Landslides are often triggered by catastrophic events, among which earthquakes and rainfall are the most depicted. However, very few studies have focused on the effect of atmospheric pressure on slope stability, even though weather events such as typhoons are associated with significant atmospheric pressure changes. Indeed, both atmospheric pressure changes and rainfall-induced groundwater level changes can generate large pore pressure changes. In this paper, we assess the respective impacts of atmospheric effects and rainfall over the stability of a hillslope. An analytical model of transient groundwater dynamics is developed to compute slope stability for finite hillslopes. Slope stability is evaluated through a safety factor based on the Mohr–Coulomb failure criterion. Both rainfall infiltration and atmospheric pressure variations, which impact slope stability by modifying the pore pressure of the media, are described by diffusion equations. The models were then forced by weather data from different typhoons that were recorded over Taiwan. While rainfall infiltration can induce pore pressure change up to hundreds of kilopascal, its effects are delayed in time due to flow and diffusion. To the contrary, atmospheric pressure change induces pore pressure changes not exceeding a few kilopascal, which propagates instantaneously through the skeleton before diffusion leads to an effective decay of pore pressure. Moreover, the effect of rainfall infiltration on slope stability decreases towards the toe of the hillslope and is cancelled where the water table reaches the surface, leaving atmospheric pressure change as the main driver of slope instability. This study allows for a better insight of slope stability through pore pressure analysis, and shows that atmospheric effects should not always be neglected.

In mountainous areas, landslides represent a major erosional process that contribute to landscape dynamics and frequently cause significant damage and losses when catastrophic failures occur (Keefer, 1994; Malamud et al., 2004). Landslides can be triggered by dynamic events, including earthquakes and storms, which drive hillslopes towards instability and catastrophic failure (Haneberg, 1991; Iverson, 2000; Collins and Znidarcic, 2004; Hack et al., 2007). These two types of triggering events have been extensively studied with numerous observations, empirical, analogical, numerical, and theoretical models. Triggering of co-seismic (i.e. during an earthquake) landslides is generally attributed to the peak ground acceleration generated by seismic waves, but more complex phenomena come into play, such as a cohesion loss, liquefaction, or topographic site effect (Hack et al., 2007; Meunier et al., 2007, 2008). Triggering of landslides by weather events involves various processes that are generally linked to rock–water interactions. Characterising and understanding how weather events trigger devastating landslides are essential (Baum et al., 2010; Rossi et al., 2012; Chen et al., 2014; Martha et al., 2015). At long time scales, weathering processes affect rock mechanical properties through chemical alterations. This rock-weakening process is known to reduce the slope stability and increase the risk of landslides (Calcaterra and Parise, 2010; Hencher and Lee, 2010). At monthly to seasonal time scales, groundwater recharge increases the water table height and the pore pressure, which alters slope stability. As the wet season increases the groundwater level, this results in seasonal increase in the frequency of catastrophic landslides – namely sudden failures leading to significant mass displacement (Gabet et al., 2004). At shorter time scales, water infiltration leads to a pressure front that modifies pore pressure and diffuses through the hillslope subsurface leading to its destabilisation (Haneberg, 1991; Iverson, 2000; Collins and Znidarcic, 2004; Tsai and Yang, 2006). Large infiltration rates and high groundwater flow gradients can also generate seepage forces that further destabilise the slope (Budhu and Gobin, 1996).

Weather events are also characterised by a drop in atmospheric pressure which could influence slope stability. This slope destabilisation factor has received little attention. Indeed, atmospheric pressure changes induce a pressure differential at the water table, which results in pore pressure evolution via diffusion in the saturated zone until equilibrium with atmospheric pressure, thereby modifying slope stability (Schulz et al., 2009). A correlation has been observed between atmospheric tides, leading to diurnal and semidiurnal atmospheric pressure changes, and displacement rate in a slow-moving landslide (Schulz et al., 2009). The amplitude of these repetitive pressure changes induced by atmospheric tides greatly depends on the latitude, but does not exceed 1.3 hPa around the Equator (Lindzen and Chapman, 1969; Dai and Wang, 1999). Other atmospheric events can lead to much larger changes in atmospheric pressure. Indeed, typhoons and major storms can yield atmospheric drop of tens of hectopascals, which could in turn significantly alter the stability of slopes.

