Hazard Assessment of Rainfall–Induced Landslide Considering the Synergistic Effect of Natural Factors and Human Activities

Abstract

Landslide hazard assessment is essential for determining the probability of landslide occurrence in a specific spatial and temporal range. The hazard assessment of potential landslides could support landslide disaster early warning and disaster prevention decisions, which have important guiding significance for urban construction and sustainable development. Due to the lack of consideration of the synergistic effect of multiple factors and geographic scene heterogeneity, the accuracy of existing landslide hazard assessment methods still needs to be improved, and the interpretability and applicability of existing models still need to be improved. In this paper, we propose a landslide hazard assessment method considering the synergistic effect of multiple factors, including natural factors and human activities, and the heterogeneity of geographic scenes. On this basis, we carry out experimental verification on rainfall–induced landslides in Dehong Prefecture, Yunnan Province, China. Firstly, rainfall–induced landslide hazards’ characteristics and impact factors are analyzed and classified. The whole study area is divided into some homogeneous sub–regions using regional dynamic constraint clustering based on the similarity of underlying environmental variables. Then, considering the spatial autocorrelation between various landslide conditioning and trigger factors, a local weighted random forest model is developed to evaluate the rainfall–induced landslide hazards comprehensively. Experimental results show that the proposed method has higher accuracy and interpretability than the existing representative methods and can provide useful references for preventing landslide hazards.

1. Introduction

Landslides are one of the world’s most critical geological hazards that significantly harm the surrounding environment and resources and threaten the security of the surrounding residents and infrastructure [1]. In China, landslides caused over 25,000 deaths from 1949 to 2011, with an average annual economic loss of around 50 million US dollars [2,3]. Rainfall is one of the primary triggers of landslides, with rainfall–induced landslides accounting for over 90% of all landslides in China [4]. The evolutionary trend of landslide hazard can be actively predicted by evaluating the probability of landslide occurrence in a specific spatial and time range, which can provide important guidance for early warning and prevent landslides [5]. It is essential to accurately and swiftly evaluate the latent landslide hazards for disaster prevention, urban planning and sustainable development, such as the planning of landslide defense facilities and site selection of urban construction, etc.

In recent years, scholars have paid much attention to landslide hazard assessment, and a series of achievements have been made. Landslide hazard assessment models are usually constructed based on static spatial susceptibility and dynamic temporal inducibility [6]. The spatial susceptibility represents the spatial probability of landslide occurrence determined by the environmental factors (also called conditioning factors) such as topographic slope, geological structure, meteorological and hydrological factors, and other features [7,8,9]. Temporal inducibility indicates the temporal probability of landslide occurrences with certain trigger factors such as rainstorms, earthquakes, and human activities [5,7,10,11,12]. It is key to effectively couple the results of susceptibility and inducibility for objectively perceiving landslide hazards [13,14,15,16]. For example, Salciarini et al. proposed a landslide hazard assessment model based on rainfall–induced slope damage probability and validated it in central Italy [13]. Pradhan et al. first quantified the spatial and temporal probabilities of landslide occurrence based on the artificial neural network and effective rainfall intensity model, and then realized landslide hazard assessment in Busan, Korea, with the help of a heuristic matrix [15]. Liu et al. input the conditioning factor and rainfall trigger factor into the machine learning model and used a data–driven strategy to realize landslide hazard assessment [16].

The existing landslide hazard assessment methods can be divided into four categories according to the differences in modeling the landslide hazards. The details are shown as follows:

(1)

Physical methods. This method usually uses various physical models to explore the possibility of landslides occurring under different trigger factors (i.e., rainfall, earthquake) for specific slope structures and constituent materials [17,18,19,20]. For example, Zhuang et al. used an infinite–slope model to evaluate the hazard of shallow landslides on the loess plateau under different rainfall conditions based on the decay law of rainfall–caused soil strength change [17]. The physical method does not rely on a large amount of historical landslide data. However, this type of method requires strict physical assumptions and complex model parameters and is usually only applicable to specific landslide areas.

(2)

Empirical methods. This method scores or ranks landslide influencing factors based on expert experience and then analyzes and evaluates regional landslide hazards [21,22,23]. For example, Chau et al. assigned and weighted the influence factors based on expert experience and realized landslide hazard assessment of Hong Kong Island, China [21]. The empirical method has the advantage of simplicity and efficiency. However, the model effect depends on the subjective knowledge of experts on the landslide occurrence mechanism and the lack of generalizability in a wide range of applications.

(3)

Probabilistic coupling methods. This method quantitatively estimates and couples the temporal, spatial, and intensity probabilities of regional or individual landslide occurrence based on heuristic matrices or continuous probabilities [24,25]. Huang et al. proposed a method to obtain the continuous–type landslide hazard probabilities with the multiplicative model based on the temporal and spatial probabilities of landslide occurrence [25]. The probabilistic coupling method can comprehensively consider various factors for a comprehensive and effective assessment of landslide hazard. However, different factors’ coupling modes and weight settings still have some subjectivity.

(4)

Statistical methods. This method provides a uniform, unified estimation of the latent landslide hazard based on a complex nonlinear correlation model with related conditioning and triggering factors [26,27]. Huang et al. proposed a landslide hazard assessment method based on an improved deep belief network and applied the method to the disaster assessment in the Wenchuan earthquake region [26]. The method overcomes the problems of poor learning ability and the weak feature extraction ability of traditional machine learning methods.

Although the existing methods for landslide hazard assessment have made remarkable achievements in the analysis of impact factors causing landslide disasters and quantitative evaluation models of landslide hazards, some limitations still need to be further solved. On the one hand, most existing methods only use rainfall as a trigger factor, resulting in low accuracy of the assessment results [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]; on the other hand, the current methods usually model hazards in different geographical scenarios as a whole or consider only one–factor variability [28,29], ignoring the impact of multi–factor spatial stratified heterogeneity and spatial correlation, which makes it difficult to explain the generation and evolution process of the assessment results. This paper proposes a method that considers the synergistic effect of multiple factors to solve these issues. The main contributions of this study are as follows:

(1)

Different from existing strategies, in this paper, the study area is first divided into some homogeneous regions by a spatial constrained hierarchical clustering method based on the similarity of underlying environmental variables, which effectively weakens the impact of geographic scene heterogeneity on landslide hazard assessment modeling;

(2)

The locally weighted random forest (LWRF) method is developed for landslide hazard assessment, which can effectively account for the synergistic effects of spatial correlation and multi–source trigger factors, including natural factors, i.e., rainfall, and human activities such as land reclamation and building roads and houses;

(3)

A typical city in Yunnan Province, China, is selected for the case study of rainfall–induced landslide hazard assessment. Experiments based on real data and comparative analysis are conducted to verify the effectiveness of the proposed method.

The rest of this paper is organized as follows. The study area and data sources used in this study are described in Section 2. Section 3 presents the details of the proposed method for landslide hazard assessment. Results are presented in Section 4. Section 5 is the discussion of this paper. Finally, we give our conclusions in Section 6.

2. Study Area and Data Sources

2.1. Study Area

Dehong Prefecture is located in the southwest of Yunnan Province, China. It has two cities—Mangshi and Ruili—and three counties—Lianghe, Longchuan and Yingjiang. Dehong Prefecture is located at longitude 97°31′40″~98°43′36″ E and latitude 23°50′40″~25°20′10″ N. With a total land area of about 11,526 square kilometers and a total population of approximately 1,138,000 [30,31], Dehong Prefecture receives an average annual precipitation of over 1000 mm [32]. The region has a wet season from mid–May to mid–October, when precipitation accounts for more than 85% of the year, and a dry season from mid–October to mid–May. As one of the most severe geological disaster areas in Yunnan Province, landslides in Dehong Prefecture have the following characteristics: frequent, extensive, sudden, and devastating. From 2015 to 2019, the region had over 400 geological hazards, causing direct economic losses of over CNY 3.5 million [33]. The distribution of historical landslide disasters in the study area is shown in Figure 1.

Dehong Prefecture generally presents a landscape of mountains, river valleys, and basins arranged in parallel [30]. It is located on the windward slope of the northeastern end of the low–altitude topographic region in central and west Myanmar, which rises towards western Yunnan. The strata in the study area are well developed, with outcrops from Sinian to Quaternary, and are geologically part of the Hengduan Trough Fold Belt of the Tibetan–Yunnan Trough Fold System. The Lushui–Ruili Rift, the Wengmai Rift and the Dayingjiang Rift run diagonally across the state, with powerful adverse geological effects, and 80% of the study area is covered with gneiss and granite. It is highly susceptible to weathering and the formation of unstable rock and soil masses under subtropical climatic conditions. The fragile geological is suitable for forming and developing landslides [34].

2.2. Experimental Data and Sources

The landslide cataloging data used in this paper came from the Yunnan Institute of Geological Environment Monitoring, including 472 landslides between 2015 and 2019. According to the topography, geomorphology, geological structure, and meteorological and hydrological conditions of the study area, relevant data such as digital elevation model, soil type, 1:2,500,000 geological map, and water system distribution were collected, and 13 conditioning factors were further generated as shown in Figure 2. In addition to rainfall (including pre–rainfall) as a trigger factor, human activities such as land reclamation and building roads and houses were also considered trigger factors. Finally, effective rainfall intensity, road density, building footprintdensity, normalized difference vegetation index (NDVI), and other factors were selected as the multi–source trigger factors of landslide. The relevant data sources are shown in

Table 1. The data sources.

Data Set	Data Description	Data Source
Digital elevation model	30 m digital elevation model	http://www.usgs.com/ (accessed on 20 March 2022)
Soil type	1:1,000,000 soil type data	http://www.ncdc.ac.cn/ (accessed on 20 March 2022)
Geological map	1:2,500,000 geological map data	https://www.resdc.cn/ (accessed on 20 March 2022)
Road network/water system distribution	1:250,000 public basic geographic data	https://kmap.ckcest.cn/ (accessed on 20 March 2022)
Rainfall data	Meteorological monitoring station data, CLDAS–V2.0	https://data.cma.cn/ (accessed on 20 March 2022)
Landsat–8 image	30 m remote sensing image data	https://www.gscloud.cn/ (accessed on 20 March 2022)
Building footprint	Building footprint map data	https://www.resdc.cn/ (accessed on 20 March 2022)

.

The following factors are generated from the above data sources, as shown in

Table 2. Factors and effect on landslides.

Category	Subcategory	Factor	Effect on Landslide
Conditioning factors	Topography	Elevation	The spatial distribution of landslides varies with different elevation values and is mainly reflected in the following aspects: vegetation coverage, vegetation type, land use intensity, and rock–soil mass distribution at the critical surface of landslides.
		Slope	The slope has great influence on the stress distribution of rock–soil mass on slopes, the surface water run of on slopes, the recharge and discharge of groundwater in slopes, the thickness of the weathered layer on slopes, the vegetation coverage, and the land use. It can affect the stability of landslides.
		Aspect	Different slope directions lead to different intensity of solar radiation and weathering, which affect factors such as the vegetation coverage, water evaporation, and soil humidity. Consequently, the distribution of the groundwater pore pressure of rock–soil mass, as well as the physical and mechanical characteristics change, thus indirectly affecting the slope stability.
		Plane curvature	Plane curvature affects slope stability by influencing slope morphology.
		Profile curvature	Profile curvature affects slope stability by influencing the structure of the sliding surface.
	Geological structure	Fault density	The vicinity of a fault is prone to vibration, which reduces slope stability. The higher the density of the fault, the more likely it is that landslides will occur.
		Distance from fault	The vicinity of a fault is prone to vibration, which reduces slope stability. The closer to the fault, the more likely it is that a landslide/failure will occur.
		Lithology	Stratum lithology is an important material basis for the formation and development of landslides, which directly affects the physical and mechanical properties of slopes and plays a decisive role in the stability of slopes.
	Meteorology and hydrology	Distance from river	The flowing water leads to distinct scour and erosion on the bank slope, which destroys the stability of the bank slope, the closer to the river, the more likely it is that a landslide/failure will occur.
		River density	The flowing water leads to distinct scour and erosion on the bank slope, which destroys the stability of the bank slope, the higher the density of the river, the more likely it is that landslides will occur.
		Average annual precipitation	Areas of high rainfall can lead to infiltration of rainwater and reduce slope stability.
Trigger factors	rainfall	effective rainfall intensity	Rainfall can infiltrate along fractures in the landslide mass and greatly affect the shear strength of slopes, and important stages in the evolution of slope morphology caused by shallow landslides are usually associated with short but intense rainfall events.
	Human activity	Road density	When a road is constructed, the cut slope causes disturbance to the natural slope and weakens the stability of the slope foot.
		Building footprint density	When a building is constructed, the cut slope causes disturbance to the natural slope and weakens the stability of the slope foot.
		Normalized Difference Vegetation Index	Vegetation can improve the shear strength of the soil and fix the soil through the interaction between the root system and the soil. It can also reduce soil erosion and maintain rock–soil mass stability. Therefore, vegetation has an important effect on the stability of rock–soil mass on slopes.

. Figure 2 shows the conditioning factors, and Figure 3 shows the trigger factors on 9 August 2017; these factors changed over time. Data such as road network density, building footprints density, and NDVI can reflect the intensity of human activities from different time periods, such as slope cutting, road construction, deforestation, and other essential information, which can be extracted based on geographic information analysis software such as ArcGIS or QGIS. The effective rainfall intensity can measure the law of rainfall–induced landslides from the aspects of effective rainfall and rainfall duration [35], and the calculation of effective rainfall intensity is as follows:

$$EI=\frac{R_c}{D}$$

(1)

where EI represents the effective rainfall intensity, $R_c$ represents the effective rainfall, calculated by Equation (2), and D represents the rainfall duration, which represents the number of rainfall days before the landslide event.

$$R_c=R_1+\alpha R_2+{\alpha }^2{R}_3+\dots +{\alpha }^{n-1}{R}_n$$

(2)

where $\alpha$ is the effective rainfall coefficient, $R_1$ is the amount of rainfall of that day, n is the duration of the rainfall process, and $R_n$ is the rainfall of the $n$th day before the occurrence of a landslide. Based on the rainy season cycle and geological conditions in Dehong Prefecture, the effective rainfall coefficient is set to 0.84 according to previous studies by Li et al. [36] and Wang et al. [37].

3. Methodology

This paper proposes a rainfall–induced landslide hazard assessment method that considers the synergistic effect of multi–source induced factors, including natural factors and human activities. As we all know, landslides rarely occur in flat areas, and landslides tend to occur in slope areas with a particular slope. In our study, the slope areas were first extracted based on the topographic features and used as the basic spatial units for landslide hazard assessment. Based on the sloped areas, the conditioning factors were first calculated and a spatial constrained hierarchical clustering algorithm was used to partition the study area into different homogenous sub–regions with similar conditioning factors. Then, the dynamic trigger factors such as effective rainfall intensity, road network density, building distribution, and NDVI for each slope area were calculated. Further, the locally weighted random forest model was developed to determine the landslide hazards. Finally, experiments and comparative analysis were conducted to evaluate the effectiveness of the proposed method. The framework of the proposed method is shown in Figure 4.

3.1. Extraction of Slope Areas

Since slopes have consistent geological properties and precise variable meanings, slopes are identified as the basic unit of analysis in this paper. The mean–curvature watersheds method [38] was used to generate the slopes, and the specific method of generation was as follows:

(1)

The horizontal surface is often uneven at the ground surface due to slope erosion and stream development, resulting in increased elevation roughness. Before solving for curvature, small–scale variations in elevation were removed using mean filtering. The processed elevation data calculated the mean curvature value for each grid.

(2)

The flow direction data were solved by assuming that the mean curvature was a value or elevation describing the undulations of the terrain. The depression units were then solved based on the flow direction data. The basin was then cracked using the flow direction as the base map and the depressions as catchment points. After vectorizing the basin raster data, the concave geomorphic element boundaries were obtained.

(3)

The mean curvature data were inverted, step 2 was repeated, and the inverted curvature data were calculated to obtain the convex geomorphic element boundaries. The two types of boundaries were then combined to extract the slope areas.

3.2. Space Partitioning

Goodchild [39] once pointed out that “geographic variables exhibit uncontrolled variance” and extended this to the second law of geography. This law describes the differences in the spatial distribution of geographical phenomena, i.e., the spatial distribution varies with the characteristics of geographical phenomena, time, place, scale, etc. Spatial heterogeneity is widely reflected in human society, such as population distribution, climate change, disaster analysis, and other areas [40,41,42]. Due to spatial heterogeneity, the relationship between conditioning factors and trigger factors changes with the change of geographical location, which violates the a priori assumption that “evaluation factors obey independently and identically distributed”. Furthermore, it is difficult for global estimation model parameters to properly describe local regions, which results in different credibility of traditional hazard assessment results between regions. Therefore, this paper adopts the spatial constrained hierarchical clustering algorithm [43] for spatial partitioning, hoping to establish adaptive landslide hazard assessment models in different homogeneous proton regions. In essence, the spatial constrained hierarchical clustering algorithm constructs a group of homogeneous regions by aggregating adjacent slopes with similar attribute values. The specific partitioning idea is as follows:

First of all, we need to define the objective of clustering. The partition object of this paper is to find the sub–regions in which the conditioning factors are similar. In this paper, we first calculate each slope area’s representative point (i.e., center point) and extract the corresponding conditioning factors as its attribute values. Then, the representative points of all slope areas in the study area are used as input for the clustering. The clustering objective is defined as the minimum sum of square deviations of each partition in the study area and is calculated as follows:

$$SSD=\sum _{r=1}^k\sum _{i=1}^{n_r}\sum _{j=1}^d{\left(x_{ij}-{\overline{x}}_j\right)}^2$$

(3)

where $k$ denotes the number of regions, $n_r$ is the number of representative points within the region $r$ (adjacent small areas), $d$ is the number of variables or factors to be considered, $x_{ij}$ is the $j$th variable value of the $i$th representative point in region $r$, and ${\overline{x}}_j$ is the average of the $j$th variable values of all representative points in region $r$. Each of the variables or factors should be normalized, and a weight can be assigned to each variable or factor in clustering.

We apply a spatially constrained hierarchical clustering algorithm [44] to obtain the homogeneous regions. In the clustering, the first step is to construct the neighborhood’s relationship of the representative points based on the Delaunay triangulation (DT) network. If two points are connected by an edge of the DT network, then the two points are spatially adjacent; otherwise, the two points are not spatially adjacent. Then, spatially adjacent points with similar conditioning factors are hierarchically aggregated to build a minimum spanning tree according to the average linkage strategy. Finally, the edges in the minimum spanning tree are pruned to find clusters using a top–to–bottom partitioning strategy until the desired number of regions is reached. Details of the clustering algorithm can be found in [43].

3.3. Landslide Hazard Assessment Method

3.3.1. Local Weighted Random Forest (LWRF) Model

Existing landslide hazard assessment studies usually estimate the probability or hazard level of a region where the landslides may occur based on conditioning or/and trigger factors of this region. However, the above studies neglected to consider the neighborhood information of sampling locations, resulting in insufficient modeling of spatial correlation and heterogeneity. The occurrence of landslide disasters is not only related to the characteristics of the geographical location but also to the characteristics of the adjacent locations. For example, roads or rivers usually surround the landslide area, and the non–landslide area is usually less prone to occurrence. Thus, this paper proposes a local weighting strategy to capture the correlation of adjacent spatial positions, as shown in Figure 5. Specifically, the Delaunay triangulation network is used to construct the adjacency relation between the neighboring slope areas (as described in Section 3.2) and then calculate the conditioning factors and trigger factors of a sloped area by considering the influence of its first–order neighboring sloped areas. The influence weights are calculated using the inverse distance weighting method [44]. In the local weighted model, the adjacency weight is calculated as follows:

$$w_{ij}=\frac{d_{ij}}{\sum _j^k{d}_{ij}}$$

(4)

where $w_{ij}$ denotes the influence weight of the $\mathrm{i}$th slope area by the $j$th adjacent slope area, $d_{ij}$ represents the distance between the $\mathrm{i}$th slope area and the $j$th adjacent slope area, and $k$ represents the number of adjacent slope areas of the $i$th slope area.

Machine learning has the advantage of processing rich data and ultra–multidimensional spatial datasets to achieve accurate classification and prediction, which is suitable for handling the estimation of non–linear relationships and is widely used in hazard assessment. Commonly used machine learning models include support vector machine (SVM), random forest (RF), logistic regression (LR), artificial neural network (ANN), and convolutional neural network (CNN); the advantages and disadvantages of different machine learning models are shown in

Table 3. Comparison of common machine learning algorithms.

Model	Advantages	Disadvantages
SVM	Simplifies the usual problems such as classification and regression.	It is difficult to evaluate the large–scale and multi–classified training samples.
RF	Good performance; fast training; balanced dataset error; good resistance to overfitting; can avoid the influence of strong samples on the evaluation results.	It is not possible to control the inner workings of the model.
LR	Suitable for scenarios with classification probability; easy to implement; good robustness to small noise in the data.	It is easy to underfit, the classification accuracy is not high, and it does not perform well when there are missing data feature.
ANN	High class accuracy; strong learning ability.	A large number of parameters are required, the learning time is too long, and the evaluation results are uncertain.
CNN	Good portability; handles high–latitude data; automatic feature extraction.	When the network level is too deep, the parameters are slow to change; the pooling layer loses a lot of valuable information, and the model is less efficient.

. The random forest model has the advantages of high stability, ease of use, and low time cost. In addition, the random forest model is less sensitive to noise and is less prone to overfitting. Compared with other machine learning methods, random forests are more suitable for modeling small samples [45]. Therefore, this paper chose the random forest model as the base model.

Random forest is a combinatorial classification algorithm in ensemble learning [46]. This model continuously generates decision trees conforming to the distribution of sampled small data sets through placing sampling on training sets through multiple random number algorithms, and then votes and scores according to the prediction results of all decision trees, finally obtaining the optimal prediction results, as shown in Figure 5. Thus, in this paper, we develop a local weighted random forest approach to achieve a nonlinear mapping between the conditioning factors and dynamic trigger factors to the occurrence possibility of landslide hazards. Different from the previous studies based on the random forest model, we build different random forest models for different homogeneous sub–regions obtained in the spatial partitioning step by considering the impact of geographic scene heterogeneity; for each random forest model, not only the features of the target sample itself but also the features of its spatial neighborhood samples are used as the input to train the model, which improves the ability to capture spatial context features.

3.3.2. Positive and Negative Sample Generation

This paper generated and labeled 1416 landslide samples by experienced experts, including 472 positive samples (some landslides occurred between 2015 and 2019) and 944 negative samples, to train the local weighted random forest model described above. Among them, the spatiotemporal position of the positive sample depends on the occurrence time and geographical coordinates of the landslide; while the spatiotemporal position of the negative sample is randomly generated outside a certain space range of the positive sample, the 500 m buffer is used in this paper and the time of occurrence is randomly generated outside the date of the disaster point. Considering the equilibrium of positive and negative sample features, the positive and negative sample ratio is set to 1:2 regarding Liu [12]. Finally, the sample divided into training set and test set according to the ratio of 7:3. The demonstration of positive and negative sample generation is shown in Figure 6.

3.3.3. Evaluation Index of the Results

The accuracy rate (Acc), recall rate (Recall), false negative rate (FNR), and false positive rate (FPR) are used to measure the effectiveness of the results. Among them, the accuracy rate represents the proportion between the number of samples correctly classified to the total number of samples, defined as Equation (5). The recall rate represents the proportion of positive samples correctly classified to the total number of positive samples, defined as Equation (6). The false negative rate represents the proportion of positive samples classified as negative samples, defined as Equation (7). The false positive rate represents the proportion of negative samples being predicted as positive samples in the total number of negative samples, defined as Equation (8).

$$Acc=\frac{TP+TN}{TP+FP+TN+FN}$$

(5)

$$Recall=\frac{TP}{TP+FN}$$

(6)

$$FNR=\frac{FN}{TP+FN}$$

(7)

$$FPR=\frac{FP}{FP+TN}$$

(8)

where TP represents the number of correctly predicted positive samples, FP represents the number of incorrectly predicted positive samples, TN represents the number of correctly predicted negative samples, and FN represents the number of incorrectly predicted negative samples.

4. Results

4.1. Experimental Results

Before conducting spatial clustering, it is necessary to select the related conditioning factors, as highly correlated factors may cause data redundancy and have a negative impact on the model’s predictions. The Pearson correlation coefficient is used to analyze the correlation between the conditioning factors and to select the significant related factors. The calculation of the Pearson correlation coefficient is shown in Equation (9). The range of the Pearson correlation coefficient is [−1, 1]. When the absolute value of the correlation coefficient between two influence factors is more significant than 0.8, it indicates a strong correlation. The Pearson correlation coefficients between the different conditioning factors are shown in Figure 7; only the Pearson correlation coefficient between the relative relief factor and slope factor is more significant than 0.8. Therefore, the relative relief factor is eliminated, and the slope factor is retained.

$${\rho }_{x_1{x}_2}=\frac{Cov(x_1,x_2)}{\sqrt{D\left(x_1\right)}\sqrt{D\left(x_2\right)}}$$

(9)

where $x_1$ and $x_2$ represent two variables and ${\rho }_{x_1{x}_2}$ represents the correlation coefficient between $x_1$ and $x_2$. $Cov(x_1,x_2)$ represents the covariance between variables $x_1$ and $x_2$, and $D\left(x_1\right)$ and $D\left(x_2\right)$ represent the variance of $x_1$ and $x_2$, respectively.

