Download Regional landslide susceptibility: Statistical distribution in space and time.

Nat Hazards
DOI 10.1007/s11069-011-9834-4
ORIGINAL PAPER
Regional landslide susceptibility: spatiotemporal
variations under dynamic soil moisture conditions
Ram L. Ray • Jennifer M. Jacobs • Thomas P. Ballestero
Received: 15 February 2011 / Accepted: 25 April 2011
Ó Springer Science+Business Media B.V. 2011
Abstract Quantification of landslide susceptibility variability in space and time in
response to static and dynamic conditions is a fundamental research challenge. Here, we
identify and apply new modeling and remote sensing observation techniques to statistically
characterize susceptibility distributions under dynamic moisture conditions. The methods
are applied at two study regions: Cleveland Corral, California, US and Dhading, Nepal.
The results show that the temporal variability of safety factors is lower during the wet
season than the dry season, but this variability, when scaled by mean seasonal stability, is
constant annually. Relative variability differs by region with lower variability in Nepal, the
highly susceptible region. L-Moment evaluations indicate that Nepal has a consistent,
regional probability distribution, but that California has two distinct distributions. The
variability in time is not normally distributed for either region. For both regions, transitional characteristic of safety factors show a strong power law relationship between the
average duration and number of periods during which sites are highly susceptible. Because
the mapped landslide locations typically had frequent crossings with brief unstable conditions, a consistent physical mechanism is pointed to as a possible cause of slope failure.
Keywords
Landslide Transitional Safety factor Variability Spatiotemporal
1 Introduction
Shallow slope failures are common throughout the world in mountainous regions (Borga
et al. 1998; Gulla et al. 2008). Landslides, whether they are large or small in size, occur
every year in mountainous regions of the world (Li et al. 2010). Intrinsic variables
R. L. Ray (&)
Department of Civil, Construction and Environmental Engineering, San Diego State University,
5500 Campanile Dr., San Diego, CA 92182, USA
e-mail: [email protected]
J. M. Jacobs T. P. Ballestero
Environmental Research Group, Department of Civil Engineering,
University of New Hampshire, 35 Colovos Rd., Durham, NH 03824, USA
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(topography, geology, soil regolith and engineering properties) and extrinsic variables
(rainfall, fire, glacier outbursts, earthquakes and volcanoes) play critical roles in slope
stability (Dai and Lee 2002; Dahal et al. 2008; Cepeda et al. 2010).
To understand the physical and dynamic processes of instability, it is necessary to
quantify a region’s landslide susceptibility both in time and in space (Wu and Sidle 1995;
Glade 1998; Guzzetti et al. 1999; Stefanini 2004). Extrinsic variable changes can cause a
stable slope to become unstable. Of the extrinsic variables, rainfall is of interest because it
evolves as a transitional process that is highly variable at multiple scales in space and time
and has a strong interaction with the near surface. Rainfall-induced landslides are triggered
by wetting soils which effect a slope’s shear strength and the shear stress (Caine 1980;
Iverson and Major 1987; Rahardjo 2000; Lee 2005; Adler et al. 2006; Meisina and
Scarabelli 2007; Cepeda et al. 2010; Ray et al. 2010a).
Most studies only provide a static representation of landslide susceptibility (Li et al.
2010) or use rainfall characteristics that are indicative of soil wetting dynamics (e.g. spatial
distribution, duration and intensity) to predict landslide initiation (Iverson 2000; Lan et al.
2005; Dahal et al. 2008; Lee et al. 2008; Jaiswal and van Westen 2009; Turner et al. 2010;
Xu and Zhang 2010). However, rainfall alone is not adequate to identify slope instability.
For example, in order for Zezere et al. (2005) to identify the appropriate number of days
used to determine antecedent precipitation, they explicitly differentiated their method
based on landslide type and geo-environmental characteristics. Even for the shallow debris
slide investigated by Jaiswal and van Westen (2009), their envelope curves show considerable variability across a modest-sized region. While these methods have advanced
considerably in regions that have a complete historical database on landslides and rainfall,
it remains a challenge to directly transfer site-specific methods using precipitation data to
other locations.
As a first-order process, slopes can become unstable when intense rainfall rapidly
increases soil water storage (Pelletier et al. 1997). Currently, the characteristics of landslide-prone regions’ soil moisture, the resulting evolution of slope instability in time and
the relative value of additional complexity are areas of active research for hill slope studies
(Jaiswal and van Westen 2009). For example, Talebi et al. (2008) used a hill slope model to
demonstrate that profile curvature effects slope stability magnitude and rates of change
during rain events.
Over longer periods and larger scales, soil moisture dynamics are linked to local vegetation and soil states that may be important to slope stability. While limited data exist for
steep terrain, a few studies have shown that vegetation type and rooting zone depths are
controlled by the evolution of soil moisture (Schwarz et al. 2010; Bathurst et al. 2010) and
the frequency of droughts (Oberhuber et al. 2001; Tosattig 2006). Soil wetting and drying
may also modify soil properties (Pires et al. 2008; Dorner et al. 2009) including cohesion
and porosity (Seguel and Horn 2006; Zemenu et al. 2009). Some of these effects have been
used in dynamic, distributed, physically based models to characterize the evolution of
quasi-static variables, vegetation strength and surcharge and their effects on landslide
susceptibility variability at monthly and annual time scales (Wu and Sidle 1995; Gorsevski
et al. 2006). While challenges remain in the prediction of susceptibility in space and time
because of soil and land cover heterogeneity as well as soil moisture variability (Saha et al.
2005), modelling and observational advancements are progressively reducing that uncertainty (Davis and Keller 1997; Gorsevski et al. 2006).
This study seeks to use a dynamic, distributed, physically based model to capture the
large-scale, temporal evolution of safety factors for hazard-prone regions due to soil water
dynamics. Here, we propose that the characterization of daily soil water and attendant
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safety factor variations over a multi-year period will show distinct slope stability spatiotemporal patterns reflecting regional geo-environmental as well as climatic variables. This
characterization of landslide-prone slopes includes standard statistical moments,
L-moment methods and transition properties of threshold values. Two landslide-prone
regions, Cleveland Corral, California, US and Dhading, Nepal, are used to demonstrate and
contrast these metrics (Fig. 1a, b). Both sites include stable and unstable regions, but differ
by location, terrain, soils and climate.
2 Theory
This paper uses the modified infinite slope stability model to develop landslide susceptibility that directly links vadose zone soil moisture and groundwater (Ray et al. 2010a). The
infinite slope method (Skempton and DeLory 1957) calculates safety factors as the ratio of
resisting forces to driving forces. The infinite slope stability model as adapted by the
several researchers (e.g. Montgomery and Dietrich 1994; van Westen and Terlien 1996;
Acharya et al. 2006; Ray and De Smedt 2009) is
Cs þ Cr
cw tan u
ð1Þ
þ 1m
FS ¼
ce H sin h
ce tan h
where Cs and Cr are the effective soil and root cohesion [kN/m2], ce is the effective unit
soil weight [kN/m3], H is the total depth of the soil above the failure plane [m], h is the
slope angle [°], m is the wetness index [dimensionless], / is the angle of internal friction of
the soil [°], and cw is the unit weight of water [kN/m3]. The effective unit weight is
estimated as
Fig. 1 a Mapped landslide (top) and slope movement (bottom) locations at Cleveland Corral, California in
2006 and b a major catastrophic landslide along Prithvi Highway, Nepal (picture was taken in August, 2003)
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ce ¼
q cos h
þ ð1 mÞcd þ mcs
H
ð2Þ
where q is any additional load on the soil surface [kN/m2] and cd is dry unit soil weight
[kN/m3] for the unsaturated soil layer.
Here, the wetness index follows Ray et al. (2010a) where
m¼
h þ ðH hÞ Sw
H
ð3Þ
where h is the saturated thickness of the soil [m] above the failure plane and Sw is the
degree of soil saturation [cm3/cm3] or vadose zone soil moisture.
The estimated safety factor (FS) values are categorized into stability classes using Pack
et al.’s (1998) and Acharya et al.’s (2006) stability classification system where the four
susceptibility classes are highly susceptible (FS B 1), moderately susceptible
(1 \ FS \ 1.25), slightly susceptible (1.25 \ FS \ 1.5) and not susceptible (stable)
(FS C 1.5). The critical threshold for slope failure occurs when the resisting force equals
the sliding force and the FS = 1 (Skempton and DeLory 1957; van Westen and Terlien
1996; Burton and Bathurst 1998; Acharya et al. 2006; Ray and De Smedt 2009).
Depending on the soil, vegetation and climatic characteristics of the region, a slope may or
may not fail at this critical safety factor value.
Application of the modified infinite slope stability model to time series analyses requires
a dynamic, distributed, physically based model. For this study, we use the VIC-3L model
(Liang et al. 1994) to estimate soil moisture in the unsaturated zone. VIC-3L is a macroscale land surface model that was used to simulate the water budget based on the
climatic, soil and vegetation characteristics. Model details, application and validation are
provided in Ray et al. (2010b). The primary model output are daily, spatially distributed
predictions of saturated zone and vadose zone soil moisture that can be directly used to
determine the wetness index in Eq. 3 (Ray et al. 2010a).
3 Application
3.1 California, United States
The Cleveland Corral study region in the Highway 50 corridor is located in the Sierra
Nevada Mountains, California, USA (Reid et al. 2003). The study area is about 22 by
28 km or 616 km2. Highway 50 is a major road located between Sacramento and South
Lake Tahoe in California (Spittler and Wagner 1998). About 600 landslides were catalogued along the 24-km-long corridor (Spittler and Wagner 1998; Reid et al. 2003). One
major catastrophic landslide occurred in 1983 (Spittler and Wagner 1998). Since 1996,
slope movement and landslides occur infrequently during the winter months. Slope
movement is defined as the transitional slow movement of slope without any slope
failures or landslides. Figure 1a shows one Cleveland Corral hill slope having mapped
landslide and slope movement. Since 1997, the United State Geological Survey (USGS)
has monitored this region using real-time data acquisition systems. The USGS observations found that elevated pore-water pressures and wet soils were coincident with
enhanced slope movement and landslides during the winter (rainy) season (Reid et al.
2003).
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Elevations in this study area range from about 902–2,379 m. Based on the 90-m SRTM
digital elevation model (DEM), slopes in this region range from 0 to 48° with 1.27% of the
area possessing slopes greater than 30°. This study region has considerable variability in
soil texture ranging from clay loam to sandy loam (Table 1). The soil is predominantly
sandy loam (72%). The total soil depth ranges from 0.6 to 1.4 m. The assumed potential
failure plane underneath the soil layer is bedrock. Conifer and wooded grassland are the
dominant land covers: 80 and 14% of the study region, respectively. Some rock outcrops
were also observed along the Highway 50 corridor during the field observation.
The climatic data were obtained from the National Climatic Data Centre (NCDC) from
2003 to 2006 (Table 1). This region has average annual rainfall of 1,101 mm and maximum and minimum temperatures of 19.6 and 5.5°C, respectively. The majority of rainfall
occurs during the winter (725 mm) in this region. This region’s wet season is defined as
January to May.
Table 1 Soil, vegetation, slope
and climatic characteristics of the
California and Nepal study
regions
Area (%)
California
Nepal
Evergreen forest
3.3
1.0
Conifer
79.9
–
Deciduous forest
2.7
–
Woodland
–
50.3
Wooded grassland
14.1
18.2
Land cover
Grassland
–
1.7
Cropland
–
28.8
Soil texture
Loamy sand
–
16.2
Sandy loam
72.0
22.5
Loam
16.0
9.8
Sandy clay
3.0
15.0
Sandy clay loam
–
36.5
Clay loam
9.0
–
0–15
71.2
19.0
15–30
27.5
53.2
30–45
1.2
27.0
45–60
0.0
0.8
1,101
1,624
Slope (°)
Climate
Average annual rainfall (mm)
Average rainfall wet season (mm)
(Jan–May, CA and Jun–Sep, Nepal)
725
1,287
Average daily max. temperature (°C)
19.6
27.0
Average daily min. temperature (°C)
5.5
16.6
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3.2 Dhading, Nepal
The Nepal study area in the Dhading region is one of the seventy-five Nepalese districts.
The transnational Prithvi highway, connecting Kathmandu and Pokhara, runs through the
southern part of the district and parallels the Trishuli River. The study area is about 25 by
14 km or 350 km2. Landslides are frequent during the monsoon season (June to September). Numerous major landslides have occurred along the Prithvi highway over the past
decade (2000–2008) with a major catastrophic landslide at Krishna Bhir in August 2003
(Fig. 1b).
The Nepal study region has distinctly different topography, soil, vegetation and climatic
characteristics from the California region. The Nepal study region is 83% mountainous
terrain and 17% southern alluvial plains. Based on the SRTM DEM, elevations range from
256 to 1,918 m. Slopes in this region range from 0 to 57° with 27.8% of the study region’s
slopes exceeding 30°. The soils are predominantly sandy clay loam (36%) and sandy loam
(22%). Woodland and cropland are the dominant land covers: 50 and 29% of the study
region, respectively. The total soil depth ranges from 1.0 to 1.5 m. The assumed potential
failure plane underneath the soil layer is bedrock.
Rainfall, temperature and wind speed measurements were obtained from the Department of Hydrology, Nepal (Table 1). This region is warmer and wetter than the California
study region. The monsoon season, June to September, averages 1,287 mm of the
1,624 mm average annual rainfall. Nepal’s wet season is defined as June to September.
