in the north and ends at Khunjerab in the south (Figure 3a–c). We define the 10 km area flanking both sides of this KKH section as the study area, and its total length is 415 km. It passes through the Kunlun Mountain and the Karakoram Mountain, which are located at the northwestern edge of the Qinghai–Tibet Plateau [43]. The area along the highway is mainly mountainous with large topographic relief, and the altitude ranges from 1200 to 7000 m. The overall altitude along the highway is relatively high, with about seventy percent of the area having an altitude exceeding 3000 m. The stratum lithology along the highway is complex, including Variscan granite, Carboniferous limestone and shale, Triassic sandstone and conglomerate, and Quaternary loose sediments. Due to active tectonic processes, there are many faults along the highway, and earthquakes occur frequently [13]. Moreover, the climate along the highway shows typical characteristics of aridity. Precipitation in the study area is scarce and is concentrated from May to September. About seventy-eight percent of the study area has annual average precipitation of no more than 100 mm. Furthermore, only about three percent of the whole area has average annual precipitation of more than 200 mm.

3.2. Landslide Inventory

A landslide inventory provides indispensable basic data for model building in LHA studies. We established an original landslide inventory based on high-resolution remote sensing images through indoor interpretation, and we further supplemented and improved the landslide inventory through field investigations. This landslide inventory was also published in China Scientific Data [43]. In the study area, we identified a total of 356 landslides that occurred from 1970 to 2024, and these were mainly rock landslides (Figure 4). According to the classification method proposed by Varnes (1978) [2], these landslides were mainly translational and rotational, complex, and topple slides. Additionally, most of these landslides were distributed in the V-shaped valleys along the KKH, especially between Aoyitake and Bulunkou (Figure 3c).
In order to evaluate the adopted LHA models, we utilized GIS software (ArcGIS v10.4) and the MATLAB R2022a software to establish a training set and validation set based on the landslide inventory [5,11,41]. Firstly, using the hydrology tools in ArcGIS 10.4, we extracted the slope units as the evaluation units (Figure 3c–e), totaling 9456 slope units. Using DEM data with a 30 m resolution, we conducted depression filling and flow direction analysis to gather essential data for the creation of hydrological units. After calculating the flow and delineating the river network, we used the GIS software to automatically produce hydrological slope units that represented watershed and catchment line features. Any unreasonable unit boundaries were manually corrected. Next, we randomly selected non-landslide evaluation units of the same quantity as in the landslide evaluation units. Then, we mixed the landslide evaluation units with the non-landslide evaluation units. Finally, we used the MATLAB R2022a software to randomly select 70% of the mixed evaluation units as the training set for model building and the remaining 30% as the validation set for model evaluation.

3.3. Landslide Predisposing Factors

A landslide is the result of the coupling action of internal and external driving forces [8,44]. In LHA studies, the predisposing factors related to landslide formation are the basic variables for the calculation of the landslide hazard. Based on field investigations and literature research, we analyzed the controlling factors of landslide occurrence in the study area. Eventually, geomorphological factors (elevation, aspect, slope, and topographic relief), geological factors (rock group, fault density, and peak ground acceleration (PGA)), hydrological factors (river density and annual precipitation), and a surface cover factor (normalized difference vegetation index (NDVI)) were selected for the LHA of the study area. We obtained the original data of these predisposing factors from existing survey data and open databases. Detailed information about these data and their sources is shown in Table 2.
Subsequently, we used the zonal statistics tool of the GIS software (ArcGIS v10.4) to assign the data of the selected predisposing factors to the generated evaluation units based on spatial relationships, thereby obtaining data layers for all predisposing factors. Most of these predisposing factor layers were divided into eight classes according to the natural breakpoint method [45]. Among them, the aspect, rock group, and PGA were discontinuous factors and were classified according to their natural attributes [19]. Finally, we analyzed the relationships between each predisposing factor and landslide occurrence using the DFR and FR methods. The analysis results and the classification of each predisposing factor are shown in Table 3.

3.3.1. Geomorphological Factors

Elevation (Figure 5a), aspect (Figure 5b), slope (Figure 5c), and topographic relief (Figure 5d) are typical geomorphological factors that play significant roles in the formation of landslides [43]. Elevation determines the climatic characteristics and hydrodynamic conditions of a certain area [46]. Climate change affects the distribution of species and the characteristics of human activities [47]. Thus, it can cause changes in surface vegetation, weathering, and the degree of human activity, which deeply affect the development of landslides. Moreover, aspect is closely related to soil moisture and the lighting conditions, thereby influencing slope stability [14]. Due to the influence of the aspect factor on solar radiation and wind conditions, the water action conditions, vegetation coverage, and weathering of these slope units show significant differences. As shown in Table 3, aspect is generally classified into nine categories, with a −1 value representing flat land [22]. Moreover, the slope can alter the stress distribution and strain accumulation in the stress field of the slope body [5]. Within a certain range of slope values, the stability of the slope body usually decreases as the slope increases. Topographic relief reflects the magnitude of the elevation variation within a certain area. With higher topographic relief, the slope generally tends to accumulate more gravitational potential energy and exhibits stronger sliding forces. In addition, excessive topographic relief can amplify the intensity of hydrodynamic actions such as overland flow and groundwater seepage, which are unfavorable for slope stability [48].

3.3.2. Geological Factors

The lithology is one of the basic geological conditions for landslide occurrence. The weathering process of the slope, the development of joints and fractures, and the rock strength often vary dramatically due to different rock types [44]. This can eventually affect the slope stability in terms of the slope morphology and rock mass strength [5]. Based on a 1:250,000-scale geological map and referring to the National Standard of China called the Standard for Engineering Classification of Rock Mass (GB/T50218-2014) [49], we classified the lithology of the study area into 6 rock groups (Figure 5e): very hard, hard, less hard, soft, very soft, and water [20]. Fault zones often control the development of landslides, and we adopted the factor of the fault density (Figure 5f) to reflect its effect on landslide occurrence. On the one hand, the structural planes are very developed near the fault zone, determining the spatial position of the failure surface of the slope and the boundary of the landslide [50]. On the other hand, due to the internal dynamics, fault zones often form landforms of fault scarps and rift valleys [51]. They are characterized by large topographic relief and provide favorable geomorphological conditions for landslide occurrence. Furthermore, Table 3 indicates that areas with a higher fault density tend to be more prone to landslides. In addition, the burst of an earthquake often leads to the occurrence of a large number of landslides, and they are distributed in clusters [52]. In this study, PGA (Figure 5g) refers to the maximum absolute value of the acceleration of surface particle motion during the propagation of seismic waves [53]. It can reflect the instantaneous intensity of the energy released by an earthquake [54].

3.3.3. Hydrological and Surface Cover Factors

The scouring and erosion effects of rivers can cause damage to the feet of slopes [5]. Moreover, seasonal changes in the river water level can lead to periodic changes in the hydrological conditions of the slope, weakening the slope structure and making it less stable. The river density (Figure 5h) is often used to reflect the ability of rivers to erode the slope [20]. Past studies have shown that vegetation is beneficial for the stability of the slope, and its related factors are also often used to evaluate the landslide hazard [55]. Reflecting the state and biomass of the surface vegetation, the NDVI (Figure 5i) was selected to analyze the impact of vegetation coverage on landslide occurrence in this study. Generally speaking, the higher the NDVI value, the higher the vegetation coverage. Table 3 shows that landslides are more likely to occur when the NDVI is lower. In addition, the melting snow and rain infiltration brought by precipitation are not conducive to the stability of the slope and often trigger landslides [56]. Therefore, the annual precipitation (Figure 5j) was used to analyze the relationship between precipitation and landslide occurrence. About seventy-eight percent of the study area has annual precipitation of no more than 100 mm. As shown in Table 3, slope units with annual average precipitation of 71–89 mm are more prone to landslides.

3.4. Vulnerability Factors

In order to evaluate the vulnerability of the study area, we adopted five vulnerability factors according to related studies and field investigations. As shown in Table 4, the natural breakpoint method was applied to divide the selected vulnerability factors into six categories. We classified the land use according to its inherent attributes, and the economic values of its classes were ranked as follows: unused land, water, grassland, woodland, farmland, and building land. Additionally, we referred to existing studies on vulnerability and assigned values to each class of the factors based on the classification results shown in Table 4 [57].
The population density is an important social component and has a significant impact on social vulnerability [58,59]. Industrial, commercial, and agricultural activities are often vigorous in regions with a high population density [60]. When landslides occur in these regions, they often cause huge casualties and economic losses. As shown in Figure 6a, the zones with a high population density in the study area are mainly distributed in Kashi City and the surrounding Shufu County and Shule County. The GDP is a commonly used macroeconomic indicator that is adopted to measure the economic operation scale of a country or region [61]. We chose the GDP density as the evaluation factor to reflect the economic level of the study area. Generally speaking, the higher the GDP density, the higher the social vulnerability [58]. As shown in Figure 6b, the regions with a higher GDP density in the study area are mainly distributed in the urban region of Kashi and its surrounding counties and in the county town of Taxkorgan County.
Additionally, the road density (Figure 6c) is frequently used in vulnerability evaluation [14]. Roads are the main trunks of the transportation network in the study area, serving as the connection channels for various human activities between the local urban and rural regions. When roads are damaged by landslides, local personnel exchanges and goods transportation are hindered. Furthermore, it is possible for vehicles to be directly buried or damaged by landslides. Thus, the higher the road density, the higher the vulnerability. Additionally, the mine density (Figure 6d) has a significant impact on the vulnerability of the study area. Mining is a common engineering activity in such areas, especially in mountainous regions prone to landslides. As landslides tend to pose a serious threat to the safety of the mining area, the vulnerability also rises with an increasement in the mine density. Land use is also an important factor in vulnerability assessment as it is closely related to human activities. Generally, the higher the economic value of the land, the higher its vulnerability. The class of building land has the highest value of vulnerability and is essentially distributed in the towns along the KKH (Figure 6e).

4. Results

4.1. Landslide Hazard

4.1.1. Results of the AHP Model

According to Equations (4) and (5), the values of the CI, RI, and CR are 0.027, 1.490, and 0.018, respectively. This indicates that the results of the judgment matrix shown in Table 5 meet the requirements of the AHP model. Next, the obtained weight of each predisposing factor was input into Equation (6) to calculate the LHI, as shown in Equation (10). Then, we normalized the LHI, and its value range was from 0 to 1. Finally, the landslide hazard maps of the AHP model were generated using the GIS software. Based on the natural breakpoint method, we highlighted the characteristics of different levels of LHIs and classified the generated LHIs into five grades (Figure 7a,b): very low, low, moderate, high, and very high. Similarly, the other LHI results obtained in this study were also classified by the natural breakpoint method.
LHIAHP = 0.216 × PF1 + 0.050 × PF2 + 0.162 × PF3 + 0.116 × PF4 + 0.079 × PF5 + 0.162 × PF6 + 0.050 × PF7 + 0.031 × PF8 + 0.019 × PF9 + 0.116 × PF10
where PF1 to PF10 are the FR values of the corresponding predisposing factors in Table 3.
Figure 7 shows that the results of the FR-AHP model (Figure 7a) and the DFR-AHP model (Figure 7b) are relatively close. Based on the FR-RF model (Figure 7a), the zones with very low (0–0.15), low (0.15–0.29), moderate (0.29–0.43), high (0.43–0.61), and very high (0.61–1) landslide hazards cover 21.96%, 31.15%, 27.36%, 12.79%, and 6.75% of the entire study area, respectively. Moreover, in the landslide hazard map generated by the DFR-AHP model (Figure 7b), the proportions of very low (0–0.13), low (0.13–0.26), moderate (0.26–0.39), high (0.39–0.58), and very high (0.58–1) landslide hazard zones are 20.85%, 30.52%, 27.45%, 13.72%, and 7.46%, respectively. Meanwhile, zones with very high and high landslide hazards are mainly distributed between Aoyitake and Bulunkou. However, compared with the FR-AHP model, the landslide hazard map obtained by the DFR-AHP model clearly displays that there are more zones with very high and high landslide hazards between Aoyitake and Bulunkou.

4.1.2. Results of the RF Model

To ensure that the RF model has good predictive performance, it is necessary to determine the number of decision trees first. For the RF model, the more decision trees there are, the better the predictive performance will be, but the calculation time will also be longer. However, if there are too few decision trees, the predictive performance of the model will be poor [36]. Thus, using the MATLAB R2022a software, we obtained the optimal number of decision trees through the analysis of the out-of-bag error [62]. The optimal number of decision trees was determined to be 100, with a min_samples_leaf value of 5. Then, the LHIs were calculated using the established model. Finally, the gained LSI results were loaded into the GIS software to generate the landslide hazard maps.
In the landslide hazard map generated by the FR-RF model (Figure 7c), the zones with very low (0–0.12), low (0.12–0.26), moderate (0.26–0.45), high (0.45–0.70), and very high (0.7–1) landslide hazards represent 34.99%, 27.72%, 20.56%, 9.97%, and 6.76% of the entire study area, respectively. However, according to the DFR-RF model (Figure 7d), the zones with very low (0–0.13), low (0.13–0.30), moderate (0.30–0.52), high (0.52–0.77), and very high (0.77–1) landslide hazards account for 36.48%, 29.17%, 14.16%, 12.51%, and 7.68%, respectively. Additionally, compared with the FR-RF model, the DFR-RF model predicts significantly fewer zones with moderate landslide hazards. Moreover, Figure 7 shows that the zones with very high and high landslide hazards predicted by the RF model are also mainly located between Aoyitake and Bulunkou.

4.1.3. Evaluation of the LHA Models

Based on the validation set, we evaluated all the LHA models using the ROC curve. Figure 8a shows that the ROC curves of the different models in this study have apparent discrepancies. In terms of the types of FRs, the AUC values of the models using the DFR method are higher than those of the same types of models using the FR method, which does not consider landslide aggregation. This indicates that the DFR method, considering landslide spatial aggregation, can effectively improve the prediction performance of the LHA model. Overall, the AUC value of the RF model is higher than that of the AHP model, suggesting that the former performs better in LHA studies. Meanwhile, the AUC value (0.913) of the DFR-RF model is also the highest among all models.
In addition, the distribution characteristics of the LHIs and the quantities of landslides under different landslide hazard levels can reflect the rationality and reliability of each LHA model. Firstly, as shown in Figure 8b, the coverage of each landslide hazard grade decreases with an increase in the hazard level on the whole. Moreover, the zones with very high and high landslide hazards only cover a very small part of the study area, ranging from 6.75% to 7.68% and 9.97% to 13.72%, respectively. Secondly, the frequency of landslide occurrence increases with an increase in the landslide hazard level. In the evaluation results of each model, the number of landslides in the zones with very high and high hazards accounts for 79.41% to 91.76% of the total number. Meanwhile, the share of landslides in the low-hazard zone is only 0.59% to 7.059%. The number of landslides in the zone with a very low landslide hazard is the lowest, not exceeding 0.59% of the total. Notably, there are fewer landslides in the zones with very low and low hazards predicted by the LHA models using the DFR method. Overall, all LHA models in this study show good predictive performance. However, the DFR method, which considers landslide aggregation, can significantly improve the predictive ability of the LHA models.

4.2. Vulnerability

As shown in Equation (11), we adopted the AHP model to calculate the vulnerability of the study area. Moreover, the weight of each vulnerability factor was obtained by quantitatively analyzing the relationships among various vulnerability factors through the judgment matrix (Table 6). In the consistency test of this judgment matrix, the values of the CI, RI, and CR are 0.024, 1.120, and 0.022, respectively, indicating that the calculation process satisfies the requirements of the AHP model. Based on the natural breakpoint method, the generated vulnerability map of the study area was divided into five grades: very low (0–0.06), low (0.06–0.17), moderate (0.17–0.38), high (0.38–0.69), and very high (0.69–1).
V = 0.378 × VF1 + 0.271 × VF2 + 0.185 × VF3 + 0.120 × VF4 + 0.046 × VF5
where V is the vulnerability value of each slope unit, and VF1 to VF5 are the values of the corresponding vulnerability factors shown in Table 4.
Figure 9 shows that the zones with high and very high vulnerability are mainly located in the northern part of the study area, including Kashi City and its surrounding towns of Shufu County and Shule County. The zones with high and very high vulnerability account for 0.55% and 1.42% of the study area, respectively. The moderate-vulnerability zones are mainly distributed in the surrounding towns of Kashi City, the county seat of Taxkorgan County, and Aoyitake Town, accounting for 5.27% of the whole area. The coverage of very low- and low-vulnerability zones is significantly larger, accounting for 60.37% and 32.39% of the study area, respectively. In addition, the vulnerability is relatively high near the mining sites and roads.

4.3. Landslide Risk

The landslide risk index (LRI) can be calculated by multiplying the LHI and vulnerability value [6,14]. We selected the result of the DFR-RF model, which performed the best in the model evaluation, as the input variable for the calculation of the landslide risk in this study. According to Equation (12), the landslide risk map was generated by the GIS software. Finally, the normalized landslide risk indices were divided into five categories using the natural breakpoint method: very low (0–0.04), low (0.04–0.12), moderate (0.12–0.29), high (0.29–0.54), and very high (0.54–1).
LRI = LHI × V
where LRI is the value of the landslide risk index of each slope unit, LHI is the value of the landslide hazard index of each slope unit, and V is the vulnerability value.
Figure 10 shows that the zones with very high and high landslide risks in the study area are mainly located on the southern side of Aoyitake Town, accounting for 0.18% and 1.16% of the whole area, respectively. These zones have very small coverage and are characterized by wide bands along the KKH. Moreover, the zones with a moderate landslide risk are mainly distributed in the Gaizi River valley between Aoyitake Town and Bulunkou and are also found around Dabudaer and the county seat of Taxkorgan. These zones account for 7.93% of the study area, and 65.88% of the landslides are distributed in them. They are strip-like, and most of them are close to the KKH. Additionally, the zones with very low and low landslide risks have a wide distribution range, accounting for 64.68% and 26.05%, respectively. Furthermore, due to the fact that most of the study area is uninhabited, many zones with high landslide hazards have also been classified as zones with a low landslide risk based on Equation (12).

5. Discussion

5.1. Application of LAIFR

The spatial aggregation of landslides is widespread in nature, bringing uncertainty to the assessment of landslide hazards and risks. However, it has often been ignored in past studies [19,20,22]. Considering landslide spatial aggregation, we proposed the DFR method with an index called LAIFR. Based on the AHP and RF models, we applied the DFR method to an LHA study and obtained the landslide hazard map along the KKH. The results show that the DFR method can significantly improve the prediction performance of the LHA models. According to the ROC curve, the AUC values of models using the DFR method are significantly higher than those of the original model. This phenomenon occurs in both the AHP and RF models (Figure 8a). Compared with the original FR method, the application of the DFR method can improve the prediction accuracy of the LHA model by 1.4% to 2.1%. However, there are also distinct differences between the AHP and RF models. Compared with the RF model, the AHP model exhibits significantly greater improvements after applying the DFR method. Previous studies have also shown that methods considering landslide spatial aggregation can effectively reduce the uncertainty, but the effects may not be the same in different models [20,22]. In addition, after the application of the DFR method, the landslides distributed in zones with very low and low landslide hazards in the prediction results also decreased conspicuously. Moreover, compared with the existing indices [19,22], the DFR method takes into account the discrepancies in the coverage of various classes of each predisposing factor [20]. In other words, the DFR method is more applicable to the anisotropic natural conditions in terms of basic principles and therefore has a better application effect.

5.2. Analysis of the Landslide Risk in the Study Area

The results regarding the landslide risk depend on the spatial distribution of both the landslide hazard and vulnerability [14]. To ensure high accuracy in the LRA study, the landslide hazard mapping for the study area was ultimately based on the DFR-RF model outputs. Figure 7 shows that the AUC value of the RF model in this study is relatively high, and its performance is superior to that of the AHP model. In previous studies on landslide hazards [16,20,48], different models often show varied performance in prediction. The prediction performance of the same model also varies significantly in LHA studies in different regions. This is closely related to the landslide inventory, the selection of predisposing factors, and the internal logic of the model itself [11]. Therefore, due to the above uncertainties, it is necessary to adopt different prediction models in the assessment of landslide hazards and risks, such as the AHP model and RF model. Among them, the model with the best prediction performance should be selected to calculate the final LHIs. However, most LRA studies only use a single evaluation model to obtain landslide hazard data [6,13,14], and the results often have much uncertainty. Additionally, by comparing Figure 7d and Figure 10, it can be found that many zones with high landslide hazards are classified as those with low or very low landslide risks. In the landslide hazard calculation results of the DFR-RF model, there are 726, 1183, and 1339 evaluation units with very high, high, and moderate landslide hazards, respectively. However, the evaluation units with very high, high, and moderate landslide risks amount to only 17, 110, and 750, respectively. The zones with very high and high landslide risks are mainly distributed along the roads on the southern side of Aoyitake Town. In addition, regions that are distant from roads and densely populated towns generally exhibit lower vulnerability and landslide risks. This phenomenon is particularly common in sparsely populated regions [14].

5.3. Prospects for Further Research

5.3.1. Selection of Predisposing Factors

The selection of predisposing factors is one of the main steps in establishing a landslide hazard model and has a significant impact on the model’s predictive ability [3]. This process requires the comprehensive consideration of the geological environment and the formation mechanism of the landslide to generate the model spatial datasets [11]. In practice, it is difficult to fully reflect the impact of related conditions in a certain area on landslide formation through the selected predisposing factors [63]. On the one hand, the predisposing factors of landslide evolution do not act in isolation, and it is difficult to fully quantify them. For example, in this study, the earthquake, lithology, and precipitation factors were only subjected to preliminary vectorization due to limitations in data acquisition and the method of quantitative analysis. This often leads to varying degrees of distortion of the predisposing factors. On the other hand, there are numerous predisposing factors for landslide occurrence, and regional differences in them are common. Existing studies indicate that the most frequently utilized predisposing factors encompass geology, geomorphology, hydrology, and land cover, with over 40 specific types [3,11]. In general, the LHR model is established by selecting the main controlling factors through field investigations and statistical analysis. This leads to the neglect of some landslide predisposing factors, and the regional differences in the development of landslides cannot be completely reflected in the LHR model. Especially in LHR studies at provincial or larger scales, the established model can only embody the general laws of the overall area and often has high uncertainty [64]. Therefore, it is necessary to explore a systematic and practical method through extensive practice for the selection of predisposing factors. This method should follow the principles of the adaptation of the physical mechanism and the optimization of the regional characteristics.

5.3.2. Evaluation Unit

The selection of the evaluation unit is a prerequisite for the LRA model. The most commonly used evaluation units include grid cells, unique condition units, and hydrological slope units [11]. Among them, the hydrological slope unit can better reflect the relationship between landslide occurrence and geomorphological factors [3,17,63]. The extraction of hydrological slope units is usually based on digital elevation model (DEM) data and GIS software [22]. This method is often time-consuming and labor-intensive when dealing with large-scale regional data, resulting in numerous distorted hydrological slope units. Some studies have found that the automatic extraction of slope units can effectively achieve rapid modeling and improve the predictive performance of the LHR model [65]. However, the existing automatic extraction methods for slope units often produce unreasonable outputs when dealing with complex geomorphological conditions. Therefore, a refined method for the extraction of hydrological slope units needs to be further studied.

5.3.3. Evaluation of the LRA Model

At present, there is a serious lack of reasonable quantitative methods for the analysis of the performance of LRA models. On the basis of the calculation results regarding the landslide hazard, LRA studies also need to further systematically analyze the attributes of the disaster-bearing bodies. Some studies adopt the ROC curve, using only the landslide inventory with disaster attributes to evaluate the LRA model. These studies do not take into account the attributes of the disaster-bearing bodies, which is contrary to the calculation principles of the landslide risk. We qualitatively analyzed the generated landslide risk results of the study area based on the spatial distribution characteristics of landslide risk indices. In the next step of the research, we will carry out the quantitative validation of the LRA model according to the principles of the LRA study and effective statistical methods. Moreover, it is indispensable to establish a validation set based on the high-risk sites obtained from on-site investigations.

6. Conclusions

In this study, considering landslide spatial aggregation, we proposed the DFR method to establish the connection between landslide occurrence and predisposing factors. Furthermore, the DFR method was applied to an LHA study in the section of the KKH between Kashi and Khunjerab, based on the AHP and RF models. Finally, a landslide risk map of the study area was generated with the landslide hazard and vulnerability. The new findings and main conclusions of this study are as follows:
(1)
The DFR method can effectively quantify the degree of landslide spatial aggregation and has a good application effect. Based on the ROC curve and distribution patterns of the LHIs, the model evaluation indicates that the DFR method can practically improve the prediction performance of LHA models.
(2)
Compared with the AHP model, the RF model has higher accuracy in this study. Furthermore, the prediction performance of the DFR-RF model is the best. The landslide hazard map generated by a single type of LHA model often has high uncertainty, and it is better to comprehensively analyze the performance of multiple LHA models to determine the final LHIs.
(3)
The coverage of zones with high and very high landslide risks is very small, and they are mainly distributed along the roads on the southern side of Aoyitake Town. The zones with medium landslide risks are largely concentrated in the Gaizi River valley between Aoyitake and Bulunkou, and some are also found around Dabudaer and the county town of Taxkorgan. Our research provides a reference for local disaster risk prevention and control.

Author Contributions

Conceptualization, X.Y. and Y.S.; methodology, Y.S.; software, X.Y.; validation, Q.M. and H.M.; formal analysis, X.Y.; investigation, Y.S., X.Y., P.S. and I.A.; resources, X.Y.; data curation, Y.S.; writing—original draft preparation, X.Y.; writing—review and editing, Y.S.; project administration, Y.S.; funding acquisition, Y.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the Science and Technology Partnership Program of the Shanghai Cooperation Organization and International Science and Technology Cooperation Program, the Xinjing Department of Science and Technology (Grant No. 2023E01005), the Third Xinjiang Scientific Expedition Program (Grant No. 2022xjkk1305) and the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019QZKK0904).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in this published article, and further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
AHPAnalytic hierarchy process
AUCArea under the curve
CIConsistency index
CRConsistency ratio
DFRDual-frequency ratio
FRFrequency ratio
GDPGross domestic product
KKHKarakoram Highway
LHALandslide hazard assessment
LHILandslide hazard index
LRALandslide risk assessment
NDVINormalized difference vegetation index
PFPredisposing factor
PGAPeak ground acceleration
RFRandom forest
RIRandom index
ROCReceiver operating characteristic
VFVulnerability factor

