1 Introduction

During a rainstorm from June 5 to June 6, 2011, many debris flows were triggered within and outside the Dayi area in the Guizhou Province of China. These debris flows were gully-type debris flows, which are dangerous and cause enormous risks (Yu et al. 2013b). Gully-type debris flows occur in areas with significant gully topography (Liu et al. 2009). The gully-type debris flows in the study area were triggered partly by flash floods causing a runoff-induced effect (Kean et al. 2013), and partly by the development of many shallow landslides. Debris flow initiation is typically attributed to runoff from low-permeability surfaces during rain storms, which at a critical discharge threshold mobilize loose sediments which can transform into a debris flow (Kean et al. 2013). The initiation of a debris flow by a runoff effect can be facilitated by the accumulation in very steep channels of abundant solid materials from old landslide debris, soil, talus, or dumped material deposits. Kean et al. (2013) pointed out that the mechanistic theories for debris flow initiation by runoff are grouped into two categories: (1) mass failure of the channel sediment by a sliding along a discrete failure plane: a sudden large impulse of sediment to be added to and/or entrained within the water flow, such as from the failure of the sediment-filled bed of the channel or the failure of the channel banks caused by channel erosion, and (2) grain-by-grain bulking by hydrodynamic forces: a critical discharge of water creating a debris flow surge by eroding the sediment by hydrodynamic forces from the top down rather than by sliding at a failure plane at a depth of several until many grains below the surface. High-speed water flows generated during unusually intense rainstorms can create also an extra shear force of the rushing water along steep slopes. In addition to the component of the driving force induced by the weight of the sediment, it may destabilize the material and initiate a debris flow (Johnson and Rodine 1984).

To mitigate and prevent hazards induced by debris flows and related risks, one must understand the formation of these in order to make reliable forecasts. Many factors are related to the occurrence of debris flows such as the basin gradient, the percentage of basin area with slopes greater than or equal to 30 %, basin ruggedness, additional measures of gradient, slope aspect, rainfall intensity, and soil properties, including the clay percentage, the percentage of organic matter, the soil granulometry and sorting, and the soil liquid limit (Cannon et al. 2010). Liu et al. (2009) among others stated that there are three groups of factors playing a major role in the formation of ordinary gully-type debris flows. They are related to topography, geology, and hydrology.

Yu et al. (2013b) introduced a formation model for gully-type debris flows for the Chenyoulan River Watershed with factors related to topography, geology, and rainfall. Their model consists of three critical values to make four classes of the probability of debris flow occurrence. The model used a limited number of lithological classes, which makes it less applicable for other areas. For the assessment of the geological factor, the chemical weathering was not considered as well as the presence of loose sediments in catchments, deposited by landslides triggered by a strong earthquake (Yu et al. 2013c). Because of the scarcity of detailed rainfall data in their research area, only the average annual rainfall was used to normalize the rainfall data for the rainfall factor, which decreases also the applicability of the model in other areas.

Therefore, in this study, a refined geological factor is introduced by including a so-called firmness coefficient for very soft rock and for landslide deposits and loose sediments in channels, and by taking into account the degree of chemical weathering. Also, a variety coefficient of the 10-min rainfall intensity is introduced for the normalization of the rainfall factor. The revised prediction model for debris flows with a runoff-induced mechanism will be calibrated on debris flows which occurred in 2011 in the Dayi area. The model will be validated on debris flows, which were triggered in a number of selected regions in southwest China.

2 Description of the Dayi study area

The calibration area with 66 gullies is located downstream of Dayi town (see Fig. 1). It is crossed in a north–south direction by the Wangmo River, a main branch of the Nanpanjiang River, which is one of the branches of the Zhujiang River, the third large river in China. The lowest place in the study area is 710 m in altitude, and the highest peaks in the catchment have altitudes between 1,500 and 1,600 m. The channel gradients in the upstream part of the gullies are very large, and some of them are larger than 35°. These are suitable topographic conditions for debris flow outbreaks. But above a critical slope gradient (around 35°), there is no solid source material to initiate debris flows by concentrated flash floods. There are only two lithological units in the calibration area: hard siltstones interbedded with thin mudstones. The thickness ratio of siltstone and mudstone is 3–4 to 1. There is no fault in the study area. The statistics of historical earthquakes give the study area a general seismic intensity of VI (NSBC 1990).