In this context, groundwater plays a crucial role in converting both atmospheric and rainfall-induced effects into mechanical pressure changes. Most of the studies using analytical models to represent slope stability use a 1D infinite slope model (Collins and Znidarcic, 2004; Iverson, 2000). However, modelling the full hillslope enables a better characterisation of the evolution of groundwater level along the hillslope through modelling of the lateral flow. Since landslides are not evenly distributed along hillslopes (Meunier et al., 2008), this work presents a 2D analytical model based on a basic hydrological model applied to a hillslope and a mechanistic safety factor to evaluate atmospheric and rainfall effects on slope stability. We use the model in this paper to investigate the role of pore pressure changes induced by rainfall and atmospheric pressure changes during major storms on slope stability, while accounting for groundwater level, pre-conditioned by seasonal rainfall and compare it with the rainfall forcing.

First, we define a slope stability model based on a classic Mohr–Coulomb criterion. As both rainfall and atmospheric effects imply pore pressure diffusion in groundwater, defining slope stability requires a model able to describe groundwater diffusion. We therefore define an analytical solution for groundwater flow in a finite hillslope, and accordingly apply infiltration and atmospheric induced pore pressures to compute slope stability changes. Second, we consider simple synthetic scenarios of pressure and rainfall changes to model their distinct contributions to slope stability. This allows us to define spatial domains along the hillslope where the instability is predominantly driven by either rainfall or atmospheric pressure changes. Third, we apply this model to observed meteorological data from Taiwan to compute the respective impact of different typhoons, through rainfall or atmospheric pressure change, on slope stability. Last, we discuss the results and the relevance of the model.

Locally, slope stability can be expressed as the stability of an infinite
homogeneous slope tilted with an angle

Geometry of the hillslope considered in this study. The water table (in blue) forms a quadratic surface between the two boundaries conditions (in red). The stability is evaluated with a Mohr–Coulomb criterion along a slope-parallel slip. The atmospheric pressure and rainfall infiltration are applied uniformly along the slope. The zoomed-in section shows the implementation of the diffusion of pore pressure due to the rise of the water table between two consecutive time steps.

Slope stability can vary under the addition of external force, or if the
mechanical properties of the slope change. While weathering processes may
weaken rocks (Calcaterra and Parise, 2010; Hencher and Lee, 2010), we will focus on short-term to seasonal processes and consider constant mechanical soil properties. However, variations of the effective normal stress

As we aim to compare these dynamic effects, the slope will be considered at
yield, and only pore pressure will be investigated. In the following
sections, we develop models that describe water table variations (Sect. 2.2), rainfall-induced pore pressure

Infinite slope models have already been developed to evaluate slope stability under rainfall forcing and the diffusion of pore pressure (e.g. Iverson, 2000), but they are inherently limited in groundwater flow characterisation. If recharge is the vertical movement of water, groundwater level gradients in the hillslope induce a lateral movement of water. Water table fluctuations will change depending on the position along the hillslope, as local flow is linked to both recharge and uphill water convergence. Such characteristics cannot be represented in infinite slope models, where groundwater level is considered parallel to the surface. A more accurate description of groundwater flow is therefore required to express the flow dynamics and water table height along a hillslope.

In the following, we develop a 2D hydrological model applied to a
finite hillslope, with a slope angle

During extreme rainfall events, groundwater recharge does not equal the amount of precipitation. Part of the rainfall will not infiltrate and generate runoff if the rainfall rate exceeds the soil infiltration capacity. This can represent a significant portion of the rainfall and is heavily
dependent on soil characteristics. Therefore a limit has been set to the
recharge

This solution for modelling the transient water table relies on the Dupuit–Forchheimer hypothesis, with two assumptions. First, the flow lines are horizontal and parallel, which is verified when the lateral extent of the aquifer is much larger than its thickness, and the hillslope is not convergent or divergent. Second, the aquifer transmissivity is not affected by water table height variations, which needs an aquifer much thicker than the amplitude of its height variations. Such hypotheses would be well suited for a long and wide hillslope with a thick saturated zone but are questionable for the steep and complex shape of hillslopes that are typically a source of landslides, and may not exactly represent the complexity and dynamics of groundwater observed under steep hillslopes. However, it allows for a first-order and broad assessment of water table dynamics through an analytical solution, which is why it was selected.

