Author Correction: Respective influence of vertical mountain differentiation on debris flow occurrence in the Upper Min River, China

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

www.nature.com/scientificreports/ mean annual temperature ranges from 5.7 to 13.5 °C, and the annual precipitation from 400 to 800 mm with an 80% concentration in the period from May to October. In addition to the deep river incision and large elevation disparity, the fact that warm and moist air flows have to climb over mountains before reaching this region results in scarce rainfall and dry climate, further promoting the formation of dry-hot valleys. With a population of 384,179, the study region is the only but one largest Qiang ethnic settlement in China, and also a poverty-stricken mountainous area with comparatively limited economic development 20 . Han, Zang, Qiang, and Hui people co-inhabit in the river valleys and mountain terraces, with Wenchuan, Townships of Yingxiu and Xuankou as the densely populated center. Due to their farming culture and large population, the river valleys have gathered most of the region's secondary and tertiary industries, while high mountains and mountain plateaus adopt animal husbandry as the main economic activity. Currently, there are 625 administrative www.nature.com/scientificreports/ villages with 66,500 rural households 68 (Table 1), demonstrating settlement characteristics of large dispersion, low density, and small scale. Environment Management System provides data on geological disasters (disaster types including slide, debris flow, ground fissure, ground subsidence, and ground subsidence) discovered during 1905-2018 in Sichuan Province, including 6,250 debris flows. The data is obtained through the field survey of the geological disaster investigation project organized and implemented by the Natural Resources Department of Sichuan Province every year and the residents' report, mainly including the coordinates of the geological disaster point, the specific geographic location, the time of occurrence, the threat of property, the number of threats, the number of threatened households, volume, scale and other parameters. Based on the data of 244 typical debris flow hazard points in the Upper Min River provided by the Sichuan Geological Environment Management System, the author uses ArcGIS 10.2 software to manually draw 244 debris flow catchments using the GDEMV2 30 m data 67 and Google Earth remote sensing images in the Upper Min River as the base map ( Fig. 1, Table 2). The Upper Min River is a typical active area of debris flow in southwestern China. The debris flow is mainly concentrated in the alpine gorge area, especially on the banks of the river below Zhenjiangguan and its tributaries in the mainstream of the Upper Min River, and the Heishui River below the Heshui and its tributaries and below the Shaheba section of the Zagunao River and its tributaries. The 9 factors and the symbols used were vertical zones (D1), annual average temperature (D2), maximum daily rainfall (D3), sunshine hours (D4), vegetation type (D5), soil type (D6), slope (D7), aspect (D8) and lithology (D9). The vertical zones, slope and aspect data are extracted from the ASTER GDEM V2 30 m data 67 . The average annual temperature sunshine was obtained from the National Meteorological Center China Meteorological Data Network (https ://www.escie nce.gov.cn/). The rainfall data comes from the Sichuan Provincial Hydrology and Water Resources Bureau. Rainfall data were collected from 79 meteorological stations in the Upper Min River during the flood season . The density of the rain gauge network is 3.59 × 10 -3 /km 2 . The elevation distribution of the rain gauges is from 886 m (Yingxiu) to 5286 m (Aotaiji). The soil-vegetation distribution data were obtained from Assessment Dataset of Habitat Suitability in the Upper Reaches of Min River, China 69 . The lithology data extracted from the 1: 200,000 Chinese geological map in the National geological data Museum (https ://ngac.org.cn/).
First of all, ArcGIS10.2 software was used to generate 23,018 square grids of 1 km × 1 km in the Upper reaches of Min River. The 1 km × 1 km grid is selected because it is smaller than the minimum watershed area of 244 debris flows. Then the grid map is superimposed with the debris flow distribution map. The area of the debris flow in each grid is counted, and the ratio of the debris flow catchment of each grid is calculated. Then, the other debris flow impact factor layers are superimposed with the grid map to obtain relevant data and exported. Finally, GEO software is used for data analysis.
The law of vertical differentiation of mountainous areas refers to the distribution pattern of mountainous natural landscapes with elevation changes 34,35,70 . Due to the change in altitude in the vertical direction, the  www.nature.com/scientificreports/ conditions such as water and heat are significantly different, resulting in various combinations, which in turn affect the development, development and formation of debris flow. The relative elevation difference of the Upper Min River is 1500-3000 m. The hydrothermal conditions are very different, and the vertical zonality of the climate is significant, which leads to obvious vertical zonal differences in vegetation, soil type and topography. The 9 factors selected for the respective influence are as follows: 1. Vertical zones (D1) The elevation difference in the Upper Min River is huge, and the hydrothermal conditions vary significantly with elevation. The climate regions in the study area are significantly different.
According to the research of Ren Meijun 39 , Chen Guojie 16 , Guo Yongming 41 and other scholars, the Upper Min River are divided into 7 zones according to the elevation: subtropical zone (< 1300 m), warm temperate zone (1301-1900 m), temperate zone (1901-3000 m), cold temperate zone (3001-3800 m), subrigid zone (3801-4400 m), frigid zone (4401-5000 m), ice-snow zone (> 5000 m) (Fig. 2a). Figure 2a is based on the ASTER GDEM V2 30m data and is reclassified using ArcMap according to the elevation distribution of the climatic zone. 2. Annual temperature (D2) the vertical temperature of the Upper Min River is significant, which is one of the main climatic factors controlling the vertical differentiation and vegetation distribution of the mountain, and also the main factor was controlling the weathering of the rock. The development and formation of the debris flow are greatly affected. The annual average temperature is divided into 7 categories using the natural breakpoint method (Fig. 2b). Figure 2b is based on the annual average temperature data of the Upper Min River Meteorological Station using ArcMap for spatial interpolation.
3. Maximum daily rainfall (D3) The spatial distribution of precipitation caused by the undulations and complex topography of the Upper Min River. In the dry-warm valleys, precipitation is small. Generally speaking, the precipitation is mainly controlled by altitude and latitude and longitude. In the horizontal direction, the arid elliptical arid center centered on the Shaba area of Mao gradually increases the precipitation from east to west. In the vertical direction, precipitation is positively correlated with altitude, relationship, and maximum daily rainfall is divided into 7 categories using natural breakpoints (Fig. 2c). Figure 2c is based on the maximum daily rainfall data of the Upper Min River Meteorological Station using ArcMap for spatial interpolation.