3.3 Model data
For the California study region, the soil and vegetation data required for the three-layer
variable infiltration capacity (VIC-3L) hydrologic model and the slope stability model
were obtained from States Soil Geographic (STATSGO) database (Soil Survey Staff 2008),
Land Data Assimilation System (LDAS; Mitchell et al. 2004) and from the literature
(Table 2). The STATSGO soil data were obtained in vector format (polygon) and converted into a 90-m raster (grid). For Nepal, soil depth and soil texture were assigned the
values from global and local databases as developed by Ray and De Smedt (2009). The
unit soil weight values (saturated and moist) were calculated from VIC-3L model soil
moisture estimates and literature values of soil porosity and specific gravity of the soils
(Table 2) using methods adapted by Ray et al. (2010a). For both regions, each land cover
class was assigned a root cohesion value adapted from Sidle and Ochiai (2006). Each soil
type was assigned soil cohesion and friction angle values from Deoja et al. (1991). The
slope of the retention curve is from Clapp and Hornberger (1978). Soil bulk density, field
capacity, wilting point and saturated hydraulic conductivity values are from Miller and
White (1998) and Dingman (2002). Slope angle was determined from a 90-m SRTM
digital elevation model (DEM). For both study regions, landslides locations were mapped
in the field using global positioning system (GPS). The field observations identified ten and
twelve landslides locations in California and Nepal, respectively.
4 Analysis methods
For these study regions, the VIC-3L model was applied at a daily time-step from October
2003 to September 2006 using a 0.0083° (*900-m) resolution. The Cleveland Corral,
California, US study region has 900 pixels sized at 0.7 km2 and Dhading, Nepal has 450
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Table 2 List of model parameters and sources by model
Parameters
Sources
Model
Soil cohesion
Deoja et al. (1991)
Slope stability
Soil porosity
Dingman (2002)
Slope stability and VIC-3L
Soil texture
STATSGO
Slope stability and VIC-3L
Soil depth
STATSGO
Slope stability and VIC-3L
Hydraulic conductivity
STATSGO
VIC-3L
Soil bulk density
Dingman (2002)
Slope stability and VIC-3L
Angle of internal friction
Deoja et al. (1991)
Slope stability
Additional load (surcharge)
Ray (2004)
Slope stability
Land cover
University of Maryland
Slope stability and VIC-3L
Root cohesion
Sidle and Ochiai (2006)
Slope stability
Root depth
LDAS
VIC-3L
Root fraction
LDAS
VIC-3L
Vegetation roughness
LDAS
VIC-3L
Vegetation height
LDAS
VIC-3L
Leaf Area Index (LAI)
LDAS
VIC-3L
Rainfall
NCDC, DOH-NP
VIC-3L
Groundwater
USGS
Slope stability
Temperature
NCDC, DOH-NP
VIC-3L
Wind speed
NCDC, DOH-NP
VIC-3L
STATSGO States Soil Geographic, LDAS Land Data Assimilation System, USGS United States Geological
Survey, VIC-3L variable infiltration capacity-3 layers, NCDC National Climatic Data Center, DOH-NP
Department of Hydrology, Nepal
pixels sized at 0.75 km2. The VIC-3L soil moisture values were assigned to the 90-m DEM
pixels using a nearest neighbour approach. This study used soil moisture values approximately at 900-m and all other model parameters at 90-m scales. Using the VIC modelled
soil moisture, groundwater and geotechnical parameters, daily safety factors were calculated for each 90-m DEM pixels using Eqs. 1–3. In total, daily safety factors were
determined for 75,988 pixels in California and 41,800 pixels in Nepal from 1 October 2003
to September 30, 2006. The maximum modelled wetness was determined at each 90-m
pixel and used to classify the pixel’s susceptibility classes as highly, moderately, slightly
susceptible or not susceptible (stable). For each region and susceptibility class, a daily
average susceptibility was calculated to present dynamic susceptibility during the study
period.
Safety factor variations were characterized using a suite of descriptive statistics,
probability distributions analyses and crossing properties for the critical slope failure
threshold. Descriptive statistics included mean, standard deviation (SD), coefficient of
variation (CV) and skewness. Statistics were calculated for the entire year as well as for the
wet season. Statistics were mapped to indentify spatial patterns.
Probability distributions were examined using histograms, and goodness of fit was
considered using L-moment diagrams (Hosking 1990). While the method of moment
method is the traditional approach to fitting distributions, L-moment diagrams are often an
improvement because they are approximately unbiased and are particularly relevant when
samples are skewed (Vogel and Fennessey 1993). L-Moment diagrams, L-skewness (s3)
versus L-kurtosis (s4) and theoretical relationships for five probability distributions were
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constructed using the theory presented by Stedinger et al. (1993), Vogel and Wilson (1996)
and Hosking and Wallis (1997). L-Moment analysis is used to compare if the region has a
consistent probability distribution and, if so, which potential theoretical probability distribution best matches the observed probability distributions of the safety factors in highly
susceptible regions.
