GIS-based landslide susceptibility mapping using frequency ratio and index of entropy models for She County of Anhui Province, China

1 Introduction

Landslide disasters frequently occur in mountainous areas, causing secondary geological hazards, enormous casualties, and losses of eco-environmental and infrastructure [1]. Landslide disasters cause thousands of casualties and several hundred billion dollars in direct economic losses worldwide [2]. In China, 6,000 landslide accidents occur annually, resulting in an estimated 5–8 billion CNY in direct economic losses and hundreds of deaths, and most of the landslides accidents occur in mountainous and hilly areas [3]. She County is located in the mountainous region of South Anhui, China, where hilly and mountainous areas account for 95%, which is the most serious landslide disaster area in Anhui Province and even China. Until now, the landslides have caused 68 casualties, 1,098 houses have been destroyed, and 1018.4 million CNY of direct economic loss [4,5]. Therefore, it is necessary to scientifically assess the regional landslide susceptibility and help local government work out effective landslide prevention and control plans to reduce negative effects.

Currently, there exists a preliminary but reasonable and applicable procedure for landslide susceptibility mapping based on the geographical information system (GIS). The main core of landslide sensitivity assessment is to determine the influencing factors of regional landslides and appropriate models to produce the landslide susceptibility maps [6]. Landslide is the external manifestation of the comprehensive action of primary geological conditions and external environmental factors. Generally, the factors considered in the regional landslide susceptibility analysis mainly include lithology, elevation, slope angle, slope aspect, human activities, water system, vegetation, rainfall, topographical structure, and geological structure. Due to the differences in regional conditions and scholars’ views, there is still no unified factors catalogue [4]. Lithology, slope angle, water system, and human activities are considered basic factors by most scholars [7]. Zou et al. considered that 8–12 factors are sufficient to meet the requirements of landslide susceptibility evaluation, not the more the better [8]. The evaluation models widely used in landslide sensitivity mapping can be divided into qualitative and quantitative. As the most prevailing tools in landslide susceptibility modeling, quantitative approaches can be divided into three groups: heuristic, deterministic, and statistical methods [9,10]. The statistical methods are the most widely used, including statistical index (SI), weight of evidence (WOE), certainty factor (CF), index of entropy (IOE), analytical hierarchy process (AHP), logistic regression (LR), and frequency ratio (FR) [11,12,13,14,15,16]. As the main technical sources of data-driven modeling, machine-learning methods are popularly applied to predict regional landslide susceptibility [7,17,18]. Some researchers have developed hybrid models, combining statistical and machine-learning approaches, to obtain more accurate results and overcome the shortcomings of individual methods [19,20]. Each method has its inherent advantages and limitations; the prior step is to comprehensively understand the application of statistical methods [12]. It is beneficial for an in-depth understanding of the application and combination with each method. In some of the literature, FR and IOE are most frequently used to evaluate landslide susceptibility [21,22,23,24]. However, there have been few studies comparing these methods, especially in the mountainous and hilly areas of China.

The main purpose of this study is to form a landslide susceptibility map of She County in Anhui Province, China, which is a landslide-prone area. For this purpose, 10 landslide-related factors are considered and overlaid by using FR and IOE models based on the GIS. Additionally, the predictive performance of these models has been evaluated and compared using receiver operating characteristic (ROC) curves. The results of this study have implications for landslide prevention and mitigation in the study area and other similar terrains.

2 Study area

She County is situated at longitudes 118°15′00ʺ to 118°53′50ʺE and latitudes 29°30′25ʺ to 30°07′00ʺN in the mountainous region of South Anhui, China (Figure 1). The county encompasses approximately 2,122 km², and hilly and mountainous areas account for about 95% of the study area.

Figure 1

Location of the study area and landslide inventory map.

