Landslide Susceptibility Mapping Considering Landslide Spatial Aggregation Using the Dual-Frequency Ratio Method: A Case Study on the Middle Reaches of the Tarim River Basin

Abstract

The phenomenon of landslide spatial aggregation is widespread in nature, which can affect the result of landslide susceptibility prediction (LSP). In order to eliminate the uncertainty caused by landslide spatial aggregation in an LSP study, researchers have put forward some techniques to quantify the degree of landslide spatial aggregation, including the class landslide aggregation index (LAI), which is widely used. However, due to the limitations of the existing LAI method, it is still uncertain when applied to the LSP study of the area with complex engineering geological conditions. Considering landslide spatial aggregation, a new method, the dual-frequency ratio (DFR), was proposed to establish the association between the occurrence of landslides and twelve predisposing factors (i.e., slope, aspect, elevation, relief amplitude, engineering geological rock group, fault density, river density, average annual rainfall, NDVI, distance to road, quarry density and hydropower station density). And in the DFR method, an improved LAI was used to quantify the degree of landslide spatial aggregation in the form of a frequency ratio. Taking the middle reaches of the Tarim River Basin as the study area, the application of the DFR method in an LSP study was verified. Meanwhile, four models were adopted to calculate the landslide susceptibility indexes (LSIs) in this study, including frequency ratio (FR), the analytic hierarchy process (AHP), logistic regression (LR) and random forest (RF). Finally, the receiver operating characteristic curves (ROCs) and distribution patterns of LSIs were used to assess each LSP model’s prediction performance. The results showed that the DFR method could reduce the adverse effect of landslide spatial aggregation on the LSP study and better enhance the LSP model’s prediction performance. Additionally, models of LR and RF had a superior prediction performance, among which the DFR-RF model had the highest prediction accuracy value, and a quite reliable result of LSIs.

1. Introduction

Landslides are one of the most widespread geohazards worldwide, characterized by their sudden occurrence, destructive force and fast movement, and often cause great damage to settlements and constructions located in landslide-prone zones [1,2,3,4,5]. Therefore, the research of landslide susceptibility prediction (LSP) is vital for providing guidance for land use, urban–rural planning and disaster prevention and mitigation [6,7,8]. According to the landslide susceptibility map (LSM) obtained by LSP studies, the site location strategy of engineering construction, including roads, hydropower stations and residential districts, can be reasonably determined to reduce or even avoid the loss of lives and property caused by landslides [9,10,11].

Landslide formation is a complicated process that involves a number of predisposing factors, such as geomorphology, tectonic action, stratum lithology, climate, hydrological condition, human activity, etc. It is the key step for LSP study to determine a link between landslide occurrence and predisposing factors [12,13,14]. Aiming to analyze this relationship, scholars have proposed many different models, including geomorphological mapping, heuristic terrain and susceptibility zoning, physically based numerical modeling and statistically based classification methods, to quantify the impact of each factor and calculate the landslide susceptibility index (LSI) [6,10,13,14,15]. Current research shows that statistically based models are widely used in regional studies with good prediction performance, such as heuristic methods [10,16,17], frequency ratio (FR) analysis [14,15,18], general statistical approaches [7,10] and machine learning models [18,19,20,21,22]. In addition, the machine learning models, including the logistic regression (LR) model, random forest (RF) model, etc., are being used more and more frequently due to their reliable results and high precision [17,19,20,21,22,23]. However, each LSP model often displays different prediction performance as a result of the discrepancies in model types, characteristics of study areas, landslide spatial datasets and predisposing factors. And it is recommended that the LSP result should not be determined by a single model, because each model usually has its own uncertainty [13,14,17].

In addition, the accuracy of model prediction is significantly influenced by the landslide inventory, which is a necessary precondition for LSP research [8,22]. Although the production of a landslide inventory is more convenient and accessible using high-resolution remote sensing imagery datasets and developed investigation techniques, there is still uncertainty in landslide inventories caused by the lack of high-level professional interpretation, the challenge of investigations in inaccessible areas and the non-homogeneity of landslide spatial distribution [14,16,24]. The non-homogeneity of landslide spatial distribution is an inherent attribute of landslide spatial datasets and is one of the challenges in creating a landslide inventory. Due to the complexity of the landslide formation mechanism, predisposing factors have a significant impact on the landslide distribution pattern. For instance, it is often found that landslides in a specific region happened in the form of clusters of landslides in areas with nearby faults or roads, and have a banding distribution. In other words, landslide distribution usually shows a high degree of heterogeneity in space and is affected by changes in controlling factors, especially when the study area is large [16,24,25]. Some scholars have introduced the relevant landslide aggregation index (LAI) to realize the quantification of landslide spatial aggregation [16,24,26,27]. In particular, the often-used FR, which does not consider landslide spatial aggregation, was modified to enhance the LSP model’s prediction performance [16,26]. A new index for quantifying the degree of landslide spatial aggregation is proposed in this study, which shows a good effect on regional LSP study.

In order to quantify the aggregation degree of landslide spatial distribution, a comparison was made between different LAIs that are used in improving FR. Four typical models including FR, the analytic hierarchy process (AHP), LR and RF, were used in calculating LSIs to test the application effect of LAIs. Then, the prediction performance of four LSP models was also analyzed in this study. The middle reaches of the Tarim River Basin, which is situated between the Tarim Basin and the South Tianshan Mountains, is seriously affected by landslides. This area was therefore selected as a study area. Based on different LSP models and modified FR values, LSMs of the study area were obtained, and the receiver operating characteristic curves (ROCs) and LSI distribution patterns were used to validate the performance of each LSP model.

2. Methods

2.1. LSP Modeling Procedure

In this study, the primary objective is to analyze the impact of landslide spatial aggregation on the LSP model’s prediction performance in the middle reaches of the Tarim River basin. As shown in Figure 1, all the processes required to complete the landslide susceptibility prediction in this study can be summarized into six steps, as follows:

(1)

Landslide inventory building through remote sensing interpretation, field investigation and historical record;

(2)

Spatial datasets collection and the integration of landslide predisposing factors;

(3)

Establishing the correlation between the incidence of landslide and corresponding impact factors by indicators including FR, adjusted FR (FRa) and DFR; the influence of landslide spatial aggregation is considered by the latter two indicators;

(4)

Creating LSP models using the FR, AHP, LR and RF models, and adopting the FRs values of each predisposing factor as input variables;

(5)

LSIs calculation by LSP models and LSMs generation using ArcGIS 10.4 software;

(6)

Model evaluation based on LSI distribution patterns and accuracy analysis.

2.2. Analysis of Landslide Spatial Aggregation

Based on the analyzed statistic correlations, the frequency ratio is often used as an indicator to reflect the impact of each subclass of predisposing factors to landslide occurrence, which can be easily applied to visually display the geographic connection of landslide distribution with related predisposing factors [7,14,15,16,24]. As shown in Equation (1), FR is also often regarded as the ratio of landslide density of a specific subclass under a predisposing factor to that of the whole study area. In general, a low correlation between landslide incidence and related factors is indicated by a FR value less than 1, and a high correlation is indicated by a FR value larger than 1 [17,18].