Based on the selected conditioning factors, we partition the study area into sub–regions with similar conditioning factors by the spatially constrained hierarchical clustering method [44]. The partitioning results with different numbers of clusters are shown in Figure 8. The commonly used silhouette coefficient index is applied in the experiments to select an optimal clustering result among these partitioning results. The silhouette coefficient is used to evaluate the clustering effectiveness, describing the contour sharpness of each category after clustering and including two factors—cohesion and separation. Cohesion reflects the closeness between a sample point and elements within the same cluster, and separation reflects the closeness between a sample point and elements outside the cluster. The silhouette coefficient is calculated as follows:

$$S=\frac{1}{N}{\sum }_{i=1}^N\frac{b\left(i\right)-a\left(i\right)}{max\{a\left(i\right),b\left(i\right)\}}$$

(10)

where $S$ is the silhouette coefficient, N is the number of samples in data, $a\left(i\right)$ is the average distance between the $i\mathrm{t}\mathrm{h}$ sample and other samples in the same cluster (i.e., cohesion), and $b\left(i\right)$ is the minimum average distance between the $i\mathrm{t}\mathrm{h}$ sample and samples in other clusters (i.e., separation).

The value range of the silhouette coefficient is [−1, 1], and the larger the silhouette coefficient is, the better the clustering result. According to the statistical silhouette coefficient, a larger silhouette coefficient index can be obtained when the number of clusters is six. Therefore, this paper divides the study area into six subregions, as shown in Figure 8.

Multiple measures are used to verify the results and analyze the proposed method’s effectiveness. The comparison method and indicator statistics of each model are shown in

Table 4. Comparison of different landslide hazard assessment methods.

Trigger Factors	Methods	Acc	Recall	FNR	FPR
Only the rainfall factors	Heuristic matrix [10]	66.04%	69.78%	30.22%	35.76%
	SVM [12]	75.52%	78.75%	21.25%	25.21%
	RF [47]	83.22%	83.19%	16.81%	16.77%
	LWRF	86.68%	84.55%	14.45%	12.89%
Rainfall factors and human activity factors	LWRF	89.51%	89.58%	10.42%	10.51%

. From Table 4, it can be found that:

(1)

Compared with the results by different methods, the local weighted random forest model has advantages over the heuristic matrix, support vector machine, and random forest. The proposed method can also achieve higher accuracy and recall rates with the same training samples and trigger factors (i.e., the rainfall factors). The false positive and false negative rates are relatively lower than other methods.

(2)

When rainfall factors and human activities are both considered, the accuracy of the proposed method is further improved. Compared with other methods, such as the SVM–based method and RF–based method, the performance indicator of the proposed method shows significant improvement, respectively, with the accuracy rate and recall rate reaching its highest percentage, and the false negative rate and false positive rate reaching their lowest percentage.

4.2. Results Analysis

The experimental results show that considering multi–source trigger factors, spatial partitioning, and the local weighting strategy can significantly improve the accuracy of landslide hazard assessment. The main reasons are the following. Firstly, the study area is divided into multiple subregions, and the models for landslide hazard assessment are carried out separately, which can weaken the influence of spatial heterogeneity to a certain extent and improve the pertinence of the sample set in the study area, reducing the complexity of the model. Secondly, compared with the existing method that only considers rainfall factors, human activities such as cutting the slope areas, building roads, houses and reservoirs, and deforestation are also some important trigger factors for landslide hazards; thus, when additional consideration is given to human activities, a more comprehensive model may be built. In addition, the local weighted random forest model can capture the influence of the adjacent slope areas on the target slope area instead of considering these slope areas as separate entities.

5. Discussion

5.1. Case Study

Figure 9 shows assessment results from different methods on 9 August 2017. On 9 August 2017, five rainfall–induced landslides occurred in Dehong Prefecture, located in Dachang village of Lianghe County, Kazi village of Lianghe County, Xianrendong village of Mangshi City, Manglong Village of Mangshi City, and Guanzhang village of Lianghe County. The disaster threatened 19 people and caused direct economic losses of 81,000 yuan, with no casualties. Based on the principle of “similar in the region and different in the region” [48], this paper uses the equal interval method to divide the probability of landslide hazards calculated by different methods into five levels—very low, low, medium, high, and very high, and the slope areas with medium or above levels are identified as the warning areas.

We evaluate the results from overall accuracy, early warning accuracy, and interpretability. For overall accuracy, since the heuristic matrix–based method is essentially based on the direct multiplication of classification indices to obtain assessment results, the warning areas are too large and heavily dependent only on rainfall factors. In contrast, the random–forest–based method, support–vector–machine–based method, and our method further consider the nonlinear relationship between conditioning and trigger factors, so that the fine early warning results are more consistent with human cognition. For the warning accuracy, the local weighted random forest model with consideration of spatial partitioning can successfully identify four of five landslides that happened in the study area. The accuracy is higher than those of random forest and support–vector–machine–based methods. Due to the additional modeling of human activity influence based on spatial partitioning, the local weighted random forest model (i.e., the proposed method) successfully identified all the landslides in the study area, which further verified the effectiveness of the proposed strategy. For interpretability, considering both natural rainfall factors and human activity factors, some potential landslides affected by the synergistic effects of nature with human activities will be at higher levels. For example, in Figure 9d, in landslide a in Dachang Village, Lianghe County, the road density is relatively high, which indicates to some extent that human reconstruction activities on the geological environment in this region are relatively intense. Only low–hazard assessment results can be obtained theoretically when only the rainfall factor is considered. However, when the synergistic effects of multi–source trigger factors (such as rainfall and human activities) are considered, a higher warning level can be obtained, thus providing a useful reference for landslide disaster prevention and early warning applications.

5.2. Limitations of the Work

There are some main limitations or challenges of the proposed method; the details are as follows:

(1)

The local weighted random forest model can mitigate the effect of spatial heterogeneity, but complete elimination is impractical, and it is worth considering how to improve the proposed model.

(2)

As records of landslide occurrence are rare, the hazard data used in this paper consist of just over 400 landslides that occurred between 2015 and 2019, resulting in a lack of accuracy in the hazard assessment results. Next, we will collect more historical landslide data for hazard evaluation.

(3)

There is a certain deficiency in responding to human activity based on information such as road distribution, land cover, and building footprint, and it is necessary to additionally consider data types that are strongly correlated with human activity, such as slope cutting and dynamic population distribution. Although different data can be processed at the same spatial and temporal resolution to participate in the modeling, data completeness is a particularly important limitation; for example, the inconsistent update interval from days to years for different trigger factors means that there may be a lag in the trigger factors considered in the hazard assessment. The inconsistent level of granularity of the data will affect the assessment results. Next, we will focus on data governance for more accurate and real–time assessment results.

6. Conclusions

This paper proposes a rainfall–induced landslide hazard assessment method that considers the synergistic effects of multi–source trigger factors, and a case study in Dehong Prefecture, Yunnan Province, China, is given. The findings of this study are as follows:

(1)

The local weighted random forest model proposed in this paper can effectively improve the accuracy of landslide hazard assessment. The proposed method identified possible warning areas with the highest accuracy and recall rate. Compared with the commonly used heuristic matrix–based method, the accuracy rate of the proposed method is 23.47% higher and the false negative rate is 19.80% lower, which indicates that the proposed method has the potential to improve the accuracy of landslide hazard warning.

(2)

Spatial partitioning can effectively weaken the impact of spatial heterogeneity on landslide hazard assessment, especially for assessment modeling under the condition of the uneven spatial distribution of positive and negative samples. Compared with the global modeling strategy, the proposed method can obtain more accurate assessment results through different subregions.

(3)

Using multiple trigger factors to evaluate the landslide hazard can improve the accuracy and interpretability of early warnings. This paper is based on natural factors and human activities, realizes the collaborative modeling of conditioning and trigger factors, and obtains rating results more consistent with cognition.