Rainfall threshold calculation for debris flow early 1 warning in areas with scarcity of data 2

Debris flows are one of the natural disasters that frequently occur in mountain ar9 eas, usually accompanied by serious loss of lives and properties. One of the most used ap10 proaches to mitigate the risk associated to debris flows is the implementation of early warning 11 systems based on well calibrated rainfall thresholds. However, many mountainous areas have 12 little data regarding rainfall and hazards, especially in debris flow forming regions. Therefore, 13 the traditional statistical analysis method that determines the empirical relationship between 14 rainstorm and debris flow events cannot be effectively used to calculate reliable rainfall 15 thresholds in these areas. After the severe Wenchuan earthquake, there were plenty of dipos16 its deposited in the gullies which resulted in lots of debris flow events subsequently. The trig17 gering rainfall threshold has decreased obviously. To get a reliable and accurate rainfall 18 threshold and improve the accuracy of debris flow early warning, this paper developed a 19 quantitative method, which is suit for debris flow triggering mechanism in meizoseismal areas, 20 to identify rainfall threshold for debris flow early warning in areas with scarcity of data based 21 on the initiation mechanism of hydraulic-driven debris flow. First, we studied the characteris22 tics of the study area, including meteorology, hydrology, topography and physical characteris23 tics of the loose solid materials. Then, the rainfall threshold was calculated by the initiation 24 mechanism of the hydraulic debris flow. The comparison with other models and with alter25 nate configurations demonstrates that the proposed rainfall threshold curve is a function of 26

Longmenshan tectonic belt has a significant effect on this region, especially the Hongkou-146 Yinxiu fault. The study area has strong tectonic movement and strong erosion, and the main 147 channel is "V"-shaped. The area is characterized by a rugged topography, and the main slope 148 gradient interval of the gully is 20° to 40°, accounting for 52.38% of the entire study area. and Table 2 (Wang et al., 2016). They indicate that the volume of materials is more than 20 × 158 10 4 m 3 , and the infiltration capable of the earth surface have much increased. Therefore, the 159 trigger rainfall for debris flow has decreased greatly. The Guojuanyan gully had no debris 160 flows before the earthquake because of the lack of loose solid materials before the earthquake; 161 however, it became a debris flow gully after the earthquake, and debris flows occurred in the 162 following years (Table 3). The specific conditions of these debris flow events were collected 163 through field investigations and interviews. The field investigations and experiments deter-164 mined that the density of the debris flow was between 1.8 and 2.1 g/cm 3 . Unfortunately, there 165 were no rainfall data before 2011, when we started field surveys in the Guojuanyan gully.

Debris flow monitoring and streambed survey of the study area 175
After the Wenchuan earthquake, continuous field surveillance was undertaken in the study area. A debris flow monitoring system was also established in the study area. To identify 177 the debris flow events, this monitoring system recorded stream water depth, precipitation and 178 real-time video of the gully (Fig. 4). The water depth was measured using an ultrasonic level 179 meter, and precipitation was recorded by a self-registering rain gauge. The real-time video 180 was recorded onto a data logger and transmitted to the monitoring center, located in the In-181 stitute of Mountain Hazards and Environment, Chinese Academy of Sciences. When a rain-182 storm or a debris flow event occurs, the realtime data, including rainfall data, video record, 183 and water depth data, can be observed and queried directly in the remote client computer in 184 the monitoring center.

Data collection and the characteristics of rainfall 195
The Wenchuan earthquake occurred in the Longmenshan tectonic belt, located on the 196 eastern edge of the Tibetan plateau, China, which is one of three rainstorm areas of Sichuan tain rainstorm area). Heavy rainstorms and extreme rainfall events occur frequently. Because 199 there were few data in the mountain areas, we collected the rainfall data from 1971-2000 and

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the total annual rainfall in this area was approximately 1148 mm, and rainfall in the monsoon tion of rainfall is seriously inhomogeneous; moreover, the rainfall intensity has great differ-218 ences. From 1971 to 2000, the maximum monthly rainfall was 592.9 mm, the daily maximum 219 rainfall was 233.8 mm, the hourly maximum rainfall was 83.9 mm, the 10-min maximum 220 rainfall was 28.3 mm, and the longest continuous rainfall time was 28 days.

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Debris flow field monitoring data and on-site investigation data were used to identify the 222 debris flow events and to analyze the characteristics of the rainfall pattern and the critical 223 rainfall characteristics. Analysing the typical rainfall process curves (Fig. 13), we can find that 224 the hourly rainfall pattern of the Guojuanyang gully is the peak pattern, displaying the single     widely. The reason is that debris flow is usually triggered by short-duration rainstorms.

