Analysis of topographic and climatic control on rainfall-triggered shallow landsliding using a quasi-dynamic wetness index

Abstract

A model for the prediction of both topographic and climatic control on shallow landslide initiation processes in hilly mountainous terrain is proposed. The model develops upon a theory for coupled shallow subsurface flow and landsliding of the soil mantle previously proposed by Montgomery and Dietrich [Water Resour. Res. 30 (1994) 1153]. The model uses a ‘quasi-dynamic’ wetness index to predict the spatial distribution of soil saturation in response to a rainfall of specified duration. The rainfall predicted to cause instability in each topographic element is characterised by duration and frequency of occurrence. The incorporation of a rainfall frequency–duration relationship into assessment of landslide hazard provides a practical way to include climate information into estimation of the relative potential for shallow landsliding. The model is applied to a mountain experimental basin where high-resolution digital elevation data are available: the Cordon catchment (5 km²), in north-eastern Italy. An inventory of landslide scars is used to document sites of instability and to provide a test of model performance by comparing observed landslide locations with model predictions. The model reasonably reproduces the observed distribution of landslides, although spatial variability of soil properties and hydrologic complexities not accounted for by the model complicate prediction of where landslides occur within areas of similar topographic-climatic control. Model predictions from the quasi-dynamic model are compared with those provided by the steady-state model [Water Resour. Res. 30 (1994) 1153]. These results suggest that the quasi-dynamic model offers significant improvement over the steady-state model in predicting existing landslides as represented in the considered landslide inventory.

Introduction

Landsliding associated to rainstorms is a major process of landscape evolution on steep hillslopes. The trigger mechanism for most of these shallow slope failures is the rapid buildup of pore water pressure above a hydrologic impeding layer in the trough of geomorphic hollows. Once the hollows fail as shallow debris slides, debris avalanches, or debris flows, they gradually fill in by localised sloughing around the headwall, soil creep, weathering of exposed bedrock or till, surface erosion, and recruitment of organic debris (Dietrich and Dunne, 1978, Benda and Dunne, 1997). The periodicity of evacuation of these hollows depends on the long-terms rates of infilling and the timing of episodic storms as well as the effects of vegetation removal.

Shallow landsliding is important not only as a geomorphological process, but also as a cause of natural hazards. The resultant need to predict landslide occurrence at landscape scales has led to the development of numerous stochastic/statistic and process-based models, with increasing emphasis on the use of GIS in the past 10 years. Statistical models rely on statistical correlation between landslide frequency and factors such as slope, lithology, and geologic structure (Pike, 1988, Carrara et al., 1991). The process-based landscape models have generally used some variation on the factor of safety equation (Selby, 1985, p. 228) coupled with geomorphic, hydrological, geological, and vegetation data to estimate slope, slope shape, cohesion, and subsurface flow characteristics (Okimura and Kawatani, 1986, van Asch et al., 1993, Montgomery and Dietrich, 1994, Miller, 1995, Wu and Sidle, 1995, Wu and Sidle, 1997, Van Westen and Terlien, 1996, Pack and Tarboton, 1997, Borga et al., 1998, Iida, 1999, Montgomery et al., 2000, Borga et al., 2002).

Dietrich et al., 1992, Montgomery and Dietrich, 1994 developed a simple physically based model (steady-state model, hereafter), based on digital terrain data, which couples a shallow saturated subsurface model with an infinite slope stability model. The steady-state model incorporates a scheme based on the formulation proposed by O'Loughlin (1986) to simulate the topographic dependence of runoff generation during transient storm events in humid environments. Based on this approach, maps of equilibrium soil saturation are generated from the analysis of the upslope contributing areas, soil transmissivity, and local slope. This hydrologic model thus reduces to a calculation of the ratio of local flux at a given rainfall to that at soil profile saturation. The utilisation of the O'Loughlin model relies upon two key assumptions: the existence of steady-state conditions; and that total potential is dominated by the elevation (topography) potential.

Simplified approaches such as the steady-state model are well suited to portray the topographic control of hydrology on shallow landsliding. However, the problem of predicting susceptibility to shallow landsliding at the landscape scale is complicated by the interaction between static and dynamic environmental factors. While topographic control of the near-surface hydrologic response can be treated as a static factor in slope stability models, relevant dynamic factors include variability of rainfall intensity and duration as well as spatial and temporal variation in the species, age, and density of vegetation.

Dynamic models of the hydrological response at the watershed scale have been developed to account for variability in both rainfall input and vegetation. Wu and Sidle, 1995, Wu and Sidle, 1997 developed and tested a dynamic, distributed, physically based slope stability model (dSLAM). The dSLAM model combines an infinite slope model, a kinematic wave groundwater model, and continuous change model for vegetation root cohesion and surcharge. In the application of dSLAM model to steep forested terrain, it is assumed that the infiltration capacity of the soil is always greater than rainfall intensity, thus only subsurface flow and non-Hortonian overland flow is simulated. Explicit routing models such as the dSLAM, are generally applied over areas where sufficient information on the spatial variability of the topographic and soil parameters that control water movement are available. The need for generalising from intensely studied sites to broader landscapes with sparse data sets presents a problem for these explicit routing approaches. There is a need therefore to develop a methodology which is able to cope with dynamic factor as the variability of rainfall intensity and duration and yet maintains the simplicity of the index approach.

In this paper, we first analyse the implications of using the steady-state assumptions incorporated into the steady-state shallow failure model and show how this assumption may be relaxed by using a quasi-dynamic wetness index, introduced by Barling et al. (1994). It is then shown how the quasi-dynamic wetness index may be derived from the kinematic wave model for subsurface flow. This shows the linkages between the index-based approach to slope stability analysis and the modelling approach based on the dynamic simulation of landscape response to storms. The quasi-dynamic subsurface runoff model is coupled with the local intensity–duration–frequency (IDF) rainfall equation and with an infinite slope, Coulomb failure model which assumes that the soil is cohesionless at failure to predict duration and frequency of the rainfall necessary for landslide initiation to occur across the catchment. The model is designed to incorporate the spatial variability of IDF relationship across the landscape, thus allowing for the inclusion of climatic control (further than topographic control) on shallow landsliding analysis. The model is applied and tested in the Rio Cordon basin (5 km²), a mountainous catchment in the Dolomites where field surveys provide a description of hydraulic and geotechnical properties of soils and an inventory of landslide scars is available. A methodology for the intercomparison of slope stability index models is introduced and a comparison with the results provided by the steady-state model is described.