Fig. 1
figure 1

The classification of the investigated gullies in Dayi area, in the Guizhou Province

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The average annual rainfall lies in a range between 1,210 and 1,320 mm, and the average annual temperature varies between 14.4 and 16 °C. Figure 2 shows the rainfall figures of the Dayi and Xintun (13.1 km in the south of Dayi) stations, before and after the outbreak of the debris flows from June 5 until June 6, 2011. The rainfall started at 22:00, June 5, at the Dayi station, while there was almost no rainfall at the Xintun station until 1:00, June 6. The maximum hourly rainfall was 105.9 mm at the Dayi station from 23:00 to 24:00, June 5. The debris flows were triggered during this period. The rainfall data for the 66 gullies, including the hourly rainfall, and cumulative rainfall before the triggering of the debris flows were obtained by interpolation of the rainfall data of the Dayi and Xintun stations (see Table 1).

Fig. 2
figure 2

Rainfall characteristics in the Dayi area from June 5 to June 6, 2011

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Table 1 Parametric values related to different debris flow prediction factors and the presence of debris flows in gullies in the Dayi area. (For an explanation see text)
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3 The classification of the gullies in the Dayi study area

Field investigations were conducted in the 66 gullies of the study area. Debris flow activity during the heavy rain storm of June 5 to June 6, 2011, was observed in 47 gullies. Some debris flows were triggered by a runoff-induced mechanism, some were initiated by shallow landslides, and some were triggered by both processes. In this study, we will only focus on debris flows which were triggered by a runoff-induced mechanism. We distinguished three classes related to the presence or absence of debris flows in gullies: (1) There are 22 gullies classified as “no debris flow,” which means there were no debris flows or debris flows that originated solely from shallow landslides because there was no material entrained in the channels. (2) There are 25 gullies classified as “debris flow” with obvious material entrained in the channels, which means that the presence of debris flows is caused by a runoff-induced mechanism, or by both a runoff-induced mechanisms and shallow landslides. (3) There are 19 gullies classified as “uncertain” without clear indications of entrainment of material in the channels; debris flows and shallow landslides are present, but it is not sure whether the debris flows are triggered by a runoff-induced mechanism. Figure 1 shows the location of the gullies subdivided into three classes according to the above given definitions. Table 1 gives for each gully the classification together with the parametric values related to the three revised debris flow prediction factors, which will be described shortly in the next paragraph.

4 The prediction factors of debris flows with a runoff-induced mechanism

The basic ideas behind the three prediction factors used in this study are the same as those in Yu et al. (2013b), but there are, as explained above, some refinements of the geological and the rainfall factor.

4.1 The topographic factor

Yu et al. (2011, 2013b) obtained a dimensionless topographic factor describing the role of topography in the formation of debris flows with a runoff-induced mechanism (Eq. 1):

$$T = FJ(A/A_{0} )^{0.2} = J(A/L^{2} )(A/A_{0} )^{0.2}$$
(1)

in which T is the dimensionless topographic factor of the source (formation) section of the gully where the debris flows are initiated; F (=A/L 2) is the form factor with A: the area (km2) and L (km): the length of the channel in the source section. J is the average slope of the channel; A 0 is the unit area of the gully in the source section (=1 km2).

The topographic factor includes the form factor, the average slope, and the area of catchment of the formation area. The form factor is highly related to the distribution of the hydrograph: a larger form factor produces a larger discharge and velocity than a smaller form factor. The discharge of the flow is the key triggering factor for debris flows with a runoff-induced mechanism. Therefore, under the same conditions, a watershed area with a large form factor has a higher likelihood to generate debris flows (Chang 2007). The parameters related to the average slope and the area of the catchment also influence the surface flow discharge and the flow velocity and thus the resulting downslope movement of sediments.

The topographic factors were calculated using a 1:10.000 topographic map. The values of the topographic factor T for all the 66 gullies are listed in Table 1.

4.2 The geological factor

Yu et al. (2012, 2013b) obtained a dimensionless geological factor to represent the role of geology in the formation of debris flows triggered by flash floods in channels. The geological factor contains a firmness coefficient (F 0) for the lithology and some correction coefficients. Yu et al. (2013a) extended the geological factor with more lithological units such as the soft rock (with an average firmness coefficient 2 ≥ F 0 ≥ 1.5) and the loose sediments in the channel (with an average firmness coefficient F 0 < 1) (see Table 2). The chemical weathering was also taken into account for the revised geological factor (Eq. 2):

$$G = F_{0} C_{1} C_{2} C_{3} C_{4}$$
(2)

in which G is the dimensionless geological factor; F 0 is the average firmness coefficient of the lithology in the source section of the gully; C 1 is a correction coefficient for seismic intensity in the source section of the gully; C 2 is a correction coefficient for tectonics (faults); C 3 is the correction coefficient for physical weathering; C 4 is the correction coefficient for chemical weathering.

