Modeling the Spatial Distribution of Debris Flows and Analysis of the Controlling Factors: A Machine Learning Approach

Abstract

Debris flows are a major geological hazard in mountainous regions. For improving mitigation, it is important to study the spatial distribution and factors controlling debris flows. In the Bailong River Basin, central China, landslides and debris flows are very well developed due to the large differences in terrain, the complex geological environment, and concentrated rainfall. For analysis, 52 influencing factors, statistical, machine learning, remote sensing and GIS methods were used to analyze the spatial distribution and controlling factors of 652 debris flow catchments with different frequencies. The spatial distribution of these catchments was divided into three zones according to their differences in debris flow frequencies. A comprehensive analysis of the relationship between various factors and debris flows was made. Through parameter optimization and feature selection, the Extra Trees classifier performed the best, with an accuracy of 95.6%. The results show that lithology was the most important factor controlling debris flows in the study area (with a contribution of 26%), followed by landslide density and factors affecting slope stability (road density, fault density and peak ground acceleration, with a total contribution of 30%). The average annual frequency of daily rainfall > 20 mm was the most important triggering factor (with a contribution of 7%). Forest area and vegetation cover were also important controlling factors (with a total contribution of 9%), and they should be regarded as an important component of debris flow mitigation measures. The results are helpful to improve the understanding of factors influencing debris flows and provide a reference for the formulation of mitigation measures.

1. Introduction

Debris flows are a major geological hazard in steep mountainous regions. They are one of the most dangerous material movements because of their high speed, long movement distance, large impact, and abruptness of onset, and for these reasons they are a major threat to life and property [1]. Therefore, it is important to determine the spatial distribution and controlling factors of debris flows in order to prevent them and mitigate their impacts [2,3].

The frequency of debris flows is mainly controlled by the coupled effects of geomorphology, material and rainfall. Many studies assumed that the material conditions were constant at the present time, and in this case the frequency of debris flows was determined entirely by the frequency of rainfall events exceeding the rainfall threshold [4,5,6]. However, if the rate of material supply is low, the frequency of debris flows is determined by the coupled effects of material and rainfall [3,7].

Hazard analysis of debris flows is typically conducted by establishing a relationship between their cause and occurrence [8]. Different studies have placed different emphases on the various factors influencing debris flows: e.g., geomorphic factors [9,10,11,12,13,14,15]; geological characteristics such as lithology and structural faults [1,2,8,16]; land cover and vegetation cover, which influence the hydrological response and the generation of debris flows [17,18,19,20,21,22]; land use [23]; climate change, such as the number of heavy rainfall events [24,25,26] and rainfall intensity [27,28]; landslides [29,30]; and wildfire [31]. Several studies analyzed the spatial distribution of debris flows [32,33,34,35,36]. In addition, landslides and rock falls induced by strong earthquakes greatly increase the number and scale of debris flows, as in the case of the 1999 Taiwan Jiji earthquake [37,38], the 2008 Wenchuan earthquake [39,40,41,42], and the 8 August 2017 Jiuzhaigou earthquake [43]. However, Dai et al. [44] confirmed that even in the presence of large quantities of debris on the slopes, the trends of landslides and debris flows seem to follow a faster recovery.

Although many studies have sought to identify the main factors controlling debris flows, it is difficult to quantitatively determine the contribution of each factor. The Bailong River Basin in central China has a complex geological environment and debris flows are extensively developed, making the area well suited to a comprehensive analysis of the various factors influencing debris flows. We used a machine learning method to model the distribution of debris flows and to quantitatively analyze their controlling factors.

2. Study Area

The Bailong River Basin is in the transition zone between the Qinghai-Tibet Plateau and the Loess Plateau, with elevations ranging from 406 to 4457 m [45]. Structurally, it is located on the eastern boundary of the Indian–Asian plate collision zone [46]. The lithology of the strata in the area is quite complicated (Figure 1). The region is strongly influenced by the Asian monsoon, with annual precipitation ranging from 300 to 900 mm; 75% of the precipitation occurs between June and September [47]. The average minimum and maximum temperatures are −14 to 3 °C in January, and 11 to 27 °C in July. As a result of large terrain differences, complex geological environments and concentrated rainfall, landslides and debris flows are very well developed [48].

3. Data and Methods

3.1. Debris Flow Inventory

Debris flow data were provided by the Gansu Provincial Geological Environment Monitoring Institute, which include details of the location, event time, frequency and casualties of each debris flow catchment (the starting year of the data is 2003) [1]. Combined with field surveys and a literature survey, a total of 652 debris flow catchments were obtained.

