Dispersion index of topographic surfaces

Geomorphology 153–154 (2012) 169–178

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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

a r t i c l e

i n f o

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

a b s t r a c t 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. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Debris flows, lahars and lava flows are natural hazards that threaten 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 programs dedicated to the environmental analysis represent digital elevation 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 properties 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 relief 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 roughness and the Hurst exponent (Shepard et al., 2001; Orosei et al., 2003; Morris et al., 2008). The latter properties are not local, and

⁎ Corresponding author. Tel.: + 39 050 8311932; fax: + 39 050 8311942. E-mail address: [email protected] (S. Tarquini). 0169-555X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2012.02.022

characterize the morphology at each point based on an increasingly wider neighborhood as the considered wavelength increases. Geomorphic parameters have been used for geographic information system (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 morphology 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 parameter, the dispersion index, which characterizes each point of a topography 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 decades, a large effusive eruption occurs every two years, often threatening 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 characterized by effusive basaltic eruptions from central craters or from

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Fig. 1. Red relief image of Mount Etna which reveals the varied morphology. Inset at lower left shows the geographical position of Etna. The white dotted line encloses the area covered by the 2005 LIDAR survey (Favalli et al., 2009a), the rest is covered by the TINITALY/01 DEM (Tarquini et al., 2007). SC: Summit Craters. PF: Pernicana Fault. TFS: Timpe Fault System. The areas of Figs. 4, 6, 7, 8 and 9 are indicated as F4 etc. Projection, UTM zone 32N; Datum WGS84. Tick marks indicate kilometer coordinates.

lateral vents accompanied by explosive activity (e.g. Behncke and Neri, 2003). The present volcanic edifice is the result of a complex geological history, including major caldera-forming plinian eruptions (Branca et al., 2004) and partial flank failures of the eastern flank (Calvari et al., 2004). All these processes shaped the main profile of the volcano leading to an asymmetric edifice and uneven slopes. The flanks of this volcano are scattered with more than 300 monogenetic scoria cones formed during flank eruptions (Mazzarini and Armienti, 2001). These cones are grossly clustered in three sectors along the NE, S and W rift zones. Several faults have an evident morphological expression on the eastern sector of the volcano (e.g. Pernicana and Timpe faults, see Fig. 1) which is experiencing an eastward sliding (Acocella et al., 2003). At a local scale, the recursive effusive activity led to the emplacement of new ′a′ā lava flow fields with a rough surface, while the frequent fall out of fine-grained tephra tends to smooth landforms (Neri et al., 2008; Favalli et al., 2009a). As an outcome, the morphology of Mount Etna is rather varied and evolves continuously at all scales. 3. Material and methods 3.1. Digital elevation models (DEMs) In this work we use two DEMs, both obtained as 10 m-cell size grids. The first DEM has been resampled from the 2 m-cell size grid obtained from the airborne LIDAR survey in September 2005

(Favalli et al., 2009a). This survey covered an area of about 622 km 2 (Fig. 1). The average density of the gathered elevation spots was 0.41 pts m − 2, and raw data have been corrected for reducing the RMS planimetric and altimetric errors to ± 0.48 m and ± 0.16 m respectively (Favalli et al., 2009a). The second DEM has been derived by gridding the TINITALY/01 DEM, which is an improved triangular irregular network (TIN) computed from the digital regional cartography of the Catania Province at 1:10,000 scale (Tarquini et al., 2007; see also Favalli and Pareschi, 2004 for details). For the TINITALY/01 DEM of Mount Etna, Neri et al. (2008) calculated a root mean square vertical error of 1.98 m. In the following we will mainly use a merge of the two DEMs, where the central and eastern parts of the volcano are covered by the LIDAR-derived DEM and the rest by the TINITALY/ 01 DEM (Fig. 1). 3.2. Maps of dispersion index 3.2.1. The steepest descent path (SDP) Considering a terrain surface as a continuous, derivable function in the form of z = f(x,y), the gradient of f is denoted as ∇ f and is given by:  ∇f ¼

 ∂f ∂f ; ∂x ∂y

ð1Þ

∇ f is a vector that points towards the greatest increase in elevation, typically this is referred to as the slope expressed as percentage.

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The arctangent of the slope gives the slope expressed in degrees. The aspect (ψ) is the direction of the greatest decrease in elevation (− ∇ f) and is usually measured clockwise from the North. A linear (hence 2D) path following locally the direction of − ∇ f, is called the steepest descent path (SDP). We consider here mass flows set in motion by the gravitational force on the Earth surface. In terms of gravitational po→ tential (ϕ), the acceleration is simply given by a ¼ −∇φ and when the movement is confined on a surface z = f(x,y) the acceleration → due to gravity becomes a ¼ −g∇f , where g is the gravitational acceleration. This means that, if we consider this mass movement over a digital model representing a portion of the Earth surface (hence a DEM), the acceleration due to the gravitational force is along the direction of the SDP at each point of the DEM. In other words, at each point the gravitational force would direct the flow along the SDP. 3.2.2. Deviations from the SDP In general, natural mass flows do not strictly follow the SDPs because of the presence of other factors (e.g. Dragoni et al., 1986; Miyamoto and Sasaki, 1997; Favalli et al. 2005). Lava flows, for example, are relatively “slow” flows in which viscous and self-gravitational terms (e.g. Dragoni et al., 1986) play a fundamental role in creating complex compound flows that can overflow obstacles, bifurcate and braid (Favalli et al., 2010a). On the other hand, for “faster” flows such as lahars, snow avalanches or pyroclastic flows, other physical properties can influence the diversion of the flow from the SDP. Whatever the physical properties that induce deviations from the local SDP, the morphology plays an important role. Let us consider two contrasting examples. In case a (Fig. 2a), the initial SDP is constrained within a preexisting valley, and the morphology itself acts against the forces which tend to deviate the flow. In case b (Fig. 2b), instead, the initial SDP runs over an “open” morphology (e.g. a convex slope), and a relatively small perturbing/deviating force will divert the path far from the initial one. Considering the same perturbing forces acting on both cases, the final contrasting result will be a channelized flow in case a, and a dispersed flow in case b (Fig. 2a,b, stage 2). This difference holds as far as the perturbing/deviating forces are not strong enough to overcome the morphological constraint of case a. Let us consider a third case c (Fig. 2c), where the initial SDP is running on a morphology with a smaller valley than in case a. In this case, the SDP spreads out from the initial morphological constraint when

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the perturbing/deviating forces overcome a threshold much lower than the one which would generate spreading in case a. In general, the morphological constraint of a site, over which an SDP passes, is given by the depth (d) of the valley (or gully) which locally bound the SDP itself (Fig. 2a, stage 1). Therefore, the stability of the SDP is greater in case a than in case c while in case b the path is unstable. From the above description, it is clear that the underlying morphology plays a crucial role in allowing channelization or dispersion of superficial flows. The present work is aimed at quantifying and mapping this feature at each point of a topography. 3.2.3. The dispersion area An SDP (let us call it SDP0) is univocally defined given a starting point p and an input topography such as a DEM in grid format. If we slightly modify the input topography by adding a noise in elevation (i.e. by randomly varying elevation values of the DEM within a given range ± Δh, see Fig. 3a), we will obtain different SDPs originating from the same point p (let us call it SDP1). Fig. 2 suggests that if the perturbation Δh is small with respect to an existing morphological constraint (d) along SDP0, SDP1 will still be contained within the constraint (Fig. 2a), otherwise it could spread out (Fig. 2b,c). If we reiterate a number N of times a similar procedure generating further SDPs starting from the same input DEM by applying a similar noise (i.e. the same Δh range), we obtain a family of N SDPs (Fig. 3b). All these SDPs will “behave” similarly to SDP1. Hence, we will obtain a family of paths confined within the morphological constraint in case a of Fig. 2 and a broad fan of paths in case b of Fig. 2. As the number of iterations N increases, the envelope of all the SDPs will progressively define all the area which is “floodable” from the starting point p (under the given perturbation Δh) and which is shown, case by case, in stage 3 of Fig. 2. The cumulative coverage (or envelope) of a family of paths is calculated as the sum of the grid cells of the DEM crossed by at least one path, times the cell area. The ideal cumulative coverage is reached when the limit for the number of iterative SDP creations N → +∞, but in practice, we will see that a few thousands of iterations (N) meet our needs. Fig. 2 shows that we will obtain the smallest coverage in case a (A1), where multiple paths will repeatedly pass over the same grid cells inside the morphological constraint, and a much wider coverage in cases b and c (A2 and A3, respectively). As a result, the different size of A1, A2 and A3 are a

Fig. 2. Concept of the perturbation of the steepest descent path (SDP) and envelope of the perturbed SDP for three schematic cases (a to c) with three stages (1 to 3). See main text for details.

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Fig. 3. Illustration of the algorithm used to trace SDPs. a) Conceptual scheme of the perturbation of the topography within ± Δh. b) 3D view of a portion of topography with 100 SDPs obtained from the point ps. The mesh is obtained by connecting the centers of the cells of the elevation grid. In general, the 3D polygons constituting such mesh connects four vertices which in general are not coplanar. c) Zoom showing the forced triangulation generating meshes with coplanar vertices, i.e. a TIN. The exact SDPs are then calculated in vector form over the TIN.

straightforward expression of the different proneness to SDP dispersion or channelization over the three topographies illustrated in Fig. 2. From the above, it is clear that the extent of the envelope of SDP families can be an indicator of the degree of local proneness to dispersion/channelization due to morphology. An SDP will end in a local minimum or at the limits of the frame. To better characterize the envelope it is necessary to truncate all the SDPs at a given maximum length (L), and the corresponding SDP coverage will be referred to as AL. The information carried by AL depends on the morphology encountered by SDPs within the bandwidth or length scale L. As an example, Fig. 3b shows that after an initial dispersion over a convex shape, the family of SDPs originated from the point ps tends to converge near point c, and to stay channelized afterwards. Fig. 4 further illustrates this concept for a point p1 on our test case (Mount Etna), for Δh = 3 m and N = 10,000. Fig. 4a shows the coverage AL for L = 1, 2, 4 and 8 km, while AL values as a function of L are plotted in Fig. 4b. In the first 1 km SDPs are well channelized, while in the second 1 km they rapidly spread; afterwards, SDPs tend to converge at ~6 km. 3.2.4. The dispersion index The basis for making a dispersion map is the measurement of AL for each cell of the computational DEM. Δh and L are set according

to specific needs. As for the number of iterations N, the determination of the smallest acceptable value is quite important, because we need to calculate AL over millions of cells (depending on the size of the computational DEM), and setting N to 1000 instead of 10,000 would mean a significant difference from a computational point of view. For this reason we have explored, for increasing N, the values of AL at different points. As an example, in Fig. 5 we show the values of AL, for Δh = 3 m and L = 2 km, measured at a selected point of dispersion (Ad) and in another selected point of channelization (Ac). The ratio Ad/Ac (Fig. 5) shows that N = 2000 is a good compromise between computational cost and reliability of results. Specific features implemented in the algorithm used to trace single SDPs are illustrated in Fig. 3b–c. Once ALi is calculated at all the ith pixels of the input DEM, we create a map where the extent of the corresponding ALi coverage is attributed to each ith pixel. This map can be designated as a dispersion map, being ALi a straightforward expression of the proneness to channelization/dispersion of SDPs from the ith point within the distance L from that point. To enable comparisons among maps generated with various Δh and L, we introduce the dimensionless dispersion index (dσ) defined as: dσ ¼ ðALi –ALave Þ=sσ

ð2Þ

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Fig. 4. Coverage AL of 10,000 SDPs from p1 at different lengths L, see main text for definition of AL and L. a) Coverage area AL (colored areas) wrapped over shaded relief map. White dotted line marks the boundary among two different sources for the DEM. b) Plot of AL vs L. Projection, UTM zone 32N; Datum WGS84. Tick marks indicate kilometer coordinates.

where ALave and σS are, respectively, the average and standard deviations of the ALi values measured at all the cells of the considered region S. It must be noted that the region S over which the analysis is carried out influences the value of dσ. In general σS ~ 1/2 ALave, and dσ is in the range −2 to 3 for DEMs having strikingly different resolutions and accuracies. Examples of the main parameters and statistics of calculated dispersion maps are shown in Table 1. Fig. 6 shows the relation between the definition of dσ and morphometric properties (slope, openness and roughness).

each volcano): Mount Etna (Δh = 3 m; e.g. Tarquini and Favalli, 2010), Nyiragongo (Δh = 0.4 m; Favalli et al., 2009b) and Mount Cameroon (Δh = 2.2 m; Favalli et al., 2012). Recently, Tarquini and Favalli (2011) have further evaluated the robustness of the Δh value originally proposed by Favalli et al. (2005) for lava flow path forecasting at Mount Etna (Δh = 3 m), finding satisfactory results in a wide range of real cases.