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Therefore, the short-durations of 10-min and 1-h rainfall have higher correlation with debris 252 flow occurrence and have the minor differences. Actually, the 10-min rainfall intensity 253 (maximum precipitation over a 10-min period during the rainfall event) is the most 254 appropriate index for early warning of debris flow, which is most representative and has 255 minor error. However, it is difficult to obtain such short-duration rainfall data in actual debris 256 flow gullies because long-term rainfall monitoring system do not exist in most debris flow 257 basins especially in areas with scarcity of data. Further analyzing the 10-min and 1-h critical 258 rainfalls, we can find that they vary with the antecedent precipitation index ( API ). They are 259 variable rather than constant. In this paper, the antecedent precipitation index ( API ) and the 260 1-h rainfall ( 60 I ) were used to calculate the rainfall threshold curve of debris flows in the 261 Guojuanyan gully.

Materials and methods 263
This study makes an attempt to analyze the trigger rainfall threshold for debris flow by 264 using the initiation mechanism of debris flow. Firstly, to analyze the rainfall characteristics of 265 the watershed by using the field monitoring data; then to calculate the runoff yield and con-266 centration progress based on field observation. Additionally, the critical runoff depth to initi-267 ate debris flow was calculated by the initiation mechanism with the underlying surface condi-268 tion (materials, longitudinal slope, etc.) of the gully. Then, the corresponding rainfall for the 269 initiation of debris was back-calculated based on the stored-full runoff generation. At last, 270 these factors were combined to build the rainfall threshold model. This method can be applied 271 to the early warning system in the areas with scarcity of rainfall data.

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The flow chart of the research is shown in Fig. 8.
where * C is the volume concentration obtained by experiments(0.812);  is the unit weight of 336 loose deposits (usually is 2.65 g/cm 3 );  is the unit weight of water,1.0 g/cm 3 ;  is the longi-

Calculation of watershed runoff yield and concentration 358
The stored-full runoff, one of the modes of runoff production, is also called as the super 359 storage runoff. The reason of the runoff yeild is that the aeration zone and the saturation zone 360 of the soil are saturated by rainfall. In the humid and semi humid areas where rainfall is 361 plentful, because of the high groundwater level and soil moisture content, the loss of precipi-362 tation is no longer increased with the rains continue, after meet plant interception and infil-363 tration, which produces a wide range of surface runoff. The Guojuanyan gully is located in Du off producing mechanism in this gully, and this runoff yield pattern is used to calculate the 366 watershed runoff. That is, it is supposed that the water storage can reach the maximum stor-367 age capacity of the watershed after each heavy rain. It is common used in the humid and semi 368 humid areas in China to analyze the runoff yield mechanism. Therefore, the rainfall loss in each time I is the difference between the maximum water storage capacity Im and the soil 370 moisture content before the rain Pa. Hence, the water balance equation of stored-full runoff is 371 expressed as follows (Ye, et al., 1992): where R is the runoff depth (mm); P is the precipitation of one rainfall (mm); I is the rain-374 fall loss (mm); m I is the watershed maximum storage capacity (mm) for a certain watershed, 375 it is a constant for a certain watershed that can be calculated by the infiltration curve or infil-  Eq. 5 can be expressed as follows: The precipitation intensity is a measure of the peak precipitation. At the same time, the 383 duration of the peak precipitation is generally brief, lasting only up to tens of minutes. There-384 fore, 10-minute precipitation intensity (maximum precipitation over a 10-minute period dur-385 ing the rainfall event) is selected as the stimulating rainfall for debris flow, which is appropri-386 ate and most representative. However, it is difficult to obtain such short-duration rainfall data 387 in areas with scarcity of data. Therefore, in this study, P and a P are replaced by 60 I (1 hour 388 rainfall) and API (the antecedent precipitation index), respectively; thus, Eq. 6 is expressed 389 as: In the hydrological study, the runoff depth R is: 392 3.6 t 3.6 = 1000 where R is the runoff depth (m); W is the total volume of runoff (m 3 ); F is the watershed area 394 (km 2 ); t  is the duration time, in this study it is 1 hour; and Q is the average flow of the water-395 shed (m 3 /s), which can be expressed as follows: where B is the width of the channel (m), V is the average velocity (m/s) and 0 h is the critical 398 depth (m).

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Eq. 5 is the expression of the rainfall threshold curve for a watershed, which can be used 400 for debris flow early warning. This proposed rainfall threshold curve is a function of the ante-

The critical depth of the Guojuanyan gully 406
The grain grading graph (Fig. 11) is obtained by laboratory grain size analysis experi-407 ments for the loose deposits of the Guojuanyan gully. Figure 11 shows that the characteristic Guojuanyan gully is 100mm. According to Eq. (5) -Eq. (7), the calculated rainfall threshold 420 curve of debris flow in the Guojuanyan gully is shown in Table 5.

The calculation of the antecedent precipitation index ( API ) 428
The rainfall factor influencing debris flows consists of three parts: indirect antecedent 429 precipitation (IAP) (it is 0 a P in this paper), direct antecedent precipitation (DAP) (it is t R in this 430 paper), and triggering precipitation (TP) (it is 60 I in this paper). The relationships among them 431 are shown in Figure 12. Obviously, IAP increases soil moisture and decreases the soil stability, 432 and DAP saturates soils and thus decrease the critical condition of debris flow occurrence.

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Although TP is believed to initiate debris flows directly, its contribution amounts to only 37%     Table 6.

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In addition to the rainfall process of the 5 debris flow events (Fig. 13), some typical rain-486 falls whose daily rainfall were greater than 50 mm but did not trigger a debris flow were also 487 calculated; the greatest 1-h rainfall is considered as 60 I (Table 6). 488 The proposed rainfall threshold curve is a function of the antecedent precipitation index ( API ) and 1-h rainfall ( 60 I ), which is a line and a negative slope. Fig. 14

About the two above points that did not trigger debris flows 501
The proposed rainfall threshold curve is a function of the antecedent precipitation index ( API ) and the 1-h rainfall ( 60 I ), which has been validated by rainfall and hazards data and 503 can be applied to debris flow early warning and mitigation. However, in Figure 14, there are 504 two points above the curve that did not trigger debris flow at all. Although we have highlight-505 ed the significance and interconnect of antecedent rainfall, critical rainfall, 1 h triggering 506 rainfall, as well as their accurate determination before the hour of debris flow triggering, it 507 should be noticed that the rainfall is only the triggering factor of debris flows. A comprehen-508 sive warning system must contain more environmental factors, such as the geologic and geo-509 morphologic factors, the distribution of source areas. The special and complex formative en-510 vironment of debris flow after earthquake caused the rainfall threshold is much more complex 511 and uncertain. The rainfall threshold of debris flow varies with the antecedent precipitation 512 index ( API ), rainfall characteristics, amount of loose deposits, channel and slope characteris-513 tics, and so on. Therefore, we should further study the characteristics of the movable solid 514 materials, the shape of gully, and so on to modify the rainfall threshold curve.
25 5 debris flow events. Furthermore, as the initiation depth in distinct watershed is different 517 from each other because of the different topography and loose solid materials, hence the rain-518 fall threshold is independent for each watershed. While most of debris flow gullies in Wen-519 chuan earthquake affected areas with scarcity of rainfall data and disaster data, therefore, the 520 approach proposed in this study hasn't been validated by other gullies except the Guojuanyan 521 gully so far. Figure 13 and Figure 14 indicated that the only 5 debris flow events all triggered 522 by the rainfalls with high-intensity and short-duration. As mentioned before, the influence of 523 the antecedent rainfall in this kind of debris flow is relatively less. However, it still can't ignore 524 the significance role of the antecedent precipitation. Due to safety concerns, in the universali-525 ty calculation of rainfall threshold for debris flow, it must fully consider the antecedent pre-526 cipitation. Therefore, the days count for antecedent rainfall in this study is selected as 20. Of 527 course, the value of the curve should be further validated and continuously corrected with 528 more rainfall and disaster data in later years.

Further studies about the debris flow early warning in earthquake-hit 530 areas 531
It should be noted that the methodological proposal of this study is based on the physical 532 process of debris flow initiation and involves modeling with physical characteristics of the 533 loose solid materials which served by the landslides triggered by earthquake; therefore, it's 534 suitable for the areas with scarcity of data especially the earthquake affected areas.

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Actually, the times of debris flow events happened in the earthquake-hit areas were de-536 creasing from 2014 on; there was even no debris flow event at all in Guojuanyan gully. Mainly 537 because of the unstable slopes as well as the materials are decreasing with the times go by.

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Therefore, the rainfall threshold would increase accordingly. However, it may need a long 539 time, perhaps 15-20 years, according to the experiences in other earthquake-hit areas, such as 10-min and 1-h critical rainfalls of different debris flow events have minor differences; how-549 ever, the 24 hour critical rainfalls vary widely. The 10-min and 1-h critical rainfalls have a no-550 tably higher correlation with debris flow occurrences than to the 24-h critical rainfalls.

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(2) The rainfall pattern of the Guojuanyan gully is the peak pattern, both single peak and 552 multi-peak. The antecedent precipitation index ( API ) was fully explored by the antecedent 553 effective rainfall and stimulating rainfall.

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(3) As an important and effective means of debris flow early warning and mitigation, the 555 rainfall threshold of debris flow was determined in this paper, and a new method to calculate 556 the rainfall threshold is put forward. Firstly, the rainfall characteristics, hydrological charac-557 teristics, and some other topography conditions were analysed. Then, the critical water depth