Risk Assessment of Population Loss Posed by Earthquake-Landslide-Debris Flow Disaster Chain: A Case Study in Wenchuan, China

: Earthquakes often cause secondary disasters in mountainous areas, forming the typical earthquake-landslide-debris ﬂow disaster chain for a long time that results in a series of losses. It is important to improve the risk assessment method from the perspective of cascading effect of such a disaster chain, by strengthening quantitative research on hazards of the debris ﬂows which are affected by landslide volume and rainstorm intensity. Taking Wenchuan County as an example, the risk assessment method for population loss of the disaster chain is established and the risks are evaluated in this paper. The results show that the population loss risk is 2.59–2.71 people/km 2 under the scenarios of the Wenchuan Ms8.0 earthquake and four rainstorm intensities. The impacts of landslide and debris ﬂow after the earthquake were long-term and profound. A comparison of risks caused by each element of the chain revealed that the risk associated with the earthquake accounted for the highest proportion, and landslide and debris ﬂow accounted for 38.82–37.18% and 3.42–7.50%, respectively. As the earthquake intensity increases, the total risk posed by the disaster chain increases signiﬁcantly. The risk caused by the earthquake is the highest in high earthquake intensity zones; while in the lower-intensity zones, landslides and debris ﬂows pose relatively high risks. The risk assessment results were veriﬁed through comparison with actual data, indicating that the simulation results are quite consistent with the existing disaster information and that the risk assessment method based on the earthquake-landslide-debris ﬂow cascade process is signiﬁcant for future risk estimation.


Introduction
Natural disasters have a huge impact on the regional population, economy, resources, and environment [1,2]. Many organizations and regional plans around the world have emphasized the importance of improving natural disaster risk prevention capabilities [3][4][5]. Earthquakes are one of the main causes of geological disasters, and they can cause huge losses to regional populations [6][7][8][9]. A variety of disaster risk prevention measures have been formulated and adopted to reduce future impacts of earthquakes [10]. However, the occurrence of secondary geological disasters such as landslides and debris flows under the influence of great earthquakes may result in severe damage and long-term accumulation [11][12][13][14][15]. Moreover, they are characterized by sudden occurrences and hidden dangers [16]. The prevention and control of these disasters are long-term and difficult, and the risk of population loss posed by these disasters has attracted widespread attention [5,8,9,17].
Wenchuan County, the risk assessment method was improved in terms of the identification and assessment of debris flow hazards under earthquake and rainstorm scenarios, and the quantitative risk assessment of the population loss was conducted to provide a scientific basis for regional seismic geological disaster prevention and management.

Study Area and Materials
Wenchuan County (Figure 1) is located on the eastern edge of the Tibetan Plateau, and it is characterized by an altitude of 783-6057 m and a large degree of undulation. The study area is constructed by 9 towns, including Bazhou, Weizhou, Miansi, Gengda, Yingxiu, Xuankou, Shuimo, Sanjiang, and Wolong. The population distribution is relatively sparse, with an average density of 28.22 people/km 2 in 2015. It is relatively high in Xuankou and Shuimo (60.66 people/km 2 and 45.15 people/km 2 , respectively). The stratum of Wenchuan County is mainly distributed with Triassic, Devonian, and Proterozoic stratum. The lithology mainly includes magmatic rocks, metamorphic rocks, sandstone, and conglomerate [30]. The Wenchuan-Maoxian fault, Yingxiu-Beichuan fault, and Guanxian-Anxian fault are the main fault zones in Wenchuan. The epicenter of the Wenchuan Ms8.0 earthquake was in Yingxiu. According to the division of the intensity zone by the China Earthquake Administration [11], Yingxiu and Xuankou are located in the XI Intensity Zone, and Bazhou, Miansi, Gengda, Wolong, and Sanjiang are mostly located in the VIII and IX Intensity Zones. The complex geological structure and steep terrain in Wenchuan have led to a large number of landslides and debris flows after earthquakes [7,30]. material source and peak discharge to achieve reliable risk assessment of landslide-generated debris flows.
The risk assessment of population loss posed by disaster chain is an important way to achieve comprehensive disaster prevention and mitigation [6]. In this study, from the perspective of the cascading effect of an earthquake-landslide-debris flow disaster chain in Wenchuan County, the risk assessment method was improved in terms of the identification and assessment of debris flow hazards under earthquake and rainstorm scenarios, and the quantitative risk assessment of the population loss was conducted to provide a scientific basis for regional seismic geological disaster prevention and management.

