Southwestern China is characterized by many steep mountains and deep valleys due to the uplift activity of the Tibetan Plateau. The 2008 Wenchuan earthquake left large amounts of loose materials in this area, making it a severe disaster zone in terms of debris flow. Susceptibility is a significant factor of debris flows for evaluating their formation and impact. Therefore, there is an urgent need to analyze the susceptibility to debris flows of this area. To quantitatively predict the susceptibility of the area to debris flows, this study evaluates 70 typical debris flow gullies, which are distributed along the Brahmaputra River, Nujiang River, Yalong River, Dadu River, and Ming River, as statistical samples. Nine indexes are chosen to construct a factor index system and then to evaluate the susceptibility to debris flow. They are the catchment area, longitudinal gradient, average gradient of the slope on both sides of the gully, catchment morphology, valley orientation, loose material reserves, location of the main loose material, antecedent precipitation, and rainfall intensity. Following this, an empirical model based on the Type I quantification theory is established for susceptibility prediction for debris flows in southwestern China. Finally, 10 debris flow gullies upstream of the Dadu River are analyzed to verify the reliability of the proposed model. The results show that the accuracy of the statistical model is 90 %.

Debris flows are a common geological hazard in mountainous areas that transport large amounts of sediment down-slope and cause serious damage to dwellings, roads, and other structural facilities. China has a chiefly mountainous topography and is one of the most debris-flow-prone countries in the world. Up to March 2019, approximately recorded 50 000 debris flows have occurred in China (Di et al., 2019). A significant percentage of these debris flows are distributed in southwestern China, particularly in the Wenchuan earthquake area, where large amounts of loose material were produced by the earthquake-induced landslides (Xu et al., 2012; Huang et al., 2015; Dai et al., 2017).

Due to the complex nature of debris flows, it is quite difficult to fully understand their initiation mechanism and precisely forecast their occurrence (Brayshaw and Hassan, 2009; Gao et al., 2019). The uncertainty of debris flows poses a significant threat to human life in downstream areas (Schürch et al., 2011). Debris flow susceptibility expresses the occurrence possibility of debris flow in an area with respect to its geomorphologic characteristics (Kappes et al., 2011; Bertrand et al., 2013). Therefore, susceptibility analysis is an essential step for conducting risk assessments of debris flow hazards (Di et al., 2019; Zou et al., 2019).

Debris flow susceptibility analyses include two steps: (1) identification of the potential source areas and (2) prediction of the possible deposition areas (Kang and Lee, 2018). In the literature, a large number of prediction models have been proposed for the susceptibility analyses of debris flows. For the first step, statistical models that use various environmental factors contributing to possible instabilities are well established. For example, Blahut et al. (2010) performed susceptibility assessment for the source areas of landslide-induced debris flows in the Valtellina Valley based on bivariate statistics. Bertrand et al. (2013) used two multivariate statistical models, a linear discriminant analysis (LDA) and a logistic regression (LR), to analyze the debris flow susceptibility of upland catchments. Jomelli et al. (2015) proposed a Bayesian hierarchical probabilistic model to investigate how debris flows respond to environmental and climatic variables in the French Alps. Carrara et al. (2008) discussed the application of different statistical models to debris flows in Val di Fassa, Trentino, Italy. Lucà et al. (2011) compare bivariate and multivariate statistical models for the evaluation of gullying susceptibility in northern Calabria, southern Italy, and concluded that multivariate statistical models were found to be the best model for predicting the debris flow susceptibility of the study area. For the second step, the concept “angle of reach” was widely used in the empirical models to predict the run out distance of debris flows (Hürlimann et al., 2012; Horton et al., 2013). Recently, many numerical models have been proposed to simulate the propagation of debris flows and predict the deposition area. For example, Pirulli and Sorbino (2008) analyzed the propagation of potential debris flows in southern Italy using two numerical codes RASH3D and FLO2D. Beguería et al. (2009) proposed a two-dimensional model based on numerical integration of the depth-averaged motion equations to predict debris flow propagation over complex terrain near Lienz, East Tyrol, Austria. Huang et al. (2015) presented a numerical model based on the smoothed particle hydrodynamic (SPH) method to calculate the run out distance of catastrophic debris flows that occurred in the Wenchuan earthquake area. Gregoretti et al. (2016) used a cell model to simulate a debris flow that occurred on the Rio Lazer. Moraci et al. (2017) performed debris flow susceptibility zoning of debris flows in the Province of Reggio Calabria based on the SPH method. Some recent analysis methods of debris flow susceptibility can be found in Cama et al. (2017), Prieto et al. (2018), and Rosatti et al. (2018).

