Landslides triggered by rainfall: A semi-automated procedure to define consistent intensity–duration thresholds

Highlights

• We present a new methodology to define rainfall thresholds for landslide initiation.

• First a software program (MaCumBA) quickly analyzes large amounts of rainfall data.

• Then a back analysis selects the most effective threshold between many possible ones.

• The procedure is fast, automated, standardized and can be consistently replicated.

• Validation proves its reliability in warning systems implementations.

Abstract

In this paper, a methodology to automate and standardize the identification of rainfall intensity–duration thresholds for landslides triggering is presented. A newly developed software called MaCumBA (MAssive CUMulative Brisk Analyzer) can be used to analyze rain-gauge records, extract the intensities (I) and durations (D) of the rainstorms associated with the initiation of landslides, plot these values on a diagram and identify thresholds that define the lower bounds of the aforementioned I–D values. Because the methodology is automated, it is possible to process a relevant amount of data in short times, while allowing for user decision input. A back analysis using data from past events that did not trigger landslides can be used to identify the threshold conditions associated with the least amount of false alarms. We applied the methodology in two test sites. A validation procedure returned satisfactory results, demonstrating the potential utility of the proposed methodology in the development of landslide warning systems.

Introduction

Since landslides are responsible for casualties and costly damages to buildings, assets and infrastructures, it is of primary importance to forecast their occurrence and define effective warning systems (Guzzetti et al., 1999; Jakob et al., 2012). The application of physically based slope stability models for effective warning systems is at present feasible only at basin scale (Guzzetti et al., 1999, Segoni et al., 2009, Mercogliano et al., 2013, Rossi et al., 2013), while on regional scales empirical approaches are traditionally considered more effective (Aleotti, 2004, Tiranti and Rabuffetti, 2010). Rainfall events are oftentimes the primary triggering cause for landslides (Wieczorek, 1996, Farahmand and AghaKouchak, 2013) and they can be analyzed to define a statistical or empirical correlation between rainfall characteristics and landslide occurrence. This correlation can be expressed by a simple mathematical law that defines a threshold. If the same relationship observed for the past is assumed valid for the future, whenever the threshold is exceeded the occurrence of one or more landslides should be expected. As a result, regional scale warning systems which make use of only rainfall data as input parameters can be implemented (Sirangelo and Versace, 1996, Aleotti, 2004, Capparelli and Tiranti, 2010, Cannon et al., 2011; Jakob et al., 2012; Martelloni et al., 2012). Concerning rainfall thresholds, an empirical relationship linking rainfall intensity (I) and duration (D) with a power law (I=aD^−b, where a and b are empirical parameters) was first described by Caine (1980). Over 3 decades this approach has been successfully applied at various scales and in different physical settings, especially for debris flows and shallow landslides, but some authors successfully applied this approach to landslides of mixed typology (Hong et al., 2005, Guzzetti et al., 2007, Brunetti et al., 2010, Rosi et al., 2012).

However, I–D thresholds are often defined resorting to subjective decisions that cannot be consistently replicated in an automated warning system, thus reducing the effectiveness of the warning system itself.

The first difficulty encountered in the process of definition of rainfall intensity–duration thresholds is the identification of the rainfall conditions that have triggered each landslide. Many studies retrieve this information from official documents, which in turn sometimes report averaged or estimated values (Guzzetti et al., 2008). In many cases, the temporal evolution of the rainstorm at the exact landslide location is often not available, and it is necessary to identify a “representative” rain-gauge. The most common choice is to consider the rain-gauge closest to the landslide or at similar elevations in the same basin as the best representation. However, Aleotti (2004) highlighted that other factors should influence this decision (e.g. aspect and prevailing wind direction). In addition, rain-gauge networks provide rainfall measurements at discrete points, while rainstorms often exhibit a strong temporal and spatial variability (AghaKouchak et al., 2011). As a result, the identification of representative rain-gauges can be constrained by their spatial distribution.

In addition, once a rain-gauge is identified as representative of the landslide triggering conditions, the critical measures of the rainfall itself must be defined. Guzzetti et al. (2007) highlighted that a standardized procedure does not exist, as an example the rainfall intensity (and associated duration) may refer to either the peak precipitation rate measured during the rainstorm or to an average estimate of the mean precipitation rate of the whole rainstorm. Many authors use the concept of “critical rainfall”, which is defined as the “…rainfall from the time in which a sharp increase in rainfall intensity is observed” (Aleotti, 2004). This definition is rather subjective and it may introduce additional inconsistency in the modeling, especially when dealing with complex rainfall paths. Another widely used definition is “the rain that falls from the beginning of the rainfall event to the landslide triggering” (Tiranti and Rabuffetti, 2010), which has the advantage of having a higher degree of objectivity but still could bring to an oversimplification of complex rainfall paths characterized by alternating peaks of varying intensity.

In the past, rainfall intensity–duration thresholds were primarily visually drawn from intensity–duration data in a log–log graph (Caine, 1980) or the power law parameters were adjusted to fit the limits of empirical data (Aleotti, 2004). The subjectivity in the definition of the thresholds has been recently reduced introducing the use of statistical methods (Guzzetti et al., 2007, Guzzetti et al., 2008, Rosi et al., 2012), but such methodologies do not completely avoid the uncertainty, as different statistical approaches may lead to different thresholds, even with the same dataset (Brunetti et al., 2010).

Lastly, a clear distinction exists between the definition of a threshold and its operational use in warning systems. The same approach of analysis of rainfall data (e.g. to define the critical rainfall) should be consistently applied both during the threshold definition and during the operational scenario. In addition, although validation is considered a fundamental part in the scientific approach and in decision-making processes, very few studies present the results of a rigorous validation procedure performed against independent data sets (Martelloni et al., 2012).

This paper presents a methodology in which several passages of the process of the identification of rainfall intensity–duration thresholds are carried out by a newly developed software. The methodology tries to address the aforementioned criticalities traditionally encountered in similar studies and is divided into two parts. First, a software program called MaCumBA (MAssive CUMulative Brisk Analyzer) (Fig. 1) is used to automatically carry out the following tasks: (i) identification of the critical rainfall; (ii) definition of the critical parameters used to describe the rainfall event (critical intensity I and critical duration D); (iii) selection of the most representative rainfall record for a given landslide; (iv) graphing of the appropriate intensity–duration values, where each point represents the rainfall conditions associated to the triggering of a landslide; (v) definition of rainfall intensity–duration thresholds using a set of standard statistical procedures. The automation of the threshold definition procedure allows for the possibility to make several runs, varying the setting parameters, obtaining different thresholds with the same confidence level. In the second part of the procedure, an extension of MaCumBA is used to perform a back-analysis to identify the threshold which, true positives being equal, minimizes false positive errors. The first part of the proposed procedure provides a fast, automatic and standardized method to analyze rainfall data and to define triggering thresholds, without completely avoiding subjective decision; the second part provides an objective criterion to select the most effective threshold and to define the specific set of parameters to be consistently used by the operational warning system to minimize errors.

The proposed procedure was applied in two different areas to test the validity of the approach in different environmental conditions. The ultimate practical aim of this paper is to define and test a methodology that in the near future could be applied to set up a system of thresholds as the core of a regional warning system for the occurrence of rainfall triggered landslides. To this end, a validation procedure was carried out as well to evaluate the reliability of the automatically defined thresholds.