Sunshine hours (D4)
The number of sunshine hours directly affects the heat distribution in different regions, which in turn affects the climate. In general, the higher the altitude, the longer the sunshine hours, the positive correlation, showing a distinct vertical differentiation. The annual average sunshine hours were divided into 7 categories using the natural breakpoint method (Fig. 2d). Figure 2d is based on the annual sunshine hours data of the Upper Min River Meteorological Station using ArcMap for spatial interpolation. According to its main distribution range, from low to high, it is yellow soil, dark brown soil, cinnamon soil, cold brown soil, marsh soil, stony soil, meadow soil, alpine remark (Fig. 2f). The soil distribution data were obtained from Assessment Dataset of Habitat Suitability in the Upper Reaches of Min River, China 35 . Figure 2f plotted in ArcMap. 7. Slope (D7) Slope directly affects the fluctuation of the regional landscape. The most direct manifestation is the difference in vegetation type and coverage, which in turn forms different vertical bands of the mountain. At the same time, the slope changes cause the stability of the soil and the surface hydrodynamics to change, that is, with the increase of the slope, the erosion ability of the precipitation, and the erosion intensity is also gradually increasing. The slopes in the Upper Min River are divided into 7 categories (Fig. 2g). Figure 2g is obtained from the aspect analysis of the DEM data using ArcMap. 8. Aspect (D8) Aspect is one of the important topographic factors that distinguish the vertical band spectrum of mountainous land. The influence of physiology characteristics of aspect is mainly explained by the fact that the light and heat conditions accepted on different slopes are different. Generally speaking, the solar radiation heat received by the shady slope is much smaller than that of the sunny slope, resulting in a difference in regional vegetation type distribution. According to the direction of the octant method: North, North East, East, South East, South, Nancy, West and North West (Fig. 2h). Figure 2h is obtained from the aspect analysis of the DEM data using ArcMap. Interaction detector compares the influence of two factors A and B on debris flow occurrence by interacting to detect whether different factors have interaction on debris flow occurrence so as to determine whether these two factors have a separate effect or interaction on debris flow occurrence. The evaluation method is to first calculate the q value of the two factors A and B for the ratio of debris flow catchments: q(A) and q(B), and calculate the q value when they interact: q(A ∩ B), and compare q (A), q(B) and q(A ∩ B) are compared. The relationship between the two factors can be divided into 5 categories (Table 3).
Risk detector is used to determine whether there is a significant difference between the mean values of the ratio of debris flow catchments in the two sub-regions of a certain factor, and perform a significance test. The sub-areas with greater mean significance, the more frequent the debris flow activity, used to search for areas where the debris flows frequently in each factor.