The previous studies mentioned above have attempted to conduct debris flow
susceptibility analysis in specified regions. Southwestern China is
characterized by steep mountains and deep valleys, and is strongly affected
by the uplift activity of the Tibetan Plateau. Moreover, southwestern China has
abundant loose material after the 2008 Wenchuan earthquake. Therefore, a
series of large-scale debris flows have been occurred during the rainy
seasons in southwestern China (Wu et al., 2019). In the literature, many models
for debris flow risk prediction in this area have been proposed. For
example, Xu et al. (2012) assess debris flow susceptibility based on
an information value model and Geographic Information System (GIS) in Sichuan,
China. Wang et al. (2016) adopted a self-organizing map method to analyze
the susceptibility to debris flows at the Wudongde Dam site in southwestern
China. Li et al. (2017) carried out a susceptibility analysis on debris
flows also in the Wudongde Dam area using the fuzzy

Distribution of the 70 debris flow gullies investigated in southwestern China (the base map is from Zhao, 2014). Publisher’s note: Please note that the above figure contains disputed territories.

Typical debris flows in the study area.

Southwestern China is characterized by steep mountains and deep valleys and is
strongly affected by the uplift activity of the Qinghai–Tibet Plateau.
Furthermore, there is abundant loose material and rainfall in this area.
Therefore, it is a severe disaster zone in terms of debris flow. In the past
3 years, 70 typical debris flows distributed along the Brahmaputra
River, Nujiang River, Yalong River, Dadu River, and Ming River are
investigated. The location of the debris flows is shown in Fig. 1, and some typical debris flows are shown in Fig. 2. Based on the field investigation, the characteristics of the five water catchments are summarized as follows.

Upstream of the Brahmaputra River, 18 debris flow gullies along the Dagu River and Jiexu River are investigated. The lithology in this area is the irruptive rock of the late Yanshanian–Himalayan epoch, with a wide distribution of granodiorite. The average annual rainfall in this area is about 540 mm and concentrates mostly in summer. Large-scale ice-melting-type debris flow once occurred in this region. However, in recent years, the debris flows in this area are mainly caused by precipitation. Material reserves are abundant in the valleys, whereas unstable materials are found less frequently and the deposit zone is small. It is found that most of the debris flows in this area are in the decline phase, and that most debris flow gullies are in the low-frequency category.

In the midstream of the Nujiang River catchment, 11 debris flow gullies located in the Zuogong River section are investigated. The stratum mainly includes the Permian Nacuo group slate and Triassic Wapu group marble. As this region is located in the subtropical zone south of the Himalayas, it is characterized by a humid climate and plentiful precipitation. This leads to an extensive distribution of debris flow gullies.

Midstream in the Yalong River catchment, 27 debris flow valleys are investigated, which belong to a plateau climate zone with complex meteorological and hydrological conditions. The concentricity and suddenness of rainfall provide hydraulic conditions for the debris flow breakouts. Collapses and landslides in the valley occur frequently, which provide abundant material resources for the debris flow occurrence. Moreover, the debris flow activity is intensified by unreasonable human engineering activities, such as deforestation and accumulation of highway waste residue.

In the Dadu River catchment, 42 gullies in the midstream and the upstream are surveyed. This area is characterized by intense new tectonic movement, high earthquake intensity, and rock fragmentation on the mountain surface. Debris flow, collapse, and other geological disasters are widely distributed, and the deposit zone of the debris flow is large. The maturity of the valley is high.

In the Minjiang River catchment, the Wenchuan River section are surveyed, and 32 debris flows are investigated. This region is characterized by abundant loose materials, frequent debris flows, and a high possibility of the breakout of large-scale debris flows. Most of these debris flows are intensive in activity and have not declined in recent times.

