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Landslides (2014) 11:877–887
DOI 10.1007/s10346-013-0421-5
Received: 12 July 2012
Accepted: 26 June 2013
Published online: 13 July 2013
© Springer-Verlag Berlin Heidelberg 2013
Wei Zhou IChuan Tang
Rainfall thresholds for debris flow initiation
in the Wenchuan earthquake-stricken area,
southwestern China
Abstract The Wenchuan earthquake-stricken area is frequently
hit by heavy rainfall, which often triggers sediment-related disas-
ters, such as shallow landslides, debris flows, and related natural
events, sometimes causing tremendous damage to lives, property,
infrastructure, and environment. The assessment of the rainfall
thresholds for debris flow occurrence is very important in order to
improve forecasting and for risk management. In the context of
the Wenchuan earthquake-stricken area, however, the rainfall
thresholds for triggering debris flows are not well understood.
With the aim of defining the critical rainfall thresholds for this
area, a detailed analysis of the main rainstorm events was carried
out. This paper presents 11 rainfall events that induced debris flows
which occurred between 2008 and 2012 after the Wenchuan earth-
quake. The rainfall thresholds were defined in terms of mean
rainfall intensity I, rainfall duration D, and normalized using the
mean annual precipitation (MAP). An ID threshold and a normal-
ized I
MAP
Dthreshold graph could be set up for the Wenchuan
earthquake-stricken area which forms the lower boundary of the
domain with debris flow-triggering rainfall events. The rainfall
threshold curves obtained for the study area were compared with
the local, regional, and global curves proposed by various authors.
The results suggest that debris flow initiation in the study area
almost requires a higher amount of rainfall and greater intensity
than elsewhere. The comparison of rainfall intensity prior to and
after the earthquake clearly indicates that the critical rainfall
intensity necessary to trigger debris flows decreased after the
earthquake. Rainfall thresholds presented in this paper are gener-
alized, so that they can be used in debris flow warning systems in
areas with the same geology as the Wenchuan earthquake-stricken
area.
Keywords Wenchuan earthquake .Debris flow .Critical
rainfall .ID threshold
Introduction
Local intense or prolonged rainfall events often trigger debris
flows in southwestern China after the Wenchuan earthquake,
causing serious casualties and economic losses. Post-earthquake
debris flow events increased significantly due to the increased
loose materials in this area with intense rainfall. These post-seis-
mic disasters will still last for 5 to 10 years (Tang et al. 2009), or
may last also longer −10 to 15 years, even up to 30 years (Cui et al.
2008; Xie et al. 2009). The typical study areas for these post-
earthquake debris flows are the Kanto earthquake zone in Japan,
the Chi-chi earthquake area in Taiwan (e.g., Lin et al. 2006; Shieh
et al. 2009; Chen and Hawkins 2009), and the Wenchuan earth-
quake-stricken area (e.g., Tang and Liang 2008; Tang et al. 2009,
2012).
To analyze the primary causes of debris flow occurrence, it is
necessary to understand the relationship between rainfall
thresholds and debris flow initiation. In the relevant literatures,
the physical approach (process-based, conceptual) and the empir-
ical approach (historical, statistical) have been proposed to define
rainfall thresholds (e.g., Caine 1980; Corominas 2000; Guzzetti et
al. 2007; Cannon et al. 2008; Saito et al. 2010). The empirical
approach is the focus of this paper. Empirical rainfall thresholds
are defined by studying rainfall events that have triggered debris
flows. Guzzetti et al. (2007) suggested that empirical rainfall
thresholds can be grouped in four categories as follows: (1) rainfall
intensity–duration (ID) thresholds, (2) thresholds based on the
total rainfall of the event, (3) rainfall event–duration thresholds,
and (4) rainfall event–intensity thresholds. ID thresholds for de-
bris flow occurrence are the most common type of thresholds and
have been widely identified in many different climates and geo-
logic settings (Guzzetti et al. 2007,2008; Brunetti et al. 2010; Saito
et al. 2010).
The Wenchuan earthquake-stricken area is characterized by its
high-relief topography and complex geological conditions. Rainfall
is one of the primary factors that have triggered debris flows in
southwestern China. Heavy rainfall frequently occurs, especially
during the monsoon season, causing sediment-related disasters
such as shallow landslides and debris flows. But the relationship
between debris flow occurrence and rainfall characteristics in the
study area, either in empirical equations or in physical interactions
of loose materials, is still unclear. Few studies have evaluated the
regional relationship between ID thresholds and debris flow oc-
currence in Wenchuan earthquake-stricken area prior to the earth-
quake using empirical models, e.g., the rainfall intensity and
cumulative rainfall (Tan 1990; Tan and Han 1992). After the
Wenchuan earthquake, the critical ID thresholds for the triggering
of debris flows have decreased, but these thresholds are hard to
quantify precisely. It is very difficult to estimate the debris flow
occurrence by the critical rainfall of debris flow prior to the
earthquake. Hence, the definition of critical rainfall of post-seismic
debris flow is needed to be redefined for the frequent debris flow
events. The redefinition of ID thresholds for triggering debris
flows can provide a crucial decision making tool in risk manage-
ment after the earthquake.
A relatively accurate prediction of post-earthquake debris flows
can help to reduce the casualties and economic losses. Right now,
it is very difficult to predict debris flows on the basis of the
initiation mechanisms. Therefore, in order to increase the capacity
of predicting possible future debris flow occurrence, this paper
assesses the relationship between post-seismic debris flows and
rainfall thresholds.
The main purposes of this paper are the following: (1) deter-
mining empirical ID thresholds for debris flows in the Wenchuan
earthquake-stricken area, (2) establishing empirical normalized
I
MAP
D(Iis rescaled by the mean annual precipitation: MAP)
thresholds for debris flows in the Wenchuan earthquake-stricken
Landslides 11 &(2014) 877
Original Paper
area, and (3) providing important information for the local gov-
ernment to mitigate debris flow hazards. To do so, rainfall records
were collected to analyze the critical cumulative rainfall for typical
debris flows which occurred in the Wenchuan earthquake-stricken
area. In accordance with more traditional methods (Giannecchini
2006), the ID thresholds and the normalized I
MAP
Dthresholds
were obtained using manual fitting methods to determine the
lower boundary of rainfall events with debris flows. The ID thresh-
olds were compared with those that had been proposed for the
world (Caine 1980; Guzzetti et al. 2008), for humid tropical and
Asian monsoon regions (Jibson 1989; Hong et al. 2005; Chen et al.
2005; Guzzetti et al. 2008; Dahal and Hasegawa 2008), and for
China (Jibson 1989; Tang et al. 2012). The method used to establish
the rainfall thresholds is similar to that by other researchers (e.g.,
Caine 1980; Larsen and Simon 1993) in different parts of the world.
Rainfall thresholds for post-seismic debris flows
In this section, rainfall thresholds for debris flow initiation after
the Chi-Chi earthquake and Wenchuan earthquake will be
reviewed. Many papers about characteristics of critical rainfall
for post-seismic debris flows in the Chi-Chi earthquake area in
Taiwan have been published before and after the Wenchuan earth-
quake (e.g., Lin et al. 2003; Shieh et al. 2009; Chang et al. 2009;
Chen 2011).
After the Chi-Chi earthquake, both maximum rainfall intensity
and critical cumulative rainfall that have triggered debris flows
reduced. Lin et al. (2003) stated that these figures reduced to as
low as one third of the pre-seismic figures in the Chenyulan River
watershed. Shieh et al. (2009) suggested that debris flows were
easily triggered with a cumulative precipitation of 200 mm in the
first year after the Chi-Chi earthquake, which was as low as 1/4 of
the pre-earthquake figures (Shieh et al. 2009; Chang et al. 2009).
The rainfall necessary to initiate debris flow quickly decreased
after the Chi-Chi earthquake, but subsequently increased with
time. The maximum effective critical cumulative rainfall reached
to 520 mm at the end of the seventh year. These values have
already recovered to 54.7 % of the original values prior to the
Chi-Chi earthquake. The effective cumulative rainfall of the
Wushikeng watershed, located in Taichung County, increased from
330 mm in the first year to 710 mm in the seventh year, recovering
to 50 % of the original values prior to the Chi-Chi earthquake
(Shieh et al. 2009). For the same rainfall duration, the lowest
rainfall intensity triggering debris flows in the 1st year after the
Chi-Chi earthquake is only one-fifth of that before the earthquake.
The critical rainfall intensity in the fifth year after the earthquake
has gradually recovered to that before the earthquake (Chen 2011).
Few rainfall thresholds for debris flows before the occurrence of
the Wenchuan earthquake can be found in literature. Researchers
started to pay attention to the characteristics of the critical rainfall
for post-seismic debris flow in this region after the Wenchuan
earthquake. Tang and Liang (2008) stated that rainfall intensity
necessary to initiate debris flow is 41 mm/h after the earthquake, a
reduction of 25–31 % compared to the pre-earthquake figures in
the Beichuan area. The cumulative precipitation necessary to ini-
tiate debris flow reduced to 15–22 % of the values before the
earthquake. Tang et al. (2012) suggested the expression
I=25.962D
−0.239
as a rainfall threshold for debris flow occurrence
in the Qingping area. Meanwhile, they proposed that antecedent
precipitation varying between 67.7 and 137.6 mm in 24 h, with a
mean rainfall intensity of about 7.3–22.5 mm/h, can trigger debris
flows in the Qingping area (Tang et al. 2012).
Study area
Before the Wenchuan earthquake, only four catastrophic earth-
quakes (M
L
>7.0) occurred in northeast Sichuan: on September 4,
1713, M
L
7.0; on August 25, 1933, M
L
7.5; on August 16, 1976, M
L
7.2;
and on August 23, 1976, M
L
7.2. Since 1976, there have been no
severe sediment disasters (i.e., large-scale landslides and debris
flows) recorded except for those associated with the Wenchuan
earthquake. Figure 1shows the locations of the Hongchun, Bayi,
Wenjia, and Dashui watersheds in Sichuan Province. The distances
of the epicenter to the Hongchun, Bayi, Wenjia, and Dashui wa-
tersheds are only 10, 13, 80, and 130 km, respectively. The impact of
the earthquake was instantaneous at the four sites.
Table 1presents geomorphological parameters which were
gathered through the study of geologic maps and topographic
maps, as well as relevant literature, official engineering reports,
and field work.
Study area 1—Dashui watershed
The Dashui watershed is a branch of Jianjiang River and located
about 2,500 m southwest of the old town of Beichuan, Sichuan
Province (Fig. 1a) and drains a total area of 0.45 km
2
(Fig. 1b). The
maximum relief is 896 m. The watershed is underlain primarily by
sandstone, marlstone, and mudstone. The daily maximum precip-
itation is about 301 mm, and the maximum hourly rainfall inten-
sity is 62 mm. The mean annual precipitation is 1,399.1 mm, and
the maximum annual precipitation is 2,340 mm. The rainfall is
largely concentrated in the period from June to September, during
which 74 % of the annual precipitation is deposited. Subsequent to
the Wenchuan earthquake, many shallow slope failures and large-
scale landslides occurred in the area. According to the official
engineering report, the volume of loose materials is 1.62 million
cubic meters after the Wenchuan earthquake. The volume of
effective loose materials reaches 0.91 million cubic meters (Hu et
al. 2009).
Study area 2—Wenjia watershed
The Wenjia watershed has a drainage area of 7.65 km
2
and is
located in the Qingping area, part of Mianzhu county in the
Sichuan Province. The main branch has a length of 4.33 km. It is
located about 80 km to the northeast of the epicenter of the
Wenchuan earthquake (Fig. 1c). The maximum relief is 1,519 m.
The slope gradients vary between 12 and 35°. The watershed is
underlain primarily by shale, sandstone and siltstone, limestone,
and dolomite. The area is situated in a subtropical humid mon-
soon climate zone with an annual average temperature of 14.4 °C.
The average annual precipitation is 1,086 mm. The rainfall is
largely concentrated in the period from June to September, with
80 % of the annual precipitation (Yu et al. 2010; Tang et al. 2012).
Rock avalanche deposits are located at the Hanjia platform (with
an estimated volume of about 23 million cubic meters) and the
1,300 platform (with an estimated volume of about 55 million cubic
meters). The most catastrophic debris flow event occurred on
August 13, 2010 and transported more than 3.1 million cubic meters
of materials from the 1,300 platform deposits of the rock avalanche
towards the Mianyuan River. The avalanche deposits remaining at
Original Paper
Landslides 11 &(2014)
878
the1,300platformarestillsusceptibletobeerodedand
remobilized as debris flows by concentrated water flow (Tang et
al. 2012).
Study area 3—Hongchun watershed
The Hongchun watershed covers an area of 5.35 km
2
and is located
near Yingxiu town, in the Wenchuan county of Sichuan Province
(Fig. 1d). The main branch has a length of 3.6 km. The maximum
relief is 1,288.4 m. The watershed is underlain primarily by granite
and diorite. The area is situated in a subtropical humid monsoon
climate zone. The average annual precipitation is 1,253.1 mm. Sixty
to seventy percent of the annual precipitation is concentrated in
the period from June to September (Tang et al. 2011). Subsequent
to the Wenchuan earthquake, many shallow slope failures and
large-scale landslides occurred in the area. The estimated volume
of landslide deposits reaches 3.843 million cubic meters after the
earthquake.
Study area 4—Bayi watershed
The Bayi watershed has a drainage area of 8.3 km
2
and is located in
the Longchi area, part of Dujiangyan City in Sichuan Province. The
main branch has a length of 2.93 km. It is located about 13 km to
the northeast of the epicenter of the Wenchuan earthquake
(Fig. 1e). The maximum relief is 1,606 m. The slope gradients vary
104°30'E
104°30'E
104°0'E
104°0'E
103°30'E
103°30'E
103°0'E
103°0'E
32°0'N
32°0'N
31°30'N
31°30'N
31°0'N
31°0'N
Jianjiang River
Dashuigouwatershed
740
840
940
114 0
1240
1340
1440
1540
Landslide
km
00.20.1
960 1060 1160 1260
1360
1460
1560
1660
1760
1860
1960
2060
Wenjiawatershed
MianyuanRiver
Landslide
km
010.5
1160
1260
1360
1060
960
1460
1560
1660
1760
1860
1960
960
Hongchunwatershed
MingjiangRiver
Landsli de
km
010.5
LongxiRiver
Bayiwatershed
940
1140
1340
1540
1740
1940
2140
Landslide
km
010.5
(d)
(c)
(b)
(e)
1300 Platform
(a)
Fig. 1 (a) Location map of the four debris flow watersheds in the Wenchuan earthquake-stricken area (SW China). Watershed maps of the Dashui watershed (b), the
Wenjia watershed (c), the Hongchun watershed (d), and the watershed (e)
Landslides 11 &(2014) 879
between 20 and 50°. The watershed is underlain primarily by
marlstone, sandstone, and mudstone. The area is situated in a
subtropical humid monsoon climate zone with an annual average
temperatureof14.4°C.Theaverage annual precipitation is
1,134.8 mm, and the maximum annual precipitation is
1,605.4 mm (Zhou et al. 2011). The rainfall is largely concentrated
in the period from May to September, during which 80 % of the
annual precipitation is deposited (Ma et al. 2011). According to the
official engineering report, the estimated volume of loose mate-
rials is 8.59 million cubic meters after the Wenchuan earthquake.
The volume of effective loose materials reaches 5.2 million cubic
meters. The most catastrophic debris flow event occurred on 13th
of August 2010 and transported more than 0.827 million cubic
meters of rock avalanche materials to the Longxihe River.
Rainfall thresholds analysis
Rainfall data
For each event, the following rainfall variables were collected: (1)
cumulative rainfall C(in millimeter), (2) rainfall duration D
(hour), (3) mean rainfall intensity I(millimeter per hour), and
(4) peak rainfall intensity I
p
(millimeter per hour). The definition
proposed by Jan and Lee (2004) is adopted to define one single
event with continuous precipitation. The start of precipitation is
defined when the rainfall intensity is >4 mm/h. The end of the
precipitation event is defined when the rainfall intensity is <4 mm/
h during six consecutive hours (Chang et al. 2011).
Knowledge of the rainfall characteristics in a particular area
requires well-recorded debris flows and corresponding rainfall-
duration data. In the Wenchuan earthquake-stricken area, howev-
er, systematically recorded debris flow data are rarely available
because few giant debris flows occurred. Besides, precipitation
gauging stations are not installed in all the debris flow gullies.
The information on the rainfall data and meteorological stations
used in this study is listed in Tables 2and 3, respectively. The
rainfall data recorded at the closest meteorological stations for
every event were plotted in its respective hyetograph to find out
their main characteristics and to get some insight into their tem-
poral behavior.
The hyetographs (Fig. 2) depict 11 rainfall events. For the
DFDB1, DFMW1, and DFMW4 events, the peak rainfall intensity
is reached very quickly (less than 2 h), and then the rainfall
terminates in less than 3 h. For the DFBD1 and DFDB2 events,
the peak rainfall intensity is also reached very quickly (less than
3 h), but the rainfall decreases much slowly (7 h). For the DFMW2,
DFMW3, and DFWH1 events, the maximum rainfall intensity is
reached slowly (during 8 h), and then the rainfall decreases also
slowly (6 h). For the DFWH2 event, the maximum rainfall inten-
sity is reached in 4 h, and then the rainfall ceases in 3 h. For the
DFBD2 event, the maximum rainfall intensity is reached in 2 h,
and then the rainfall decreases very slowly (12 h).
According to the previous collection of rainfall records of
typical debris flows and analysis of debris flow occurrence, cumu-
lative rainfall and rainfall intensity of debris flow occurrence were
shown in Fig. 2. Inspection of Fig. 2shows that the peak rainfall
intensity for Dashui, Wenjia, Hongchun, and Bayi watersheds, are
41.8–61.8, 31.9–75.2, 32–56.5, and 68.5–75 mm/h, respectively.
The 11 rainfall records can be summarized by the following two
simple statements: (1) the hourly peak intensities vary from 31.9 to
Table 1 Geomorphological parameters of four watersheds assessed by field investigation (volumes), geologic maps, topographic maps, and archives
Debris flow gully Dashui watershed Wenjia watershed Hongchun
watershed
Bayi watershed
Catchment area (km
2
) 0.45 7.65 5.35 8.3
Stream length (km) 0.99 4.33 3.6 2.93
Mean channel gradient (‰) 525 467 358 376
Maximum/minimum elevation (m a.s.l.) 1,609/713 2,402/883 2,168.4/880 2,456/850
Maximum relief, H(m) 896 1,519 1,288.4 1,606
Volume of effective loose materials (10
4
m
3
)
91 7,490 3,84.3 520
Geology Sandstone, marlstone, and
mudstone
Shale, sandstone and siltstone, limestone and
dolomite
Granite and diorite Marlstone, sandstone, and
mudstone
Original Paper
Landslides 11 &(2014)
880
75.2 mm/h, and (2) the cumulative rainfalls are between 89.5 and
245.8 mm. Inspection of Fig. 2indicate that the majority of debris
flows occurred when rainfall persisted for 1–11 h. Meanwhile, not
all debris flows were triggered at the maximum rainfall intensity.
This is influenced by the impact factors such as site-specific me-
teorological and hydrological conditions or the distance between
the debris–flow event and the rain gauge (Guzzetti et al. 2007).
ID thresholds
In order to construct the ID thresholds, all the duration Dand
mean rainfall intensity Idata were plotted together in double-
logarithmic coordinates (Don the x-axis, Ion the y-axis), and
the rainfall thresholds were defined as the level above which debris
flow can be triggered (Guzzetti et al. 2007,2008). Then, the critical
threshold curve was drawn by computer-aided software. Figure 3
depicts an ID threshold graph associated with typical debris flows
in the Wenchuan earthquake-stricken area. Values of the duration
Drange from 2 to 15 h and mean rainfall intensity Ifrom 10.2 to
44.8 mm/h.
Threshold s can be described in the form of I=αD
−β
, where α
and βare constants. The threshold curve, which was defined by the
lower boundary of the points representing rainfall events for
triggering debris flow in the study area, is expressed as (Eq 1):
I¼66:36D−0:79 2≤D≤15ðÞ ð1Þ
Where Iis the mean rainfall intensity (in millimeter per hour), Dis
the rainfall duration (hour). It shows how the mean rainfall inten-
sity that is likely to initiate debris flow decreases with an increase
in rainfall duration.
Normalization
The normalized intensity (i.e., the ratio of the mean rainfall inten-
sity to mean annual precipitation) can be plotted against rainfall
duration. Figure 4presents I
MAP
D conditions associated with
typical debris flows in the Wenchuan earthquake-stricken area.
The range of rescaled rainfall intensity is 0.0081 to 0.041 (h
−1
)of
MAP. The rescaling slightly reduced the variation of rainfall
intensity.
The I
MAP
Dthreshold graph, which forms the lower boundary of
the plotted points with debris flow events, can be expressed as
follows:
IMAP ¼0:036D−0:61 2≤D≤15ðÞ ð2Þ
Where I
MAP
is the normalized rainfall intensity (in millimeter per
hour), Dis the rainfall duration (hour).
It is sometimes instructive in estimating critical rainfall inten-
sities for debris flow events to express the values as a percentage of
the MAP. For example, in our case, rainfall events of a short
duration, such as less than 2 h, require a normalized rainfall
Table 2 Information on meteorological stations
Dashui watershed Wenjia watershed Hongchun watershed Bayi watershed
Meteorological station Tangjiashan Nanmu Yingxiu Longchi
Recording interval (h) 1 1 1 1
Altitude (m a.s.l.) 764 771 880 717
Distance to debris flow source area (km) 1 2 1 7
Mean annual precipitation (mm) 1,399.1 1,086 1,253.1 1,134.8
Table 3 Rainfall data for post-seismic debris flows in the Wenchuan earthquake-stricken area
Study site Debris flow
code
Rainfall
event date
Peak rainfall
intensity (mm/h)
Mean rainfall
intensity (mm/h)
Cumulative
rainfall (mm)
Duration
rainfall (hour)
Dashui DFBD1 2008-9-23 41.8 30.0 90.0 3
DFBD2 2008-9-24 61.8 15.1 226.5 15
Wenjia DFMW1 2010-7-31 39.1 44.8 89.5 2
DFMW2 2010-8-13 38.7 24.5 163.9 8
DFMW3 2010-8-19 31.9 12.5 176.0 14
DFMW4 2012-8-14 75.2 22.6 112.9 5
DFMW5 2012-8-19 67.0 29.6 237.0 8
Hongchun DFWH1 2010-8-14 32.0 10.2 143.2 14
DFWH2 2011-8-21 56.5 18.8 131.6 7
Bayi DFDB1 2010-8-13 75.0 13.7 123.5 9
DFDB2 2010-8-19 68.5 30.7 245.8 8
Landslides 11 &(2014) 881
0
20
40
60
80
100
0
10
20
30
40
50
00 01 02 03 04 05 06 07 08 09 10
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(a)
DFBD1
0
50
100
150
200
250
0
10
20
30
40
50
60
70
20 22 00 02 04 06 08 10 12 14
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(b)
DFBD2
0
20
40
60
80
100
120
0
10
20
30
40
50
60
00 01 02 03 04 05 06 07 08 09 10 11 12
Cumulati ve rainfa ll (mm)
Rai nfall i ntensity (mm/h)
Time
(c)
DFMW1
0
30
60
90
120
150
180
0
10
20
30
40
50
17 18 19 20 21 22 23 00 01 02 03 04 05
Cumulati ve rainfa ll (mm)
Rai nfall i ntensity (mm/h)
Time
(d)
DFW2
0
50
100
150
200
0
10
20
30
40
21 23 01 03 05 07 09 11 13
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(e)
DFMW3
0
50
100
150
0
20
40
60
80
09 11 13 15 17 19 21 23
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(f)
DFMW4
0
50
100
150
200
250
300
0
20
40
60
80
14 16 18 20 22 00 02 04 06 08 10
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(g)
DFMW5
0
30
60
90
120
150
180
0
5
10
15
20
25
30
12 14 16 18 20 22 00 02 04 06 08 10
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(h)
DFWH1
0
40
80
120
160
0
20
40
60
18 20 22 00 02 04 06 08
Cumulati ve rainfa ll (mm)
Rainfall intensity (mm/h)
Time
(i)
DFWH2
0
40
80
120
160
0
20
40
60
80
13 14 15 16 17 18 19 20 21 22 23 00
Cumulative rainfall (mm)
Rainfall intensity (mm/h)
Time
(j)
DFDB1
0
50
100
150
200
250
300
0
20
40
60
80
17 19 21 23 01 03 05
Cumulati ve rainfa ll (mm)
Rai nfall i ntensity (mm/h)
Time
(k)
DFDB2
Fig. 2 Hyetographs and cumulative
rainfalls of the debris flows studied.
Black star indicates an estimated
time of debris flow occurrence
Original Paper
Landslides 11 &(2014)
882
intensity of at least 0.0236 h
−1
(which is 2.36 % of the MAP) to
trigger debris flows.
Guidicini and Iwasa (1977) introduced the normalized event
rainfall (E
MAP
), i.e., the cumulative rainfall divided by the MAP.
On the basis of the same empirical approach used for the identi-
fication of the ID thresholds, two threshold curves were drawn
(Figs. 5and 6). The E
MAP
Iand the E
MAP
Dthresholds are expressed
by the Eqs. (3) and (4), respectively:
EMAP ¼0:26I−0:45 10:2≤I≤44:8ðÞ ð3Þ
EMAP ¼0:0376D0:37 2≤D≤15ðÞ ð4Þ
Where E
MAP
is the normalized event rainfall (in percent), Iis the
mean rainfall intensity (in millimeter per hour), and Dis the
rainfall duration (hour).
Figure 5indicates that the E
MAP
decreases with the increasing
mean rainfall intensity I. Figure 6indicates that the E
MAP
increases
with increasing rainfall duration. The results depend on the MAP
value.
Discussion
Comparison of rainfall thresholds
Guzzetti et al. (2007) have listed 36 previous works of ID thresh-
olds and 13 previous works of normalized ID thresholds for debris
flows initiation in global, regional, and local contexts. The ID
threshold for the Wenchuan earthquake-stricken area can be
compared with some of these relations available in the literature
(Fig. 7and Table 4). The thresholds obtained in this work (red in
Fig. 7) fall in the range of rainfall intensity and duration defined by
other thresholds (1–16 in Fig. 7). The ID threshold for the
Wenchuan earthquake-stricken area is higher than other global,
regional, and local thresholds. In particular, it is slightly higher
than the thresholds of Jibson (1989) for China and Tang et al.
(2012) for the Qingping area. Inspection of Fig. 7also depicts that
the thresholds resemble that proposed by Larsen and Simon (1993)
for humid tropical Puerto Rico and Dahal and Hasegawa (2008)
for Nepal Himalaya but with a slightly lower threshold value.
The global thresholds proposed by Caine (1980) and Guzzetti et
al. (2007), however, are quite lower than the threshold for the
Wenchuan earthquake-stricken area. It is an interesting phenom-
enon. Despite the drop down in threshold due to the enormous
loose material, it is still a high threshold compared to the rest of
the world. In some parts of the world, the loose materials are more
vulnerable for debris flows. It indicates that the impact of climates
and geologic settings on the debris flow occurrence may not be
significant when the catchment undergoes a prolonged rainfall
event with large amounts of precipitation.
Guzzetti et al. (2007) pointed out that the thresholds defined by
various researchers for mid-latitude climates are steeper (power
value of Din between −0.70 and −0.81) than the thresholds
obtained for the mountains and cold climates (power value of D
in between −0.48 and −0.64). It is also true for the threshold in the
Wenchuan earthquake-stricken area based on the observation,
which lies in the middle latitudinal area.
The normalized ID thresholds were also compared with similar
thresholds obtained from different parts of the world by various
I = 66.36D
-0.7 9
1
10
100
110
Mean rainfall intensity
/(mm/ h)
Durati on /h
Fig. 3 ID threshold graph associated with typical debris flows in the Wenchuan
earthquake-stricken area
I
MAP
= 0. 036 D
-0. 61
0.001
0.01
0.1
110
Mean ra infall intensity /MAP
/h
-1
Duration /h
Fig. 4 I
MAP
Dthreshold line for typical debris flows in the Wenchuan earthquake-
stricken area
E
MAP
= 0.26I
-0. 4 5
0.01
0.1
1
550
Cumulative rainfall /MAP /%
Mean rainfall intensity /(mm/h)
Fig. 5 E
MAP
Ithreshold graph for typical debris flows in the Wenchuan
earthquake-stricken area
E
MAP
= 0.0376D
0.37
0.01
0.1
1
110
Cumulative rainfall /MAP /%
Durati on /h
Fig. 6 E
MAP
Dthreshold graph for typical debris flows in the Wenchuan
earthquake-stricken area
Landslides 11 &(2014) 883
researchers, as presented in Fig. 8and Table 5.InFig.8,the
normalized ID threshold for debris flow in the Wenchuan earth-
quake-stricken area is similar to the regional threshold proposed
Table 4 ID thresholds for the debris flow initiation
# Extent Reference Area Equation Range (h) Number in
Fig. 7
1 G Caine (1980) World I=14.82D
−0.39
0.167<D<240 1
2 G Jibson (1989) World I=30.53D
−0.57
0.5<D<12 2
3 G Guzzetti et al. (2008) World I=2.20D
−0.44
0.1<D<1000 3
4 G Guzzetti et al. (2008) World I=2.28D
−0.20
0.1<D<48 4
5 G Guzzetti et al. (2008) World I=0.48D
−0.11
48≤D<1000 5
6 L Jibson (1989) Hong Kong I=41.83D
−0.58
1<D<12 6
7 R Jibson (1989) Japan I=39.71D
−0.62
0.5<D<12 7
8 R Larsen and Simon
(1993)
