Contribution of dendrochronology to the determination of magnitude–frequency relationships for landslides Jordi Corominas ⁎, Jose Moya Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, UPC, Jordi Girona 1-3, D-2 Building, 08034 Barcelona, Spain abstract article info Article history: Received 5 September 2009 Received in revised form 7 July 2010 Accepted 1 September 2010 Available online 8 September 2010 Keywords: Landslides Rockfalls Debris flows Complex slides Magnitude–frequency Dendrogeomorphology The determination of magnitude–frequency (M–F) relationships is necessary for landslide hazard assessment. Ideally, this is achieved by using inventories of past landslide events recorded by technical units or aerial photo interpretation. However, direct sources of landslide data are often unavailable. Dendrogeomorpho- logical techniques allow us to determine the frequency of events, but few attempts have been made to estimate landslide magnitude by analysing the spatial distribution of disturbed trees. This paper addresses M– F determination for rockfalls, debris flows and complex slides obtained by dendrogeomorphology. The cases presented require the appropriate understanding of both the geomorphological context and the disturbance caused by landslide motion on trees. Both small and large rockfalls can be identified and dated by reconstructing the trajectories in the forest stand. The larger the rockfall size, the longer the path, the higher the number of affected trees and the greater the area of deposition of rock fragments. The area of damaged trees is proposed as an indicator of the rockfall magnitude. The frequency and extent of a series of debris flows were reconstructed by mapping their deposits using relative dating criteria and by dating damaged trees. Local and global mudslide reactivations were deduced by sampling various tree generations and by analysing the location of the disturbed trees in the landslide units. Magnitude–cumulative frequency curves were determined for the three cases. © 2010 Elsevier B.V. All rights reserved. 1. Introduction The total risk at a given site results from exposure to small and frequent landslide events and large and infrequent landslides. Areas threatened by potential landslides with catastrophic consequences might be classed as low hazard areas if the probability of occurrence is very low whereas areas with frequent landslides of low magnitude may be considered as moderate or high hazard areas (Lateltin, 1997, 2002). One of the main challenges faced by the authorities when considering possible risk mitigation measures and allocating funds is to evaluate the risk level of a given area in terms of expected annual losses. Quantitative risk analysis can play a role in this evaluation but data on the magnitude and frequency distribution of the landslides are indispensable (Hungr et al., 1999). These two parameters are usually presented in plots of landslide magnitude versus cumulative (or non-cumulative) frequency curves (Guzzetti et al., 2002). The construction of these curves is essential for hazard assessment. The magnitude–frequency relationships for landslides have been discussed by a number of researchers (i.e. Hovius et al., 1997; Pelletier et al., 1997; Hungr et al., 1999; Guzzetti et al., 2002; Malamud et al., 2004; Picarelli et al., 2005). These authors have consistently found that the M–F distribution of landslides appears to have a power-law similar to that observed in seismology. The Gutenberg–Richter relation- ship between earthquake magnitude and cumulative frequency of earthquakes is expressed as follows: log Nm ð Þ = a-bM ð1Þ where:N(m) is the cumulative number of earthquake events of magnitude equal or greater than M, and a and b are constants. It can be shown that this equation is equivalent to a fractal (power law) relationship between the number of earthquakes and the characteristic size of the rupture (Turcotte, 1997). The magnitude of landslides may be represented by either the area (Hovius et al., 1997; Pelletier et al., 1997; Guzzetti et al., 2002) or the volume of the deposits (Hungr et al., 1999; Dai and Lee, 2001; Guzzetti et al., 2003). Magnitude–cumulative frequency (MCF) relationships have been developed for rockfalls (Bunce et al., 1997; Hungr et al., 1999; Dussauge-Peisser et al., 2002; Chau et al., 2003; Guzzetti et al., 2003), rock avalanches (Whitehouse and Griffiths, 1983), debris slides and debris flows (Brardinoni and Church, 2004; Guthrie and Evans, 2004; Hungr et al., 2008) and landslides (Guzzetti et al., 2002). Recent reviews of M–F relationships for landslides may be found in Guzzetti et al. (2002), Malamud et al. (2004) and Picarelli et al. (2005). Geomorphology 124 (2010) 137–149 ⁎ Corresponding author. Tel.: +34 93 401 68 61; fax: +34 93 401 72 51. E-mail address: jordi.corominas@upc.edu (J. Corominas). 0169-555X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2010.09.001 Contents lists available at ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph