Dispersion index of topographic surfaces

The dispersion index (dσ) of topography is introduced. This index is a geomorphic parameter which characterizes each point of topography with respect to the stability/instability of the steepest descent path (SDP) originating from it. The procedure for calculating dσ 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, dσ 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, dσ 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 dσ 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 dσ, besides being a tool for viewing morphologies, have interesting applications for hazard assessment related to lava flows.