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Figure 1. Flowchart of the methodology for landslide risk assessment.
Figure 1. Flowchart of the methodology for landslide risk assessment.
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Figure 2. The main cases of landslide spatial aggregation phenomena: (a) case 1; (b) case 2; (c) case 3; (d) case 4.
Figure 2. The main cases of landslide spatial aggregation phenomena: (a) case 1; (b) case 2; (c) case 3; (d) case 4.
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Figure 3. Location map and landslide distribution of the study area: (a) the location of the study area in China; (b) the location of the study area in Xinjiang Province; (c) landslide distribution; (d) example 1 of the hydrological slope units; (e) example 2 of the hydrological slope units.
Figure 3. Location map and landslide distribution of the study area: (a) the location of the study area in China; (b) the location of the study area in Xinjiang Province; (c) landslide distribution; (d) example 1 of the hydrological slope units; (e) example 2 of the hydrological slope units.
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Figure 4. Examples of past and recent landslides alongside the KKH: (a–d) the landslides distributed along the roads. The red dash line indicates the boundary of the landslide.
Figure 4. Examples of past and recent landslides alongside the KKH: (a–d) the landslides distributed along the roads. The red dash line indicates the boundary of the landslide.
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Figure 5. Landslide predisposing factors: (a) elevation; (b) aspect; (c) slope; (d) topographic relief; (e) rock group; (f) fault density; (g) PGA; (h) river density; (i) NDVI; (j) annual precipitation.
Figure 5. Landslide predisposing factors: (a) elevation; (b) aspect; (c) slope; (d) topographic relief; (e) rock group; (f) fault density; (g) PGA; (h) river density; (i) NDVI; (j) annual precipitation.
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Figure 6. Vulnerability factors of the study area: (a) population density; (b) GDP density; (c) road density; (d) mine density; (e) land use.
Figure 6. Vulnerability factors of the study area: (a) population density; (b) GDP density; (c) road density; (d) mine density; (e) land use.
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Figure 7. Landslide hazard maps based on different LHA models: (a) FR-AHP model; (b) DFR-AHP model; (c) FR-RF model; (d) DFR-RF model.
Figure 7. Landslide hazard maps based on different LHA models: (a) FR-AHP model; (b) DFR-AHP model; (c) FR-RF model; (d) DFR-RF model.
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Figure 8. The characteristics of different LHA models’ results: (a) the ROC curves of different LHA models’ results; (b) the distribution characteristics of the LHIs.
Figure 8. The characteristics of different LHA models’ results: (a) the ROC curves of different LHA models’ results; (b) the distribution characteristics of the LHIs.
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Figure 9. Vulnerability map of the study area.
Figure 9. Vulnerability map of the study area.
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Figure 10. Landslide risk map of the study area.
Figure 10. Landslide risk map of the study area.
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Table 1. RI values under the variation in the total number of selected factors.
Table 1. RI values under the variation in the total number of selected factors.
n123456789101112
RI000.520.891.121.261.361.411.461.491.521.54
Table 2. The sources of the spatial databases used in this study.
Table 2. The sources of the spatial databases used in this study.
Predisposing FactorData SourceResolution or Scale
Elevation, slope, aspect, and topographic reliefGeospatial Data Cloud (https://www.gscloud.cn) (accessed on 6 June 2024)30 m
Rock group and fault densityGeological map (accessed on 6 June 2024)1:250,000
PGAChina Earthquake Administration (https://www.cea.gov.cn/cea/index/index.html) (accessed on 24 June 2024)1:250,000
Annual precipitationWorldClim (https://www.worldclim.org) (accessed on 26 December 2024)1 km
Population density and GDP densityResource and Environmental Science Data Platform (https://www.resdc.cn) (accessed on 26 December 2024)1 km
River density, road density, and mine densityNational Platform for Common Geospatial Information Services (https://map.tianditu.gov.cn) (accessed on 26 December 2024)30 m
NDVI and land useNational Cryosphere Desert Data Center (http://www.ncdc.ac.cn) (accessed on 23 January 2025)1:10,000