Study Area and Materials
Wenchuan County (Figure 1) is located on the eastern edge of the Tibetan Plateau, and it is characterized by an altitude of 783-6057 m and a large degree of undulation. The study area is constructed by 9 towns, including Bazhou, Weizhou, Miansi, Gengda, Yingxiu, Xuankou, Shuimo, Sanjiang, and Wolong. The population distribution is relatively sparse, with an average density of 28.22 people/km 2 in 2015. It is relatively high in Xuankou and Shuimo (60.66 people/km 2 and 45.15 people/km 2 , respectively). The stratum of Wenchuan County is mainly distributed with Triassic, Devonian, and Proterozoic stratum. The lithology mainly includes magmatic rocks, metamorphic rocks, sandstone, and conglomerate [30]. The Wenchuan-Maoxian fault, Yingxiu-Beichuan fault, and Guanxian-Anxian fault are the main fault zones in Wenchuan. The epicenter of the Wenchuan Ms8.0 earthquake was in Yingxiu. According to the division of the intensity zone by the China Earthquake Administration [11], Yingxiu and Xuankou are located in the XI Intensity Zone, and Bazhou, Miansi, Gengda, Wolong, and Sanjiang are mostly located in the VIII and IX Intensity Zones. The complex geological structure and steep terrain in Wenchuan have led to a large number of landslides and debris flows after earthquakes [7,30]. The data sources are summarized in Table 1, including the geographical, disaster, and statistical data. The geographical data include the elevation, relief degree, population, geologic map, soil and water erosion, Normalized Difference Vegetation Index (NDVI), Fractional Vegetation Cover (FVC), faults, and human activity index data used to evaluate the debris flow hazards. Soil and water erosion refers to [49] to evaluate and classify the mean soil erosion modulus. The human activity index is based on the interpretation data of remote sensing images and is obtained by converting the construction land area [50]. The disaster data include earthquake intensity, several disaster points, The data sources are summarized in Table 1, including the geographical, disaster, and statistical data. The geographical data include the elevation, relief degree, population, geologic map, soil and water erosion, Normalized Difference Vegetation Index (NDVI), Fractional Vegetation Cover (FVC), faults, and human activity index data used to evaluate the debris flow hazards. Soil and water erosion refers to [49] to evaluate and classify the mean soil erosion modulus. The human activity index is based on the interpretation data of remote sensing images and is obtained by converting the construction land area [50]. The disaster data include earthquake intensity, several disaster points, and the corresponding population losses, which are used to analyze the result of the risk assessment. The statistical data include the earthquake-landslide hazards and the population loss vulnerability due to earthquakes, landslides, and debris flows from previous studies. Vulnerability curves or indexes for different disasters Vulnerability to earthquakes (V eq ): L peop = 1/(0.01 + 1.534 × 10 8 × 0.13 I ) [51] Vulnerability to landslides (V ls ):

Risk Assessment Method for Disaster Chain
The risk assessment method for the disaster chain was used to quantify the potential population loss caused by an earthquake-landslide-debris flow chain under various scenarios in Wenchuan. Among the expressions of various risk assessment methods, it is widely recognized that the risk composition consists of three aspects and is usually defined as where H stands for hazards, indicating the probability of disaster occurrence, and is mainly determined by the scale, intensity, and frequency. V is the vulnerability to a specific hazard intensity, and E is the exposure of the element at risk [54,55]. According to the theory of multi-disaster risk [20,40,41], the expression of the disaster chain risk is the accumulation of the primary disaster risk and the secondary disasters risks: where R dc is the risk of population loss posed by the earthquake-landslide-debris flow disaster chain; R eq , R ls , and R df are the risks of the earthquake, landslide, and debris flow in the chain, representing a population loss step by step; V eq , V ls , and V df are the vulnerabilities to population loss caused by the earthquake, landslide, and debris flow in Table 1, respectively; and E eq , E ls , and E df are the population densities in the earthquake, landslide, and debris flow areas, respectively (people/km 2 ). H eq is the hazard posed by the earthquake, which is represented by the Wenchuan Ms8.0 earthquake's intensity in this paper. H ls is the hazard posed by landslides, which was obtained by [41] through the analysis of the probability and movement of landslides (Table 1). H df is the hazard posed by debris flows, which was calculated by constructing an evaluation method and consists of the hazard area and intensity: where S df ( Figure 2) is the potential hazard area of the debris flow, which is related to a landslide factor; and y represents the factors used to construct the indicator system. cific hazard intensity, and E is the exposure of the element at risk [54,55]. According to the theory of multi-disaster risk [20,40,41], the expression of the disaster chain risk is the accumulation of the primary disaster risk and the secondary disasters risks: where Rdc is the risk of population loss posed by the earthquake-landslide-debris flow disaster chain; Req, Rls, and Rdf are the risks of the earthquake, landslide, and debris flow in the chain, representing a population loss step by step; Veq, Vls, and Vdf are the vulnerabilities to population loss caused by the earthquake, landslide, and debris flow in Table 1, respectively; and Eeq, Els, and Edf are the population densities in the earthquake, landslide and debris flow areas, respectively (people/km 2 ). Heq is the hazard posed by the earthquake, which is represented by the Wenchuan Ms8.0 earthquake's intensity in this paper Hls is the hazard posed by landslides, which was obtained by [41] through the analysis of the probability and movement of landslides (Table 1). Hdf is the hazard posed by debris flows, which was calculated by constructing an evaluation method and consists of the hazard area and intensity: where Sdf ( Figure 2) is the potential hazard area of the debris flow, which is related to a landslide factor; and y represents the factors used to construct the indicator system.

Method for Delimiting the Hazard Area of the Debris Flow
The Sdf includes the potential path in the gully (Sgully) and the resultant alluvial fan (Sfan): Based on the DEM for Wenchuan, the sub-basins with areas of mostly less than 5 km 2 were extracted [30]. The study area is dominated by gulley-type debris flows that threaten the population after the earthquake [30,[56][57][58]. In each sub-basin, the potential  The S df includes the potential path in the gully (S gully ) and the resultant alluvial fan (S fan ): Based on the DEM for Wenchuan, the sub-basins with areas of mostly less than 5 km 2 were extracted [30]. The study area is dominated by gulley-type debris flows that threaten the population after the earthquake [30,[56][57][58]. In each sub-basin, the potential flow paths were mainly determined by the terrain in Wenchuan [26,[56][57][58]. The edges of paths in the gully were detected using the Laplacian of the Gaussian (LOG) operator [59] according to the zero points of the second derivative: where a and b are the elevation of points and σ is the variance of the pixel in each window. A 3 × 3 window and a threshold of 1.20 (σ) were used in this study. The possible debris-flow runout zones on the alluvial fans were predicted using the empirical formula for its radius [48]: where L is the maximum accumulation length of the deposition fan (km); H is the elevation difference in the sub-basin (km), and V D is the volume of the non-compacted materials (10 4 m 3 ). In this study, an empirical formula was used to estimate V D [57,60]: where A is the area of the sub-basin (km 2 ) and A l is the area of the landslide in this basin (km 2 ).