Results
Distribution characteristics. The distribution characteristics of debris flows in the study region are summarized as follows: 1. Concentration in deeply incised river valleys with high relief energy. The deeply incised river valleys are usually characterized by crust uplifting, tectonic activity, high relief and deep slopes, providing favorable development conditions for debris flows. Therefore, a high concentration is often witnessed in these valleys. For instance, the valleys along the Min River banks downstream below Zhenjiangguan Village of Songpan, along the Heishui River downstream below Luhua Township of Heishui, and along the Zagunao River downstream below Saba Village of Li. 2. Concentration in areas with abundant precipitation and frequent rainstorms. Intensive precipitation (rainstorms in particular) is a major trigger of mountain hazards, causing a high concentration of well-developed landslides and debris flows. The precipitation of the study region differs greatly. The period from May to September is the wet season, during which the precipitation takes up 80-85% of the total. In this period of time, mountain hazards frequently occur, proving a positive correlation with precipitation. Generally speaking, a year of abundant precipitation or climate anomalies is likely to witness mountain hazards, especially when heavy rains, rainstorms, and hailstorms are simultaneously functioning. According to statistics, the www.nature.com/scientificreports/ mountain hazards including debris flows, landslides, and collapses occurred during the wet season take up more than 90% of the total.

The dominant factors of influence of vertical differentiation factors on debris flow occurrence.
The factor detector is used to measure the intensity of the influence of nine factors on debris flow occurrence. The larger the value of q, the greater the intensity of the influence of this factor on debris flow occurrence. According to the analysis results (Fig. 3), D3 (maximum daily rainfall), D7 (slope), D5 (vegetation types), D1 (sunshine hours) and D1 (vertical zones) have a influence on the debris flow of 53.92%, indicating that the occurrence of debris flow is mainly affected by the vertical differentiation of mountain, and maximum daily rainfall , slope factors in the Upper Min River has the greatest impact on debris flow occurrence in the study area, followed by the slope, vegetation types, sunshine hours and elevation.

The interaction of vertical differentiation factors on debris flow. The interaction detector is used to
test whether the two factors act independently or interact with each other. If they interact, the effect is enhanced or weakened. The interactive detector module was used to obtain the interaction of nine factors in the mountain to the debris flow ( Table 4). The diagonal in Table 4 is the q value calculated by the interaction detector of 9 factors that affect debris flow occurrence. Due to local correlations and regional differences, individual factors have little effect on the occurrence of debris flows in the study area. For the comprehensive interaction of a factor with the other seven factors, the interactions with the strongest effects are: D5 ∩ D3 (vegetation type ∩ maximum daily rainfall), D3 ∩ D7 (maximum daily rainfall ∩ slope), D9 ∩ D3 (lithology ∩ maximum daily rainfall), the interaction between factors are above 5%. The interaction of nine factors in vertical mountain differentiation is nonlinearly enhanced. The effect, that is, the interaction of any two factors is greater than the independent effect of a single factor, and the additive effect of maximum daily rainfall is the most significant.
Risk detection of factors on debris flow occurrence. The risk detector answers the question of the geographical location of the debris flow distribution and is used to search for areas where debris flows occur frequently. In the results of the risk detector, the result information for each factor is represented in two tables. The first table gives the mean value of the area of debris flow in each zone. The second table gives a statistical difference in the mean of the attributes between every two partitions; if there is a wet difference, the corresponding value is "Y", otherwise it is "N". Taking vertical zones as an example, the results of the risk detector are shown in Table 5. It can be seen from Table 5 that the elevation is divided into seven partitions, represented by the numbers 1, 2, …, 7. According to the  www.nature.com/scientificreports/ mean value of the ratio of debris flow catchment, the elevation band is sorted, 3 > 4 > 7 > 6 > 2 > 5 > 1, and the mean value of the temperate debris flow area is the largest in vertical zone 3 (temperate zone 1901-3000 m). (Table 5).
Other factors can be similarly analyzed to find areas of frequent debris flow in the vertical differentiation of the mountains (Table 6). Table 6 revealed that the most frequent mountainous vertical belt of the debris flow is the temperate mixed wood stony soil.

Discussion
According to the results of the factor detector and the risk detector, maximum daily rainfall, slope factors are the main spatial drivers of debris flow. Maximum daily rainfall in the main risk area of debris flow is 71-86 mm, which happens to be in the intense rainstorm area in the middle and eastern part of the Upper Min River. Among them, arid and dry valleys with the mainstream of the Min River in Zhenjiangguan of Songpan County and Mianzhu Town of Wenchuan County are typical. Although its annual precipitation is very small, concentrated rainfall during the flood season is prone to induce debris flow. The slope of the main risk area for debris flow is 5 (40°-50°). With the increase of the slope, the scouring ability and erosion intensity of rainfall also gradually increase. The great height difference makes the loose material sources such as slop deposits have higher potential energy conditions. At the same time, the slope of the gully has more restrictive effects on the movement speed of the debris flow, runoff conditions and deposition. Therefore, the debris flow is concentrated in deeply incised river valleys with high relief energy.
Being ecologically fragile within Upper Yangtze and prone to mountain hazards, the study area demonstrates distinct characteristics of mountain vertical zonality (Fig. 4). Figure 4 is obtained by extracting climate zone grids from 244 debris flow gully basins in ArcMap. An obvious respective influence of vertical mountain differentiation on debris flow occurrence is witnessed. The debris flow accumulation area and propagation area on the Upper Min River are mainly distributed on the banks of the Min River and its tributary valleys at an altitude of Wenchuan (1300 m)-Songpan (2800 m), located in the subtropical and warm temperate arid valleys. With limited annual precipitation of 400-800 mm, the subtropical and warm temperate arid valleys provide favorable conditions for the debris flow occurrence. Intensive and concentrated precipitation brought by storms may induce a simultaneous burst of several or even a dozen debris flows around the rainstorm center. The debris flow formation and clear-water confluence areas usually cover one or two base zones: a debris flow deposed in the subtropical zone will have its formation and clear-water confluence areas in the warm temperate and temperate zones; while that deposed in the warm temperate zone will often have its formation and clear-water confluence areas in the temperate and cold temperate zones (Fig. 4).
On the one hand, the deposition and propagation areas of the above-mentioned gullies are all located within base zones (within the base zone transiting from the subtropical zone to the warm temperate zone: Fotangba gully; within the warm temperate base zone: Tea garden gully, Longdong gully, Haermu gully, and Ridi Village gully; within the temperate base zone: Luhua gully, Luoba Street gully, and Longtanbao gully). On the other hand, the formation and clear-water confluence areas are often situated in the warm temperate and temperate zones (Fotangba gully), in the temperate zone (Tea garden gully, Longdong gully, Haermu gully, and Ridi Village gully), and in the cold temperate and temperate zones (Longtanbao gully).

Conclusions
In this study, the Upper Min River was used as the study area, and vertical zones, annual average temperature, maximum daily rainfall, sunshine hours, vegetation type, soil type, slope, aspect and lithology 9 factors representing the vertical differentiation characteristics of the mountain were selected. The model quantitatively analyzes the relationship between the debris flow and the nine factors that characterize the vertical zone of the mountain and conducts the respective influence of vertical mountain differentiation on debris flow occurrence. It will expand the understanding of the development law of the debris flow disaster, and also determine the debris flow disaster on the Upper Min River. The research provides guidance and provides a richer scientific basis for Table 5. Mean value of the ratio of debris flow catchments in each vertical zone.  www.nature.com/scientificreports/ disaster prevention and mitigation management of debris flow disasters. This study mainly got the following three conclusions: 1. Debris flows of the study region are mainly distributed along the Min River and its tributaries downstream below Zhenjiangguan, along the Heishui River and its tributaries downstream below Heishui County, along the Zagunao River and its tributaries downstream below Shaba. These valleys are also prone to rainstorms and landslides, due to deep incision, high relief, and abundant precipitation. 2. Our results reveal that maximum daily rainfall, slope factors are the main spatial drivers of vertical mountain differentiation on debris flow occurrence. The factor detector reveals the consistency and difference of the P D, H interpretation of the influence factor on the debris flow. The spatial data analysis of debris flow indicates  www.nature.com/scientificreports/