3.2.5. Dispersion map vs actual mass flows The defined map of SDP dispersion is a straightforward tool for the visualization of topographic surfaces, without a need to ensure a correlation between specific mass flows and the parameters selected for the map (Δh and/or L). However, in the case of Mount Etna a well established relationship between the perturbation range Δh and lava flows emplacement already exists. This is demonstrated by the successful application of the DOWNFLOW code (Favalli et al., 2005). DOWNFLOW is a probabilistic, DEM-based method to determine the area inundated by lava flows. Both the DOWNFLOW code (Favalli et al., 2005) and dispersion maps rest on the same principle of SDPs determination over a topography randomly affected by an elevation noise within ± Δh. Moving from a dimensional analysis of the momentum equation of lava flow (Miyamoto and Sasaki, 1997), Favalli et al. (2005) argued that, for this specific mass flow and setting Δh to half the characteristic flow height, the SDP perturbations are able to take into account first-order variations in lava flow spreading. DOWNFLOW has been extensively applied to lava flow hazard analysis at some basaltic volcanoes (setting specific Δh values for

4.1. Dispersion maps for Mount Etna

Fig. 5. AL as a function of N for a dispersive point (Ad) and a for a channelizing point (Ac). Note the ratio Ad/Ac becomes almost stable for N > 1000.

4. Application

At Mount Etna hazardous flows are typically represented by streams of basaltic lava (Favalli et al., 2009c,d; Crisci et al., 2010). As discussed in the previous section, we set Δh = 3 m, so that the obtained dispersion maps should be considered representative for the behavior of lava flows. We calculated ALi for L = 1, 2, 4 and 8 km at all the pixels in a 13 km radius centered on the summit craters and a 6 km radius around a secondary peak of probability of future vent opening determined from Favalli et al. (2009c); then we derived dσ values to build the dispersion maps of Fig. 7. Fig. 8 shows details of these maps along with maps of shaded relief, slope, openness and roughness to allow a direct comparison between different morphological descriptors. 4.2. Dispersion index along an actual lava flow The lowermost of the lava flow fields formed during the 2001 Mount Etna eruption (L2001 flow in the following) from the effusion of about 21.4 × 10 6 m 3 of lava (Coltelli et al., 2007). This flow has been extensively studied and simulated by using several lava flow simulation codes (e.g. SCIARA, Crisci et al., 2004; MAGFLOW, Vicari et al., 2007; LavaSIM, Proietti et al., 2009). To explore if there is a relationship between dσ of the pre-emplacement topography and the shape of the actual flow, we calculated the dispersion map over the 1998 DEM. We set Δh = 3 m as above and L = 0.5 km, to explore shortdistance variations (Fig. 9b). Then, we measured and plotted flow width, average slope and average dσ as a function of the down-flow distance (i.e. averaging slope and dσ values over all the pixels set at the same distance from the vent; Fig. 9c,d). We found a substantial agreement between the distance downflow of the three broad, relative maxima of the first part of the plot of the average dσ value and the relative maxima of the plot of the flow width (i.e. peaks are almost superimposed along the abscissas axis; Fig. 9d). On the other hand, in the remaining part of the flow any agreement disappears (gray area in Fig. 9d). Interestingly the same partition was detected by Favalli et al. (2010b) who distinguished the initial-central part of the L2001 flow, characterized by

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Table 1 Main parameters and statistics of calculated dispersion maps. Figure

7b, 8e 8b 7c, 8c 7d, 8d a

9b

Region

Etna Etna Etna Etna Etna Etna

DEM

Dispersion index

Source

Year

Resolution (m)

RMSE (m)b

Δh (m)

L (km)

LIDAR/TINITALY LIDAR/TINITALY LIDAR/TINITALY LIDAR/TINITALY LIDAR TINITALY

2005/1998 2005/1998 2005/1998 2005/1998 2005 1998

10 10 10 10 2 10

0.16/1.98 0.16/1.98 0.16/1.98 0.16/1.98 0.16 1.98

3 3 3 3 1 3

1 2 4 8 0.1 0.5

Area (km2) Average

σ

0.14 0.32 0.71 1.55 0.0021 0.062

0.06 0.15 0.35 0.8 0.0010 0.024

a

Maps not shown in the present work. Elevation accuracy of the 2005 LIDAR is from Favalli et al. (2009a). All other vertical root mean square errors (RMSE) were calculated at Mount Etna by using as reference surface a high resolution LIDAR-derived DEM (2007 LIDAR, Favalli et al., 2009a). b

the existence of a “stable channel”, from the distal segment, where the flow became transitional and eventually dispersed (the extreme downhill reach of the flow front). Those authors found that this distinction is marked by the presence of a clear break in slope along the main axis of the flow (see Fig. 4 in Favalli et al., 2010b). In comparison, the similar plot of the average slope (Fig. 9c) seems to be less informative, being dominated by short wavelength peaks

which do not show an evident agreement with the ones of the plot of the flow width. 5. Discussion Fig. 6a,c,e shows the envelope of 10,000 SDPs from point p1 (also shown in Fig. 4a), which is used to define dσ at p1, overlaid to maps