Table 2 The classification of rock types by firmness
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The average firmness coefficient for lithology F 0 is based on the Protodyakonov coefficient (Protodyakonov 1962) for rock strength, which was revised after investigations in the field (Yu et al. 2012, 2013a, b, see Table 2). The values of this coefficient for the 66 gullies are the same in the Dayi area: 77.8 % hard siltstone (F 0 = 8) interbedded with 22.2 % mudstone (F 0 = 4), which gives a weighted average firmness coefficient of F 0 = 7.11.

The correction coefficients C 1, C 2, and C 3 (see Eq. 2) of respectively the seismic intensity, tectonics (faults), and physical weathering in the formation area of the gullies are listed in Table 3 (Yu et al. 2012). The correction coefficients C 4 (see Eq. 2) for chemical weathering for the formation area of the gullies are listed in Table 4 (Yu et al. 2013a).

Table 3 Correction factors for seismic intensity, faults (tectonics), and degree of physical weathering
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Table 4 Correction factors for degree of chemical weathering
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The seismic intensity in the study area is VI, which gives a correction coefficient C 1 of 1 (see Table 3). The correction factor C 2 with respect to the tectonics is 1 because there is no fault in the research area. The physical weathering scores based on the data of the average annual rainfall and temperature in the study area, and the figure of weathering classification with average annual rainfall and temperature are provided by Fookes et al. (1971). The coefficient C 3 for physical weathering in the research area is 1. The chemical weathering is a second factor which plays a role. The intensity of the chemical weathering is controlled by the amount of \({\text{CO}}_{3}^{ 2- }\) in rocks such as in limestones, dolomites, etc (see Table 4, Yu et al. 2013a). Chemical weathering in limestone leads to the formation of cracks which hampers the formation of surface runoff (Yu et al. 2013a, b). Therefore, the stronger the chemical weathering, the more difficult it is to form runoff-induced debris flows. So the coefficient C4 increases with increasing intensity of chemical weathering (see Table 4). As there is no \({\text{CO}}_{3}^{ 2- }\) in the rocks of the Dayi area, the coefficient C 4 in the research area is 1. The resulting final geological value for all the 66 gullies is therefore G = 7.11 (see Table 1). In the validation areas, we will find more catchments with limestone (see Table 5).

Table 5 Parametric values related to different debris flow-forming factors and the presence of debris flows in gullies of the validation areas
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4.3 The rainfall factor

Short-duration high-intensity rainfall is the main triggering factor for the gully-type debris flows (Shieh et al. 2009; Wu et al. 1990; Tan and Han 1992). Yu et al. (2013b) used the 1-h rainfall intensity and cumulative precipitation in the period before the triggering of the debris flow to describe the critical rainfall index for the runoff-induced debris flows.

$$X = B + 12.5I$$
(3)

in which X is the critical rainfall index (mm); B is the cumulative precipitation, until the start of the debris flow (mm); I is the amount of rainfall in the hour before the start of the debris flow (mm).

Yu et al. (2013b) used the annual precipitation to normalize the critical rainfall in the Chenyoulan River Watershed. The normalization is very important because rainfall values vary widely between the different areas. The difference may be reduced by introducing a good normalization. Only annual precipitation is not enough to normalize the rainfall. The coefficient of variation represents the local heterogeneity of rainfall. The larger the coefficient of variation, the more heterogeneous is the rainfall. Therefore, the coefficient of variation was introduced here for the normalization of the rainfall factor in this paper (Ma and Zhang 1991):

$$C_{v} = \sigma /H$$
(4)

in which C v is the coefficient of variation; σ is the standard deviation of rainfall (mm); H is the average rainfall (mm) over a certain period.

The average rainfall can be calculated over a period of 10 min, 1 h, 6 h, 24 h, and 1 year. So there are corresponding coefficients of variation that can be calculated over these periods. For the same average rainfall, larger amount of rainfall in an area shows always larger coefficients of variation. The coefficient of variation has the same effect as the annual precipitation: the larger the coefficient of variation and annual precipitation, the larger the rainfall threshold.

