Introduction
Landslides are one of the most common natural hazards causing significant damage and casualties every year. Landslides often occur in the soil mantle due to extreme rainfall and can present hazards to human life, property, and activities. They can also trigger rapidly moving debris flows (Iverson, 1997). The Republic of Korea also frequently suffers from landslides and slope instabilities with mountainous regions covering more than 70% of the land area. Statistics provided by the Korea Forest Service in 2013 showed that landslides in Korea are becoming more frequent and severe in recent years. The 10-year average for recorded landslide-damaged areas increased from 321 ha in the 1980s to 349 ha in the 1990s and 713 ha in the 2000s; this is more than double the values of previous decades. Since the year 2000, in particular, more than 1,000 ha of landslide-damaged
areas have been recorded (Kim et al., 2014). Additionally, landslides are responsible for the loss of approximately 23 lives each year, which comprises approximately 25% of the annual casualties as a result of a natural disaster in Korea (Lee and Park, 2014).
An accurate landslide-susceptibility assessment is fundamental for preventing landslides and minimizing damages. Especially, the increasing trend in landslide occurrence in mountainous areas in recent decades caused by climate change has set off an alarm for researchers to seek more reliable methods for landslide prediction and warning systems. However, analyzing the stability of a natural slope is not an easy task because it depends on numerous factors such as those related to vegetation, soil properties, soil moisture distribution, the amount and duration of rainfall, earthquake, etc. The factors causing landslide hazards can be categorized into two groups: intrinsic variables, such as geological conditions or vegetation, and extrinsic variables such as rainfall, earthquake, or human activity. The probability of landslide occurrence depends on both of the above variables. The spatial distribution of the intrinsic variables determine the spatial distribution of landslide susceptibility in the study region (Huabin et al., 2005); and the time of occurrence of extrinsic variables is important for estimating the time of landslide occurrence.
A variety of different methods and techniques for evaluating landslide susceptibility have been proposed, but up to now, no specific method or technique has been accepted as the standard approach because it is very difficult to assess the different methods with entirely different intrinsic and extrinsic data. There is hardly any systematic comparison of different methods, in terms of respective advantages and limitations (Carrara et al., 1995; Westen et al., 1997; Huabin et al., 2005). Landslide prediction methods can fall into three categories: empirical, statistical, and physical approaches. This paper reviews previous research and surveys three groups of landslide prediction methods.
Empirical approaches
One of the most common approaches for the prediction of landslide occurrence is the estimation of rainfall threshold, which is derived from two or more rainfall parameters such as rainfall intensity and duration. Since the pioneering works of Caine (1980), Campbell (1975), Guidicini and Iwasa (1977), and Lumb (1975), the rainfall threshold approach has been widely used and many thresholds levels for rainfall-induced shallow landslides have been proposed based on a large variety of rainfall parameters. Huang et al. (2015) classify those methods according to the type of data the threshold is based on, such as (i) hourly rainfall intensity and duration (Keefer et al., 1987; Guzzetti et al., 2007b; Cannon et al., 2008; Segoni et al., 2014), which is the most popular among rainfall threshold methods; (ii) daily rainfall and antecedent rainfall intensity (Glade et al., 2000; Guo et al., 2013); (iii) cumulative rainfall and duration (Aleotti, 2004); (iv) cumulative rainfall and average rainfall intensity (Hong et al., 2005); and, (v) a combination of different thresholds such as (i) - (iv) (Baum and Godt, 2009). The rainfall threshold method is useful for early warning systems due to its simplicity and applicability. The performance of the rainfall threshold method has been proven in many studies ( Keefer et al., 1987; Baum and Godt, 2009; Glade et al., 2000; Guzzetti et al., 2007a; Osanai et al., 2010; Greco et al., 2013; Segoni et al., 2014; Zêzere et al., 2014; Segoni et al., 2015).
The empirical rainfall threshold can be simply estimated by drawing lower-bound lines to the rainfall conditions that resulted in landslides plotted in Cartesian, semi-logarithmic, or logarithmic coordinates without any rigorous mathematical, statistical, or physical criterion. Guzzetti et al. (2007b) listed 25 rainfall and climate variables used in previous studies of empirical rainfall thresholds for shallow landslide as listed in Table 1.