FR_ij = (l_ij/a_ij)/(L/A)

(1)

where FR_ij denotes the frequency ratio of subclass i under the predisposing factor j; l_ij refers to the count of landslides under subclass i of the predisposing factor j; a_ij stands for the area of class i under the predisposing factor j; L denotes the whole amount of landslides in the total research area and A refers to the total area.

However, the heterogeneity of landslide spatial distribution is a result of the fact that landslide formation is influenced by a variety of internal and external dynamics and varies significantly across different regions [5,12,25,28]. Therefore, using the FR alone without taking into account the landslide spatial aggregation makes it irrational to create a correlation between the occurrence of landslides and the associated predisposing factors [16,24,26,27]. In other words, the principle of the FR method ignores the influence of landslide spatial aggregation, which leads to uncertainty in the results.

In order to quantify the degree of landslide spatial aggregation and to eliminate the associated uncertainty, some scholars have introduced new adjusted indexes used in improving FR calculation, such as the class landslide aggregation index (CLAI), the normalized spatial-correlated scale index (NSCI) and the normalized spatial distance index (NSDI) [16,24,26,27]. Among these indexes, the CLAI has been widely used in LSP studies, because it is easy to be adopted in combination with FR and its form is more closely related to FR [16,26]. The first two cases in Figure 2 served as the foundation for the initial introduction of CLAI. The level of landslide aggregation in four distinct scenarios can be observed in Figure 2, representing the typical situations of landslide spatial distribution. The chosen area is split into the same grid with an equal area of S_a in each of the cases depicted in Figure 2. Since the subclass i₁ in case 1 and subclass i₂ in case 2 both have the same number of grids (five) and landslide points (ten), the l_ij/a_ij in each of the above two cases is same as 10/(5 × S_a). They are equally susceptible to landslides, as indicated by their identical FR values. However, since only one grid of subclass i₁ has landslide points in case 1, and every grid of subclass i₂ has landslide points in case 2, it is evident that the degree of landslide spatial aggregation varies in each case. According to this situation, the CLAI was proposed to quantify the degree of landslide spatial aggregation and its calculation is shown in Equation (2) [16]:

CLAI = U_L/U_T

(2)

where U_L is the number of basic evaluation units in which landslide points are present in a specific subclass i under certain predisposing factor, and U_T denotes the total number of basic evaluation units in the subclass i. In general, the smaller the CLAI, the higher the degree of landslide spatial aggregation. Then, the FR can be modified by applying CLAI, as shown in Equation (3) [16,26]:

FR_a = FR × CLAI

(3)

where FR_a represents the adjusted frequency ratio.

However, there are also other cases, such as case 3 and case 4. In particular, the subclass i is divided into ten identical grids in case 4, just as the area of each subclass is usually different. Both case 3 and case 4 reflect other different situations in which the uncertainty may be caused by the landslide spatial aggregation. Regarding case 2 and case 3, since the subclass i is divided into five identical grids in each case, the CLAI value in each case is equal to 1. However, in case 3, there is actually less landslide spatial aggregation, because each grid only has one landslide point. In addition, the CLAI in case 4 is unreasonably reduced to 0.1 compared to the CLAI value of 1 in case 2. In summary, CLAI cannot really quantify the degree of landslide spatial aggregation due to its theoretical limitations. Aiming to achieve a quantitative degree assessment of landslide spatial aggregation, a new indicator, called LAI_FR, is proposed in this study, which can be conveniently obtained on the basis of CLAI, as shown in Equation (4):

LAI_FR = CLAI/(L_S/U_T)

(4)

where LAI_FR represents the landslide spatial aggregation index calculated in the form of the frequency ratio; CLAI can be obtained from Equation (2); L_S stands for the total number of landslide points of a certain subclass i under specific predisposing factor; U_T represents the total number of basic evaluation units in subclass i. Similarly, the smaller the LAI_FR, the higher the degree of landslide spatial aggregation. Significantly, the LAI_FR is equal to 0 when there is no landslide point in a subclass. In fact, it is can be found that the LAI_FR is able to be deduced as U_L/L_S. However, for the sake of visual expression and comparison with CLAI and FR, we decided to display the LAI_FR as Equation (4) in this study. Furthermore, FR can be improved by the LAI_FR considering landslide spatial aggregation, as shown in Equation (5):

DFR = FR × LAI_FR

(5)

where DFR is the optimized frequency ratio expressed in the form of the dual-frequency ratio participating in the calculation. In this study, FR, FRa and DFR are also collectively referred to as the FRs.

2.3. LSP Modeling Approaches

To test the related LAI methods, four LSP models including FR, AHP, LR and RF are applied to LSIs. FR and AHP are often-used classical statistical models, while LR and RF belong to typical machine learning models. Furthermore, the FR values without considering landslide spatial aggregation, and values of FR_a and DFR considering landslide spatial aggregation are input as the basic data in the four abovementioned LSP models.

2.3.1. FR Model

The frequency ratio model is a popular statistical methodology that may be applied to GIS methods to quantitatively obtain the LSM. Equation (1) shows how the frequency ratio model is used to ascertain the spatial relationships between the location of landslides and contributing factors. Then, the frequency ratio of each factor is obtained using Equation (6) to calculate the LSIs [7,14,15,17].

LSI_FR = FR₁ + FR₂ + FR₃ + … + FR_j,

(6)

where FR_j stands for the FR value of the type or range of each factor.

2.3.2. AHP Model

As a typical multi-criteria heuristic method, the AHP model is a semi-qualitative decision-making approach which is usually used to resolve complicated multi-objective decision-making problems, such as engineering location selection, resource allocation, etc. [9,11,29]. Each factor’s weight value in the AHP model ranges from 1 to 9 and is calculated by comparing different factors in pairs. The consistency of the comparison matrix made up of the aforementioned weight values is tested using the consistency ratio (CR), which is determined by Equation (7). The comparison matrix is approved if the CR value is less than 0.1 [8,10,16]:

CR = CI/RI

(7)

where RI stands for the random index for the comparison matrix and CI is the consistency index of the matrix as determined by Equation (8). In Equation (8), λ_max refers to the comparison matrix’s maximum eigenvalue, and n denotes the total amount of factors (twelve in this case).

CI = (λ_max − n)/(n − 1)

(8)

Then, the normalized weight value of each predisposing factor is gained according to the comparison matrix. And finally, the LSIs can be calculated using Equation (9):

LSI_AHP = FR₁ × w₁ + FR₂ × w₂ + FR₃ × w₃ + … + FR_j × w_n

(9)

where FR_j is the type or range rating of each factor, and w_n indicates the weight value of the corresponding predisposing factor.

