Supplementary materialS1. Confort 15 assumptions and limitationsModeling procedure and related assumptions adopted in Conflow and Confort 15 models

are briefly listed in Section 2. Here we would like to outline and comment on the major

assumptions of the procedures and possible future directions.

Conflow program considers the magma-gas mixture as a single homogeneous fluid. This

assumption allows the mixture to be treated as a single fluid whose density, viscosity and

other properties are bulk values for the mixture.

This is the same assumption on which classic conduit models (e.g. Wilson et al., 1980)

have been based although some more recent models (e.g., Dobran, 1992; Papale and

Dobran, 1993; Papale et al., 1998, Melnik and Sparks, 2002; de’ Michieli Vitturi et al.,

2010, Kawaguchi et al., 2013) solve separate equations for the mass and momentum of

the gas and melt+crystal phases.

The assumption of homogeneity is most appropriate when applied to eruptions of rapidly

ascending magma, such as vigorous lava-fountain, Plinian or sub-Plinian eruptions, where

the rise velocity of bubbles in magma is small relative to the ascent velocity of the magma.

The model also assumes that gas exsolution maintains equilibrium with pressure in the

conduit. This assumption is used by most modelers of volcanic eruptions (e.g. Wilson et

al., 1980; Dobran, 1992; Papale and Dobran, 1993; Papale et al., 1998; Mastin, 1995,

2002; de’ Michieli Vitturi, 2010, Kawaguchi et al., 2013), though Mangan and Sisson

(2000) conducted experimental studies suggesting that bubble growth may be limited by

kinetics. Only few modelers attempt to consider non-equilibrium conditions along the

conduit (e.g. Proussevitch and Sahagian, 1996; Mangan et al., 2004).

Another model’s assumption is to consider the flow one-dimensional, which disregards

effects that take place at the walls and centers of conduits. As volatiles exsolve and

viscosity increases, ascending magma near the conduit margins where shear strain rates

are largest may be subjected to non-Newtonian, shear-thinning behavior. Locally, this may

enhance magma permeability and outgassing (Tuffen, 2003; Gonnermann and Manga,

2012) and the loss of volatiles and decrease of pressure promote crystallization, leading

to an increase in viscosity. Furthermore, Conflow considers that flux of heat and gas

through the conduit wall are negligible relative to their flux up the conduit. The gas

consists only of H2O and maintains thermal equilibrium conditions with melt and crystals

during the mixture ascent. This assumption is reasonable because of the very short

thermal equilibration times for particles of the size typically produced during volcanic

eruptions (Wilson et al., 1980; Mastin and Ghiorso, 2000). The assumption of a cylindrical

conduit is an approximation regarded to be valid in modeling literature (e.g. Dobran, 1992;

1

Mader et al., 1994; Papale et al., 1998; Mastin, 2002; Kawaguchi et al., 2013), but during

real eruption frequently the conduit geometry changes due to erosion (e.g. Macedonio et

al., 1994; de’ Michieli Vitturi et al., 2010).

In addition to Conflow assumptions and limitations (for other details see Mastin and

Ghiorso, 2000), in Confort 15 it is important to consider the ability to input decompression

rate. Our results indicate that input decompression rates strongly affect magma dynamics,

acting mostly on the fragmentation depth, initial velocity and the mass fluxes.

Decompression rates obtained from textural analysis and Toramaru (1995, 2006)

formulations are very high. Several factors can cause a high decompression rate, such as

a sector-collapse, as in the Chaitén eruption (Alfano et al., 2012) or the increase in

crystallinity (Shea et al., 2010). In our cases, the calculated decompression rates refer to

maximum values achievable during an eruption during the final nucleation and growth

event, which could be related to the rapid decompression immediately below the

fragmentation depth. For this reason, it would be incorrect to insert the calculated dP /dt at

the base of the conduit and thus in Confort 15 we insert this value at exsolution level.

Then, in order to satisfy choked conditions, the program adjusts initial velocities, dP /dz

and hence the dP /dt iteratively. In general, we observe that the recalculated dP /dt are

slightly lower (up to 1 MPa/s less than the input values) at the base of the conduit and

reach the Toramaru values at about 30 to 60 meters from fragmentation level, which is in

perfect agreement with the rapid decompression expected at fragmentation level. The

current model does not allow to control a priori the effective point at which the

decompression rate is applied throughout the conduit. This is a limitation of the model that

should be overcome in the future. High decompression rates, such as those we

calculated, may only be plausible within a short distance of the fragmentation depth,

where viscosity may increase considerably over short distances, especially due to water

exsolution (e.g. Papale, 1999; Mastin, 2002; Koyaguchi and Mitani, 2005; Massol and

Koyaguchi, 2005; Melnik et al., 2005). According to this, our decompression rates are

indeed rightly located in the proximity of fragmentation.

In spite of these limitations and approximations, Confort 15 model is a useful tool to be

used not only to predict eruption characteristics, but especially to illustrate how flow

parameters may affect eruption dynamics. Of course, we strongly hope and wish that

significant improvements will be seen in the next future to overcome such simplifications

and to allow more realistic modeling of conduit dynamic.