The threshold based on hourly rainfall intensity and duration has a general form as follows:
(1)
where I is mean rainfall intensity, D is rainfall duration, and a, b, and c are parameters. Note that if c = 0, Eq. (1) is a simple power law. The above equation covers a wide range of rainfall duration between 1 and 100 hr and intensities between 1 and 200 mm/hr. Guzzetti et al. (2007b) listed 52 rainfall intensity-duration thresholds from previous studies. Among them, 45 thresholds use a simple power law (c = 0). The range of parameter a is from 4.0 to 176.4 and b is from -1.5 to -0.19. As stated above, this method can straightforwardly be applied to a wide range of rainfall intensities and durations. However, its limitation is that a very small rainfall intensity with very long duration may result in landslides, which is unrealistic. In order to overcome this limitation, some studies proposed the minimum value of rainfall intensity for long rainfall durations in the range from 0.48 to 6.90 mm/hr. By analyzing variety of rainfall intensity-duration thresholds as listed in Table 2, Guzzetti et al. (2007b) found that those local thresholds are slightly higher than the regional thresholds and that global thresholds are positioned in a lower part than the regional and local thresholds. They also found that there are significant differences in thresholds even for the same geographical areas. The reason for this is that landslides do not only depend on the rainfall conditions but also physiographical, geological, or geomorphological conditions.
A few studies proposed probabilistic rainfall thresholds (e.g., Berti et al., 2012; Huang et al., 2015). A rainfall threshold is defined as the value that must be exceeded to result in landslides. This definition is based on a deterministic view: the system of the landslide can be predicted by comparing the input value (rainfall) with the threshold, and no randomness is involved in the system. Such a deterministic approach can be successfully used to define the rainfall threshold in the ideal cases, where a triggering mechanism is directly controlled by rainfall (Berti et al., 2012). In most of the real cases, however, the separation between critical and non-critical rainfall is not clear. Fig. 1 shows a conceptual example to demonstrate the difficulty of determining rainfall threshold. Since the landslide events are triggered by the combination of various factors, the occurrence of the landslide cannot be predicted by rainfall alone. Therefore, the deterministic approach has limitations, and a probabilistic model is required for more accurate prediction. Berti et al. (2012) proposed the probabilistic rainfall thresholds using a Bayesian approach as follows:
|
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Fig. 1. Illustration of rainfall intensity-duration or intensity-cumulative rainfall thresholds in real cases (retraced following Berti et al., 2012). |
(2)
where 
is the conditional probability of observing a landslide when a rainfall event of magnitude B occurs, 
is the prior probability of landslide occurrence regardless of whether a rainfall event of magnitude B occurs or not, 
is the marginal probability of observing a rainfall of magnitude B irrespective of whether a landslide occurs or not, and 
is the conditional probability of observing a rainfall event of magnitude B when a landslide occurs. Huang et al. (2015) proposed the probability of landslide occurrence (PLO) as follows:
(3)
(4)
where 
is the accumulated rainfall (mm), I is the rainfall intensity (mm/hr), a is the gradient of line in R-I graph of landslide events, and 
is maximum (minimum) constraint of value of C. The probabilistic rainfall thresholds have an advantage over the determinant thresholds in terms of the consideration of uncertainties. However, it still has the fundamental limitation that only rainfall is taken into account for landslide prediction.
Statistical approaches
The empirical approach has been successfully applied in landslide early warning systems, but it has limitations for the prediction of the spatial distribution of landslide occurrence. The statistical approach can be a good alternative to overcome this limitation. The main advantage of this method is that it considers several geo-environmental factors. Based on spatial distribution and analysis of those factors, the landslide risk map can be produced. Pardeshi et al. (2013) categorized the statistical methods into two groups as bi-variate statistical methods and multi-variate statistical methods.
The bi-variate statistical method compares data layers of geo-environmental factors to the observed landslide distribution data, and the weight is estimated by the landslide density. There are several bi-variate statistical methods: weights of evidence method, weighted overlay method, frequency ratio method, information value method, and fuzzy logic method.