The crest of the hillslope,

The solution to the partial differential equation (Eq. 4) can be separated
into a static part

For the transient part of the recharge, Townley (1995) provided a solution to Eq. (4) in Fourier space, describing groundwater level variations under periodic recharge. However, the weather events investigated here are not periodic, and using the solution as is would result in a partly acausal signal due to a limitation in the computation of the fast Fourier transform algorithm. This numerical issue is avoided by considering the temporal impulse response function corresponding to Townley's solution. The transient recharge

The hydrostatic pore pressure

The propagation of the pore pressure induced by rainfall and water table
variations can be described by a diffusion model. Iverson (2000) developed a
1D model that characterised the rainfall-induced pore pressure through a
homogeneous material. While the hydrological model considers a 2D geometry, a 1D vertical model is deemed sufficient to represent pore pressure diffusion in the hillslope. Starting from Richard's equation and assuming a fully vertical diffusion and wet initial conditions, the pore pressure front

The partial differential equation (Eq. 6) is mathematically identical to the
heat diffusion equation, for which Carslaw and Jaeger (1959) provided a set of analytical solutions (see Sect. 2.9 of Carslaw and Jaeger, 1959). In this case, a semi-infinite solid with a Neumann condition at its surface represents well the pressure diffusion under a recharge flux at its surface. The solution to a constant loading

The response to any recharge can be computed by a linear combination of these two solutions. Our model computes an impulse response function by replacing in Eq. (7)

The pore pressure

Rainfall is not the only process that impacts pore pressure. As a fluid, air
also contributes to pore pressure but its impact on slope stability is
generally disregarded. Indeed, atmospheric pressure adds to pore pressure
but also applies an equal normal load on the slope, directly increasing

As air is a low-viscosity fluid, pressure diffusion of the air through the
unsaturated zone is considered quick enough that atmospheric pressure variations can be directly applied to the top of the water table. The diffusion process is therefore the same as for rainfall infiltration (Eq. 7), with a Dirichlet boundary condition at the top of the semi-infinite solid instead of a Neumann boundary condition (see Sect. 2.5 of Carslaw and Jaeger, 1959). The pressure
input equals

The response of atmospheric- and rainfall-induced pore pressures to a weather
event are assessed both at the toe and the crest of a modelled hillslope.
For the purpose of this study, the slope is considered at yield, near the
failure. The finite slope model considers a

Rainfall recharge and atmospheric pressure variations used for the synthetic tests. The 24 h event corresponds to a cumulated rainfall of 86.4 mm, during which the atmospheric pressure drops 1 kPa.

Rainfall-induced pore pressure change

Temporal evolution of

The atmospheric pore pressure disequilibrium

The slight discrepancy between

We now consider in Fig. 4 the role of the initial water table height on the
impact of rainfall and atmospheric pressure change on slope stability.
During the event, the same input functions are used as for the previous case
(Fig. 2), but a constant recharge of 10

Initial state of the water table in the hillslope

If the initial water table height does not significantly impact

Taiwan is a mountainous island coming from the convergence between the Eurasian and the Philippines plate. A large portion of the island is composed of steep slopes and mountains, which culminates at 3952 m a.s.l. (above sea level). The reliefs are very steep and composed of sandstone, slate, schist and mudstone (Lin et al., 2011; Tsou et al., 2011). However, a large portion of the surface material is significantly weathered due to the annual precipitation of 2.5 m. As a region undergoing several typhoons each year and subjected to landslides, Taiwan is a relevant study area.

