Dispersion index of topographic surfaces Massimiliano Favalli, Simone Tarquini ⁎, Alessandro Fornaciai, Enzo Boschi Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Pisa, Via della Faggiola, 32, 56126 Pisa, Italy abstract article info Article history: Received 30 July 2011 Received in revised form 17 February 2012 Accepted 25 February 2012 Available online 3 March 2012 Keywords: Dispersion index DEM Lava flow Geomorphic parameter Mount Etna The dispersion index (d σ ) of topography is introduced. This index is a geomorphic parameter which charac- terizes each point of topography with respect to the stability/instability of the steepest descent path (SDP) originating from it. The procedure for calculating d σ is based on the assessment of SDP variations as the initial topography is also varied within a given elevation Δh, while a length scale L defines the maximum extent of the SDP. As a result, d σ can be derived for different ranges Δh and different bandwidths L. Since at each point the gravitational force would direct a surface flow along the SDP, d σ appears to have a strong influence on the behavior of gravity-driven mass flows, influencing local topographic widening, spreading or channelization. Considering Mount Etna (Italy) as a test case, we present maps of d σ for Δh = 3 m and L =1, 2, 4 and 8 km, demonstrating also the relationship between the range Δh = 3 m and Etnean lava flows. Focusing on the 2001 lava flow, we show that the presented maps of d σ , besides being a tool for viewing morphologies, have interesting applications for hazard assessment related to lava flows. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Debris flows, lahars and lava flows are natural hazards that threat- en life and property in mountainous, volcanic, coastal and seismically active areas. Collectively known as gravitational flows, they occur when an unstable mass is located on a slope (e.g. a mobilized debris or lavas poured out from a vent). The mass tends to accelerate as gravity pulls it down the slope, and will slow down on gentler slopes, when driving forces wane. While several factors determine velocity and final run-out of a moving mass, local topography is fundamental in determining modulus and direction of the resulting driving force. To help in understanding landscape morphology, computer pro- grams dedicated to the environmental analysis represent digital ele- vation models (DEMs) in the form of 2D maps of some geometrical descriptors (e.g. Yokoyama et al., 2002). The simplest and most used representation is surface shading (or shaded relief map), which provides a perception of a digital surface similar to the one in the real world. Slope and aspect are the first order geometrical prop- erties of a DEM, while curvature and openness (Prima and Yoshida, 2010) are examples of geometrical properties of the second order. Chiba et al. (2008) introduced a new visualization method, the red re- lief image map, which allows the visualization of topographic slopes, concavities and convexities at the same time (Fig. 1). Surfaces can also be characterized through statistical descriptors such as rough- ness and the Hurst exponent (Shepard et al., 2001; Orosei et al., 2003; Morris et al., 2008). The latter properties are not local, and characterize the morphology at each point based on an increasingly wider neighborhood as the considered wavelength increases. Geo- morphic parameters have been used for geographic information sys- tem (GIS)-based classification of landforms at regional (e.g. Prima et al., 2006; Benito-Calvo et al., 2009) or continental scale (Iwahashi and Pike, 2007). In the present work we focus on the effect of Earth surface mor- phology on surficial flows. The topography underlying active mass flows is known to affect flow morphological characteristics (e.g. Gregg and Fink, 2000; Mazzarini et al., 2005). We introduce a new pa- rameter, the dispersion index, which characterizes each point of a to- pography according to local proneness of mass flows originating at (or passing on) that point to spread over topography or otherwise to stay channelized. We use Mount Etna as a case study, exploring the relationship of dispersion maps with the coverage of an actual lava flow. 2. Regional settings Mount Etna, in Sicily (Italy), is one of the most active and densely populated volcanoes of the world. On average, over the last three de- cades, a large effusive eruption occurs every two years, often threat- ening buildings and civil infrastructures. Today, about 900,000 people live on the flanks of this volcano (Behncke et al., 2005). Rising 3329 m a.s.l. (Neri et al., 2008), Mt. Etna is a stratovolcano located on the continental crust on the eastern coast of Sicily at the tectonic boundary marked by the subducting Ionian oceanic slab (Gvirtzman and Nur, 1999). Current activity of the volcano is charac- terized by effusive basaltic eruptions from central craters or from Geomorphology 153–154 (2012) 169–178 ⁎ Corresponding author. Tel.: + 39 050 8311932; fax: + 39 050 8311942. E-mail address: tarquini@pi.ingv.it (S. Tarquini). 0169-555X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2012.02.022 Contents lists available at SciVerse ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph