Rainfall thresholds of the debris ows based on various rainfall intensity types in Beijing

Empirical rainfall thresholds derived from various types of rainfall intensities have widely used in characterizing rainfall conditions that cause debris ows and landslides. However, few works have studied the differences among these various thresholds, due to limited information on the instantaneous intensity triggering debris ows. The detail records of the storms on 21 July, 2012, 20 July, 2016, and 16 July, 2018, together with the occurrence time of debris ows, provide an opportunity to evaluate the thresholds based on various rainfall intensities. Based these data, a new rainfall threshold of debris ows is derived from the instantaneous rainfall intensity in Beijing. At the same time, the thresholds based on average rainfall intensities as used in most previous studies, including the average over the periods from the beginnings of rainfall to the occurrences of the debris ows and over the whole period of the rainstorms, are reconstructed. The result shows that the instantaneous rainfall threshold has a higher ability in separating the rainstorms inducing from those without reducing debris ows than those derived from average intensities, indicating a high accurate of the instantaneous threshold. Our data also indicate that the debris ows in Beijing should be triggered by the concert works of rainfall intensity and cumulative precipitation. Only when enough water to inltrate, saturate, mobilize the debris sediments, and sucient high water ows and surges caused by intensive storms to incorporate and retain the mobilized sediments, are satised simultaneously do the debris ows occur.


Introduction
Debris ow is the major geo-disasters in Beijing, and many heavy disasters occurred in the past. The debris ows in 1888 destroyed 39 villages and caused a great loss of both human lives and assets.
According to the geo-disaster survey of Beijing, more than 9 hundreds sites including many villages and tourism sites are under thee threaten of debris ows. Therefore, the early and accurate forecast of debris ows is of special signi cance for the disaster prevention and mitigation in Beijing. Though many factors, such as geological and geomorphological characteristics, compositions of sediments, and vegetation cover, have a potential impact on debris ows, it is well known that intensive storm is often the initial trigger (David-Novak et al. 2004, Guzzetti et al. 2007, Iverson 1997, Kean et al. 2011). As a result, the rainfall threshold becomes the key to forecast debris ows and landslides (Baum and Godt 2010, Fausto et al. 2008).
The empirical model is the method widely used to estimate rainfall thresholds (Aleotti 2004, Caine 1980 Wieczorek et al. 2000). This threshold is established based on statistical analysis of the past rainstorms causing debris ows, mainly based the relationships between rainfall intensities and durations of the storms (Caine 1980, Guzzetti, Peruccacci, Rossi andStark 2007). Therefore, the de nition of rainfall intensity is the key to establishment of empirical model and forecast debris ows (Guzzetti, Peruccacci, Rossi and Stark 2007). There are various types of rainfall intensities, which have different geophysics implications (Guzzetti, Peruccacci, Rossi and Stark 2007). Theologically, the thresholds derived for various intensities should have some differences. However, few works have evaluated the differences among the various thresholds before.
Rainfall intensity is the amount of precipitation accumulated in a period, or the rate of precipitation in a period, most commonly measured in millimeters per hour. The average rainfall intensity is the main type of intensity used to establish the empirical model, due to lack of the information about the occurrence time of debris ows. Based on the length of observation periods, average intensities can be divided into the average intensity over hours (peak intensity), days or longer periods, such as average over the period of whole rainfall or over the durations before the occurrences of debris ows (Guzzetti, Peruccacci, Rossi and Stark 2007). The peak intensity indicates the average rainfall rate of the maximum rainfall period, while the average over long periods re ects the "average" value that underestimates the peak (maximum) rainfall rate occurred during the observation period (Guzzetti, Peruccacci, Rossi and Stark 2007 (Ma et al. 2018, Wu 2001, showed that the occurrences of debris ows didn't always correspond to the maximum rainfall intensity. Therefore, the research on the instantaneous rainfall intensities, which coincide to the occurrences of debris ows, is of special signi cance in accurately estimating the rainfall thresholds. However, to our knowledge, few studies as such have been reported in previous studies.
Three extreme storms occurring on 21 July, 2012, 20 July, 2016, and 16 July, 2018, caused serious debris ows in Beijing. The detail processes of the storms including their spatial and temporal changes have been registered by the intensive automatic weather stations, FY-2E infrared images, and Doppler weather radar (Lei et al. 2020, Yang et al. 2018, Zhong et al. 2015. Furthermore, the occurrence time of the debris ows was well known. This provides the rst opportunity to test the reliability of the rainfall thresholds derived from various rainfall intensities and make a deep insight on the dynamics of debris ows in Beijing. This paper made a systematic analysis on the evolution of the three storms, particularly the changes of rainfall intensity and precipitation, and its association with the occurrence of debris ows. A new rainfall threshold was established based on the relationship between the instantaneous rainfall intensities (I i ) and the rainfall durations before debris ow occurrences by the empirical model (Caine 1980, Guzzetti, Peruccacci, Rossi andStark 2007). The rainfall thresholds based on the average intensities, including the average over the periods before the occurrence of debris ows (I b ) and over the whole rainstorm durations (I w ), were also established. The accurate of different rainfall thresholds was evaluated through comparing their abilities in separating the storms inducing debris from those without causing debris ow.
At the same time, the dynamic of debris ows were discussed based on the intensities and precipitations triggering the debris ows.

