NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-18-765-2018Radar-based quantitative precipitation estimation for the identification of
debris flow occurrence over earthquake-affected regions in Sichuan, ChinaShiZhaoshi_zhao@foxmail.comWeiFangqiangChandrasekarVenkatachalamKey Laboratory of Mountain Hazards and Earth Surface Process,
Chengdu, 610041, ChinaInstitute of Mountain Hazards and
Environment, Chinese Academy of Sciences, Chengdu, 610041,
ChinaUniversity of Chinese Academy of Sciences, Beijing, 100049,
ChinaDepartment of Electrical and Computer Engineering, Colorado State University, Fort Collins, 80523, USAKey Laboratory of Atmospheric Sounding,
Chengdu University of Information and Technology, Chengdu
610225, ChinaZhao Shi (shi_zhao@foxmail.com)8March201818376578031August201719September201731January20182February2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://nhess.copernicus.org/articles/18/765/2018/nhess-18-765-2018.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/18/765/2018/nhess-18-765-2018.pdf
Both Ms 8.0
Wenchuan earthquake on 12 May 2008 and Ms 7.0 Lushan earthquake on
20 April 2013 occurred in the province of Sichuan, China. In the
earthquake-affected mountainous area, a large amount of loose material caused a high
occurrence of debris flow during the rainy season. In order to evaluate the
rainfall intensity–duration (I–D) threshold of the debris flow in
the earthquake-affected area, and to fill up the observational gaps
caused by the relatively scarce and low-altitude deployment of rain gauges in
this area, raw data from two S-band China New Generation Doppler Weather
Radar (CINRAD) were captured for six rainfall events that triggered 519
debris flows between 2012 and 2014. Due to the challenges of radar
quantitative precipitation estimation (QPE) over mountainous areas, a series
of improvement measures are considered: a hybrid scan mode, a
vertical reflectivity profile (VPR) correction, a mosaic of reflectivity, a
merged rainfall–reflectivity (R-Z) relationship for convective and
stratiform rainfall, and rainfall bias adjustment with Kalman filter (KF). For
validating rainfall accumulation over complex terrains, the study areas are
divided into two kinds of regions by the height threshold of 1.5 km from the
ground. Three kinds of radar rainfall estimates are compared with rain gauge
measurements. It is observed that the normalized mean bias (NMB) is decreased
by 39 % and the fitted linear ratio between radar and rain gauge
observation reaches at 0.98. Furthermore, the radar-based I–D threshold
derived by the frequentist method is I=10.1D-0.52 and is underestimated by uncorrected raw radar data.
In order to verify the impacts on observations due to spatial variation, I–D thresholds are identified from the nearest rain gauge observations and
radar observations at the rain gauge locations. It is found that both kinds
of observations have similar I–D thresholds and likewise underestimate I–D thresholds due to undershooting at the core of convective rainfall.
It is indicated that improvement of spatial resolution and measuring accuracy
of radar observation will lead to the improvement of identifying debris flow
occurrence, especially for events triggered by the strong small-scale
rainfall process in the study area.
Introduction
Rainfall-induced debris flow is a kind of ubiquitous natural hazard for
mountainous areas with complex terrain. It is a geomorphic movement process which
scours the sediment from steep areas into alluvial fans. The formation of
rainfall-induced debris flow is generally related to three main factors,
including gravitational potential energy, abundant loose materials and
meteorological events (Guzzetti et al., 2008). The gravitational potential
energy remains relatively stable for a long period of time. The loose
materials are normally made up of sand, unsorted silt, cobbles, gravel,
boulders and woody debris (Wang et al., 2016). High-magnitude
earthquake events can generate abundant loose solid material from co-seismic
rock falls and landslides and deposited in gullies (Shieh et al., 2009).
During the rainy season, the occurrence of debris flow after an earthquake
becomes more frequent (Yu et al., 2014; Guo et al., 2016a). Both the Ms 8.0
Wenchuan earthquake on 12 May 2008 and the Ms 7.0 Lushan earthquake on 20 April 2013 occurred in the province of Sichuan, China, and have changed the formation conditions for
debris flow. A large number of debris flows occurred from 2008 to 2014 and
caused many casualties and extensive property damage.
Early warning systems (EWS) for rainfall-induced landslide and debris flow
are widely implemented in many parts of the world (Baum and Godt, 2010; Glade
and Nadim, 2014; Segoni et al., 2015). The performance of EWS relies highly
on the updating of precipitation thresholds (Rosi et al., 2015). Furthermore,
a large amount of loose materials caused by earthquake highly increases the occurrence of debris flow (Tang et al., 2009,
2012), it is necessary to revaluate the precipitation threshold. The model of
rainfall intensity–duration (I–D) is widely used to represent the
precipitation thresholds of triggering landslides and debris flow (Aleotti,
2004; Guzzetti et al., 2007). Some literature concluded that the I–D
relationships for some of the regions were severely affected by the Wenchuan
earthquake (Su et al., 2012; Cui et al., 2013; Zhou and Tang, 2014; Guo et
al., 2016b). However, most of these I–D relationships are derived from
rain gauge observation. This is a common technical way to estimate the
I–D thresholds of debris flows using rainfall observation from the
nearest rain gauge. However, the uncertainty of I–D thresholds from rain
gauge observations could not be ignored. This is related to two critical
limitations which probably lead to underestimation of observation of strong
convective events occurring at high-altitude areas. The first limitation is
the relatively sparse network density of rain gauges in the mountainous
region (Marra et al., 2014); the other one is the altitude of gauge
deployments, which is at low elevation for sustainability. The same
limitations of rain gauge observation also exist in the mountainous regions
of Sichuan. The technique of microwave remote sensing has become a necessary
way for observing rainfall events in complex terrain. The radar-based
quantitative precipitation estimation (QPE) has been shown to be useful for
the study of debris flows, as its unique advantage of high spatial and
temporal resolution. Radar observations offer the unique merit of estimating
rainfall over the actual debris flow location (David-Novak et al., 2004;
Chiang and Chang, 2009; Marra et al., 2014; Berenguer et al., 2015). However,
there are many challenges when radar-based QPE in the mountainous area is
applied to the study of debris flow. Commonly, keeping the elevation angle
close to the ground and estimating the sample cut at the same height is a
basic requirement for radar QPE to represent the actual rainfall distribution
on the ground. The radar beam blocked by the mountain is a serious problem
for the low angle observation. The radar beam angle has to be elevated to
avoid the blockage. However, doing this introduces another problem: rainfall
distribution at higher heights is different from that at the surface and
varies greatly according to the precipitation type (Zhang et al., 2012).
Errors due to radar system calibration and uncertainty in hydrometeor's DSD
(drop size distribution) also decrease the accuracy of rainfall estimates.
Therefore, the combination of radar and rain gauges to provide accurate
rainfall estimates in complex terrain is attracting increasingly more
interest for improving warnings of future precipitation and situational
awareness (Willie et al., 2017). Furthermore, debris-flow-triggering events
are often related to high precipitation gradients of storms which occur for a
short duration and are on a small scale (Nikolopoulos et al., 2015).