S2. Confort 15 rheology equations

2

In Confort 15 the liquid viscosity is calculated using the GRD model (Giordano et al.,

2008). The temperature dependence of viscosity (η) is modeled by the Vogel–Fulcher–

Tammann (VFT) equation:

logη=A+ BT (K )−C S.1

where T (K )is the temperature in Kelvin, A is a constant independent of composition and

B and C are adjustable parameters.

The compositional dependence of viscosity is taken into account in the B and C

parameters as linear combinations of oxide components (mol%) and several multiplicative

oxide cross-terms:

B=∑i=1

7

[biM i ]+∑j=1

3

[b1 j(M 11 j ∙ M 21 j)] S.2

C=∑i=1

6

[c i N i ]+¿ [c11(N 111∙ N 211)]¿ S.3

where M and N are combinations of mol% oxides for B and C respectively. The 17

unknown coefficients (b i, b1 j, c i, c11) are used to compute the values of B and C for any

individual melt composition (for details see Giordano et al., 2008).

For peralkaline melts Confort 15 uses the Di Genova et al. (2013) equation:

log η= A+b5+b6 ×log (1+H2O)

T ( K )−[ c5+c6×log (1+H 2O)AEX ]

S.4

where A is a constant independent of composition and has a value of −4.55 Pa s (as in

Giordano et al., 2008), b5, b6 , c5 , c6 are fitting parameters, T is the absolute temperature,

H 2O is the water concentration in mol% and AEX is the alkali excess in mol% (for details

see Di Genova et al. 2013).

The crystal-bearing rheology is determined using the Vona et al. (2011) equation in which

the relative viscosity (ηr) is expressed as:

ηr=(1− ϕϕm )−2 [1−α log (γ̇ )] S.5

where γ̇ is the applied strain rate, α is a constant equal to 0.06 and ϕmrepresents the

maximum packing fraction.

The values of ϕmare calculated on the basis of the average aspect ratio using the equation

by Mueller et al. (2010):

3

ϕm=2

0.321 R+3.02S.6

which has been calibrated to empirically fit their data on analog suspensions containing

monodisperse particles of fixed aspect ratio. We calculate the average aspect ratio R

according to the following equation (Vona et al., 2011):

R=∑ ϕiRi

ϕS.7

where ϕi and Ri are the crystal fraction and the mean aspect ratio of phase i.

When ϕ>ϕm, Confort 15 considers the Costa et al. (2009) model, where the relation

between relative viscosity and the solid fraction is given by:

η (ϕ )= 1+φδ

[1−F (φ , ε , γ ) ]Bϕ¿

S.8

where

F=(1−ξ ) erf [ √π2 (1−ξ )

φ (1+φ γ)] S.9

with φ = ϕ ¿ϕ¿ where ϕ¿, ξ, γ and δ are empirical parameters that depend on the

deformation rate and B is the Einstein coefficient. Although this model can successfully

predict the multiphase rheology of suspensions containing ϕ = 0.1-0.8 with isotropic

particles for a wide range of strain rates, it can produce appreciable errors when the

aspect ratio of the solids increases.

S3. Confort 15 decompression rate calculationsIn Confort 15 input of decompression rates are calculated using textural analysis and Eq.

1 (Toramaru 1995, 2006).

In this calculation we did not consider larger vesicles that may have experienced

expansion and possibly coalescence, but we utilized only number densities calculated for

the size range 0.01-0.001 mm to capture the decompression rates corresponding to the

final stages of rapid ascent prior to fragmentation (only to the final accelerating portions of

the ascent path). The threshold was chosen according to the cumulative vesicle size

distribution, taking into account the change in slope at the smallest size.

Thus, we have to recalculate the water content X 0 at the porosity ϕ (i.e. taking into

account the porosity of the selected vesicle size range), by rearranging the equilibrium

model presented in Gardner et al. (1999) as demonstrated by Shea et al. (2011):

X 0=X i−ϕ

ρZ

V w(1−ϕ )

S.10

4

where X i is the original initial water content, Z is the molecular weight of water, V w is the

molar volume of water in the vapor phase, and ρ the magma density. For each measured

clast, we used the porosity value obtained by summing the contributions from all vesicles

with sizes L ≥ 0.01 mm to derive X 0 using FOAMS software (Shea et al., 2010).

To calculate decompression rates according to Eq. 1, curves of Number densities per unit

volume as a function of ascent rate log(dP/dt) as predicted by the model of Toramaru

(1995, 2006) for varying “effective” surface tensions (in the range 0.01-0.09 N/m) were

built (Fig. S1 Green Tuff Member A and Etna 122 as examples). In the case of resulting

multiple surface tensions, we chose the one that best matched literature data for

heterogeneous nucleation (e.g. Massol and Koyaguchi, 2005; Cluzel et al 2008; Shea et

al, 2010) paying particular attention to the composition and the water content of the

selected samples. In particular, we chose surface tension of 0.09 N/m for Member A of

Green Tuff, comparable with the range 0.078-0.09 N/m found by Cluzel et al. 2008 and

Gardner and Ketcham, 2011 on rhyolites. For the trachytic Member H we adopted a

surface tension of 0.035 N/m, similar for composition and water content to the phonolites

of Shea et al. 2011. Direct studies on basaltic compositions are not available in literature,

so values of surface tension for the case of Etna 122 are more difficult to constrain.

In this case, we adopted a surface tension of 0.035 N/m, in agreement with values for

dacites of Mourtada Bonnefoi and Laporte, 2004 (for similar water and alkali content). This

leads to a possible overestimation of the real surface tension which, for the Etna case,

ranges between 0.01 (dP/dt = 1.4 MPa/s) and 0.035 N/m (dP/dt = 2.2 MPa/s).

Because “heterogeneous” surface tension is lower than the “homogeneous” one (e.g.,

Cluzel et al. 2008), decompression rates estimated from heterogeneously nucleated

vesicle number densities are approximately one order of magnitude lower than if

homogeneous nucleation were assumed (e.g. Toramaru 2005, Giachetti et al., 2010).

A decompression rate of up to an order of magnitude lower (i.e. heterogeneous

nucleation) clearly raises the fragmentation level, corresponding to higher pressure

distributions and lower acceleration along the conduit.

5

Figure S1: Number densities per unit volume (VND) in function of ascent rate log(dP/dt) as predicted by the model of Toramaru (1995, 2006) for varying effective surface tensions σeff=0.010–0.090 Nm−1 (black lines). The red and blue lines represent the values pertaining to VNDs of the Green Tuff Member A and Etna 122BC in the selected bubble size range (0.01-0.001 mm). In green the resulting dP/dt (3.82 MPa/s for the Green Tuff Member , 2.2 MPa/s for Etna 122 BC).

S4. Density determination and image strategyScoria clasts were cleaned and dried at T>100 °C for 24 h and then ranked by decreasing

size and numbered from large to small (e.g. Shea et al., 2010). Density measurements

were performed by a combination of pycnometer and hydrostatic balance according to the

method described by Houghton and Wilson (1989). We selected few median density

clasts pumices in the -2/-3ϕ grain size interval from Member A and Etna 122 BC and three

massive samples from Member H, excluding deposits showing welding deformation. This

approach, valid for a general description of the eruptive dynamics, involves a certain

degree of uncertainty (due to the scarce representativeness of the samples), and we

stress that a more specific analysis of the pyroclastic succession would require a more

statistical quantitative textural analysis. Images were collected by scanner and Philips

XL30 SEM at the LIME laboratory of Roma Tre University at five different magnifications

for Pantelleria samples (1x, 20x, 200x, 400x and 800x) and four for Etna 122 BC (1x, 20x,

350x and 700x) to ensure that all vesicles and crystal sizes were adequately represented.

At each magnification, twice as many images were collected as the images collected at

6

the next lower magnification. The obtained images were processed and analyzed via

Adobe Photoshop and the ImageJ software, thresholded automatically, when possible,

otherwise completely manually redrawn. We measured number densities in the smallest

size range (0.001-0.010 mm diameter) to capture the decompression rates during the final

stages of ascent before fragmentation using FOAMS software (Shea et al., 2010).

S5. The importance of VND in disequilibrium degassingBecause VND is directly proportional to the thickness of the film of melt surrounding the

vesicles, it strongly influences the diffusion time and the onset of disequilibrium conditions.

It is important to point out that, using Conflow modeling, vesicle number densities are

calculated on the basis of the mass fraction of SiO2 in the melt, whereas with the new

Confort 15 program, VNDs derived from textural analysis can be directly inserted as input

values. To assess the importance of using textural-derived VNDs, we run a simulation

considering VNDs SiO2-based values (about 103.8 cm-3) for the basaltic Etna eruption (Fig.

S2). The very low VND yields to low overpressure build-up in this simulation and does not

allow fragmentation to occur, testifying to the importance of observational constraints as

input to modeling. In order to assess the importance of VND variation on the

disequilibrium degassing, simulations were repeated in the VND range obtained from

textural analysis (108-109 cm-3 for GT and 106-107 cm-3 for ET; Fig. S2). Increasing VNDs

increase, as expected, the overall bubble overpressure, but reduce the onset pressure of

disequilibrium conditions (GT = 10 and 8 MPa, ET = 7 and 5 MPa).

7

Figure S2: Confort 15 model results for bubble growth calculation (solid lines) and the required fragmentation threshold (dotted lines; Spieler et al., 2004). (a) Pantelleria Green tuff Member A results at T = 750°C, H2O = 3 wt.% and VNDs of 108

and 109 cm-3 (derived from textural analysis). (b) Etna 122 BC microlite-bearing results at T = 1100 °C, H2O = 1.85 wt.% and VNDs of 106 and 107 cm-3 (derived from textural analysis) and 103.8 cm-3 (SiO2-derived). At P < 10 MPa for GT and 7 MPa for ET, magma pressure decreases more rapidly than bubble pressure until the bubble overpressure (Pg-Pm) reaches the fragmentation threshold pressure. For VNDs SiO2-derived no fragmentation occurs.

8

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