2.3.3. LR Model

The LR approach is a commonly used analysis model that enables a quantitative assessment of the correlationship between a set of independent variables (impact factors in this study) and a dependent variable (landslide occurrence in this study) [18,21,22]. It explains how a series of independent variables contribute to a binary dependent variable (whether a landslide occurs). In this study, the dependent variable is the likelihood that landslide will occur, and the corresponding predisposing factors are taken as independent variables in the SPSS Statistics 27 software. In the LR model, the dependent variable is the binary variable of whether landslide occur (1) or not (0). Additionally, the following Equation (10) can be used to determine the likelihood of landslide occurrence:

P = 1/(1 + e^−z)

(10)

where Z denotes the linear combination given by Equation (11) and P is the likelihood of landslide incidence, which ranges from 0 to 1.

Z = b₀ + b₁ × x₁ + b₂ × x₂ + … + b_n × x_n

(11)

where the regression intercept is denoted by b₀, b_n (n = 1, 2, 3,..., n) refers to regression coefficient and the independent variable is represented by x_n (n = 1, 2, 3,..., n), which is the corresponding FRs value of each predisposing factor in this study.

2.3.4. RF Model

The RF model, which was first presented by Breiman in 2001, is an ensemble technique made up of a series of tree classifiers that combines the random subspace and bagging ensemble learning [30]. The RF model is one of the most frequently used methods for addressing multi-classification and prediction issues, including LSP study [19,20,26]. In terms of missing and unbalanced data, the RF algorithm’s outcomes are comparatively consistent and its susceptibility to multicollinearity is low. The RF model’s primary steps are as follows [23,30]: (1) using bootstrap to resample the original dataset in order to produce a subset that is equivalent to the original dataset; (2) the optimal segmentation index is chosen for segmentation after a random selection of m indexes is made from n indexes in each classification tree node; (3) combining the classification or prediction outcomes of every decision tree to arrive at the final findings. Furthermore, the RF model’s prediction performance is significantly impacted by the quantity of decision trees and candidate attributes included in the subsets [31].

2.4. Performance Evaluation Indexes

2.4.1. ROCs

Receiver operating characteristic curves (ROCs), one of the most popular methods for model evaluation in LSP research, are used to assess the prediction performance of each LSP model [7,14,22]. As shown in Equations (12) and (13), when plotting ROCs, the horizontal coordinate is the false positive rate (FPR), while the vertical coordinate is the true positive rate (TPR). The model’s accuracy in forecasting the likelihood of landslide events is indicated by the area under the curve (AUC), which ranges from 0.5 to 1. Generally, the AUC values can be classified into following grades, such as 0.5~0.6 (very low accuracy), 0.6~0.7 (low accuracy), 0.7~0.8 (moderate accuracy), 0.8~0.9 (good accuracy) and 0.9~1 (excellent accuracy) [32,33,34].

TPR = TP/(TP + FN)

(12)

FPR = FP/(FP + TN)

(13)

where TP indicates the quantity of correctly categorized landslide samples, FN represents the quantity of incorrectly categorized non-landslide samples, FP denotes the quantity of incorrectly categorized landslide samples and TN refers to the quantity of correctly categorized non-landslide samples. As shown in Equation (14), the model’s prediction performance improves with a greater AUC value [26].

AUC = (ΣTP + ΣTN)/(P + N)

(14)

2.4.2. Distribution Patterns of LSIs

The mean and standard deviation values in this study are adopted to describe the distribution patterns of LSIs, which are displayed as a type of histogram. As assistant indexes for assessing LSP model performance, the mean value can give an index to the predicted LSIs’ central tendency, and the degree of dispersion is reflected by standard deviation [26]. In general, LSIs deviate from the mean value less when the standard deviation is lower, and vice versa. Furthermore, a low mean value and a high standard deviation generally mean low calculated results of LSIs on the whole, which can illustrate the strong ability of the LSP model to differentiate between LSIs of various grid cells. In addition, if the model also has a high AUC value of landslide prediction, it indicates that this model is not only reliable, but also has high prediction accuracy [17].

3. Study Area and Data

3.1. Description of Study Area

The Tarim River basin is composed of nine river systems, including the Aksu River, the Hetian River, the Yerqiang River, the Qarqan River, the Keriya River, the Dina River, the Kashgar River, the Kaidu–Kongque River and the Ugan–Kuqa River [35]. As shown in Figure 3, the study area is located in the middle reaches of the Tarim River basin, which is situated in Xinjiang Province of China (38°47′04″~42°38′44″N, 76°36′23″~86°30′53″E), adjacent to the republic of Kyrgyzstan and the republic of Kazakhstan in the northwest, bounded by the middle beam of the South Tianshan Mountains. It covers a total area of 185,829 km², being about 818 km long from east to west and 428 km wide from north to south. The entire population of the study area is around 4.86 million.

The study area’s elevation spans from 655 to 7435 m, and it is located on the northern edge of the Tarim Basin and the southern edge of the South Tianshan Mountains. Additionally, the overall terrain decreases from north to south, characterized with a three-step pattern, with continuous mountains in the north, the vast Taklimakan Desert in the south, and gravel fan-shaped foothills, an alluvial plain area, and the Gobi Desert and oasis sites alternating in the middle. The Tomur Peak in the South Tianshan Mountains is the highest point in the study area at 7435.3 m. Geologically, the study area is situated on the southwest margin of the Central Asian orogenic belt and the junction of the Kazakhstan–Yili block and the Tarim block [36,37,38], so it is characterized by active structures and developed faults. The strike of most active faults is close to E-W, and the distribution density of faults in the south is less than that in the north. Furthermore, faults can produce canyons with large surface fluctuations, and their vicinity is often a landslide-prone area.

In addition, the Tarim River basin belongs to the typical temperate continental climate zone and arid–semiarid region, with rare rainfall, high evaporation and a dry climate. The average annual temperature, average annual precipitation and potential evaporation for the majority of the study area are 9.2 to 11.5 °C, 64 mm and 1890 mm, respectively [39]. Moreover, the study area’s precipitation distribution is incredibly unequal in space. The north mountainous regions near the Tomur Peak and the Khan–Tengri Peak receive almost 600 mm of precipitation annually, while the annual precipitation in the southern Tarim Basin is less than 50 mm.

3.2. Landslide Inventory Information

The necessary initial operation in the LSP study is creating a landslide inventory [14,40]. The landslide dataset of the study area was obtained, validated and further enhanced based on remote sensing interpretation, field work and literature research. The production of landslide inventory was based on the analysis of historical landslide records (past survey materials and previous news reports), as well as the interpretation of Google Earth images and Gaofen-2 (GF-2) satellite images. Google Earth is a data platform that integrates high-resolution satellite images, aerial photographs and geographic information into a three-dimensional model. It allows users to observe the features of slope surface from different viewing angles, which is convenient for the identification of landslide areas. In addition, researchers can view historical images on Google Earth to analyze the evolution of disaster. In some areas where available Google Earth images were not provided, we used GF-2 satellite images for the interpretation of landslides. The GF-2 satellite images used in this study had a resolution of 1.0 m and were obtained from Geospatial Data Cloud (https://www.gscloud.cn, accessed on 17 June 2023). Based on ArcGIS and Google Earth, a total of 663 landslides between 1985 and 2023 were identified. Landslides are widely developed in the study area, especially in northern mountains (Figure 3). According to the classification of landslide types proposed by Varnes in 1978 [41], the main types of the identified landslides in the study area are rotational sliding, translational sliding, fall and topple. Debris flow is not considered in this study, because the susceptibility prediction of it is different from that of other landslide types [14]. The formation of debris flow is greatly influenced by the quantity and type of unconsolidated materials in the source area and channel.

