Mountain torrents are sudden surface runoff with severe fluctuations, often caused by rainstorms in small watershed in mountain regions and accompanied by landslides, debris flows and collapses^[1]. It is one of the most severe natural hazards around the world posing a severe damage to infrastructure, life, and property in the mountain area^[2-3]. Due to the influence of global climate change and development of economy and society, the occurrence frequency and magnitude of mountain torrents have presented an increase trend in recent years^[4-5]. For China, mountain torrents cause thousands of people death and hundreds of million yuan economic losses each year. For example, from June 3 to 10, 2019, Guangxi, Jiangxi, Fujian, Guangdong suffered different degrees of torrents induced by heavy rainfall, causing 83 deaths, 6.75 million people affected, more than 15 000 houses damaged and about 10-billion-yuan economic loss^[6]. On June 19, 2016, Zhenxiong town, Yunnan Province, a heavy rainfall triggered a large scale of torrents causing more than 300 households and 2 000 people affected and 4 people died^[7]. For Guangdong Province, according to the statistics from Guangdong Provincial Hydrographic Bureau, mountain torrents directly threaten 770 000 urban populations and 3.08 million rural populations in hilly and mountain areas, as well as enterprises with fixed assets of 3.12 billion yuan and annual output value of 33.15 billion yuan^[8]. For instance, on June 10, 2019, a heavy rainfall caused mountain torrents in Heyuan city, Guangdong Province, resulting in 8 people died and 3 people injured, 114 550 people affected, 956 houses damaged, 14 540 people displaced, and direct economic loss of 600 million yuan^[9]. Therefore, the research of distribution characterises and key influencing factors of mountain torrents aimed to mountain torrents mitigation is extremely important.

The extent and magnitude of mountain torrents are controlled by various factors related to geology, lithology, topography, meteorology and hydrology, soil, vegetation, and human activity^[10]. The formation mechanism is complicated and still lacking the reasonable theories, which limits the research progress on mountain torrents forecasting^[11]. However, mountain torrents are the result of interactions between rainfall and various background factors. Previous researches have highlighted the impact of various factors on the manifestations of mountain torrents, including meteorological, hydrological and geomorphological parameters. Some scholars have found that the meteorological characteristics of heavy rains affect the occurrence of mountain torrents, especially in small mountainous watershed areas^[12-13]. The research also showed that hydrological processes, including mountain torrents, were greatly affected by topography, such as slope, watershed area and hydrogeological parameters^[14]. For example, Diakakis, et al.^[10] tested the statistical correlation between mountain torrents and environmental factors by using the method of binary logistic regression. Lee et al.^[15] applied a bivariate statistical analysis method to determine the relationship between environmental factors and the occurrence of mountain torrents. Pradhan et al.^[16] studied the relationship between mountain torrents and multivariate variable by using the multivariate regression method. Currently, many researchers have devoted to this issue. However, the distribution characteristics of mountain torrents and their relationships with environmental factors in Guangdong Province have not been discussed in detail.

The overall objective of the study is to explore the geospatial distribution regularity of mountain torrents and relationships between occurrence probability of mountain torrents and various factors in Guangdong Province. The spatial distribution regularity of mountain torrents was explored first from the perspective of river basins, municipal administrative regions and disasters scales. Then, the examined factors on spatial distribution of mountain torrents were selected based on the formation mechanism. Finally, the relationship between occurrence probability of mountain torrents and the examined factors was put forward.

1 Study area 1.1 Geographical location

Guangdong Province is located in the southernmost part of mainland China, which extends from 20°13′ N to 25°31′ N latitude and 109°39′ E to 117°19′ E longitude. The geographical location is shown in Fig. 1. The land area of Guangdong Province is approximately 179.80×10³ km² and the island area is about 1 592.7 km^2[17].

1.2 Topography

Affected by the combined effect of crustal movements, lithology, faulted structures, and external forces, the landform types in Guangdong Province are complex and diverse, with mountains, hills, terraces, plains, and waters, accounting for 33.6%, 24.8%, 14.3%, 21.8%, and 5.5% of the province’s land area, respectively^[18]. The overall terrain of Guangdong Province is high in the north and low in the south. Its northern part is mostly mountainous and high hilly. In the south, it is plain and terraced, with the largest is the Pearl River Delta plain. The slope angles are mainly small than 5°, accounting for 42.92% of the total slope area. The steep slope above 20° is account for 16.36% of the whole land area. Using the digital elevation model (DEM) with 30 m resolution, the statistical analysis of the slope in Guangdong Province can be obtained (Table 1).

1.3 Geological settings

The bedrock rocks making up all kinds of landforms are most common in granite, sandstone and metamorphic rocks, and there is a large distribution of limestone in north-western Guangdong. In addition, there are some unique red rock series, such as the famous Danxia Mountain. Danxia Mountain and Huguangyan in western Guangdong have been rated as World Geoparks. The coastal areas along the river are mostly Quaternary sedimentary layers, which are material basis of the cultivated land resources^[19].

1.4 Climate

The study area belongs to the East Asian monsoon region. It is a mid-subtropical, south-subtropical and tropical climate from North to South. The province’s average sunshine hours are 1 745.8 h, and the annual average temperature is 22.3 ℃. Guangdong Province has abundant rainfall, with an average annual precipitation of between 1 300 and 2 500 mm, and an average of 1 777 mm^[20]. The rainfall is mostly bimodal during the year. The main peak is in May and the secondary peak is in August. The precipitation is sever unevenly distributed. The precipitation amount of the monsoon season from April to September accounts for more than 80% of the whole year. June to October each year is the main period affected by typhoons and tropical depressions which are generally accompanied by heavy rains triggering landslides, torrents, debris flows, and other disasters in mountainous regions.

1.5 Overview of mountain torrents

Controlled by various factors related to geology, lithology, topography, meteorology and hydrology, soil, vegetation, and human activity, mountain torrents are extremely developed and are distributed widely in Guangdong Province. Through extensive data collections and field works of mountain torrents, we eventually identified more than 3 000 recorded disaster sites (Fig. 1). The collected data mainly come from the provincial, municipal, and county government departments. Field works included field investigations, remote sensing image surveys, and unmanned aerial vehicle surveys. We also establish an information database based on GIS, recording the key information of these mountain torrents, such as geographic coordinates, disaster categories, scales, threat objects, potential losses, disaster treatments, and occurred times. The major mountain torrents in recent years are shown in Table 2. For instance, on June 10, 2019, a heavy rainfall caused mountain torrents in Heyuan city, Guangdong Province, resulting in 8 people died and 3 people injured, 114 550 people affected, 956 houses damaged, 14 540 people displaced, and direct economic loss of 600 million yuan^[9].

2 Materials and methods 2.1 Geospatial distribution regularity of mountain torrents

With the support of geographic information system (GIS), the study area was classified into 179 801 grid cells first. According to the identified mountain torrent sites as well as their recorded key information, the mountain torrent information for each grid was determined by using spatial statistical analysis function of ArcGIS. Then, the geospatial distribution regularity of mountain torrents can be further analysed by counting the information of each grid. Due to the short time span, the temporal variability of mountain torrents is not discussed, but the spatial variability characteristics of mountain torrents in river basins, municipal administrative regions and disasters scales is discussed in detail providing a basis for the spatial control of mountain torrents in Guangdong Province.

2.2 Selection of examined factors affecting mountain torrents

Generally, the formation of mountain torrents is high related with the topographic, material and hydrodynamic conditions. The following is a detailed description of selection of key influencing factors affecting mountain torrents in Guangdong Province.

2.2.1 Topographic condition

The influence of the topographic condition on the convergence process and evolution directly affects the formation of mountain torrents^[21]. Among these factors, the relative relief, slope and drainage density are the most important ones. The relative relief is controlling the energy of mountain torrents movement. Slope gradient provides energy conversion for the movement of mountain torrents. The drainage density affects the occurrence possibility of mountain torrents and the ground convergence. The complexity and diversity of landform types of the study area provide the favourable topographic condition for the formation and movement of mountain torrents. In our analysis, the relative relief (Fig. 2(a)), slope gradient (Fig. 2(b)) and drainage density (Fig. 2(c)) are chosen as the key factors to describe the topographic condition which are derived from the DEM with 30 m resolution.

2.2.2 Material condition

The occurrence of mountain torrents must have certain material conditions. The amount of loose solid material is a key factor of material condition because it not only determines whether a torrent could occur, but affects the critical rainfall triggering mountain torrents. In general, the stratigraphic lithology controls the loose solid material formation and affects mountain torrents formation^[22]. The soils with weaker corrosion resistance developed by granite weathering, shale, mudstone, sandstone and shale in the hilly areas of Guangdong Province are widely distributed, combined with unreasonable production methods of humans, resulting in a large amount of loose solid materials. Under the combined affection of storms and runoff, it is easy to produce mountain torrents in the mountain region. Therefore, the lithology is chosen as a key factor describing the material condition (Fig. 2(d)). Based on the lithology of the study area, the lithology can be classified into five classes reflecting the resistance to weathering and sensitivity to mountain torrents (Table 3).

2.2.3 Hydrodynamic condition

Sudden and persistent heavy rain is the basic driving force for the formation, dumping and erosion of mountain torrents. Generally, the 24-hour rainfall is one of the most important rainfall parameters presenting a high correlation with the mountain torrents occurrence^[23]. The distance to the river is also an extremely important factor affecting mountain torrents formation. To some extent, it represents the intensity of human activity and the development of mountain torrents. Therefore, the average annual 24-hour rainfall (Fig. 2(e)) and the distance to river (Fig. 2(f)) are selected as key factors to describe the hydrodynamic conditio.^[24] and the latter is derived from drainage network vector data derived from the 30 m DEM.

In summary, key factors influencing the formation of mountain torrents in Guangdong Province are selected as relative relief, slope gradient, drainage density, stratum lithology, average annual 24-hour rainfall, and distance to the river in this paper. With the support of GIS, the information of each selected factor for each grid (in total 179 801 grids) can be determined by using the spatial statistical analysis method.

2.3 Relationships between mountain torrents and key influencing factors

The statistical analysis method was used to analyse the quantity distribution and occurrence probability of mountain torrents. Since the watershed area of mountain torrents ranges from less than 1 km² to more than 100 km², it is obviously not appropriate to use the mountain torrent site as a unit of statistical analysis. Therefore, the size of studied grid cell must be conformed first. According to related statistics, the mountain torrents in Guangdong Province mainly occur in a small watershed with a catchment area of less than 10 km^2[25]. The result is similar to the study result of the whole China derived from Li et al.^[26]. Therefore, the calculated grid cell in this study was fixed into 1 km² (1 km×1 km) and the whole Guangdong Province was classified into 179 801 grid cells. The information of selected factors for each grid can be obtained in ArcGIS. The probability statistic calculated as follows:

${P_i} = \frac{{{N_i}}}{{{S_i}}}, $

(1)

where P_i is the probability of torrents under the condition of i factor, N_i is the number of torrents in a grid cell under the condition of i factor, and S_i is the total number of grid cells under the condition of i factor.

3 Results and discussion 3.1 Distribution characteristics of mountain torrents 3.1.1 Watershed distribution characteristics

According to the drainage network characteristics of Guangdong Province, the area can be divided into six major river basins: Hanjiang River, Beijiang River, Xijiang River, Dongjiang River, Yuexi Coast River, and Pearl River. Then the number, proportion, and disaster density in each river basin were counted, respectively (Fig. 3). It is found that the number of mountain torrents in the Hanjiang River basin is the largest, accounting for 42.16% of the total, followed by the Beijiang River basin, and the Pearl River basin is the least, the number is only 5.13% of the total. In terms of the disaster density, the Hanjiang River basin has the highest disaster density, reaching 0.021/km², followed by Beijiang River basin, Xijiang River basin, Dongjiang River basin, Yuexi Coast River, and Pearl River Delta.

3.1.2 Distribution characteristics of administrative regions

According to the municipal administrative boundaries of Guangdong Province, the number, proportion, and disaster density of mountain torrents in each administrative region were counted respectively in ArcGIS (Fig. 4). As shown in Fig. 4, we can find that the number of mountain torrents in Meizhou is the largest, accounting for 14.19% of the total, followed by Heyuan, Zhaoqing, Chaozhou, Shaoguan，and Qingyuan, total accounting for 54.72%, Shenzhen and Zhuhai have the least number. However, in terms of disaster distribution density, Chaozhou has the highest disaster density, reaching 0.045 8/km², followed by Jieyang, Meizhou, Heyuan, Shanwei, and Shantou.

3.1.3 Distribution characteristics of disaster scale

We counted the scale of occurred mountain torrents which could be divided four categories: small, medium, large, and super large scales (Fig. 5(a)). The statistically analysis result is in Fig. 5(b). It is found that medium-sized mountain torrents are the most, accounting for 54.68% of the total number, and widely distributed throughout the mountain or hill areas. The super large-scale disasters have the least distribution, only accounting for 4.53%.

3.2 Relationships between mountain torrents and key influencing factors 3.2.1 Relative relief

The relative relief of each grid cell was classified into 28 categories with Natural Breaks (Jenks) method in ArcGIS. The number of mountain torrents in each class was counted. It can find that the distribution of mountain torrents by category is skewed showing a trend of increasing first and then decreasing. About 80% mountain torrents are distributed in the relative relief less than 200 m.

To further explore the most favourable interval of relative relief for mountain torrents, the occurrence probability of mountain torrents under various categories of relative relief can be obtained by using (1), seen in Fig. 6(a). The occurrence probability of mountain torrents increases first and then decreases with the increase of relative relief. The probability has one peak when relative relief reaches about 100 m. When the relative relief reaches about 100 m, the probability reaches maximum and then sudden drops. The relationship between relative relief and occurrence probability can be expressed as

$y = {a_1}{{\rm{e}}^{{b_1}x}} + {a_2}{{\rm{e}}^{{b_2}x}}, $

(2)

where y is the occurrence probability of mountain torrents and x is the relative relief. Eq.(2) is a fitted model using MATLAB software (R2010a). The curve is as Fig. 6(a) when a₁=0.014 7, b₁=-0.002 2, a₂=-0.015 2, b₂ =-0.029 2 with 95% confidence bounds and 0.636 9 R².

3.2.2 Slope gradient

The slope of each grid cell was classified into 15 categories with Natural Breaks (Jenks) method in ArcGIS. The number in each category of slope was counted. It can be found that the distribution of mountain torrents by categories is also skewed and can be expressed by a generalized exponential distribution. About 64% mountain torrents are distributed in grid cells of slope less than 10°.

The probability of mountain torrents under various categories of slope was obtained according to (1) (Fig. 6(b)). When the slope is less than 10°, the probability increases sharply with the increase of slope and then decrease slowly when the slope is more than 10°. The relationship between the slope categories and the probability ca be fitted as

$y = {a_1}{{\rm{e}}^{{b_1}x}} + {a_2}{{\rm{e}}^{{b_2}x}}, $

(3)

where y is the occurrence probability of mountain torrents and x is the slope. Eq.(3) is the fitted model using ATLAB software (R2010a). The fitting curve is as Fig. 6(b) when a₁=0.009 0, b₁ =-0.002 0, a₂=-0.008 9 and b₂=-0.520 1 with 95% confidence bounds and 0.601 8 R².

3.2.3 Drainage density

The drainage density can be divided into several categories with the equal range of 0.25 km/km². The number of torrents increases with the increase of drainage density and then decreases when the value exceeds 1.75 km/km². About 64% are distributed within the drainage density less than 1.75 km/km².

The probability of torrents in each category was calculated using (1) which can be seen in Fig. 6(c). The occurrence probability increases with the increase of drainage density and then sudden drops when the value exceeds 1.75 km/km². The relationship between drainage density and the probability is fitted as

$y = {a_1}{{\rm{e}}^{{b_1}x}} + {a_2}{{\rm{e}}^{{b_2}x}}, $

(4)

where y is the occurrence probability of mountain torrents and x is the drainage density. Eq.(4) is the fitted model by the MATLAB software (R2010a). The fitting curve is as Fig. 6(c) when a₁=-0.004 3, b₁=1.05, a₂=0.008 4，and b₂=0.822 8 with 95% confidence bounds and 0.789 4 R².

3.2.4 Stratigraphy

The strata can be divided into five categories according to the Table 2. The number of mountain torrents among these categories was counted in ArcGIS. It is found that the third category has the largest number of torrents and the first category has the least number.

The probability of mountain torrents under each stratigraphic category can be seen in Fig. 6(d). From Fig. 6(d), the probability of torrents increases with the increases of weakness of the stratigraphy. The weak and less resistant rock is more favourable for torrents. The relationship between stratigraphy and probability can be fitted as

$y = a{{\rm{e}}^{bx}}, $

(5)

where y is the occurrence probability of mountain torrents and x is the stratigraphic categories. Eq.(5) is the fitted model by using the MATLAB software (R2010a). The fitting curve is as Fig. 6(d) when a=0.005 3 and b=0.146 7 with 95% confidence bounds and 0.874 6 R².

3.2.5 Average annual 24-hour rainfall

The average annual 24-hour rainfall of each grid cell can be divided into 15 categories based on the values derived from Ref. [24]. The number of mountain torrent in each class was counted in ArcGIS, from which we can find that the average annual 24-hour rainfall presents bimodal. The one peak is between 100 mm and 110 mm, and the other is between 150 mm and 160 mm. About 60% of mountain torrents are distributed with the average annual 24-hour rainfall ranging from 100 mm to 160 mm.

The probability occurring in various categories of average annual 24-hour rainfall is calculated according to (1) (Fig. 6(e)). As shown in Fig. 6(e), the occurrence probability of mountain torrents increases with the average annual 24-hour rainfall, indicating that the greater the rainfall, the more disasters are likely to occur. The relationship between the probability and the average annual 24-hour rainfall can be fitted as a model

$y = a{{\rm{e}}^{bx}}, $

(6)

where y is the occurrence probability of mountain torrents and x is the average annual 24-hour rainfall. Eq.(6) is the fitted model by using the MATLAB software (R2010a). The fitting curve is as Fig. 6(e) when a = 0.002 8 and b = 0.005 8 with 95% confidence bounds and 0.806 5 R².

3.2.6 Distance to the river

Distance to the river can be divided into ten classes with an interval of 1 km. The number of mountain torrents among these categories is counted in ArcGIS. It is found that the number of mountain torrents is significantly decrease with an increase of distance to rivers. The mountain torrents are concentrated in the cells with distance to rivers between 0 km and 5 km, accounting for 65.84% of the total disasters.

The probability of mountain torrents by distance to rivers is calculated using (1), which can be seen in Fig. 6(f). The probability decreases with the increase of distance to rivers. The relationships between the distance to rivers and the probability can be fitted as

$y = a{{\rm{e}}^{bx}}, $

(7)

where y is the occurrence probability of mountain torrents and x is the distance to rivers. Eq.(7) is the fitted model by using the MATLAB software (R2010a). The fitting curve is as Fig. 6(f) when a=0.010 9 and b =-0.112 5 with 95% confidence bounds and 0.624 9 R².

As described above, the relationships between the occurrence probability of mountain torrents and various background factors in Guangdong Province can be descried by a generalized exponential distribution which can be seen in Table 4. The confidence bounds, RMSE, and R² are also shown in Table 4.

3.3 Discussion

At present, there are many related researches on the temporal and spatial distribution characteristics and influencing factors of mountain torrents. For example, Xiong et al.^[27] found that the spatial differences of mountain torrents in the Southwestern region were significant, and the distribution of disaster number showed a significant spatial positive correlation. Zhang et al.^[28] found that the low-altitude small undulating mountains and hilly areas with a height of 200 m and a slope below 15 ° and a hilly area of 1 000 to 1 300 mm rainfall are high incidence areas of mountain torrents in Chongqing. It can be seen that the mountain torrent is closely related to its impact factors. In this paper, we explored the relationships between the number and probability of mountain torrents and impact factors and found that the relationship between probability and impact factors showed a generalized exponential model with different fitting constants. The number of mountain torrents, size of statistical grid, and uncertainty of selecting background factors are the main cause affecting the accuracy of the research result. Therefore, we will continue to collect mountain torrent sites, test the more important factors and modify the model parameters so that they can better reflect the actual situation and can be better applied to disaster mitigation.

4 Conclusions

1) The number and disaster density of mountain torrents in the Hanjiang River basin are the largest compared with Beijiang River, Xijiang River, Dongjiang River, Yuexi Coast River, and Pearl River Delta. The number of mountain torrents in Meizhou is the largest, accounting for 14.19 of the total. However, Chaozhou has the highest disaster density. The super large-scale torrents are mainly distributed in the cities of Shaoguan, Heyuan, Zhaoqong, Chaozhou, Yunfu, and Gaozhou.

2) For relative relief, about 80% of mountain torrents are distributed in the grid cells with relative relief less than 200 m. For slope, about 64% of mountain torrents are distributed in cells of the slope less than 10°. For drainage density, the number and probability of mountain torrents increase with increasing drainage density and then drops abruptly when the value exceeds 1.75 km/km². For stratigraphy, the probability of mountain torrents increases with the increases of weakness of the stratigraphic lithology. For average annual 24-hour rainfall, about 60% of mountain torrents are distributed in cells with average annual 24-hour rainfall ranging from 100 mm to 160 mm. For distance to rivers, mountain torrents are concentrated in the cells with distance to rivers between 0 km and 5 km, accounting for 65.84% of the total.

3) The relationships between the occurrence probability and the relative relief/slope/drainage density can be fitted as the model of y=a₁e^b₁x+a₂e^b₂x with different fitting constants. The relationships between the probability and stratigraphy/average annual 24-hour rainfall/distance to rivers can be described by y=ae^bx with different fitting constants.