The selected study site is situated on the lower slope of a ravine on a hillside in the city of Castries, Saint Lucia (eastern Caribbean), in which informal construction of houses has led to increased landslide risk. The slope section is approximately 50 m in height and has an overall angle of about 30∘. The material strata comprise up to 6 m of residual soils overlying a similar depth of decomposed rock (weathering grades III–IV; after GEO, 1988) overlying volcanic bedrock. As is typical for the humid tropics, the dominant landslide trigger in the Caribbean is rainfall (Lumb, 1975; De Graff et al., 1989), and shallow rotational slides are the most common type of landslide in the deep weathered tropical residual soils on the mid to lower slopes of steep hillsides (Migon, 2010). Such locations tend to be the only land available to the most socio-economically vulnerable families, so even small landslide events can have a high societal impact (UNISDR, 2015). These “everyday disasters” are also increasingly seen as indicators of risk accumulation (low disaster resilience) and represent a potential hindrance to national economic development (Bull-Kamanga et al., 2003).

In 2011 a landslide hazard reduction project was implemented at the study site location using a community-based approach – Management of Slope Stability in Communities (Mossaic) – developed by Anderson and Holcombe (2006). At the time, estimates of geotechnical, hydrological and geometrical parameters for the study site were derived from a combination of: topographic maps, site surveys, interviews with residents to estimate soil strata depths and weathering grades (based on their experiences of excavating the soils to construct house foundations), elicitation of local engineering knowledge of soils, and information from shear box and ring infiltrometer testing of similar soils in Saint Lucia. Soil properties were also benchmarked against extensive triaxial and permeameter test data for similar undisturbed tropical residual soils in Hong Kong (GCO, 1982).

Deterministic physically based modelling of slope stability has previously been carried out at the study site using the Combined Hydrology And slope Stability Model (CHASM) to diagnose landslide drivers and estimate the benefit–cost ratio of landslide mitigation (Holcombe et al., 2012). In a validation exercise in Hong Kong CHASM was shown to be numerically robust and capable of correctly classifying 78 % of failed slopes and 68 % of stable slopes (i.e. true positives, TP = 78 %; false positives, FP = 22 %; true negatives, TN = 68 %; false negatives, FN = 32 %) for a specified rainfall event (Anderson, 1990), corresponding to an accuracy of 72.5 % ((TP + TN) / (total observed failed slopes + total observed stable slopes)). This is comparable with, or exceeds, the performance of spatially distributed GIS-based models such as a statistical analysis of landslide susceptibility in Central America (using the Hurricane Mitch landslide inventory) that attained an accuracy of 68 % (Kirschbaum et al., 2012); and a physically based infinite-slope analysis (using modified SINMAP) in the data-rich region of Calabria, Italy, that achieved a maximum TP rate of 71 % and accuracy of 72 % (Formetta et al., 2014, p. 639). This level of accuracy might typically enable disaster risk managers and practitioners (such as engineers and planners) to identify slopes exhibiting potentially high hazard and prioritize further investigation and/or risk reduction accordingly. CHASM has been extensively used by slope stability researchers and practitioners to assess landslide hazards along roads and in urban and rural areas, and to propose appropriate mitigation in Malaysia, Indonesia, the eastern Caribbean, United Kingdom and New Zealand (Anderson et al., 1997; Lloyd et al., 2001; Wilkinson et al., 2002a, b).

A brief overview of CHASM is given here – full descriptions of the numerical scheme and principal equations can be found in Anderson and Lloyd (1991) and Wilkinson et al. (2002b). CHASM represents the slope cross-section as a regular two-dimensional mesh of columns and cells with geotechnical and hydrological parameters specified for each soil type (Fig. 2). Initial hydrological conditions are the matric suctions (negative pore pressure) in the top cells of each column and the water table position. Subsequent dynamic forcing conditions are rainfall events of specified intensities and durations imposed on the top cells. For each hydrological time step (usually 10–60 s) a forward-explicit finite difference scheme is used to solve Richards' equation (Richards, 1931) and Darcy's law (Darcy, 1856) for rainfall infiltration, unsaturated and saturated groundwater flows. Cell moisture conditions, pressure heads and unsaturated hydraulic conductivities are updated at each time step using soil moisture characteristic curves and the Millington–Quirk procedure (Millington and Quirk, 1959). At the end of each simulation hour the pressure head fields are used to calculate pore water pressures (positive and negative) for input to a two-dimensional limit equilibrium method (LEM) calculation of slope stability. In LEM analysis the slope factor of safety (F) is calculated as the ratio of destabilising forces to resisting forces for a potential landslide slip surface location, such that F<1 indicates failure. In CHASM either Bishop's simplified circular method of slices (Bishop, 1955) or Janbu's non-circular method (Janbu, 1954) is implemented using an automated search algorithm to identify the location of the slip surface with the minimum value of F for that hour.