Geological Setting And Methods
Beijing is located at the northern tip of the North China Plain, near the meeting point of the Xishan and Yanshan mountain ranges. The city of Beijing lies on low and at land, which is bounded by Xishan Mountain to the west and Yanshan Mountain to the north. The Yanshan and Xishan ranges meet at Nankou, in Changping District, northwest of the city. Xianshan belongs to Yanshan mountain range, which runs a north-south up the spine of Hebei province. Xishan covers nearly all of Fangshan and Mentougou Districts, and the western part of Haidian. The highest peak in Beijing (Lingshan with an altitude of 2303m) is located in Xishan mountain areas. The high mountain meadows and river gorges, such as Shidu and Juma River, are developed across Xishan. To the north of Beijing city, Yanqing and Miyun Counties, and Huairou and Pinggu Districts are located in the Yanshan range running from west to east across north Heibei Province.
Faults, folds, bedrock ssures are developed intensively in the mountain areas of Beijing. This tectonic factor, together with rock weathering, results in a large amount of unsolid sediments accumulated in the mountain valleys, providing enough debris materials for debris ows. Therefore, the debris ows occur mainly in these mountain areas (Wang 2008, Wu 2001, Zhong et al. 2004).
The climate of Beijing is semi-humid continental climate, which is controlled by Asia Monsoon, characterized by hot, humid climate in summer and dry, cold climate in winter. The annual average precipitation is around 600 mm with a little high precipitation in the northeast and southwest areas. The rainfall concentrates in summer season, particularly from June to August, the precipitation of June-August accounts for more than 80% of the annual total precipitations. Almost all of the debris ows of 1949-2018 occurred during the interval from June to August (Wang 2020).
The detail processes of the storms occurred on 21 July, 2012, 20 July, 2016, and 21 July, 2018 are reconstructed based on continuous monitoring data of the meteorological stations, which are located in or nears the areas where debris ows occurred. The occurrence times of debris ows are taken from news reports, geo-disaster survey reports, and the interview with local residents. Though the total precipitation brought by the rainstorm on 20 July, 2016 is larger than the storm on 21 July, 2012, the damage and loss caused by the later one is much serious. Debris ows and landslides occurred mainly in Fangshan District, where a total of 22 debris ows and 10 landslides were triggered by the storm in 2012 (Fig.1). The large scale debris ows and landslides occurred in Heibeizhen (7 events), Xiayunling (13 events), and Nanjiao (3 events) coinciding to the heavy storms (Fig.1). The debris ows caused by the rainstorm on 20 July 2016 and 16 July 2018 is few. Each rainstorm causes only one debris ows, which occurred in Jiangxintai, Fangshan District and Xibailianyu, Miyun District, respectively.

Discussion
Rainfall intensities and durations triggering debris ows The rain fall durations before the debris ow occurrence show a signi cant difference among the three rainstorms. The debris ow triggered by the rainfall with the longest duration (15 hours) occurred on 20 July, 2016, while the debris ow induced by the shortest duration rainfall (5 hours) presented on 16 July, 2018 (Fig. 2). The rainfall durations of the debris ows in 2012 change little among various sites, centering around 8-9 hours. The rainfall intensities show a decreasing trend with increased cumulative precipitations. The rainfall intensity is only 46 mm/h with a cumulative precipitation of 217.6 mm for the debris ows in Nanjiao site, while it is as high as 98.9 mm/h corresponding to the cumulative precipitation of 180 mm for the debris ows in Fangshan site (Fig.2).

Rainfall thresholds based various rainfall intensity
For the rainfall-induced debris ows, a rainfall thresholds is de ned by rainfall reaching or exceeding a hydrological condition that is likely to trigger a debris ow (Guzzetti, Peruccacci, Rossi and Stark 2007). It has been demonstrated that rainfall-induced debris ows and landslides are closely related to rainfall intensities and durations (Caine 1980 The thresholds derived various types of rainfall intensities differed signi cantly between each other (Fig.3). The I i -D a threshold is the largest one of the three thresholds, and Ia-Da model is the smallest.
When the data of rainfalls without causing debris ows are available, the threshold is de ned as the best separator of the rainfall conditions that resulted and did not result in debris ows (Guzzetti, Peruccacci et al. 2007). To test the reliabilities of the various thresholds, we plot the data that the rainfall intensities are more than 10 mm/h during the three storms, but did not cause debris ows in the Fig. 3a. The reason for the application of 10 mm is that 10 mm is used to delimit a rainfall event in the studied regions susceptible to debris ow, and the overland ow on the surface of a slope is generated before The rainfall threshold derived from instantaneous intensity show high ability in separating the rainfalls inducing from those without inducing debris ows. Almost all of the data without causing debris ows, particularly those with similar rainfall durations, fall into the safety region delimited by the I i -D a threshold (Fig. 3a). Furthermore, the instantaneous intensity of the debris ows occurred on 21-22 July, 1989 (Wu 2001) also fall into the risk region delimited by our Ii-Da threshold (Fig.3a). In contrast, many data of the average intensities that did not result in debris ows fall into the risk region de ned by the I a -D a threshold ( Fig. 3a ). Similar to the Ia-Da threshold, the threshold derived from the intensity over the whole rainstorms also show a low ability in separating the rainfalls inducing from those without inducing debris ows. Most importantly, the I w values of many rainfall storms, which caused debris, falls into the safety region of the I w -D w thresholds, indicating a low accurate. These data consistently suggest that the occurrences of the debris ows are closely related to the instantaneous intensities and antecedent durations of rainfall events, and thus the I i -D a threshold is more accurate than those derived from other two intensity types. In contrast, the I a -D a and I w -D w thresholds might underestimate the precipitation or intensity triggering debris ows, and thus have a high rate of false alarm. This conclusion is consistent with the coincidence of the debris ows to the high rainfall intensities identi ed in both the three and previous storms in Beijing. Of course, this postulation need further research in consideration of the limited spatial and temporal coverage of the three storms in this study.

Comparison with previous thresholds
The rainfall threshold as the lower boundary of rainfall conditions, permits a direct comparison of thresholds based on various intensity types, though the rainfall thresholds are derived from various intensities, (Aleotti 2004  (2020), particularly, when the rainfall duration exceed 6 hours (Fig.3b). The I a -D a threshold in this study, together with the threshold of Wang (2020) and local thresholds of Ma et al. (2016), can well de ne the average rainfall condition that resulted in debris ows, whereas they might have a high rate of nuisance alarms as pointed above.