In total, 70 debris flow gullies distributed in five water catchments in southwestern China were investigated from the gully outlet to the watershed over the past 3 years. This work includes the investigation of the watershed terrain, geological structure, outbreak scale, loose material distribution, processes of occurrence and movement, frequency of debris flows, and so on. The role of each factor causing instability of the source materials are analyzed.

The antecedent precipitation can reduce the soil shear strength, and has an important influence on the formation and the scale of debris flows (Shieh et al., 2009). Therefore, the precipitation data before the outbreak of debris flows was collected from local meteorological bureaus and used as one of the main influence factors to assess the susceptibility of debris flows in this study. In this work, the antecedent precipitation is classified into three categories: inadequate, medium, and adequate. The classification criteria are listed in Table 1.

Qualitative grading criteria of antecedent precipitation.

Bulk density tests and soil screening tests are carried out in the 70 debris
flow deposit areas. Figure 3 shows the results of the bulk density tests.
The bulk densities of the soil material in the debris flow deposits are
mainly between 1.3 and 1.8 g cm

Density characteristics of debris flow deposits in the study area.

The geologic condition in the active debris flow gullies in southwestern China is very complicated. To investigate the material composition and the thickness of the deposit area, the geological drilling was conducted in the active debris flow gullies along the Dadu River, Yalong River, Yaluzangbo River, and Minjiang River. The drilling information, such as the drilling location, drilling depth, and soil characteristics, are provided in Table 2.

Information and results of the geological drilling in the study area.

Continued.

The statistical techniques can be grouped into bivariate and multivariate methods. A bivariate statistical method analyses each parameter individually; therefore, the calculation and application in bivariate statistical models are straightforward and efficient (Suzen and Doyuran, 2004). On the other hand, a multivariate statistical method considers the interaction of all parameters in controlling the occurrence of a phenomenon and is considered one of the best methods in predicting debris flow susceptibility (Lucà et al., 2011). Hayashi's quantification theory is a well-known multivariate statistical method developed by Hayashi (1961). The Type I quantification theory applies multiple linear regression methods, which can simultaneously process qualitative and quantitative variables, and evaluate the weight of each variable. Therefore, it is widely used in various fields (Matsumura, 2004; Ishihara et al., 2007; Inoue et al., 2009; Shen and Chen, 2018). In this method, the qualitative and quantitative variables can be mutually transformed based on a reasonable principle. Therefore, this method has very good applicability for processing the quantitative and qualitative influencing factors of debris flow risk.

In Hayashi's Type I quantification theory , qualitative variables are
termed items. All possibilities for each item are termed categories. A dummy
variable

The response matrix

To establish an analysis model of debris flow susceptibility, some necessary steps should be followed based on Hayashi's Type I quantification theory: (1) building an index system, (2) selecting samples and assigning values, (3) establishing the analysis model using single slopes, (4) conducting a significance test of the regression equation and each variable, and (5) applying this analysis model to regional debris flow hazards evaluation.

There are many factors that affect debris flow formation and development. From the perspective of source material of the debris flows, the main influence factors are catchment area, loose material position, and loose material reserves. The antecedent precipitation and

The nine indexes used in the prediction model of debris flow susceptibility.

Grading criteria of the evaluation indexes in the prediction model of debris flow susceptibility.

Note that

A total of 70 debris flow gullies in southwestern China are selected as the sample to evaluate the performance of the statistical model. Detailed information about these debris flow gullies is given in Table 5. The values of the samples are assigned according to Eq. (1), and the response from each category is obtained. The sample data then can be transformed into a “0–1” reflection matrix.

Typical characteristics of the Danba section in the upper reaches of the Dadu River.

Sample data for debris flow examples from southwestern China.

Continued.

When the quantitative theory and regression analysis take the binary-state
variables 0 and 1, the equation can be revised as the following linear
regression expression:

Score values of each index after normalization.

Substituting the numerical values in Eq. (4), the susceptibility prediction
model of debris flow is established, which can be represented as follows:

Quantitative model eigenvalue.