Weather data were obtained from the Data Bank for Atmospheric Research at
the Taiwan Typhoon and Floods Research Institute. The data are an hourly
report of rainfall and atmospheric pressure, from 1 January 2003 to 30 June 2017. The weather station is located in the Taroko National Park, in northeastern Taiwan (C0U650, 24.6753

In the model, the recharge is assumed to be equal to the observed rainfall, neglecting evapotranspiration. Atmospheric tides are observed in the atmospheric pressure data, with a diurnal and semidiurnal period and amplitudes of about 0.03 to 0.1 kPa, respectively. These tides are removed using notch filters to focus only on typhoons. In a similar way, a high-pass filter is applied to only keep signals with a period of less than 30 d and remove seasonal components. In the following, we assume that any remaining change in atmospheric pressure is attributable to weather events.

A total of 36 major typhoons are identified in the data. Rainfall peak
intensity ranges roughly between 0 and 57.6 mm h

On top of these three events, a theoretical typhoon is tested by taking the arithmetic mean of rainfall and atmospheric pressure of all 36 events in the data (Fig. 5b). The atmospheric pressure profile of this “average typhoon” is similar to the form of the pressure cross-section of a typhoon described by the empirical Griffith model (Griffith, 1978).

The impact of typhoons Matsa, Krosa, Morakot and the average typhoon was investigated through the hillslope stability model. The initial state – as previously established with the synthetic tests – plays an important role when computing

Initial state of the water table in the hillslope

For most typhoons, the amount of rainfall received during the preceding 6 months is significant, with average rates ranging between

At the toe of the hillslope, Morakot and the synthetic mean event are the
only events showing a non-zero

At the crest of the hillslope, for a high diffusivity

The atmospheric-induced instability

The models presented in this study consider simplification hypotheses, for both the failure mechanism and the hydrological characterisation of the slope. The finite hillslope hydrological model, which proposes a more realistic formalism for groundwater flow than the infinite slope model, allows for a simple characterisation of both rainfall and atmospheric effects on slope stability along the slope. However, the finite hillslope model is based on a Dupuit hypothesis and considers small water table level variations compared to the aquifer width (Townley, 1995). Therefore, this model describing the water table is less adapted to steep hillslopes such as those found in Taiwan.

While considering the full hillslope and groundwater dynamics helps represent pore pressure diffusion and the resultant instabilities, considering a homogeneous hillslope with a single unconfined aquifer is still a simplification, which neglects the potential role of perched aquifer within the hillslope. However, the model can be applied at any scale as long as the boundary conditions and the hypothesis of the hydrological model are respected.

Another limitation of the infinite and finite hillslope models is the independent computation of rainfall-induced and atmosphere-induced pore pressure diffusion. Indeed, rainfall infiltration tends to create a downward fluid displacement, while a drop of atmospheric pressure tends to induce an upward fluid flow, as it moves from high- to low-pressure areas. These two mechanisms happen simultaneously during a weather event and can, in turn, interact with each other. Since the model limits lateral water movement as a diffusion process, the time delay between rainfall and the hydromechanical response can be overestimated. We also consider that a fully saturated hillslope does not show any response to rainfall in terms of stability in the model. However, if the water table reaches the surface, even though the charge of the column of water does not change, the water flowing out of the slope induces a destabilising force function of the flow rate. This phenomenon, known as seepage, can lead to slope failure induced by rainfall near the toe of the hillslope (Budhu and Gobin, 1996; Ghiassian and Ghareh, 2008; Marçais et al., 2017). However, accounting for this process would require a dynamic computation of flow.

Finally, the hillslope model considers a fully homogeneous material, with no changes in mechanical properties along the slope or with depth. This simplification hypothesis sets aside the complexity of the soil, especially with regard to the weathering.