The study site slope cross-section, as represented in CHASM, is illustrated in Fig. 2. Slope input factors (slope geometry, geotechnical and hydrological properties) are assumed to be random variables characterized by different statistical distributions. These distributions and their statistical parameters have been obtained from different sources as described in Sect. 2.1, and summarized in Table 1. For each set of CHASM input factors generated via random sampling, checks are undertaken to ensure that any combination of the input factor values that is physically unrealistic (for example, with saturated unit weight smaller than unsaturated unit weight) is discarded from further analysis (and replaced by another randomly generated, feasible combination). The complete list of such feasibility checks is given in the footnote of Table 1. For the purposes of this study the model discretization parameters – such as the cell size (1 m × 1 m), hydrological time step (60 s), and slip search grid location and dimensions – and physical and mathematical constants are not varied. These discretization parameters are selected based on preliminary model simulations and our previous experience of applying CHASM to similar slopes, and they ensure the numerical stability and conservation of mass (water) of the hydrological component throughout the simulation period. These choices are thus meant to minimize the number of failed model runs during the Monte Carlo simulation process.

The dynamic hydrological scheme of CHASM requires the specification of hourly rainfall intensities to drive the dynamic hydrological component of CHASM for the selected hydrological time step (60 s). While the uncertainties in slope properties are characterized by probability distributions based on past experience of applying the model to the study area, the potential variability of future rainfall is difficult to define with a probability distribution, hence the term of “deep” uncertainty. We therefore represent our lack of knowledge by varying rainfall intensity–duration combinations widely to ensure that any feasible future design storm in a changing climate is captured in our sampling. The ranges of rainfall intensity and duration used in this analysis are based on intensity–duration–frequency (IDF) relationships derived for the design of the Roseau Dam in Saint Lucia (Fig. 3). Engineering consultants, Klohn-Crippen (1995), applied Gumbel analysis of 40 years of daily rainfall data from weather stations around the island to estimate the intensities and durations of 1:5 to 1 : 500-year return periods events. From these IDF relationships we define ranges of possible rainfall intensities of 0 to 200 mm h-1 and durations of 0 to 72 h, which we sample independently and uniformly.

For this experiment the first 168 h of rainfall forcing are set to an intensity of 0 mm h-1 to allow the moisture distribution within the unsaturated zone to be established based on the suction–moisture curve. This is necessary because the initial moisture content in each unsaturated cell at time step zero is a linearly interpolated value between the initial surface suction and position of the estimated water table (where the pressure head is 0 m). Then after the first iteration of the hydrological function in CHASM the Millington–Quirk equation is used to update the moisture content based on the suction–moisture curve. The implementation of a 168 h start-up (zero rainfall) period should be sufficient to establish a representative moisture distribution and potentially steady-state seepage (equilibrium). However, if hydrological equilibrium is not attained, this is still an acceptable representation of the physical processes that may be observed in such slopes. For instance, it may replicate the high groundwater tables that often exist in our study area towards the end of a rainy season.

Rainfall of the selected intensity and duration is then imposed on the slope to determine the stability of the slope for that storm event. In the absence of information on typical hourly rainfall rates for events longer than 1 h, rainfall intensity is assumed to be uniform across the rainfall duration sampled. The storm is followed by a further 168 h of zero-rainfall simulation time to consider the continued effects of the groundwater response on slope stability.

While different algorithms have been used to implement the mapping step in bottom-up approaches in past studies, we have chosen to use classification and regression trees (CART). Comparison between the most popular algorithms, CART and PRIM, did not show either algorithm to be superior (Lempert et al., 2008), while CART has the advantages of simplicity and an ability to work with minimal input from the user. CART is a machine-learning method for constructing prediction models from data (Breiman et al., 1984). In our application, such model takes the form of a binary tree, where a categorical dependent outcome (i.e. slope failure versus stability) is predicted from a set of continuous independent variables (i.e. slope and design storm properties). The tree is composed of nodes and branches. At each node, an if-then condition is applied to one of the independent variables (e.g. “slope angle above or below 30 degrees”) to generate two different branches. Several strata of nodes and branches compose the tree up to a stratum of terminal nodes (leaf nodes) where a prediction of the categorical dependent outcome is made (e.g. “slope fails”).