Hazard Assessment of Seismic Landslide-Generated Debris Flow
In this study, the hazard intensity of the debris flow was estimated using the indicators in the hazard area: The landslide intensity (simulation volume) (y 1 ), debris flow intensity (peak discharge (y 2 ) and velocity (y 3 ), altitude (y 4 ), relief degree (y 5 ), degree of basin cutting (y 6 ), lithology (y 7 ), distance to the fault (y 8 ), NDVI (y 9 ), FVC (y 10 ), soil erosion (y 11 ), water erosion (y 12 ), and human activity index (y 13 ) were selected as the hazard factors for the debris flow and were divided into five levels according to different thresholds and were assigned values of 0.2, 0.4, 0.6, 0.8, or 1.0. w is the weight of each factor, which was synthesized using the Entropy Method (EM) and the Analytic Hierarchy Process (AHP) which need to refer to the explanation of factor weight in the existing research [61][62][63][64].
The debris flow intensity (y 2 and y 3 ) was simulated based on different rainstorm scenarios. The peak discharge is [65]: where Q c is the peak discharge of the debris flow (m 3 /s); Q p is the peak discharge of clear water (m 3 /s); φ c is the correction coefficient of the debris flow; D c is the obstructive coefficient; ϕ is the peak discharge coefficient of the clear water; F is the area of the basin (km 2 ), and i is the maximum rainstorm intensity under different scenarios (mm/h) based on the historical rainfall and researches about triggering rainfall of debris flows [66][67][68].
The velocity of the debris flow is one of the important parameters describing its dynamics. The formula for a sparse debris flow in the southwestern region was adopted [65]: where V c is the peak velocity of the debris flow (m/s); γ H is the density of the solid material in the debris flow (t/m 3 ), H c is the hydraulic radius, which can be approximated as the depth of the mud (m); and 1/n is the roughness coefficient of the river bed, with a value of 10. I c is the hydraulic slope of the debris flow and is replaced by the vertical drop (‰). The parameters usually vary with rainstorm intensity, and the information in Table 2 is based on experience and previous research [56,69,70].

Spatial Statistical and Analysis Methods
This article uses some spatial analysis and statistical tools in GIS. Hydrological tools are used to extract sub-basins based on DEM, and spatial statistics tools are used to analyze regional hazard factors and risks of the disaster chain.
The regional average elevation in Wenchuan is 2967 m, with higher elevations in the southwest region. The land relief ranges from 0.55 to 9.22 m, exhibiting an overall downward trend toward the southeast. Based on the GB50218T-2014 (China) engineering rock mass grading standards, the rock masses were divided into five types. The engineering geological group is soft in Xuankou and Shuimo. Soft layers mainly consist of mudstone and shale which are prone to be damaged. In terms of faults, the area within 1000 m of the fault was the most affected by the earthquake and the post-earthquake landslides [12,15,30]. The regional NDVI is 0.024-0.900, and the value is higher than the average in 77.78% of the region. The FVC in the study area is 0.12-0.61, with an average of 0.40. The spatial distributions of the NDVI and FVC both reflect the characteristics of lower vegetation coverage in the higher altitude areas. A total of 13.20% of the region has a soil erosion degree of greater than 8000, and these regions are mainly located in the high-altitude western area. The areas with high water erosion account for 5.61% of the total area and are mainly located in Gengda.
The results of the weight analysis of the hazard factors based on Equation (8) are shown in Table 3. The landslide volume and altitude are relatively higher based on the EM, accounting for 27.29% and 15.01%, respectively. The weights based on the AHP are 11.16%, 10.29%, 14.55%, 28.48%, 1.49%, 2.94%, 4.98%, 8.45%, 2.22%, 2.83%, 5.63%, 2.36%, and 4.61% with a Consistency Index of 0.138 and a Consistency Ratio of 0.08, which means that they pass the consistency test. The comprehensive weights obtained using the two methods indicate that the weight of the landslide volume is highest (20.92%), followed by that of the altitude (21.75%). The comprehensive weights are used in the debris flow hazard assessment.  The results of the weight analysis of the hazard factors based on Equation (8) are shown in Table 3. The landslide volume and altitude are relatively higher based on the EM, accounting for 27.29% and 15.01%, respectively. The weights based on the AHP are 11.16%, 10.29%, 14.55%, 28.48%, 1.49%, 2.94%, 4.98%, 8.45%, 2.22%, 2.83%, 5.63%, 2.36%, and 4.61% with a Consistency Index of 0.138 and a Consistency Ratio of 0.08, which means that they pass the consistency test. The comprehensive weights obtained using the two methods indicate that the weight of the landslide volume is highest (20.92%),

Debris Flow Hazard Analysis
The total debris flow hazard area in Wenchuan is 425.12 km 2 , and the radius of the alluvial fan is 0.20-0.65 km (Figure 4). The areas in Wolong and Gengda are relatively high at 88.12 km 2 and 84.93 km 2 , respectively, while those in Shuimo and Xuankou are lower at 2.78 km 2 and 5.87 km 2 , respectively, due to difficulties in delimiting the gully areas in the mainstream area of the Minjiang River. Using the indicator system for debris flows, the results of the regional hazards were obtained ( Figure 4). In the potential area, the average hazard gradually increases with rainstorm intensity; and the values under scenarios RS1, RS2, RS3, and RS4 are 0.25, 0.37, 0.49, and 0.57, respectively. This value is generally low under scenario RS1, ranging from 0.14 to 0.35. Under scenario RS4, the regional debris flow hazard is 0.34-0.78, and 60.31% of the hazard area is higher than 0.5. The hazard in Miansi, Shuimo, and Xuankou in the southwestern part of the study area is significantly higher, with the highest increment of 0.12.

Debris Flow Hazard Analysis
The total debris flow hazard area in Wenchuan is 425.12 km 2 , and the radius of the alluvial fan is 0.20-0.65 km (Figure 4). The areas in Wolong and Gengda are relatively high at 88.12 km 2 and 84.93 km 2 , respectively, while those in Shuimo and Xuankou are lower at 2.78 km 2 and 5.87 km 2 , respectively, due to difficulties in delimiting the gully areas in the mainstream area of the Minjiang River. Using the indicator system for debris flows, the results of the regional hazards were obtained ( Figure 4). In the potential area, the average hazard gradually increases with rainstorm intensity; and the values under scenarios RS1, RS2, RS3, and RS4 are 0.25, 0.37, 0.49, and 0.57, respectively. This value is generally low under scenario RS1, ranging from 0.14 to 0.35. Under scenario RS4, the regional debris flow hazard is 0.34-0.78, and 60.31% of the hazard area is higher than 0.5. The hazard in Miansi, Shuimo, and Xuankou in the southwestern part of the study area is significantly higher, with the highest increment of 0.12.  , which has the largest hazard area. As the intensity of the heavy rain increases, the hazard increases significantly, but the growth rate decreases. The debris flow hazard under scenario RS2 in the township increases by 0.11-0.15, and the growth rate is 47.65-51.00% compared with scenario RS1. The hazard under scenario RS4 increases by 0.07-0.12, and the growth rate is 15.72-19.26% compared with scenario RS3. From the perspective of the hazard anomaly percentage of each township, Xuankou, Shuimo, and Yingxiu are significantly higher than the regional average; Gengda, Sanjiang, and Weizhou are slightly higher; Bazhou and Wolong are lower. bris flow hazard under scenario RS2 in the township increases by 0.11-0.15, and the growth rate is 47.65-51.00% compared with scenario RS1. The hazard under scenario RS4 increases by 0.07-0.12, and the growth rate is 15.72-19.26% compared with scenario RS3. From the perspective of the hazard anomaly percentage of each township, Xuankou, Shuimo, and Yingxiu are significantly higher than the regional average; Gengda, Sanjiang, and Weizhou are slightly higher; Bazhou and Wolong are lower.

Risk of Earthquake-Landslide-Debris Flow Disaster Chain
According to the improved risk assessment method, the population loss risks posed by an earthquake-landslide-debris flow disaster chain under the Wenchuan Ms8.0 earthquake and four rainstorm scenarios were evaluated ( Figure 6). The risks of population loss are 10,579, 10,761, 10,928, and 11,045 people (when the population risk is measured in people, less than 1 is counted as 1) under scenarios RS1, RS2, RS3, and RS4, respectively. The regional average risk is 2.59 people/km 2 , 2.64 people/km 2 , 2.68 people/km 2 , and 2.71 people/km 2 under scenarios of RS1, RS2, RS3, and RS4, respectively, and these differences are mainly caused by the debris flow.
As the rainstorm intensity increases, the proportion of the population loss caused by the earthquake and landslides decreases, while the proportion caused by the debris flow increases significantly, with a growth rate of 119.22%. The population loss risk posed by the earthquake accounts for 57.76-55.32%, the landslide accounts for 38.82-37.18%, and the debris flow accounts for 3.42-7.50%. From the perspective of the spatial distribution, the risk in southeastern Wenchuan is significantly higher. In particular, the risks are relatively high in the high earthquake intensity area and the mountainous western area.
On the township scale, the population risks in Yingxiu, Gengda, and Miansi are relatively high at 3903, 2120, and 1062 people, accounting for 36.89%, 20.04%, and 10.03%, respectively, under scenario RS1. Yingxiu has the highest risk at 10.15 people/km 2 , which is 3.90 times the regional average, followed by Xuankou and Weizhou at 7.86 people/km 2 and 3.21 people/km 2 , respectively, and the risks in the other towns are lower than the average. As the rainstorm intensity increases, the population risk in the townships increases steadily. The proportions of the total population risk in Yingxiu, Gengda, Xuankou, and Sanjiang decrease mainly due to the low risk of debris flows in this region. The proportion in Yingxiu decreases by 1.23%, while the proportion in Weizhou increases significantly (1.12%).

Risk of Earthquake-Landslide-Debris Flow Disaster Chain
According to the improved risk assessment method, the population loss risks posed by an earthquake-landslide-debris flow disaster chain under the Wenchuan Ms8.0 earthquake and four rainstorm scenarios were evaluated ( Figure 6). The risks of population loss are 10,579, 10,761, 10,928, and 11,045 people (when the population risk is measured in people, less than 1 is counted as 1) under scenarios RS1, RS2, RS3, and RS4, respectively. The regional average risk is 2.59 people/km 2 , 2.64 people/km 2 , 2.68 people/km 2 , and 2.71 people/km 2 under scenarios of RS1, RS2, RS3, and RS4, respectively, and these differences are mainly caused by the debris flow.
As the rainstorm intensity increases, the proportion of the population loss caused by the earthquake and landslides decreases, while the proportion caused by the debris flow increases significantly, with a growth rate of 119.22%. The population loss risk posed by the earthquake accounts for 57.76-55.32%, the landslide accounts for 38.82-37.18%, and the debris flow accounts for 3.42-7.50%. From the perspective of the spatial distribution, the risk in southeastern Wenchuan is significantly higher. In particular, the risks are relatively high in the high earthquake intensity area and the mountainous western area.
On the township scale, the population risks in Yingxiu, Gengda, and Miansi are relatively high at 3903, 2120, and 1062 people, accounting for 36.89%, 20.04%, and 10.03%, respectively, under scenario RS1. Yingxiu has the highest risk at 10.15 people/km 2 , which is 3.90 times the regional average, followed by Xuankou and Weizhou at 7.86 people/km 2 and 3.21 people/km 2 , respectively, and the risks in the other towns are lower than the average. As the rainstorm intensity increases, the population risk in the townships increases steadily. The proportions of the total population risk in Yingxiu, Gengda, Xuankou, and Sanjiang decrease mainly due to the low risk of debris flows in this region. The proportion in Yingxiu decreases by 1.23%, while the proportion in Weizhou increases significantly (1.12%).
The population loss rates (Figure 7) caused by an earthquake-landslide-debris flow disaster chain in Wenchuan are 9.06%, 9.21%, 9.35%, and 9.45% under rainstorm scenarios RS1, RS2, RS3, and RS4, respectively. For each element of the disaster chain, the population risk loss rate is 5.23% for the earthquake, 3.71% for the landslides, and 0.34%, 0.51%, 0.67%, and 0.78% for the debris flows under scenarios RS1, RS2, RS3, and RS4, respectively. At the township scale, all towns are strongly affected by the earthquake with a generally high population loss rate. Among them, Yingxiu Town is the most significant, which is located at the epicenter. The population loss rate of secondary geological disasters in Weizhou Town and Shuimo Town is relatively high. The population loss rate in Yingxiu is 25.82-26.07%, of which the earthquake population loss rate is 23.74%. The population loss rates caused by debris flows in Weizhou under scenarios RS3 and RS4 (2.38% and 2.75%, respectively) are higher than those caused by landslides. The mortality rates are greatly affected by landslides in Shuimo, Bazhou, and Wolong, with loss rates of 1.69%, 4.59%, and 2.29%, respectively. In addition to the relatively high population risks posed by landslides in Shuimo and Wolong, the population loss rates caused by debris flows under a high rainstorm intensity are 0.86% and 0.42% in Shuimo and Wolong, respectively, which exceed the risks posed by an earthquake.
According to the statistical results of the risks under different earthquake intensities (Table 4), the population risk and loss rate of the disaster chain increase as the earthquake intensity increases. For example, as earthquake intensity increases, the population loss risks increase from 1.16 people/km 2 to 10.17 people/km 2 , and the loss rates increase from 4.52% to 29.28% under scenario RS1. For the elements of the disaster chain, the loss rate caused by the earthquake increases the most significantly with increasing earthquake intensities, while those caused by the landslides and debris flows fluctuate. The population loss caused by the earthquake is the highest under intensities X and XI, followed by that caused by landslides, and that caused by debris flows is the lowest. In the IX and VIII intensity zones, the landslides and debris flows have relatively high risks, and the earthquake risk is relatively low. Under intensity XI, the loss rate caused by an earthquake is the highest (26.67%), and that caused by landslides is the lower (3.27%). Under intensity VIII, the population loss rate caused by landslides and debris flows is higher than that caused by the earthquake, i.e., 4.15% and 0.29-0.66%, respectively. The population loss rates (Figure 7) caused by an earthquake-landslide-debris flow disaster chain in Wenchuan are 9.06%, 9.21%, 9.35%, and 9.45% under rainstorm scenarios RS1, RS2, RS3, and RS4, respectively. For each element of the disaster chain, the population risk loss rate is 5.23% for the earthquake, 3.71% for the landslides, and 0.34%, 0.51%, 0.67%, and 0.78% for the debris flows under scenarios RS1, RS2, RS3, and RS4, According to the statistical results of the risks under different earthquake intensities (Table 4), the population risk and loss rate of the disaster chain increase as the earthquake intensity increases. For example, as earthquake intensity increases, the population loss risks increase from 1.16 people/km 2 to 10.17 people/km 2 , and the loss rates increase from 4.52% to 29.28% under scenario RS1. For the elements of the disaster chain, the loss rate caused by the earthquake increases the most significantly with increasing earthquake intensities, while those caused by the landslides and debris flows fluctuate. The population loss caused by the earthquake is the highest under intensities X and XI, followed by that caused by landslides, and that caused by debris flows is the lowest. In the IX and VIII intensity zones, the landslides and debris flows have relatively high risks, and the earthquake risk is relatively low. Under intensity XI, the loss rate caused by an earthquake is the highest (26.67%), and that caused by landslides is the lower (3.27%). Under intensity VIII, the population loss rate caused by landslides and debris flows is higher than that caused by the earthquake, i.e., 4.15% and 0.29-0.66%, respectively.   The population loss risk posed by the earthquake-landslide-debris flow disaster chain was analyzed using probability statistics at an interval of 0.5 ( Figure 8). As the risk value increases, the corresponding probability value decreases, and the rate of decrease of the frequency under scenario RS1 is larger than those under the other scenarios. The frequencies of risks of less than 1.0 person/km 2 are 0.53, 0.52, 0.51, and 0.50 under scenarios RS1, RS2, RS3, and RS4, respectively. When the risk is higher than 3.5 people/km 2 , the frequencies are 0.26, 0.27, 0.28, and 0.28, respectively. In the RS1 heavy rain scenario, as the risk increases, the rate for the frequency reduction is more obvious. According to the curve fitting, when the risk of population loss is lower, the lower the rainfall intensity, the higher the risk frequency. By contrast, when the risk is higher, the frequency is higher under the higher rainfall intensity scenario. frequencies of risks of less than 1.0 person/km are 0.53, 0.52, 0.51, and 0.50 under sce-narios RS1, RS2, RS3, and RS4, respectively. When the risk is higher than 3.5 people/km 2 , the frequencies are 0.26, 0.27, 0.28, and 0.28, respectively. In the RS1 heavy rain scenario, as the risk increases, the rate for the frequency reduction is more obvious. According to the curve fitting, when the risk of population loss is lower, the lower the rainfall intensity, the higher the risk frequency. By contrast, when the risk is higher, the frequency is higher under the higher rainfall intensity scenario.

