Estimation of debris flow triggering rainfall: Influence of rain gauge density and interpolation methods
Introduction
Rainfall-induced landslides and debris flows pose a significant and widespread hazard, resulting in a large number of casualties and enormous economic damages worldwide (Salvati et al., 2010, Petley, 2012, Borga et al., 2014, Dowling and Santi, 2014, Melillo et al., 2014). Considerable research efforts have been made so far to determine the rainfall amount required for rainfall-induced landslides or debris flows (Salvati et al., 2010). Rainfall thresholds are often used to identify the local or regional rainfall conditions that, when reached or exceeded, are likely to result in landslides or debris flows (e.g., Caine, 1980, Wieczorek, 1996, Deganutti et al., 2000, Cannon and Gartner, 2005, Guzzetti et al., 2008, Frattini et al., 2009, Saito et al., 2010, Chen et al., 2011, Jakob et al., 2012). Following the pioneering works of Caine (1980) and Innes (1983), rainfall thresholds for shallow landslides and debris flows (collectively termed ‘debris flows’ hereinafter) were determined at the local, regional, and global scales. Guzzetti et al. (2008) proposed a review of the literature on rainfall thresholds for the possible initiation of debris flows. The identification of rainfall thresholds is affected by a number of uncertainties that limit the accuracy of debris flow forecasts and warnings (Guzzetti et al., 2008, Kirschbaum et al., 2012, Nikolopoulos et al., 2014). A specific source of uncertainty lies in the estimation of the rainfall amounts that are responsible for debris flows (Guzzetti et al., 2007, Nikolopoulos et al., 2014).
Rain gauge data are the typical source of information for the definition of the rainfall thresholds. This implies that, with the exception of the very rare cases when rain gauge data are available at the debris flow initiation site, rainfall data for debris flow events are estimated based on data from more or less remote neighboring stations. This rainfall estimation is difficult for two main reasons. First, debris flow triggering storms are often characterized by large rainfall gradients, possibly influenced by complex topography (Marra et al., 2014). Second, unknown precipitation must be estimated at points where it exceeds a threshold and it often forms a local peak (Marra et al., submitted for publication). As a result, findings from the literature on rainfall spatial estimation (see Masson and Frei, 2014 and references therein), where the whole rainfall distribution is sought, may not be completely relevant for the case of debris flow triggering storms.
Inspection of the literature shows that little attention has been dedicated to the problem of rainfall estimation for debris flow triggering storms (Chiang and Chang, 2009, Melillo et al., 2014). While the spatial variability of rainfall fields is often identified as a potential problem, researchers often overlook it in debris flow threshold modeling primarily because of the scarcity of rain gauges, especially in mountainous areas (Jakob and Weatherly, 2003, Guzzetti et al., 2004). Debris flow triggering rainfall is often estimated based on the concept of the reference gauges (e.g., Jakob and Weatherly, 2003, Aleotti, 2004, Godt et al., 2006, Brunetti et al., 2010, Berti et al., 2012, Schneuwly-Bollschweiler and Stoffel, 2012), which relies on the observation at the gauge nearest to the debris flow location. Nikolopoulos et al. (2014) have shown that inferring rainfall properties at initiation points from the closest rain gauge is associated with significant uncertainty. Furthermore, they showed that application of the closest gauge estimates leads to significantly underestimated thresholds of debris flow occurrence with a subsequent degradation of the efficiency of the warning procedures based on these thresholds. However, the work of Nikolopoulos et al. (2014) is based on a simulation exercise; hence, results may be claimed dependent on the realism of the simulation experiment itself.
The work presented in this paper has two main objectives. Firstly, we aim to quantify the dependence of the accuracy of debris flow-triggering rainfall estimation on rain gauge density and the use of various rainfall estimation procedures. Secondly, we evaluate the impact of the rainfall estimation errors on the identification of the intensity–duration (ID, hereinafter) thresholds used for predicting landslide and debris flow occurrence. These questions are examined by using high-resolution, carefully corrected radar rainfall data to represent space–time patterns of true precipitation at the debris flow initiation points and in the surrounding area. These rainfall fields are sampled by simulated rain gauge networks, stochastically generated with varying gauge densities. This approach is ideally suited to assess the properties of rainfall estimation errors in areas with strong gradients, where alternative methods are lacking. As such, this approach has been used in a number of studies for the assessment of the influence of rainfall sampling on areal rainfall estimation and rainfall–runoff modeling (Seed and Austin, 1990, Duncan et al., 1993, Fabry et al., 1994, Bradley et al., 2002, Volkmann et al., 2010). The present work is based on the availability of accurate radar-based estimates of rainfall fields for 10 storms, which triggered 82 debris flows in a mountainous region in the Eastern Italian Alps (the Upper Adige River basin).
Based on such simulated networks, four gauge densities are considered and three interpolation techniques are used to derive rainfall estimates at the debris flow initiation points. The rainfall estimation procedures considered here are: i) the nearest neighbor technique; ii) the inverse distance method; and iii) ordinary kriging. These estimates are then used to identify the ID thresholds for debris flows occurrence. Results are compared against the reference threshold obtained by using the actual rainfall data at debris flow initiation locations. In order to isolate the properties of the interpolation algorithms and to assess the effects of varying rain gauge density, we do not apply here further criteria for the reconstruction of rainfall events, i.e. application of minimum rainfall depth thresholds (Melillo et al., 2014, Nikolopoulos et al., 2014).
Section snippets
Study area and data
The area of study is part of the Upper Adige River basin in Northern Italy (Fig. 1), a mountainous region with more than 64% of the area located above 1500 m a.s.l., whereas only 4% of the area is located below 500 m a.s.l. The south-eastern sector of the region belongs to the Dolomites, the north-eastern part to the Noric Alps and the western sector to the eastern Rhaetian Alps, including the highest peak of Mt. Ortles (3902 m) (Norbiato et al., 2009a, Piacentini et al., 2012). The climate pattern
Methodology
To study issues related to rainfall estimation errors, the radar data were assumed to be the “true” observed rainfall and were therefore used as the reference for comparative analysis. An advantage of this is that variations in precipitation, as observed by radar and gauges, are represented empirically. In mountainous regions where orography influences precipitation patterns in complex ways (Molinié et al., 2012), the space–time patterns of non-stationary storm precipitation are very difficult
Analysis of the rainfall estimation error
For each realization of simulated rain gauge networks, rainfall estimates at DF locations were obtained from the three interpolation methods (NN, IDW, and OK). Interpolated values were then compared against the radar rainfall observations at the actual DF location, which serves as reference throughout the analysis. Error in rainfall estimation is expressed in terms of relative error, εr, defined aswhere RtotiDF and RtotDF are interpolated and reference total event
Conclusions
The main objective of this work is to examine the problem of rain gauge-based estimation for rainfall events responsible of debris flows. We analyzed first the effect of rain gauge network density and spatial interpolation methods on the estimation of rainfall at the DF locations and then investigated the propagation of the rainfall estimation errors in the identification of ID thresholds. We have examined these issues by simulating rain gauge networks based on a random sampling exercise of
Acknowledgments
This work is supported by EU FP7 Marie Curie Actions IEF project PIEF-GA-2011-302720) (HYLAND, http://intra.tesaf.unipd.it/cms/hyland/). We sincerely acknowledge Ripartizione Opere Idrauliche, Autonomous Province of Bolzano (Italy), for providing access to the archive of debris flows and Ufficio Idrografico, Autonomous Province of Bolzano (Italy), for providing hydrological and meteorological data and for providing access to the weather radar information. We express our sincere gratitude to
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