Puerto Rico I=91.46D
−0.82
2<D<312 8
9 R Jan and Chen (2005) Central Taiwan I=13.5D
−0.20
0.7<D<40 9
10 R Jan and Chen (2005) Central Taiwan I=6.7D
−0.20
0.7<D<40 10
11 R Hong et al. (2005) Shikoku Island, Japan I=1.35+55D
−1.0
24<D<300 11
12 R Chien-Yuan et al.
(2005)
Taiwan I=115.47D
−0.80
1<D<400 12
13 R Cannon et al. (2008) Southern California I=14.0D
−0.5
0.167<D<12 13
14 R Dahal and Hasegawa
(2008)
Nepal Himalaya I=73.90D
−0.79
5<D<720 14
15 R Jibson (1989) China I=49.11-6.81D
1.0
1<D<5 15
16 L Tang et al. (2012) Qingping, China I=25.962D
−0.239
1<D<24 16
17 L This study Wenchuan earthquake-stricken
area, China
I=66.36D
−0.79
2≤D≤15 17
Extent: Gglobal threshold, Rregional threshold, Llocal threshold
0.1
1.0
10.0
100.0
0.1 1.0 10.0 100.0 1000.0
Mean ra infall intensity (mm/h)
Duration /h
1
2
3
4
5
678
9
10
11
12
13 15
16
14
17
Fig. 7 Comparison between the ID threshold graphs determined by this study
(red line) with some local, regional, national, and global threshold graphs
(presented in Table 4). Thick lines (black and gray): global thresholds. Thin lines
(black and gray): regional thresholds. Blue lines: local thresholds. Area: 1World
(Caine 1980),2World (Jibson 1989), 3–5World (Guzzetti et al. 2008), 6Hong Kong
(Jibson 1989), 7Japan (Jibson 1989), 8Puerto Rico (Larsen and Simon 1993), 9–10
Central Taiwan (Jan and Chen 2005), 11 Shikoku Island, Japan (Hong et al. 2005), 12
Taiwan (Chien-Yuan et al. 2005), 13 Southern California (Cannon et al. 2008), 14
Nepal Himalaya (Dahal and Hasegawa 2008), 15 China (Jibson 1989), 16 Qingping,
China (Tang et al. 2012)
0.0001
0.0010
0.0100
0.1000
1.0000
0.1 1.0 10.0 100.0 1000.0
Mean ra infall intensity/MAP /h
-1
Duration /h
3
1
4
5
6
7
8
9
2
10
Fig. 8 Comparison between the normalized ID threshold graphs determined by
this study (red line) with some local, regional, national, and global thresholds
(presented in Table 5). Thick lines (black and gray): global thresholds. Thin lines
(black and gray): regional thresholds. Blue lines: local thresholds. Area: 1World
(Jibson 1989), 2–4World (Guzzetti et al. 2008), 5Japan (Jibson 1989), 6Hong
Kong (Jibson 1989), 7Hong Kong (Jibson 1989), 8central and southern Europe
(Guzzetti et al. 2007), 9Nepal Himalaya (Dahal and Hasegawa 2008)
Original Paper
Landslides 11 &(2014)
884
by Jibson (1989) for Puerto Rico. Compared to other places, such
as Japan (Jibson 1989) and Central and southern Europe (Guzzetti
et al. 2007), the normalized ID threshold value is high, whereas it is
less than the thresholds obtained from Puerto Rico (Jibson 1989)
and Nepal Himalaya (Dahal and Hasegawa 2008).
Comparison of thresholds prior to and after the earthquake
It is difficult to assess the precise rainfall data which triggered a
specific debris flow, because after the earthquake it was hard to
determine the time of debris flow occurrence in the uninhabited
gullies. Meanwhile, few precipitation gauging stations were
installed in these gullies. The rainfall data recorded at the nearest
precipitation gauging stations of a debris flow gully were consid-
ered to be representative for the triggering of a debris flow. For
DFBD1 and DFDB2, the cumulative rainfall triggering debris flows
in some gullies near Tangjiashan precipitation gauging station was
90–173 mm, and the critical rainfall intensity was 14.2–41.8 mm/h.
According to the research on critical rainfall prior to Wenchuan
earthquake, the critical rainfall intensity was 50–60 mm/h, and the
cumulative rainfall was 320–350 mm (Tang and Liang 2008). The
critical rainfall intensities and cumulative rainfall have reduced to
23.6–69.6 and 25.7–49.4 % of the original values prior to the
Wenchuan earthquake.
The cumulative rainfall and rainfall intensity necessary to ini-
tiate debris flows can be determined from the debris flow events
after the Wenchuan earthquake. The cumulative precipitation in
some gullies close to Yingxiu station was 104–118 mm, while the
critical rainfall intensity was 16.4–56.5 mm/h. The cumulative
rainfall triggering debris flows in some gullies near Dujiangyan
station was 134.4–245.8 mm, and the critical rainfall intensity was
15.8–47.3 mm/h. In some gullies close to Nanmu station, the
cumulative rainfall was 89.5–176 mm, while the critical rainfall
intensity was 16.4–39.1 mm/h. The rainfall intensities necessary to
initiate debris flows in the Yingxiu and Longchi area are poorly
known because no significant debris flow events were recorded
prior to the Wenchuan earthquake. Tan and Han (1992) pointed
out that the critical rainfall intensity in the Longmenshan area is
greater than 30–50 mm/h, with a total rainfall of at least 80–
100 mm. Comparing the characteristics of the triggering rainfall
with the thresholds reported by Tan and Han (1992), the results
indicate that only the minimum critical rainfall intensities have
reduced to as low as one half of the pre-earthquake figures.
Apart from the increase in volume of loose material after the
earthquake, it is also the structure of these materials which increased
the susceptibility for debris flows. Field investigation showed that the
void ratio of this new loose materials is relatively large, which lowers
the rain intensity threshold to mobilize this material.
Despite the fact that the critical rainfall data before and after
the earthquake are scarce, one can conclude, also thanks to the
findings about the Chi-Chi earthquake, that the critical rainfall
intensity and duration necessary to trigger debris flow decreased
after the earthquake.
Use of rainfall thresholds
The ID thresholds that are determined for the Wenchuan earth-
quake-stricken area in this work can provide guidance for setting
up debris flow warning systems and planning emergency actions.
Three or four scenarios of rainfall monitoring can be listed, and
the corresponding emergency actions can be proposed. One sce-
nario can be adopted and an emergency system activated based on
critical rainfall data. If a real-time rainfall monitoring system is
available, the rainfall evolution can be analyzed step by step. The
possibility of triggering debris flows can be judged by real-time
rainfall data from rain gauges. Debris flows can be triggered when
the combination of mean rainfall intensity and duration exceeds
the ID threshold curve. In the historical data, the minimum effec-
tive rainfall intensities for the study areas to initiate a debris flow
ranged between 15.8 and 33 mm/h. The critical mean rainfall
intensities based on the ID threshold curve are between 7.8 and
38.4 mm/h. On the basis of the comparison of the rainfall forecasts
and real-time measurements in combination with the threshold
curves, decisions on warning and emergency response can be
made by the local government.