The quality of data collection and compilation is controllable as a whole, mainly in the following measures: (1) The interpretation of landslide points was based on comparisons of high-precision remote sensing images, considering the morphological structure of landslides and altered landscapes. And the influence of other background conditions such as surrounding engineering facilities and vegetation growth can also provide guidance. Generally, the landslide area is characterized by a tongue shape or an oval shape, and the back wall is armchair-shaped. Images of a landslide often display variegated light gray tones or a bright white elongated strip [11]. Furthermore, the vegetation in the landslide area is generally sparse or undeveloped. In addition, the landslide movement would also cause the change in river channel. (2) Field research studies were performed in the landslide areas to eliminate the wrong data caused by construction excavations or misjudgments of remote sensing interpretations. For instance, some temporary spoil dumping sites caused by mining activities were easily misjudged as landslide deposits because of their similar shapes. And through the field investigations, we found some unstable slopes in the deformation stage which were difficult to identify through remote sensing interpretation. (3) The landslide points were identified according to multi-period historical images, which can not only overcome the identification limitations of snow and clouds, but also comprehensively compare the spatial relationship between the geohazard and threatened target. Some landslide deposits were destroyed by subsequent debris flows, and the boundaries of landslides were better determined through field investigations. Additionally, the comparison of images from different periods is helpful to approximately determine the occurrence time of landslides, such as a series of landslides in a certain region that may be associated with a mining activity or rainfall event. Furthermore, based on multi-phase images, it can be inferred that some landslides may tend to develop further in the rainy season, which can guide the selection of predisposing factors. Based on the above data verification and selection, the dataset has reliable quality and good usability [4,42].

3.3. Landslide Predisposing Factors

Numerous factors influence the formation of landslides, which are the consequences of both internal and external dynamics [14,43,44]. Predisposing factors that cause landslide were chosen for this study based on field investigation and previous studies on landslide susceptibility, which could reflect the local geomorphologic conditions (slope, aspect, elevation and relief amplitude), geological settings (engineering geological rock group (EGRG) and fault density), hydrological factors (river density and average annual rainfall) and surface cover factors (NDVI, distance to road, quarry density and hydropower station density). According to some recent studies [40,45], the continuous factors such as fault density and river density are more feasible than discrete linear factors including the distance to river and distance to fault. Therefore, the factors of fault density, river density, quarry density and hydropower station density were selected in this study. However, as the influence of road on landslide occurrence in the study area usually has a narrow scope, we used the factor of distance to road rather than road density factor [14]. There is often a certain correlation between the predisposing factors, and the high correlation is not conducive to the prediction accuracy of the LSP model. Therefore, a Pearson correlation test was applied to validate these factors’ independence in this study. Each of the twelve predisposing factors satisfied the independence criterion, since the absolute values of their pairwise correlation values were all less than 0.5 [8]. Next, as shown in

Table 1. FRs values considering landslide spatial aggregation.