Topographically, the altitudes gradually decrease from the southeast to the northwest, in which the maximum and minimum are 1,787 and 100 m according to a DEM++ with a grid of 30 m. Geologically, the tectonic structure within the study area is complex, with abundant folds and faults formed by multi-stage tectonic movements, mainly including Indo-china Movement, Yanshanian Movement, and Wannan Orogeny. The exposed strata include Sinian of Proterozoic, Cambrian of Paleozoic, Ordovician, Jurassic and Cretaceous of Mesozoic, and Quaternary loose soil and deposition. With regard to climate, the study area belongs to the subtropical monsoon climate zone, which provides abundant rainfall in spring and summer. It is reported that the annual average precipitation is 1582.7 mm, and the annual average temperature is 16.3°C. Xin’an, Lian, Fengle, Fengyuan, Changyuan, Jieyuan Rivers, and their tributaries form a network drainage system. In 2020, the population of this county was approximately 362.9 thousand. The coupling effect of special geological and climatic conditions and the influence of human engineering activities make this area prone to landslides. The coupling effects of special geology, climate, and human engineering activities make this area prone to landslides.

3 Data used

The spatial characteristics of landslides in the study area were ascertained using 1:50,000 scale aerial photograph interpretation, historical landslide records, and extensive field surveys and observations. Resultantly, a total of 502 landslides (source areas) were detected in the study area, including 463 slides and 39 falls. In terms of size, the smallest landslide volume is about 1,880 m³, and the largest is larger than 9 × 10⁶m³, and large-scale (10⁶–10⁷m³), medium-scale (10⁵–10⁶ m³), and small-scale (≤10⁵m³) landslides (Figure 2) accounted for about 1, 8, and 91% of the total, respectively. The detected landslides were randomly divided into two groups: 351 cases (70%) were randomly selected for modeling and the remaining 151 (30%) cases were used for validation [25].

Figure 2

Landslide photos: (a) small-scale landslide; (b) medium-scale landslide; and (c) medium-scale landslide (part).

The landslide is caused by the combined action of the internal elementary geological conditions and external environmental factors of the slope [26,27]. The former refers to the factors that control the occurrence and development of landslides, mainly including stratigraphic lithology, topography, and geological structure. The latter refers to the factors that trigger the occurrence of landslides, such as the hydrogeological environment and human engineering activities. According to relevant research [28,29,30], the availability of data sources, and the characteristics of local geological environments, 10 influencing factors including slope angle, slope aspect, curvature, landform, lithology, distance to faults, distance to roads, distance to rivers, rainfall, and normalized difference vegetation index (NDVI), are considered for landslide susceptibility analysis. The digital elevation model (DEM), which depicts the accurate representation of the land surface, is suitable for medium-scale mapping [11]. Geomorphological-related thematic data layers, including slope angle, slope aspect, and curvature, are extracted from the 30 m × 30 m DEM covering our study area. Other parameters are mainly collected from available resources, such as geological map, environment geology map, road map, and drainage map. All of the landslide-influencing factors are reclassified and expressed as corresponding thematic maps (Figure 3) with an identical resolution of 30 m × 30 m.

Figure 3

Landslide influencing factor maps: (a) slope angle; (b) slope aspect; (c) curvature; (d) landform; (e) distance to faults; (f) lithology; (g) distance to roads; (h) distance to rivers; (i) rainfall, and (j) NDVI.

Slope angle is an indispensable parameter in landslide susceptibility evaluation, and its important influence on landslide occurrence has been widely discussed [31]. Generally, the slope angle is firmly connected with the stress distribution, groundwater, loose deposits, and human engineering activities, thus affecting the failure modes and dynamic characteristics of a landslide [32,33]. In this study, the slope angle was reclassified into five categories: 0–10°, 10–18°, 18–26°, 26–35°, and 35–73°.

The slope aspect determines the rainfall direction, solar radiation intensity, and the morphologic structure of the area, which impacts the physical environment and vegetation around the slope [34]. For the landslide susceptibility assessment, the slope aspect is classified into nine categories: Flat, North, North-East, East, South-East, South, South-West, West, and North-West.