3.2. Factors Influencing Debris Flows

The formation of a debris flow is influenced by geomorphic conditions, material conditions and triggering conditions [49,50]. The parameters related to them are described below.

3.2.1. Factors Related to Geomorphic Conditions

The geomorphic characteristics of a catchment determine its gravitational potential energy conditions, water flow process [50], and hydrological characteristics [51]. (See [52] for parameter calculation methods.)

Basin area [9], main channel length [1] and curvature of the main stream [53] reflect basic information of a catchment.

The area proportions of slopes > 30°, >35°, >40°and slopes between 30° and 40° reflect the slope stability and runoff speed [54,55,56]. The average aspect affects the directions of water flows and soil humidity [57].

Basin relief [58], relief ratio [59] and relative relief ratio [60] reflect the gravitational potential energy condition of a catchment. Drainage density reflects the degree of drainage development [61]. Circularity ratio [62,63], form factor [61] and elongation ratio [58] reflect the basin shape.

The hypsometric integral [64] reflects the evolution of the basin geomorphology [65] and the slope distribution [13]. The Melton ratio reflects the susceptibility of debris flows [60].

Profile curvature refers to the curvature along the maximum slope direction, which affects the acceleration and deceleration of the flow, which in turn affects erosion and deposition. Plane curvature is the curvature perpendicular to the maximum slope direction, which affects the convergence and dispersion of flow.

The ruggedness number [64] is influenced positively by the structural terrain complexity [66]. The Terrain Ruggedness Index and Topographic Position Index reflect the difference between a central pixel and its surrounding cells [67].

The Topographic Wetness Index is a physically-based index or indicator of the effect of local topography on runoff flow direction and accumulation [68]. The Stream Power Index is a measure of the erosive power of flowing water [69]. The fitness ratio is the ratio of the main channel length to the basin perimeter [60].

3.2.2. Factors Related to Material Conditions

The quantity of materials and the ease with which they can be converted to a debris flow will affect its formation process, rainfall threshold and frequency.

The lithology data were divided into very hard, hard, medium, soft, and very soft according to the hardness of the rock (

Table 1. Lithologies in the study area and their hardness classification.

Stratigraphic Age	Major Lithology	GSI	Relative Strength
Quaternary loose material	Pebbles, gravel, silty clay	0–10	very soft
Neogene stratified clastic rocks	Conglomerate, shale, sandstone
Paleogene stratified clastic rocks	Conglomerate
Cretaceous stratified clastic rocks	Conglomerate, sandstone, mudstone	10–20	soft
Jurassic stratified clastic rocks	Sandstone, mudstone, conglomerate, shale	30–40	medium
Silurian metamorphic rocks	Sandstone, limestone, phyllite, slate
Devonian carbonate rocks	Slate, phyllite, limestone
Permian layered metamorphic rocks	Sandstone, sandy slate, tuff, phyllite
Carboniferous carbonate rocks	Limestone	60–70	hard
Devonian carbonate rocks	Limestone, shale, slate, sandstone
Triassic and Permian layered carbonate	Limestone, sandstone, shale
Triassic and Permian intrusive rocks	Granite, diorite, granite gneiss, basalt, diabase	80–90	very hard

; Figure 2, lithology). In this study, the geological strength index (GSI) estimation was used as the estimation value of rock mass quality [70,71]. The area proportion of different hardness lithology in each catchment was calculated to analyze the influence of different lithologies on debris flows. (Lithology and fault data were obtained from a published geological map with a scale of 1: 200,000).

The linear density of faults was calculated using the line density tool in GIS software (Fd, Figure 2), and the average value in each catchment was determined to analyze the impact of faults on debris flows.

The point density of landslides was calculated using the point density tool in GIS software (Ld, Figure 2), and the average value in each catchment was calculated to analyze the impact of landslides on debris flows. (The data were provided by Gansu Provincial Geological Environment Monitoring Institute).

Earthquakes affect slope stability. The average value of peak ground acceleration (PGA, Figure 2) in each catchment was calculated to analyze the influence of earthquakes on debris flows. (The data are from the public version of China’s seismic peak ground acceleration zonation map of 2016, published by the China Seismological Bureau).