Wu et al. (1990) indicated that the 10-min rainfall intensity is strongly correlated with the triggering of debris flows with a runoff-induced mechanism. Although we use here the 1-h rainfall intensities (Eq. 3), it is better to use for the normalization the coefficient of variation of 10 min instead of the coefficient of variation of 1 h. Therefore, we normalized the critical rainfall with the annual precipitation and the coefficient of variation of 10 min (when available) to obtain the dimensionless rainfall factor R (Eq. 5):

$$R = \frac{X}{{R_{0} C_{v} }} = \frac{B + 12.5I}{{R_{0} C_{v} }}$$
(5)

in which R is the dimensionless rainfall factor; R 0 is the annual precipitation of the site (mm); C v is the coefficient of variation of 10 min. The annual precipitation R 0 for each gully is obtained from the spatial distribution of the annual rainfall in the study area by the interpolation of the rainfall data of the Dayi and Xintun stations. In the Dayi area, only the coefficient of variation for a 24-h period (C v  = 0.45) and a 1-h period (C v  = 0.4) is available. So we were obliged to use in the Dayi test area the coefficient of variation for 1 h instead of the 10-min coefficient of variation: C v  = 0.4. The values of the hydraulic factor R for all the 66 gullies are listed in Table 1.

5 The calibration of the prediction model in the Dayi area and the validation in some areas of southwest China

5.1 Model calibration in the Dayi area

Yu et al. (2013b) obtained a formation model with data of debris flows with a runoff-induced mechanism in the Chenyulan River watershed (Taiwan) triggered during the Typhoon Toraji. With the refined geological factor given by Yu et al. (2013a) and the rainfall factor proposed in this study, a prediction model for debris flows with a runoff-induced mechanism is obtained using the data of the rainstorm event from June 5 to June 6, 2011, in the Dayi region. The prediction factor P can be expressed by T (Eq. 1), G (Eq. 2), and R (Eq. 5) (Yu et al. 2013b) as in Eq. 6 by empirical statistic analyses:

$$P = RT^{0.2} /G^{0.5} \ge C_{r}$$
(6)

in which P is the prediction factor; C r is a critical value for the prediction of debris flows.

The values for the prediction factor P for all the 66 gullies are listed in Table 1. Figure 3 shows a scatter plot of R against T 0.2/G 0.5 (from Eq. 6) for all the 66 gullies and two graphs for two different values of P, marking two critical probability values for debris flow prediction. All the debris flows lie beyond the critical line C r1 = 0.35 in Fig. 3, while 80 % of the debris flows lie beyond the line, C r2 = 0.47. These critical boundaries deliver a subdivision into three classes of the probability of debris flow occurrence. Debris flows are hardly formed in the area with P < 0.35. This area can be considered as a very low probability or safe area. Some debris flows (5 out of a total of 25, 20 %) are formed in the area between 0.35 ≤ P < 0.47, which makes this area a medium probability or an alarm area. When P ≥ 0.47, debris flows are triggered in most gullies (20 out of 25, 80 %), which makes it a high-probability area. In this area, people have to be evacuated to safer places.

Fig. 3
figure 3

The critical lines for the probability of debris flow occurrence in the calibration area of Dayi. J > 0.7 means gullies with steep channels (>35°) without source material for debris flows

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5.2 Validation in southwest China

Also, in southwest China, many debris flows are triggered every year with a runoff-induced mechanism. Some of them cause enormous damage and many casualties (Yu et al. 2010). Figure 4 shows the location of five regions with debris flows in southwest China. The topographic, geological, and rainfall factors in the gullies of these regions are quite different (see Table 5): The topographic factor ranges from 0.048 to 0.405, the geological factor from 0.5 to 10.29, and the rainfall factor from 0.295 to 3.29 (the annual precipitation varies between 410 and 1,718 mm, and the 10-min rainfall coefficient of variation between 0.35 and 0.73). The value of T 0.2/G 0.5 for the investigated gullies is concentrated between 0.2 and 0.4, and between 1.0 and 1.2 (see Fig. 5). The difference in debris flow frequency is also very large (see Table 5). In the range of T 0.2/G 0.5-values between 1.0 and 1.2, the debris flows may occur several times each year in one location, while for T 0.2/G 0.5-values between 0.2 and 0.4, the frequency is only once in 10 years.

Fig. 4
figure 4

The validation regions in southwest China

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Fig. 5
figure 5

The validation of the prediction model for debris flows in different regions of southwest China

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Equation 6 and Figs. 3 and 5 show us how the critical rainfall threshold R for a certain catchment is controlled clearly by the topographic (T) and lithological characteristics (G) of the catchment. The predictive factors (T, G, and R) and the final predictive score P are listed in Table 5 for the different areas.

Figure 5 shows the validation of the prediction model for the selected areas in southwest China. All the points beyond the line of P ≥ 0.47 are debris flows. Almost all the points with debris flows are located in the domain P ≥ 0.35, and more than half of these points are located in the domain P ≥ 0.47 (see Table 6). So the two critical P lines subdivide classes with almost the same probability in the Dayi area and areas in southwest China. The prediction model obtained from data of a rain event with debris flows around Dayi, in the Guizhou Province, is applicable in other areas in the southwest of China and may be also a good predictor in other areas.

Table 6 The percentages of debris flow (DF) and no debris flow (no DF) in the three classes
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6 Discussion

Landslides, channel bed erosion, and destruction of natural dams are three common causes that trigger debris flows (Takahashi 2000). In this study area, only the runoff-induced mechanism (channel bed erosion) is considered as the trigger mechanism of debris flows in the study area. The prediction factor P is not suitable for the other mechanisms of debris flow formation.

In 2011, a heavy rainstorm that occurred in the Dayi area (Guizhou Province) provided an unprecedented amount of data to establish a model for the prediction of debris flows with a runoff-induced mechanism. For our revised prediction model proposed in this study, we had to include the category “uncertain” for gullies where the triggering mechanism of the debris flows was not sure. Neglecting the impact of these uncertain cases in the results, the distinction of the probability of occurrence of debris flows by means of the prediction factor P is acceptable despite the fact that some gullies with no debris flows are found in the domain with very high probability, and no data in the domain P < 0.35. The validation of the prediction model in southwest China was reasonable good withstanding the fact that the characteristics of these gullies are quite different to those of the calibration area. In the high-probability domain (P ≥ 0.47) of the Dayi events, there are still some gullies with the absence of debris flows. Some of these gullies have very steep channel gradients in the formation (source) area: J > 0.7 (35°). Since the angle of repose of rock particles is around 35° (Yang et al. 2009), one can hardly expect sediment deposits in such steep channel sections which means there is no source material for debris flow development. Therefore, the channel gradient J for the topographic factor (Eq. 1) is only valid for J ≤ 0.7. The points with “No debris, J > 0.7” and “Uncertain, J > 0.7” in Fig. 3 represent unrealistic (false) values because the debris flow cannot take place whatever the values of the geological and rainfall factor. This hypothesis needs to be proved in future research.

Without the “false” data, there are still nine gullies with the absence of debris flows in the high-probability area (P ≥ 0.47) during the Dayi events. This study cannot explain why no debris flows were triggered in these gullies. Future work is needed to give an explanation for these cases.

Some rainstorm events produce extreme values for the rainfall factors leading to P-values far above the critical value P = 0.47. For example, the rainfall event of Zhouqu on August 7, 2010, causing the death of 1,744 people (Yu et al. 2010), produced P-values in the range of 0.743–0.776 and huge debris flows in the catchments. Another extreme case is the rainfall event in the Wenjia Gully on August 13, 2010 (Yu et al. 2013c), which produced 3.1 million cubic meters of debris flow material, with a P value of 1.513. Lower debris flow volumes were produced in the same catchment with a P-value near the critical value (see Table 7). Figure 6 shows the exponential relationship (R 2 = 0.93) between P-values and related dimensionless debris flow volumes S expressed by Eq. 7:

$$S = 0.07e^{2P} - 0.14$$
(7)
$$S = \frac{V}{{AR_{0} C_{v} }}$$
(8)

in which S is the dimensionless volume of a debris flow; V is the volume of a debris flow (m3); A is the area of the formation section of the gully (m2); R 0 is the annual precipitation of the site (m); and C v is the 10-min coefficient of variation.

Table 7 Some gullies with P-values and debris flow volumes
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Fig. 6
figure 6

The relationship between the P value and a dimensionless volume S of debris flows

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The only outlier in Fig. 6 is the debris flow, which occurred in the Wenjia Gully on July 31, 2010. The predicted volume is much higher than the observed volume because the debris flow prevention works kept most of the sediment behind the last dam of the Wenjia Gully (Xu 2010; Xu et al. 2012). We can conclude that the prediction model may not only forecast the probability of occurrence of debris flows, but also the scale of the debris flows. The area A (see Eq. 8) of the formation section varies in the data set between 0.1 and 100 km2. However, we have only a limited amount of rainfall data in combination with related debris flow volumes to set up the relationship given in Eq. 7 and depicted in Fig. 6. The areas A (Eq. 8) of these gullies have in addition a narrow range between 1.75 and 9.18 km2. Therefore, more work should be conducted to verify Eq. 7.

In this study, many lithologies were involved in the determination of the geological factor in the Dayi area and the five regions of southwest China. It appeared that we had to introduce a low firmness coefficient values for very soft and loose materials in order to forecast the high sensitivity for debris flows in these catchments. For example, in the Hunshui Gully, debris flows were triggered many times within 1 year (Zhang and Liu 1989). This is caused by the presence in this gully of extremely strong weathered granite which we found during our field investigations. So a low value of 2 was given for the average firmness coefficient F0 of this extremely strong weathered granite (see Table 2).

Han et al. (2011) divided the frequency of debris flows in gullies in 4 classes: extremely high: occurring several times each year; high: occurring once in 1–5 years; medium: occurring once in 5–20 years; and low: occurring once in 20 years or more. The return periods (in years) of debris flows in southwest of China are shown in Table 5. Figure 7 shows the relationship between the return period (frequency) and geological factor G-value, and T 0.2/G 0.5-value of debris flows. Figures 5 and 7 show debris flow gullies with a T 0.2/G 0.5-value within the range of 1.0–1.2. These gullies have a minimum geological factor (G = 0.5) with a low firmness coefficient (0.5) because these catchments are filled with plenty of fine sediments. The debris flow may occur several times each year in one location and are therefore high-frequency debris flow gullies. Figure 5 shows also gullies with a value of T 0.2/G0.5 in the range of 0.2–0.4, with much higher G values such as limestone (10.29), sandstones (7.14), granite and diabase (10.7), etc (see Fig. 7). These gullies may be low-frequency debris flow gullies (20 years or more). No data were collected in this study for T 0.2/G 0.5-values in the range of 0.4–1.0 (See Figs. 5, 7). The frequency of debris flows within this range may be once in 5–20 year (medium) or once in 1–5 year (high). From the relationship between frequency and T 0.2/G 0.5-values and G-values, one can conclude that the debris flow activity in gullies may be determined by the topographic and geological factors, or only by the geological factor. But that have to be verified by future studies with new data.

Fig. 7
figure 7

The relationship between the return period (frequency) and geological factor G, and T 0.2/G 0.5 of debris flows

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The runoff-induced effect may be more related to short-duration rainfall intensity. Kean et al. (2011) pointed that the post-fire debris flow stage was best cross-correlated with time series of 5-min rainfall intensity and lagged the rainfall by an average of just 5 min. Wu et al. (1990) indicated that the 10-min rainfall intensity is strongly correlated with the triggering of the runoff-induced debris flows. In this paper, we suggest to use for the normalization the coefficient of variation of 10 min instead of the coefficient of variation of 1 h. It may be better to use the 10-min rainfall factors instead of the 1-h rainfall factors. Unfortunately, it is difficult to obtain the information of 10-min intensities. We have to use the 1-h rainfall factors in this paper. To get better results of the prediction of debris flows with a runoff-induced mechanism, 10-min rainfall intensity should be used in future research.

The critical value C r2 is 34.3 % higher than the critical value C r1 (Eq. 6), which shows a moderate performance of the prediction model. For a more accurate prediction of the occurrence of debris flows, more research is needed to reduce the difference between C r1 and C r2.

7 Conclusions

The heavy rainstorm from June 5 to June 6, 2011, caused a severe debris flow activity in the Dayi area, Guizhou Province, China. Short-duration high-intensity rainfall was the main triggering factor for these gully-type debris flows with a runoff-induced mechanism. This research proposed a prediction model for debris flows based on a refined, geological, and rainfall factor. These dimensionless factors are not totally deduced from the statistical analyses of a given area but partly based on the mechanism for the formation of debris flows. The model was calibrated on the June 5–6 storm event in the Dayi area. The prediction model has a generic nature, because it could be validated with reasonable success in other areas of southwest China with complete different gully characteristics.

In our view, the prediction model offers a new and exciting way to forecast the probability of occurrence of the runoff-induced debris flows. However, to improve the understanding of the occurrence and triggering mechanisms of debris flows, future research is needed to include the effect of large channel gradients, to discover the reason for the miss-classification of the absence of debris flows in the high-probability domain (large P-value), to prove the usability of the model in areas with a medium and high debris flow activity, and to reduce the difference between critical probability values.