Population Loss Risk Posed by Each Element of the Disaster Chain
Under the Wenchuan Ms8.0 earthquake scenario, the population loss risk posed by the Wenchuan earthquake is 1.5 people/km 2 (Figure 9). It is higher in areas with an earthquake intensity of XI, with an average value of 9.61 people/km 2 . It is 1.89 people/km 2 , 0.16 people/km 2 , 0.02 people/km 2 in the areas with earthquake intensities of X, IX, and VIII, respectively. At the township scale, the risks in Yingxiu, Xuankou, and Weizhou are higher than the average risk level in the study area. It is highest in Yingxiu (9.29 people/km 2 ), followed by Xuankou (6.51 people/km 2 ) and Weizhou (1.90 people/km 2 ). Bazhou is mainly located in the VIII zone and has the lowest risk (0.02 people/km 2 ). Under the Wenchuan Ms8.0 earthquake scenario, the population exposure of the landslide was 27.16 people/km 2 after 6111 people were lost during the earthquake. The risk of population loss posed by the landslides in Wenchuan is 1.01 people/km 2 . The risks in Sanjiang, Gengda, Bazhou, and Xuankou are higher than the average risk level in the study area, at 1.10 people/km 2 , 1.53 people/km 2 , 1.15 people/km 2 , and 1.23 people/km 2 , respectively, while the risk in Wolong is the lowest (0.69 people/km 2 ).

Population Loss Risk Posed by Each Element of the Disaster Chain
Under the Wenchuan Ms8.0 earthquake scenario, the population loss risk posed by the Wenchuan earthquake is 1.5 people/km 2 (Figure 9). It is higher in areas with an earthquake intensity of XI, with an average value of 9.61 people/km 2 . It is 1.89 people/km 2 , 0.16 people/km 2 , 0.02 people/km 2 in the areas with earthquake intensities of X, IX, and VIII, respectively. At the township scale, the risks in Yingxiu, Xuankou, and Weizhou are higher than the average risk level in the study area. It is highest in Yingxiu (9.29 people/km 2 ), followed by Xuankou (6.51 people/km 2 ) and Weizhou (1.90 people/km 2 ). Bazhou is mainly located in the VIII zone and has the lowest risk (0.02 people/km 2 ). Under the Wenchuan Ms8.0 earthquake scenario, the population exposure of the landslide was 27.16 people/km 2 after 6111 people were lost during the earthquake. The risk of population loss posed by the landslides in Wenchuan is 1.01 people/km 2 . The risks in Sanjiang, Gengda, Bazhou, and Xuankou are higher than the average risk level in the study area, at 1.10 people/km 2 , 1.53 people/km 2 , 1.15 people/km 2 , and 1.23 people/km 2 , respectively, while the risk in Wolong is the lowest (0.69 people/km 2 ). From the perspective of an earthquake-landslide disaster chain (Figure 10), the population loss risk in the study area is 10,217 people (2.51 people/km 2 ), with relatively high values in Yingxiu and Xuankou (10.04 people/km 2 and 7.75 people/km 2 , respec- From the perspective of an earthquake-landslide disaster chain (Figure 10), the population loss risk in the study area is 10,217 people (2.51 people/km 2 ), with relatively high values in Yingxiu and Xuankou (10.04 people/km 2 and 7.75 people/km 2 , respectively). The earthquake and landslides accounted for 59.80% and 40.20%, respectively, of the risk posed by this disaster chain. As the earthquake intensity increases, the risk posed by the earthquake increases significantly, but the risk posed by the landslides in the lower-intensity areas increases even more significantly than the earthquake risk. The earthquake-landslide disaster chain risk in the XI zone is 10.09 people/km 2 , and the risk posed by the earthquake accounts for 91.76%, which is significantly higher than that caused by the landslides. The risk in the VIII zone is 1.10 people/km 2 , and the risk posed by the earthquake accounts for 2.37%, while that posed by the landslides accounts for 97.63%. From the perspective of an earthquake-landslide disaster chain (Figure 10), the population loss risk in the study area is 10,217 people (2.51 people/km 2 ), with relatively high values in Yingxiu and Xuankou (10.04 people/km 2 and 7.75 people/km 2 , respectively). The earthquake and landslides accounted for 59.80% and 40.20%, respectively, of the risk posed by this disaster chain. As the earthquake intensity increases, the risk posed by the earthquake increases significantly, but the risk posed by the landslides in the lower-intensity areas increases even more significantly than the earthquake risk. The earthquake-landslide disaster chain risk in the XI zone is 10.09 people/km 2 , and the risk posed by the earthquake accounts for 91.76%, which is significantly higher than that caused by the landslides. The risk in the VIII zone is 1.10 people/km 2 , and the risk posed by the earthquake accounts for 2.37%, while that posed by the landslides accounts for 97.63%. The population loss risks posed by debris flows in Wenchuan are 0.09 person/km 2 , 0.13 person/km 2 , 0.17 person/km 2 , and 0.20 person/km 2 under rainstorm scenarios ( Figure  11). As the intensity of the heavy rains increases, the risk of population loss posed by debris flows increases steadily, and the frequency of the higher risk of population loss increases. Under scenario RS1, the regional population loss risk posed by debris flows is mainly 0.20-0.60 people/km 2 , of which 40.31% of the debris flow valley area has a risk of The population loss risks posed by debris flows in Wenchuan are 0.09 person/km 2 , 0.13 person/km 2 , 0.17 person/km 2 , and 0.20 person/km 2 under rainstorm scenarios ( Figure 11). As the intensity of the heavy rains increases, the risk of population loss posed by debris flows increases steadily, and the frequency of the higher risk of population loss increases. Under scenario RS1, the regional population loss risk posed by debris flows is mainly 0.20-0.60 people/km 2 , of which 40.31% of the debris flow valley area has a risk of fewer than 0.40 people/km 2 and 78.86% of the debris flow valley has a risk of fewer than 0.60 people/km 2 . Under scenario RS4, 70.56% of the debris flow valley area has a risk of 0.60-1.20 people/km 2 and 48.39% of the debris flow valley area has a risk of greater than 1 person/km 2 . At the township scale, the debris flow risks in Weizhou, Shuimo, Xuankou, and Miansi are higher than the regional average. The debris flow risk in Weizhou is relatively high, at 0.46 people/km 2 , 0.70 people/km 2 , 0.90 people/km 2 , and 1.04 people/km 2 under rainstorm scenarios. The risk in Gengda is the lowest, at 0.04 people/km 2 , 0.06 people/km 2 , 0.07 people/km 2 , and 0.09 people/km 2 , respectively.