Different land use types affect surface runoff and sediment transport and may control the slope stability [2]. The area proportions of unused land, forested land, grassland, cultivated land, residential land and industrial land in each catchment were calculated to analyze the impact of different land use types on debris flows (Figure 2, Land use). (The land use data were obtained from the interpretation of remote sensing images).

The average NDVI (Figure 2, NDVI) of each catchment was calculated to analyze the impact of vegetation coverage on debris flows (NDVI was derived from Gaofen-1 images in August 2020).

Soil type influences rainfall runoff processes [72]. The average values of soil depth, soil clay fraction and soil bulk density in each catchment were calculated to analyze the influence of soil types on debris flows (Sde, Scf and Sbd, Figure 2). (Soil data were from the FAO, International Institute for Applied Systems Analysis. The soil map for China is based on Harmonized World Soil Database (HWSD, v1.1, 2009), National Tibetan Plateau Data Center, 2019).

The sum of the population and GDP of each catchment was calculated to reflect the impact of human activities on debris flows (Pop and GDP, Figure 2) (data source: [73]).

Roads may cut the original slopes, change the original surface confluence, and affect the slope stability. The linear density of roads was calculated (Rd, Figure 2), and the average value in each catchment was calculated to reflect the impact of roads on debris flows.

3.2.3. Factors Related to Triggering Conditions

Rainfall is the main triggering factor of debris flows in the study area. The average annual frequencies of daily rainfall > 15, >20, >30, >40 and >50 mm (F15, F20, F30, F40 and F50) at each meteorological station were calculated, and Figure 3 was produced by an interpolation method. The average value of each catchment was calculated to reflect the impact of rainfall on debris flows. (The rainfall data are from 41 meteorological stations in the study area).

Finally, a total of 52 factors influencing debris flows were selected and calculated, as shown in

Table 2. Factors influencing debris flows. (H_max and H_min are the maximum and minimum elevations in a catchment. Lt is the total length of stream channels. p is the basin perimeter).

No.	Parameter	Abbr.	Formula	Unit
1	Basin area	A	GIS analysis	km2
2	Main channel length	Lmc	GIS analysis	km
3	Curvature of the main stream	Cms	Cms = Lmc/Ls	/
4	Average slope	Sa	Average value	°
5	Area proportion of slopes > 30°	S30	Area of slopes > 30°/A	%
6	Area proportion of slopes > 35°	S35	Area of slopes > 35°/A	%
7	Area proportion of slopes > 40°	S40	Area of slopes > 40°/A	%
8	Area proportion of slopes between 30° and 40°	S30–40	Area of slopes 30–40°/A	%
9	Average aspect	Aa	Average value	°
10	Basin relief	H	H = Hmax − Hmin	km
11	Relief ratio	Rr	Rr = H/L	/
12	Relative relief ratio	Rrr	Rrr = H*100/p	/
13	Drainage density	Dd	Dd = Lt/A	/
14	Circularity ration	Cr	Cr = 4πA/P2	/
15	Form factor	Ff	Ff = A/L2	km
16	Elongation ratio	Er	$Er=2\sqrt{A/\pi L^2}$	/
17	Hypsometric Integral	HI	HI = (Hmean − Hmin)/(Hmax − Hmin)	/
18	Melton ratio	Mr	$Mr=H/\sqrt{A}$	/
19	Plane curvature	Cpl	GIS analysis	/
20	Profile curvature	Cpr	GIS analysis	/
21	Ruggedness number	Rn	Rn = H*Dd	/
22	Terrain Ruggedness Index	TRI	GDAL analysis	/
23	Topographic Position Index	TPI	GDAL analysis	/
24	Topographic Wetness Index	TWI	TWI = ln(As/tan(S))	/
25	Stream Power Index	SPI	SPI = ln(As*tan(S))	/
26	Fitness ratio	Rf	Rf = Lmc/p	/
27	Area proportion of very hard lithology	Lvh	Area of very hard lithology/A	/
28	Area proportion of hard lithology	Lh	Area of hard lithology/A	/
29	Area proportion of moderate lithology	Lm	Area of moderate lithology/A	/
30	Area proportion of soft lithology	Ls	Area of soft lithology/A	/
31	Area proportion of very soft lithology	Lvs	Area of very soft lithology/A	/
32	Fault density	Fd	Linear density	/
33	Area proportion of unused land	Lun	Area of unused land/A	/
34	Area proportion of forest land	Lfo	Area of forest land/A	/
35	Area proportion of grass land	Lgr	Area of grass land/A	/
36	Area proportion of cultivated land	Lcu	Area of cultivated land/A	/
37	Area proportion of residential land	Lre	Area of residential land/A	/
38	Area proportion of industrial land	Lin	Area of industrial land/A	/
39	Normalized Difference Vegetation Index	NDVI	Average value	/
40	Soil depth	Sde	Average value	cm
41	Soil clay fraction	Scf	Average value	%
42	Soil bulk density	Sbd	Average value	kg/dm3
43	Landslide density	Ld	Point density	/
44	Peak ground acceleration	PGA	Average value	/
45	Population	Pop	Average value	/
46	Gross domestic product	GDP	Average value	/
47	Road density	Rd	Linear density	/
48	Average annual frequency of rainfall > 15 mm/d	F15	GIS analysis	times/yr
49	Average annual frequency of rainfall > 20 mm/d	F20	GIS analysis	times/yr
50	Average annual frequency of rainfall > 30 mm/d	F30	GIS analysis	times/yr
51	Average annual frequency of rainfall > 40 mm/d	F40	GIS analysis	times/yr
52	Average annual frequency of rainfall > 50 mm/d	F50	GIS analysis	times/yr

.

3.3. Machine Learning Analysis

3.3.1. Machine Learning Algorithms

Four machine learning algorithms (MLA) were selected, including Ensemble methods (Extra Trees (ETs), Gradient Boosting (GB) and Random Forest (RF)) and XGBoost (XGB). Ensemble methods combine multiple classifiers and classify new data by taking a vote of their predictions. XGBoost is a type of lifting tree model with a boosting algorithm. (See DF_distribution.ipynb for code).

3.3.2. Data Processing

Highly correlated factors may cause the instability of the models [74,75]. A cross-correlation heat map was produced (Figure 4; see features_Correlation.xlsx for details). The highly correlated factors were eliminated, including Lmc (0.93), S30 (0.98), S35 (0.96), S40 (0.90), TRI (0.99), SPI (0.91), Rr (0.97), Rrr (0.93), Rn (0.89), Er (0.99), F30 (0.94) and F40 (0.89).

3.3.3. Cross−Validation

The cross−validation method was chosen to randomly select 70% of the samples for training, and the remaining 30% were used to test the model performance. This process was repeated 10 times to reduce the sampling uncertainty.

3.3.4. Model Evaluation and Optimization

The average accuracy (Acc) and standard deviation (Std) of the validation set were used to evaluate model performance. The two parameters can effectively evaluate the accuracy and stability of the models. The models were optimized by grid search for the optimal parameters. The Recursive Feature Elimination and Cross-Validation (RFECV) [76] method was used to determine the optimal number of factors.

3.3.5. Feature Importance

The feature importance method based on the mean decrease in impurity was used to calculate the importance of each factor [77]. The importance of a feature is computed as the (normalized) total reduction in the criterion brought by that feature.

4. Results

4.1. Spatial Distribution Division

The spatial distribution of 652 debris flow catchments has an obvious regularity and can be divided into three frequency zones: high zone (>2 times/year), medium zone (0.5–2 times/year) and low zone (<0.5 times/year) (Figure 5).

4.2. Model Evaluation and Optimization

After modeling and parameter optimization, the optimal parameters and the Acc of the validation set are listed in

Table 3. Optimization results of models.

MLA	Optimal Parameter	Acc	Std
ETS	n_estimators = 200; max_depth = 22; criterion = entropy	0.952	0.0166
XGB	n_estimators = 50; learning_rate = 0.25; max_depth = 6	0.948	0.0153
GB	n_estimators = 50; learning_rate = 0.25; criterion = friedman_mse; max_depth = 6	0.947	0.0173
RF	n_estimators = 500; criterion = gini; oob_score = True; max_depth = 14	0.936	0.0169

. The results show that the ETs performed the best and hence was selected for further optimization. The optimal number of factors of ETs was determined using RFECV (

Table 4. Feature selection results of ETs.

	Acc	Std	Factors	Number
Before RFECV	0.952	0.0166	A, Cms, Sa, S30–40, Aa, H, Dd, Cr, Ff, HI, Mr, Cpl, Cpr, TPI, TWI, Rf, Lvs, Ls, Lm, Lh, Lvh, Fd, Lun, Lfo, Lgr, Lcu, Lre, Lin, NDVI, Sde, Scf, Sbd, Ld, PGA, Pop, GDP, Rd, F15, F20, F50	40
After RFECV	0.956	0.0149	Sa, Mr, Cpl, Cpr, Lvs, Lm, Lh, Fd, Lfo, Lgr, Lcu, NDVI, Sbd, Ld, PGA, Rd, F15, F20	18

). It can be seen that the number of factors was reduced from 40 to 18, and the Acc of the models had been slightly improved. The final Acc of ETs is 95.6%, indicating that the model can correctly judge which frequency zone most catchments belong to.

4.3. Importance of the Factors

The importance scores of 18 factors were calculated (Figure 6). It can be seen that the most important factor is lithology, including Lm (with a contribution of 13%), Lh (with a contribution of 8%) and Lvs (with a contribution of 5%). The second most important factors are landslide density (Ld, with a contribution of 10%) and road density (Rd, with a contribution of 10%), flowed by fault density (Fd, with a contribution of 5%) and peak ground acceleration (PGA, with a contribution of 5%). The average annual frequency of daily rainfall > 20 mm (F20, with a contribution of 7%) is the most important triggering condition of debris flows. The area proportion of forest land (Lfo, with a contribution of 5%) and vegetation cover (NDVI, with a contribution of 4%) are also important factors controlling debris flows in the study area.

5. Discussion

5.1. Spatial Distribution and Influencing Factors

The spatial distribution of 652 debris flow catchments was divided into three zones according to their differences in debris flow frequencies. Such typical regional distribution characteristics are suitable for a comprehensive analysis of the relationship between various factors and debris flows.

In order to analyze the distribution characteristics of various factors, a box plot of each factor in the high, moderate and low zones were produced in Figure 7. The high zone and moderate zone have similar high rainfall conditions (F15, F20, F50), and the moderate zone has more favorable geomorphic conditions (higher Sa, S30, S30–40, H, Ff, HI and Mr). However, debris flow frequency in the moderate zone is lower than in the high zone, which indicates that the difference between them is mainly caused by material conditions. Compared with the moderate zone, the high zone has more favorable material supply conditions (higher Fd, Ld and Lvs), and is more affected by human activities (higher Rd, Lcu and Pop). In addition, the moderate zone has a higher vegetation coverage (higher Lfo and NDVI). Therefore, the high zone has a higher debris flow frequency.

Compared with the high and moderate zones, the low zone has less favorable rainfall conditions (lower F15, F20, F30 and F40), material supply conditions (lower Lh), and geomorphic conditions (lower Sa, H, Dd and Mr). The other factors for the low zone are generally intermediate between the high and moderate zones. Therefore, the low zone has the lowest debris flow frequency.

In summary, the conditions of more favorable rainfall and material supply and more intensive human activities are responsible for the high debris flow frequency in the high zone. Under similar rainfall conditions with the high zone, a lower material supply, less intense human activities, and higher forest cover are responsible for the moderate debris flow frequency in the moderate zone. The less favorable rainfall, material supply and geomorphic conditions are responsible for the lowest debris flow frequency in the low zone.

5.2. Feature Importance Analysis

The importance of factors in Figure 6 shows that lithologies (with a total contribution of 26%) control the main distribution of debris flow catchments in the study area. Many studies showed that lithology was an important factor controlling the spatial distribution of debris flows [1,2] and affecting the supply of loose debris [78]. Our study quantitatively calculates the contribution of different lithologies to the spatial distribution of debris flows, and we can better understand the relationship between lithology distribution and debris flows. Figure 8 (Lithology) shows that the high zone is mainly distributed in Lvs and Lm areas, the moderate zone is mainly distributed in Lm areas, and the low zone is mainly distributed in Lh areas.

The second most important factor is landslide density (Ld, with a contribution of 10%). Many studies showed that the frequency of debris flows would increase significantly within 1–8 years after a large landslide [30]. Landslides and rock falls caused by an earthquake would reduce rainfall thresholds of debris flows and increase the number and scale of debris flows [38,39,40,43]. However, some studies indicated that there was no direct relationship between landslide distribution and debris flows [79], and coseismic landslide was not the main material source driving debris flows after an earthquake [20], so landslides need a certain process to mobilize to form debris flows [80].

Road density (Rd, with a contribution of 10%) mainly reflects the influence of human activities on slope stability. Fault density (Fd, with a contribution of 5%) and peak ground acceleration (PGA, with a contribution of 5%) also affect the slope stability. This is an important reason for the significant decrease in the rainfall threshold of debris flows after an earthquake.