Table 5 Normalized ID thresholds for the debris flow initiation
# Extent Reference Area Equation Range (h) Number in
Fig. 8
1 G Jibson (1989) World I
MAP
=0.02D
−0.65
0.5<D<12 1
2 G Guzzetti et al. (2008) World I
MAP
=0.0016D
−0.40
0.1<D<1000 2
3 G Guzzetti et al. (2008) World I
MAP
=0.0017D
−0.13
0.1<D<48 3
4 G Guzzetti et al. (2008) World I
MAP
=0.0005D
−0.13
48≤D<1000 4
5 R Jibson (1989) Japan I
MAP
=0.03D
−0.63
1<D<12 5
6 L Jibson (1989) Hong Kong I
MAP
=0.02D
−0.68
1<D<12 6
7 R Jibson (1989) Puerto Rico I
MAP
=0.06D
−0.59
1<D<12 7
8 R Guzzetti et al. (2007) Central and Southern Europe I
MAP
=0.0064D
−0.64
0.1<D<700 8
9 R Dahal and Hasegawa
(2008)
Nepal Himalaya I
MAP
=1.10D
−0.59
5<D<720 9
10 L This study Wenchuan earthquake-stricken
area, China
I
MAP
=0.036D
−0.61
2≤D≤15 10
Extent: Gglobal threshold, Rregional threshold, Llocal threshold
Landslides 11 &(2014) 885
Limitations of this research
Limitation of the rainfall data
Before the Wenchuan earthquake, few debris flows occurred in the
study area. Therefore, precipitation gauging stations were not
installed in potential dangerous debris flow gullies. After the
Wenchuan earthquake, stations were installed in the middle and
lower parts of the watersheds with frequent debris flows. However,
few precipitation gauging stations were installed in the source area
of the large watersheds, and the data are of limited access. In this
work, for each debris flow, the corresponding effective rainfall data
on the day of debris flow occurrence were obtained from the
nearest rainfall station. The rainfall data in the source area at
higher altitudes is different from that of the lower lying meteoro-
logical stations. Although the rainfall data is few, they can be used
to analyze the relationship between ID thresholds and debris flow
occurrence. To some extent, the limitations of the rainfall data can
reduce the precision of ID thresholds but cannot affect the analysis
of ID thresholds.
Limitations of the rainfall ID analysis
Figure 2shows that some debris flows occur during high-intensity
short-term rainfall events. Figures 3and 4show that ID thresholds
obtained for the Wenchuan earthquake-stricken area are charac-
terized by short rainfall duration (<15 h). However, ID plots depict
only mean rainfall intensities and do not necessarily reflect high
rainfall intensity or low rainfall intensity at the time of debris flow
occurrence. This paper does not take into account the role of
antecedent rainfall in triggering debris flows in the Wenchuan
earthquake-stricken area. Further studies are necessary to estab-
lish local ID thresholds considering the variation of rainfall inten-
sity, antecedent rainfall, and other variables such as topography
and geology.
Conclusion
This paper constructs empirical ID thresholds for debris flow
initiation in the Wenchuan earthquake-stricken area based on
the intensity–duration (ID) approach. The ID thresholds were
identified quantitatively. To compare the ID thresholds with
those of other studies, Iwas normalized by the mean annual
precipitation (MAP) data. The results indicate that rainfall
intensities of 7.8–38.4 mm/h have the potential to initiate
debris flows in the Wenchuan earthquake-stricken area, with
rainfall durations between 2 and 15 h. Despite the fact that the
threshold graph must have dropped significantly after the
earthquake, it is still higher than those previously proposed
for the global, regional, and local scale in almost all previous
studies. It means that the Wenchuan earthquake-stricken area
is less prone to debris flows. This is due to the high MAP and
the high frequency of rainstorms hitting the study area, which
induce in the long term a natural and dynamic equilibrium
between climatic features and slopes.
The computer-aided software used to construct the threshold
curves led to cautionary results. However, mathematical and sta-
tistical approaches will be tested and compared with the present
results in the next stages of this research. The threshold curves
which are constructed by this work can be the basis to set up the
debris flow warning systems. This requires reliable weather fore-
cast systems to be in operation. Then the local government can
make decisions on warning and emergency response based on the
proposed rainfall thresholds for the Wenchuan earthquake area.
Acknowledgments
This work was supported by the National Natural Science Foun-
dation of China (no. 41202253), research fund of the State Key
Laboratory of Geo-Hazard Prevention and Geo-Environment Pro-
tection (no. 2011Z020) and the Special Program for the Fundamen-
tal Research of Science and Technology of the Ministry of Science
and Technology, China (no. 2011FY110100-3). We express our grat-
itude to Zhou Chunhua for the collection of rainfall data and Xia
Tian for the figures. Dr. ThWJ van Asch (Utrecht University, The
Netherlands) helped to improve the language of the paper. The
authors thank the anonymous reviewers for their helpful sugges-
tions to improve the paper.
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W. Zhou ()):C. Tang
State Key Laboratory of Geo-Hazard Prevention and Geo-Environment Protection,
Chengdu University of Technology,
Chengdu 610059, People’s Republic of China
e-mail: chouvw@163.com
Landslides 11 &(2014) 887