Here we compare the finite hillslope model, considered in this manuscript,
with a classic 1D model which considers an infinite slope and slope-parallel
water table and flow (Iverson, 2000). In this 1D model, the water table is fixed and the rainfall-induced pore pressure

The main difference between the 1D infinite slope model and the finite hillslope model is the presence of a dynamic water table in this latter.
Another significant difference is the point at which rainfall-induced pore
pressure is applied. Indeed, the infinite slope model diffuses

The atmospheric effect

However, the results are significantly different for the rainfall-induced
pore pressure

These differences between the 1D and finite hillslope models can lead to
significant changes when applied to specific typhoons, with large implications for hazard assessment. For example, these two models lead to
stark difference for

Pore pressure changes induced by rainfall and atmospheric pressure changes
are both diffusive mechanisms (Eqs. 7 and 8) and are both sensitive to
hydraulic diffusivity. Hydraulic diffusivity is highly variable in space,
and its estimation is complex and scale dependent (Jiménez-Martínez et al., 2013). As an example, measurements can vary over several orders of magnitude inside a single slope, and the scale of the hillslope or the presence of preferential flowpaths may lead to biased values and overestimation of the diffusivity (Handwerger et al., 2013). When focusing on soils, hydraulic diffusivities are typically low, ranging between 10

Media hydraulic diffusivity is a key factor controlling pore pressure and
its effect on slope stability. The higher the diffusivity, the greater the impact of rainfall (Fig. 4). The atmospheric effect is also affected
by diffusivity. The higher the diffusivity, the faster pore pressure readjusts to the atmosphere and the quicker

The water table is also diffusivity dependent (Eq. 4), for both its static
level and its variations. The static level is inversely proportional to the
hydraulic diffusivity (Eq. 5), and thus a decrease in diffusivity will result in
increasing water table height. A low-diffusivity hillslope is therefore more
susceptible to be initially fully saturated by the mean recharge of the
previous months, nullifying the dynamic effect of rainfall

Even though rainfall-induced pore pressure and atmospheric effects are both
based on the same diffusivity mechanism, their impact on slope stability is
very different.

While

The geomorphological and hydrogeological context of the location considered
plays an important role when assessing slope stability. For instance, the
position along the hillslope has a major influence on the dynamics of the water table. Indeed, water table variation depends on the boundaries of the
hillslope, namely the water divide and outlet. The position along the hillslope of the maximum variations of the water table is a function of the
diffusivity, but also the length of the slope and the period of the rainfall
recharge (Townley, 1995). Water table variations tend to reach a maximum near the crest of the hillslope when recharged by intense rainfall events such as typhoons. This implies higher values of

The initial elevation of the water table constrains the maximum amplitude of
the rain-induced pore pressure. Typhoons Krosa and Matsa occurred at a state
where the modelled water table reached the surface at the toe of the slope,
for a high diffusivity

Generally, towards the crest of the hillslope, where the hillslope is not fully saturated, rainfall effects are dominant (Fig. 7). Downslope, below the point where the water table reaches the topography, atmospheric effects are potentially dominant since they are the only dynamic effects. The limit between the atmospheric-driven domain and the rainfall-driven one will shift along the hillslope as a function of the past rainfall and initial height of the water table. In a wet season, where most of the hillslope is fully saturated, the limit shifts upwards, promoting atmospheric effects, while in a dry context, the limit shifts downwards, promoting rainfall effects.

Diagram representing the hillslope and the main driving effect for
a potential landslide during a typhoon. If the water table is deep

The geometry of the hillslope controls this distribution as well: the water table is less likely to reach the topography in a very steep and highly diffusive hillslope than in a shallow low-diffusivity hillslope. Moreover, the shape of the hillslope also plays an important role when determining the water table profile. In this case, the model assumes a hillslope of constant angle and width, water divide and outlet lines of the same lengths. However, a converging or diverging topography will change the drainage area and the steady state of the water table (Troch et al., 2002; Marçais et al., 2017). Converging topography will increase the saturation near the toe of the slope, while a diverging one will have the opposite effect.