Implication for the dynamics of debris ow in Beijing
The data of this study suggest that the rainfall intensity should play a dominant role in triggering the debris ows in the mountain areas of Beijing. As discussed above, all the debris ows in Beijing occurred during the interval with high intensity. Another obvious characteristics is that the high intensive rainfall sustained at least two hours before the debris occurred (Fig. 2). The serious disasters occurred in the regions where the long-term high intensive storms occurred. The most serious disasters occurred in Hebeizhen and Xiayunling areas during the storm on 21 July, 2012. In both sites, the heavy rainfall lasted about 3 hours before triggering a debris ow. The rainfall intensities from 9 to 11 hours are 65, 84, and 92 mm/h in Hebeizhen (Fig. 2), reaching the level of a 500-year storm. Similarly, the debris ows in Xiayunling were caused by 3-hour storm with an intensity of >48.5 mm/h, reaching the level of a 100-year storm. All these evidences suggest that the high intensive, continuous rainfall might play a dominant role in triggering debris ows in Beijing.
However, rainfall intensity cannot interpret the debris ows in Beijing alone. The cumulative precipitation from the beginning of the rainfall to the occurrence of debris ows may also play a substantial role. In many sites, the occurrences of the debris ows do not always correspond to the maximum rainfall intensity. Only when both accumulative rainfall and intensity reach a threshold could the debris ows be triggered (Fig. 2). During the storm on 21 July, 2012, no debris ows occurred when the cumulative precipitations were relative small in Mentougou (118.4 mm) and Longquan sites (84.3 mm), despite the rainfall intensity reached the maximum (Fig.2). Only when the cumulative rainfall reached 187.4 and 203.9 mm (3-4 hours delay to the maximum intensity) did the debris ows occurred (Fig. 2a). Similarly, the rainstorms with high intensity and low precipitations during the storm on 16 July, 2018 also caused few debris ows (Fig. 2). The intensities on the site of Bangheyan, Xiwanzi, and Yunmengshan are higher than 55 mm/h, but the corresponding cumulative precipitations are small. No debris ows or landslides occurred in these regions, though serious oods occurred. These evidences indicate that neither the rainfall intensity nor cumulative rainfall can interpret the debris ows in Beijing alone. Only when both rainfall intensity and cumulative rainfall reach a threshold simultaneously do debris ows occur. This Above evidences indicate that the debris ows in Beijing are triggered by the combination of high intensive rainstorm with high cumulative precipitation. This provides some deep insights into the dynamics of debris ows in Beijing. It is well known that high intensive rainstorms must lead to ood occurrences, but mustn't result in debris ows. This is related to the underlying forcing of ood and debris ows. Debris ows are distinguished from oods in major forcing. The debris ow is that masses of poorly sorted sediments agitated and saturated with water, surge down slopes in response to gravitational attraction (Iverson 1997). As pointed by Iverson (1997), there are three factors for the development of debris ows: 1) failures of debris masses, 2) enough water to saturate the mass, and 3) su cient conversion of gravitational potential energy to internal kinetic energy to change the style of motion that can be recognized as ow. The three factors must be satis ed almost simultaneously for debris ow occurrences (Anderson and Sitar 1995, Ellen and Fleming 1987, Iverson 1997. For the debris ows in Beijing, the long-term rainfall and its resultant high cumulative rainfall before debris ow occurrences provide enough time for water in ltrating and saturating debris sediments, mobilizing sediments by increasing the pore pressures of the sediments. Simultaneously, the high water ows and surges caused by intensive storms incorporate and retain the mobilized sediments, owing down the slope and forming debris ows.

Conclusion
This paper made a systematic analysis on the evolution of recent three rainstorms and their association with the occurrence of debris ows in Beijing. The rainfall durations before the occurrences of debris ow are relative long, ranging from 5 to 15 hours. The debris ows occurred during the intervals with high rainfall intensity, whereas don't always correspond to the maximum of rainfall intensities, some of which are 3-4 hours delay to the maximum rainfall intensity. All of the debris ows occurred under the condition when both the intensities and cumulative precipitations reached a certain level, indicating a concerted work of rainfall intensity and cumulative precipitations.
The rainfall thresholds are estimated by various types of rainfall intensity, and the differences among them have been compared. The thresholds derived from the instantaneous intensity (I i -D a ) display a high ability in separating the storms inducing from those without inducing debris ows. In contrast, the I a -D a and I w -D w thresholds show a low discriminating ability and thus high rate of false alarm, though the Ia-Da model might be a high safe threshold indicated by its low value. These evidences demonstrate a signi cant role of instantaneous rainfall density in triggering debris ows, and a necessary of using instantaneous rainfall intensity and in situ monitoring in accurately estimating rainfall thresholds in future works.