Fig. 6. The envelope of 10,000 SDPs of Fig. 4 wrapped over maps of geomorphic parameters. White dotted line marks the boundary among two different sources for the DEM. a) Slope map. b) Width of the SDPs envelope (black curve) and average slope down-flow from p1 (red curve, see also main text). c) Openness map (Yokoyama et al., 2002; length scale 500 m). d) Width and openness down-flow. e) Roughness map at 50 m bandwidth (from Shepard et al., 2001). f) Plot of width and roughness calculated as above. Note the effect of the different DEM sources on the texture of the surface, mainly due to a different roughness. Projection, UTM zone 32N; Datum WGS84. Tick marks indicate kilometer coordinates.

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Fig. 7. Etna case study. a) Slope map of the DEM of Mount Etna; source data for the area enclosed by the orange dotted line is a LIDAR survey (Favalli et al., 2009a), the rest is TINITALY/ 01 (Tarquini et al., 2007). The areas of Figs. 4, 6, 8 and 9 are indicated as F4 etc. b) to d) show dispersion maps for different length scales L and Δh = 3 m. The legend in b) applies also to c) and d).

of slope, openness and roughness. Fig. 6b,d,f provides the values of respective parameters averaged over all the pixels of the envelope at the same down-path distance from p1 and plotted versus the downflow distance itself. In each plot, the relevant geomorphic parameter is compared to the width of the SDPs' envelope. Initially, the path are well constrained within a deep and narrow valley. This is evidenced by the plots in Fig. 6 which display high slopes and openness in the initial part. Fig. 6b shows an overall negative correlation between the width of the envelope and slope in the first 2–3 km downhill p1. A similar correlation holds also between width and openness (Fig. 6d). Interestingly, none of the considered geomorphic parameters tell anything about the SDP envelope portion beyond the first 2–3 km. For example, the sudden narrowing between 5.5 and 6.5 km shows no evidence in the slope, openness or roughness plots. In any case, even if there might be a piecewise correlation between slope (or openness) and width of the SDP envelopes, the value of dσ at p1 takes into account contribution along a distance L down-path. For this reason, in general, dispersion maps are not correlated with slope, openness, and roughness (Fig. 8).

Dispersion maps can be used as a straightforward way to characterize topographic surfaces at different length scales. Concerning practical uses of dispersion maps, we established in our test case a clear association between Δh and Etnean lava flows. The expected behavior of future lava flows at each (mapped) point over Mount Etna is best displayed by Fig. 7. In particular, these maps show if flows starting at, or passing through a given point are likely to spread or otherwise to stay channelized within the next 1, 4 or 8 km downhill from that point. Areas of minimum dispersion suggest that SDPs originating there are not easily diverted from the original path, and prediction of flow evolution in these cases is easier. In contrast, areas of maximum dispersion indicate that flows tend to divert in multiple directions and locally the ability to predict future scenarios is less accurate. In other words, the lower dσ values encountered (i.e. channelized flow), the easier the prediction of the direction followed by the related flow. This information can be easily combined with existing hazard and/or risk maps (e.g. Favalli et al., 2009c,d; Crisci et al., 2010) during an ongoing crisis, to adequately tune the alert level on the basis of an increased awareness.

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Fig. 8. Zoom on the Etna case study. a) Shaded relief. b) Slope map. c) Openness map (Yokoyama et al., 2002, length scale 500 m). d) Roughness map at 50 m bandwidth (Shepard et al., 2001). (e to h) Dispersion maps for different length scales L (indicated in each panel) and Δh = 3 m. The legend in e) applies also to f) to h). Projection, UTM zone 32N; Datum WGS84. Tick marks indicate kilometer coordinates.

Dispersion maps of Fig. 7 show that existing volcano morphologies create evident corridors of low and high dispersion values. The most evident example is the impressive channelization corridor trending NE from the summit craters (SC in Fig. 1) which is clearly visible in the maps obtained at all the considered length scales L (as shown also in Fig. 8). Another example can be found in the portion of the

south flank where the L2001 flow emplaced. This area still shows low dσ values on the DEM updated to 2005 (then already including the L2001 flow), indicating that possible future flows entering the same area from uphill will probably evolve southwards in a narrow corridor as occurred in 2001. On the contrary, the same maps show that immediately at the southeast of the L2001 vent, a future flow

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Fig. 9. Coverage of the L2001 lava flow wrapped over maps of slope and dσ of the 1998 topography of Mount Etna (see Figs. 1 and 7 for location on the southern flank of the volcano). a) Slope map. b) Dispersion map (Δh = 3 m and L = 0.5 km). (c and d) Average down-flow values for slope and dσ, respectively, along with down-flow width. Red arrow in b) points to a dispersion maximum which eventually led to a flow bifurcation (see main text). dσ values are shifted along the abscissas by half the length scale L, because dσ, per se, stores information about the topography from the considered point up to a distance L. Gray area in the right-end portion of d) indicates the distal segment of the L2001 flow, where a drastic decrease of down-channel slope led to a different behavior of the flow. UTM zone 32N; Datum WGS84. Tick marks indicate kilometer coordinates.

would likely spread along different paths, then away from the L 2001 flow. Similar analyses could be of use also in designing artificial diversions of future flows, suggesting areas where a possibly diverted flow could follow a well constrained path (low dσ) and areas where a flow could be less easily controlled (high dσ). At a more local scale, Fig. 9 illustrates that the plot of the average dσ value of the topography underneath an actual flow shows peak values (relative maxima) in agreement with peaks of flow width. In particular, it is worth noting that the relative maximum at 3.5 km down-slope in Fig. 9d originates from an area of maximum dispersion on the left side (facing the down-flow direction) of the flow (red arrow in Fig. 9b), which has been ultimately the site of a major, late bifurcation of the 2001 flow field (Coltelli et al., 2007). Published simulations of the L2001 flow testify that existing deterministic codes were not able to reproduce the mentioned bifurcation without adding ephemeral vents in a position that could hardly be guessed before (Crisci et al., 2004; Vicari et al., 2007). Thus dispersion maps turn out to be an useful tool to estimate points of possible flow bifurcation, and it is evident that a dispersion map provides an additional information that can help in assessing the reliability of simple simulations. The dispersion map (Figs. 7 and 8) rests on the collection of 2000 SDPs at each of the six million pixels representing the mapped coverage (Fig. 7), for a cumulative 1.2 × 10 10 SDPs for each considered L. This data layout has a density 64 times higher than current highresolution lava flow hazard and risk maps (Favalli et al., 2009c,d), and can help in estimating the possible behavior of future flows at a very detailed scale. Dispersion maps neither substitute simple simulations of natural flows nor replace hazard maps, but should be used jointly with simulations and hazard maps to improve the assessment of expected scenarios.

6. Conclusions Dispersion maps are a new tool for the visualization of topography. We illustrated the procedure to derive dispersion maps as matrices (grids) of dσ. The dσ value of a given point p on a topography is relative to a given elevation range Δh and to the length L of the considered SDP. A negative dσ means proneness to channelization (or to flow narrowing) and a positive dσ proneness to dispersion (or flow widening). We showed an application of the dispersion maps at Mount Etna. dσ is univocally determined by local morphology (within the distance L from the considered point), but a relation between the range Δh and a specific kind of superficial mass flows (i.e. lava flows at Etna) can be established. In this particular case, dispersion maps result in an interesting information layer to support hazard management of ongoing effusive events. Beyond the case shown here, further assessments of possible relations between different kinds of mass flows and specific values of Δh and L are promising, and could contribute to a better understanding of processes that shape landforms.

Acknowledgments This manuscript benefited from thorough and insightful reviews of O.D.A. Prima and J. Procter. Eric Pirard contributed to improve the clarity of the manuscript. This work benefited from funding provided by the Italian Dipartimento della Protezione Civile in the frame of the 2007–2009 agreement with the Istituto Nazionale di Geofisica e Vulcanologia—INGV. Scientific papers funded by the DPC do not represent its official opinion and policies.

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References Acocella, V., Behncke, B., Neri, M., D'Amico, S., 2003. Link between major flank slip and 2002–2003 eruption at Mt. Etna (Italy). Geophysical Research Letters 30, 2286. doi:10.1029/2003GL018642. Behncke, B., Neri, M., 2003. The July–August 2001 eruption of Mt. Etna (Sicily). Bulletin of Volcanology 65, 461–476. Behncke, B., Neri, M., Nagay, A., 2005. Lava flow hazard at Mount Etna (Italy): new data from a GIS-based study. In: Manga, M., Ventura, G. (Eds.), Kinematics and Dynamics of Lava Flows: Geological Society of America Special Paper, 396, pp. 189–208. Benito-Calvo, A., Pérez-González, A., Magri, O., Meza, P., 2009. Assessing regional geodiversity: the Iberian Peninsula. Earth Surface Processes and Landforms 34, 1433–1445. Branca, S., Coltelli, M., Groppelli, G., 2004. Geological evolution of Etna volcano. In: Bonaccorso, A., Calvari, S., Coltelli, M., Del Negro, C., Falsaperla, S. (Eds.), Mt. Etna Volcano Laboratory. : Geophys. Monogr. Ser., vol. 143. American Geophysical Union, Washington, D.C., pp. 49–63. Calvari, S., Tanner, L.H., Groppelli, G., Norini, G., 2004. Valle del Bove, eastern flank of Etna volcano: a comprehensive model for the opening of the depression and implications for the future hazards. Mt. Etna: Volcano Laboratory, Geophys. Monogr. Ser., vol. 143, edited by A. Bonaccorso et al. AGU, Washington, D.C., pp. 65–75. Chiba, T., Kaneta, S., Suzuki, Y., 2008. Red relief image map: new visualization method for three dimensional data. The international Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. : Part B2, vol. XXXVII. Beijing. Coltelli, M., Proietti, C., Branca, S., Marsella, M., Andronico, D., Lodato, L., 2007. Analysis of the 2001 lava flow eruption of Mt. Etna from 3D mapping. Journal of Geophysical Research 112, F02029. doi:10.1029/2006JF000598. Crisci, G.M., Rongo, R., Di Gregorio, S., Spataro, W., 2004. The simulation model SCIARA: the 1991 and 2001 lava flows at Mount Etna. Journal of Volcanology and Geothermal Research 132, 253–267. Crisci, G.M., Avolio, M.V., Behncke, B., D'Ambrosio, D., Di Gregorio, S., Lupiano, V., Neri, M., Rongo, R., Spataro, W., 2010. Predicting the impact of lava flows at Mount Etna, Italy. Journal of Geophysical Research 115, B04203. doi:10.1029/2009JB006431. Dragoni, M., Bonafede, M., Boschi, E., 1986. Downslope flow models of a Bingham liquid: implications for lava flows. Journal of Volcanology and Geothermal Research 30, 305–325. Favalli, M., Pareschi, M.T., 2004. Digital elevation model construction from structured topographic data: the DEST algorithm. Journal of Geophysical Research 109, F04004. Favalli, M., Pareschi, M.T., Neri, A., Isola, I., 2005. Forecasting lava flow paths by a stochastic approach. Geophysical Research Letters 32, L03305. doi:10.1029/2004GL021718. Favalli, M., Fornaciai, A., Pareschi, M.T., 2009a. LiDAR strip adjustment: application to volcanic areas. Geomorphology 111, 123–135. Favalli, M., Chirico, G.D., Papale, P., Pareschi, M.T., Boschi, E., 2009b. Lava flow hazard at Nyiragongo volcano, D.R.C. 1. Model calibration and hazard mapping. Bulletin of Volcanology 71, 363–374. Favalli, M., Mazzarini, F., Pareschi, M.T., Boschi, E., 2009c. Topographic control on lava flow paths at Mt. Etna (Italy): implications for hazard assessment. Journal of Geophysical Research 114, F01019. doi:10.1029/2007JF000918. Favalli, M., Tarquini, S., Fornaciai, A., Boschi, E., 2009d. A new approach to risk assessment of lava flow at Mount Etna. Geology 37, 1111–1114. Favalli, M., Fornaciai, A., Mazzarini, F., Harris, A., Neri, M., Behncke, B., Pareschi, M.T., Tarquini, S., Boschi, E., 2010a. Evolution of an active lava flow field using a multitemporal LIDAR acquisition. Journal of Geophysical Research 115, B11203. doi:10.1029/2010JB007463. Favalli, M., Harris, A., Fornaciai, A., Pareschi, M.T., Mazzarini, F., 2010b. The distal segment of Etna's 2001 basaltic lava flow. Bulletin of Volcanology 72, 119–127.

Favalli, M., Tarquini, S., Papale, P., Fornaciai, A., Boschi, E., 2012. Lava flow hazard and risk maps at Mount Cameroon volcano. Bulletin of Volcanology 74, 423–439. doi:10.1007/s00445-011-0540-6. Gregg, T.K.P., Fink, J.H., 2000. A laboratory investigation into the effects of slope on lava flow morphology. Journal of Volcanology and Geothermal Research 96, 145–159. Gvirtzman, Z., Nur, A., 1999. The formation of Mount Etna as the consequence of slab rollback. Nature 401, 782–785. Iwahashi, J., Pike, R.J., 2007. Automated classifications of topography from DEMs by an unsupervised nested-means algorithm and a three-part geometric signature. Geomorphology 86, 409–440. Mazzarini, F., Armienti, P., 2001. Flank cones at Mount Etna volcano; do they have a power-law distribution? Bulletin of Volcanology 62, 420–430. Mazzarini, F., Pareschi, M.T., Favalli, M., Isola, I., Tarquini, S., Boschi, E., 2005. Morphology of basaltic lava channels during the Mt. Etna September 2004 eruption from airborne laser altimeter data. Geophysical Research Letters 32, L04305. doi:10.1029/ 2004GL021815 (September). Miyamoto, H., Sasaki, S., 1997. Simulating lava flows by an improved cellular automata method. Computers & Geosciences 23, 283–292. Morris, A.R., Anderson, F.S., Mouginis-Mark, P.J., Haldemann, A.F.C., Brooks, B.A., Foster, J., 2008. Roughness of Hawaiian volcanic terrains. Journal of Geophysical Research 113, E12007. Neri, M., Mazzarini, F., Tarquini, S., Bisson, M., Isola, I., Behncke, B., Pareschi, M.T., 2008. The changing face of Mount Etna's summit area documented with Lidar technology. Geophysical Research Letters 35, L09305. doi:10.1029/2008GL033740. Orosei, R., Bianchi, R., Coradini, A., Espinasse, S., Federico, C., Ferriccioni, A., Gavrishin, A.I., 2003. Self-affine behavior of Martian topography at kilometer scale from Mars Orbiter Laser Altimeter data. Journal of Geophysical Research 108, 8023. doi:10.1029/2002JE001883. Prima, O.D.A., Yoshida, T., 2010. Characterization of volcanic geomorphology and geology by slope and topographic openness. Geomorphology 118, 22–32. Prima, O.D.A., Echigo, A., Yokoyama, R., Yoshida, T., 2006. Supervised landform classification of Northeast Honshu from DEM-derived thematic maps. Geomorphology 78, 373–386. Proietti, C., Coltelli, M., Marsella, M., Fujita, E., 2009. A quantitative approach for evaluating lava flow simulation reliability: LavaSIM code applied to the 2001 Etna eruption. Geochemistry, Geophysics, Geosystems 10, Q09003. doi:10.1029/2009GC002426. Shepard, M.K., Campbell, B.A., Bulmer, M.H., Farr, T.G., Gaddis, L.R., Plaut, J., 2001. The roughness of natural terrain: a planetary and remote sensing perspective. Journal of Geophysical Research 106, 32,777–32,795. Tarquini, S., Favalli, M., 2010. Changes of the susceptibility to lava flow invasion induced by morphological modifications of an active volcano: the case of Mount Etna, Italy. Natural Hazards 54, 537–546. Tarquini, S., Favalli, M., 2011. Mapping and DOWNFLOW simulation of recent lava flow fields at Mount Etna. Journal of Volcanology and Geothermal Research 204, 27–39. Tarquini, S., Isola, I., Favalli, M., Mazzarini, F., Bisson, M., Pareschi, M.T., Boschi, E., 2007. TINITALY/01: a new Triangular Irregular Network of Italy. Annals of Geophysics 50, 407–425. Vicari, A., Herault, A., Del Negro, C., Coltelli, M., Marsella, M., Proietti, C., 2007. Modeling of the 2001 lava flow at Etna volcano by a cellular automata approach. Environmental Modelling and Software 22, 1465–1471. Yokoyama, R., Shirasawa, M., Pike, R.J., 2002. Visualizing topography by openness: a new application of image processing to digital elevation models. Photogrammetric Engineering and Remote Sensing 68, 257–265.