Considering this, raw S-band radar reflectivity data are used to estimate
rainfall and assess the impact of estimation errors on the identification of
the I–D threshold over the study area.
The main aim of this study is to merge the radar QPE, thereby improving its
estimation over complex terrain, and to assess the impact of rainfall estimate
accuracy on the identification of I–D threshold over the study area. To
do that, a series of accuracy-improving measures have been adopted including
a hybrid scan mode, a vertical reflectivity profile (VPR) correction, a
mosaic of reflectivity, a combination of rainfall–reflectivity (R-Z)
relationship for convective and stratiform rainfall, and rainfall bias
adjustment with Kalman filter (KF). Three radar rainfall estimation scenarios
are evaluated with the rain gauge observations for six debris-flow-triggering
rainfall events to validate the accuracy of radar estimate. I–D thresholds
are identified from 519 rainfall-induced debris flow events with the
frequentist method (Brunetti et al., 2010; Peruccacci et al., 2012). Another
aim of this study is to understand the impact on the I–D identification
due to spatial variability of rainfall observation. Rain gauge observations
nearest to the debris flow within 10 km and radar observations at the rain
gauge locations are used to get the I–D relationship.
Location and topography of the study area. Asterisks show the
location of Chengdu and Mianyang S-band weather radars which
monitor the study area within 150 km (dash black circle) from the radar
location. Rain gauges in the study area are marked with black triangles and
mostly deployed in the valley. The two blue circle dots are the epicenter of
the
Ms 8.0 Wenchuan earthquake on 12 May 2008 and the Ms 7.0 Lushan earthquake on
20 April 2013.
Land use map (a) and lithology map (b) for the
study area.
Study domain and data
The study area is located in Sichuan in southwest China, which
consists of 16 administrative districts and counties. The area of study is
about 38 000 km2 and occupies nearly 8 % of the land area of
Sichuan (see Fig. 1). This area was strongly affected by the Ms 8.0
Wenchuan earthquake which occurred on 12 May 2008 and the Ms 7.0 Lushan
earthquake which occurred on 20 April 2013. In the following years, debris
flow happened frequently. During the period from 2012 to 2014, the debris
flow occurring in this area accounted for 58.3 % of the annual debris flow events which occurred in the entire province. The area is in the
transitional zone of the Qinghai–Tibet Plateau to the Sichuan Basin. Terrain
changes steeply and the average altitude above sea level (a.s.l.) for this
area is between 500 m and 6 km. The geological structure of the study area
shows a northeast to southwest orientation. The rocks over this region are
mainly comprised of volcanic rocks, mixed sedimentary rocks, siliciclastic
sedimentary rocks, carbonate sedimentary rocks, acid plutonic rocks,
intermediate volcanic rocks, intermediate plutonic rocks, unconsolidated
sediments, metamorphic rocks, basic plutonic rocks and pyroclastic rocks.
Figure 1a shows the lithological map. Quaternary deposits were distributed in
the form of river terraces and alluvial fans. Owing to frequent tectonic
activities, most of the gully is steeply sloped over this area, as shown in
Fig. 2b. The main land use types in this region are mixed forest,
cropland and grassland, as shown in Fig. 2a. Potential debris flow watersheds
over the study area were extracted from morphological variables, using the
logistic regression method. Berenguer et al. (2015) simplified the
geomorphological variables, as the watersheds maximum height
(hmax), mean slope (smean), mean aspect (θmean) and Melton ratio (MR) are the variables
with the smallest overlapping areas for assessing the susceptibility of the
watersheds. The hmax, smean, θmean and MR were retrieved from DEM data. Combined
with the debris flow occurrence over this area during 3 years, the potential
susceptibility map was calculated with the logarithm regression method, as
shown in Fig. 3. The identification results show that there are 673 potential
debris flow watersheds in this region.
Morphology and potential debris flow watersheds map over study
area: (a) slope; (b) aspect; (c) potential debris flow
watersheds (gray polygon) with debris flow observation (blue circle).
The climate type of the study area is humid subtropical. The monthly
precipitation distribution is commonly affected by the plateau monsoon, the
East Asian monsoon and complex terrain. The mean annual rainfall over the
central and southern parts of this region varies from 1200 to 1800 mm,
sometimes even reaching 2500 mm (Xie et al., 2009). The mean annual rainfall
over the western part of this area is less than 800 mm. The northern and
southwestern areas of this region are in the transition zone from hot dry to
humid climates, with mean annual precipitation ranging between 800 and
1200 mm.
The area is monitored by two well-maintained S-band Doppler weather radars
(see Fig. 1). One is deployed in Chengdu city at an altitude of
596 m a.s.l. and the other one is deployed at Mianyang city at a height
of 557 m a.s.l. Both of the radar systems have same system specifications,
which can be seen in Table 1. The system provides radar rainfall estimates at
a radial range resolution of 300 m and an angular resolution of 1∘.
There is a rain gauge network consisting of 551 gauges equipped at the
meteorological surface station in the study areas. The number of rain gauges
seems to be a lot, but most of them are deployed at the valleys. The density
of rain gauges is severely scarce at the high altitude of the mountains,
resulting in observation gaps where the debris flow initially takes place.
The average altitude above sea level of those rain gauges is far lower than
3 km.
Characteristics of S-band Doppler weather radar.
ItemsValueWavelength10.4 cmPolarized modehorizontalAntenna gain45First side lobe level-29 dBcPeak transmitted power750 kWNoise figure4 dBDynamic range90 dBRange resolution300 mVolume scanning elevation0.5, 1.5, 2.4, 3.4, 4.3,6.0, 9.5, 14.5, 19.5∘Altitude above sea level595 m for Chengdu siteof radar location557 m for Mianyang siteMethodsRadar-accumulated rainfall estimation methods
S-band weather radar has a unique advantage of being unaffected by
attenuation, as it is subjected to Rayleigh scattering for almost all
hydrometeors. However, in complex terrain conditions, S-band radar
observations still face serious challenges. The main problem comes from
ground clutter and severe beam blockage, resulting in inaccurate estimates of
radar rainfall. A number of signal processing techniques have been developed
to detect and remove clutter and anomalous propagation, including fuzzy
logic, ground echo maps and Gaussian model adaptive processing (GMAP) filters (Harrison et al., 2000; Berenguer et al., 2006; Nguyen and Chandrasekar,
2013). For the radar data used in this study, ground clutter is filtered with
the GMAP algorithm configured in the Vaisala Sigmet digital processor.
Furthermore, in order to overcome the beam blockage and improve the rainfall
estimation accuracy, radar data are corrected concerning the following
issues: (i) beam shielding and hybrid scan, (ii) vertical profile of
reflectivity, (iii) mosaic of hybrid scan reflectivity, (iv) combination of
reflectivity rainfall relationship and (v) rainfall bias adjustment.