The weight of evidence technique is based on the Bayesian probability approach. It uses different combinations of geophysical factors to find their interrelation. This method has been successfully applied in many reteaches (Ghosh et al., 2009; Blahut et al., 2010; Neuhäuser et al., 2011; Piacentini et al., 2012; Schicker and Moon, 2012; Martha et al., 2013). In the weighted overlay method, the weight is estimated based on the relationship of geophysical factors with the landslide frequency (Sarkar et al., 1995; Cardinali et al., 2002; Parise, 2002; Preuth et al., 2010). The frequency ratio method assesses the landslide susceptibility index by summing of the frequency ratios of each geophysical factor. The frequency ratio for each individual factor is estimated from the relationship between the factors and the landslide occurrence (Lee, 2005; Bălteanu et al., 2010; Goswami et al., 2011). In the information value method, the information values are determined for each subclass of landslide-related parameter on the basis of the presence of landslides in a given mapping unit. This approach has proved to be a useful tool for determining the degree of influence of individual causative geophysical factor (Zêzere, 2002; Arora et al., 2004; Wang and Sassa, 2005; Champatiray et al., 2006). The fuzzy logic method defines explanatory variables between 0 and 1 based on the fuzzy theory. These variables are integrated using a fuzzy gama operator or a fuzzy algebraic sum to generate the spatial distribution map of the landslide.
As stated above bi-variate statistical methods consider individual geo-physical factor to the observed landslide occurrences, which may lead to a limitation of the method because the interrelation which exists among the landslide-causing factors and the landslide is basically the result of several causing factors. Therefore, approaches considering several factors at a time have been proposed for more accurate predictions of landslides. These methods are called multivariate statistical methods. The multivariate approach has widely been used since the past decade and proved to be a more objective method for assessing landslide hazards with complex geophysical data (Ercanoglu et al., 2004; Conoscenti et al., 2008; Van Den Eeckhaut et al., 2009). These methods compute the percentage of landslide area for each pixel based on multivariate analysis such as logistic regression, discriminant analysis, multiple regression, conditional analysis, and artificial neural network methods (Pardeshi et al., 2013).
The logistic regression predicts the presence or absence of a characteristic or outcome based on values of predictor variables. This model is useful for dichotomous events such as landslides. The logistic regression method finds the best fitting relationship between presence (or absence) of landslides and a set of geophysical factors such as slope angle, slope aspect, and land use (Ayalew and Yamagishi, 2005). Recently, this method has been applied in many reteaches (Ohlmacher and Davis, 2003; Chau et al., 2004; Ayalew et al., 2005; Ayalew and Yamagishi, 2005; Wang and Sassa, 2005; Chang et al., 2007; García-Rodríguez et al., 2008; Nefeslioglu et al., 2008; Ghosh et al., 2009; Erener and Düzgün, 2010; Akgun, 2011; Das et al., 2011).
The discriminant analysis method is one of the frequently used statistical methods for producing landslide hazard maps. The maximum difference for the landslide-causing factors between landslide group and non-landslide group can be found and weights for these factors are estimated by the discriminant analysis (Lee et al., 2008). This method has been successfully applied in several studies (Ohlmacher and Davis, 2003; Lee et al., 2008; Van Den Eeckhaut et al., 2009).
The artificial neural network method has also been applied for the prediction of landslide occurrence, which is triggered by complexly interrelated many factors. The complex correlations among many landslide-causing factors are expressed by the neurons and the layers (Catani et al., 2005; Ercanoglu, 2005; Pradhan and Lee, 2009; Tien Bui et al., 2012). Clerici et al. (2002) applied conditional analysis method for landslide prediction in GRASS (Geographical Research Analysis Support System), which is widely used open source GIS software.
Physical approaches
The empirical rainfall threshold can be used to predict the timing of landslide occurrence while the statistical approach can predict the spatial distribution of landslide susceptibility. Both methods have advantages and limitations as previously stated. On the other hand, the physically based models have the ability to predict both the spatial distribution of landslide susceptibility and the timing of landslide occurrence. They describe the physical triggering processes of shallow landslides and provide spatially variable slope - stability information, often as a safety factor (FS), which is an index expressing the ratio between the local resisting and driving force.
Most of the physically based model estimate FS based on the infinite slope stability model. Fig. 2 shows a schematic of an infinite slope - stability model. With assumption of an infinite slope and failure parallel to the slope surface the shear and normal stress are derived as follows:
(3)
(4)
where 
is the soil weight (kg/m), 
is the shear force (kg/m), 
is the normal force (kg/m), 
is the soil depth (m), 
is the slope width (m), 
is the slope angle (rad), and 
is the unit weight of the soil (kg/m3). According to the Mohr - Coulomb theory, the shear strength of an infinite slope is as follows:
(5)
where 
is the cohesion (kg/m2), 
is the effective stress (kg/m2), which was expressed as 
, 
is the pore water pressure (kg/m2), and 
is the angle of internal friction (rad). Then, the 
is defined as
(6)
Substituting Eqs. (3) - (5) into Eq. (6) yields the following equation:
(7)
Substituting 
into Eq. (7) gives
(8)
where 
is the unit weight of water (kg/m3), and 
is the pressure head of the subsurface water (m). Eq. (8) is rewritten by separating the time-variant term and steady terms as (Iverson, 2000)
(9)
Note that time-variant variable in Eq. (9) is only the pressure head and the other variables are steady in time. The pressure head can be estimated for steady and unsteady state.