Plane curvature is defined as the curvature of contour formed by the intersection of horizontal plane and surface [35]. It affects the convergence and divergence of water flowing through the surface. Curvature is employed and arranged into three categories: <(–1), –1 to 1, and >1 in the study.

The dependence of landslides on landform has been demonstrated by relevant studies, and mechanisms behind the effects of various landform types, such as hilly and mountain areas, on landslide activity have been discussed as well [36]. Landforms in She County include hills and mountains. Mountainous and hilly areas account for 95% of the county area, and plains account for 5% [5]. More specifically, the landforms are divided into eight categories: 1 (plain), 2 (shallow hill plain), 3 (middle hill), 4 (high hill), 5 (low undulating low mountain), 6 (high undulating low mountain), 7 (low undulating mountain), and 8 (high undulating mountain).

Faults usually break rock mass structure and reduce rock strength. In complicated structure areas, landslides often occur along the faults and decrease sharply with the distance to the faults [37]. The distance from faults, formed by multi-stage tectonic movements, is calculated at 400-m intervals using the geological map at a scale of 50,000. Euclidean metric and visual inspection were implemented to analyze the correlation between faults and landslides.

Lithology, which can reflect rock physical and mechanical properties including strength, weathering resistance, etc., is generally considered to be the decisive interfering factor for landslide stability [32,38]. In the study area, a total of six categories (Table 1) are identified according to the geological ages and lithofacies using the bedrock geological map with a 1:50,000 scale.

Generally, landslides tend to spread along road cuts due to the changed slope conditions and artificial free surfaces during road construction [39]. Many investigations and research results show that the probability of landslides decreases with the distance to roads [15,29,40]. In this study, a total of four road buffer zones have been generated: <400 m, 400–1,200 m, 1,200–2,000 m, and >2,000 m.

River erosion is one of the important factors scouring the slope toe and reducing slope stability [41]. The characteristics and mechanism of landslides triggered by river erosion have been revealed through investigations and experiments [42,43]. Typically, it can be concluded that the probability of landslide occurrence decreases with increasing distance to rivers. In the present study, five buffer zones are generated with an interval of 400 m, including <400 m, 400–800 m, 800–1,200 m, 1,200–2,000 m, and >2,000 m.

Rainfall can accelerate the rate of slope erosion and is always considered one of the most crucial negative factors in the stability of the landslide, especially in mountainous and hilly areas [14]. In this study, data from 18 meteorological stations provided by the Anhui Provincial Meteorological Bureau (http://www.weather.org.cn) are used to produce the mean annual rainfall map. Thus, the rainfall is reclassified into four classes: <1,530 mm/year, 1,530–1,580 mm/year, 1,580–1,650 mm/year, and >1,650 mm/year.

Vegetation fixes the soil through roots and improves the shear capacity of soil, which can effectively prevent the occurrence of landslides [44]. NDVI is always regarded as a critical index reflecting vegetation characteristics in landslide susceptibility mapping [45]. In the current study, the NDVI map of She County is obtained from the operational land image (OLI) of Landsat 8. The value is calculated by the following formula:

where IR is the infrared band of the electromagnetic spectrum, and R is the red band of the electromagnetic spectrum.

Ultimately, the NDVI value is reclassified into five categories including <0.2, 0.2–0.3, 0.3–0.35, 0.35–0.4, and >0.4.

4 Landslide susceptibility mapping

4.1 Application of frequency ratio model

The movement of rock-soil mass and controlling factors of landslide occurrence is assumed to be similar to those observed in the past. Based on this assumption, future landslides occurring in an unspecified time span can be predicted [12]. The frequency ratio (FR) is defined as the ratio between the percentage of landslides and the percentage of pixels within a category. The FR is the ratio of the area where landslides have occurred to the total area and is also the ratio of the probability of the landslide occurrence to nonoccurrence for a given attribute [46]. In the present study, the FR for each factor’s type or range is calculated based on its relationship with landslides. The larger the value, the stronger the correlation between the given factor and the landslide [47]. The landslide susceptibility index (LSI) has been acquired by summing the ratios of each factor as the given equation:

(2) LSI = ∑ FR ,

where FR is the ratio of each factor’s type or class and can be expressed by the following equation:

(3) FR = NLS pix ∑ 1 n NLS pix NC pix ∑ 1 m NC pix ,

where NLS_pix is the number of pixels of landslides, and NC_pix is the number of pixels of a class.

Based on the FR model, each class of the factors used in this study is characterized by a certain landslide occurrence density (Table 2).

Table 2

Spatial relationship between conditioning factor and landslide by FR and IOE models

Conditioning factor	Class	% Total of area (a)	% Total of landslide area (b)	FR (b/a)	(P ij )	H j	H jmax	I j	W j
Slope angle (°)	0–10	8.55	6.77	0.79	0.21	1.98	2.32	0.15	0.55
	10–18	24.79	25.50	1.03	0.28
	18–26	44.26	50.80	1.15	0.31
	26–35	22.15	16.93	0.76	0.20
	35–73	0.25	0	0	0.00
Slope aspect	F	0.31	0	0	0.00	2.99	3.17	0.06	0.46
	N	10.97	10.96	1.00	0.12
	NE	11.17	8.96	0.80	0.10
	E	12.48	10.76	0.86	0.11
	SE	13.47	11.75	0.87	0.11
	S	12.38	14.74	1.19	0.15
	SW	12.81	14.74	1.15	0.14
	W	13.20	12.95	0.98	0.12
	NW	13.20	15.14	1.15	0.14
Curvature	Concave	43.99	43.03	0.98	0.34	1.58	1.59	0.00	0.01
	Flat	9.34	7.97	0.85	0.30
	Convex	46.67	49.00	1.05	0.36
Landform	1	2.28	0.20	0.09	0.02	2.45	3.00	0.18	1.07
	2	2.39	0	0	0.00
	3	4.25	5.78	1.36	0.23
	4	7.85	1.00	0.13	0.02
	5	15.23	15.34	1.01	0.17
	6	23.75	32.27	1.36	0.23
	7	28.01	35.86	1.28	0.22
	8	16.25	9.56	0.59	0.10
Distance to faults (m)	<400	10.41	21.51	2.07	0.32	2.21	2.32	0.05	0.32
	400–800	10.26	15.34	1.50	0.23
	800–1,200	10.01	9.56	0.96	0.15
	1,200–2,000	18.62	24.90	1.34	0.21
	>2,000	50.71	28.69	0.57	0.09
Lithology	1	54.47	70.32	1.29	0.25	2.53	2.59	0.02	0.11
	2	25.40	14.94	0.59	0.12
	3	1.05	1.00	0.95	0.19
	4	3.65	3.39	0.93	0.18
	5	5.44	3.78	0.70	0.14
	6	9.98	6.57	0.66	0.13
Distance of roads (m)	<400	18.63	30.88	1.66	0.39	1.93	2.00	0.04	0.15
	400–1,200	27.62	25.30	0.92	0.22
	1,200–2,000	20.79	17.13	0.82	0.20
	>2,000	32.96	26.69	0.81	0.19
Distance of Rivers (m)	<400	22.69	39.84	1.76	0.34	2.10	2.32	0.09	0.49
	400–800	19.67	18.53	0.94	0.18
	800–1,200	17.24	11.35	0.66	0.13
	1,200–2,000	14.41	22.71	1.58	0.30
	>2,000	25.99	7.57	0.29	0.06
Rainfall (mm/year)	<1,530	50.69	65.74	1.30	0.39	1.93	2.00	0.03	0.12
	1,530–1,580	29.41	21.12	0.72	0.22
	1,580–1,650	7.86	4.98	0.63	0.19
	>1,650	12.03	8.17	0.68	0.20
NDVI	<0.2	2.89	6.37	2.20	0.34	2.20	2.32	0.05	0.35
	0.2–0.3	9.78	14.14	1.45	0.23
	0.3–0.35	24.41	29.68	1.22	0.19
	0.35–0.4	35.52	33.47	0.94	0.15
	>0.4	27.40	16.33	0.60	0.09

As a result of the FR model, an LSI map (Figure 4) has been constructed by ArcGIS 10.0 software, in which the LSI values vary from 2.88 to 8.01. Obviously, larger LSI values indicate a higher susceptibility for land sliding.

Figure 4

Landslide susceptibility map derived by the FR model.

For the visual interpretation of LSI maps, considering data distribution histogram, the quantile and natural break methods are applied to classify the data in this study. The comparison results show that the quantile data classification method is able to produce better classification results. After which the LSI map is classified into four sensitivity classes (low, moderate, high, and very high) using the quantile classifier. The corresponding area proportions for low, moderate, high, and very high susceptibility classes are 25.67, 25.33, 22.60, and 25.50%, respectively.

4.2 Application of ratio index of entropy model

Another model used for evaluating landslide susceptibility is the index of the entropy model based on the bivariate analysis principle. The entropy indicates the extent of instability, disorder, imbalance, and uncertainty of a system [48]. The model can calculate the weight of various factors referring to the extent that each landslide conditioning factor influences the occurrence of landslides in the natural environment [49]. The weight value for each variable obtained separately is expressed as the entropy index [10]. The equations used to calculate the weight value for each variable as a whole are as follows:

(4) P i j = b a ,

(5) ( P i j ) = P i j ∑ j = 1 S j P i j ,

(6) H j = − ∑ j = 1 S j ( P i j ) log 2 ( P i j ) , j = 1 , … , n ,

(7) H j max = log 2 S j , S j is the number of classes,

(8) I j = H j max − H j H j max , I = ( 0 , 1 ) , j = 1 , … , n ,

(9) W j = I j P i j W ,

where a and b are the percentages of domain and landslide, respectively, (P _ij ) represents the probability density, H _j and H _jmax are entropy values, I _j represents the information coefficient, and W _j is the resultant weight value for the factor as a whole. The LSM is finally prepared by the following equation:

(10) Y IOE = ∑ i = 1 n z m i × C × W j ,

where Y _IOE is the sum of all classes, i is the number of specific parameter mappings, z is the number of classes with the largest number of classes in a parameter mapping, m _i is the number of classes in a specific parameter map, C represents the value of the class after reclassification, and W _j represents the weight of the parameter. The summation results reflect the different sensitivities of landslide susceptibility.

The weight W _j of each conditioning factor in landslides is calculated and presented in Table 2. The results show that each class of the selected factors has a certain landslide occurrence density, and the landform, slope angle, distance of rivers, and NDVI are the most important factors that influence landslide distribution. Before LSM development, LSI is calculated by using the following equation:

(11) Y IOE = ( Slope angle × 0 .55 ) + ( Slope aspect × 0 .46 ) + ( Curvature × 0 .01 ) + ( Landform × 1 .07 ) + ( Distance to faults × 0 .32 ) + ( Lithology × 0 .11 ) + ( Distance to roads × 0 .15 ) + ( Distance to rivers × 0 .49 ) + ( Rainfall × 0 .12 ) + ( NDVI × 0 .35 ) . .

As a result of the IOE model, an LSI map (Figure 5) is constructed, in which the LSI value varies from 4.14 to 20.59. Obviously, the larger LSI value indicates a higher susceptibility to land sliding. After which the LSI map is classified into four sensitivity classes (low, moderate, high, and very high) by using the quantile classifier. The corresponding area proportions for low, moderate, high, and very high susceptibility classes are 4.18, 22.71, 41.63, and 31.47%, respectively.

Figure 5

Landslide susceptibility map derived by the IOE model.