Blockage ratio of beam shielding for the radar main lobe beam and
hybrid scan map. Panels (a)–(c) represent the blockage
ratio of Chengdu radar at elevations of 0.5, 1.5 and 2.4∘,
respectively. Panels (e)–(g) represent the blockage ratio
of Mianyang radar at elevations of 0.5, 1.5 and 2.4∘, respectively.
Hybrid scan maps for Chengdu (d) and Mianyang (h) are merged as long as the blockage ratio is
lower than 0.5.
Beam shielding and hybrid scan
The hybrid scan mode is used to form the initial reflectivity field for
rainfall estimate by keeping the radar main beam away from the blockage of
the complex terrain (Zhang et al., 2012). In the study area, the grids with
0.36 km2 resolution on the ground are aligned with radar bins of each
elevation angle. The blockage coefficients of the low elevation angles at
0.5, 1.5 and 2.4∘ are calculated according to the digital elevation
model (DEM), earth curvature, antenna pattern and the wave propagation model
(Pellarin et al., 2002; Krajewski et al., 2006). The blockage ratio
distribution of two S-band radars can be seen in Fig. 4. There is almost no
topographical shielding in the near-field within a distance of 50 km from
each radar. The main factor considered in the hybrid scan within 50 km is to
meet the estimated rainfall from the same vertical height as much as
possible. Thus the area within 20 km from radar is assigned with elevation
angle of 3.4∘, the area from radar between 20 and 35 km is assigned
the elevation angle of 2.4∘ and the area from radar between 35 and
50 km is assigned the elevation angle of 1.5∘. It is assigned with
the elevation angle of 0.5∘ by default when there is no blockage over
50 km distance from the radar. The terrain transforms from plain land to a
mountainous region over about 70 km westward of each radar. At this region
the altitude rises sharply, and the elevation angle of 0.5∘ is
totally obscured. Therefore, the lowest angle at which the blockage ratio
does not surpass 0.5 is assigned to the aligned grid. Meanwhile, the blockage
ratio is correspondingly used to compensate the energy loss of reflectivity.
The final adaptive-terrain hybrid scan maps are combined as shown in Fig. 4d
and h. It can be seen that most of the study area is covered by the 1.5 and
2.4∘ radar scans.
Vertical profile of reflectivity
Due to the hybrid scan, the radar elevation angle is raised, resulting in the
majority of the observed reflectivity coming from the upper levels of
precipitation profiles. This is quite different from the actual reflectivity
on the ground. It is necessary to account for the reflectivity correction at
the ground level. This study adopts the VPR method to adjust the reflectivity
(Zhang et al., 2012). The processing steps applied in this study are as
follows: (i) convection precipitation is discriminated from stratiform based
on the composite reflectivity > 50 dBz or
VIL > 6.5 kg m-2, where VIL is vertically integrated
liquid water content, an estimate of the total mass of precipitation in the
clouds (Amburn and Wolf, 1997). (ii) The parameterization of VPR is carried
out to generate bright band top, peak, bottom heights and piecewise linear
slopes S1, S2 and S3 (see Fig. 5). (iii) Observed reflectivity
is adjusted based on the parameterized VPR to piecewise extrapolate the
corresponding reflectivity at the ground. Figure 5 shows a sample scatter
plot of the vertical reflectivity profiles from 11:30 to
12:30 UTC+8 on 21 July 2012.
Impacted by the temperature, air dynamics, particle size and phase are
changed along the vertical falling. Figure 5 shows the vertical profile of
reflectivity varied approximately as three piecewise linear sections.
Altitude is one the critical factors affecting the atmosphere physics
parameters and the performance of VPR. The areas of study are classified into
two types, region types I and II, in relation to the height from the
ground (≤ 1.5 km for region type I and > 1.5 km for
region type II) and the distance from the radar (≤ 100 km for region
type I and > 100 km for region type II). Figure 6 shows the
identification results for both radars. Apart from the VPR adjustment, these
two kinds of regions are assessed during the validation of radar QPE in order
to understand the actual impact of distance and height of radar observations
on the rainfall estimation.
A real sample of VPR model processed in the study on 21 July 2012.
The blue circle represents azimuthal mean of reflectivity over 1 h. The
orange line represents the idealized VPR with piecewise linear slope α, β and γ. The horizontal blue line is the bright band (BB)
top and dashed blue line is BB bottom. The solid red line and dashed red
line are BB peak and the 0 ∘C height, respectively.
The height from the ground of hybrid scan for two S-band
radar (a) radar located at Chengdu (b) radar located at
Mianyang. The regions surrounded by green dash lines meet the condition of
that the height from the ground is 1.5 km below and the distance from radar
is inner 100 km and is recognized as region type I. The regions surrounded
by the red dash lines represents the area under the opposite condition and is
recognized as region type II.
Mosaic of hybrid scan reflectivity
Both S-band radars have common coverage areas where reflectivity data
should be mosaicked to construct a large-scale sensing for rainfall events.
Taking the distance and altitude as weighing parameters, the mosaic formula
is defined as
ZM=∑iwi×ki×Zi∑iwi×ki,
and
wi=exp-di2L2,ki=exp-hi2H2.
Here, ZM represents the mosaicked hybrid scan reflectivity,
Zi is the single radar hybrid scan reflectivity, i is the radar index,
w is weighing component for the horizontal weighting and k is weighing
component for the vertical weighting. The variable d is the distance between
the analysis grid and the radar, and h is the height above the ground of
the single radar hybrid scan. The parameters L and H are
scale factors of the two weighting functions.
Combination of rainfall relationship
Rainfall rates are calculated from radar reflectivity by a power law
empirical relationship called the R-Z relationship (Austin, 1987;
Rosenfeld et al., 1993) and, theoretically, the R-Z relationships should be
adjusted when the DSDs change over the rainfall
duration. However, it is still a challenge to obtain fine spatial
distribution of DSDs with changes of time over complex terrains. This study
adopts the two widely verified R-Z relationships defined as
Z=300R1.4 for convective precipitation (Fulton et al., 1998) and Z=200R1.6 for stratiform (Marshall et al., 1955), and the rainfall
type is identified during VPR processing.
Rainfall bias adjustment
The errors of the R-Z relationship mainly come from DSD variation, radar calibration errors, etc. (Berne and
Krajewski, 2013), so the rainfall biases change over time. The mean field bias
correction is a method to calculate the ratio of the means of radar estimate
and the rain gauge observation (Anagnostou and Krajewski, 1999; Chumchean et
al., 2003; Yoo and Yoon, 2010). In this study, the bias is calculated based
on hourly radar rainfall accumulation and rain gauge accumulated observation.
It is defined as
BIAS=1N∑iNri1N∑iNgi,
where BIAS is mean rainfall bias in 1 h, g is 1 h accumulated rainfall of
rain gauge, i is rain gauge index, r is the radar-based 1 h accumulated
rainfall over the ith rain gauge and N is the total number of rain
gauges. As described above, the density of rain gauge deployment over the
mountainous area is relatively scarce. Therefore the precipitation measured
by individual gauges at high and low altitudes may lead to overestimation and
underestimation, respectively. Therefore, the KF is adopted to
alleviate the measurements noise of the bias
(Ahnert, 1986; Chumchean et al., 2006; Kim and Yoo, 2014).