A CART is constructed through a recursive algorithm applied to a sample of independent variables (inputs) and associated categorical outcomes (outputs). In this study, the input/output sample is generated by the Monte Carlo simulation of CHASM. The algorithm automatically selects which input variable and threshold value to use at every node. The selection is based on maximizing the homogeneity of the output samples in the subsequent nodes. The level of homogeneity can be measured by different criteria. Here, we use the Gini impurity measure, which is defined as 1-∑i=1mp2i, where m is the number of categories for the output (2 in our case), and pi is the fraction of output samples in the node belonging to category i. A Gini impurity index equal to 0 corresponds to a pure node, i.e. a node where all output samples belong to the same category. In general, pure nodes cannot be obtained, but the algorithm seeks to minimize the Gini impurity index.

A key question in constructing a classification tree is that of the optimal sizing (i.e. number of nodes and branches). Increasing the size of the tree generally increases its predictive accuracy over the sample used for its construction, but it might reduce its ability to generalize to new samples (overfitting). Moreover, a tree with simpler structure might be easier to interpret and communicate. Once a CART has been constructed, a machine learning technique called “pruning” can be applied to reduce the size of the tree by removing sections that provide little classification power. More details about the pruning technique can be found, for example, in Hastie et al. (2009).

For our study site the ratio of the topsoil stratum's effective cohesion to stratum thickness is shown to be a dominant factor in the stability of the slope. Inspection of selected model outputs indicates that the critical slip surface generally tends to be located within this top stratum (weathering grade V–VI) with the deepest part of the slip circle at the interface with the weathered material stratum (grade III–IV), as illustrated in Fig. 2. The slip surface location within the topsoil stratum is explained by the site-specific parameters (Table 1) in which: (i) the higher strength weathered material stratum constrains the failure surface to within the weaker soil stratum above; and (ii) as rainfall infiltrates, the lower hydraulic conductivity of the weathered material is likely to cause loss of soil matric suction and thus a reduced apparent strength at the soil/weathered material interface.

Of the two topsoil stratum strength parameters, it is effective cohesion, rather than angle of friction, that shows up in the CART analysis because the study site slope is likely to be cohesion controlled rather than friction controlled – i.e. the slope angle is typically greater than the friction angle. Figure 6 shows that when the topsoil stratum is thin it can remain stable even for very low values of effective cohesion, whereas, thicker soils tend to require a much higher effective cohesion for stability. This result is in keeping with other physically based modelling studies of the relationships between the geometry of slopes, strata and shallow landslides in cohesion controlled slopes (Frattini and Crosta, 2013; Milledge et al., 2014). Ignoring the effects of water table location and pore water pressures, the greater self-weight of soil at the base of a thicker soil stratum generates higher shear stresses and requires greater shear resistance for stability than in a shallower soil.

The importance of cohesion for the stability of tropical residual soil slopes, such as our study site, and its inclusion in stability analysis is the subject of an ongoing debate amongst geotechnical engineering, researchers and practitioners. Laboratory analysis of the shear strength of remoulded clays show that the value of the effective cohesion parameter is affected by measurement uncertainties (Parry, 2004) and that peak cohesion is lost with seasonal cycles of dilatancy (Take and Bolton, 2011). The known sensitivity of slope stability to cohesion and the uncertainties associated with its measurement thus lead some engineers to adopt a highly conservative approach to the value of effective cohesion used in slope design – often assigning it a value of zero (Schofield, 2006). Yet, landslide hazard assessment scientists and engineering practitioners in the humid tropics argue for its inclusion as an observable strength parameter in the analysis of existing slopes comprised of undisturbed tropical residual soils which exhibit relict structures from the weathered parent rock (Burland et al., 2008). For the study site, our modelling approach supports the inclusion of non-zero values of effective cohesion in the analysis to account for its observable stability in the field. Our results also indicate that any data acquisition strategy for this site should target both soil thickness and effective cohesion values (both undisturbed and remoulded) to improve landslide hazard predictions.

The second most important factor in the stability of our study site is the nature of rainfall events in terms of their intensity and duration. As noted in Sect. 4, when the predicted failed and stable slopes are plotted on log–log axes of associated rainfall intensities and durations (Fig. 8) a negative linear threshold is found above which landslides are more likely to occur. This relationship is observed in landslide inventories which are widely used to generate empirical regional rainfall intensity–duration (I–D) thresholds of the form I = a1 D-a2, where a1 and a2 are parameters specific to a site or region (e.g. Larsen and Simon, 1993; Guzzetti et al., 2007). In the absence of empirical data, physically based models may be used to generate synthetic thresholds using Monte Carlo methods (e.g. Peres and Cancelliere, 2014). Our method thus demonstrates the importance of representing the dynamic hydrological processes involved in triggering landslides, while also providing a starting point for generating site-specific rainfall I–D thresholds in data-scarce locations.

We have to reiterate that our results are valid within the context of the assumptions made in our study. For example, changing a particular input factor distribution may influence the importance of other factors. This is not a limitation of our study only, but of any model-based study and sensitivity analysis application. Particularly relevant for our study is that we evaluate the occurrence of slope failure for individual rainfall events and we do not consider explicitly the impacts of varying initial hydrological conditions that may result from sequences of rainfall events. This limitation is partially mitigated by the fact that we jointly vary the intensity–duration of individual events and the initial depth of water table. The approach presented here is a useful contribution for identifying dominant landslide preparatory and triggering factors, guiding data acquisition and refining the hazard assessment.

In this study, we have evaluated how uncertainty about slope characteristics and future rainfall change may influence risk of slope failure. Our findings have demonstrated that, for our study site, physical slope properties, namely effective cohesion and thickness of the topsoil, are significant drivers of slope stability. For this slope, these physical properties have a more significant impact on landslide hazard risk than variability in future rainfall intensity and duration. Extending this type of study to other slopes would allow further exploration of the complex interactions between soil depth, permeability, rainfall intensity-duration, antecedent rainfall and the resulting slide depth (see, for example, Lumb, 1975; van Asch et al., 2009).

Our findings have a number of important implications for landslide hazard research. Previous studies typically have analysed the impacts of uncertainty related to slope characteristics and future climate independently. For example, Dehn and Buma (1999), Collison et al. (2000) and Ciabatta et al. (2016) consider the impacts of climate change on slope stability, but ignore uncertainty around soil properties; while Rubio et al. (2004) account for uncertainty introduced by slope hydrology and geotechnical properties, but ignore uncertainty relating to design storms. However, our results suggest that the failure to consider both sources of uncertainty simultaneously may lead to a significant underestimation of slope susceptibility to landslides under potential climate change. Furthermore, we have demonstrated how physically based models, like CHASM, can be utilized to rapidly assess the impacts of multiple interacting and uncertain drivers of landslide occurrence in ways that would not be possible using simpler statistical models (e.g. Dixon and Brook, 2007).

To date, only Melchiorre and Frattini (2012) have attempted to analyse slope failure considering both uncertainty arising from slope properties and future climate. Their research used a top-down approach to quantify the impacts of multiple uncertainties. Specifically, they used Monte Carlo simulations and sensitivity analysis to assess the impacts of uncertainty in soil properties on predictions of slope stability for a pre-defined set of precipitation scenarios. We conclude that deep uncertainty due to potential future climate characteristics is not yet fully considered in landslide hazard assessment, and, as a result, policy recommendations may lead to undesirable outcomes given the difficulty in predicting impacts of climate change on future rainfall. In contrast, bottom-up approaches, such as that proposed in this study, consider a much wider range of possible system drivers (rainfall) and other uncertainties, without introducing assumptions regarding the probability of future precipitation. This insight is particularly relevant for small islands like the Caribbean, where the variety of different processes that contribute to rainfall change, some of which are poorly resolved by GCMs, make it very difficult to provide projections of future rainfall (Seneviratne et al., 2012).

Bottom-up approaches to natural hazard risk assessment provide valuable knowledge to inform management decisions and to target data acquisition, especially in situations where resources may be limited. This study has shown how dominant physical slope properties driving landslide occurrence for a particular class of slope can be identified. As a result, decision makers may seek to provide funding for targeted data acquisition to reduce uncertainty about the values of these parameters (e.g. thickness and effective cohesion of topsoil) in order to improve understanding of how likely a slope is to fail. Decision makers could also use the knowledge gained from CART to target management practices to improve slope stability (e.g. improving slope drainage or land cover) or to develop options to mitigate consequences of slope failure (e.g. restricting development in high-risk areas). In this regard, the methodology developed in this study could be used to quantify the impact of different management options on landslide occurrence thresholds, providing an objective measure of the potential value of each strategy that can support debate amongst disaster risk reduction practitioners.

CART also has the distinct advantage that trees can provide useful knowledge for decision makers even when uncertainties about future changes in climate are large, as is the case with rainfall projections in the Caribbean islands that are predominant areas where landslides occur globally. Any available climate information can be used a posteriori to assess the plausibility of threshold tipping points being crossed, and support the discussion whether improved management is required to improve slope stability in the future. Ultimately, the decision to implement any given action depends on how risk averse stakeholders are and how much they are willing to spend on an adaptation strategy. However, CART provides the tools and information to enable managers to make informed choices that are robust under a wide range of plausible future conditions, reducing the risk of wasted investment and/or unanticipated negative outcomes.