The average annual frequency of daily rainfall > 20 mm (F20, with a contribution of 7%) is also an important factor. The high and moderate zones are mainly distributed in the areas with higher F20, and the low zone is mainly distributed in the areas with lower F20.

The area proportion of forest and vegetation cover are also important factors (with a total contribution of 9%), which gives us a new understanding of the role of vegetation in reducing debris flows. Forest cover mainly reduces the supply of loose materials and slows down the confluence speed [81,82,83]. Comparison of the high and moderate zones indicates that, even if the moderate zone has more favorable geomorphic conditions (higher Sa, S30, S30–40, H, Ff, HI and Mr) and precipitation conditions (Figure 8, F20), but the material conditions are less favorable than the high zone (Figure 8, Ld, Rd and Lithology), and the vegetation cover (especially forest cover) is higher than the high zone (Figure 8, Land use and NDVI), the result is lower debris flow frequency in the moderate zone. This is consistent with the results of Guo et al. [20], who found that a lower material supply and higher vegetation coverage can effectively reduce the frequency of debris flows and increase the rainfall threshold. Therefore, vegetation cover, especially forest cover, is an important factor to be considered when formulating debris flow mitigation measures [84,85,86].

It appears that factors related to geomorphology have little influence on debris flows in the study area. One of the most important factors is the Melton ratio (Mr), which may be because the terrain difference in the study area is generally large and there is little differentiation.

Among the important factors, except for the vegetation coverage and the proportion of forest, another factor that can be readily controlled is the road density. Reducing road construction can reduce the material supply on unstable slopes to debris flows. However, it would potentially impact the economic development of the region and would require careful evaluation by decision makers.

The contribution of this section is to quantitatively evaluate the importance of each factor for the spatial distribution of debris flows, which helps us better understand their relationship. Through the above analysis, we have a new understanding of the factors influencing the spatial distribution of debris flows, which has reference value for better formulating disaster reduction measures.

5.3. Estimation of Daily Rainfall Threshold

The average annual frequencies of daily rainfall >15, >20, >30, >20, >40 and >50 mm in each zone were determined in

Table 5. Debris flow frequencies and average annual frequencies of daily rainfall >15, >20, >30, >40 and >50 mm in different zones (times/year).

Zone	Debris Flow Frequency	>15 mm	>20 mm	>30 mm	>40 mm	>50 mm
High	>2	5–9.5	1–7	1–2	<0.5	<0.25
Moderate	0.5–2	5–8	2–5	1–3	0.3–1	<0.25
Low	<0.5	5–7	1–3	0.5–1.5	<0.5	<0.25

. Taking the daily rainfall with the average annual rainfall frequencies equal to the debris flow frequencies as the daily rainfall threshold, the daily rainfall threshold is ~15–30 mm in the high zone, ~30–40 mm in the moderate zone, and >40 mm in the low zone. The daily rainfall thresholds can provide a reference for regional debris flow early warning.

5.4. Uncertainties

The data used in this paper includes detailed investigation data (debris flow inventory) and the data obtained from public websites (DEM, remote sensing images, geological data, soil data, population, GDP, road and rainfall), which ensure the quality of the data. However, compiling data related to debris flows is challenging. Therefore, like other related studies, our study had some uncertainties due to the influence of the amount and quality of available data.

6. Conclusions

The main contribution of this study has been to analyze and model the spatial distribution of debris flows with different frequencies in the Bailong River Basin, central China, where debris flows are very well developed. To do this, we divided 652 debris flow catchments into three frequency zones and analyzed a comprehensive range of factors using statistical and machine learning methods. The factors controlling the distribution of debris flows were analyzed quantitatively. The results potentially provide a deeper understanding of factors controlling debris flows and have an important reference value for formulating debris flow mitigation measures. The major findings are summarized below.

• The main factor controlling debris flows in the study area is lithology. The medium, hard and very soft lithologies control the major distribution of debris flow catchments.
• Landslides and the factors affecting slope stability (including roads, faults and earthquakes) are the second most important factors. The factor that can be easily controlled is road construction, although controlling this may adversely affect regional economic development.
• The most important triggering factor of debris flows is the average annual frequency of daily rainfall >20 mm. We also estimated the daily rainfall thresholds of debris flows in different zones.
• The area proportion of forest and vegetation cover are also important factors controlling debris flows, which can be an important part of debris flow mitigation measures.