Predisposing Factors	Values	FR	CLAI	FRa	LAIFR	DFR
Slope (°) (F1)	0~4	0.008	0.000000	0.000000	1.000	0.008
	4~10	0.149	0.000003	0.000001	1.000	0.149
	10~17	1.314	0.000029	0.000038	0.939	1.234
	17~25	3.469	0.000072	0.000251	0.894	3.102
	25~33	5.331	0.000092	0.000493	0.742	3.956
	33~41	6.308	0.000136	0.000857	0.922	5.816
	41~52	10.064	0.000220	0.002214	0.936	9.417
	52~90	8.354	0.000179	0.001498	0.919	7.677
Aspect (°) (F2)	−1	0.000	0.000000	0.000000	0.000	0.000
	0~22.5, 337.5~0	0.829	0.000017	0.000014	0.885	0.734
	22.5~67.5	0.856	0.000020	0.000017	1.000	0.856
	67.5~112.5	0.708	0.000013	0.000009	0.769	0.544
	112.5~157.5	1.418	0.000029	0.000041	0.866	1.228
	157.5~202.5	1.597	0.000032	0.000051	0.847	1.352
	202.5~247.5	1.218	0.000023	0.000028	0.802	0.977
	247.5~292.5	0.717	0.000016	0.000012	0.964	0.691
	292.5~337.5	0.905	0.000021	0.000019	1.000	0.905
Elevation (m) (F1)	655~1209	0.112	0.000002	0.000000	0.854	0.096
	1209~1623	1.261	0.000028	0.000035	0.946	1.193
	1623~2104	1.503	0.000033	0.000049	0.935	1.405
	2104~2643	3.384	0.000075	0.000254	0.956	3.234
	2643~3212	6.130	0.000115	0.000707	0.811	4.969
	3212~3817	4.531	0.000093	0.000423	0.888	4.023
	3817~4587	0.463	0.000011	0.000005	1.000	0.463
	4587~7444	0.000	0.000000	0.000000	0.000	0.000
Relief amplitude (m) (F4)	0~17	0.010	0.000000	0.000000	0.800	0.008
	17~47	0.691	0.000013	0.000009	0.829	0.572
	47~83	3.336	0.000067	0.000223	0.857	2.859
	83~118	4.053	0.000095	0.000384	1.000	4.053
	118~155	5.650	0.000111	0.000625	0.838	4.732
	155~204	9.098	0.000180	0.001636	0.846	7.698
	204~285	10.305	0.000224	0.002307	0.930	9.581
	285~989	5.239	0.000140	0.000733	1.143	5.988
Engineering geological rock group (F5)	Hard	1.940	0.000045	0.000087	1.000	1.940
	Less hard	3.649	0.000071	0.000260	0.841	3.070
	Less soft	2.769	0.000062	0.000173	0.972	2.692
	Soft	2.864	0.000059	0.000169	0.887	2.541
	Softer	0.187	0.000004	0.000001	1.000	0.187
	Water	0.000	0.000000	0.000000	0.000	0.000
Fault density (F6)	0~0.06	0.000	0.000000	0.000000	0.000	0.000
	0.06~0.18	0.015	0.000000	0.000000	1.000	0.015
	0.18~0.29	1.461	0.000033	0.000049	0.981	1.433
	0.29~0.4	0.484	0.000011	0.000005	1.000	0.484
	0.4~0.5	3.471	0.000065	0.000226	0.808	2.804
	0.5~0.6	2.197	0.000050	0.000110	0.981	2.155
	0.6~0.76	1.896	0.000036	0.000068	0.811	1.538
	0.76~1.00	0.121	0.000003	0.000000	1.000	0.121
River density (F7)	0~0.08	0.000	0.000000	0.000000	0.000	0.000
	0.08~0.18	1.252	0.000023	0.000029	0.790	0.989
	0.18~0.28	1.506	0.000035	0.000052	0.989	1.490
	0.28~0.38	1.067	0.000024	0.000026	0.979	1.045
	0.38~0.49	1.320	0.000024	0.000032	0.795	1.050
	0.49~0.59	1.018	0.000020	0.000021	0.855	0.870
	0.59~0.69	1.598	0.000031	0.000050	0.844	1.349
	0.69~1.00	0.709	0.000016	0.000012	1.000	0.709
Average annual rainfall (mm) (F8)	31~59	0.000	0.000000	0.000000	0.000	0.000
	59~88	0.456	0.000010	0.000005	0.986	0.450
	88~123	0.301	0.000007	0.000002	1.000	0.301
	123~168	1.299	0.000026	0.000034	0.870	1.130
	168~223	4.467	0.000091	0.000406	0.876	3.914
	223~283	4.325	0.000096	0.000415	0.955	4.129
	283~346	4.037	0.000073	0.000294	0.777	3.136
	346~609	0.109	0.000001	0.000000	0.500	0.054
NDVI (F9)	−1.00~−0.40	2.246	0.000031	0.000070	0.600	1.348
	−0.40~−0.23	2.885	0.000065	0.000188	0.974	2.810
	−0.23~−0.15	0.767	0.000015	0.000011	0.830	0.636
	−0.15~−0.06	1.232	0.000026	0.000032	0.900	1.109
	−0.06~0.08	1.071	0.000022	0.000023	0.873	0.935
	0.08~0.26	1.325	0.000028	0.000037	0.920	1.219
	0.26~0.45	0.734	0.000019	0.000014	1.143	0.839
	0.45~1.00	0.104	0.000002	0.000000	1.000	0.104
Quarry density (F10)	0~0.03	0.188	0.000010	0.000002	0.797	0.149
	0.03~0.1	0.436	0.000030	0.000013	1.000	0.436
	0.1~0.19	1.273	0.000085	0.000108	0.970	1.235
	0.19~0.3	1.852	0.000127	0.000235	1.000	1.852
	0.3~0.42	2.960	0.000199	0.000590	0.981	2.903
	0.42~0.57	4.560	0.000308	0.001403	0.983	4.482
	0.57~0.76	2.271	0.000156	0.000354	1.000	2.271
	0.76~1.00	9.046	0.000576	0.005206	0.927	8.384
Distance to road (m) (F11)	0~100	9.496	0.047747	0.008396	0.703	6.675
	100~200	2.258	0.003842	0.000676	1.000	2.258
	200~400	1.273	0.001220	0.000215	1.000	1.273
	400~800	0.550	0.000228	0.000040	1.000	0.550
	800~1600	0.399	0.000104	0.000018	0.870	0.347
	1600~3200	0.537	0.000165	0.000029	0.759	0.408
	3200~6400	0.367	0.000074	0.000013	0.726	0.267
	>6400	0.104	0.000008	0.000001	0.980	0.102
Hydropower station density (F12)	0~0.04	0.309	0.000017	0.000005	0.932	0.288
	0.04~0.14	1.435	0.000047	0.000068	0.565	0.811
	0.14~0.24	1.713	0.000095	0.000163	0.952	1.631
	0.24~0.35	2.269	0.000088	0.000201	0.667	1.512
	0.35~0.47	8.546	0.000389	0.003324	0.778	6.647
	0.47~0.62	4.410	0.000258	0.001138	1.000	4.410
	0.62~0.77	1.712	0.000100	0.000171	1.000	1.712
	0.77~1.00	2.900	0.000170	0.000492	1.000	2.900

, the discrete factors were categorized under the actual determined state or homologous action mechanism, while the continuous factors were categorized into eight subtypes based on the natural breakpoint method [13,17]. In Table 1, considering landslide spatial aggregation, the FRs values were attained to reflect whether each subclass of a predisposing factor was conducive to the formation of landslide. Additionally, the data layers of the above factors were processed into a raster format, with the size of each grid being 30 × 30 m² for LSIs calculation.

3.3.1. Geomorphologic Factors

In terms of geomorphologic conditions, the slope (Figure 4a), aspect (Figure 4b), elevation (Figure 4c) and relief amplitude (Figure 4d) are the primary controlling factors of landslide formation in the study area, and the relevant data from these three factors can be generated by a digital elevation model (DEM). Therefore, slope degree could change the stress field of slope body, so as to affect slope evolution, including stress distribution, strain accumulation and the formation of a potential slip surface. Therefore, landslide development has a close correlation with the slope, and within a certain range, a lower slope gradient is usually associated with a higher slope stability [3,14]. Aspect has an impact on hydrothermal conditions, including sunshine and precipitation, which plays a controlling role in rock weathering, vegetation growth and the melting of ice and snow. Thus, there is a certain relationship between aspect and landslide distribution in space [8,26]. As with many LSP studies, the aspect factor has nine subclasses in Table 1, with the subclass of −1 representing the plane area [7,17,19]. Various climate elements change with the increase in elevation, among which precipitation and temperature change quite acutely. The resulting changes in some conditions, such as microclimatic characteristics, types of plant communities and human activities, would affect the evolution of a landslide [44]. Relief amplitude denotes the difference between the highest and lowest elevation points in a given area. In general, a higher relief amplitude can cause an increase in landslide potential energy, which in turn improves the landslide velocity and ultimately raises the intensity of landslide activity [46,47].

3.3.2. Geological Factors

With respect to geological setting, the lithology factor controls the strength of slope material, which profoundly determines the slope stability [7,48]. In this study, according to the National Standard of China (GB/T 50218-2014) [49], the engineering geological rock group (EGRG) (Figure 4e) used in reflecting the influence of lithology is divided into six subclasses, as shown in

Table 2. The classification criteria of EGRG in the study area.

Class	Major Rock Types
Hard	Unweathered to slightly weathered: granite, syenite, diorite, diabase, basalt, andesite, gneiss, siliceous slate, quartzite, siliceous consolidated conglomerate, quartz sandstone, siliceous limestone, etc.
Less hard	(1) Moderately (weakly) weathered hard rock; (2) unweathered to slightly weathered: fused tuff, marble, slate, dolomite, limestone, calcareous sandstone, coarse crystal marble, etc.
Less soft	(1) Strongly weathered hard rock; (2) moderately (weakly) weathered less hard rock; (3) un-weathered to slightly weathered: tuff, phyllite, sandy mudstone, marl, argillaceous sandstone, siltstone, sandy shale, etc.
Soft	(1) Strongly weathered less hard rock; (2) moderately (weakly) weathered less soft rock; (3) unweathered to slightly weathered mudstone, argillaceous shale, chlorite schist, sericite schist, etc.
Softer	(1) Completely weathered rock; (2) strongly weathered less soft rock; (3) moderately (weakly) weathered to strongly weathered soft rock; (4) various semi-diagenetic rock; (5) quaternary loose accumulation.
Water	Lakes, reservoirs, etc.

