Abstract The dispersion index ( d σ ) 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 d σ is based on the assessment of SDP variations as the initial topography is also varied within a given elevation Δ h , while a length scale L defines the maximum extent of the SDP. As a result, d σ can be derived for different ranges Δ h 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 Δ h = 3 m and L = 1, 2, 4 and 8 km, demonstrating also the relationship between the range Δ h = 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.