5 Validation of the landslide susceptibility maps

Without validation, any try or effort to ascertain the landslide sensitivity in an area is meaningless [12]. In this study, the raster distributions (RD) histogram (Figure 6) and the ROC curve (Figure 7) have been drawn to validate and compare the performance of the two models.

Figure 6

Raster distributions of landslides within different classes. (a) FR, and (b) IOE.

Figure 7

Success and prediction rate curves for the LSMs produced in this study. (a) Success; (b) prediction.

In Figure 6, the blue and green bars represent the proportions of the landslide-prone areas in the total area and known landslide points in each classed area, respectively. Generally, a higher green bar in the higher class with a lower blue bar in the corresponding class indicates more accuracy and better fitting of the model is validated, which can provide a scientific basis for the prediction and management of landslide hazards [2]. Here, the proportions of landslide points in the high class are divided by the corresponding proportions of area for two models, the results are 1.49 (FR) and 1.52 (IOE), respectively. It indicates that both models can be used for assessing landslide susceptibility, while the IOE model is more accurate and better fitting in our study area.

The ROC curve is also adopted to check the quality of deterministic and probabilistic detection and forecast systems. In this study, 351 landslide locations (70%) are randomly selected from the observed dataset as the training data, and the remaining 151 landslide locations (30%) are used for validation. Then, the success rate curves were plotted by Python using training data (Figure 7(a)). In Figure 7(a), the x-axis is 1-specificity indicating the probability of predicted disaster points, and the y-axis is susceptibility, which represents the probability of disaster points correctly predicted in the total area. The AUC is used to qualitatively analyze the prediction accuracy of the landslide susceptibility map. When the AUC value close to 1.0 indicates fitting better, the value below 0.5 indicates fitting randomly [50]. The analysis results of the success rate curve indicated that the IOE model has a higher AUC value (0.816), whereas the FR model has 0.808. Because the success rate method used the data in the previous modeling, its results are less meaning for the prediction capability evaluation of the models. Therefore, the prediction rate is adopted to measure the prediction performance. The AUC plot assessment results of prediction rate curves (Figure 7(b)) found that the AUC values for FR and IOE models are 0.786 and 0.802, respectively. It can be concluded that both the success rate and the prediction rate curve show a similar result, and the models used in this study exhibited reasonably good accuracy in landslide susceptibility prediction. The IOE model is more suitable for landslide susceptibility mapping in the study area.

In this paper, FR and IOE models were used to develop the landslide vulnerability map of Shexian County. It can provide a comprehensive and inexpensive assessment of the study area and its ability to support individual or comprehensive uses, such as road construction and logging. Managers and foresters can then make decisions and develop prescriptions that will produce highly predictable results to produce sustainable products, maintain site quality, and significantly reduce the risk of any adverse effects.

6 Conclusion

In this study, two widely accepted models – frequency ratio (FR) and index of entropy (IOE) – are used to produce landslide susceptibility mappings for She County in the mountainous region of South Anhui, China. A total of 502 landslide locations has been identified and randomly divided into two groups as training (70%) and validation (30%) datasets. To perform sensitivity mapping, 10 landslide-influencing factors, including slope angle, slope aspect, curvature, landform, lithology, distance to faults, distance to roads, distance to rivers, rainfall, and normalized difference vegetation index (NDVI), are selected. Four susceptibility classes – low, moderate, high, and very high – are derived with the quantile data classification method in the susceptibility maps produced by FR and IOE models. The success rate and prediction rate methods are adopted to validate and compare the performance of the two models. The results indicate that the IOE model has a success rate of 0.816 and a predictive accuracy of 0.802, which is higher than that of the FR model, with AUC values of 0.808 and 0.786, respectively. The validation process also indicates that the models utilized in this study exhibit reasonably good accuracy in predicting landslide susceptibility. The interpretation of the susceptibility map indicates that landform, slope degree, and distance to rivers play a major role in landslide occurrence and distribution. The research results are worthy of preliminary land use planning and hazard mitigation in the next future.