The basic steps of KF in this study are as follows.
State the estimate prediction:BIASPn=BIASKFn-1,
where BIASP represents the bias prediction, BIASKF represents the bias estimate update and n is
discrete time.
State the estimate error covariance prediction:PPn=F2×PKFn-1+Q,
where PP represents the bias estimate error covariance
prediction, PKF represents the bias estimate error covariance
update and Q represents covariance function of the system error.
Calculate the Kalman gain:Gn=PPn×PPn+S-1,
where G represents the Kalman gain. S represents covariance function of
the measurement error.
Update the state estimate:BIASKFn=BIASPn+Gn×BIASmn-BIASPn,
where BIASm represents the bias measurement.
Update the estimate error covariance:PKFn=1-Gn×PPn.
It is assumed that the variation of the real bias within each hour is
negligible, and the initial estimator for mean field radar rainfall logarithmic
bias and its error variance are assumed to equal their updated values, which
are, respectively, BIASKF0 and PKF0.
Rainfall thresholds for the possible initiation of debris flows are
identified according to the I–D power law relationship (Guzzetti et al.,
2007), it is defined as follows:
I=αD-β.
Calculating the event duration (D) and the average intensity (I) requires
the start and end times of the rainfall event. The duration and intensity of
each debris flow can be directly identified with the time-sequential radar
rainfall estimate. These times are determined by an interval of at least
24 h, rain rates of less than 0.1 mm h-1 (Guzzetti et al., 2008;
Marra et al., 2014) or corresponding radar reflectivity of less than
10 dBz to separate two consecutive rainfall events. The parameters of a
and β are estimated with the frequentist method (Brunetti et al.,
2010).
In order to illustrate the impacts of radar rainfall estimate on I–D
threshold, basic procedures of the frequentist method are applied to radar
rainfall accumulation and are described below:
Radar-identified rainfall durations and average intensities are log
transformed as log(I) and log(D). Both of them are fitted
by least-squares method to form a linear equation as log(If)=log(α50)-βlog(D), where α50
and
β are the fitted intercept and slope, respectively.
For each debris flow, the difference δ(D) between
the actual rainfall average intensity log[I(D)] and the
corresponding fitted intensity value log[If(D)] is
calculated: δ(D)=log[I(D)]-log[If(D)].
The probability density function (PDF) of the δ(D)
distribution is determined through kernel density estimation and furthermore
fitted with a Gaussian function, which is defined asfδ=a×exp-δ-b22c2,
where a > 0, c > 0 and a, b and
c∈R.
The threshold for expected minimum exceedance probability (Pmep)
is determined by PDF function, as∫-∞δmepf(δ)dδ=Pmep,
where δmep is the intercept parameters. δmep can be resolved through Eq. (12) for given Pmep
and
then the αmep corresponding to the Pmep
is calculated asαmep=α50expδmep.
Finally, αmop and β are the best-fitted parameters
for exceedance probabilities Pmep.
The minimum exceedance probability is set to 5 % for this study.
Images of radar-estimated rainfall accumulation for the six rainfall
events (a–f). Circles represent the location of triggered
debris flows. Events are shown in chronological order:
(a) 9 July 2012; (b) 21 July 2012;
(c) 17–18 August 2012; (d) 19 June 2013;
(e) 8–12 July 2013; (f) 10, 12 July 2014.
Characteristics of the rainfall events.
EventDateNumber ofEvent durationEvent durationMax. rainfallMax. rainfallno.triggeredby rainby radaraccumulation byaccumulation bydebris flowsgauge (h)(h)rain gauge (mm)radar (mm)19 Jul 20129121117.529.6221 Jul 20129101229.323.6317–18 Aug 201220074919.2195.8419 Jun 20131551255.3101.858–12 Jul 20132615573562.2416.9610–12 Jul 201425202128.517.8Events, results and discussion
Six debris-flow-triggering rainfall events which occurred in the area of
study between 2012 and 2014 are analyzed. Those events happened at the most
severely earthquake-affected region during rainy season and triggered a total
of 519 debris flows that caused casualties and extensive property damage.
Table 2 summarizes the characteristics of the rainfall events. Three events
occurred in August, two events occurred in July and one occurred in June.
These events are deemed to be representative of the debris-flow-triggering
precipitation in the region during the rainy season. The event duration and
maximum rainfall accumulation are also retrieved by the rain gauge nearest to
debris flow location and radar observations. The identification of the
rainfall event was determined by an interval of at least 24 h, during which
the rain rate is less than 0.1 mm h-1 (Guzzetti et al., 2008; Marra et
al., 2014). Table 2 indicates that the durations and rainfall accumulations
identified by gauge and radar are different due to the precipitation type and
density of rain gauges. The identification differences of event nos. 1, 2 and
6 between gauge and radar are not as large as event nos. 3, 4 and 5. From
Fig. 7, showing radar-estimated rainfall accumulation for the six rainfall
events (the improving measures described below are applied in Fig. 7), it can
be seen that the precipitation of event nos. 3, 4 and 5 is dominated by
convection and the strong core of rainfall regions is located in the
high-altitude area where rain gauges are relatively scarce. A few debris flow
events occurred in the long range, approaching radar detection edges, while the rainfall measured
there was low. This may be caused by the decreasing resolution at long radial
range. In following section, rainfall estimation accuracy, I–D, the
distance and height are considered as evaluation factors to assess the
radar-based rainfall estimate.
Considering the accuracy and robustness of the I–D threshold of the
debris flow are determined by the accuracy of rainfall observation and
positioning, a series of processing steps including hybrid scan, VPR correction, a
combined R-Z relationship and mean bias adjustment are performed on six
rainfall events to improve the accuracy of radar-based accumulated rainfall.
In order to evaluate the overall performance and verify the impact on I–D
threshold due to rainfall accumulation accuracy, the assessment was performed
on three scenarios of radar-based estimates: scenario I, the estimate
from raw data of hybrid scan without VPR and bias adjustment; scenario II,
the estimates with VPR adjustment after scenario I; and scenario III, the
estimates with rainfall bias correction after scenario II. According to
rainfall estimate evaluation, I–D thresholds are derived from those
scenarios and also assessed with regard to accuracy and spatial resolution.
Scatter plots of radar and rain gauge event–rainfall
accumulations. (a) Scenario 1: radar estimate from hybrid
scan. (b) Scenario 2: radar estimate from hybrid scan and
VPR. (c) Scenario 3: radar estimate through the hybrid scan, VPR and
bias correction.
The comparison of radar and rain gauge for each estimate
scenario.