Several studies (Montgomery and Dietrich, 1994; Pack et al., 1999) consider a simple steady-state hydrological process under constant rainfall to estimate the pressure head. They used the topographic wetness index, which is commonly used to quantify topographic control on hydrological processes. This index is a function of both the slope and the upstream contributing area per unit width orthogonal to the flow direction. The index can be converted to the pressure head with the assumption that the water is accumulated at the bottom of the slope. Therefore, the accuracy of the models is highly related to the estimation of the wetness index. Lee et al. (2012) compared the effects of several of the upstream contributing area estimation methods for wetness index. Many studies have applied steady-state approaches for the prediction of landslides (Acharya et al., 2005; Terhorst and Kreja, 2009; Gomes et al., 2013; Michel et al., 2014; Pradhan et al., 2014). The steady-state approaches are useful for producing spatially distributed slope stability but are limited to the temporal prediction of the slope stability because of the steady-state description of hydrological fluxes.
In order to estimate the unsteady pressure head in slope, the subsurface flow should be computed. The subsurface flow system of partially saturated soil is formulated by the Richards equation as follows
(10)
where 
is the pressure head (m); 
is the volumetric moisture content; 
is the hydraulic conductivity (m/s); 
is time (s); 
is the vertical dimension, which is assumed to be positive in the upward direction; and 
is the general source term (1/s), including rainfall.
Simoni et al., (2008) solved the three-dimensional (3D) subsurface flow numerically on the basis of Eq. (10) and considers the physical hydrological process for the estimation of landslide susceptibility. The computation of 3D subsurface flow usually requires a large amount of computational resources because fully implicit temporal discretization is essential for the numerical stability owing to the high nonlinearity of the Richards equation.
On the other hand, (Iverson, 2000; Baum et al., 2008) computed the transient pore-water pressure based on the one-dimensional (1D) Richards equation as follows:
(11)
Note that the above equation is not able to consider the effect of horizontal subsurface flow in slope. With the assumption of a simple exponential soil-water retention relationship, the analytical solution can be used, which can reduce the computational cost significantly. This model has been widely used in the past decade (Liu and Wu, 2007; Baum et al., 2010; Liao et al., 2010; Montrasio et al., 2011; Saadatkhah et al., 2014; Peres and Cancelliere, 2016), and its parallelized version has been developed (Alvioli and Baum, 2016).
Lu and Likos (2006) insist that Eq. (9) is only valid for saturated soil and Terzaghi’s effective stress is unsatisfactory for unsaturated soil. If the soil is highly dried, the large negative pressure head causes an excessive suction force with a Terzaghi’s effective stress of 
. They generalized the effective stress as follows:
(12)
where 
is the air pressure, and 
is the suction stress, which is a characteristic function of the saturation or matric suction and is expressed in a closed form as follows:
(13)
Here, 
is the water pressure, and 
is the effective saturation, which is defined as
(14)
where 
is the saturated moisture content, and 
is the residual moisture content. The assumption of 
and 
leads an effective stress of 
. Therefore, Eq. (9) is generalized for variably saturated soil as
(15)
Note that if the soil is saturated, the effective saturation becomes zero, and Eq. (15) is equivalent to Eq. (9).
An et al. (2016) proposed the landslide prediction model based on Eqs. (10) and (15). They also proposed the numerical scheme to reduce the computational requirement. They found that the proposed scheme significantly reduced the computation cost required for 3D physical modelling approaches.
Conclusion
For last two decades, landslide prediction techniques have achieved a significant progress with the remarkable advance of the computer, GIS, and remote sensing technology. However, there are still many unknowns and uncertainties on the triggering process of the landslide because the landslide is a fundamentally complex hazard, which is related to hydrology, soil physics, meteorology, etc., and shows very different behaviors depending on the region. Several prediction methods are surveyed, and many previous studies are introduced in this article. There is no perfect methodology for landslide prediction to be applied everywhere since all of the prediction methods have limitations and strengths. Therefore, it is recommended that users or researchers consider the purpose of the prediction, the available data, human resources, social issues, and research period when selecting a landslide prediction method.