: hard, less hard, less soft, soft, softer and water. The original data on EGRG factor is generated based on the 1:250,000 scale geological map. And because of more structure planes and lower strength, landslides in the study area are prone to developing in areas of the less hard, less soft and soft rock groups (Table 1). Fault density (Figure 4f) is positively correlated with landslide occurrence [8,11]. Faults result in the formation of rock mass structural planes and considerable topographic relief [46,48]. Thus, landslides are common in the northern mountainous regions with a high fault density in the research area.

3.3.3. Hydrological Factors

River density (Figure 4g) can affect slope stability by causing pore water pressure and scouring the slope foot, which is generally unfavorable to the structural strength of the slope body and conductive to landslide occurrence [14]. In addition, groundwater often develops near rivers, which can lead to infiltration failure and soften the structural surface, resulting in slope instability [15]. Rain infiltration and direct ground erosion caused by rainfall is less favorable to slope stability, and thereby landslide is often triggered by rainfall in the study area [50]. The average annual rainfall data (Figure 4h) of the research area is produced using ArcGIS 10.4 software, based on rainfall data gathered from the local meteorological service and an open database published by the WorldClim website (https://www.worldclim.org/, accessed on 24 January 2024). Table 1 shows that the regions with high average annual rainfall are exactly associated with a high frequence of landslide occurrence.

3.3.4. Surface Cover Factors

Based on the spectral characteristics of vegetation cover, NDVI (Figure 4i) can reflect the status and biomass of surface vegetation, which is adopted to measure the surface vegetation cover in this study. Generally speaking, the higher the NDVI value, the better the vegetation growth [17]. The research area’s NDVI values, varying from −1 to 1, are separated into eight subclasses using the natural breakpoint approach, as indicated in Table 1. On the whole, Table 1 also shows that a relatively high NDVI value is more closely connected with a low landslide occurrence.

Furthermore, human activities are also important predisposing factors to landslide occurrence [1]. According to field investigation, engineering constructions including roads, hydropower stations and quarries are considered as the main human activities triggering landslides in the study area. These engineering activities could not only break the original stress equilibrium of slope by hill cutting or variation in reservoir level, but also cause the occurrence of unstable slopes due to unreasonable surface loading [15]. In Table 1, the natural breakpoint approach is used to categorize the quarry density (Figure 4j) and the hydropower station density (Figure 4l) into eight different groups. However, according to related studies [11,14], the factor of distance to road (Figure 4k) is classified into eight classes under the specific intervals of distance: 0–100 m, 100–200 m, 200–400 m, 400–800 m, 800–1600 m, 1600–3200 m, 3200–6400 m, >6400 m. Moreover, Table 1 shows a negative correlation between landslide occurrence and the distance to road as a whole.

4. Results

4.1. Preparation of Spatial Datasets for Building LSP Model

Twelve landslide predisposing factors’ FRs values are utilized in this study as input independent variables for LSP models, as follows: (1) FR value without considering landslide spatial aggregation; (2) FRa value considering landslide spatial aggregation based on CLAI; (3) DFR value considering landslide spatial aggregation based on LAI_FR. The purpose of the LSP study is to infer whether a landslide would occur in a certain area, and it is usually an analysis of binary classification (0~1). Therefore, the spatial dataset used as the dependent variable in the LSP models contains two types of data, including landslide and non-landslide. A total of 663 landslide grid units were extracted according to the central point of each identified landslide area and assigned a value of one. Then, using the Create Random Points tool in ArcGIS 10.4 software, 663 non-landslide grid units were randomly selected in the area without landslide events, and each non-landslide grid unit was assigned to 0. For the sake of model validation in the LSP process, all of the landslide and non-landslide samples were arbitrarily split into two groups: 70% were used as training data to construct the model, and the remaining 30% were utilized to assess the LSP model’s performance [7,26].

4.2. LSP by FR Model

The FRs values, including FR, FRa and DFR, were calculated through Equations (1)–(5), and Table 1 displays each factor’s results. Then, according to Equation (6), values of each FRs type are summed up, respectively, to achieve the LSIs by ArcGIS 10.4 software. With the frequently used natural breakpoint method, the LSMs obtained by the FR models are categorized into five susceptibility levels (Figure 5a–c): very low, low, moderate, high and very high [20,40]. Additionally, the other three LSP models also follow the natural breakpoint approach for LSM classification.

As shown in Figure 5, the majority of the high and very high LSI areas are scattered in northern mountains, and all the gained LSMs have high similarity in this respect. However, the LSM based on the FRa model clearly displays the fewest areas in high and very high LSIs (Figure 5b), accounting for 3.06% and 1.68% of the entire area, respectively, mostly around constructions of quarries and hydropower stations. In addition, due to the gentle topography, most districts of the study area, such as Aksu, Awati, Keping, Alar, Tiemenguan, Tumushuke, Shaya and Bachu, are almost entirely have a very low degree of landslide susceptibility.

4.3. LSP by AHP Model

As the values of the CI, RI and CR are 0.0305, 1.54 and 0.0198, respectively, this shows that the pairwise comparison matrix (

Table 3. Pairwise comparison matrix and weight values of the data layers in AHP model.

Factors	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12	Weight
F1	1												0.170
F2	1/6	1											0.031
F3	1/7	1/2	1										0.020
F4	1/2	5	6	1									0.127
F5	1/3	4	5	1/2	1								0.092
F6	1/2	5	6	1	2	1							0.127
F7	1/5	2	3	1/4	1/3	1/4	1						0.046
F8	1/3	4	5	1/2	1	1/2	3	1					0.092
F9	1/8	1/3	1/2	1/7	1/6	1/7	1/4	1/6	1				0.012
F10	1/3	4	5	1/2	1	1/2	3	1	6	1			0.092
F11	1/2	5	6	1	2	1	4	2	7	2	1		0.127
F12	1/4	3	4	1/3	1/2	1/3	2	1/2	5	1/2	1/3	1	0.065

) provided in the calculation process of AHP model has a reasonable consistency. Then, according to Equation (9), the calculated weight value of each predisposing factor is input into the AHP model to calculate LSIs, as shown in Equation (15). Next, the LSMs of AHP model are generated using ArcGIS 10.4 software. Finally, the LSMs of study area are also listed as five grades based on the natural breakpoint approach (Figure 5d–f): very low, low, moderate, high and very high.

LSI_AHP = 0.170 × F₁ + 0.031 × F₂ + 0.020 × F₃ + 0.127 × F₄ + 0.092 × F₅ + 0.127 × F₆ + 0.046 × F₇ − 0.092 × F₈ + 0.012 × F₉ + 0.92 × F₁₀ + 0.127 × F₁₁ + 0.065 × F₁₂

(15)

On the whole, it is evident that the high and very high susceptibility areas are almost all concentrated in alpine valleys of the South Tianshan Mountains, especially in the upper and middle reaches of the Tarim River’s tributaries (Figure 5d–f). Most of the aforementioned areas are primarily found in the northern portions of Kuqa, Wensu, Luntai, Baicheng, Akqi, Wushi and Korla. In addition, the results of the FR-AHP model and the DFR-AHP model are significantly similar in the spatial distribution characteristics of LSIs. But according to Figure 5e, the LSM by FRa-AHP model has fewest areas with very high (0.63%) and high (3.85%) landslide susceptibility levels, which is consistent with the result based on the FRa model.