CriteriaScenario I (hybrid scan) Scenario II (VPR) Scenario III (bias adjustment) RegionRegionAll studyRegionRegionAll studyRegionRegionAll studytype Itype IIregionstype Itype IIregionstype Itype IIregionsNSE (%)46.45050.745.849.046.143.547.244.0NMB (%)-40.9-42.8-41.1-17.1-21.2-18.61.710.81.91CORR0.800.770.780.820.770.800.850.820.84Assessment of rainfall estimation accuracy
The accuracy of the radar-based rainfall event accumulation is assessed
with the rain gauge observations. In order to perform an evaluation, a set of
criteria is calculated including normalized standard error (NSE), normalized
mean bias (NMB) and correlation coefficient (CORR), defined as
NSE=1N∑iNri-gi1N∑iNgi×100%,NMB=1N∑iNri-gi1N∑iNgi×100%,CORR=∑iNgi-g‾ri-r‾∑iNgi-g‾2∑iNri-r‾2,
where NMB and NSE are in percent, CORR is dimensionless, ri and gi represent the rainfall accumulation from radar and gauge and N is
the total sampling number. The statistical criteria comparisons between
rain gauges and the three radar
estimate scenarios are shown in Table 3, and the scatter plot of radar-based
estimates and rain gauge rainfall observations is shown in Fig. 8. The
comparison of scenario I indicates that the NSE, NMB and CORR of the study
areas are 50.7, -41.1 % and 0.78, respectively. The radar-based rainfall
is underestimated. The linear ratio is estimated from linear regression of
radar rainfall estimation and rain gauge observation, with the predefined
intercept of zero. The linear ratio approximates to 1 when radar-based
rainfall estimation is consistent with rain gauge observation. The linear
ratio of rainfall observation between radar and gauge for scenario I is 0.51,
as shown in Fig. 8a. The reason for the underestimation is the systematic
bias and uncertainty of reflectivity on the ground. From the comparison of
two types of regions, it can be observed that the NSE, NMB and CORR of region
type I are relatively better than region type II. It is revealed that
improved measures are needed for the hybrid scan estimate.
The comparison of scenario II indicates that the NSE, NMB and CORR for the
study areas are 46.1, -18.6 % and 0.80, respectively. This is an
improvement over scenario I. The radar-based rainfall is also underestimated
through the VPR adjustment, and the linear ratio of rainfall observation between
radar and gauge is 0.76, as shown in Fig. 8b. This means rainfall biases
still exist in the estimate. The NSE and CORR of region type I are also
slightly better than region type II.
The comparison of scenario III indicates that the NSE, NMB and CORR of the entire
study area are 44.0, 1.91 % and 0.84, respectively. The linear ratio of
rainfall observation between radar and gauge is 0.98, as shown in Fig. 8c,
and this means the consistency between rainfall and radar observation is
achieved through the KF-based bias correction. Figure 9 shows the
average and covariance of bias estimation by KF and mean field
bias method for six rainfall events. The CORR and NSE improvement also
verifies
the efficiency of the KF for radar QPE in mountainous areas. Kalman
filtering frees the entire rainfall event estimate of large significant
overestimation or underestimation.
The average and covariance of bias estimation by Kalman filter and
mean field bias method for six rainfall events.
Scenario III provides the optimum rainfall estimation for this study. In the
following, all three scenarios are used to assess the impact of QPE
accuracy on I–D relationship identification.
Intensity–duration thresholds based on radar QPE
The radar rainfall estimates with high spatial resolution can retrieve
rainfall duration and average intensity for each rainfall-triggered debris
flow, so an abundant of sample data are captured to induce the I–D
relationship. Scatter distribution of event duration–intensity for the three
radar-estimated scenarios is shown in Fig. 10. Comparisons of scatter
distribution between scenarios I, II and III indicate that the average rainfall intensity and duration are
incrementally increased when applying the improvement measures. The PDF
estimations reveal that the number of positive differences δ(D) is
more than the number of negative differences. This can be accounted for by
storm triggering, which is relatively dominant. The parameters of the
Gaussian function are summarized in Table 4. Parameter a incrementally
decreases. When applying the improvement measures, parameter c has the
opposite trend and parameter b randomly changes in a small range around
zero.
The parameters of Gaussian fitting, which are used by the frequentist
method to account for I–D threshold.
The I–D threshold derived from the scenario III is 10.1D-0.52 . It
is higher than the other two I–D thresholds derived from scenario I and
scenario II, due to application of accuracy improving measuring.
Scatter plots of radar and rain gauge event–rainfall accumulation
and probability density functions (PDFs). Panels (a), (b) and (c) are
the scatter plots of scenario I, II and III,
respectively. Panels (d), (e) and (f) are the Gaussian
fitted PDF of scenario I, II and III, respectively.
Event–rainfall scatter plots of rain gauges nearest to debris flow
locations and radar-based estimate from scenario III over the same location
of rain gauge.
Comparison with intensity–duration thresholds from rain gauge
observations
In order to analyze the impact of the spatial sampling variability on
identification of I–D threshold for radar estimates and rain gauge
observations, I–D thresholds are derived from the rain gauge nearest to the
debris flow and radar estimates at the corresponding co-location of the rain
gauge (Marra et al., 2014). There are some same predefined conditions for
comparison: (1) duration times are identified separately by two kinds of
sensors, rainfall duration time is required to be more than 1 h and minimum
mean rainfall rate is 0.1 mm h-1. (2) The maximum distance from debris flow location is less than 10 km. (3) The identification of I–D threshold
is calculated from frequentist methods with exceedance probabilities of
0.5 %. Firstly, the event's rainfall accumulation is compared between rain
gauge observations nearest to the location of debris flows and radar
estimates at the location of the corresponding rain gauge. The scatter plot
of rain gauge and radar estimates is shown in Fig. 11. The corresponding
metrics are calculated. The CORR is 0.88, NMB is 17.07 %, NSE is
28.32 % and the linear ratio is 1.13, indicating that rainfall observations
from the rain gauge nearest to the debris flow location and radar estimates at
co-location have the tendency of consistency. The I–D thresholds are
derived from rain gauge and radar estimates. Scatter plots of I–D pairs
are shown in Fig. 12. The I–D threshold estimated from rain gauges is I=5.1D-0.42. The other I–D threshold estimated from radar is
I=5.8D-0.41. Both I–D thresholds seem slightly lower than
I=10.1D-0.52, since the scarce gauge network did not capture the strong
core of rainfall which triggered the debris flow. It is interesting to note
that I–D thresholds of both radar and rain gauge are very similar,
although there are some measurement errors between them, as shown in Fig. 11.
Intensity–duration thresholds (black line) derived
from (a) rain gauges nearest to debris flow locations
and (b) radar rainfall estimation at the same location of the rain
gauges nearest to the debris flow.
Scatter plot of relative changes versus distance. Blue circles
represent relative change between radar estimate at debris flow location and
rain gauge observation nearest to debris flow location. Red asterisks
represent relative change between radar estimate at debris flow location and
radar estimate at the co-location of the nearest rain
gauge. (a) Accumulated rainfall relative
change. (b) Duration relative change. (c) Rainfall intensity relative change.