Crossing properties have been used extensively in soil moisture studies to identify
critical thresholds of plant water stress (e.g. Porporato et al. 2001). This concept is applied
to slope stability in order to present a statistical analysis of the duration and frequency of
instability. A crossing property analysis determines the number of crossings and the
average duration of all crossings. For this study, the critical crossing threshold is defined as
the transition from moderately susceptible to highly susceptible (Fig. 2). The crossing
duration corresponds to a single crossing and is the number of days that a pixel remains
classified as highly susceptible before returning to a moderately susceptible state. The
crossing properties are mapped and evaluated using observed landslide events.
5 Results and discussion
5.1 Dynamic landslide susceptibilities
Using the VIC modeled soil moisture, groundwater and geotechnical parameters, daily
safety factors were calculated for the study period (2003–2006) in the Nepal and California
study regions. The maximum modeled wetness was determined at each 90-m pixel and
used to classify the pixel’s susceptibility classes as highly, moderately, slightly susceptible
or not susceptible (stable). Regionally, Nepal has a much greater proportion of susceptible
area than California (Table 3).
For each region and susceptibility class, a daily average susceptibility was calculated as
the average safety factor value for all pixels in each study region and susceptibility class.
Figure 3 shows the time evolution of these average safety factors by region and class as
well as the threshold (FS = 1) indicating when a typical hazard-prone area becomes
Fig. 2 Demonstration of crossing and duration properties based on safety factor transitions from stable to
unstable and return to stable
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Table 3 Safety factor statistics for the 2003–2006 study period and wet season (Jan–May) for California
and (Jun–Sep) for Nepal
Statistical
parameter
California
Nepal
Highly
susceptible
Moderately
susceptible
Slightly
susceptible
Highly
susceptible
Moderately
susceptible
Slightly
susceptible
Area (%)
0.49
1.69
2.89
11.59
23.30
21.12
Number of pixels
339
1,169
2,007
4,748
9,545
8,653
Average
1.09 (0.12)
1.44
1.75
1.02 (0.13)
1.30
1.57
SD
0.14 (0.03)
0.18
0.23
0.11 (0.03)
0.12
0.14
Skewness
0.03 (0.23)
-0.05
-0.05
-0.09 (0.05)
-0.09
-0.09
CV
0.13 (0.02)
0.12
0.13
0.10 (0.03)
0.09
0.08
Average
0.98 (0.10)
1.29
1.56
0.92 (0.11)
1.19
1.43
SD
0.08 (0.02)
0.11
0.13
0.04 (0.01)
0.05
0.06
Skewness
1.10 (0.19)
1.10
1.12
1.37 (0.14)
1.39
1.39
CV
0.08 (0.02)
0.09
0.09
0.05 (0.01)
0.04
0.04
Annual
Wet season
Parentheses indicate standard deviation. Classifications are based on maximum modeled susceptibility on
8 May 2005 for California and 18 August 2004 for Nepal
CV coefficient of variance
susceptible. The parallel time evolution across susceptibility classes is likely due to similar
climatic patterns for the regions. While hazardous seasons in California and Nepal differ,
the transition from dry (high FS) to wet conditions (low FS) occurs over a short period in
both regions. Intense rainfall, increasing vadose zone wetness and rising groundwater
levels, rapidly decrease safety factors. The regions’ safety factor variations during the wet
and dry seasons also differ. The California slopes have fairly large variations when they are
unstable, and, on average, a region is typically unstable for a short period of time. In Nepal,
once regions become unstable, they tend to stay unstable for the remainder of the monsoon
season with more limited variations. During stable periods, California’s slope stability is
fairly consistent due to relatively constant dry conditions. Nepal’s stable periods differ by
year. Some years have constant stability similar to California, while other years have
variations that are not markedly different than its unstable periods.
Descriptive statistics of the safety factors, mean, SD, CV and skewness, were calculated
for each pixel from the time series of daily safety factors at that pixel. The average and
standard deviation of these statistics are summarized by susceptibility category (Table 3).
On an annual basis, the average, SD and CV statistics are lower in Nepal than California.
Results show that these differences are not notable for the highly susceptible areas, but that
the range of conditions is much greater in California than Nepal. The SD typically
increases with decreasing susceptibility. The CV is nearly identical for all susceptible
classes. Statistics differ during the wet season as compared to the annual period. The
average, SD, and CV of the estimated safety factors are all lower during the wet season
than on an annual basis. The negative and positive skew during the annual period and wet
season, respectively, suggest that there are two distinct populations of safety factors
depending on the period of interest.
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2.50
0
2.00
1.50
100
1.00
150
Rainfall
0.50
Rainfall (mm)
Safety Factor
50
High Susceptible
Moderately Susceptible
(a)
Slightly Susceptible
0.00
O-03 D-03 F-04 A-04 J-04 A-04 O-04 D-04 F-05 A-05 J-05 A-05 O-05 D-05 F-06 A-06 J-06 A-06
2.50
200
0
2.00
1.50
100
1.00
0.50
(b)
Rainfall
Highly Susceptible
Moderately Susceptible
Slightly Susceptible
0.00
O-03 D-03 F-04 A-04 J-04 A-04 O-04 D-04 F-05 A-05 J-05 A-05 O-05 D-05 F-06 A-06 J-06 A-06
Rainfall (mm)
Safety Factor
50
150
200
Fig. 3 a Average safety factors and rainfall distribution by susceptibility class at the Cleveland Corral, CA,
USA study region; b average safety factors and rainfall distribution by susceptibility class at the Dhading,
Nepal study region
The spatial distribution of CV values for all susceptibility classes differs by location,
and there is some spatial coherence (Figs. 4, 5). The California study region has a higher
CV throughout the study area as compared to Nepal. This relative high variability may be
an indicator of regions with localized susceptible areas. Both study regions have a highway
and a river passing through the center of their study region. While the DEM scales make it
difficult to discern how the highway impacted regional susceptibility, the CVs along the
highway are very different between the two regions. In Nepal, a highway divides the steep
southern region from the modest slopes in the northern region which includes the river.
Very low CV values are found in the North along the river and highway with higher
variability along the steep southern terrain. In California, steep slopes border the highway,
and high CV values occur along the highway and stream. Thus, there is a strong geomorphic control that appears to be independent of the river or highway presence on
stability variations. The California study region also has lower CV values in the highly
susceptible class (Fig. 4) near to the natural water body (mapped landslide no. 1).
These landslide susceptibility variability results are comparable to the 3-day study by
Wu and Sidle (1995), the 20-day study by Talebi et al. (2008) and the 30-year temporal
susceptibility analysis by Gorsevski et al. (2006). These studies also identified landslide
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Fig. 4 The safety factor coefficient of variance for all susceptible classes during the wet season, in
Cleveland Corral, CA, USA. Stable portions of the region are assigned zero values
susceptibility changes due to soil wetness changes over time. Wu and Sidle (1995) found
an increase in susceptibility after rainfall than prior to rainfall, and Talebi et al. (2008)
observed increasing patterns of susceptibility with increase in wetness, whereas Gorsevski
et al. (2006) observed landslide susceptibility had monthly and annual patterns.
5.2 Susceptibility temporal distribution
Because landslides mainly occur during the wet season, this section further examines
safety factor probability distributions exclusively during the wet season. The histogram
plot and L-moment diagrams are used to examine the safety factor probability density
functions (PDF) in both regions. The histograms show that safety factor distributions differ
by region with higher center of mass and thinner tails in Nepal than California (Fig. 6). In
Nepal, there is almost a 95% probability that the estimated safety factor will be under the
FS = 1, 1.25 and 1.5 class delineations during the wet season. In contrast, California has a
70% probability of the FS being below the critical value. Moreover, the California region
has a bimodal probability distribution, whereas Nepal has a unimodal probability
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Fig. 5 The safety factor coefficient of variance for all susceptible classes during the wet season in Dhading,
Nepal. Stable portions of the region are assigned zero values
distribution. Results clearly show two populations of safety factors in California, and
therefore, this mode cannot be considered the best measure of central tendency as for
Nepal. Although both study regions have positively skewed safety factors, the California
region has less variability in susceptibility than Nepal.
For each highly susceptible site, the safety factors’ L-Skewness s3 and L-Kurtosis
s4 were computed and plotted for the wet season values. Figure 7 compares theoretical
probability distribution relationships to the individual L-moment values for each site as
well as the mean s3 and s4 values for each region. Nepal’s susceptible areas have a
consistent distribution that is distinctly different from the California region. For Nepal, the
clustering of sites indicates the region has a common probability distribution. The threeparameter lognormal (LN3) distribution does a reasonable job of capturing the temporal
variability of safety factors for Nepal’s highly susceptible sites. The unstable areas in
California have one of three distinct populations. The two populations having a relatively
high kurtosis and following a generalized Pareto distribution are located near the natural
water body (mapped landslide no. 1). The region along the CA highway has a different,
distinct pattern with a much lower kurtosis. While the normal or gamma distributions are
frequently associated with hydrological processes, neither distribution fits the observed
variability for these landslide-prone regions. Thus, a single underlying distribution for
landslide susceptibility cannot be used for different locations.
5.3 Crossing properties of landslide safety factors
The crossing properties associated with the time evolution of stability were quantified for
each highly susceptible location (339 locations/pixels in California, 4,748 in Nepal).
Boxplots used to summarize these values show that California and Nepal have nearly equal
median crossing and duration values, but have different ranges (Fig. 8). The median
duration under the threshold is slightly shorter in California (18 days) than in Nepal
(26 days), whereas the median number of crossings is the same in Nepal and California.
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0.20
(a)
Probabilitty-NP
Probability
0.16
Probabilitty-CA
0.12
0.08
0.04
0.00
0.8
0.20
0.85
0.9
0.95
1
1.05
1.1
(b)
Probability
0.16
0.12
0.08
0.04
0.00
1
1.1
1.2
1.3
1.4
0.20
(c)
Probability
0.16
0.12
0.08
0.04
0.00
1. 25
1.5
1.75
Safety Factor
Fig. 6 The histogram of daily safety factors at each region during the wet season. a Highly susceptible,
b moderately susceptible, c slightly susceptible, CA California, NP Nepal
About 25% of Nepal’s highly susceptible area has more than nine crossings per year with
each crossing lasting on average less than 20 days. California has no region that exceeds
nine crossings annually. Twenty-five percent of California’s unstable region sustains
highly susceptible conditions for more than 100 days annually. This may be the primary
reason that California has frequent slope movements and less slope failures, while Nepal
has frequent slope failures and no routine slope movements during their respective wet
seasons.
Figure 9 shows the relationship between the number of crossings and average duration
for each highly susceptible site. Both regions have a similar nonlinear decrease in duration
with increasing crossings. Nepal’s relationship is well defined by the power law function,
y = 365x-0.43 (R2 = 0.69), where y is the duration and x is the number of crossings. For
the equivalent number of crossings, California’s locations typically have shorter durations
than Nepal, but are within the Nepalese range. This further explains why Nepal has
frequent slope failures, while California has fewer failures and more frequent slope
movements. This result is further supported by the findings of Lan et al. (2005) who found
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0.40
L-Kurtosis, τ 4
0.20
Generalized Pareto (GPA)
Gamma (P3)
Lognormal (LN3)
0.00
Gumbel
Normal
California
Nepal
Mean SF-CA
Mean SF-NP
-0.20
0.00
0.10
0.20
0.30
0.40
0.50
0.60
L-Skewness, τ 3
Fig. 7 L-Moment diagrams for each highly susceptible location by region and potential probability
distribution functions during the wet season for generalized Pareto (GPA), gamma (P3), normal, Gumbel and
three parameter lognormal (LN3) distributions
(b) 250
Average duration (days)
Number of crossings
(a) 20
15
10
5
200
150
100
50
0
0
Nepal
California
Nepal
California
Fig. 8 The quantile box plots of a the number of transitions (crossings) below the safety factor threshold
value and b the average duration that the safety factor stayed below the threshold on an annual basis by
region (complete year)
that while some slopes can fail rapidly, others can take a long time to fail under similar
saturation.
Landslide locations were mapped by each region (Figs. 4, 5), and their crossing
properties are indicated in Fig. 9. Interestingly, most of these highly susceptible regions
and mapped landslides have frequent crossings and briefly unstable conditions. Of the ten
mapped landslides in California, seven have short duration, unstable conditions and frequent crossings. In Nepal, eleven out of the twelve slide locations have the same short
unstable conditions and frequent crossings. A gradual decrease or increase in stress over
time that causes cyclic stress relaxation associated with subsequent material failures
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250
Nepal
Mapped Landslides (Nepal)
California
Average Duration (Days)
200
Mapped Landslides (California)
Power-law distribution
150
100
50
y = 365x-0.43
R2 = 0.69
0
0
2
4
6
8
10
12
14
16
Crossings per Year (Counts)
Fig. 9 The average duration that the safety factor stayed below the critical threshold versus the number of
crossings per year for each highly susceptible pixel. Mapped landslides in CA, USA and Dhading, Nepal
study regions are indicated with open triangle and open circle, respectively. Solid line is the best fit
regression relationship for the Nepal region
(Borzdyka 1974) may explain why slope failures occur at locations that have frequent
crossings.
Crossing properties maps reveal that the Nepal region has a uniform distribution of
crossing frequencies while California’s properties differ by area (Figs. 10, 11). Along
California’s highway, crossings are more frequent than in the northwest region. Physically,
Nepal has no preferential steep terrain locations, whereas California has localized areas of
steeper terrain along the highway and in the northwest portion of the study region. In
California, the northwest region has longer susceptible periods, but fewer crossings than
along the highway. This regionalized difference is supported by the frequent slope
movements observed by the USGS (‘‘Current Landslide Status’’, 2011) along the highway,
but not in the Northwest region. These differences may be caused by different physical
characteristics, geotechnical variable distributions and hydrological variable distributions
between regions.
A safety factor is calculated using static parameters such as slope and soil characteristics that temporally change very little (Li et al. 2010) and dynamic parameters such
as soil wetness that can change dramatically both in space and time. The change in soil
wetness is directly linked with changes in climatic parameters such as temperature and
precipitation (Bonnard et al. 2008). The daily variations in safety factor or transitional
and crossing properties of the safety factor in a particular region can be linked with the
local and/or regional climatic variation. Therefore, these transitional and crossing
properties of susceptibility/safety factor can help to predict the timing of slope failures.
In addition, dynamic safety factor time evolution and crossing properties provide an
additional source of information that can be used to differentiate among identified hazard
zones in a region.
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Fig. 10 a Number of annual crossings below the threshold safety factor and b average duration (days)
below threshold for highly susceptible location from Oct. 2003 to Sep. 2006 in CA, USA
5.4 Regional analysis limitations
This study’s spatiotemporal landslide susceptibility analysis approach may be useful for
regional and local scale studies including in remote regions where detailed information is
not available. In contrast to site-specific studies, the methodology has limitations due to the
resolution of datasets as well as knowledge of the engineering design practices on hill
slopes.
This study used datasets that are larger than many landslides; the VIC-3L modeled soil
moisture at a 900-m scale and the soil, vegetation and slope parameters characterized slope
stability analysis at a 90-m scale. Soil moisture is highly variable at these scales (Choi et al.
2007). Although this study assumes that the mean soil moisture is a reasonable estimate of
the 90-m values, Jacobs et al. (2004) and Choi and Jacobs (2011) demonstrated that soil
moisture varies in space as a function of soil porosity and slope position. Future studies
might consider using physical parameters to downscale soil moisture. Similarly, the
STATSGO and SRTM DEM values do not capture the variability of soils and slope within
the 90-m. Here, a challenge is finding consistent methods to downscale multiple parameters that can reproduce patterns of stability and identify failure slopes that do not rely on
detailed in situ observations.
The presence of instability along the major roadway in the California study region also
points to a limitation of regional studies. For this study, it appears that the road cut
disturbed the slope, and if the slope is steep, there is the possibility that this cut increased
slope instability as compared to the natural steep slope. Natural slopes are more stable than
the disturbed or cut slope. The impact of the road depends on construction methods and
precautions taken regarding drainage and slopes stability. Thus, the application of slope
stability analysis using regional datasets can only point to areas of interest. Regional
studies cannot take the place of site-specific analyses.
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Fig. 11 a Number of annual crossings below the threshold safety factor and b average duration (days)
below threshold for highly susceptible location from Oct. 2003 to Sep. 2006 in Dhading, Nepal
6 Conclusion
An infinite slope stability model coupled with a hydrologic model was used to develop
dynamic landslide susceptibility maps in Cleveland Corral, California, US and Dhading
Nepal. We presented a spatiotemporal slope stability model that assessed the daily safety
factor variation in two different study regions. Spatial analysis predicts highly susceptible
zone, whereas temporal analysis compares daily, seasonal and annual variability in safety
factors or in susceptibility among predicted highly susceptible pixels/locations. We also
compared the transition property of safety factor or susceptibility in highly susceptible
pixels. The mean, standard deviation, skewness and coefficient of variation of safety
factors and L-moments were calculated to characterize the temporal variability and
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probability distribution of safety factors. The statistical results show higher relative variability in California than in Nepal. Both study regions’ safety factors are positively
skewed; however, for the wet season, Nepal’s safety factors are more positively skewed
than California’s. The Nepal study region, which has low spatial and temporal variability
in susceptibility, is more prone to failure than California.
A strong relationship was observed between the number of crossings and the average
duration, which follows a power law. Results show that the safety factors may fluctuate
around the critical threshold, but a slope does not always fail when the safety factor is
below the critical threshold. This study provides preliminary insights as to how slopes
reach and sustain potential hazardous conditions not revealed by static spatial distribution
studies.
In summary, this paper presents two important findings derived from stability analysis
over a multi-year period based on two study regions. In landslide-prone regions, the joint
spatial and temporal analysis of susceptibility shows regional patterns with distinct statistical characteristics that are consistent across years but change seasonally. The longerterm data sets, which allowed transitional characteristics of susceptibility to be quantified,
demonstrate a consistent relationship between crossing properties below the critical
threshold (FS = 1) value. The crossing property and transitional characteristics analysis of
safety factor or susceptibility and dynamic time evolution can be used in landslide hazard
forecasting using relative simple models and limited climatic data. It is recommended that
these metrics be extended beyond the two study regions to sites having longer and more
robust records of landslide to understand the global spatiotemporal patterns of susceptibility across different landslide-prone regions.
Acknowledgments We acknowledge NASA’s research funding through Earth System Science Fellowship, Grant No: NNG05GP66H, for this research. We would also like to thank Dr. M. E. Reid for providing
information about Cleveland Corral Landslide area and in situ groundwater measurements. We are also
indebted to three reviewers whose extensive comments greatly improved the manuscript.
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