4.4. LSP by LR Model

In the initial step of the LR model’s prediction process, the datasets about twelve various predisposing factors and related samples should be first converted into XLS-formatted data for the SPSS software to access. Then, the FRs of each predisposing factor are imported into LR model through adopting binary logistic regression analysis, where the occurrence of landslide corresponds to the dependent variable, and the input factors are the independent variables [7]. According to the initial result of LR model analysis, the significance values of aspect and annual mean rainfall are both greater than 0.05. Hence, they should be removed from the LR model in the later model building process [17]. Next, the remaining 10 predisposing factors are re-input into the LR model. Then, each factor’s regression coefficient is determined, as shown in Equations (16)–(18). These regression coefficients are all positive, indicating that each factor contributes to the landslide occurrence of the middle reaches of the Tarim River basin.

The equation for the FR-LR model:

Z_FR = −7.022 + 0.170 × F₁ + 0.177 × F₃ + 0.278 × F₄ + 0.200 × F₅ + 0.512 × F₆ + 1.348 × F₇ + 0.283 × F₉ + 1.168 × F₁₀ + 0.696 × F₁₁ + 0.356 × F₁₂

(16)

The equation for the FRa-LR model:

Z_FRa = −4.078 + 446.474 × F₁ + 982.629 × F₃ + 1101.208 × F₄ + 6273.457 × F₅ + 5954.789 × F₆ + 22037.404 × F₇ + 2714.528 × F₉ + 3586.338 × F₁₀ + 593.037 × F₁₁ + 894.978 × F₁₂

(17)

The equation for the DFR-LR model:

Z_DFR = −6.086 + 0.153 × F₁ + 0.210 × F₃ + 0.372 × F₄ + 0.226 × F₅ + 0.591 × F₆ + 1.009 × F₇ + 0.124 × F₉ + 1.145 × F₁₀ + 0.995 × F₁₁ + 0.479 × F₁₂

(18)

Furthermore, because each model’s chi-square significance is greater than 0.05, the Hosmer–Lemeshow test indicates that the goodness-of-fit of these equations based on the FR-LR model (0.232), FRa-LR model (0.210), and DFR-LR model (0.830) can be adopted [22]. In addition, the values of Cox–Snell R² and Nagelkerke R² tests are also much higher than 0.05 and close to 1, indicating that the performance of models is good. Finally, through Equations (16)–(18), the LSMs are acquired by calculating the LSI of each grid unit based on ArcGIS 10.4 software. Additionally, the natural breakpoint approach is applied to reclassify the LSMs predicted by the LR models into five grades; namely, very low, low, moderate, high and very high (Figure 5g–i).

On the whole, compared with models of FR and AHP, the discrepancy of LSIs distribution patterns in each LSM obtained by the LR model is not very apparent under different types of FRs. Figure 5g–i shows that high and very high landslide susceptibility zones are mainly distributed in Akqi, Kuqa, Wushi, Luntai, Baicheng, Wensu and Korla, accounting for 4.92~5.33% and 4.36~4.63% of the total area, respectively.

4.5. LSP by RF Model

In general, for an RF model, more decision trees could result in more modeling time, whereas less decision trees would result in errors [23,26,31]. Hence, in the first step of establishing the RF model for LSP, the optimal numbers of factor features, and decision trees used in the models are attained by using MATLAB R2022a software through the analysis of the factor feature number and out-of-bag error [51,52,53]. Then, the RF model under the optimal parameters is adopted to carry out LSI prediction. Finally, the calculated results of the LSI are loaded into ArcGIS 10.4 software for producing the LSMs (Figure 5i–l).

Similarly, the LSMs obtained by the RF model are ranked into five different categories based on natural breakpoint approach, including very low, low, moderate, high and very high. Furthermore, the LSM obtained by the FR-RF model has the most areas of high and very high landslide susceptibility among these LSMs by RF model, making up 9.59% and 10.21% of the total area, respectively. Meanwhile, the LSM by the FRa-RF model has the fewest areas of high and very high landslide susceptibility, covering the proportion of 5.6% and 4.3% of the total area, respectively. Likewise, the majority of the high and very high landslide susceptibility zones in the middle reaches of the Tarim River basin are primarily found in the northern part of the South Tianshan Mountains, where gullies and valleys developed.

5. Discussion

In this section, the predictive performance of the adopted LSP models is validated by the AUC values and LSIs distribution characteristics. Then, according to the LSP results of this study and existing studies, the features of the LSP model and FRs are discussed. In addition, the limitations of the LSP model are analyzed, and briefly, the prospects of future potential research work are also given.

5.1. Evaluation of LSP Models

5.1.1. AUC Values of the LSP Models

Based on the validation datasets, the LSP models are evaluated by the ROCs and the AUC values are obtained to reflect models’ prediction accuracy. As shown in Figure 6, based on the DFR datasets, the LSP models considering the landslide spatial aggregation have higher AUC values, indicating that the accuracy of the LSP model can be improved by the application of the DFR method. Compared with the prediction results under unadjusted FR datasets, the prediction accuracy of the LSP model using the DFR method is significantly improved, by 0.9–3.0%. On the contrary, as far as the AUC value is concerned, the models using FRa datasets are even lower than the models using FR datasets that do not consider landslide spatial aggregation.

From the perspective of the whole results of the AUC (Figure 6), the AUC value of the RF model is greater, indicating a good prediction ability, followed by the LR model, the AHP model and the FR model. In terms of the RF models, the variation trend of the AUC value is as follows: DFR-RF (0.910) > FR-RF (0.880) > FRa-RF (0.861). Furthermore, because of the very good performance and distinctly higher accuracy, the DFR-RF model’s prediction result is the most reliable and accurate when compared to the other LSP models. And the FR model using the FRa dataset has the lowest AUC value, of 0.828. Additionally, regardless of which type of FRs dataset is used, the AHP model and the FR model both have lower AUC values. On the other hand, in the LSP of this study area, the LR and RF models both perform better in terms of prediction precision.

In addition, it is evident that the RF models based on different FRs datasets differ greatly in terms of accuracy, while the difference in accuracy in the FR or AHP models is smaller. This phenomenon suggests that the performance of RF models with better prediction ability is more affected by the type of FRs datasets.