The metric for assessing the relative changes of the accumulated
rainfall, duration and rainfall intensity versus distance.
FactorsRain gauge observation nearest to debris flow location versus radar estimate at debris flow locationRadar estimate at the co-location of rain gauge versus radar estimate at debris flow locationAccumulated rainfall relative change (ARRC)ARRCgs=∑i=1N(s)Rdfi-Rgi∑i=1N(s)Rdfi×100%ARRCrs=∑i=1N(s)Rdfi-Rri∑i=1N(s)Rdfi×100%Duration relative change (DRC)DRCgs=∑i=1N(s)Ddfi-Dgi∑i=1N(s)Ddfi×100%DRCrs=∑i=1N(s)Ddfi-Dri∑i=1N(s)Ddfi×100%Rainfall intensity relative change (RIRC)RIRCgs=∑i=1N(s)Idfi-Igi∑i=1N(s)Idfi×100%RIRCrs=∑i=1N(s)Idfi-Iri∑i=1N(s)Idfi×100%
Note: R represents accumulated rainfall for debris flow event,
D represents duration for rainfall event and I represents the mean intensity
for rainfall event. The variables with subscript df, g and r
represent the observation from radar at debris flow location, rain gauge
nearest to debris flow location and radar at the co-location of the nearest
rain gauge,
respectively. s represents the distance between the nearest rain gauge
location and debris flow location with the range resolution of 300 m. N(s)
represent the number of rain gauge observation for debris flow at the
distance of s.
Impact of rainfall spatial variation on intensity and duration
The accumulated rainfall, duration and rainfall intensity identified from the
nearest rain gauge probably are different from the realities occurred at the
debris flow location, since the rainfall varies in space especially for
convective precipitation with sharp variation in short distance. The observed
rainfall differences rely on the distance from the nearest rain gauge to the
debris location and could be considered as rainfall spatial change. To this
end, relative changes of the accumulated rainfall, duration and rainfall
intensity versus distance are calculated from the comparisons with the
radar-based estimate at the location of debris flow. The metrics for
evaluating relative change versus distance are defined in Table 5. There are
also some predefined conditions for the comparison of relative changes versus
distance. (1) The radar rainfall estimations used for comparison are all from
scenario III. (2) The radar rainfall estimations and duration identification at
the debris flow location are considered as the referred value. (3) The maximum
distance from debris flow location to the nearest rain gauge is predefined
within 10 km and the distance resolution is set equal to the range resolution of 300 m of the China New Generation Doppler Weather
Radar (CINRAD). (4) In order to assess the rainfall spatial
variation using a multi-sensor, the radar-based estimate at the co-location of
the nearest rain gauge, as well as rain gauge observations, is also compared
with the radar-based estimate at the location of debris flow.
Parameters of the identified ID thresholds and relative changes.
αα-αS3αS3×100%ββ-βS3βS3×100%Scenario I7.62-24.50.6728.8Scenario II8.7-13.80.43-17.3Scenario III10.10.00.520.0Rain gauges5.1-49.50.42-19.2Radar estimate at the co-locationof the nearest rain gauge5.8-42.60.41-21.2
Note: αS3 and βS3 are α and
β, respectively, estimated from scenario III.
The metrics of accumulated rainfall relative change (ARRC), duration relative
change (DRC) and rainfall intensity relative change (RIRC) are calculated for
the nearest rain gauge and radar estimate at the co-location.
The results of ARRC, DRC and RIRC versus distance are shown in Fig. 13. The
main findings from the evaluation results are summarized as follows:
The results of ARRC, DRC and RIRC all have an enlarging tendency along
with the increasing distance. The maximum ARRC, DRC and RIRC for rain gauge
observations are 42.2, 41.67 and 55.88 %, respectively. The maximum ARRC,
DRC and RIRC for radar-based estimate at the co-location of the nearest rain
gauge are 43.33, 41 and 45.2 %, respectively.
Nonlinear regression is applied for ARRC, DRC and RIRC versus distance to
investigate the average tendency, as shown in Fig. 13. The regression
curves of ARRC and DRC for rain gauge and radar are similar,
within 10 and 4 km, respectively, indicating the observed difference as a
function of distance is dominated by the natural spatial variability and the
potential impact from differences in rainfall estimates coming from different
sensors is secondary, especially for estimating duration.
It is clear from the above discussion that the rainfall estimation accuracy
and spatial variation impact the identification of I–D threshold. We
further take the α and β estimated from scenario III as a
reference value and calculate the relative
change of α and β for each scenario, as shown in Table 6. The
relative change of α for scenarios I, II and III is -24.5, -13.8
and 0 %, respectively. The relative change of β for scenarios I,
II and III is -28.8, -17.3 and 0 %, respectively. It is indicated
that improving the accuracy of rainfall estimate is able to decrease the
relative changes of α and β. Concerning rainfall spatial
variation, the relative change of α for the nearest gauge observation
and radar-based estimate at the co-location is -49.5 and -42.6 %,
respectively. The relative change of β for the nearest gauge
observation and radar-based estimate at the co-location is -19.5 and
-21.2 %, respectively. The relative change of α is remarkably
larger than the one derived from radar-based estimate on the debris flow
location, but the differences of α and β for rain gauges and
radar-based estimate at the co-location are not significant.
I–D thresholds determined for this study (red line) and those
of various other studies. G is global and R is region. G-1: Guzzetti et
al. (2008); G-2: Caine (1980); R-1: Wenchuan earthquake area (Zhou and Tang,
2014); R-2: Qingping, a region in Wenchuan earthquake area (Tang et al., g120
2012); R-3: Wenchuan earthquake area (Guo et al., 2016a); R-4: Italy (Marra
et al., 2014); R-5: central Taiwan (Jan and Chen, 2005); R-6: Japan
(Jibson, 1989).
Comparison with previous results
The I–D threshold for the study regions is compared with other global
and
regional thresholds in the literature. It can be seen from Fig. 14 that the
threshold obtained in this work (red in Fig. 14) falls in the range of other
I–D thresholds. The results were also compared with the rainfall
thresholds previously proposed in the Wenchuan earthquake area (Tang et al.,
2012; Zhou and Tang, 2014; Guo et al., 2016a). Our result lies in the middle
range of them. The difference comes from the database we used, the radar data
which are used to fill the observation gap of rain gauges, and the
identification method of I–D threshold that was also different due to a
different exceedance probability. The I–D threshold of this study was
cross-checked with that proposed in the area affected by the Chi-Chi earthquake in
Taiwan (Chien Yuan et al., 2005), mainly due to the climatic differences
like storm occurrence duration and intensity. The result nearly overlapped
with the one proposed in Adige, Italy (Marra et al., 2014).
Guzzetti et al. (2008) updated the global I–D threshold, which is significantly lower than the global threshold first proposed by Caine (1980).
Our result is higher than that for the world (Guzzetti et al., 2008).
