1
FORECASTING
LAVA FLOW
HAZARDS DURING THE 2
006
ETNA
ERUPTION: USING
THE MAGFLOW CELLULAR
AUTOMATA MODEL
Herault Alexis
1,2
,
Annamaria Vicari
1,
*
,
Alessia Ciraudo
1,3
,
Ciro Del Negro
1
1
Istituto Nazionale di Geofisica e Vulcanologia

Sezione di Catania, I
tal
y
2
Laboratoire de Science de Information

Université de Marne La Vallée

Paris XIII, France
3
Dipartimento di Matematica e Informatica
–
Università di Catania, Italy
* Corresponding author:
Annamaria Vicari
E

mail address: vicari@ct.ingv.it
Phone Number
: +390957165800
Fax Number: +39095435801
Abstract
The MAGFLOW cellular automata model was able to
fairly
accurately reproduce the time of
the lava flow
advance
during the 2006 Etna eruption
leading to very plausible flow
predictions.
MAGFLOW is intended f
or use in emergency response situation
s
during an
eruption to quickly forecast the lava flow path over some time interval from
the
immediate
future to
a
long

time forecast. Major discrepancies between the observed and simulated
paths occurred in the early
phase of the 2006 eruption due to an underestimation of the initial
flow rate, and at the time of the
overlapping
with the 2004

2005 lava flow. Very good
representations
of the areas likely to be inundated by lava flows were
obtained when we
adopt a time

v
arying effusion rate and include the 2004

2005 lava flow field
in the Digital
Elevation Model (DEM) of topography
.
Keywords:
Lava Flow, Etna volcano, Numerical Simulation
, MAGFLOW model
Introduction
Timely predictions of the areas likely to be inundated
by lava flows are of
major
interest to
hazard managers during a volcanic eruption.
Although most volcanic lava flows do not result
in loss of human life, they can potentially cause enormous damage to property. Lava flows
can bury homes and agricultural lan
d under
several
meters of hardened rock. Typical
2
examples of lava flows are from the Etna
volcano
,
where
its frequent effusive eruptions
can
pose hazard to several
villages
(
Behncke et al., 2005
).
In order to estimate the amount of
damage that can be cause
d by a lava flow, it is useful to be able to predict the size and
extent of such flows. Numerical simulation is a good tool to examine such
events
. With such
simulations, one can explore various eruption scenarios and these can specifically be used
to esti
mate the extent of
the
inundation area, the time required for the flow to reach a
particular point and resulting morphological changes (
Del Negro et al., 2006
).
Forecasting lava flow paths on a volcanic edifice requires the development, validation and
appl
ication of accurate and robust physical

mathematical models able to simulate their
spatial and temporal evolution. Methods for modeling lava flows attempt to simulate how the
complex interaction between flow dynamics and physical properties of lava lead to
the final
flow dimensions and morphology observed in the field. Many attempts have been made to
simulate and predict lava flow fields based on various simplifications of the governing
physical
equations and on analytical and empirical modelling
(Hulme, 19
74;
Crisci et al.,
1986;
Young and Wadge, 1990;
Miyamoto and Sasaki, 1997;
Harris and Rowland, 2001;
Costa and Macedonio, 2005; Del Negro et al., 2005
).
The use of cellular automata (CA)
methods for forecasting lava flow inundation is well established, and
several algorithms have
been presented in the literature. Our
Laboratory for the Technological Advance in Volcano
Geophysics (called TecnoLab) has been developing a different approach of CA for physically
based modeling of lava flows. In particular, we de
veloped
the
MAGFLOW Cellular Automata
model
which
involves
a steady state solution of the
Navier

Stokes equations coupled to heat
transfer due to radiative losses and solidification effects modeled via a temperature
dependent viscosity.
MAGFLOW
was designe
d
a
s a
tool
to simulate
lava flow
behavior
,
with regard
to real
physical data operating during the eruptive event
s
. Th
e model
is intended for use in
emergency
response situation
during an eruption to quickly forecast the lava flow path over
some time inter
val from
the
immediate future to long

time
prediction
.
The MAGFLOW model
was
successfully
applied to reproduce lava flows formed during the 2001 and 2004 eruptions
3
at Mt Etna (Del Negro et al., 2006; Vicari et al., 200
7
). These eruptions provided the
oppor
tunity to verify our model
’s
ability
to simulate the path of lava flows. This operation was
possible due to the availability of the necessary data for both modeling and subsequent
validation. The latest eruption of Mt Etna, occurring in July 2006, represen
ted a further step
towards defini
ng
the real potential of the MAGFLOW model as an effective tool for real

time
forecasting of lava flow hazards. We will briefly summarize results obtained by comparing the
simulated and the real events.
Model Description
T
he MAGFLOW model is based on Cellular Automata (CA) in which the states of the cells
are the thickness of lava and the quantity of heat. The states of the cells are synchronously
updated according to local rules that depend on the cell’s own values and the
neighbor’s
values within a certain proximity. The evolution function of MAGFLOW is a steady state
solution of Navier

Stokes equations for the motion of a Bingham fluid on an inclined plane
subject to pressure force
,
in which the conservation of mass is gu
aranteed both locally and
globally.
However, t
his kind of evolution function induces a strong dependence on the cell
geometry and position of the flux, with respect to the symmetry axis of the cell: flows on a
horizontal plane spread preferentially in the
direction of the mesh (the calculated length of
lava flows depends on the relative directions of flow and the mesh).
This problem was
overcome using a Monte Carlo approach, which allows
obtaining
cell geometry free results
as well
as
calculat
ing
large

scal
e lava flows with no artificial anisotropy (Vicari et al., 200
7
).
A simplified flow diagram summarizing the MAGFLOW model is given in Figure 1.
The
necessary data to run MAGFLOW are
a) a knowledge of the
rheological properties
of the
lava (as this places c
onstraints on the eruption temperature of the lava and the relationships
between temperature and viscosity and temperature and yield strength, which are used to
compute the rate at which the lava solidifies), b) a digital representation of the topography
o
ver which the lava is to be emplaced, c) the location of the eruptive vent, and d) an estimate
of the lava effusion rate
(Appendix A)
(
Del Negro et al., 2006;
Vicari et al., 200
7
)
.
4
At the initial state, the
lava
thickness at each cell is set to zero. The l
ava flow starts
discharging at a certain rate from a cell (or more cells) corresponding to
the
vent. The
thickness of lava at the vent cell increases by a rate calculated from the volume of lava
extruded during each time interval (of course, the flow rate
for each vent can change in time).
When the thickness at the vent cell reaches a critical level, the lava spreads over the
neighbor cells. Next, whenever the thickness at any cell exceeds the critical thickness, the
lava flows to the adjacent cells
.
At thi
s time, the heat content of lava in each cell is carried in
accordance with the flow motion, and solidification effects are modeled considering the
radiative heat loss from the surface of the flow (
Appendix B).
In order to obtain a stable solution, and to
complete a simulation in a short time, it is
important to make a proper choice of the time stepping (Δt). In this regard, it is
essential
to
note that the thickness at each cell can’t assume a negative value. This condition is satisfied
if Δt is selected a
s follows:
q
h
x
const
t
cells
the
all
over
2
max
(
1
)
where
x is the distance between two adjacent cells, h is lava thickness and q is the
volumetric flow rate, computed by the basic formula of Dragoni et al. (1986).
T
he time
stepping is adaptive in the sense that for
each iteration we choose the maximum value that
satisfies the relationship (
1
).
Simulation setup
The MAGFLOW model proposed here was applied to reproduce
the
lava flow
outpoured
during the 2006 Etna eruption.
Simulations of the volcanic lava flow were ca
rried out using
realistic three dimensional topography
of Etna volcano
, obtained from the
University of Rome
by
data collected during an aerophotogrammetric flight in August 2004.
The topographic data
w
ere
in the form of a Digital
Elevation
Model (D
E
M) wit
h a
horizontal
resolution of
5
m
. A
DE
M is a digital file consisting of terrain elevations for ground positions at regularly spaced
horizontal intervals
.
However, this DEM was
only
updated until August 2004, and this means
5
that it doesn’t take into account
the modification
of the topography
produced from the pile

up
of the lava flow
occurr
ing
during the 2004

2005
Etna eruption
in an area near the vents of
the
2006 eruption
.
Rheological properties were modeled using a variable viscosity
relationship
by Gior
dano and
Dingwell (2003), parameterized in terms of temperature and water content
, and linearized
between solidification (1143°K) and extrusion temperature (1360°K), as:
bT
a
T
)
(
log
(2)
where a and b, for
a fixed water content of 0.02 wt% H
2
O,
are 22.9153 and

0.0146
,
respectively
.
Typical material properties of many basaltic rocks occurring in volcanic regions
were chosen for Etnean basaltic lava
(Kilburn and Guest, 1993
, Harris et al., 1997
)
.
The
average density and specific heat of the lava
are
2600
kg/m
3
and 1150 J kg

1
K

1
,
respectively. The eruption temperature of the lava at the point of discharge from the crater
was chosen to be 1360 K with the ground temperature being 300 K. At 1360 K, the viscosity
of the lava (as given in equation (2
)) is about 1300 Pa s (which is very free flowing). Based
on equation (2), a decrease in temperature to about 1100 K gives a viscosity of about
1.9X10
6
Pa s (an increase by a factor 1000) demonstrating that the lava becomes
significantly viscous with even
moderate decreases in temperature.
Many factors combine to determine how far lava will flow. However, for a given composition,
the lava effusion rate (i.e. the volumetric flux of lava from the vent) is the principal factor
controlling final flow dimension
s. As such, simulations that take into account the way in which
effusion rate changes during an eruption, and how this influences the spread of lava as a
function of time, are of special interest, particularly as effusion rates can be highly variable
(
Laut
ze et al., 2004)
.
During a hypothetical eruption
,
lava effusion rates can vary by orders of
magnitude over a matter of hours
(
Wright et al., 2001
)
, and are difficult to determine in

situ.
However, lava eruption rates can be estimated using thermal infrared
satellite data.
Since
they can be obtained from low spatial/high temporal resolution remote sensing data (e.g.
MODIS, AVHRR), such effusion rates can be determined at regular intervals (i.e. up to four
times per day) during an eruption.
In Figure 2, both
the field observations and
satellite

6
derived estimates of lava
effusion
rates
are reported.
These time

varying
effusion
rates were
used to
guide
lava flow simulations using the MAGFLOW cellular automata algorithm
(
Wright
et al.,
2001
).
It is clear that for
using MAGFLOW as
a
forecasting tool, it was necessary
to
establish preliminarily a time

varying curve representing the variation of flux rate in relation to
the time of eruption (for example 30 days)
using the
set of
available
discrete values of
effusion
rate
.
O
f course, this
curve
was updated every time
some new values were available
(the green bell

shaped curve in Figure 2)
.
The reconstruction of the effusion rate trend is in
accordance with discharge variations discussed by Wadge (1981) for eruptions fr
om
pressurized sources, showing a rapid increase followed by a slower decline.
Application to 2006 Etna eruption
The 2006 Etna eruption provided the opportunity to verify our model
’s
ability
to predict the
path of lava flows while the event was ongoing an
d to produce different scenarios as eruptive
conditions
changed
.
At 23:30 local time on 14 July 2006, a fissure opened on the east flank
of the South

East Crater (SEC) summit cone of Mt Etna. Two vents (B1 and B2) along the
fissure produced a lava flow spr
eading east to the Valle del Bove (a wide depression that
cuts the eastern flank of the volcanic edifice).
We simulated
step

by

step
the
whole
effusive
activity
,
during the period of 14 July
–
29 July 2006,
produced from two vents
:
B1
(UTM
coordinates: 500
125.66; 4177661.25) and B2 (UTM coordinates: 500197.06; 4177624.69),
opened between 3000 m and 3100 m a.s.l.
The
initial
scenario
was
produced
taking
into account the
first
field
measurement
s
of the
effusion rate carried out
o
n the morning of
15
July
(see
Figure
2).
In particular
, Figure
3
show
s
the
prediction
at 17 July 2006
(INGV

CT
Report
,
2006b
)
calculated on 15 July using a
constant
effusion rate value of 1.5 m
3
/s for each vent
.
A helicopter survey carried out on 16
July at 7:30 showed a braided lava f
low field up to 1.7 km long (INGV

CT
Report
,
2006a
).
Preliminary mapping of the lava flow field allowed calculati
ng
its surface area and
approximate volume, leading to an estimation of the mean output rate of about 2.6 m
3
/s
during the first 32 hours of eru
ption. In Figure 3
,
the real flux (red contour)
proved
more
7
sustained
than the simulated one, and for this reason we increased the average value of
effusion rate to 3 m
3
/s for each vent. The result of
the new
simulation is reported in Fig
ure
4
(INGV

CT
Rep
ort
, 2006
c
)
.
This simulation
foresees/predicts
the formation of a lava flow
field
entirely
confined in
the
Valle del Bove
,
spreading north
of
the
Serra Giannicola Piccola
ridge
.
I
t
reached
about
1700 m a.s.l.
and overlapped
the 2004

2005 lava flow field (b
lue contour in
Figure 4). At this point,
it was necessary
to consider how
the path of the simulated lava flow
was influenced by the presence of 2004
–
2005 lava flow
field
.
Firstly, the old lava flow field
was included
in
the DEM attributing a
preliminary
th
ickness of 100 m to the
whole
2004
–
2005 lava flow
. Clearly in this way, we constructed an insuperable obstacle. The
aim
of this
simulation was to see the effects produced
by
the presence of the old lava flow, and if this
could in some way deviate the new f
low in potentially no
n

flooded areas. Moreover, we
introduced time

varying
effusion
rates to drive lava flow simulations
(the green bell

shaped
curve in Figure 2)
.
From
the knowledge of past eruptions, the effusion rate curve was
extended to 30 days for
pr
oduction of real

time forecasts, and it was
constrained by
the early
satellite

derived estimates of lava
effusion
rates, calculated
between 15 and 16 July 2006.
In Fig
ure
5
,
we report
two
simulation
s
dated
17
and 23 July 2006
computed on 17 July 2006
usin
g time

varying
effusion
rates (
equivalent to
an eruption rate
of 5 m
3
/s for each vent).
It is
worth noting
that
the first simulation (17 July 2006) r
eproduce
s
an event
that had
already
happened
, while the second (23 July 2006)
predict
s
the lava flow
path
o
f an ongoing event.
At the moment in which the simulations were made (17 July 2006), we
didn’t have any
idea
about the trend of effusion rate for the future days
. The bell

shape of the green curve in
Figure 2 represents exclusively a hypothetical trend nee
ded to produce such forecasts (until
30 days of eruption) faster than real time. However, the field observations confirmed that the
lava flow field emplacement reached a peak on 20 July, when an effusion rate ranging
between 10 and 14 m
3
/s allowed the lava
flow to reach a maximum distance of about 3 km
within the Valle del Bove.
T
wo
interesting
features
can be noted
now
:
(i)
the
time

varying
effusi
on
rate
generates
a lava flow path
that is
more similar in shape and times
to
real
one
(Fig
ure
5)
, and (ii)
the
insertion in the DEM
of 2004

2005
lava flow
field
produces
a deviation
8
in the path of
the simulated flow, which
lean
t
to the old
lava flow
.
For this reason, we
modified
the thickness of 2004

2005
lava flow
in order to
allow
the
overlapping
between
the
new
and older
flows
in some areas
.
T
he
inset of the
F
ig
ure
5
b
clearly
shows
that a branch of
2006
lava flow
field
is
overlapped
on the
2004

2005
lava
flow
.
Since
measures of the real
thickness
of
2004

2005 lava flow are not available yet
,
we
adopted a procedu
re of trial and
error in order
to determine
the
mo
st likely
thickness
value
. After
several
attempts
, we fixed
the thickness to
10 m
. In Fig
ure
6
,
we
report
two simulations
dated
19
and
2
3
July
2006, in
which
it is possible to see
the formation of the main
branch leaned to 2004

2005
lava flow
,
but also
a
new branch that
is able to
surmount
the obstacle
, rejoining
the main branch
subsequently
at
1800 m
a.s.l.
Figure
7
shows the comparison between the observed and
simulated lava
in 3D
relative
to 2
3
July, when
the flow
attained its maximum expansion
(INGV

CT Report, 2006d).
The real lava flow front widened at the base of Monte Centenari,
at 1800 m a.s.l. and at least 15 km
away
from the closest villages. The effusion rate on 23
July decreased to about 3
m
3
/s
,
with the lava channels narrowed and levees partially
collapsed. The eruption finished on 24
July.
Conclusi
on
The MAGFLOW model was used to simulate
the
real lava flow event occurring on the
eastern
flank of Etna volcano during the 200
6
eruption.
We
w
ere
a
ble to
fairly
accurately
reproduce the time of
the lava flow
advanc
e
and
effectively
forecast the path of lava
.
MAGFLOW appears to be a highly
efficient
technique for predicting lava flow
s
with very good
representations of the fluid free surface, close int
eraction with the complex topography, easy
inclusion of the thermal and solidification effects
, thereby
leading to very plausible flow
predictions.
The good performance obtained makes the model an efficient and robust tool for
estimating the areas
that mig
ht
be affected by potentially destructive lava flows.
Consequently, this tool could be a key extension of an efficient monitoring system of the lava
flow eruption, like that operating at Etna volcano. The reliability of parameters derived from
the analysis
and interpretation of field data, such as those
of use
for the estimation of the
9
flow rate, has allowed verify
ing
the
effective
capability and
high
performance of the modeling
implemented in MAGFLOW. It was also demonstrated that in order to simulate real
istic
scenarios, data collected on site during the evolution of the eruption are necessary.
Despite the
reasonably
satisfactory results obtained in this work, it should be noted that lava
flow propagation depends on many factors such as the characteristics
of magma feeding
system, the lava’s physical and rheological properties, the topography
,
and the
environmental conditions. Many of these parameters may change rapidly during an eruption
and
modify lava flow behavior. Thus
it is important to have a tool
su
ch
as
MAGFLOW
, which
is able to
produce
a number of
simulations in a short time
, guaranteeing
a good
representation
of the areas likely to be inundated by lava flows.
ACKNOWLEDGMENTS
Study performed with financial support from the ETNA project (DPC

INGV 2
004

2006
contract).
This work was developed in the frame of the TecnoLab, the laboratory for the
technological advance in geophysics organized by DIEES

UNICT and INGV

CT.
Thanks are
due to Maria Marsella
and Mauro Coltelli
for making the Digital Elevation
Model of Etna
available, Andrew Harris and Fabrizia Buongiorno for the
satellite

derived estimates of lava
effusion rates
, and
the
INGV

CT
volcanological team
for the mapping of the lava flow field
during the 2006 Etna eruption
.
APPENDIX A
An example of c
onfiguration file.
Free text can be placed anywhere in the file, and the order of the variable can be changed.
density:
2600.0
// density (kg
m

3
)
Tground:
300
// ground
temperature
(K)
Tlsolid:
1143
// Solidification temperature
(K)
Tlliquid:
1450
// molten temperature
(K)
Tclinker:
1303
//
clinkers
temperature
(K)
emissivity:
0.9
// emissivity
10
hcapacity:
1150.0
// thermal capacity
(J kg

1
K

1
)
avisc:
22.9153
// a viscosity coefficient
bvisc:

0.0146
// b viscosity coefficient
ays:
13.999
7
// yield strength coefficient
bys:

0.0089
// yield strength coefficient
tend:
2592000
// end of simulation
(second)
dt1:
2
// initial time step of
simulation
(second)
dt2:
2
// time step of
simulation
after the end of the eruption
(second)
d
tsave:
21600
// save time
(second)
niter:
10
// Monte Carlo iteration
cellradius:
2.5
// cell radi
u
s
(m)
neibnum:
8
//
neighbors
number (8

>square cells, 6

>
h
exagonal cells)
r:
5
// influence
radius
(m)
problem:
0
// type of simulation (DEM 0,
inclined plane 1)
cooling:
1
// problem with cooling
dtadapt:
1
// adaptive time step
APPENDIX B
Starting from the general form of the Navier

Stokes equations, we used the basic equations
governing fluid motion considering the flow driven by the pres
sure gradient as a result of the
variation of flow depth. In this way, it is possible to examine flows on a slightly inclined or
horizontal plane (steady state solution of Navier

Stokes equations). In our simulation code,
we assume that the lava flow is a
Bingham fluid characterized by a yield strength (S
y
) and
plastic viscosity (
), and that it advances as an incompressible laminar flow. The basic
formula to calculate the flux on an inclined plane was introduced in volcanology by Dragoni et
al. (1986). The
y deduced a steady solution of Navier