Verification of the Risk Assessment Results
In this study, information obtained from the literature showed that the population loss in Wenchuan was 15.94 thousand people for the earthquake events in 2008. The population risk posed by the earthquake-landslide-debris flow disaster chain was about 11.00 thousand people in this paper, which is not significantly different from the actual data. Moreover, the population risk posed by debris flows was compared with data for several debris flow events to verify the reliability of the simulation results ( Table 5). The results are in good agreement with the actual losses or casualties caused by events in several gullies. fewer than 0.40 people/km 2 and 78.86% of the debris flow valley has a risk of fewer than 0.60 people/km 2 . Under scenario RS4, 70.56% of the debris flow valley area has a risk of 0.60-1.20 people/km 2 and 48.39% of the debris flow valley area has a risk of greater than 1 person/km 2 . At the township scale, the debris flow risks in Weizhou, Shuimo, Xuankou, and Miansi are higher than the regional average. The debris flow risk in Weizhou is relatively high, at 0.46 people/km 2 , 0.70 people/km 2 , 0.90 people/km 2 , and 1.04 people/km 2 under rainstorm scenarios. The risk in Gengda is the lowest, at 0.04 people/km 2 , 0.06 people/km 2 , 0.07 people/km 2 , and 0.09 people/km 2 , respectively.

Verification of the Risk Assessment Results
In this study, information obtained from the literature showed that the population loss in Wenchuan was 15.94 thousand people for the earthquake events in 2008. The population risk posed by the earthquake-landslide-debris flow disaster chain was about 11.00 thousand people in this paper, which is not significantly different from the actual data. Moreover, the population risk posed by debris flows was compared with data for several debris flow events to verify the reliability of the simulation results ( Table 5). The results are in good agreement with the actual losses or casualties caused by events in several gullies. For example, a debris flow in Taoguan Gully in 2013 lost 1 person, while the simulation results provided a risk of 0.53-1.31 people under the different rainstorm

Reliability of Population Risk for the Disaster Chain
The risk assessment results of this study were verified through comparison with data for actual disaster events, indicating that the method proposed in this study has a certain scientific value for risk assessment of earthquake-landslide-debris flow disaster chains. However, the accuracy of the risk results in some gullies needs to be improved which may be related to regional disaster prevention and mitigation measures [41,71]. In 2013, the population loss caused by a debris flow in Qipan Gully was 15 people, including 13 tourists and 2 workers [72]. However, the simulation results indicated 82-188 people, which is much higher than the actual value. This discrepancy may be related to the timely implementation of emergency measures [71]. In 2019, 15 people were lost in a debris flow in Zhaobi Village, but the simulation results were slightly lower (4-8 people). During this disaster event, village officials strengthened inspections after heavy rains, carried out monitoring and prevention measures, and the timely relocation of villagers to safer areas. There were no deaths in some gullies in Qiangfeng, mainly due to timely weather warnings, monitoring, and population relocation [34,72]. Risk assessment for disaster chains is closely related to regional risk management and prevention. Therefore, considering the interactions between the current regional disaster prevention and the disaster scenarios in the risk assessment process is of great significance for enhancing the reliability of future risk assessments.
The population loss risk posed by an earthquake-landslide-debris flow disaster chain simulated in this paper is about 11.00 thousand people, including the risks posed by the earthquake, landslides, and debris flows, which occurred at different times and sequentially. There is still some data gap that may be caused by the occurrence of a large number of other co-seismic disasters (dammed lakes, floods, etc.), or may be related to errors in the risk assessment [73]. The results show that the risks posed by landslides in high earthquake intensity areas may be lower than those in low earthquake intensity areas, which may be related to the influence of the regional geological conditions and the errors in the existing earthquake-landslide hazard assessments [41,74]. In view of the uncertainty of regional risk results, factor analysis methods can be further used to explore the sensitivity of risks to topography, environment, and other factors to further clarify the characteristics of disaster chain risks [63,64,75]. In summary, it would be valuable to collect more disaster data, strengthen field investigations, and improve research on mechanism processes and verify the simulation results from multiple aspects [63,64,75].
In this study, the earthquake intensity used the classification result based on Chinese standards to analyze risks [11,51]. The measurements of earthquake intensity scales have great influences on earthquake prevention and disaster mitigation [76]. Many earthquake intensity scales have been used around the world, such as Environmental Seismic Intensity (ESI) [12,13,77], European Microseismic Scale (EMS) [14], the Chinese seismic intensity scale [11], shake map in America [78], Japan Meteorological Agency (JMA) Instrumental Seismic Intensity [79], etc. There are some differences between these classifications of earthquake intensity. ESI mainly considers earthquake environmental effects and quantifies the size and distribution of some disasters such as landslides and tsunamis [77]. EMS and Chinese standards have 2-3 quantitative terms of damage degree for each type of house in each intensity, but there are differences in the description of house type and earthquake damage degree [11,14]. The earthquake intensity of JMA is divided by 8 degrees, and the quantification related to house damage is rarely mentioned [79]. The shake map uses instrument monitoring data to estimate the earthquake intensity based on empirical formulas. These methods and standards will result in different intensity values. However, basic seismic data (such as house damage), which is necessary to estimate the results of the earthquake intensity according to different scales, is difficult to obtain. Earthquake intensity scales are also constantly being developed [79,80]. In the future, regional risks can be further studied according to different earthquake intensity scales to enhance the comparability of research results on a global scale.