Summary
The main purpose of this paper is to evaluate the debris flow occurrence
thresholds of the rainfall intensity–duration in the earthquake-affected
areas of Sichuan over the rainy seasons from 2012 to 2014. The
paper calculates the intensity–duration threshold from radar-based rainfall
estimates, which is different from the common method of using rain gauge
observation. Radar observations have high spatial resolutions sensitive to
convective precipitation, which is a critical issue for rain gauge
observation due to its scarcity and low-altitude deployment over mountainous
areas. However, the accuracy of radar-based QPE over complex areas is
affected by the terrain and remains a challenge for hydrological
application. The following work was done to draw the conclusions.
Two S-band Doppler radars covered the study area. Radar
observations for six rainfall events were processed with a series of
mountain-oriented QPE algorithms, including a terrain-adapted hybrid scan,
VPR correction, a reflectivity mosaic, a combination of R-Z
relationships a rainfall bias correction. Three types of estimation from
radar are performed and compared with rain gauge observations to validate the
accuracy. The results show that the combination of all correction
procedures reduces the bias to 1.91 % and the NSE to 44 % and
improves the correlation coefficient to 0.84 and the linear ratio to 0.98.
Intensity–duration rainfall thresholds for the triggering debris flow are
calculated with a frequentist approach. The I–D threshold of
I=10.1D-0.52 is derived from the KF-corrected radar
estimates. The accumulated rainfall is lower than rain gauge observations and
the derived I–D is also underestimated. The hybrid scan, VPR correction
and combination of R-Z relationship are strongly required.
The I–D deduced from rain gauge observations nearest to the
occurrence of debris flow is highly similar to the one deduced from the radar
estimates at the same location as rain gauge: I=5.1D-0.42 and
I=5.8D-0.41, respectively. These I–D thresholds are underestimated
due to the rainfall spatial variation and the noncontinuous sampling effect.
Finally, it is clear that radar-based rainfall estimates and thresholds
supplement the monitoring gaps of EWS where rain gauges are scarce. A better
understanding of the relationship between rainfall and debris flow initiation for
earthquake-affected areas can be gained by improving the spatiotemporal
resolution and low-elevation-angle coverage of radar observation, especially
for monitoring the convective storm occurring at the mountains.
The data used in this research can be made available on demand. Please contact the authors for requests.
The authors declare that they have no conflict of
interest.
This article is part of the special issue “Landslide early
warning systems: monitoring systems, rainfall thresholds, warning models,
performance evaluation and risk perception”. It is not associated with a
conference.
Acknowledgements
This research was supported by the National Natural Science Foundation of
China (no. 41505031), the Science and Technology Support Project of Sichuan
(no. 2015SZ0214), China Meteorological Bureau Meteorological
Sounding Engineering Technology Research Center funding, China Scholarship
Council (no. 201508515021), and scientific research funding of CUIT (no. J201603).
We thank the weather bureau of Sichuan for the data services.
The participation of VC is supported by the US National Science Foundation
through the Hazard SEES program. Edited by:
Samuele Segoni
Reviewed by: three anonymous referees
References
Ahnert, P.: Kalman filter estimation of radar-rainfall field bias, Preprints
of the 23rd Conference on Radar Meteorology, 1986.Aleotti, P.: A warning system for rainfall-induced shallow failures, Eng.
Geol., 73, 247–265, 10.1016/j.enggeo.2004.01.007, 2004.
Amburn, S. A. and Wolf, P. L.: VIL density as a hail indicator, Weather Forecast., 12, 473–478, 1997.
Anagnostou, E. N. and Krajewski, W. F.: Real-time radar rainfall estimation.
Part I: Algorithm formulation, J. Atmos. Ocean. Tech.,
16, 189–197, 1999.
Austin, P. M.: Relation between measured radar reflectivity and surface
rainfall, Mon. Weather Rev., 115, 1053–1070, 1987.
Baum, R. L. and Godt, J. W.: Early warning of rainfall-induced shallow
landslides and debris flows in the USA, Landslides, 7, 259–272, 2010.
Berenguer, M., Sempere-Torres, D., Corral, C., and Sánchez-Diezma, R.: A
fuzzy logic technique for identifying nonprecipitating echoes in radar scans,
J. Atmos. Ocean. Tech., 23, 1157–1180, 2006.Berenguer, M., Sempere-Torres, D., and Hürlimann, M.: Debris-flow
forecasting at regional scale by combining susceptibility mapping and radar
rainfall, Nat. Hazards Earth Syst. Sci., 15, 587–602,
10.5194/nhess-15-587-2015, 2015.Berne, A. and Krajewski, W. F.: Radar for hydrology: Unfulfilled promise or
unrecognized potential?, Adv. Water Resour., 51, 357–366,
10.1016/j.advwatres.2012.05.005, 2013.Brunetti, M. T., Peruccacci, S., Rossi, M., Luciani, S., Valigi, D., and
Guzzetti, F.: Rainfall thresholds for the possible occurrence of landslides
in Italy, Nat. Hazards Earth Syst. Sci., 10, 447–458,
10.5194/nhess-10-447-2010, 2010.
Caine, N.: The rainfall intensity: duration control of shallow landslides and
debris flows, Geogr. Ann. A, 62, 23–27, 1980.Chiang, S.-H. and Chang, K.-T.: Application of radar data to modeling
rainfall-induced landslides, Geomorphology, 103, 299–309,
10.1016/j.geomorph.2008.06.012, 2009.
Chien Yuan, C., Tien-Chien, C., Fan-Chieh, Y., Wen-Hui, Y., and Chun-Chieh,
T.: Rainfall duration and debris-flow initiated studies for real-time
monitoring, Environ. Geol., 47, 715–724, 2005.
Chumchean, S., Sharma, A., and Seed, A.: Radar rainfall error variance and
its impact on radar rainfall calibration, Phys. Chem. Earth, 28, 27–39,
2003.
Chumchean, S., Seed, A., and Sharma, A.: Correcting of real-time radar
rainfall bias using a Kalman filtering approach, J. Hydrol., 317, 123–137,
2006.
Cui, P., Zou, Q., Xiang, L.-Z., and Zeng, C.: Risk assessment of simultaneous
debris flows in mountain townships, Prog. Phys. Geog., 37, 516–542, 2013.
David-Novak, H. B., Morin, E., and Enzel, Y.: Modern extreme storms and the
rainfall thresholds for initiating debris flows on the hyperarid western
escarpment of the Dead Sea, Israel, Geol. Soc. Am. Bull., 116, 718–728,
2004.
Fulton, R. A., Breidenbach, J. P., Seo, D.-J., Miller, D. A., and O'Bannon,
T.: The WSR-88D rainfall algorithm, Weather Forecast., 13, 377–395, 1998.Glade, T. and Nadim, F.: Early warning systems for natural hazards and risks,
Natural Hazards, 70, 1669–1671, 10.1007/s11069-013-1000-8, 2014
Guo, X., Cui, P., Li, Y., Ma, L., Ge, Y., and Mahoney, W. B.:
Intensity–duration threshold of rainfall-triggered debris flows in the
Wenchuan earthquake affected area, China, Geomorphology, 253, 208–216,
2016a.
Guo, X., Cui, P., Li, Y., Zou, Q., and Kong, Y.: The formation and
development of debris flows in large watersheds after the 2008 Wenchuan
Earthquake, Landslides, 13, 25–37, 2016b.
Guzzetti, F., Peruccacci, S., Rossi, M., and Stark, C. P.: Rainfall
thresholds for the initiation of landslides in central and southern Europe,
Meteorol. Atmos. Phys., 98, 239–267, 2007.
Guzzetti, F., Peruccacci, S., Rossi, M., and Stark, C. P.: The rainfall
intensity–duration control of shallow landslides and debris flows: an
update, Landslides, 5, 3–17, 2008.
Harrison, D., Driscoll, S., and Kitchen, M.: Improving precipitation
estimates from weather radar using quality control and correction techniques,
Meteorol. Appl., 7, 135–144, 2000.
Jan, C. D. and Chen, C. L.: Debris flows caused by Typhoon Herb in Taiwan,
in: Debris Flow Hazards and Related Phenomena, edited by: Jakob, M. and
Hungr, O., Springer, Berlin Heidelberg, 363–385, 2015.
Jibson, R. W.: Debris flows in southern Puerto Rico, Geol. S. Am. S., 236, 29–56, 1989.Kim, J. and Yoo, C.: Use of a dual Kalman filter for real-time correction of
mean field bias of radar rain rate, J. Hydrol., 519, 2785–2796,
10.1016/j.jhydrol.2014.09.072, 2014.
Krajewski, W. F., Ntelekos, A. A., and Goska, R.: A GIS-based methodology for
the assessment of weather radar beam blockage in mountainous regions: two
examples from the US NEXRAD network, Comput. Geosci., 32, 283–302,
2006.
Marra, F., Nikolopoulos, E. I., Creutin, J. D., and Borga, M.: Radar rainfall
estimation for the identification of debris-flow occurrence thresholds,
J. Hydrol., 519, 1607–1619, 2014.
Marshall, J., Hitschfeld, W., and Gunn, K.: Advances in radar weather,
Adv. Geophys., 2, 1–56, 1955.Nguyen, C. M. and Chandrasekar, V.: Gaussian Model Adaptive Processing in
Time Domain (GMAP-TD) for Weather Radars, J. Atmos. Ocean. Tech., 30, 2571–2584, 10.1175/jtech-d-12-00215.1, 2013.Nikolopoulos, E. I., Borga, M., Creutin, J. D., and Marra, F.: Estimation of
debris flow triggering rainfall: Influence of rain gauge density and
interpolation methods, Geomorphology, 243, 40–50,
10.1016/j.geomorph.2015.04.028, 2015.
Pellarin, T., Delrieu, G., Saulnier, G.-M., Andrieu, H., Vignal, B., and
Creutin, J.-D.: Hydrologic visibility of weather radar systems operating in
mountainous regions: Case study for the Ardeche catchment (France), J. Hydrometeorol., 3, 539–555, 2002.Peruccacci, S., Brunetti, M. T., Luciani, S., Vennari, C., and Guzzetti, F.:
Lithological and seasonal control on rainfall thresholds for the possible
initiation of landslides in central Italy, Geomorphology, 139–140, 79–90,
10.1016/j.geomorph.2011.10.005, 2012.
Rosenfeld, D., Wolff, D. B., and Atlas, D.: General probability-matched
relations between radar reflectivity and rain rate, J. Appl. Meteorol., 32, 50–72, 1993.
Rosi, A., Lagomarsino, D., Rossi, G., Segoni, S., Battistini, A., and
Casagli, N.: Updating EWS rainfall thresholds for the triggering of
landslides, Nat. Hazards, 78, 297–308, 2015.Segoni, S., Battistini, A., Rossi, G., Rosi, A., Lagomarsino, D., Catani, F.,
Moretti, S., and Casagli, N.: Technical Note: An operational landslide early
warning system at regional scale based on space–time–variable rainfall
thresholds, Nat. Hazards Earth Syst. Sci., 15, 853–861,
10.5194/nhess-15-853-2015, 2015.
Shieh, C.-L., Chen, Y., Tsai, Y., and Wu, J.: Variability in rainfall
threshold for debris flow after the Chi-Chi earthquake in central Taiwan,
China, Int. J. Sediment. Res., 24, 177–188, 2009.
Su, P., Wei, F., and Cheng, Z.: Debris flow activity of Mozi Gully after
Wenchuan earthquake on May 12, J. Yangtze River Sci. Res. Inst., 29, 16–22,
2012.
Tang, C., Zhu, J., Li, W., and Liang, J.: Rainfall-triggered debris flows
following the Wenchuan earthquake, B. Eng. Geol. Environ., 68, 187–194,
2009.Tang, C., van Asch, T. W., Chang, M., Chen, G., Zhao, X., and Huang, X.:
Catastrophic debris flows on 13 August 2010 in the Qingping area,
southwestern China: the combined effects of a strong earthquake and
subsequent rainstorms, Geomorphology, 139, 559–576, 2012.
Wang, Q., Kong, Y., Zhang, W., Chen, J., Xu, P., Li, H., Xue, Y., Yuan, X.,
Zhan, J., and Zhu, Y.: Regional debris flow susceptibility analysis based on
principal component analysis and self-organizing map: a case study in
Southwest China, Arab. J. Geosci., 9, 718–735, 2016.Willie, D., Chen, H., Chandrasekar, V., Cifelli, R., Campbell, C., Reynolds,
D., Matrosov, S., and Zhang, Y.: Evaluation of Multisensor Quantitative
Precipitation Estimation in Russian River Basin, J. Hydrol. Eng., 22,
E5016002, 10.1061/(asce)he.1943-5584.0001422, 2017.
Xie, H., Zhong, D., Jiao, Z., and Zhang, J.: Debris flow in Wenchuan
quake-hit area in 2008, J. Mt. Sci., 27, 501–509, 2009.
Yoo, C. and Yoon, J.: A proposal of quality evaluation methodology for radar
data, Journal of The Korean Society of Civil Engineers, 30, 429–435, 2010.
Yu, B., Wu, Y., and Chu, S.: Preliminary study of the effect of earthquakes
on the rainfall threshold of debris flows, Eng. Geol., 182, 130–135, 2014.Zhang, J., Qi, Y., Kingsmill, D., and Howard, K.: Radar-Based Quantitative
Precipitation Estimation for the Cool Season in Complex Terrain: Case Studies
from the NOAA Hydrometeorology Testbed, J. Hydrometeorol., 13, 1836–1854,
10.1175/jhm-d-11-0145.1, 2012.
Zhou, W. and Tang, C.: Rainfall thresholds for debris flow initiation in the
Wenchuan earthquake-stricken area, southwestern China, Landslides, 11,
877–887, 2014.