Stokes equations for a Bingham fluid
with constant thickness (
h
), which flows downward due to gravity. The volumetric flow rate
(
q
) is:
2
1
2
3
3
2
3
2
a
a
x
h
S
q
cr
y
(
B.
1)
where
cr
h
h
a
/
, h
cr
is the critical
thickness and
x the distance between two adjacent cells.
11
Other models based on this formulation were proposed in the past (e.g. Ishihara et al., 1990),
but they did not consider the flow driven by the effect of self

gravity. This case was
introduced by Mi
yamoto and Sasaki (1997), and Mei and Yuhi (2001).
The critical thickness (h
cr
) depends on the yield strength and the angle of the slope (
), as
described by:
h
z
g
x
z
S
x
h
g
S
h
y
y
cr
2
2
cos
sin
(
B.
2)
where
is the density of lava, g the acceleration due to gravity,
z the difference in height
between two cells, and
h the increase in cell thickness. Equations (1) and (2) are applied to
the numerical calculation of flux of lava between two adjacent cells.
At any time
t
, the heat content of lava (
Q
t
) in each cell is
carried in accordance with the flow
motion. The temperature of the lava in a cell is considered uniform: vertical temperature
variation is neglected. For the cooling mechanism, we consider the radiative heat loss (
∆Q
t,r
)
only from the surface of the flow (
the
effects of conduction to the ground and convection to
the atmosphere are
neglected), and the change of heat (
∆Q
t,m
) due to the mixture of lava
between cells with different temperatures, hence:
r
t
m
t
t
t
t
Q
Q
Q
Q
,
,
(
B.3
)
where:
t
c
T
q
T
q
Q
v
q
q
i
i
i
m
t
i
i
0
0
,
(
B.4
)
and
t
T
A
Q
r
t
4
,
(
B.5
)
where T is the temperature of the central cell, T
i
is the temperature of neighbor cells, q
i
is the
flux between the central cell (i.e. the cell for which the state variables are updated) and its i

th neighbor,
c
v
is the specific heat per unit mass, ε is the emissivity of lava, A is area of the
12
cell and σ is the Stefan

Boltzmann constant (5.68*10

8
J m

2
s

1
K

4
). Then, the new
temperature from the calculated heat change is:
A
h
c
Q
T
t
t
v
t
t
t
t
(
B.6
)
where
t
t
h
is the new thickness.
References
Behncke, B., Neri, M., Nagay, A., 2005. Lava flow hazard at Mount Etna (Italy): new data
from a GIS

based study.
Geolog
ical
Soc
iety
of Ame
rica 13,
189

208
.
doi:10.1130/2005.2396
.
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15
FIGURE CAPTIONS
Figure 1.
Simplified flow diagram of MAGFLOW mode
l.
Figure
2
.
Variation function of effusion rate for the whole period of the eruption: (pink
curve)
mi
nimum values measured
by remote sensing technique
, (blue
curve
) maximum values
measured
remote sensing technique
, (
orange triangles
)
values measured by
field
measurement
, (green
curve
) values used in the simulations, when no other information was
available.
Effusion rate values measured by remote sensing
technique
have been furnished
from different research teams (Remote Sensing Group INGV

Roma
, Hawaii
In
stitute of
Geophysics and Planetology
)
. Effusion rate values measured by field measurement have
been furnished
by
INGV

CT volcanological team
.
Figure
3
.
Simulated
scenario of
17 July
200
6
computed using
an average value of effusion
rate of 2.6 m
3
/s (1.3 m
3
/s for each vent)
.
R
ed contour is the real map of lava flow updated to
17 July 2006.
Figure
4
.
Simulated scenario of 23
July 2006 computed without taking into account the
presence of 2005

2005 Etna lava flows.
A
verage value of effusion rate us
ed for the
simulation is 3 m
3
/s for each vent.
R
ed contour is the real map of lava flow updated to 17 July
2006.
Figure
5
.
Simulated s
cenario
of
a) 17
July
2006
and
b) 23
July
2006
.
2004

2005 Etna lava
flow has been overlapped to the DEM, attributing a
thickness of 100 m to the entire lava flow
field. Effusion rate used for the simulation is represented by the green bell shaped in Figure
2.
I
nset show
s
a picture of
the
real lava flow updated to 19 July 2006.
16
Figure
6
.
Simulated scenario of a) 19 July 20
06 and b) 23 July 2006
.
2004

2005 Etna lava
flow has been overlapped to the DEM, attributing a thickness of 10 m to the entire lava flow
field.
Figure
7
.
Simulated scenario in 3D of 23 July 2006.
B
lue contour is the real map of 2004

2205 Etna lava flow,
and yellow one is the real map of 2006 Etna eruption updated to 23 July
2006
.
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