Limitations on Hazard Assessment of Debris Flows
In this study, the hazard posed by a debris flow is based on multiple indicators, and the weight and classification of each factor may lead to controversy because the thresholds of the classifications may not apply to all gullies. Rainfall intensity is an important factor to be discussed since it is related to the intensity of debris flows [81]. The amount of precipitation recorded during different debris flow events fluctuates within a relatively large range, usually ranging from 4.3 to 75.2 mm/h [68,70,82]. Therefore, relevant monitoring data should be established or improved, and the classification threshold should be further clarified in future studies. Moreover, in the context of climate change, the scale and frequency of extreme rainstorm events have increased, and the impact of geological disasters has also expanded. Therefore, it is necessary to carry out the risk assessment of geological disasters affected by climate change to reduce the potential loss induced by meteorological factors [37,61].
As for the study of debris flow hazard areas, empirical formulas from previous studies were used to delimit the alluvial fans. At present, related functional equations (such as the functional relationship between the run-out distance of the debris flow, the scale of the debris flow, and the height difference) are commonly constructed using statistical regression methods [48,83,84]. Studies have also been conducted to estimate the temporal and spatial distributions of alluvial fans using numerical simulation methods [16,81,85]. Therefore, more factors, such as the rainstorm intensity, should be considered to simulate the hazard area more accurately and to provide a more scientific basis for risk assessment research.
Some parameters were used to evaluate the debris flow factors. For example, the density of the debris flow is highly correlated with the recurrence period of the rainfall and the deposits [70,86]. The amplification coefficient usually ranges from 0.3 to 0.8, but it is 1.92 in some studies that took into account the intensity of short-duration rainstorms and the particular characteristics of the earthquake area [87]. The obstructive coefficient is generally 1.1-2.5, but can also range from 2.5 to 5 when a large amount of accumulated materials is considered [30]. As the rainstorm intensity increases, the debris flow may transform from a general type to a dam-breaking type, and thus, the amount of the breaking maybe dozens or even hundreds of times larger [57]. It is difficult to directly set the parameters and test the reliability for lots of debris flows because the existing data and studies are mostly based on the statistics of and prediction data for general types. Further studies with refined parameters can provide a theoretical basis for such debris flows that occur after an earthquake.

Uncertainties in the Vulnerability Curves or Indices
The population's vulnerabilities to earthquakes, landslides, and debris flows have mainly been studied using surface, curve, matrix, and coefficient in existing studies [51][52][53][88][89][90]. The determination of the vulnerability to earthquakes mostly uses an empirical formula that considers the epicentral intensity and the entire population affected while there is difficulty converting between the epicentral intensity and the earthquake intensity [11,51]. The determination of the vulnerability to landslides usually involves using key factors such as the hazard, depth, and impact pressure to construct a mortality curve [31,88]. The vulnerability to debris flows is based on the parameters at the administrative unit scale based on parameters such as the age structure of the population. In addition, the eruption characteristics of the debris flow and the natural conditions can also be considered [91]. However, the lithology is not considered in the vulnerability curve according to [52] because it may be a complex work because of difficulties in obtaining the loss rate of each lithology. As a large amount of data is not generally available, many studies refer to the vulnerability results of existing studies and have a reference value. In recent years, in the context of future population growth and climate change, and due to the continuous attention paid to the uncertainty of the vulnerability assessment, innovative equipment, and risk assessment, further research on the analysis and quantification of population vulnerability is very important for regional disaster prevention and mitigation [37,90].

Conclusions
The earthquake-landslide-debris flow disaster chain in Wenchuan poses a huge threat to the population. Population loss risk assessment is conducive to disaster reduction in advance and reduces the number of fatalities. Based on the cascading effect of this disaster chain, this study focused on the influence of the landslide volume and rainstorm intensity on debris flows and assess the population loss risk posed by each element of the disaster chain. The main conclusions are as follows.
(1) The population loss risks posed by an earthquake-landslide-debris flow disaster chain are 2.59 people/km 2 , 2.64 people/km 2 , 2.68 people/km 2 , and 2.71 people/km 2 under scenarios RS1, RS2, RS3, and RS4, respectively. For the elements of the disaster chain, the risk posed by the earthquake accounts for the highest proportion (57.76-55.32%), and that posed by the debris flow accounts for the lowest proportion. As the rainstorm intensity increases, the hazard and risk posed by debris flows increase steadily, and the frequency of higher risks of population loss increases.
(2) The population risk and loss rates caused by the disaster chain increase as the earthquake intensity increases. The loss rate caused by the earthquake increases most significantly (0.10-26.27%) with increasing earthquake intensity, and those caused by the landslides and debris flows fluctuate. The population loss caused by the earthquake is the highest in the high earthquake intensity zones; in the lower intensity zones, landslides and debris flows pose relatively high risks.
(3) The simulation results in this study assess the population risk posed by a regional disaster chain well based on a comparison between the simulated population loss risk and data for actual disaster events. By reducing the uncertainty of the comparison results, the debris flow risk assessment, and the population vulnerability, the reference value of the risk assessment method for disaster chains and for estimating future risks can be further improved.

Data Availability Statement:
The data presented in this study are available from the author upon reasonable request.