Table 3. FRs of the landslide predisposing factors.
Table 3. FRs of the landslide predisposing factors.
Predisposing FactorValueFRLAIFRDFR
Elevation (m)
(PF1)		1254–17260.0131.0000.013
1726–23044.8470.5072.456
2304–29043.2830.4771.567
2904–34822.1930.4230.929
3482–39321.1310.4740.536
3932–43810.1320.5000.066
4381–49170.3120.8460.264
4917–67150.0000.0000.000
Aspect (°)
(PF2)		−10.0000.0000.000
0–22.5, 337.5–00.0000.0000.000
22.5–67.50.2410.5000.121
67.5–112.50.4920.7310.360
112.5–157.51.5120.3930.593
157.5–202.51.1710.4240.496
202.5–247.50.8760.6180.541
247.5–292.50.5220.6320.330
292.5–337.50.1981.0000.198
Slope (°)
(PF3)		0–70.0460.4000.018
7–120.5630.5000.281
12–161.0690.4000.428
16–212.7730.3611.001
21–261.0280.7320.752
26–301.7000.4430.752
30–352.8420.5251.491
>350.9630.7500.722
Topographic relief (m)
(PF4)		0–520.0430.4000.017
52–1080.6040.4880.295
108–1631.7530.3970.697
163–2142.0280.4460.904
214–2621.2200.5000.610
262–3202.3080.4591.059
320–3982.2350.7141.596
398–6211.3190.5710.753
Rock group
(PF5)		Very hard1.5870.5260.835
Hard0.9450.8240.778
Less hard1.7050.4400.750
Soft1.2880.4950.638
Very soft0.5290.3560.188
Water0.7380.5000.369
Fault density (km/km2)
(PF6)		0–0.120.3170.5100.162
0.12–0.281.1740.3500.411
0.28–0.401.5230.5350.814
0.40–0.501.4060.5450.767
0.50–0.623.3700.4931.660
0.62–0.782.1670.5431.176
0.78–0.980.6960.3330.232
0.98–1.221.7020.8001.362
PGA (g)
(PF7)		0.200.6410.6840.439
0.301.1220.4660.522
0.400.0720.5000.036
River density (km/km2)
(PF8)		0–0.150.0820.5000.041
0.15–0.361.0970.5000.549
0.36–0.601.6190.4960.803
0.60–0.902.6390.4301.134
0.90–1.270.4140.5830.241
1.27–1.700.1510.6670.101
1.70–2.360.0000.0000.000
2.36–3.350.0000.0000.000
NDVI
(PF9)		−1.00–−0.130.0000.0000.000
−0.13–0.060.3930.8570.337
0.06–0.171.9360.4260.824
0.17–0.270.8780.5630.494
0.27–0.400.2880.5000.144
0.40–0.560.6370.5880.375
0.56–0.710.0461.0000.046
0.71–1.000.0000.0000.000
Annual precipitation (mm)
(PF10)		50–710.4370.5880.257
71–892.7120.4221.143
89–1030.4190.6510.273
103–1240.2130.8000.170
124–1510.0511.0000.051
151–2030.0000.0000.000
203–2870.0000.0000.000
287–4200.0000.0000.000
Table 4. The classification results of the vulnerability factors.
Table 4. The classification results of the vulnerability factors.
Vulnerability FactorValue
0.10.20.30.40.50.6
Population density (persons/km2) (VF1)0–827827–28932893–54755475–10,12310,123–17,45717,457–26,339
GDP density (CNY 10,000/km2) (VF2)0–55–1515–2929–4545–6161–76
Road density (km/km2) (VF3)0–0.270.27–1.061.06–2.342.34–3.923.92–6.026.02–9.58
Mine density (points/km2) (VF4)0–0.100.10–0.320.32–0.550.55–0.770.77–1.001.00–1.38
Land use (VF5)Unused landWaterGrasslandWoodlandFarmlandBuilding land
Table 5. The judgment matrix and weight values of the predisposing factors in the AHP model.
Table 5. The judgment matrix and weight values of the predisposing factors in the AHP model.
Predisposing FactorPF1PF2PF3PF4PF5PF6PF7PF8PF9PF10Weight
PF11 0.216
PF21/51 0.050
PF31/241 0.162
PF41/331/21 0.116
PF51/421/31/21 0.079
PF61/241231 0.162
PF71/511/41/31/21/41 0.050
PF81/61/21/51/41/31/51/21 0.031
PF91/71/31/61/51/41/61/31/21 0.019
PF101/331/2121/234510.116
Table 6. The judgment matrix and weight values of the vulnerability factors.
Table 6. The judgment matrix and weight values of the vulnerability factors.
Vulnerability FactorVF1VF2VF3VF4VF5Weight
VF11 0.378
VF21/21 0.271
VF31/31/21 0.185
VF41/41/31/21 0.120
VF51/61/51/41/310.046
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Yi, X.; Shang, Y.; Meng, H.; Meng, Q.; Shao, P.; Ahmed, I. Regional Landslide Hazard and Risk Assessment Considering Landslide Spatial Aggregation and Hydrological Slope Units. Appl. Sci. 2025, 15, 8068. https://doi.org/10.3390/app15148068

AMA Style

Yi X, Shang Y, Meng H, Meng Q, Shao P, Ahmed I. Regional Landslide Hazard and Risk Assessment Considering Landslide Spatial Aggregation and Hydrological Slope Units. Applied Sciences. 2025; 15(14):8068. https://doi.org/10.3390/app15148068

Chicago/Turabian Style

Yi, Xuetao, Yanjun Shang, He Meng, Qingsen Meng, Peng Shao, and Izhar Ahmed. 2025. "Regional Landslide Hazard and Risk Assessment Considering Landslide Spatial Aggregation and Hydrological Slope Units" Applied Sciences 15, no. 14: 8068. https://doi.org/10.3390/app15148068

APA Style

Yi, X., Shang, Y., Meng, H., Meng, Q., Shao, P., & Ahmed, I. (2025). Regional Landslide Hazard and Risk Assessment Considering Landslide Spatial Aggregation and Hydrological Slope Units. Applied Sciences, 15(14), 8068. https://doi.org/10.3390/app15148068

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