This non-uniform distribution of the destabilising mechanisms along the hillslope suggests a non-uniform distribution of landslides triggered by
weather events. This in accordance with observations of landslides distribution in Taiwan, where typhoon-induced landslides were found to occur
close to the toe of hillslopes, in contrast to the relatively uniform
distribution of earthquake-induced landslides along hillslopes (Meunier et al., 2008). Therefore landslides triggered by typhoons tend to occur in the atmosphere-driven zone (Fig. 7), suggesting they occur due to atmospheric pressure changes. No direct conclusions should be drawn, however, as other phenomena can explain this distribution. This study focuses on the dynamic effects on

Most datasets on landslides occurring during a triggering event are based on
comparisons between pre- and post-event satellite images (Cheng et al., 2004; Nichol and Wong, 2005; Martha et al., 2015) or even Lidar data (Bernard et al., 2021), often acquired days or weeks apart. The timing of landslide occurrence during the event itself remains poorly constrained. This is problematic when trying to attribute landslides to their triggering factor, whether rainfall or atmospheric pressure drop. This results in most landslides being by default attributed to rainfall. At first order, this is a reasonable assumption given that it is the effect leading to the greatest disturbances compared to atmospheric effects. However, this prevents a better understanding of landslide triggering during storms, as

The rainfall-induced pore pressure follows a diffusion mechanism and is
delayed from the rainfall infiltration as a function of diffusivity and depth
(Fig. 4). The response time of the water table (Eq. 4) can be approximated to the first order by

On the contrary, the atmospheric effect

Hillslope's length also affects the timing of the response. Indeed, the
length

Maximum characteristic timescale of hillslopes response depending on diffusivity

As already mentioned, Typhoon Morakot triggered more than 10 000 landslides
in the south of Taiwan, leading to major damage and casualties (Lin et al.,
2011; Hung et al., 2018; Mihai and Grozavu, 2018). Landslides triggered by this event show a wide range in size, spanning from 576 m

The devastating effect of Typhoon Morakot might be due to the combination of heavy precipitation and a deep water table accommodating large pore pressure variations under hillslopes.

We developed a model to assess the respective role of hydrological and atmospheric forcing on slope stability. This model, based on a 2D hydrological computation of the water table, is an improvement of the well-known 1D infinite slope, as it makes it possible to better account for the along-slope geometry of the water table and its temporal variations following typhoons. We then used 1D diffusion equations to simulate pore pressure variations induced by rainfall and atmospheric perturbations.

The model was applied to several typhoons that struck Taiwan in order to understand the failure mechanisms leading to landsliding. Consistent with previous studies (Vassallo et al., 2015), our results show that rainfall can lead to significant pore pressure increases – more than 100 kPa in the case of Typhoon Krosa – especially towards the crest of the slope, where the water table elevation gains are maximum. On the other hand, for similar typhoons, atmospheric-induced pore pressure is usually around 1 kPa all along the slope, 1–2 orders of magnitude less than the rainfall contribution. However, the rainfall history plays a key role when assessing slope stability. Indeed, many typhoons strike over already fully saturated slopes, especially during or after the wet season, preventing further infiltration and leaving the atmospheric-induced pore pressure as the main destabilising factor. In more general terms, if models show that saturated slopes with low diffusivity could potentially fail simply in response to atmospheric pressure drop, rainfall infiltration remains by far the dominant destabilising factor for relatively dry slopes with high diffusivity. As a striking example, our results show that Typhoon Morakot occurred after a relatively dry period, leading to significant infiltration, water table rise and pore pressure increase, especially towards the toe of the slopes. Accounting for such groundwater dynamics is fundamental to explain the large number of triggered landslides that ruptured close to the hillslope toes (West et al., 2011). Our model outcomes also corroborate the preferential location of storm-triggered landslides at the toe of hillslopes (Meunier et al., 2008). As a long-term insight, we believe that a better characterisation of the timing of landslide failure during heavy storms or typhoons, for instance thanks to the development of SAR imagery (Singhroy and Molch, 2004; Xu et al., 2019; Esposito et al., 2020), could help to separate the respective role of atmospheric pressure drop and rainfall in slope destabilisation.

The code and the data used for this study are available at

LP and PS conceptualised the mechanical stability model. LP and LL worked on the hydrological model. MM helped by providing data. The codes were written by LP. All authors participated in improving the paper by editing.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors acknowledge the Taiwan Typhoon and Flood Research Institute, National Applied Research Laboratories, for providing the Data Bank for Atmospheric & Hydrologic Research service (

This research has been supported by the European Research Council, H2020 European Research Council (FEASIBLe (grant no. 803721)).

This paper was edited by Mario Parise and reviewed by three anonymous referees.