5.1.2. Distribution Patterns of Obtained LSIs

The mean value and standard deviation are employed as the two primary indicators in this study to analyze the LSIs features of each LSP model using the histogram, and to compare the prediction performance of various models. The former can reflect the central tendency of all calculated LSIs, while the latter is proposed to indicate the degree of dispersion of LSIs. Generally speaking, a low mean value suggests that the majority of the LSIs generated by the LSP model fall within the low-value category. In terms of the standard deviation, the higher the standard deviation, and the more the LSIs deviates from the mean value, the better the distinguishing capacity for the differences in LSIs, and the lower the uncertainty of the prediction results, and vice versa. In summary, a low mean value and a high standard deviation illustrate that the corresponding LSP model can better reflect each grid unit’s landslide susceptibility by using fewer high LSIs; namely, the prediction performance of this model is reliable and accurate [17,26].

As shown in Figure 7, the LSIs distribution histogram of each LSP model is generated according to the prediction results. And in this process, the LSIs of FR models and AHP models are normalized using the ArcGIS 10.4 software in advance. As far as the FRs dataset type is concerned, compared with the FR datasets, the LSIs results predicted with the DFR datasets considering landslide spatial aggregation have a lower mean value and a higher standard deviation. In other words, the DFR method can actually enhance the LSP model’s prediction performance. However, the standard deviation in the LSP model based on FRa datasets is the lowest in each corresponding LSP model group. Especially in the models of RF and LR, the models based on FRa datasets also have the highest mean values. In addition, due to the limitations of the CLAI method, the LSIs obtained by the FR model and the AHP model built on the FRa datasets are generally very low, resulting in extremely low mean values. That is to say, in this study, the FRa datasets based on the CLAI method do not perform well in improving the LSP models’ prediction abilities.

In the case of different LSP models, the RF model and LR model have obviously better prediction performance than other LSP models according to the lower mean value and higher standard deviation. Furthermore, the DFR-RF model has the lowest mean value and the highest standard deviation, indicating that its prediction performance is very good in this study. On the whole, according to the histograms shown in Figure 7, the LSP models are ranked by the prediction performance, as follows: the RF model is the best, followed by the LR model, AHP model and FR model.

In summary, each LSP model built on DFR datasets not only has a higher AUC value, but also shows better prediction capacity, with a lower mean value and a higher standard deviation. In other words, the results show that DFR method can effectively enhance the prediction performance of LSP model. Oppositely, according to the AUC values and distribution patterns of LSIs, the FRa dataset based on the CLAI method performs poorly in improving the LSP models’ prediction performance in this study. Furthermore, machine learning models, including the RF model and the LR model, have a much better performance in LSP study, with the RF model performing the best.

5.2. Synthetical Analysis of LSP Results

Although they are based on different LSP models and FRs datasets, all the LSMs with various ranges of LSIs show generally consistent features as a whole: the northern mountains, which range in elevation from 2104 to 3817 m, are the primary areas of high and very high landslide susceptibility zones. In addition, these mountains are characterized by active tectonic activities and intense human activities, such as road construction and mining. This phenomenon suggests that these landslide predisposing factors can play a significant role in landslide occurrence, and the reasonable selection of landslide predisposing factors should not be underestimated [7,13,14].

Meanwhile, the LSP results also are affected by the LSP model’s prediction performance. Generally speaking, the traditional statistical models, including the FR model and the AHP model, are inherently linear and cannot reflect the nonlinear relationship between landslide occurrence and correlative predisposing factors, so their prediction ability is relatively low. In contrast, this complex relationship can be well-handled by machine learning models, such as the LR model and the RF model. Furthermore, the RF model can improve prediction accuracy by integrating multiple decision trees, which is helpful to avoid overfitting and enhance generalization ability [23,26,31]. By and large, the RF model outperforms the other LSP models with regard to prediction performance in this study.

Landslide spatial aggregation is worth considering in the study of LSP, as it brings uncertainty to model building [24]. According the LSP results and model evaluation, there is no doubt that the DFR method proposed in this study can practically enhance the LSP model’s prediction capacity. However, the CLAI method, which has been used successfully in some past studies [16,26], does not have a good performance. As explained within Section 2.2, the CLAI method’s poor performance is caused by theoretical limitations that would result in significant levels of uncertainty in LSP studies, especially when the research region is broad, and landslide predisposing factors are complex. In any case, the DFR method shows a more stable and favorable effect on enhancing the prediction performance of LSP model.

5.3. For Further Study

As the basic premise of LSP study, the establishment of reliable and complete landslide inventories is generally determined by skilled professional interpreters and high-resolution remote sensing datasets used for landslide identification [4]. The combination of multi-period remote sensing datasets analysis and landslide samples’ validation by field investigation is conducive to reducing the uncertainties caused by interpreters’ misjudgment and overlapping areas of multiple landslides [26,42]. In addition, automatic landslide identification using deep learning methods can lighten the workload of obtaining landslide datasets, especially when the study area is large.

In addition, evaluation units like the hydrologic slope unit, which are frequently employed in the current study, are capable of better describing the relationship between the incidence of landslides and geomorphic factors [11,14,20]. The DFR method considering landslide spatial aggregation should be applied and even optimized in different evaluation unit types, such as a hydrologic slope unit, to play a better role in improving landslide prediction ability. Additionally, the techniques employed for automatic slope unit extraction can effectively achieve quick modeling and improve the aforementioned studies, ensuring that the LSP model’s prediction performance is continuously enhanced going forward. However, the existing automatic extraction methods of slope units often produce unreasonable results when processing the datasets with complex geomorphological conditions, so the elaborate extraction method still needs further research [54].

Furthermore, the LSM produced by a single type of LSP model frequently contains inevitable uncertainty, because the association between landslide formation and numerous predisposing factors is typically complicated [7,48,55]. Since each LSP model has its own data classification principle, adopting multiple models in the study of LSP would contribute to lessening the uncertainty raised by the feature importance analysis of a series of predisposing conditions. Furthermore, some studies have shown that integrating deep learning methods with more progressive semi-supervised machine learning approaches can enhance the LSP model’s capacity to predict landslide susceptibility [14,33,56].

6. Conclusions

In this study, the LSP process of the middle reaches of the Tarim River basin has been performed using four different LSP models applying different FRs datasets, taking into account the landslide spatial aggregation. Based on the landslide inventory with 663 identified landslide points, 12 landslide predisposing factors are adopted in LSP study, and a series of LSMs are obtained with various LSIs distribution patterns. The novel findings and main conclusions of this study can be drawn:

(1)

The DFR method proposed in this study can not only perform well in quantifying the degree of landslide spatial aggregation, but also improve the prediction performance of LSP model effectively. According to the obtained LSMs and model evaluation, every LSP model using the DFR method in this study has a better prediction performance.

(2)

On the whole, the RF model outperforms the other LSP models in terms of prediction ability, followed by the LR model, the AHP model and the FR model. Furthermore, the machine learning models, including the RF model and the LR model, have a much better prediction performance than the traditional statistical models represented by the AHP model and the FR model.

(3)

The vast majority of the high and very high landslide susceptibility zones are primarily located in the northern mountainous regions of the study area, according to a combination of the different LSMs produced by LSP models. In addition, the LSP result of a single type of model is often uncertain, and the final LSM should be determined by the comprehensive analysis of the various LSP models’ results.