The values of each index are used in the established model to calculate the predicted values of the susceptibility based on Eq. (5), and then the predicted values are compared with the actual susceptibility. In this study, self-test coincidence rate is defined as the ratio of the predicted result to the actual susceptibility. As shown in Fig. 4, the predicted values of debris flow susceptibility are graded. For the calculated results listed in Table 8, the prediction accuracy for the low-susceptibility, medium-susceptibility, and high-susceptibility debris flows are 78.5 %, 92.3 %, and 82.0 %, respectively, which indicates that the proposed model can predict the debris flow susceptibility well.

Comparison of actual susceptibility and predicted actual susceptibility.

Prediction model accuracy.

Residual error is the difference between a group of values observed and their arithmetical mean. As shown in Fig. 5, the residual error of the model mainly fluctuates by

Residual distribution in the regression model of debris flow susceptibility.

The Kaka basin is located on the upper part of the Dadu River, southeast of
the Qinghai–Tibet Plateau. The valley is deep and the river runs from north
to south. The regional topography is characterized by high altitudes in the
east and low altitudes in the west. The terrain is composed of high
mountains with elevations of 2000 m. There are three layers of wide valley
mesas, and the uplift of mountains and river erosion is significant in this
area. The river elevation in the Kaka basin is approximately 1800 m, the
river width is 140–185 m, and the slope angle is approximately 45–60

Distribution of debris flow gullies in the Dadu river basin.

A total of 10 typical debris flow gullies upstream of the Dadu River are selected as samples for the model validation (as shown in Fig. 7, and listed in Table 9). The accuracy of the established model is verified through the comparison with field investigation results. Table 9 provides the relevant basic data for the samples. Each secondary index is transformed into a 0–1 mode, and all the samples are adopted to construct a

Sample data from Kaka area upstream of the Dadu River.

Comparison of predicted values and actual measured values.

Distribution of loose deposits of Linong Gully.

Figure 8 shows the catchment of the Linong Gully. The total area of the
catchment is about 10.09 km

Soil material in the Linong Gully deposit.

Debris flows frequently occurred in southwestern China and resulted in severe
damage to dwellings and lifelines. Based on Hayashi's Type I quantification
theory , an initiation susceptibility model of debris flows in southwestern China was proposed in this work. The following conclusions can be
drawn.

According to the topography and geomorphology characteristics in southwestern China, the following nine indexes were used as evaluation factors of debris flow initiation susceptibility: the catchment area, longitudinal gradient, average gradient of the slope on both sides of the gully, catchment morphology, valley orientation, loose material reserves, location of the main loose material, antecedent precipitation, and rainfall intensity.

A total of 70 typical debris flow gullies distributed along the Brahmaputra River, Nujiang River, Yalong River, Dadu River, and Ming River were investigated as statistical samples. The parameters of the prediction model were obtained based on Hayashi's quantitative theory and regression analysis.

The proposed model was applied to analyze the initiation susceptibility of 10 debris flow gullies located upstream of the Dadu River, and the result showed that the judgment coincidence rate is 90 %, indicating that the proposed model can accurately predict the initiation susceptibility of debris flow gullies in southwestern China.

The data in this paper are not provided due to the confidentiality. Notwithstanding, the authors will try to address specific requests for scientific purposes.

FJ developed the model. RL did the field investigation. ZD prepared the manuscript with contributions from all co-authors.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Advances in extreme value analysis and application to natural hazards”. It is not associated with a conference.

The presented work was supported by the Sichuan Science and Technology Program (no. 2018JY0471), Sichuan Provincial Youth Science and Technology Innovation Team Special Projects of China (no. 2017TD0018), the Open Fund of Key Laboratory of Geological Hazards on Three Gorges Reservoir Area (China Three Gorges University) (no. 2018KDZ01), the Chinese Ministry of Education, and the JSPS Grant-in-Aid for Early Career Scientists (no. 19K14804).

This research has been supported by the Sichuan Science and Technology Program (grant no. 2018JY0471), the Open Fund of State Key laboratory of Geohazard Prevention and Geoenvironmental Protection (Chengdu University of Technology (grant no. SKLGP2017K005), the Open Fund of Key Laboratory of Geological Hazards on Three Gorges Reservoir Area (China Three Gorges University) (grant no. 2018KDZ01), the Chinese Ministry of Education, and the JSPS Grant-in-Aid for Early Career Scientists (grant no. 19K14804).

This paper was edited by Yasser Hamdi and reviewed by three anonymous referees.